text:
Angiogram of the Head and Neck
Test Overview
An angiogram of the head and neck is an X-ray test that uses a special dye and camera (fluoroscopy) to take pictures of the blood flow in the blood vessels of the head and neck. An angiogram of the neck (carotid angiogram) can be used to look at the large arteries in the neck that lead to the brain. An angiogram of the head (cerebral angiogram) can be used to look at the veins or the four arteries (four-vessel study) carrying blood to the brain.
During an angiogram, a thin, soft tube called a catheter is placed into a blood vessel in the groin or just above the elbow. The catheter is guided to the head and neck area. Then an iodine dye (contrast material) is injected into the vessel to make the area show clearly on the X-ray pictures. The angiogram pictures can be made into regular X-ray films or stored as digital pictures in a computer.
An angiogram can find a bulge in a blood vessel (aneurysm). It can also show narrowing or a blockage in a blood vessel that slows or stops blood flow. An abnormal pattern of blood vessels (arteriovenous [AV] malformation) or abnormal vessels near a tumor can be seen.
A magnetic resonance angiogram (MRA) or computed tomography angiogram (CTA) may be an option instead of a standard angiogram. Each of these tests is less invasive than an angiogram. Some MRA tests and all CTA tests require an injection of dye. A CTA also involves radiation exposure.
Why It Is Done
An angiogram of the head or neck is done to:
- Look for blockage or narrowing of the arteries in the neck that carry blood to the brain. The test may help your doctor decide if a procedure is needed to open a narrowed or blocked artery to increase blood flow. Blood flow to the brain that is slowed or stopped increases the chance of having a stroke or a transient ischemic attack (TIA).
- Study symptoms that might mean problems with the blood flow to the brain. Symptoms may include severe headaches, memory loss, slurred speech, dizziness, blurred or double vision, weakness or numbness, or loss of coordination or balance.
- Detect an aneurysm in the brain or in a blood vessel leading to the brain. The test may help your doctor decide if a procedure is needed to repair the aneurysm.
- Check the pattern of blood flow to a tumor. This can show if the tumor has spread and can help guide treatment.
How To Prepare
Before an angiogram, tell your doctor if you:
- Are or might be pregnant.
- Are breastfeeding. Use formula (throw out your breast milk) for 1 to 2 days after the angiogram until the dye has passed from your body. This generally takes 24 hours.
- Are allergic to iodine dye used in the test.
- Have ever had a serious allergic reaction (anaphylaxis) from any substance, such as the venom from a bee sting or from eating shellfish.
- Have asthma.
- Are allergic to any medicines.
- Have any bleeding problems or are taking blood-thinning medicines.
- Have a history of kidney problems or diabetes, especially if you take metformin (such as Glucophage) to control your diabetes. The dye used during an angiogram can cause kidney damage in people who have poor kidney function.
Do not eat or drink for 4 to 8 hours before the angiogram. You may be asked to not take aspirin, aspirin products, or blood thinners for several days before the test and for 1 day after the test. If you take these medicines, talk with your doctor.
An angiogram can be done as an inpatient or outpatient. If you are an outpatient, you will stay in a recovery room for several hours before you go home. You may want to bring something to do or read to pass the time. Arrange to have someone take you home because you may get a sedative before the test. If you stay overnight in the hospital, you will likely go home the next day.
The test may take several hours, so you will empty your bladder just before it begins.
Also before the angiogram you may have other blood tests, such as blood clotting (coagulation) studies, blood urea nitrogen (BUN), and creatinine.
You will be asked to sign a consent form that says you understand the risks of the test and agree to have it done.
Talk to your doctor about any concerns you have regarding the need for the test, its risks, how it will be done, or what the results will mean. To help you understand the importance of this test, fill out the medical test information form( What is a PDF document? ).
How It Is Done
An angiogram can be done by different types of doctors, including a radiologist, cardiologist, or surgeon. Your doctor may be helped by a radiology technologist or a nurse.
You will need to take off any jewelry. You may need to take off all or most of your clothes. You will be given a gown to wear during the test.
During the test
You will likely have an intravenous (IV) line in a vein in your arm so your doctor can give you medicine or fluids if needed. A device called a pulse oximeter, which measures oxygen levels in your blood, may be clipped to your finger or ear. Small pads (electrodes) are placed on your arms, chest, or legs to record your heart rate and rhythm.
You will lie on your back on an X-ray table. Ask for a pad or blanket to make yourself comfortable. A strap, tape, or sandbags may be used to hold your body still. A lead apron may be placed under your genital and pelvic areas to protect them from X-ray exposure.
A round cylinder or rectangular box that takes the pictures during fluoroscopy will be moved above you. The fluoroscope will move under you during the test.
The place where the catheter will be inserted (in the groin or above the elbow) will be shaved and cleaned. Your doctor will numb the area with a local anesthetic. Then he or she will put a needle into the blood vessel. A guide wire will be put through the needle into the blood vessel and the needle will be removed. The catheter then will be placed over the guide wire and moved into the blood vessel. The catheter will be guided through the blood vessels until the tip is in the area to be studied. Your doctor will use the fluoroscope to watch the movement of the catheter in the blood vessels.
When the catheter is in place, the dye is injected through it. You may be asked to take a breath and hold it for several seconds. Several X-ray pictures will be taken one after another. These will be available right away for your doctor to look at. You need to lie very still so the pictures are clear. More pictures may be taken.
An angiogram takes 1 to 3 hours.
After the test
The catheter is taken out after the angiogram, and pressure is put on the needle site for 10 to 15 minutes to stop any bleeding. A bandage or compression device is put on the site. This will prevent bleeding. You will be given pain medicine if you need it.
If the catheter was put in your groin, you will need to lie still and keep your leg straight for several hours. The nurse may put a weighted bag on your leg to keep it still. If the catheter was put in your arm, you may be able to sit up and get out of bed right away. But you will need to keep your arm still for at least 1 hour.
Your doctor will give you specific instructions after the test. You can use an ice pack on the needle site to relieve pain and swelling.
The place in your hands and feet where your heartbeat (peripheral pulse) can be felt may be marked with a pen. Your pulse may be checked before and after the angiogram.
How It Feels
You may feel a brief sting or pinch from the numbing medicine. Most people do not have pain when the catheter is in the blood vessel.
You may feel pressure in the blood vessel as the catheter is moved. Let your doctor know if you are having pain.
You will probably feel some warmth when the dye is put in. This feeling lasts only a few seconds. For some people, the feeling of heat is strong and for others it is very mild.
You may have a headache, flushing of the face, or a salty or metallic taste in your mouth after the dye is used. These feelings do not last long. Some people may feel sick to their stomachs or may vomit, but this is not common.
After the test, you may have some tenderness and bruising at the site where the catheter was inserted.
You can drink extra fluids to pass the dye from your body unless your doctor has told you not to.
The chance of any major problem from an angiogram is very small, but some problems can occur. In most cases, the problems occur within 2 hours after the test when you are in the recovery room. If the problem occurs during the angiogram, the test may not be completed. You may need urgent treatment that could include surgery.
- There is a chance for an allergic reaction to the iodine dye. The reaction can be mild (itching, rash) or severe (trouble breathing or sudden shock). Most reactions can be treated with medicines. Be sure to tell your doctor if you have hay fever, asthma, or iodine allergy or food allergies.
- There is a small chance that the catheter may damage a blood vessel or dislodge a piece of clotted blood or fat from the vessel wall. The clot or fat can block blood flow to the brain, arm, leg, or intestine (bowel).
- Bleeding from the needle site may occur. Also, a blood clot can form where the catheter was inserted. This may cause some blockage of the blood flow in the arm or leg.
- The iodine dye used for the test can cause water loss or direct damage to the kidneys. This is a special concern for people who have kidney problems, diabetes, or who are dehydrated. Special measures are used during the test to prevent problems for people who need an angiogram and have these conditions.
- There is always a small chance of damage to cells or tissue from being exposed to any radiation, even the low level used for this test.
Angiogram of the head and neck is an X-ray test that uses a special dye and camera (fluoroscopy) to take pictures of the blood flow in the blood vessels of the head and neck. Your doctor may tell you some results right after the test. Full results are usually ready the same day.
Normal: |
The blood vessels are normal in size, shape, location, and number. |
The dye flows evenly through the blood vessels. |
No narrowing, blockage, bulging, or other problem of the blood vessels is seen. |
Abnormal: |
A narrow spot in an artery may mean that a fat deposit, calcium deposit, or clot is reducing blood flow through the blood vessel. |
Blood vessels that are not in their normal position may mean that a tumor or other growth is pushing against them. |
A bulge in a blood vessel may point to a weakness in the blood vessel wall ( aneurysm). |
An abnormal pattern of blood vessels may mean that a tumor is present. |
Dye that leaks out of a blood vessel may mean that there is a hole in the blood vessel. |
There is abnormal branching of blood vessels present since birth (congenital). |
What Affects the Test
Reasons you may not be able to have the test or why the results may not be helpful include:
- Being pregnant. An angiogram is not usually done during pregnancy because the radiation could damage the developing baby (fetus).
- Blockage or curving of the blood vessels caused by atherosclerosis, high blood pressure, or aging. This may make it hard to guide the catheter through the blood vessels or hard to inject the dye.
- Not being able to lie still during the test.
What To Think About
- A magnetic resonance angiogram (MRA) or computed tomography angiogram (CTA) may be an option instead of an angiogram. Each of these tests is less invasive than a standard angiogram. Some MRA tests and all CTA tests require an injection of dye. A CTA also involves radiation exposure. Some surgeons may want results from a standard angiogram before doing surgery to repair a damaged or abnormal blood vessel.
- For people with kidney problems, diabetes, or dehydration, steps are taken to prevent kidney damage. Less dye may be used or more fluids may be given before, during, and after the test. If you have a history of kidney problems, other blood tests (creatinine, blood urea nitrogen) may be done before an angiogram to make sure that your kidneys are working well.
- In rare cases, surgery may be needed to repair a hole in the blood vessel where the catheter was placed. There is also a substance that can be used to help plug the hole in the vessel and stop the bleeding. The substance used to plug the hole in the vessel is normally absorbed by the body over several months.
- Other angiogram tests can be done, including:
- A four-vessel study. The catheter is placed in each of the four arteries carrying blood to the head and neck (two carotid arteries and two vertebral arteries).
- An arch study. The catheter is pulled back from the head and neck area until the tip is at the large artery (aorta) where it leaves the heart. This study lets your doctor check the arteries where they branch off the aorta.
Other Works Consulted
- Chernecky CC, Berger BJ (2008). Laboratory Tests and Diagnostic Procedures, 5th ed. St. Louis: Saunders.
- Fischbach FT, Dunning MB III, eds. (2009). Manual of Laboratory and Diagnostic Tests, 8th ed. Philadelphia: Lippincott Williams and Wilkins.
- Pagana KD, Pagana TJ (2010). Mosby's Manual of Diagnostic and Laboratory Tests, 4th ed. St. Louis: Mosby Elsevier.
Current as ofSeptember 26, 2018
Author: Healthwise Staff
Medical Review: Rakesh K. Pai, MD – Cardiology, Electrophysiology
E. Gregory Thompson, MD – Internal Medicine
Martin J. Gabica, MD – Family Medicine
Adam Husney, MD – Family Medicine
Elizabeth T. Russo, MD – Internal Medicine
Howard B. Schaff, MD – Diagnostic Radiology
Current as of: September 26, 2018
Author: Healthwise Staff
Medical Review:Rakesh K. Pai, MD – Cardiology, Electrophysiology & E. Gregory Thompson, MD – Internal Medicine & Martin J. Gabica, MD – Family Medicine & Adam Husney, MD – Family Medicine & Elizabeth T. Russo, MD – Internal Medicine & Howard B. Schaff, MD – Diagnostic Radiology
This information does not replace the advice of a doctor. Healthwise, Incorporated, disclaims any warranty or liability for your use of this information. Your use of this information means that you agree to the Terms of Use. Learn how we develop our content.


text: Alex Reymundo is a Mexican-American comedian and actor, who was featured on the 2007 ALMA Awards. He was born in Acapulco, Mexico, where he lived until his family moved to Texas in the United States where lived from the age of two to twenty-two. He lived in Kentucky for seven years. Reymundo is married and has two children, a boy and a girl. Reymundo had a one-hour special that aired on Comedy Central in 2007 called Alex Reymundo Hick-Spanic: Live in Albuquerque. He was also featured in the Showtime and Comedy Central special The Original Latin Kings of Comedy along with other Latin comedians such as George Lopez and Paul Rodriguez. He received an ALMA Award in 2008 for "Outstanding Comedy Special" for his one-hour comedy special "Alex Reymundo Hick-Spanic, Live in Albuquerque." He is currently opening up for fellow comedian (and ex-brother-in-law) Ron White on his tour. His sister is Margo Rey.

subset: commoncrawl


text:
You begin from a scratch. Those mastered in playing the online slots didn't know how to play before. These kinds of one of the easiest casino games web based. There is no real knowledge needed for these quests.
Another thing to investigate when choosing mobile casino slots for slots is these people offer flexible betting rules. You should be able perform both high and minimal stakes and not just one along with other. You'll also understand of the winning lines, betting tiers and pay table.
You do not need worry about anything about Super Slot Casino. They are assuring each and every players the player have one of the most secure and safe gaming in the web. So may refine 온라인슬롯 in being fair for their games. Relax, enjoy and aim for the huge jackpot that waits for a success.
Fun casinos mean you can play with or win real money, as that will be illegal the license. These games are played with 'fun' or fake money to buy chips. During a charity event, real money is which is used to buy the chips refund policy goes in as donation.
Perform slots there aren't any strategies to memorize; but playing casino slots intelligently does require certain skills. These are the basics of the right way to increase it is likely that hitting a major jackpot.
So, anyone want to play slots games for free, than occur online. There you have numerous and exciting slots games to decide upon. There are a games available there you daily.
You must always be careful about the vendors which claim to sell a system that can beat the online slots. There are many who have been trying to come i'll carry on with a mathematical formula or a system prevented beat online slots. However, none of those have prevailed enough. Lastly, it is very important to browse the directions around slot machines before actually playing them. Online slots usually have this information before the play because they introduce the winning lines and symbols clearly.


text:
We firmly believe that infertility programs work best when designed specifically for each client and that personalized support makes all the difference. As either patients, industry veterans, or even surrogates, every member of our staff has deep ties to both the industry and the process and is committed to making the experience of becoming a parent through assisted reproduction as stress free as possible. We believe strongly in ethics, fair pricing, and efficiency.
As experts in our field, we are frequently consulted by world media outlets and our work has been featured by both international and national news organizations such as CNN, HLN, The Los Angeles Times, and Sunday Night Australia. Through our unique concierge services we provide personalized support, access to priority appointments, exclusive pre-negotiated packages, and pharmacy discounts. We are the first US based agency ever to negotiate lower pharmaceutical fees on behalf of our clients and we are proud to offer an exclusive pharmacy discount card.
We take great pride when we hear that there is something genuine and special about Nest Egg. We believe the work we do is significant and we sincerely care for the people who trust us to guide them with their future family planning. We want our clients to feel a human-to-human interaction and feel supported throughout their fertility planning, and the confidence to know that they are being guided by a company with over 20 years of personal and professional experience. In short, we are extremely proud of the way we run our business and the families we are helping to create.
"I wanted to combine my passion for science with my love of family and my compassion for people.
Nest Egg Fertility is the result of that dream."
Shalene Petricek
With seventeen years in the biotech industry, our founder, Shalene Petricek is not only an industry veteran, but a client, having preserved her own fertility through cryopreservation before most people even knew what that was. The recipient of several awards of excellence in her previous career, Shalene started Nest Egg Fertility with the intention of creating the experience she wishes she had had. Shalene has always had a passion for science and helping others. She is driven by her desire to make a difference and change the way we approach women's healthcare. Today, she's a leading expert in the field of infertility, frequently consulted by world media outlets such as HLN, CNN, The Los Angeles Times, and Sunday Night Australia. When not busy helping create families, Shalene loves cooking, traveling, and finding the human connection with people across the globe.


text:
Swirled Flower for polymer clay jewelry creations.
Size: 13×13 cm
This template is great to use in your polymer clay jewelry projects, which can be used with any kind of paint: acrylic, watercolor, crackle paints, and other mediums on polymer clay surfaces! As well this stencil is very easy to use with metallic foils and transfer foils!
How to use:
– Condition and roll out your polymer clay on your pasta machine in a nice sheet of clay;
– Press the stencil on the surface of the clay and roll it lightly with an acrylic rolling pin;
– Use one or different colors of paints on the template and then remove the stencil;
– Rinse the stencil in warm water;
– Cut out the designs or use the veneer for any of your projects!
The numerous stencil designs are giving you endless creative results!


text:
Blog Archives
Are you bold enough to accept that challenge for a moment? To let go of your current perception of reality, and consider the fact that there is an alternative way of earning a living, that will actually enable you to, well, live.
If you are, then I'd like to welcome you to the world of online marketing. (more…)
You might not be aware of it, but I first entered the arena of Click & Mortar Business back in 1996, when my late wife and I launched NiceIce.com which specialized in round brilliant ideal cut diamonds and custom jewelry, I know operate the web site as a blog which provides in-depth diamond grading tutorials and consumer education. Today's question being posed by Natalie Sisson, as part of her 30 Day Blog Challenge is "Whose online business do you admire most and why?" and the answer is… (more…)
So if you've been following along for the past week, today is Day 8 of the 30 Day Blog Challenge, presented by Natalie Sisson, author of The Suitcase Entrepreneur. The purpose of which is to teach us how to create the lifestyle of your dreams, by building a successful online business. Natalie is pulling out all the stops to teach us, step-by-step, the exact formula which she used to build her online business. (more…)
As I hurry to catch up on my commitment to participate in The Suitcase Entrepreneur's 30 Day Blog Challenge, after taking the weekend off to just enjoy time here on planet earth, it's currently Day 7, so we have the questions from Days 6 and 7 to address. The question for Day 6 is "What are my three priorities for the next 30 days that will move me closer towards living life on my own terms?" and I hope that you'll read Natalie's blog, because she shared some very cool, real life examples of people who are already living the dream! (more…)
I took the entire weekend off, as I often do, to completely unplug and just enjoy being with somebody who is incredibly special to me. For a short time on Sunday, we both took time to catch up on email, check in with our friends on Facebook, and check our phones, and then we met back up at an agreed upon time to resume our time together. If there is one gift that I could give everybody in the world, it would be the realization that the secret to a good relationship, is the ability to sever our ties with electronics and social media, and get back to just enjoying the company of those we love, and who we truly want to connect with. (more…)
This is Day 3 of The Suitcase Entrepreneur's 30 Day Blog Challenge, today Natalie asks "What's your definition of freedom in business and adventure in life?"
This is something that I've thought about quite a bit over the past few years, because I believe that Imagination is the Key to Life, and that Reality is Shaped by Our Dreams…
But far too many of us stopped dreaming during our transition from childhood to adulthood, we learned to limit our imagination and set our dreams aside, in an effort to conform to the demands which friends and family imposed upon us. (more…)
I was speaking with a client a few years back, who happens to be an attorney for the National Park Service. I asked him if he was working on anything interesting at the moment, and he responded by telling me that they were being sued by the mother of a child who had bitten while feeding a bear in Yellowstone… he muttered something about it being a wild bear, Yellowstone being a nature park, that there had been a sign three feet away from the family which read "Do not feed the bears" and people failing to realize that the real world is a dangerous place, it's not Disneyland! (more…)
I am grateful that I have had the benefit of strong fatherly influences in my life, however none of them have been of a traditional nature. Neither my natural father, nor step-father, are men of character who I choose to associate with. Rather both of them served primarily as examples of men who are unworthy of the title of father, and not only because they failed to live up to the expectations of a young man who was raised in the era of Leave It To Beaver re-runs on television. Thus over the years when I have required fatherly advice, I have sought the counsel of other men in the community who I have respected and admired. (more…)


text:
An official website of the United States government
Here's how you know
Official websites use .gov A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS A lock (LockA locked padlock) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.
The Council's past reports and meeting materials are provided on this website for the public's use.
The Advisory Council on Clean Air Compliance Analysis (the Council) completed its work under Section 312 of the Clean Air Act (CAA) and terminated in November 2014
The Advisory Council on Clean Air Compliance Analysis (COUNCIL) was established in 1991 pursuant to the Clean Air Act (CAA) Amendments of 1990 (see 42 U.S.C. §7612) to provide advice, information and recommendations to the agency as the EPA prepared periodic reports to Congress on the costs and benefits of CAA programs. In over 30 advisory reports to the Administrator, the Council provided advice and peer review of numerous technical studies and reports leading up to three EPA reports (often called "Section 812 Studies" after the section in the CAA Amendments of 1990 that established the requirement) on the costs and benefits of the CAA. See the 2012-2014 Council Charter for additional details on the Council's objectives and scope. This website provides information on the Council's advisory activities and reports from 1993 to 2011. Please contact the SAB Staff Office for other information.


text:
Our standard The Simpsons X Family Guy Stash Box is made from 100% solid maple hardwood. You can choose to have your box painted to match the design choice or leave it as the maple wood finish. The standard box comes with chosen design on the lid and internally it has built in storage compartments and a paper cradle.
All our rolling boxes are handmade and made to order, please allow 3-5 days for production. All of our boxes are made to the highest quality.
You'll love your new Stench Rolling Box!!
STANDARD The Simpsons X Family Guy Stash Box Size 15cm x 17cm x 6cm
Load It!!
You can choose to load your box with your favourite smoking papers, you can choose from Elements, RAW, Bulldog, Juicy Jays or you can have it empty. The choice is yours. Load it option consists of the following
Love our products? We have new designs coming out weekly!
Check out our classics and our newest designs in the stench designs gallery at https://stenchcustoms.co.uk/stench-designs
Make sure you follow us on all of our socials!
You can send us any suggestions of designs that you'd love to see on your box or any new products that you'd like to see in the shop! Add our socials to be in with a chance to be involved in one of the giveaways we run all the time! On our Tik Tok channel we make our boxes live. Send us a message on one of the socials we may be able to let you know when your box is being made so you can watch it being made and boxed for shipping! All of our socials are on the following link
Thank you for checking out the best Stench Boxes available


text:
Many people are unaware of the security cameras power supply requirements. There are several different types of power supplies to meet the needs of the camera and accessory equipment. Most all digital video cameras run off a low-voltage power supply so there are not as many factors to be concerned about as there is if they used full household AC current.
There are actually two major security cameras power supply. One power supply type produces AC current while the other produces DC current. Most cameras utilize either 24 Volts AC (VAC) or 12 Volts DC (VDC). There are some cameras that are designed to be used with either security camera power supply type. However, the power supplies are generally dedicated to one type of voltage or the other and not both. This means that a DC camera must have a DC security camera power supply. Likewise, an AC camera will only operate off an AC security camera power supply.
Why use two different types of power? For one thing, manufacturers make that decision when they create the camera. Also, if your system is going to include a very long run from the power supply to the camera, DC power will degrade over distance but AC won't. Therefore, using AC power is not always a personal preference or choice but can be a requirement for your system.
Most of Security Camera King's cameras operate on 12 VDC but there are many cameras in our on-line catalog that are dual voltage so they can utilize either type. As far as the camera goes Security Camera King offers two basic types of security camera power supplies.
The first type is a 4 channel output switching supply such as product# PWR-MINI-4. It basically the same thing as a plug-in transformer (sometimes referred to as an adapter) that has four power leads complete with connecting jacks. Some people prefer this type of security cameras power supply because it has a tendency to look sleek and small versus what could be construed as a "bulky" wall mounted power supply.
Which leads us to the second type of security cameras power supply, the multi channel Closed Circuit TeleVision (CCTV power distribution box). This power distribution box comes in 4, 8, 9, or 16 channel versions. One such example is product# PWR-4. The power supply normally is hard wired or plugged into normal house current. The power leads to each device are usually attached to screw terminals in the power distribution box.
There are benefits to using a power distribution box for the security cameras power supply. Power distribution boxes can be purchased with up to 16 channels or terminals for cameras and other devices. So instead of the mini unit which can only handle 4 devices at one time, all power sources are connected in one common spot (this good if you ever have to troubleshooting too).
Another interesting item, product# CV-24AC-12VDC is a voltage converter 24 VAC to 12 VDC at 1.5 A. Since AC power can be run further than DC without as much degradation, you can use this adapter to run AC power to the camera and then convert it into 12 VDC. This is also helpful when using thin gauged wires also.
Remember when designing and purchasing your system that there are more components that require power besides your camera. For those users that need systems that will be taking advantage of the InfraRed (IR) capability of a camera, you may also need an illuminator. An illuminator is an IR LED flood light that extends the nighttime range of the infrared function on your camera. Or you may want to use a powered microphone or other apparatuses that require power so make sure you purchase a power distribution box with enough available channels.
If you have any doubts or questions about what type and size power system you should use for your security cameras power supply, please contact one of our security experts. They can help you design a new system or improve and old one at no extra cost! You can contact them through Live Chat or by telephone at 866-573-8878 Monday through Friday at 866-573-8878 from 9AM to 6 PM EST.


text:
Richtlijn 2000/76 - Verbranding van afval - Hoofdinhoud
Waste incineration
The European Union (EU) has introduced measures to prevent or reduce air, water and soil pollution caused by the incineration or co-incineration of waste, as well as the resulting risk to human health. These measures specifically require a permit be obtained for incineration and co-incineration plants, and emission limits for certain pollutants released to air or to water.
Directive 2000/76/EC of the European Parliament and of the Council of 4 December 2000 on the incineration of waste [See amending act(s)].
Incineration of both hazardous and harmless wastes may cause emissions of substances which pollute the air, water and soil and have harmful effects on human health. In order to limit these risks, the European Union (EU) shall impose strict operating conditions and technical requirements on waste incineration plants * and waste co-incineration plants *.
This Directive not only applies to solid or liquid waste incineration plants, but also to co-incineration plants.
Experimental plants which aim to improve the incineration process and which treat less than 50 tonnes of waste are excluded from the scope of the Directive, as are plants which only treat:
-vegetable waste from agriculture and forestry;
-vegetable waste from food processing, if the heat generated is recovered;
-certain fibrous vegetable waste from pulp paper or paper production if it is co-incinerated at the place of production and the heat generated is recovered;
-certain wood waste;
-cork waste;
-radioactive waste;
-animal carcasses;
-waste resulting from the exploration of oil and gas and incinerated on board off-shore installations.
All incineration or co-incineration plants must have a permit to carry out their activities. The permit will be issued by the competent authority on the condition that the requirements defined in this Directive are complied with. The permit specifies the categories and quantities of waste which may be treated, the plant's incineration or co-incineration capacity and the procedures for sampling and measuring air and water pollutants to be used.
Delivery and reception of waste
During delivery and reception of waste, the operator of the incineration plant or co-incineration plant shall take all necessary precautions to prevent or limit negative effects on the environment and risks to people.
Furthermore, prior to accepting hazardous waste at the incineration plant or co-incineration plant, the operator of the plant must have at their disposal the administrative information on the generating process, the physical and chemical composition of the waste, as well as on the hazardous characteristics of the waste.
The operating conditions
In order to guarantee complete waste combustion, the Directive requires all plants to keep the incineration or co-incineration gases at a temperature of at least 850°C for at least two seconds. If hazardous waste with a content of more than 1 % of halogenated organic substances, expressed as chlorine, is incinerated, the temperature has to be raised to 1 100 °C for at least two seconds.
The heat generated by the incineration process has to be put to good use as far as possible.
Air emissions limit values
The limit values for incineration plant emissions to air are set out in Annex V to the Directive. They concern heavy metals, dioxins and furans, carbon monoxide (CO), dust, total organic carbon (TOC), hydrogen chloride (HCl), hydrogen fluoride (HF), sulphur dioxide (SO2) and the nitrogen oxides (NO and NO2).
The determining of limit values for co-incineration plant emissions to air is set out in Annex II. In addition, special provisions are laid down relating to cement kilns and combustion plants which co-incinerate waste.
Water discharges from the cleaning of exhaust gases
Incineration and co-incineration plants must have a permit which authorises them to discharge used water caused by exhaust-gas clean-up. This permit will ensure that the emission limit values set out in Annex IV to the Directive are complied with.
Incineration or co-incineration residues must be reduced to a minimum and, as far as possible, recycled. When dry residues are transported, precautions must be taken to prevent their dispersal in the environment. Tests must be carried out to establish the physical and chemical characteristics, and polluting potential, of residues.
Monitoring and surveillance
The Directive requires the installation of measurement systems to monitor the parameters of an installation and relevant emissions. Emissions to air and to water must be measured continuously or periodically in accordance with Article 11 and Annex III of the Directive.
Access to information and public participation
Applications for new permits must be made accessible to the public so that the latter may comment before the competent authority reaches a decision.
For plants with a nominal capacity of two tonnes or more per hour, the operator must provide the competent authority with an annual report on the functioning and monitoring of the plant, to be made available to the public. A list of plants with a nominal capacity of less than two tonnes per hour must be drawn up by the competent authority and made available to the public.
Implementation reports
By 31 December 2008, the Commission must report to Parliament and the Council on the application of the Directive, progress achieved in emission control techniques and experience with waste management. This report has been included in the Communication COM(2007) 843 final.
Other reports on the implementation of the Directive will also be produced.
The Member States must determine the penalties applicable to breaches of the Directive.
This Directive aims to integrate into existing legislation technical progress in terms of monitoring emissions from incineration processes and to ensure compliance with the international commitments made by the Community with regard to reducing pollution, specifically concerning the setting of emissions limit values for dioxides, mercury and dust produced by waste incineration. The Directive is based on an integrated approach: limits relating to water discharges have been introduced alongside value limits set for emissions into air.
Key terms of the Act
-Incineration plant: any stationary or mobile technical unit and equipment dedicated to the thermal treatment of wastes with or without recovery of the combustion heat generated. This includes the incineration by oxidation of waste as well as other thermal treatment processes such as pyrolysis, gasification or plasma processes in so far as the substances resulting from the treatment are subsequently incinerated.
-Co-incineration plant: any stationary or mobile plant whose main purpose is the generation of energy or production of material products and:
Act |
Entry into force |
Deadline for transposition in the Member States |
Official Journal |
Directive 2000/76/EC |
28.12.2000 |
28.12.2002 |
OJ L 332 of 28.12.2000 |
Amending act |
Entry into force |
Deadline for transposition in the Member States |
Official Journal |
Regulation (EC) No 1137/2008 |
11.12.2008 |
- |
OJ L 311 of 21.11.2008 |
The successive amendments and corrections to Directive 2000/76/EC have been incorporated in the original text. This consolidated version is of documentary value only.
Directive 2010/75/EU of the European Parliament and of the Council of 24 November 2010 on industrial emissions (integrated pollution prevention and control) [Official Journal L 334 of 17.12.2010].
Commission Decision 2006/329/EC of 20 February 2006 laying down a questionnaire to be used for reporting on the implementation of Directive 2000/76/EC on the incineration of waste [Official Journal L 121 of 06.05.2006].
See also
Last updated: 27.10.2011
Deze samenvatting is overgenomen van EUR-Lex.
Richtlijn 2000/76/EG van het Europees Parlement en de Raad van 4 december 2000 betreffende de verbranding van afval


text:
Andrew Romanoff John Hickenlooper wins Colorado's Democratic Senate primary
Andrew Romanoff
DENVER — Former Colorado Gov. John Hickenlooper won the Democratic nomination Tuesday to face Republican Sen. Cory Gardner in November, overcoming a series of stumbles and beating back a challenge from his left.
Hickenlooper's defeat of former Colorado House Speaker Andrew Romanoff was the second win by a centrist Democrat in a Senate primary Tuesday, after a late vote count from last week's Kentucky Senate primary gave Amy McGrath the win over State Rep. Charles Booker. Romanoff is a former moderate who turned himself into a populist, running against the moderate favorite of the Democratic establishment and promising a Green New Deal and single-payer health care.
But he could not overcome both Hickenlooper's immense financial edge — the former governor out-raised Romanoff by about 7-to-1 — and his deep name ID and reservoir of goodwill among voters stemming from two terms in the governor's mansion.
That's why Senate Democrats recruited Hickenlooper, 68, to take on Gardner, widely seen as the most vulnerable Republican in the Senate. Democrats need to net three seats in November to win control of the chamber if they win the White House, and they see Colorado as their most promising opportunity. Senate Democrats convinced Hickenlooper to run as his ill-fated bid for the Democratic presidential nomination fizzled last summer.
Hickenlooper's relatively easy win against Romanoff, Democrats argue, showed his resilience as a candidate whom Coloradans trust as a gaffe-prone, but authentic, leader.
"I've never lost an election in this state and I don't intend to lose this one," Hickenlooper said Tuesday night as he previewed his line of attack against Gardner: "We know what Donald Trump told us himself: Cory Gardner is with him 100% of the time."
In an interview, Gardner previewed how he intends to fight back. In contrast to Hickenlooper's attempt to link the election to national issues like Trump, the coronavirus pandemic and collapsing economy, Gardner rattled off some of his recent accomplishments — luring the headquarters of U.S. Space Command and the Bureau of Land Management to Colorado and passing a sweeping public lands bill.
"I'm with the people of Colorado 100% of the time," Gardner, 45, said.
The Republican Senator also called Hickenlooper "the most corrupt governor in the history of Colorado." It was a reference to the state ethics commission finding in early June that Hickenlooper violated the state's ethics law by failing to reimburse for a private plane flight and limousine ride while he was governor. Hickenlooper had refused to testify during a virtual hearing, insisting on an in-person one, earning a contempt citation from the nonpartisan commission.
The ethics case was part of a miserable final stretch for Hickenlooper in June. Amid the protests over police violence against Black people, Hickenlooper garbled the meaning of the slogan "Black Lives Matter." The following week, an African American Romanoff supporter tweeted a 6-year-old video of Hickenlooper jokingly comparing politicians to slaves being whipped to row "an ancient slave ship."
The combination of the gaffes and setbacks was enough to lure Republicans to launch millions of dollars in ads attacking Hickenlooper. Democrats responded with defensive ads, and Romanoff then jumped in and added his own attack ad versus the former governor.
Colorado's Democratic establishment, from Gov. Jared Polis to Sen. Michael Bennet, condemned Romanoff for the move. Then, days later, a big-money group that will not disclose its donors launched a $1 million ad campaign slamming Romanoff for spearheading an anti-illegal immigrant bill in 2006. Romanoff has since apologized for the bill.
Republicans always expected Hickenlooper to win the primary, though many rooted for Romanoff and the GOP hopes that Hickenlooper has been banged up enough to give Gardner a chance in the November election.
But Colorado Democrats are eager to oust Gardner. Romanoff quickly called Hickenlooper to congratulate him on the victory after polls closed Tuesday evening. "For all the differences that we had, and there were many in this race, I am equally committed to making sure Cory Gardner is a one-term senator," Romanoff told supporters during a virtual victory party on Zoom.
No Republican has won a statewide election in Colorado since 2014, when Gardner won by less than 2 percentage points in a strong year for Republicans. Hickenlooper was reelected as governor that year by a wider margin.


text:
Power Stoplight – Know when to use power!
Thank you for visiting PowerStoplight.com, but this service is no longer operating!
Power Stoplight was designed to help you determine when to use and/or generate power (items such as a dishwasher, air-conditioner, solar panels or wind turbines that you may have), helping both your checkbook and the environment!
The pages listed above are intended to help both you with your use of Power Stoplight and Smart Power Devices with its discontinued development.
What's New!
November 2014: After over 4 years and over 10,000 downloads, due to a hard drive failure as well as a number of bigger picture items, Power Stoplight is no longer operating. Thank you for your dedicated use and support – it's been fun!
October 11, 2012: Power Stoplight – Pay What You Want! At over two years in operation and looking forward to more, Power Stoplight is now following the Pay What You Want model. Please consider the value that Power Stoplight offers you and donate your choice of payment amount through the Secure Transaction PayPal Donate button below:
November 3, 2011: Power Stoplight Live launches today, bringing the power of social networking to all potential users of Power Stoplight, not just the 5,000+ who have downloaded Power Stoplight Mobile since its launch in May 2010. This unique capability means it's now easier than ever to know when to use and generate electricity for participants in Power Stoplight's regions' dynamic pricing programs, via Power Stoplight Live and its Facebook and Twitter feeds. Like and Follow Power Stoplight with the above buttons today!
May 27, 2011: Power Stoplight Mobile marks one year of operation! To support this free app and service, please follow the links on the right of this page to any Google Ads that may interest you. Additionally, if your organization or company is interested in sponsoring Power Stoplight through in-app messages & links or web page links, please contact Smart Power Devices via email.
November 8, 2010: Power Stoplight Mobile for Android is now free for download on Android Market! This change is designed to greatly add to the Power Stoplight user base while increasing consumers' grid & environmental awareness.
Smart Power Devices Ltd is seeking partner organizations to sponsor Power Stoplight Mobile's Smart Power Generation links that guide users to regional installation or consultation services of power generation, usage, conservation, etc. If your company is interested in sponsoring your region's link-through page, contact Smart Power Devices with your web address and other pertinent information on your organization.
October 12, 2010: Power Stoplight Mobile for iPhone is now free for download on iTunes! Additionally, Power Stoplight's XML feed is now open for use by outside applications, devices, etc – contact Smart Power Devices for access to this groundbreaking data!
August 20, 2010: Power Stoplight Mobile for iPhone is available today for free (normally 99cents)! Please help spread the word on this app to raise your friends', family's and colleagues' grid + environmental awareness.
August 2, 2010: Power Stoplight Mobile for Android is now available, also for only 99cents. Search for Power Stoplight Mobile from the Android Market App with keywords Power Stoplight.
July 28, 2010: Power Stoplight Mobile for iPhone v1.10 is now available. The App features multiple improvements to the user interface including vastly improved image selection, especially helpful for some Regions' Enhanced Image content. These plots or clock images show price vs. time in a powerful graphical format that is still very easy to understand.
July 26, 2010: The Smart Power Devices Ltd Press Release for Power Stoplight Mobile, Smartphone App for Home Energy Demand Response and Power Generation Control.
June 2010: Power Stoplight Mobile, the smartphone App, is now available for both the iPhone and BlackBerry platforms! Look for it in iTunes by searching for keywords Power Stoplight or by following this link.
Feel free to leave any questions or comments that you may have & be sure to visit again soon!


text:
India's central bank has responded to a representation about its crypto banking ban. The Supreme Court gave the central bank seven days to reply following a hearing last week of the petition by the Internet & Mobile Association of India against the ban.
Also read: Yahoo! Japan Confirms Entrance Into the Crypto Space
RBI's Response
India's central bank, the Reserve Bank of India (RBI), has responded to a representation submitted by the Internet & Mobile Association of India (IAMAI), as directed by the country's Supreme Court.
Nischal Shetty, the CEO of crypto exchange Wazirx, told news.Bitcoin.com that the representation is "a detailed document explaining blockchain, cryptos and how they function," noting that it was "made with the belief that if the RBI gets a deep understanding of blockchain and crypto then they may go easy on the ban and think about regulations."
This representation was sent to the central bank on July 3 during the IAMAI petition hearing. The Court ordered the central bank to reply within seven days. On July 11, RBI finally sent its response to the association.
According to Sohail Merchant, the CEO of Indian crypto exchange Pocketbits, RBI's reply is a "2 page generic response." While stating that "as of now the response cannot be made public" but there is "not much to read though," he commented:
IAMAI received the response from RBI as directed by SC [Supreme Court], the response is generic with the same language as the public circulars. They have not even given deliberate thought to the points made by us, all the basis of their arguments is 'Investor Protection.'
Shetty reiterated, "RBI has responded to IAMAI…They aren't changing their stand."
Until Next Hearing on July 20
The central bank issued a circular on April 6 banning all financial institutions under its control from providing services to companies dealing in cryptocurrencies, including crypto exchanges.
RBI gave banks three months to sever their relationships with crypto businesses. As the ban went into effect on July 5, banks began closing accounts of crypto exchanges. One by one, the exchanges stopped supporting fiat deposits and withdrawals.
To bypass banking restrictions, a number of exchanges are launching peer-to-peer (P2P) trading services. Koinex and Coindelta are reportedly launching their P2P services on July 15. Wazirx, on the other hand, already launched its P2P service. The company wrote, "Wazirx P2P goes live today, 10th July at 3PM. With Wazirx P2P, a buyer and seller can buy and sell cryptos for INR directly with each other."
Meanwhile, industry participants and stakeholders are trying to get the RBI ban lifted by filing petitions with the Supreme Court, which will all be heard on July 20.
Do you think RBI will soon lift the banking ban on crypto? Let us know in the comments section below.
Images courtesy of Shutterstock, IAMAI, and the RBI.
Need to calculate your bitcoin holdings? Check our tools section.
The post Indian Central Bank Responds About Crypto Restrictions appeared first on Bitcoin News.
Powered by WPeMatico


text:
Not enrolled in online banking? Enroll today!
Not enrolled in business online banking? Enroll Here
Leasing a car is a great way to get lower monthly payments on brand new or late model cars. It is one way for people who are not mechanically inclined, or who love the new-car smell, to make sure they can have a new vehicle every few years. There is a price to pay for that privilege, however, and sometimes people leasing cars need to find creative and intelligent ways to extricate themselves from these leases.
People want to get out of car leases for a variety of reasons:
Regardless of the reason, getting out of a car lease can be difficult. For those who go about getting out of a car lease in the wrong way, the process can be complicated, disastrous to credit scores, and expensive.
Avoiding Default
The last thing you want to do to get out of a car lease is to stop making payments and go into default. That will leave a lasting black mark on your credit record, making it difficult for you to get financing for future vehicles, homes, and any other credit you may require for several years.
Financial hardships do happen, though, which makes it essential to understand and explore your options for getting out of a lease without going into default. Merely stopping payments and waiting for the dealership to repossess the vehicle is the worst thing you can do. Not only does it add repossession fees to the amount you owe, but it doesn't absolve you of your debt to the dealership. According to your contract, you could still be on the hook for the remaining lease payments, early termination fees, and more.
Options for Getting Out of Car Leases
There are generally three options available to consumers looking to get out of a car lease. They include:
Each option offers its own set of pros and cons according to individual circumstances. Be aware, however, that the way depreciation works, automobiles depreciate at much faster rates earlier in the lease. That means that early termination may carry the risk of owning a substantial sum even when terminating the contract early.
Early termination of the lease can get you in hot water, depending on the language in the lease contract. If you are seeking to get out of the contract to "trade up" or into a different vehicle, it may be easier to do so, provided you pay the required early exit fees. In some cases, it is possible to trade down and only pay exit fees, saving you more money over time. One thing to consider is that there are "lease swapping" sites where people will list leases available to those interested in taking them over. Some people like the lower monthly payments that leasing delivers over buying, and these sites allow you to find willing individuals that might be interested in helping you find relief from your current contract.
Transferring the lease allows you to find someone interested in taking over the contract. Of course, the other person in question must meet the rigorous credit requirements many dealerships require for leasing vehicles. However, it gives you another option to consider. The problem, or consideration, with this method, is that it is not always easy to find someone willing to take over a lease. It is much easier to find buyers for vehicles than people interested in taking over a lease. However, it does remain a viable option if you do have an interested party in mind.
Buying out the lease is another consideration. This option would have you buy the vehicle outright. The benefit of this option is that you now own the car and can do anything you want with it. You can sell it, give it to a family member, or trade it in for another vehicle you wish to purchase. Additionally, you could drive it around without paying a monthly note.
Looking for ways to get out from under a car lease that no longer benefits your situation? You do have options, including trading up, buyouts, early termination, and lease transfers. The one thing you don't want to do is risk default by taking no action to relieve yourself from your lease burden.


text:
Size Guide
"The correct size is the one that looks good on the body, not the label." - Altuzarra
US Sizing:
US Numerical:
UK Sizing:
True to size.
Men's fit.
Once MODISTE's founder, Jami-lyn, created the retail concept, she knew an in-house line would come eventually. However, it came a bit sooner than she anticipated. The reception of the collaborations MODISTE worked on with other brands inspired her private label collection, and she couldn't be more thrilled to incorporate menswear and womenswear into it. She knew Nashville needed a more fashionable destination for women to shop at, and soon realized men needed this, too. We're excited to be able to begin to provide unique designers and in-house pieces for everyone.


text:
Paris G-String Brief - Ivory Jasmine
Intimate essential for a seamless look at the back.
- Briefs made from eco-friendly wood pulp fibres called Modal which feature natural anti-bacterial property
- Softer than silk and smoother than cotton
- Minimalist design and comfortable fit
- G-string cut
- 1 People brass logo
- 100% natural dyed - no harmful chemicals
- Available in 4 colours - each colour is named after a flower name: Jasmine (white), Peony (dusted rose), Sage (grey) and Orchid (black)
Materials: 93% TENCEL™ Modal, 7% Spandex
Care Instruction: Machine wash 40°C, gentle cycle with like colours. Only non-chlorine bleach when needed. Lay flat to dry. Cool iron if needed.
Size Chart: Elena wears size S (Height 173 cm, Bust 87 cm, Waist 62 cm, Hip 92 cm)
More styles can be found here


text:
Welcome to IAFF Local 1624 Sanford Professional Firefighters and Paramedics Offical Website
This is the offical website for the Local IAFF 1624 Sanford Professional Firefighters and Paramedics . This site is undergoing changes so please excuse our apperance while these changes are being made.
Happy Retirement: We wish a happy retirement to Captain Harold Smith. Captain Smith rode out his last shift on Halloween night. Captain Smith will not be going very far from us in his retirement. Captain Smith will be overseeing instruction of Fire Science at the Sanford Vocational Center. Best wishes in retirement Captain Smith.
Welcome New Firefighters: Recently hired Firefighters Joseph Wilber, Jason Porter, and Sarah Jarvis have all started working on their assigned shifts. Joseph Wilber of Sanford previously served with the Portland Maine Fire Department and will be assigned to C Shift on Rescue 3. Jason Porter of Wells, Maine will be assigned to Rescue 3 on D Shift. Sarah Jarvis of Rye New Hampshire will also be assigned to Rescue 3. Best wishes to all new hires.
Happy Retirement: Happy retirement to Captain Ron Grondin. Captain Grondin provided 44 years of service to the City of Sanford. Captain Grondin held many positions within the department and brought his skill and pride into each position. Captain Grondin retired as the acting Assistant Fire Chief. Best wishes in retirement.
Happy Retirement to Al Noble. Al proudly served the communities of Sanford and Springvale for 34 years. Al's last shift was followed by a breakfast with many department members in attendance. For those wondering, yes there was bacon!
Sanford Fire Department is now streaming its radio channel online click the link below to listen. You may also download apps within your smartphone's app store to listen.
FIRE MARSHALL PATRICK COTTER: (Appointed April 2014): Fire Marshall Patrick Cotter joined the Sanford Fire Department in September of 2013. Fire Marshall Cotter is actively involved in the community his office is located at City Hall.
PARAMEDIC JARRETT CLARKE: (Appointed March 2014): Paramedic Clarke joined the Sanford Fire Department in August of 2013. Paramedic Clarke is assigned to B-Shift on Rescue 3


text:
Home » Gutters, Fascias & Soffits » Areas covered » Gutters, Fascias, Soffits – Eglwys Cross, SY13
Gutters, Fascias, Soffits – Eglwys Cross, SY13
We're your Local Roofer in Eglwys Cross that provide expert gutters, facias & soffits.
Rated Excellent
Request a FREE, no obligation quote.
Gutters, Fascias, Soffits – Eglwys Cross, SY13
Gutters, fascias, and soffits are important components of any Eglwys Cross, SY13 roofing system. Here's a brief overview of each:
- Gutters: Gutters are channels that run along the edge of the roof and collect rainwater, directing it away from the building's foundation. They are typically made of aluminum or vinyl and come in various sizes and shapes to suit different roof types.
- Fascias: Fascias are the vertical boards that run along the lower edge of the roof and support the bottom row of tiles or shingles. They also provide a surface to which the gutter can be attached. Fascias are typically made of wood, PVC, or aluminum.
- Soffits: Soffits are the horizontal boards that run underneath the eaves of the roof, closing off the underside of the roof overhang. They are typically made of wood, aluminum, or vinyl and provide ventilation to the attic space.
When you book us for a job, we'll be there on time and complete the work to an exceptional standard.
As one of the leading roofing contractors in Eglwys Cross, SY13 you can trust us to complete the job at hand to a very high standard. 100% Satisfaction.
You can be sure that the finished product will be of exceptional quality. Our years of experience as a local roofing company in Eglwys Cross, SY13 means we won't settle for anything less.
No Job Too Big Or Small
Professional Gutters, Fascias & Soffits Eglwys Cross
If you're looking for professional gutter, fascia, and soffit services in Eglwys Cross, SY13, look no further. Our services can help protect your roofline from water damage, improve the overall appearance of your building, and increase the value of your property.
Our professional trained team is capable of installing new gutters, fascias, and soffits with guaranteed quality and longevity in Eglwys Cross, SY13.
Your Eglwys Cross Gutters, Fascias & Soffits Contractor
We use only the highest quality materials and the latest techniques to ensure that your Eglwys Cross gutters, fascias, and soffits are functioning properly and efficiently.
We also pride ourselves on our exceptional customer service, working closely with you to understand your needs and budget and provide you with a tailored solution that meets your specific requirements in Eglwys Cross, SY13.
Yes, gutters, fascias, and soffits are very important components of your roofing system. Gutters are designed to collect rainwater and divert it away from your building's foundation, preventing water damage and erosion. Fascias are the boards that cover the ends of your roof rafters, providing support for your gutter system and enhancing the overall appearance of your building. Soffits are the panels that cover the underside of your roof overhangs, providing ventilation and preventing moisture buildup.
There are several reasons why you may need new gutters, fascias, or soffits. One common reason is age and wear and tear. Over time, gutters, fascias, and soffits can become damaged or deteriorated, compromising their ability to function properly and protect your building from water damage. If you notice cracks, rust, or other signs of damage, it may be time to replace these components.
Another reason to consider new gutters, fascias, or soffits is a change in the design or layout of your roofing system. If you're adding an extension or changing the pitch of your roof, you may need to modify your gutter, fascia, or soffit system to accommodate these changes.
The cost of gutters, fascias, and soffits can vary depending on a variety of factors, including the size and layout of your roofing system, the materials used, and the complexity of the installation process.
If you want a more accurate price, dont hesitate to get in touch.


text:
Come and do an internship in Granada, Spain. Join our young, friendly and dynamic team during your internship in our Spanish language school, located in the very centre of Granada. You will get all the professional training and supervision that you need during your internship in the south of Spain, Andalusia.
For internships in Spain and study abroad students, make the most of your internship or year abroad with Escuela Delengua.
- Everyday administration tasks
- Creation and update of databases
- Market research and promotion
- Translations
- Knowledge of MS Office, Internet, Social network
- Motivated university student
- Spanish from B2 level. Mother tongue: English. Any other language is an advantage
- Period: from 3 months
- Starting date: May-June 2020
We offer
- 2 weeks Intensive Spanish course
- Accommodation during your stay


text:
Important information regarding your privacy
Policy last updated and effective: January 1, 2021
This section describes how we collect, use and share your Personal Information in operating our business and your rights with respect to that Personal Information. For purposes of this section, "Personal Information" has the meaning given in the California Consumer Privacy Act of 2018 ("CCPA") but does not include information exempted from the scope of the CCPA.
Your privacy rights.
You have the rights listed below. However, these rights are not absolute, and in certain cases we may decline your request as permitted by law.
- Information. You can request the following information about how we have collected and used your Personal Information during the past 12 months:
- The categories of Personal Information that we have collected.
- The categories of sources from which we collected Personal Information.
- The business or commercial purpose for collecting and/or selling Personal Information.
- The categories of third parties with whom we share Personal Information.
- Whether we have disclosed your Personal Information for a business purpose, and if so, the categories of Personal Information received by each category of third-party recipient.
- Whether we've sold your Personal Information, and if so, the categories of Personal Information received by each category of third-party recipient.
- Access. You can request a copy of the Personal Information that we have collected about you during the past 12 months.
- Deletion. You can ask us to delete the Personal Information that we have collected from you.
- Nondiscrimination. You are entitled to exercise the rights described above free from discrimination in the form of legally prohibited increases in the price or decreases in the quality of our Service.
How to exercise your rights
You may exercise your privacy rights described above as follows:
- Right to information, access and deletion. You can request to exercise your information, access and deletion rights by:
- Clicking here
- calling us toll free at 1-888-958-4308
- emailing [email protected]
We will need to confirm your identity to process your requests to exercise your information, access or deletion rights. As part of this process, government identification may be required. Additionally, you may designate an authorized agent to make a request on your behalf. In order to designate an authorized agent to make a request on your behalf, you must provide a valid power of attorney, the requester's valid government-issued identification, and the authorized agent's valid government issued identification. We cannot process your request if you do not provide us with sufficient detail to allow us to understand and respond to it. We strive to respond to a verifiable consumer request within thirty (30) days of receipt. If we require more time, we will inform you of the reason and extension period in writing. We do not charge a fee to process or respond to your verifiable consumer request. As stated above, we may deny your request as permitted by law. If we do deny your request, we will provide you with the reason for doing so.
Other privacy rights for California residents
California Civil Code Section 1798.83 allows California residents who have provided personal information to us or our third-party advertisers and marketing partners, if any, to request certain information regarding our disclosure of personal information to third parties for direct marketing purposes. Requests should be submitted via email to [email protected].
Within thirty (30) days of receiving such a request, we will provide a list of the categories of personal information disclosed to third parties for direct marketing purposes during the immediately preceding calendar year, if any, along with the names and addresses of these third parties, if any. Please be aware that not all information sharing is covered by the requirements of Section 1798.83 and only information on covered sharing will be included in our response.
How we collect, use and share your Personal Information
The following sections summarize how we collect, use and share Personal Information and describe our practices during the 12 months preceding the effective date of this Privacy Policy.
Personal Information that we collect
For purposes of this policy, "Personal Information" consists of information that identifies, relates to, describes, is reasonably capable of being associated with, or could reasonably be linked, directly or indirectly, with a particular consumer or household. The following list includes "Personal Information" about you that we may collect, use, store and/or share (some categories listed below may overlap):
- Identifiers – first name, middle name, last name, maiden name, alias, postal address, phone number(s), email address, unique personal identifier, student ID number, account name, social security number, driver's license number, passport number, state identification card number, criminal background status, physical description or characteristics, age, race, color, disability status, marital status, date of birth, ethnicity, place of birth, ancestry, sex (including gender, gender, gender identity, gender expression, pregnancy or childbirth and related medical conditions), sexual orientation, tribal affiliation, religion or creed, citizenship information, national origin, immigration status, veteran or military status, or other similar identifiers.
- Educational Information – Personal information from an educational record, which could include: a student's name, the names of the student's parent or other family members, the address of a student or student's family, a student's personal identifier (e.g., SSN, student number), other indirect identifiers of the student (e.g., date of birth, place of birth, mother's maiden name), other information that, alone or in combination, is linked or linkable to a specific student that would allow a reasonable person in the school community, who does not have personal knowledge of the relevant circumstances, to identify the student with reasonable certainty, or information requested by a person who the educational agency or institution reasonably believes knows the identity of the student to whom the education record relates.
- Financial Information – financial aid information, tax records, bank account number(s), debit or credit card number(s), account balance(s), and payment details.
- Health Information – medical records, drug testing results, immunization history and other personal health history.
- Commercial Information – records of personal property, products or services purchased, obtained, or considered, or other purchasing or consuming histories or tendencies.
- Professional or Employment Information – any information relating to a person's current, past or prospective employment or professional experience (e.g., resume, performance evaluations, references, etc.).
- Audio/Visual Information – videos and digital photographs.
- Internet or Network Information – Browsing history, search history, and information regarding a person's interaction with an Internet website, application, or advertisement.
- Online Identifiers – an online identifier or other persistent identifier that can be used to recognize a person, family or device, over time and across different services, including but not limited to, a device identifier; an Internet Protocol address; cookies, beacons, pixel tags, mobile ad identifiers, or similar technology; customer number, unique pseudonym, or user alias; telephone numbers, or other forms of persistent or probabilistic identifiers (i.e., the identification of a person or a device to a degree of certainty of more probable than not) that can be used to identify a particular person or device.Please read our Cookie Declaration for more information on what cookies we use.
- Inferences – the derivation of information, data, assumptions, or conclusions from any other category of Personal Information to create a profile about a person reflecting the person's preferences, characteristics, psychological trends, predispositions, behavior, attitudes, intelligence, abilities and aptitudes.
Along with the data criteria listed above, we may also collect, use and share other Aggregated Data, such as demographic or statistical data. Although this Aggregated Data may be derived from personal information you provide, it does not directly or indirectly reveal your identity. If Aggregated Data is ever combined with Personal Information and that combination reveals your identity, we would treat that combination of data as Personal Information as defined under this policy.
Additionally, we may include links to third-party websites on our own websites, such as Facebook, Instagram and Twitter. Please note that we do not control these third-party websites and we are not responsible for any information they may collect. We encourage you to read the respective privacy policies for any third-party websites if you choose to enter any of these websites.
Lastly, our services are intended for adults and are not directed towards minors or anyone under the age of 16. Children under the age of 13 are not authorized to provide us with Personal Information. If a parent or guardian believes that their child under the age of 13 has provided us with Personal Information, the parent or guardian should contact us at the phone number or email address listed above and request that the Personal Information be deleted from our records.
How we collect your Personal Information
We may collect your Personal Information in a variety of methods and from various sources. These methods and sources include the following:
- When you call, email or text us
- When you submit a "Get Started" form via our website
- When you submit an enrollment application
- When you enroll in any of our educational programs
- When you apply for federal financial aid or other financial assistance
- When you create a student account, such as student portal, LMS or other accounts
- When you attend classes or other events where we may collect your information
- When you purchase educational or other products and services
- When you submit a review or testimonial
- When you use interactive tools, such as the student portal and LMS
- When you use our career assistance services
How we use your Personal Information
We use your Personal Information to provide you with educational services that you request. This includes the following business processes:
- Determining your eligibility to enroll in an educational program
- Processing your enrollment into an educational program
- Determining your eligibility for federal financial aid or other financial assistance
- Providing you with information, products and services you request
- Creating your student account(s)
- Providing you with tutoring and career services assistance
- Communicating in written, electronic and verbal formats
- Analyzing learning outcomes and academic preferences
- Customizing advertising content
- Providing you with information about products or services which may be of interest to you
- Collecting payment for services that we provide to you, including payments through financial aid
- Processing reimbursements and refunds
- Applying for licensure on your behalf
- Verifying necessary information, such as educational and employment records
- Complying with internal policies and procedures and legal requirements
How we share Personal Information with third parties
We only share your Personal Information with third parties to provide you with the educational services you request from us and in accordance with the agreements we enter into with you and third parties. In this regard, below are the reasons we may share your information with third parties:
- We may use third-party service providers to perform business services on behalf of us, and therefore, may disclose Personal Information to these service providers as necessary for them to perform these business services. These third-party service providers are only allowed to use, disclose or maintain the Personal Information to provide these services and are prohibited from selling Personal Information.
- We may share Personal Information with our parent company and subsidiaries owned or controlled by Unitek, who may use the Personal Information for the purposes described above.
- You may be provided with an option to have us send information to third parties or grant them access to it. If you choose to do so, your Personal Information may be revealed to these third parties and all information you disclose will be subject to the third-parties' privacy policies and practices.
- We may disclose information about you if we are required to by law or regulation, such as in response to a subpoena. We may also disclose information in response to requests by government entities, such as law enforcement authorities or when we believe disclosure is necessary or appropriate to prevent physical, financial or other harm, injury or loss, or in connection with a criminal investigation.
- Some Personal Information is disclosed as a result of your use of certain services. Any Personal Information shared via any public forum using our services or on another website (such as Google, Facebook, Instagram or Twitter) may become public information. We cannot control the use of information disclosed in these public forums and recommend that you exercise caution when disclosing information in these public areas.
- We may seek to acquire other businesses or merge with them. If a change such as this happens to our business, the new owners may use your Personal Information in the same way as set out in this policy.
How we protect your Personal Information
We exercise reasonable measures to help protect and secure your Personal Information. However, any data transmitted or shared over the Internet and cellular networks cannot be guaranteed to be 100% secure. Third parties may be able to intercept or access transmissions or private communications unlawfully. Therefore, any such transmission is done at your own risk.
Updates and changes to our privacy policy
We reserve the right, at any time and without notice, to add to, change, update or modify this Privacy Policy, simply by posting such change, update or modification on the website. Any such change, update or modification will be effective immediately upon posting on the website.


text:
Appraisals of popular output from Nashville, where convention holds sway in the shadow of the country music industry, tend to interpret a performer's stance either as conformist or rebellious. Joy Oladokun is one Nashville contender who's no more confined to those polarized possibilities than any other type of binary. She's a Black, queer woman, and a child of Nigerian immigrants. An ex-evangelical worship leader, she long since moved on to the realm of pro songwriting and major label affiliation. On social media, she lists "she/they" pronouns and jokes about dressing like a dad and being called "sir" in the grocery store. In years' worth of selfie-style diaristic dispatches, she's espoused therapeutically knowledgeable and enthusiastically stoned insight into mental health crises.
It's not like Oladokun is trying to be transgressive, not in the least. She learned well the principles by which congregational praise choruses and arena-friendly pop compositions alike can summon a sense of shared common ground. Sincerity is her strong inclination. She simply operates with awareness that the artists seen as speaking for the masses have historically been cishet, white men, who've enjoyed cultural centrality without having to acknowledge or interrogate the particulars of their own identities. Or, to put it another way, only those with the luxury of presuming the dominance of their viewpoint have gotten to be the "everyman." And she just so happens to possess the ambition and ability to connect that broadly with her music.
In Oladokun's new songs, facets of who she is and what she's lived, seen and imagined, matters politicized by other people's prejudices, are what provide the evocative details that serve as normalizing entry points to her anthemic expression. The great theme of her newly released second album Proof of Life is what all-consuming work it is to lead an alert and searching existence, to break with oppressive orthodoxies and, in the face of the systemic devaluing of her life and the lives of other LGBTQIA+ people and Black Americans, to strain toward self-healing and put real trust in closeness and mutuality. "I pray it's worth the heartache when I'm done," she sings of the daily emotional labor of withstanding despair in "Keeping the Light On."
Initially self-released, 2020's In Defense of My Own Happiness was created in pandemic isolation; she doodled her way to emotional, relational and social verities, mainly using the instruments, microphones and software she had on hand. For Proof of Life, she entered into a partnership with Verve Forecast and Republic that didn't break her of DIY recording habits so much as vastly expand her cast of collaborators and enable her to pursue a wider array of sonic ideas. Written and co-produced with some of the more flexible minds that operate out of or occasionally visit Nashville (Ian Fitchuk, Mike Elizondo, Alysa Vanderheym, Dan Wilson) and featuring country, alt-rock, folk-pop and hip-hop guests (Chris Stapleton, Manchester Orchestra, Mt. Joy, Noah Kahan, Maxo Kream), Oladokun ultimately arrived at a very homey version of pop maximalism.
Oladokun began "Somebody Like Me" by strumming a chord pattern into her iPhone in her backyard. That became the woolen, almost lo-fi acoustic guitar loop beneath a plea of gospelly proportions. Halfway through, the McCrary Sisters join her in mass choir-style call-and-response, underscoring the way Oladokun, while conveying anguish, also invites prayer.
A number of tracks open with personalized vignettes from as far back as elementary school. During "Taking Things For Granted," a solo Oladokun production that gradually gathers emo intensity before taking on a Pet Sounds-esque harmonic grandeur, she summons the memory of the eighth birthday she spent alone in the swimming pool when all of her schoolmates bailed on her party. The pain of going unseen and unconsidered, she acknowledges in a refrain that seems destined for live singalongs, still lingers.
"Keeping the Light On," whose burbling combo of lite-funk drums, Afrobeats syncopation and folkie guitars she cooked up with Elizondo and Fitchuk, begins by zooming in on the weight of her life decisions. "Found a girl and found a job, just like they say good people do," she testifies, her phrasing subtly sinking toward melancholy. "But every now and then I turn to salt inside her wounds." She broadens and brightens the view considerably during the chorus, the push she gives each line conveying the capaciousness of determined hope.
At the beginning of "The Hard Way," the album's most country-leaning track, Oladokun recounts freeing herself from the Christian culture and creeds that defined her early life with a tight couplet: "Jesus raised me / Good weed saved me."
"I feel like nothing's hotter right now than religious trauma and cannabis," she jokes when we speak in the upstairs bedroom she converted into a home studio. "So I think that's probably the most relatable lyric on there." When she left the religious settings where she'd too often seen racism and homophobia receive a righteous varnish, she resolved to continue working out for herself what it means to live a good and spiritual life. Whether or not listeners identify with how she traded one salve for another, her insistence during the chorus that revelations don't come easily, that she "learned the hard way," has wistful resonance.
Oladokun doesn't mind imperfect takes and much prefers in-the-moment feeling to flawless precision, but she's not at all opposed to refining her abilities; she's been taking voice lessons, in fact. Now she'll seize on occasions that call for singing more freely and demonstratively, but that's still tempered by her ruminative inclinations. Even when she paints a picture of a world in chaotic flux during "Changes," the kind of stock inventory of bad news that might prompt another artist to perform as if from a soapbox, she slips down descending vocal lines with engrossed, and engrossing, worry. So present is she in her singer-songwriter pop, through those variations in inflection and tone, that her grandest gestures have powerfully modest magnetism.
Oladokun has her own standards for measuring the success of her efforts, as she lays out in our conversation: "As I continue to be a musician, the question I keep at the forefront is, 'Is this helping build bridges or is it hurting?' Like, 'Am I becoming a weird corporate shill, or something like that?' "
A greater and more heartening possibility is that this album and the tours and exposure to come will establish her with mainstream crowds as a trustworthy voice, and one that speaks for Nashville as much as any Music Row export. "I try to contribute to the community for good," she allows thoughtfully, "so I think it's fair to say that I can represent the city on some front."
Copyright 2023 WPLN


text:
Episode 350 – Ed Ward
Virtual Memories Show 350: Ed Ward
Podcast: Play in new window | Download
Subscribe: Spotify | TuneIn | RSS | More
"I don't like nostalgia. I consider it destructive to a rational understanding of history."
From the Sex Pistols' last show to the backseat of Elvis' gold Cadillac, Ed Ward has had a front-row seat to the history of rock & roll. He returns to the show to talk about The History of Rock & Roll, Volume 2: 1964–1977: The Beatles, the Stones, and the Rise of Classic Rock (Flatiron Books), and we get into the challenges of chronicling the form in that that era (both narratively and chronologically), his novelistic approach to history, the destructive nature of nostalgia, and how glad he was to get corroboration on the circumstances of Jim Morrison's death. Along the way, we get into his oft-quoted but misunderstood review of the first Stooges record (and how Iggy validated him), how Woodstock predicted the collapse of the music industry, why he thought (incorrectly) that the '70s were a nostalgia-proof generation, why he doesn't listen to music anymore, and his answer to the key question of the era: Beatles or Stones? Give it a listen (and check out our 2016 podcast)! And go buy The History of Rock & Roll, Volume 2: 1964–1977!
"I was there and I know how the story of rock & roll ends."
"Music is no longer central to youth culture."
"Disco was rhythm & blues by other means."
Enjoy the conversation! Then check out the archives for more great episodes!
Lots of ways to follow The Virtual Memories Show! iTunes, Spotify, Twitter, Instagram, YouTube, TuneIn, Tumblr, and RSS!
About our Guest
Ed Ward was the rock-and-roll historian on Fresh Air for more than thirty years, reaching fourteen million listeners. Currently he is the cohost of the Let It Roll podcast. His writing has appeared in The New York Times, The Wall Street Journal, and countless music magazines. He is the author of The History of Rock & Roll, Volume 1 and of Michael Bloomfield: The Rise and Fall of an American Guitar Hero. His new book is The History of Rock & Roll, Volume 2: 1964–1977: The Beatles, the Stones, and the Rise of Classic Rock. He lives in Austin, Texas.
Credits: This episode's music is Fella by Hal Mayforth, used with permission from the artist. The conversation was recorded at the Fairfield Inn near Penn Station in NYC on a pair of Blue enCORE 200 Microphones feeding into a Zoom H5 digital recorder. I recorded the intro and outro on a Heil PR-40 Dynamic Studio Recording Microphone feeding into a Cloudlifter CL-1 and a Mackie Onyx Blackjack 2×2 USB Recording Interface. All processing and editing done in Adobe Audition CC. Photos of Mr. Ward by me. It's on my instagram.


text:
The Essence of the Chinese Calendar |
The Chinese calendar combines the lunar and solar systems together. The Year and Day cycles use the solar system. However, there are two different Month cycles in the Chinese calendar. One uses the lunar system and the other uses the solar system. In the lunar system of Month, the new moon day is the first day of a lunar month. The length of a lunar month is the length of time between two new moon days. The name of a lunar Month is taken from the solar system. The Chinese solar months are not like the months of a modern calendar. The Chinese calendar divides the year into 24 solar segments according to the sun positions on the tropical zodiac (Similar to western astrology). Each segment's name was given for ancient Chinese farmers' use. To understand the whole picture view the following chart.
Solar Segment |
Astrology |
Sun Longitude |
Month Name |
Start of Spring | 315 | 1 - Tiger | |
Rain Water | Pisces | 330 | |
Excited Insects | 345 | 2 - Rabbit | |
Vernal Equinox | Aries | 0 | |
Clear and Bright | 15 | 3 - Dragon | |
Grain Rains | Taurus | 30 | |
Start of Summer | 45 | 4 - Snake | |
Grain Fills | Gemini | 60 | |
Grain in Ear | 75 | 5 - Horse | |
Summer solstice | Cancer | 90 | |
Slight Heat | 105 | 6 - Sheep | |
Great Heat | Leo | 120 | |
Start of Autumn | 135 | 7 - Monkey | |
Still Hot | Virgo | 150 | |
White Dew | 165 | 8 - Chicken | |
Autumnal Equinox | Libra | 180 | |
Cold Dew | 195 | 9 - Dog | |
Frost Descends | Scorpio | 210 | |
Start of Winter | 225 | 10 - Pig | |
Light Snow | Sagittarius | 240 | |
Heavy Snow | 255 | 11 - Rat | |
Winter Solstice | Capricorn | 270 | |
Little Cold | 285 | 12 - Cow | |
Severe Cold | Aquarius | 300 |
The solar months are defined by the sun longitudes. The first month, Tiger month, begins from the "Start of Spring" segment or when the sun enters the 315th degree on the tropical zodiac. The second month, Rabbit month, begins from the "Excited Insects" segment or when the sun enters 345th degree. The beginning of a solar month is called the Segment Point. In the middle of a solar month is called the Center Point. For example, the segments of "Rain Water" and "Vernal Equinox" are Center Points. The astrology names of "Pisces" and "Aries" apply to these Center Points.
The lunar month name is derived from the Solar Center Point. For example, If a lunar month contains the "Rain Water" Center Point, then it is the first month of the lunar calendar, as known as the Tiger month.
If a lunar month does not contain any Solar Center Point, that month is known as a Leap Month. The name of this leap month is the same as previous lunar month. The reason to assign leap months is that we want the moon cycle to harmonize with the sun cycle. Because one year has about 365.2425 days and one month has about 29.53 days, one year has about 12.3685 months. 12.3685 is about 12 and 7/19. If we put seven extra months in 19 years, sun and moon should be back to the same sky position. "Seven Leap Months in 19 years" is easy for people to remember. However, 12.3685 is almost equal to 12 and 144/391. That means "144 Leap months in 391 years" is a more accurate way to assign Leap months. So far, no one has lived long enough to observe the entire cycle.
Anyway, the principles of the Chinese Calendar use the following three rules which the ancient Chinese made them thousand years ago.
In the Chinese Lunar Calendar, the new moon day is the first day of a lunar month and the length of a lunar month is the length between two new moon days. In the Chinese Fortune-Telling (Astrology) Calendar, the first day of a month is the day on a Solar Segment Point and the length of a month is the length between two Solar Segment Points. Therefore there is no Leap Month in the Chinese Fortune-Telling System.
Without this knowledge, above-mentioned, most people will be confused about the solar months and lunar months. They may think all Chinese Fortune-Telling system use lunar months. Actually, the Fortune-Telling system called Eight Characters only uses the solar month, not the lunar month. The other popular system called Dipper uses solar month and lunar month together.
The counting system of Day is the Stem-Branch 60-day cycle system. No one knows who invented the Stem-Branch for Day counting system, but legend has it that characters of Day Stem-Branch were found on Oracle bones. The Animal names of Stem-Branch were applied into the Month system around 206 B.C. (between the Chin and Han dynasties). The Stem-Branch was applied into the Year system around 164 B.C..
Almost every Chinese dynasty had its own calendar. One reason was that the new emperor needed to announce the new rules including the new calendar to the public. The other reason was that the astronomer's officers had to make some adjustments on the calendar in order to match the sun and moon in the sky.
The first day of a year has been changed many times in Chinese calendars. The current Chinese calendar uses the first day of the first month of Tiger month as the first day of a year, which was initially adopted by the Shiah dynasty (2183-1752 B.C.). Today, some people consider the Winter Solstice as the first day of a year in the Chinese Fortune-Telling System, because that makes more sense from the astronomy view.
There is no simple conversion table for converting the western calendar to the Chinese calendar, if you want to get the precise date and time. For most accurate calculation, we need to use high precision Sun and Moon astronmical data to do the conversion. Now the complete information about programming, sample Visual Basic program and Sun and Moon astronmical data for Chinese Lunar Calendar are available in the CD.
about Chinese Lunar Leap Month
Lunar Calendar Conversion
Show you How to Convert Lunar Calendar


text:
Or search by topic
Published 2012 Revised 2015
Some teachers might think that proof has no place in the primary mathematics classroom but we would argue that it has. At NRICH we believe that the ideas underlying mathematical proof are central to the understanding of mathematics as a whole. Generalising, justifying and convincing are key elements of mathematical thinking and they form the building blocks of proof. As Haylock (2006) says:
proof is 'a complete and convincing argument to support the truth of an assertion in mathematics which proceeds logically from the assumptions to the conclusion'. Another significant article about proof in primary mathematics classrooms is quite an old one by Lesley Jones (1994) but is is nonetheless worth reading and still relevant.
This idea of proof involves notions of conviction as John Mason (1982) has pointed out. He characterises these levels as being equivalent to convincing oneself, convincing a friend and convincing a sceptical 'enemy'. In our experience of working with young children on proof we find that they are responsive to the idea, easily start looking for opportunities to prove whether things are true, and
offer reasons for their arguments. These reasoned arguments can then be developed into fully fledged proofs.
Generic proof is a special kind of proof that works in rather a different way from the usual idea of logical steps progressing through to a reasoned conclusion, although that is a part of the process. However this is not generalising from a sequence or pattern but it is about situations when the structure of a specific example shows how it all works. This is a great idea for young children to come to terms with and offers lots of opportunities to examine the underlying reasons about why numbers work as they do.
Tim Rowland defines generic proof as 'carefully selecting a particular example that enables one to see, in that example, the general structure'. So what might this mean for us in primary mathematics classrooms? This month we have created a set of primary problems exploring some of the structures in our number system, particularly the properties of odd and even numbers, but also looking at the external angles of polygons so we are presenting ideas about generic proof in the sphere of geometry as well as number theory.
As an example let us look at this month's problem Take Three Numbers. The idea underlying this is of taking a run of three consecutive counting numbers. The children can choose a run for themselves such as 4, 5, 6 and look at the sum of the numbers. They can choose any sequence like this that they like. It doesn't matter where they start as long as the three numbers are all 'next door neighbours'. We are asking them to explore what happens when we add these three numbers together. Is there anything special about the result? Is this special result always true? If it is, can you convince me just through examining your one example? This leads us into a 'generic proof' by careful reasoning with our chosen example.
So how might we support children to do this? We will illustrate this by showing you how it might work for 'Take Three Numbers' and leave you to apply a similar approach to the other problems for this month. First of all ask them to explore their three consecutive numbers and find their sum. Encourage them to use diagrams and 'stuff' like multilink cubes to create models of the numbers and their sum. Make sure you actually do this yourself before you let them loose on it so that you are aware of all the obstacles and opportunities this modelling offers to us in finding a result.
Questions and prompts to use:
Can you tell me three consecutive numbers?
Make multilink towers, use Numicon or draw a picture to represent each.
What is their total?
How can you re-organise your numbers and their representations to show this?
Can you carry out this exploration yourself? Can you prove that your result holds for any three consecutive numbers by unpacking this one?
Don't click on this until you have convinced yourself of your result!
The key point to get across is that the proof lies in the structure of just this one example. How good is that?
On the website this month we provide some more opportunities to explore this idea of the structure of one example giving us generic proof - another opportunity to embed proof in primary classrooms. In addition to the context of number, there are also some geometric problems about polygons in which the generic proof relies on the idea of closing up the shape. See whether you can see, and help your learners to see, how the notion of 'Walking round a square' links with 'How much to turn' in giving a generic proof for the external angle sum of a polygon. As Tim, whose suggestions have formed the basis of this month's problems has said: 'It would be nice to have some more examples of this kind and we would be delighted to hear from any of you who find something similar'. Just email us at NRICH.
Haylock, D. (2006) Maths explained for primary teachers. London, Sage.
Mason, J., L. Burton & K. Stacey. (1982) Thinking mathematically. Addison-Wesley Publishers Ltd.
Jones, L. (1994) Reasoning, Logic and Proof at Key Stage 2. Mathematics in School. Leicester: Mathematical Association