text:
Church leader heads walks to 130 Lancashire churches
The leader of Lancashire's Methodists has successfully completed a walk to each of the denomination's churches in the county.
The Reverend Stephen Poxon visited 130 Methodist churches, chapels, schools and homes for the aged in the county.
The walk took 30 days to complete and finished at a celebration in Silverdale Methodist Church.
The Reverend Poxon said the walk had given him a "new perspective of Lancashire".
He said: "I'm in my 13th year in this post and I wish I had done this walk 12 years ago because it has given me a new perspective of Lancashire, the people and the churches I seek to serve."
'Year of Prayer'
Mr. Poxon, who is soon to leave his post for a yet to be announced new position in the church, began his walk in the Ribble Valley, at Paythorne, on Palm Sunday.
Since then, in two and three-day bursts across the summer, Mr. Poxon has visited his entire district.
He said: "We designated 2012 as a Year of Prayer.
"I thought I was making a joke when I suggested I should pray in each of our churches but people took me seriously and out of that came this prayer walk across Lancashire."
Forty people joined Mr. Poxon for the final leg of the walk which began in north Lancashire at St Cuthbert's in Over Kellet. They walked through Tewitfield and Warton before finishing in Silverdale.
Some of the party had taken part in over two thirds of the prayer walk.
Ian Kitchen from Rishton completed 23 of the 30 stages.
He said: "We've probably spoken to around 500 people in 90 odd churches.
"We have heard wonderful stories about what God's doing in these churches and it's been an inspiration."
Another walker, Madeline Riley, also from Rishton, said: "I've heard recurring stories from various people about the problems they face and the different ways they have tackled them.
"I've heard how they have come out of the other side and it is wonderful to hear."
Walker Steve Colling believes visiting different churches has given him a chance to experience new ways of church.
"I've learned different ways of working with children and young people," said Mr Colling.
"We've seen new ideas for fellowship and how buildings have changed."
Mr. Colling is already thinking of revisiting some of the venues he has been to.
He remarked: "We've also made lots of contacts across Lancashire and now have some new places to stay."
Lancashire Methodist's Dave Davenport highlighted how the walk had taken him to places he would never have seen.
"I've met lots of people I would never ever have met in any other way. I've heard stories that I would never have heard in any other place," he said.
As the prayer walk came to a close, Mr. Poxon reflected on the challenges of his journey.
"On August Bank Holiday Monday we'd asked people to come out as we were leaving the Church at the Mount in Fleetwood.
"When we got to the church it was pouring with rain. To be fair, 30 people turned up," said Mr Poxon.
"We took the ferry, and then, walking from Knott End to Pilling along the sea wall was horrendous with the wind and rain hammering down. Yet people's spirit kept up, so it turned out to be good day."
He said: "I think the high point has been the people we have met and also hearing what the church is doing.
"I'm proud to be part of a church that seeks to serve the community and show that the love of God is active amongst them."
Joe Wilson presents the faith programme on BBC Radio Lancashire from 06:00 each Sunday.


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text:
Some of the most common types of antique safes were the cannonball, hobnail and wooden cabinet safes. The time period was a factor in a safe's popularity, as safes went through many transformations and upgrades throughout time.
Cannonball safes were named for their round shape. This type of safe was often used by banks in the latter half of the 1800s as their large size and formidable shape gave a feeling of security to the bank's clients. A smaller version of this type of safe was also available for home use. The Marvin Safe Co. was the first manufacturer of this type of safe. Hobnail safes were popular in the early to middle 1800s. They were a very sturdy form of antique safe, often featuring raised bumps on the outside to resemble armor. They often weighed around 200 pounds, but some models weighed as much as 700 pounds.
The wooden cabinet safes were safes hidden in ornate wooden cabinets. The cabinets often featured ornately carved legs and detailing to fit in with a high-end decor and hide the fact a safe was held within. Some of the more upscale of these cabinets featured framed paintings on the front door panel.


text:
Newell G. Meyer
July 31, 1916 - Aug. 31, 2006
Newell G. Meyer, 90, of Eagle, died Aug. 31, 2006, at Waukesha Memorial Hospital.
He was born on July 31, 1916, and was retired from the Milwaukee Journal newspaper, where he had worked for 25 years. He was a resident of Eagle since 1976 and a veteran of the U.S. Army.
He is survived by nieces, nephews, other relatives and friends.
He is preceded in death by his wife, Ann.
Funeral services will be held at noon Thursday, Sept. 7, 2006, at the Family Center (South Chapel) at Wisconsin Memorial Park, 12875 W. Capitol Drive., Brookfield.
Visitation will be from 10 a.m. until the time of services on Thursday. Entombment will be at Wisconsin Memorial Park.
Mealy's Funeral Home in Eagle serving the family. For more information, please call the funeral home at 594-2442.


text:
There has been plenty of speculation about the launch of Apple's next iPhone, and thankfully it looks like we're only going to have to sift through the rumors and fakes for another week or so. Apple has sent their invites out for the launch of the iPhone 6, and September 9th is the big day.
Via Geek.com


text:
All righty then. You got the gear? And of course, then you got more gear. Then you bought some goodies that you didn't need but really wanted. Then you bought some duplicates incase something went bad, you wanted to be prepared. And of course, there are TWO divers in the house, not just one.
So then what? Build on an extra room for storage???
In the beginning, storage was a MAJOR problem for us so we had to limit what we bought. Then we got a bigger apartment and had a two car garage, so we felt unlimited.
Despite finally having a place to put everything, we struggled as we would pack to leave for diving. What to do with it all? We didn't need something so fancy as a nice big piece of luggage because we weren't flying and the stuff would sit wet in it.
So we opted for a PERFECT solution. We went and got a rubbermaid tote. The biggest they make. It has wheels on one end. And it holds EVERYTHING but our tanks - for two people! We can even throw our wet suits and wet swimming suits and towels in it and drive home in comfy dry warm clothes.
What's in our tote?
2 bc's
2 weight belts with weights
2 sets of fins (and of course he wears xl so they are super long)
2 regulators with octos
2 3mm wetsuits
2 pair of boots
2 pairs of gloves
2 sets of slates
2 inflatables (orange ones)
1 flashlight (long story - don't ask)
2 knives
1 repair kit (extra straps, flaps, velcro, tools, etc)
bag of ziploc baggies
1 spare air
1 tarp
Yep. It all fits. And while it is heavy when you have to lift it into the truck/car (like I do that, yeah right) I can easily roll it on the ground AND carry a lounge chair :)
It was one of the best things we ever bought for diving. And in the off season, it is sealed and stored in the garage all nice and neat, out of the way. So if you are having problems with storage, check into it.


text:
If you are a User who needs information about their Personal Data, contact the Owner directly using the contacts below.
If you are the owner of this privacy policy, head to the iubenda website to understand why this policy has been deactivated.
CTPartisans - Alameda Ribeirão Preto, 410 - 01331-000 São Paulo (Brazil), email@example.com


text:
The Fundraiser in Chief
Since taking office, President Obama has attended almost 400 events to hit up donors.
As de facto party leader, presidents raise political money. Since he makes time for it no matter how pressing world or national affairs are, President Obama apparently likes raising campaign funds. He has attended 34 fundraisers so far this year. What is unusual is how much time he devotes to it, his timing and his lack of judgment.
For example, the afternoon following the Sept. 11, 2012, murder of Ambassador Christopher Stevens in Libya, Mr. Obama left the White House for a fundraiser in Las Vegas and a campaign appearance...


text:
Scotty Phillips, Debate Coach at The Potomac School in McLean, VA, Roy Levkovitz Director of Debate at Woodward Academy in Atlanta, & Bill Batterman, Director of Debate at Marquette University High School in Milwaukee, jointly started a blog on debate earlier this year. While it tends to be geared towards NFL style debating, the strategy, research, & theory articles on the blog will be useful to any debater who wants to improve. Todays article on basic search terms is a prime example.
03 September, 2009
The 3NR
Posted by Frank Wyer at 10:01 PM
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text:
Cockroaches are one of the most common household pests in the world. They are attracted to your home in search of food and water mostly. The three most common types are the German, Oriental and American roaches.
These tiny creatures are not only ugly to look at, but also harmful to your health. They act as carriers of different germs and bacteria that cause diseases.
They contaminate the space and items around them with waste products, which can cause allergic reactions in people and pets.
They can also damage household items like books, clothes, electronics, wires and more. Plus, when present in large numbers, they produce a mild musty smell.
As cockroaches reproduce quickly, you need to take measures to get rid of them as quickly as possible. When they are present in small numbers, you can easily control their growth with little effort and time.
There are plenty of commercial products in the market that can help reduce a roach infestation, but such products pose health risks for you and your family.
There are certain natural methods that, while they may require repeated use, can surely help in getting rid of them.
Here are the top 10 ways to get rid of cockroaches.
1. Borax and Sugar
Borax is a good option to try at home to control the growth of roaches and prevent the insects from entering your premises.
Borax dehydrates the pests' exoskeleton and damages their digestive system, which ultimately leads to their death.
To increase the effectiveness of borax, it should be used along with sugar. Sugar helps attract the roaches to the trap.
-Mix three parts of borax and one part of sugar.
-Put this mixture along places where you usually see the roaches at night. (Wash your hands thoroughly after distributing this mixture. It is recommended to wear gloves.)
-The next morning, you will see many dead roaches, which you need to discard.
-Repeat for a few days.
In place of borax, you can also use boric acid or simple baking soda.
Note: This remedy is not recommended if you have kids or pets at home.
2. Neem
Neem oil or powder is a good alternative to the synthetic and biological methods of insect control. It contains highly volatile components that act as insect deterrents.
Plus, it is less toxic to non-target organisms and economically cheaper than chemical repellents.
A 2014 study published in the International Journal of Pure and Applied Bioscience reports that neem is one of the plants reported to have the ability to kill or keep away the pests.
Other effective plants include turmeric, clove, sage, Chinese chaste tree and Malabar nut.
-Put 1 tablespoon of neem oil in a regular-sized spray bottle and fill it with water. Spray the solution in the affected areas at night. Repeat as needed.
-Another option is to sprinkle neem powder around the affected areas before going to bed. Repeat as needed.
3. Kaffir Lime Essential Oil
The oil derived through steam distillation of kaffir lime (makrut lime) leaves also works as an effective natural repellent for roaches.
In a 2007 study published in the Southeast Asian Journal of Tropical Medicine and Public Health, researchers analyzed the repellent activity of seven essential oils and found that kaffir lime leaf essential oil showed the best repellency against three types of cockroaches under laboratory conditions.
In fact, it showed 100 percent repellency against the American and German roach species.
-Add 8 to 10 drops of kaffir essential oil to 2 cups of water.
-Pour the solution in a spray bottle.
-Spray the solution in areas where you notice roaches at night.
-Pour the remaining solution around drains and sinks.
-Repeat as needed for several days.
Other essential oils that have insect repellent properties are peppermint and tea tree oil.
4. Catnip
The herb catnip also works as a natural repellent to cockroaches. The active ingredient nepetalactone offers the repellency property. Plus, it is nontoxic to humans and pets (except cats).
A 2006 report by American Chemical Society found that catnip essential oil can act as an effective insect repellent for common household pests.
-Put a small amount of fresh catnip leaves in small porous bags or sachets. Leave them in areas where you see cockroach activity. Change the leaves after a few days, and repeat as needed.
-You can also simmer 1 tablespoon of catnip leaves in 2 cups of water for 5 minutes. Strain and allow it to cool. Spray the solution on kitchen cabinets, behind counters and anywhere you suspect the presence of roaches at night.
5. Diatomaceous Earth
Diatomaceous earth is another nontoxic alternative to get rid of roaches. It works as a gentle abrasive and is highly effective in hidden areas, such as cabinet tops and behind appliances, where roaches congregate.
When the insects come in contact with the sharp tiny particles of diatomaceous earth, they die due to the damage caused to their waxy exoskeletons. Diatomaceous earth is also considered good for repelling bed bugs.
-Lightly dust food grade diatomaceous earth on suspected areas.
-Repeat once daily until all the roaches are gone.
Note: Always wear a mask and rubber gloves when handling diatomaceous earth. Avoid using it in wet and damp areas as it will not work.
6. Coffee Grounds
The aroma of coffee grounds lures cockroaches out the dark, quiet corners of your house. It's one of the most effective natural options to get rid of roaches. However, it is still not known whether the caffeine in coffee kills the roaches.
1.Fill a few glass jars with water.
2.Put wet coffee grounds in small paper cups and place them inside the jars.
3.Put the jars against walls or baseboards or any other place where you see roaches at night. The roaches are attracted to the aroma of the coffee grounds and enter the jar, from which they can't escape.
4.The next morning, dump the contents of the jars.
5.Repeat the process for a few days.
Full article you can read here: top10homeremedies.com


text: Thirty Five years of Automath Heriot-Watt University, Edinburgh Wednesday 10-Saturday 13 April 2002 http://www.cee.hw.ac.uk/~fairouz/automath2002/ FINAL CALL FOR PARTICIPATION Registration closes on 25 March 2002 Final call for registration which closes on 25 March 2002 at 5 pm. Automath started in 1967 by N.G. de Bruijn. Automath (automating mathematics) was the first system to use computer technology to check the correctness of whole books of mathematics. During his work on Automath, de Bruijn discovered many concepts that still remain of great relevance to the theory and practice of computation. For example, de Bruijn indices still play an important role in the implementation of programming languages and theorem provers, de Bruijn's new type systems were influential in the discovery of new powerful type systems, and de Bruijn re-invented the Curry-Howard isomorphism (which should be referred to as the Curry-Howard-de Bruijn isomorphism). The Landau book on the foundations of analysis remains the only fully encoded and checked mathematical book in any theorem prover. The Landau book was encoded by Bert van Benthem-Jutting in Automath in the early seventies. This workshop is to celebrate the 35th year of Automath and some of the impressive directions in using computers for mathematics. Lecturers and Topics: --------------------- +Peter Aczel (Manchester, UK): Formalising Mathematics --for mathematicians and by mathematicians +Andrea Asperti (Bologna, IT): The challenge of the Web for Mathematics +Henk Barendregt (Nijmegen, NL): Proof-assistants for Mathematics +Bert van Benthem-Jutting (Eindhoven, NL): Proof Checking the Full Book of Landau on the Foundations of Analysis +N.G. de Bruijn (Eindhoven, NL): The Design of Automath +Bob Constable (Cornell, USA): Recent Results in Type Theory and their Applications in MetaPRL and Nuprl +Catarina Coquand (Chalmers, SE): Structured Type Theory and the Proof Checker Agda +Ingo Dahn (University of Koblenz, Germany): Personalising Mathematical Textbooks +Gilles Dowek (INRIA, FR): Binders, models, projections and de Bruijn indices +Jacques Fleuriot (Edinburgh, UK): A Theory of Infinite Hyperreal Base Logarithms in Isabelle/HOL +Therese Hardin (Paris 6 and INRIA-Rocquencourt, FR): FOC, a certified computer algebra library + Gerard Huet (INRIA, FR): Title to be announced +Tudor Jebelean (RISC-Linz, Austria): Theorema: a System for the Working Mathematician +Michael Kohlhase (Carnegie Mellon, USA) OMDoc: An Open Markup Format for Mathematical Documents (A Building Block for Web-Based Math) +Jan-Willem Klop (Amsterdam, NL): Title to be announced +Claude Kirchner (LORIA, Nancy, FR): The ELAN System + Helene Kirchner (LORIA, Nancy, FR): Proof assistants and rewriting techniques: an experiment with Coq and Elan +Daniel Leivant (Indiana University, USA): Incorporating computational complexity into mathematical libraries +Jonathan Seldin (Lethbridge, Canada): Logic and Type Theory in Theorem Provers +Andrzej Trybulec (Poland): Towards practical formalization of mathematcis +Benjamin Werner (INRIA, FR): Formalizing the 4-color theorem's proof (or: "500 hundred million lemmatas") +Freek Wiedijk (Nijmegen, NL): A contemporary Implementation of Automath and The Fundamental Theorem of Algebra In addition to the above list of lectures, there are also accepted talks. Program can be found at: http://www.cee.hw.ac.uk/~fairouz/automath2002/program.html For registration and accommodation check the URL http://www.cee.hw.ac.uk/~fairouz/automath2002/ Registration closes at 5 pm on 25 March. If you have any questions, email email@example.com


text:
Version End of Life. 31 October 2018
This is a recommended release for all customers as it contains important updates and improvements to the stability of the manager component, specifically with respect to stalls and memory usage that would cause manager failures.
We recommend Java 7 for all Continuent Tungsten 2.0 installations. Continuent are aware of issues within Java 6 that cause memory leaks which may lead to excessive memory usage within the manager. This can cause the manager to run out of memory and restart, without affecting the operation of the dataservice. These problems do not exist within Java 7.
The following changes have been made to Continuent Tungsten and may affect existing scripts and integration tools. Any scripts or environment which make use of these tools should check and update for the new configuration:
Within composite clusters, TCP/IP port 7 connectivity is now required between managers on each site to confirm availability.
The following issues may affect the operation of Continuent Tungsten and should be taken into account when deploying or updating to this release.
The default behavior of the manager is to not fence a datasource for which a replicator has stopped or gone into an error state. This was implemented to prevent reducing the overall availability of the deployed service. There are cases and deployments where clusters should not operate with replicators in stopped or error states. This could be configure by changing the following properties to
trueaccording to the master or slave role requirements:policy.fence.slaveReplicator=false policy.fence.masterReplicator=false
If they are set to true, the manager should fence the datasource by setting it to a 'failed' state. When this happens, and the datasource is a master, failover will occur. If the datasource is a slave, the datasource will just stay in the failed state indefinitely or until the replicator is back in the online state, in which case the datasource will be recovered to online.
At present the setting of these properties are not honored.
Issues: TUC-2241
Improvements, new features and functionality
The default buffer sizes for the Section 6.5, "Using Bridge Mode" have been updated to 262144 (256KB).
To ensure that the correct number of the managers and witnesses are configured within the system, tpm has been updated to check and identify potential issues with the configuration. The installation and checks operate as follows:
If there are an even number of members in the cluster (i.e.
provided to
If witnesses are provided through
--witnesses, continue
If witnesses are not provided through
--witnesses, an error
is thrown and installation stops.
If there are an odd number of members in the cluster (i.e.
provided to
If witnesses are provided through
--witnesses, a warning
is raised and the witness declaration is ignored.
If witnesses are not provided through
installation continues as normal.
The number of members is calculated as follows:
Explicitly through the
--members option.
Implied, when
then the list of hosts declared in
--master and
Implied, when
then the list of hosts declared in
--master and
--slaves and
Issues: TUC-2105
If ping traffic was denied during installation, then installation could hang while the ping check was performed. A timeout has now been added to ensure that the operation completes successfully.
Issues: TUC-2107
The connector will now re-connect to a MySQL server in the event that an opened connection is found closed between two requests (generally following a wait_timeout expiration).
Issues: TUC-2163
When initially starting up, the connector would open a connection to the configured master to retreive configuration information, but the connection would never be closed, leading to open unused connections.
Issues: TUC-2166
The cluster status output by the tungsten cluster status within a multi-site cluster would fail to display the correct states of different data sources when an entire data service was offline.
Issues: TUC-2185
When the connector has been configured into read-only mode, for
example using
the connector would mistakenly route statements starting
set autocommit=0 to the
master, instead of being routed to a slave.
Issues: TUC-2198
When operating in bridge mode, the connector would retain the client connection when the server had closed the connection. The connector has been updated to close all client connections when the corresponding server connection is closed.
Issues: TUC-2231
The manager could enter a situation where after switching a relay on one physical service, remote site relay is incorrectly reconfigured to point at the new relay. This has been corrected so that reconfiguration no longer occurs in this situation.
Issues: TUC-2164
Recovery from a composite cluster failover could create a composite split-brain situation.
Issues: TUC-2178
A statement of record (SOR) cluster would be unable to recover a failed dataservice.
Issues: TUC-2194
A composite datasource would not go into failsafe mode if all the managers within the cluster were stopped.
Issues: TUC-2206
If a composite datasource becomes isolated due to a network partition, the failed datasource would not go into failsafe mode correctly.
Issues: TUC-2207
If a witness became isolated from the rest of the cluster, the rules would not exclude the failed witness and this could lead to memory exhaustion.
Issues: TUC-2214
The descriptions and definitions of the
archive and
standby roles has been
clarified in the documentation.
For more information, see Section 5.3.3, "Understanding Datasource Roles".
The documentation for the recovery of a multi-site multi-master installation has been updated to provide more information when covering.
Issues: TUC-2175
For more information, see Section 3.2.6, "Resetting a single dataservice".


text:
Omega 3 and Omega 6 are both essential fatty acids that support cellular health and overall health and well-being in horses. They are termed "essential" since they are compounds that
As a fertilizer, alfalfa tea provides a good source of nitrogen, calcium, iron, magnesium, phosphorus, zinc, vitamins (A, D, B1, B6, E, K and U) and triacontanol, which is a
Preventing Toxoplasmosis in Your Goats What is Toxoplasmosis? Toxoplasmosis is a disease that causes abortion in sheep and goats. Cats are the main carriers of this protozoan known as
I've been feeding Chaffhaye to my goats for 3 years now and I'm very very satisfied with the results. My distributor is Cathy Phaneuf, and she's such a wonderful lady.
There are many choices when selecting a dairy goat breed for your small farm. Such factors as: milk production, milk fat content, and temperament are just a few of things to consider when selecting your farm's dairy goat breed. To help with this difficult decision, we've compiled a list of our top 5 dairy goat breeds for small farms.


text:
The public has unanimously loved the #Nexus phones that were outed by #LG. There were three in total – the #Nexus4 (2012), the #Nexus5 (2013) and the recently unveiled #Nexus5X. But it seems like this is all the Nexus handsets that we'll see in the markets. A company spokesperson has mentioned that there will be no Nexus smartphone launching from the company this year, confirming once and for all that there won't be a LG Nexus 5X successor, well not from LG at least.
The company apparently wants to focus on its own brand, which is why it has decided to leave the Nexus line. We're not sure if this is good news, but if this means that the company will bring more devices like the recently launched LG G5, we have no reason to be concerned at this point.
Given that LG has produced some of the best Nexus handsets to us stock Android lovers, this does come as a bit of a disappointment to me personally. But we're sure that Google will team up with an equally capable manufacturer for the production of the upcoming Nexus handset. HTC is supposedly launching two Nexus handsets this year, which does sound exciting.
What do you make of this news? Will you miss LG's Nexus handsets?
Source: CNET
Via: GSM Arena


text:
Privacy Policy
© Copyright 2011 Deer Park Hall. The contents of this site ("the website") are protected by copyright of Deer Park Hall and / or its clients and suppliers. Reproduction of part or all of "the website" is prohibited other than in accordance with this Notice. All rights are reserved.
Use of content
We grant you the non-exclusive right to download the files supplied provided that the material shall not be amended or modified in any way and shall only be used for promotional reasons on behalf of Deer Park Hall.
If you supply us with personal information in order to receive information from us, we collect and store that information. That information enables us to fulfil your information request. If you review or download information, we track the visit. That information is helpful to provide you with tailored information and to give us information about your use of "the website". Information submitted via "the website" will not be passed on to any other organisation.


text:
The mother of convicted killer Dale Cregan has been cleared by a jury of obtaining confidential information from a police call handler during the manhunt for her son.
Anita Cregan, 56, was found not guilty of aiding and abetting misconduct in a public office after a nine-day trial at Manchester crown court.
The jury took three hours to clear her and two co-accused, police call handler Kathryn Smith, 25, and her former boyfriend Sean Booth, 31.
Smith was accused of supplying information to Booth, who in turn was alleged to have passed it to his neighbour Anita Cregan, the mother of his childhood friend.
At the time Dale Cregan was the prime suspect in a double killing and subject to a nationwide manhunt. The victims were father and son David and Mark Short and a £50,000 reward was put up for Creegan's arrest.
Smith, the daughter of a police inspector for Greater Manchester police (GMP), burst into tears and covered her face as the verdict was given.
Outside court Cregan said: "I thank the jury for coming to their decision and it should never have come to court anyway in the first place.
"I feel sorry for Kathryn and Sean. They were only here because they were linked to me and my name is Cregan."
The prosecution alleged that Smith, a civilian call handler with GMP, used computer systems while at work to check developments in the manhunt for Dale Cregan with intent to share the information.
The charges arose after one of Cregan's neighbours called police over an unfamiliar car with camping gear inside, parked near their home on Sutton Drive, Droylsden. This caused armed police to swoop on the Cregans' house.
Kathryn Smith was alleged to have told her then partner Booth which neighbour called police.
Anita Cregan then interrogated the neighbour about a "grass on the street", claiming she had inside information about who made the call. But she denied ever asking Booth to get information from Smith.
Smith told the jury any information she discussed with Booth was just idle chat while talking about work after her shift and that she trusted Booth not to pass the information on to the Cregans.
She admitted sometimes looking at computer-generated items for which she did not have clearance. But the court heard the culture at GMP was for workers to look at details of police incidents where they lived out of curiosity and this was tolerated by supervisors.


text:
The proposals will give police and security services the power to snoop on every single communication made by the public with the data then likely to be stored in an enormous national database.
The British government's spy-a-thon campaign is getting crazy!
I noticed recently there were more than 20 fixed CCTV cameras able to see me in Glasgow's Central Station concourse - that number does not include the ones on trains and in the shops.
Bring on Paranoid Linux:
an operating system that assumes that its operator is under assault from the government
~Cory Doctorow (Little Brother, 2008)
In the meantime, use the Tor project:


text:
A Ledyard man suffered a serious head injury when a car and moped collided on Route 117 on Thursday, state police said.
Jeremy J. Traxier, 24, of 3 Hickory Drive, Ledyard, was transported by Life Star to Hartford Hospital, police said. His condition was not immediately available.
The accident happened about noon on Route 117 at the intersection of Village Drive in Ledyard.
According to a state police news release, Sean T. Peavey, 25, of 10 Cathcart Drive, Griswold, was driving a 2011 Ford Taurus south on Route 117 at the same time Traxier was driving a 1978 Puch Maxi-Luxe, also south.
The two vehicles crossed paths at the intersection of Village Drive. Peavey was not injured, police said. Ledyard Fire Chief John R. Doucette said in an earlier release that at 11:59 a.m. responders found a 24-year-old male lying in the travel portion of the roadway with serious injuries.
Because of the nature and extent of the injuries, he stated, a Life Star helicopter was called to the scene. The Gales Ferry Fire Company established a landing zone at the nearby Ledyard Center School.
After being taken by Ledyard Ambulance to the landing zone, the injured man was flown to Hartford Hospital, according to the release. American Ambulance paramedics also assisted.
Ledyard police are investigating.
Route 117 at Village Drive was closed after the accident and reopened to traffic about 3:30 p.m.


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AN INTRODUCTION TO O-MINIMAL GEOMETRY. Michel COSTE Institut de Recherche Mathématique de Rennes
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1 AN INTRODUCTION TO O-MINIMAL GEOMETRY Michel COSTE Institut de Recherche Mathématique de Rennes November 1999
2 Preface These notes have served as a basis for a course in Pisa in Spring A parallel course on the construction of o-minimal structures was given by A. Macintyre. The content of these notes owes a great deal to the excellent book by L. van den Dries [vd]. Some interesting topics contained in this book are not included here, such as the Vapnik-Chervonenkis property. Part of the material which does not come from [vd] is taken from the paper [Co1]. This includes the sections on the choice of good coordinates and the triangulation of functions in Chapter 4 and Chapter 5. The latter chapter contains the results on triviality in families of sets or functions which were the main aim of this course. The last chapter on smoothness was intended to establish property DC k - all k which played a crucial role in the course of Macintyre (it can be easily deduced from the results in [vdmi]). It is also the occasion to give a few results on tubular neighborhoods. I am pleased to thank Francesca Acquistapace, Fabrizio Broglia and all colleagues of the Dipartimento di Matematica for the invitation to give this course in Pisa and their friendly hospitality. Also many thanks to Antonio Diaz-Cano, Pietro Di Martino, Jesus Escribano and Federico Ponchio for reading these notes and correcting mistakes. 1
3 2
4 Contents 1 O-minimal Structures Introduction Semialgebraic Sets Definition of an O-minimal Structure Cell Decomposition Monotonicity Theorem Cell Decomposition Connected Components and Dimension Curve Selection Connected Components Dimension Definable Triangulation Good Coordinates Simplicial Complex Triangulation of Definable Sets Triangulation of Definable Functions Generic Fibers for Definable Families The Program The Space of Ultrafilters of Definable Sets The O-minimal Structure κ(α) Extension of Definable Sets Definable Families of Maps Fiberwise and Global Properties Triviality Theorems Topological Types of Sets and Functions
5 4 CONTENTS 6 Smoothness Definable Functions in One Variable C k Cell Decomposition Definable Manifolds and Tubular Neighborhoods Bibliography 79 Index 81
6 Chapter 1 O-minimal Structures 1.1 Introduction The main feature of o-minimal structures is that there are no monsters in such structures. Let us take an example of the pathological behaviour that is ruled out. Let Γ R 2 be the graph of the function x sin(1/x) for x>0, and let clos(γ) be the closure of Γ in R 2. This set clos(γ) is the union of Γ and the closed segment joining the two points (0, 1) and (0, 1). We have dim(clos(γ) \ Γ)=dimΓ=1. Observe also that clos(γ) is connected, but not arcwise connected: there is no continuous path inside clos(γ) joining the origin with a point of Γ. The o-minimal structures will allow to develop a tame topology in which such bad things cannot happen. The model for o-minimal structures is the class of semialgebraic sets. A semialgebraic subset of R n is a subset defined by a boolean combination of polynomial equations and inequalities with real coefficients. In other words, the semialgebraic subsets of R n form the smallest class SA n of subsets of R n such that: 1. If P R[X 1,...,X n ], then {x R n ; P (x) =0} SA n and {x R n ; P (x) > 0} SA n. 2. If A SA n and B SA n, then A B, A B and R n \ A are in SA n. On the one hand the class of semialgebraic sets is stable under many constructions (such as taking projections, closure, connected components...),and on the other hand the topology of semialgebraic sets is very simple, without 5
7 6 CHAPTER 1. O-MINIMAL STRUCTURES pathological behaviour. The o-minimal structures may be seen as an axiomatic treatment of semialgebraic geometry. An o-minimal structure (expanding the field of reals) is the data, for every positive integer n, of a subset S n of the powerset of R n, satisfying certain axioms. There are axioms which allow to perform many constructions inside the structure, and an o-minimality axiom which guarantee the tameness of the topology. One can distinguish two kinds of activities in the study of o-minimal structures. The first one is to develop the geometry of o-minimal structures from the axioms. In this activity one tries to follow the semialgebraic model. The second activity is to discover new interesting classes statisfying the axioms of o-minimal structures. This activity is more innovative, and the progress made in this direction (starting with the proof by Wilkie that the field of reals with the exponential function defines an o-minimal structure) justifies the study of o-minimal structures. The subject of this course is the first activity (geometry of o-minimal structures), while the course of A. Macintyre is concerned with the construction of o-minimal structures. 1.2 Semialgebraic Sets The semialgebraic subsets of R n were defined above. We denote by SA n the set of all semialgebraic subsets of R n. Some stability properties of the class of semialgebraic sets follow immediately from the definition. 1. All algebraic subsets of R n are in SA n. Recall that an algebraic subset is a subset defined by a finite number of polynomial equations P 1 (x 1,...,x n )=...= P k (x 1,...,x n )=0. 2. SA n is stable under the boolean operations, i.e. finite unions and intersections and taking complement. In other words, SA n is a Boolean subalgebra of the powerset P(R n ). 3. The cartesian product of semialgebraic sets is semialgebraic. If A SA n and B SA p, then A B SA n+p. Sets are not sufficient, we need also maps. Let A R n be a semialgebraic set. A map f : A R p is said to be semialgebraic if its graph Γ(f) R n R p = R n+p is semialgebraic. For instance, the polynomial maps are semialgebraic. The function x 1 x 2 for x 1 is semialgebraic.
8 1.2. SEMIALGEBRAIC SETS 7 The most important stability property of semialgebraic sets is known as Tarski-Seidenberg theorem. This central result in semialgebraic geometry is not obvious from the definition. 4. Denote by p : R n+1 R n the projection on the first n coordinates. Let A be a semialgebraic subset of R n+1. Then the projection p(a) is semialgebraic. The Tarski-Seidenberg theorem has many consequences. For instance, it implies that the composition of two semialgebraic maps is semialgebraic. We shall say more on the consequences of the stability under projection in the context of o-minimal structures. The semialgebraic subsets of the line are very simple to describe. Indeed, a semialgebraic subset A of R is described by a boolean combination of sign conditions (< 0, = 0 or > 0) on polynomials in one variable. Consider the finitely many roots of all polynomials appearing in the definition of A. The signs of the polynomials are constant on the intervals delimited by these roots. Hence, such an interval is either disjoint from or contained in A. We obtain the following description. 5. The elements of SA 1 are the finite unions of points and open intervals. We cannot hope for such a simple description of semialgebraic subsets of R n, n>1. However, we have that every semialgebraic set has a finite partition into semialgebraic subsets homeomorphic to open boxes (i.e. cartesian product of open intervals). This is a consequence of the so-called cylindrical algebraic decomposition (cad), which is the main tool in the study of semialgebraic sets. Actually, the Tarki-Seidenberg theorem can be proved by using cad. A cad of R n is a partition of R n into finitely many semialgebraic subsets (which are called the cells of the cad), satisfying certain properties. We define the cad of R n by induction on n. A cad of R is a subdivision by finitely many points a 1 <... < a l. The cells are the singletons {a i } and the open intervals delimited by these points. For n>1, a cad of R n is given by a cad of R n 1 and, for each cell C of R n 1, continuous semialgebraic functions ζ C,1 <...<ζ C,lC : C R.
9 8 CHAPTER 1. O-MINIMAL STRUCTURES The cells of R n are the graphs of the functions ζ C,i and the bands in the cylinder C R R n delimited by these graphs. For i =0,...,l C, the band (ζ C,i,ζ C,i+1 )is (ζ C,i,ζ C,i+1 )={(x,x n ) R n ; x C and ζ C,i (x ) <x n <ζ C,i+1 (x )}, where we set ζ C,0 = and ζ C,lC +1 =+. Observe that every cell of a cad is homeomorphic to an open box. This is proved by induction on n, since a graph of ζ C,i is homeomorphic to C and a band (ζ C,i,ζ C,i+1 ) is homeomorphic to C (0, 1). Given a finite list (P 1,...,P k ) of polynomials in R[X 1,...,X n ], a subset A of R n is said to be (P 1,...,P k )-invariant if the sign (< 0, = 0 or > 0) of each P i is constant on A. The main result concerning cad is the following. Theorem 1.1 Given a finite list (P 1,...,P k ) of polynomials in R[X 1,...,X n ], there is a cad of R n such that each cell is (P 1,...,P k )-invariant. It follows from Theorem 1.1 that, for every semialgebraic subset A of R n, there is a cad such that A is a union of cells (such a cad is called adapted to A). Indeed, A is defined by a boolean combination of sign conditions on a finite list of polynomials (P 1,...,P k ), and it suffices to take a cad such that each cell is (P 1,...,P k )-invariant. We illustrate Theorem 1.1 with the example of a cad of R 3 such that each cell is (X X X 2 3 1)-invariant (a cad adapted to the unit sphere). Such a cad is shown on Figure 1.1. Exercise 1.2 How many cells of R 3 are there in this cad? Is it possible to have a cad of R 3, adapted to the unit sphere, with less cells? We refer to [Co2] for an introduction to semialgebraic geometry. Semialgebraic geometry can also be developed over an arbitrary real closed field, instead of the field of reals. A real closed field R is an ordered field satisfying one of the equivalent conditions: Every positive element is a square and every polynomial in R[X] with odd degree has a root in R. For every polynomial F R[X] and all a, b in R such that a<band F (a)f (b) < 0, there exists c R, a<c<b, such that F (c) =0. R[ 1] = R[X]/(X 2 + 1) is an algebraically closed field.
10 1.3. DEFINITION OF AN O-MINIMAL STRUCTURE 9 Figure 1.1: A cad adapted to the sphere A semialgebraic subset of R n is defined as for R n. The properties of semialgebraic sets that we have recalled in this section also hold for semialgebraic subsets of R n. We refer to [BCR] for the study of semialgebraic geometry over an arbitrary real closed field. 1.3 Definition of an O-minimal Structure We shall now define the o-minimal structures expanding a real closed fied R. The fact that we consider a situation more general than the field of reals will be important only in Chapter 5. Otherwise, the reader may take R = R. An interval in R will always be an open interval (a, b) (for a<b)or(a, + ) or (,b). We insist that an interval always has endpoints in R {, + }. For instance, if R is the field of real algebraic numbers (which is the smallest real closed field), the set of x in R such that 0 <x<π(π = ) is not an interval, because there is no right endpoint in R. Occasionally, we shall also use the notation [a, b] for closed segments in R. The field R has a topology for which the intervals form a basis. Affine spaces R n are endowed with the product topology. The open boxes, i.e. the
11 10 CHAPTER 1. O-MINIMAL STRUCTURES cartesian products of open intervals (a 1,b 1 ) (a n,b n ) form a basis for this topology. The polynomials are continuous for this topology. Exercise 1.3 Prove that the polynomials are continuous. When dealing with the topology, one should take into account that a real closed field is generally not locally connected nor locally compact (think of real algebraic numbers). Definition 1.4 A structure expanding the real closed field R is a collection S =(S n ) n N, where each S n is a set of subsets of the affine space R n, satisfying the following axioms: 1. All algebraic subsets of R n are in S n. 2. For every n, S n is a Boolean subalgebra of the powerset of R n. 3. If A S m and B S n, then A B S m+n. 4. If p : R n+1 R n is the projection on the first n coordinates and A S n+1, then p(a) S n. The elements of S n are called the definable subsets of R n. The structure S is said to be o-minimal if, moreover, it satisfies: 5. The elements of S 1 are precisely the finite unions of points and intervals. In the following, we shall always work in a o-minimal structure expanding a real closed field R. Definition 1.5 A map f : A R p (where A R n ) is called definable if its graph is a definable subset of R n R p. (Applying p times property 4, we deduce that A is definable). Proposition 1.6 The image of a definable set by a definable map is definable. Proof. Let f : A R p be definable, where A R n, and let B be a definable subset of A. Denote by Γ f = {(x, f(x)) ; x A} R n+p the graph of f. Let be the algebraic (in fact, linear) subset of R p+n+p consisting of those (z, x, y) R p R n R p such that z = y. Then C = (R p Γ) (R p B R p ) is a definable subset of R p+n+p. Let p p+n+p,p : R p+n+p R p be the projection on the first p coordinates. We have p p+n+p,p (C) =f(b), and, applying n + p times property 4, we deduce that f(b) is definable. Observe that every polynomial map is a definable map, since its graph is an algebraic set.
12 1.3. DEFINITION OF AN O-MINIMAL STRUCTURE 11 Exercise 1.7 Every semialgebraic subset of R n is definable (Hint: the set defined by P (x 1,...,x n ) > 0 is the projection of the algebraic set with equation x 2 n+1p (x 1,...,x n ) 1 = 0). Hence, the collection of SA n is the smallest o-minimal structure expanding R. Exercise 1.8 Show that every nonempty definable subset of R has a least upper bound in R {+ }. Exercise 1.9 Assume that S is an o-minimal structure expanding an ordered field R (same definition as above). Show that R is real closed. (Hint: one can use the second equivalent condition for a field to be real closed, the continuity of polynomials and property 5 of o-minimal structures.) Exercise 1.10 Let f =(f 1,...,f p ) be a map from A R n into R p. Show that f is definable if and only if each of its coordinate functions f 1,...,f p is definable Exercise 1.11 Show that the composition of two definable maps is definable. Show that the definable functions A R form an R-algebra. Proposition 1.12 The closure and the interior of a definable subset of R n are definable. Proof. It is sufficient to prove the assertion concerning the closure. The case of the interior follows by taking complement. Let A be a definable subset of R n. The closure of A is clos(a) = { x R n ; ε R, ε > 0 y R n,y A and } n (x i y i ) 2 <ε 2 i=1. where x =(x 1,...,x n ) and y =(y 1,...,y n ). The closure of A can also be described as clos(a) =R n \ ( p n+1,n ( R n+1 \ p 2n+1,n+1 (B) )), where { B =(R n R A) (x, ε, y) R n R R n ; } n (x i y i ) 2 <ε 2, i=1
13 12 CHAPTER 1. O-MINIMAL STRUCTURES p n+1,n (x, ε) =x and p 2n+1,n+1 (x, ε, y) =(x, ε). Then observe that B is definable. The example above shows that it is usually boring to write down projections in order to show that a subset is definable. We are more used to write down formulas. Let us make precise what is meant by a first-order formula (of the language of the o-minimal structure). A first-order formula is constructed according to the following rules. 1. If P R[X 1,...,X n ], then P (x 1,...,x n )=0andP (x 1,...,x n ) > 0 are first-order formulas. 2. If A is a definable subset of R n, then x A (where x =(x 1,...,x n )) is a first-order formula. 3. If Φ(x 1,...,x n ) and Ψ(x 1,...,x n ) are first-order formulas, then Φ and Ψ, Φ or Ψ, not Φ, Φ Ψ are first order formulas. 4. If Φ(y, x) is a first-order formula (where y = (y 1,...,y p ) and x = (x 1,...,x p )) and A is a definable subset of R n, then x A Φ(y, x) and x A Φ(y, x) are first-order formulas. Theorem 1.13 If Φ(x 1,...,x n ) is a first-order formula, the set of (x 1,...,x n ) in R n which satisfy Φ(x 1,...,x n ) is definable. Proof. By induction on the construction of formulas. Rule 1 produces semialgebraic sets, which are definable. Rule 2 obviously produces definable sets. Rule 3 works because SA n is closed under boolean operation. Rule 4 reflects the fact that the projection of a definable set is definable. Indeed, if B = {(y, x) R p+n ;Φ(y, x)} is definable and p p+n,p : R p+n R p denotes the projection on the first p coordinates, we have {y R p ; x A Φ(y, x)} = p p+n,p ((R p A) B), {y R p ; x A Φ(y, x)} = R p \ p p+n,p ((R p A) (R p+n \ B)), which shows that both sets are definable. One should pay attention to the fact that the quantified variables have to range over definable sets. For instance, {(x, y) R 2 ; n N y = nx} is not definable (why?). We refer the reader to [Pr] for notions of model theory.
14 1.3. DEFINITION OF AN O-MINIMAL STRUCTURE 13 Exercise 1.14 Let f : A R be a definable function. Show that {x A ; f(x) > 0} is definable. Hence, we can accept inequalities involving definable functions in formulas defining definable sets. Exercise 1.15 Let A be a non empty definable subset of R n. For x R n, define dist(x, A) as the greatest lower bound of the set of y x = ni=1 (y i x i ) 2 for y A. Show that dist(x, A) is well-defined and that x dist(x, A) is a continuous definable function on R n. Exercise 1.16 Let f : A R be a definable function and a clos(a). For ε>0, define m(ε) = inf{f(x) ; x A and x a <ε} R { }. Show that m is a definable function (this means that m 1 ( ) is definable and m m 1 (R) is definable). Show that lim inf x a f(x) exists in R {, + }.
16 Chapter 2 Cell Decomposition In this chapter we prove the cell decomposition for definable sets, which generalizes the cylindrical algebraic decomposition of semialgebraic sets. This result is the most important for the study of o-minimal geometry. The proofs are rather technical. The main results come from [PS, KPS], and we follow [vd] rather closely. 2.1 Monotonicity Theorem Theorem 2.1 (Monotonicity Theorem) Let f :(a, b) R be a definable function. There exists a finite subdivision a = a 0 <a 1 <...<a k = b such that, on each interval (a i,a i+1 ), f is continuous and either constant or strictly monotone. The key of the proof of the Monotonicity Theorem is the following Lemma. Lemma 2.2 Let f :(a, b) R be a definable function. There exists a subinterval of (a, b) on which f is constant, or there exists a subinterval on which f is strictly monotone and continuous. Proof. Suppose that there is no subinterval of (a, b) on which f is constant. First step: there exists a subinterval on which f is injective. It follows from the assumption that, for all y in R, the definable set f 1 (y) is finite: otherwise, f 1 (y) would contain an interval, on which f = y. Hence the definable set f((a, b)) is infinite and contains an interval J. The function g : J (a, b) defined by g(y) = min(f 1 (y)) is definable and satisfies f g =Id J. Since g is injective, g(j) is infinite and contains a subinterval I of (a, b). We have g f I =Id I, and f is injective on I. 15
17 16 CHAPTER 2. CELL DECOMPOSITION Second step: there exists a subinterval on which f is strictly monotone. We know that f is injective on a subinterval I of (a, b). Take x I. The sets I + = {y I ; f(y) >f(x)} I = {y I ; f(y) <f(x)} form a definable partition of I \{x}. Therefore, there is ε>0 such that (x ε, x) (resp. (x, x+ε)) is contained in I + or in I. There are four possibilities Φ +,+ (x), Φ +, (x), Φ,+ (x) and Φ, (x) which give a definable partition of I. For instance, Φ +, (x) is ε y I ( (x ε<y<x f(y) >f(x)) and (x <y<x+ ε f(y) <f(x)) ). We claim that Φ +,+ and Φ, are finite. It is sufficient to prove the claim for Φ +,+ (for Φ,, replace f with f). If Φ +,+ is not finite, it holds on a subinterval of I, which we still call I. Set B = {x I ; y I y > x f(y) >f(x)}. If B contains an interval, then f is strictly increasing on this interval, which contradicts Φ +,+. Hence, B is finite. Replacing I with (max(b), + ) I if B, we can assume ( ) x I y I (y >x and f(y) <f(x)). Take x I. The definable set C x = {y I ; y>x and f(y) <f(x)} is nonempty. If C x were finite, its maximum would be an element of I contradicting the property (*). Therefore, C x contains an interval. Let z be the greatest lower bound of the interior of C x. We have z>xbecause f>f(x) on some interval (x, x + ε). We have also f>f(x) on some interval (z ε, z) and f<f(x) on some interval (z,z+ε). Hence, the following formula Ψ +, (z) holds: ε >0 t I u I (z ε<t<z<u<z+ ε f(t) >f(u)). We have shown ( ) x I z I (x <z and Ψ +, (z)). The definable set of elements of I satisfying Ψ +, is not empty and it is not finite: otherwise, its maximum would contradict (**). It follows that, replacing
18 2.1. MONOTONICITY THEOREM 17 I with a smaller subinterval, we can assume that Ψ +, holds on I. Consider the definable function h : I R defined by h(x) =f( x). The property Φ +,+ for h holds on I. Hence, by the preceding argument, there is a subinterval of I on which Ψ +, for h holds. This means that there is a subinterval of I on which Ψ,+ for f holds (exchange left and right). On this subinterval we have both Ψ +, and Ψ,+, which are contradictory. This contradiction proves the claim. Since Φ +,+ and Φ, are finite, replacing I with a smaller subinterval, we can assume that Φ,+ holds on I or Φ +, holds on I. Say Φ,+ holds on I. Then f is strictly increasing on I. Indeed, for all x I, the definable set {y I ; y>xand f>f(x) on(x, y)} is nonempty and its least upper bound is necessarily the right endpoint of I (Otherwise, this l.u.b. would not satisfy Φ,+ ). Similarly, if Φ +, holds on I, f is strictly decreasing on I. Last step: there is a subinterval on which f is strictly monotone and continuous. Recall that f is strictly monotone on I. The definable set f(i) is infinite and contains an interval J. The inverse image f 1 (J) is the interval (inf(f 1 (J)), sup(f 1 (J))). Replacing I with this interval, we can assume that f is a strictly monotone bijection from the interval I onto the interval J. Since the inverse image of a subinterval of J is a subinterval of I, f is continuous. Proof of the Monotonicity Theorem. Let X = (resp. X, resp. X )bethe definable set of x (a, b) such that f is constant (resp. continuous and strictly increasing, resp. continuous and strictly decreasing) on an interval containing x. Then (a, b) \ (X = X X ) is finite: otherwise, it would contain an interval, and we get a contradiction by applying Lemma 2.2 to this interval. Hence, there is a subdivision a = a 0 <a 1 <...<a k = b such that each (a i,a i+1 ) is contained in X = or in X or in X. Clearly, f is continuous on each (a i,a i+1 ). Take x in (a i,a i+1 ). If (a i,a i+1 ) is contained in X = (resp. X, resp. X ), let D x be the set of y (a i,a i+1 ) such that x<yand f = f(x) (resp. f>f(x), resp. f<f(x)) on (x, y). The definable set D x is nonempty and its least upper bound is necessarily a i+1. It follows that f is constant or strictly monotone on (a i,a i+1 ). Exercise 2.3 Let f :(a, b) R be a definable function. Then lim x b f(x) and lim x a+ f(x) exist in R {, + }.
19 18 CHAPTER 2. CELL DECOMPOSITION 2.2 Uniform Finiteness, Cell Decomposition and Piecewise Continuity The notion of a cylindrical definable cell decomposition (cdcd) of R n is a generalization of cylindrical algebraic cell decomposition. We define the cdcd by induction on n Definition 2.4 A cdcd of R n is a finite partition of R n into definable sets (C i ) i I satisfying certain properties explained below. The C i are called the cells of the cdcd. n =1: A cdcd of R is given by a finite subdivision a 1 <...<a l of R. The cells of R are the singletons {a i }, 0 <i l, and the intervals (a i,a i+1 ), 0 i l, where a 0 = and a l+1 =+. n>1: AcdcdofR n is given by a cdcd of R n 1 and, for each cell D of R n 1, continuous definable functions The cells of R n are the graphs and the bands ζ D,1 <...<ζ D,l(D) : D R. {(x, ζ D,i (x)) ; x D}, 0 <i l(d), (ζ D,i,ζ D,i+1 )={(x, y) ; x D and ζ D,i (x) <y<ζ D,i+1 (x)} for 0 i l(d), where ζ D,0 = and ζ D,l(D)+1 =+. Note that the fact that a cell of a cdcd is definable follows immediately from the definition and the axioms of o-minimal structure. Note also that if p n,m : R n R m, m<n, is the projection on the first m coordinates, the images by p of the cells of a cdcd of R n are the cells of a cdcd of R m. We define by induction the dimension of a cell. The dimension of a singleton is 0 and the dimension of an interval is 1. If C is a cell of R n, its dimension is dim(p n,n 1 (C)) if C is a graph and dim(p n,n 1 (C)) + 1 if C is a band. Proposition 2.5 For each cell C of a cdcd of R n, there is a definable homeomorphism θ C : C R dim(c).
20 2.2. CELL DECOMPOSITION 19 Proof. Let D = p n,n 1 (C) and assume θ D : D R dim(d) is already defined. Let (x, y) C, where x D. We define θ C (x, y) asθ D (x) ifc is a graph, and as ( ) 1 θ D (x), ζ D,i (x) y + y + 1 ζ D,i+1 (x) y if C is the band (ζ D,i,ζ D,i+1 ) (fractions where infinite functions appear in the denominator have to be omitted). Exercise 2.6 Prove (by induction on n) that a cell is open in R n if and only if its dimension is n. Prove that the union of all cells of dimension n is dense in R n (hint: show by induction on n that every open box in R n meets a cell of dimension n). We have already said that the notion of connectedness does not behave well if R R. It has to be replaced by the notion of definable connectedness. Definition 2.7 A definable set A is said to be definably connected if, for all disjoint definable open subsets U and V of A such that A = U V, one has A = U or A = V. A definable set A is said to be definably arcwise connected if, for all points a and b in A, there is a definable continuous map γ :[0, 1] A such that γ(0) = a and γ(1) = b. Exercise 2.8 Prove the following facts: The segment [0, 1] is definably connected. Definably arcwise connected implies definably connected. Every box (0, 1) d is definably connected. Every cell of a cdcd is definably connected. We now state the three main results of this section. In the following, we denote by S the number of elements of a finite set S. Theorem 2.9 (Uniform Finiteness UF n ) Let A be a definable subset of R n such that, for every x R n 1, the set A x = {y R ; (x, y) A} is finite. Then there exists k N such that A x k for every x R n 1. Theorem 2.10 (Cell Decomposition CDCD n ) Let A 1,...,A k be definable subsets of R n. There is a cdcd of R n such that each A i is a union of cells.
21 20 CHAPTER 2. CELL DECOMPOSITION A cdcd of R n satisfying the property of the theorem will be called adapted to A 1,...,A k. Exercise 2.11 Prove the following consequence of CDCD n : Let X be a definable subset of R n such that clos(x) has nonempty interior. Then X has nonempty interior. (Hint: use Exercise 2.6 for a convenient cdcd of R n.) Theorem 2.12 (Piecewise Continuity PC n ) Let A be a definable subset of R n and f : A R a definable function. There is a cdcd of R n adapted to A such that, for every cell C contained in A, f C is continuous. Exercise 2.13 Prove the following consequence of PC n : Let X be an open definable subset of R n and f : X R a definable function. Then there is an open box B X such that f B is continuous (hint: use Exercise 2.6). We prove the three theorems simultaneously by induction on n. Forn = 1, UF 1 is trivial (R 0 is just one point), CDCD 1 follows immediately from the o- minimality, and PC 1 is a consequence of the Monotonicity Theorem 2.1. In the following we assume n>1 and UF m, CDCD m and PC m hold for all integers m such that 0 <m<n. Proof of UF n. We can assume that, for every x R n 1, the set A x is contained in ( 1, 1). Let µ : R ( 1, 1) be the semialgebraic homeomorphism defined by µ(y) =y/ 1+y 2. We can replace A with its image by (x, y) (x, µ(y)), which satisfies the assumption. For x R n 1 and i =1, 2,..., define f i (x) tobethei-th element of A x, if it exists. Note that the function f i is definable. Call a R n 1 good if f 1,...,f (Aa) are defined and continuous on an open box containing a and a does not belong to the closure of the domain of f (Aa)+1. In other words, a is good if and only if there is an open box B a in R n 1, such that (B R) A is the union of graphs of continuous definable functions ζ 1 <...<ζ (Aa) : B ( 1, 1) (ζ i = f i B). Call a R n 1 bad if it is not good. First step: the set of good points is definable. Let a beapointofr n 1.If b belongs to [ 1, 1], we say that (a, b) R n is normal if there is an open box C = B (c, d) R n containing (a, b) such that A C is either empty or the graph of a continuous definable function B (c, d).
22 2.2. CELL DECOMPOSITION 21 Clearly, if a is good, (a, b) is normal for every b [ 1, 1]. Now assume that a is bad. Let f l be the first function f i such that a is in the closure of the domain of f i and there is no open box containing a on which f i is defined and continuous. We set β(a) = lim inf x a f l (x) [ 1, 1]. We claim that (a, β(a)) is not normal. Suppose (a, β(a)) is normal. There is an open box B (c, d) containing (a, β(a)) whose intersection with A is the graph of a continuous function g : B (c, d). We can assume that f l (x) >cfor all x B such that f l (x) is defined. If l>1 and β(a) =f l 1 (a), we would deduce g = f l 1 B since B is definably connected. We would have f l (x) d for all x B such that f l (x) is defined, which contradicts β(a) <d. Hence, we can assume l =1 or f l 1 <con B. It follows that g = f l B, which contradicts the definition of l. Therefore the claim is proved. We have shown that a R n 1 is good if and only if, for all b [ 1, 1], (a, b) is normal. From this we deduce easily that the set of good points is definable. Second step: the set of good points is dense. Otherwise, there is an open box B R n 1 contained in the set of bad points. Consider the definable function β : B [ 1, 1] defined as in Step 1. By PC n 1, we can assume that β is continuous (see Exercise 2.13). For x B, we define β (x) (resp. β + (x)) to be the maximum (resp. minimum) of the y A x such that y<β(x) (resp. y>β(x)), if such y exist. Using PC n 1 and shrinking the box B, we can assume that β (resp. β + ) either is nowhere defined on B or is continuous on B. Then the set of (x, y) A (B R) such that y β(x) is open and closed in A (B R). Shrinking further the box B, we can assume that the graph of β B is either disjoint from A or contained in A. The first case contradicts the definition of β. In the second case, (x, β(x)) would be normal for every x B, which contradicts what was proved in the first step. We have proved that the set of good points is dense. Third step. By CDCD n 1, there is a cdcd of R n 1 adapted to the set of good points. Let C be a cell of dimension n 1ofR n 1. Since good points are dense, every x C is good. Take a C. The set of x C such that (A x )= (A a ) is definable, open and closed in C. By definable connectedness of C, it is equal to C. IfD is a cell of R n 1 of smaller dimension, we can use the definable homeomorphism of θ D : D R dim(d) and the assumption that UF dim(d) holds to prove that (A x ) is uniformly bounded for x D. Since there are finitely many cells, the proof of UF n is completed. Proof of CDCD n. Let A be the set of (x, y) R n 1 R such that y belongs to the boundary of one of A 1,x,...,A k,x (the boundary of S in R is clos(s) \ int(s)). Clearly A is definable and satisfies the assumptions of UF n. Hence
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from The American Heritage® Dictionary of the English Language, 4th Edition
- transitive v. To restore to health or soundness; cure. See Synonyms at cure.
- transitive v. To set right; repair: healed the rift between us.
- transitive v. To restore (a person) to spiritual wholeness.
- intransitive v. To become whole and sound; return to health.
from Wiktionary, Creative Commons Attribution/Share-Alike License
- v. To make better; to revive, recover, or cure.
- v. To become better.
- n. health
- v. To hide; conceal; keep secret.
- v. To cover, as for protection.
from the GNU version of the Collaborative International Dictionary of English
- n. Health.
- intransitive v. To grow sound; to return to a sound state; ; -- sometimes with up or over.
- transitive v. To cover, as a roof, with tiles, slate, lead, or the like.
- transitive v. To make hale, sound, or whole; to cure of a disease, wound, or other derangement; to restore to soundness or health.
- transitive v. To remove or subdue; to cause to pass away; to cure; -- said of a disease or a wound.
- transitive v. To restore to original purity or integrity.
- transitive v. To reconcile, as a breach or difference; to make whole; to free from guilt; as, to heal dissensions.
from The Century Dictionary and Cyclopedia
- To make whole or sound; restore to health or soundness; cure: as, to heal the sick.
- To restore to wholesome conditions; remove something evil or noxious from: purify; cleanse; strengthen.
- To remedy; remove, repair, or counteract by salutary or beneficial means: as, to heal a quarrel or a breach.
- To grow whole or sound; return to a sound state: with reference to a wound, sometimes with up or over.
- To hide; conceal; keep secret.
- To cover, as for protection.
- To cover (the roots of trees and plants), usually in an inclined or slanting position, with soil, after they have been taken out of the ground, and before setting them permanently: generally used with in.
- A variant spelling of heel.
- n. Health; well-being.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
- v. get healthy again
- v. provide a cure for, make healthy again
- v. heal or recover
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/Share-Alike License
from Wiktionary, Creative Commons Attribution/Share-Alike License
Thou promisest to heal their waters, but _their miry places and standing waters_, thou sayest there, _thou wilt not heal_. [
Devotions Upon Emergent Occasions Together with Death's Duel
The English word heal appears in this passage, as the Greek word iomai, meaning "cure."
And we were able to give each other enough space to heal from the wounds we inflicted upon ourselves and each other.
For me, sharing my pain with the world is how I was able to heal from a lot of hurt in my life.
When Should You Use Your Personal Pain In Your Writing? | The Creative Penn
I am so encouraged to hear that it is helping people all across the country to heal from the ravages of child abuse.
Book Promotion: 5 top tips for being on TV and lessons from a TV appearance | The Creative Penn
We cannot heal from the scourge of christianity until we are honest about some of its worse perpetrators.
The wound would heal from the inside out -- they call it healing by secondary intention, and if you think I haven't tried to write a poem with that fabulously symbolic phrase in it, you don't know me very well.
As banks continue to heal from the financial crisis, being small isn 't necessarily a disadvantage.
It's it can take congregations decades, generations to really heal from the pain that that causes.
The best thing for both of them would be to go their separate ways and try to heal from the emotional and physical damage they have both caused eachother.


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If trying to maintain balance in your life makes you feel like a tightrope walker, you're not alone. Most of us have so many demands on our time and energy, the endless pursuit of life-balance can feel like a three-ring circus! Striking a balance between work responsibilities, roles you play and all the other things you'd like to accomplish takes a high degree of alignment with your core … [Read more...]
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Staying sane over the Thanksgiving break can be a big challenge! Traditionally our family has come together for this holiday over any others. I've hosted as many as 29 people for the traditional meal, but we all know that you need to be prepared for much more than just a meal! … [Read more...]
8 Best Back To School Scheduling Strategies for Mompreneurs
It's back to school time again! Back to school time is also back to sanity time for most moms with school-aged children! Here are some great back to school strategies that are never too late to implement for more sanity! … [Read more...]
3 Simple Self-Care Strategies for Mompreneurs
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Archive for April, 2011
Who Can Separate Us From the Love of God?
by Bill Brant on Apr.25, 2011, under Hope
He knew the answer before he asked the question. He was one of the outstanding Hebrew scholars of his time, noted author, recognized speaker, leader, prisoner and eventually martyr for a religious cause.
His treatise is a letter he sent to Christians in the city of Rome and it is in the eighth chapter that he poses the question and notes that no external influence can cause separation.
Yet Paul, the Apostle, knew the whole answer which began in Moses' book of Genesis, in Chapter 3 when God asks of His creation "where are you?", Adam was afraid for he had disobeyed the Lord God and hid himself. The answer was finalized by the visionary prophet Isaiah when God used his pen say:
"Your iniquities have separated you from your God; and your sins have hidden His face from you, so that He will not hear." Isa 59:2
The question remains, who can separate us from the love of God? And the answer is—we can when we choose not to follow his ways. We can when we disobey his rules for living. We can when we hide behind our habitual sin. We can when we decide to be unholy and unworthy.
But, if we choose to allow Jesus to redeem us, save us, make us Holy, affirm that we are worthy—Then NOTHING can separate us from the love of God which is in Christ Jesus our Lord!
Sooooo.. Are you separated from God?
Why have you chosen to be so distant from Him?
Are you like Adam, having disobeyed God that you have hidden yourself from him?
Garage Junk
by Steve Ridgell on Apr.18, 2011, under Hope
My wife recently had me help her clean out our garage and I was amazed. I carried off old, used up furniture that was no longer usable. I threw away toys that were no longer played with and lots of … well, junk. But I remembered when some of that furniture was new. I can remember saving up and being so proud when we bought the item that was going to be just perfect for our house. And now it is not. I remember when the toys were absolutely the must have item on the Christmas and birthday wish list. I smiled when I remembered the fun times watching my children play with them. Now nobody wants them. The junk I was carting away was something that at one time we thought we needed – or wanted. Not now.
At first I objected to getting rid of them because I remembered how special they had been. Of course, I know they cannot last forever. No toy does. Neither does furniture. They are not designed to last forever. They do not last. They are like everything else in this world. They have a limited shelf life.
As I thought about it, I realized the memories were not so much about the items themselves. It was what they represented: good times with family and friends. I did not mind getting rid of the things so much when it dawned on me I would always have my family. My kids are grown and their grandparents are getting old. Now my wife and I have grandchildren. We are buying toys that will be thrown out someday. But our family will be together forever. That is the special blessing for those of us that believe in Jesus. He died so we could live. Forever. My family believes that.
Cleaning out the garage reminded me of what does – and what does not – last forever. It reminded me of what is – and is not – really important. It helped me to remember to focus on what matters. If you would like to know about families that last forever, I can help you. If you want to know that you will last forever, I would enjoy visiting with you. You are not junk. You are special, and you can know that.
by Tim Archer on Apr.11, 2011, under Hope
My head gets sunburned. It didn't used to, but now I have to be careful when I go out. If I'm in the sun for more than a few minutes without some sort of hat, I'll probably spend the next few days with an itchy scalp. For some reason, my head burns more easily than it used to.
I'd like to blame it on the ozone layer or global warming or something of the sort, but I know the truth: with every passing year, I've got less hair on the top of my head.
My body is wearing out. There are other signs of this, like my need for reading glasses, and more things seem to show up all the time.
I have what the Bible calls a "perishable body." It will eventually deteriorate. And, as the Bible promises, someday I will get an "imperishable body," one that won't ever wear out. It's the way that God originally wanted things to be, but mankind chose to disobey God, and the consequence of that rebellion was death, the decaying of our bodies.
Did you know that the world around us had the same thing happen to it? Where creation was once in a state of perfection, man's sin affected that as well. The Apostle Paul wrote to the Christians in Rome: "For the creation was subjected to futility, not willingly, but because of him who subjected it, in hope that the creation itself will be set free from its bondage to decay and obtain the freedom of the glory of the children of God." (Romans 8:20-21)
That word "decay" is the same word Paul uses to talk about what happens to our bodies. Just as my body is not the perfect body I will one day have, so our creation is in a state of imperfection. Not because God made it that way, but because our sin affects the world around us.
Today we see earthquakes, hurricanes, tsunamis and floods. One day, all of that will be gone. Creation will be set free from its "futility," from its imperfection.
On that day, we Christians will also be set free. We will be given bodies that will never grow old nor wear out. We'll live in a world that won't experience the disasters we see today.
And my head won't get sunburned any more!
(photo by Henk L, from www.sxc.hu)
My Dog Just Thinks He Understands Me
by Steve Ridgell on Apr.04, 2011, under Hope
I can tell from the way he looks and acts that my dog Lucky thinks he understands me. The truth is that he does not have a clue. He knows I love him, he knows I feed him, and he knows I provide shelter when it gets really cold. He adores me, minds me most of the time, and really enjoys being in my presence. But does he really understand me?
Does he really understand when I discipline him that it is for his own good? Does he understand how dangerous it is outside of his yard? Does he know why the leash has to be on before we walk? Sometimes he whines to come in, or he begs for a treat. I think he believes that I am there to make his life function exactly the way he wants it to be. He must actually think that he knows how my mind works.
He doesn't. He cannot reason on my level. He cannot think the way I do. I doubt he thinks in terms of the future. He may recognize things I do, but does he understand why? We have a relationship, but we are not equals. We love each other, but I am the master.
So I wonder if this is how it is with me and God. We are not equal. We operate on completely different levels of thought. I cannot think like God. I cannot understand God. I may get glimpses of His character. I may see the fruits of His action. I can even communicate with Him. But for me to assume I understand God is a serious mistake. I might end up thinking God is the way I want Him to be, or imagine He should be.
So I pay close attention to what He has said to me. I do not have to understand it, but I do believe it. I read His Word, the Bible. I try to do what it says. God is God, and I am me. When I remember that, life works. When I get the roles reversed, life falls apart. He is the Master, not me.


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T-SQL Tuesday is a monthly blog party for the SQL Server community (or Microsoft Data Platform community. Although it's called T-SQL Tuesday, it's not limited to SQL Server database engine only). It is the brainchild of Adam Machanic (blog | twitter) and I'm honored to host this month's edition. Each month a blog hosts the party and everybody who wants to contribute can write a post about the selected topic. You can find a list of all topics at http://tsqltuesday.com/.
This months topic is inspired by the blog post Will the Cloud Eat My DBA Job? by Kendra Little. Technology has changed a lot in the past years, especially with cloud/globalization/automation. What an impact has this had on your job? Do you feel endangered? Or do you have more exciting features/toys to work with? Do you embrace the change and learn new skills? Or do you hide in your cubicle and fear the robot uprising? Let us know how you handle all these changes, or how you feel there are no changes at all for your current job. I'm looking forward to learn how you feel about the future of data management/analysis and how you plan to deal with it.
Want to contribute? The rules are simple:
- Blog about the topic at Tuesday 11th of April. If the post is up that day in your timezone, that's fine. Include the TSQL2sDay logo and a link back to this invitation.
- Notify me about your blog post in the comments, so I can gather them for a round-up.
- If you tweet about your post , please use the hashtag #tsql2sday.


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Khelti Hai Zindagi Aankh Micholi 16th December 2013 Written Episode Update
Khelti Hai Zindagi Aankh Micholi 16th December 2013 Written Episode, Khelti Hai Zindagi Aankh Micholi 16th December 2013 Written Update
The episode starts with everyone eating soup. Then everyone start going to the toilet one by one and prabha acts and tells that why Is everyone going to the toilet. Then trisha asks that why are they going to the toilets. Then prabha says that someone must have mixed something in the soup. Then riddhi tells that she had seen ami go in the kitchen. Then trisha goes to see and then brings out the bottle of castor oil and then tells that ami must have put castor oil in the soup. then trisha calls ami loudly and ami comes and tells that why is she calling so loudly. Trisha tells that why did she put castor oil in her friends soup. Ami says she did not. Then prabha and riddhi tell that see how ami is trying to run away from her mistakes.then ami tells
in the room prabha goes to make ami and then she goes and sits on the rocking chair kept there. she then tells ami that her mom shruti is so shameless and that she has captured over sanjay and all her manners have come to her. then ami tells her to get out of the room and not talk to her, prabha smiles cunningly and is going when she stops and with her own hand she then scratches her hand by herself very badly till a lot of blood comes out. then she goes out. she tells that ami is very angry and prabha acts of crying and then sanjay sees her hand and tells that who did this, prabha tells that forgive ami, sanjay tells that ami is now a child and he should take her under control, then sanjay goes in ami's room angrily and prabha is telling him to leave ami. in ami's room sanjay goes and tells her that why did she do this, ami tells that she will do this to anyone if they tease her and make fun of her mother and that she will not leave anyone. sanjay gets sad and is thinking that ami had scratched prabha's hand, then he tells ami that she is still small and that she should learn to act as a good person, then ami tells him to go from there or else she will go and then tells that he can never be her dad neither her friend.
in prabha's room riddhi and prabha are making their first celebration of having put ami in trouble and then they are discussing about how they both did their own tricks. then they take a glass of juice and cheer and prabha tells that she will soon throw shruti out of the house.
in the room sanjay is thinking about ami and how she back answered and is also thinking that she is very sad.
next day, everyone are at the breakfast table and are having breakfast, khushboo is also there and then dad asks that where is ami? khushboo tells that she does not want to eat anything. dad tells khushboo to call, khushboo goes to call her but ami sends her back. then riddhi and prabha re telling dad that this all is drama and that ami just wants everyone's attention towards her. then khushboo tells that she will also not have the breakfast and then sanjay also goes without doing breakfast. in the room sanjay is thinking about ami and then khushboo comes and sanjay asks her that what did shruti did when ami was sad and how did she tell her to eat food. khushboo whispers in his ears.
precap: ami and khushboo are finally having food and then riddhi and prabha tell that ami is so small and that she gave up and that just wanted sanjay's attention and then they tell that what ami was doing was drama and that she finally came to eat. ami gets angry and throws the plate and tells them " shut up", the plate falls in sanjay,s legs.
Update Credit to: Vishwal


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Separate names with a comma.
Discussion in 'HTC ThunderBolt' started by atmcgill97, Feb 23, 2011.
Is is a droid or not? I think "Droid ThunderBolt" sounds nice.
"Droid" is a Motorola copyrighted name. Thats why the only "Droids" are Droid 1, Droid 2, Droid Pro and Droid X.
HTC "Droid" Incredible. Whats copyrighted now?
Wrong... Droid is a Lucasfilms copyright licensed to Verizon, not Motorola. Thus Droid Incredible is part of the Droid family, and it is made by HTC.
Copyrighted wasnt the right word, I meant licensed. LucasFilm has the copyright to the name "Droid".
And my understanding from something I had read in the past was that HTC wasnt going to continue to use the term "Droid"....prolly not wanting to pay the licensing fees.
Thanks, I was just wondering.
They are all Android based phones so yes yes and yes lol
just because it is an android phone doesnt mean it is a "droid"
"droid" was a marketing scheme that verizon and motorola and android came up with to announce the "game changing" original Droid.
anything with the "droid" ringtone/notification is considered a droid...anything else is just and android phone.
And we also had Droid Eris.... for those that try to say only flagship phones get the Droid name..
I've got an Eris, but I don't call it a "droid", seems disrespectful to the real droids.
But it actually is called a Droid eris so you're in the clear..I always get tickled though when people say "Droid ally". Lol


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Outline.. The Global Education ParadoxLeading Internationalization. Developing a StrategyAttention to ProcessWhy Develop Global SkillsDeveloping a Shared vision of global competence. The Global Education Paradox. We say Global Education is ImportantBut our schools and universities offer limi
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


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Thousands of British holidaymakers face delays after the Government suspended flights from the Egyptian resort of Sharm el-Sheikh amid security fears.
Downing Street has said the plane that crashed in Egypt at the weekend "may well have been brought down by an explosive device" and has suspended all flights.
All 224 people on board on the Russian Airbus 321 were killed in Saturday's disaster.
David Cameron's office said British aviation experts were travelling to the resort to assess the standard of security before British flights will be allowed to leave.
No British flights were due to fly there on Wednesday.
Downing Street said: "We have become concerned that the plane may well have been brought down by an explosive device."
The Irish Aviation Authority has also directed Irish airlines not to fly to or from the area until further notice.
Transport Secretary Patrick McLoughlin said the flight freeze would allow the British investigators to ensure "the right security measures are in place".
"We can not categorically say why the Russia jet crashed but we have become concerned that the plane may well have been brought down as a result of an explosive device," he said.
EasyJet has delayed flights to Gatwick and Luton this evening. "We are doing all possible to keep passengers informed," a spokesman added.
Thomson has also suspended flights, one from Manchester.
Manchester Airport which was due to land at 2330.
The company apologised for any inconvenience caused to customers and said they would be in touch as more information became available.
The Government has sent extra consular staff to the airport and is advising anyone due to fly to the resort to check with their airline or tour operator.
It is estimated there are around 2,000 British holidaymakers in the resort.


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Extension Master Gardener
Extension Master Gardeners are a vital part of K-State Research and Extension. Donating time in return for horticultural training, Extension Master Gardeners help local agents meet the need for horticultural information in their communities. The means of providing this information are diverse, including horticultural "hotlines," demonstration gardens, garden shows, public presentations, and tours. In 2014, Extension Master Gardeners in Kansas donated more than 101,000 hours for a total volunteer value exceeding $2.1 million.
See the list in the left column for more specific information.


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Rapper Tim Dog Dead From Seizure
Bronx, New York rapper Tim Dog has died from a seizure according to numerous reports.
The rapper, born Timothy Blair, suffered from a seizure, from complications associated with diabetes, according to The Source.
Tim Dog, 46, recorded early tracks with legendary rap collective Ultramagnetic MC's, but he was best known for his debut album Penicillin on Wax, which contained the diss song "F**k Compton."
The song, which was one of the first shots fired in a mounting feud between rappers on the East and West Coasts, helped fuel a series of replies from rappers on the West coast, including Compton's Most Wanted, DJ Quik, Dr. Dre and others.
In later years, Tim Dog recorded with Kool Keith in the group Ultra with Kool Keith.