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These are great tips! I'm moving in with my significant other in a few months. I'll keep some of these in mind.
If splitting the cost of rent and utilities with your significant other sounds like a good idea, you're not alone. According to the 2010 U.S. Census, 7.5 million unmarried couples are living together, which is a 13% jump from last year. The economy may be playing a role in the increase — both partners have jobs in only 49% of cohabitating couples.
Saving money on rent is obviously not a reason to move in with your boyfriend or girlfriend. But the truth is it can be a nice benefit — if you do it right. Below are five tips to make the financial side of moving in together a smooth experience.
Discussing trivial things like "will we make the bed every morning?" can be a lot easier than talking about money. Start small and work your way up. Actions may speak louder than words, but when you're moving in with a significant other, communication is key.
If one partner wants a significantly nicer apartment than the other and can afford it, great. But that doesn't mean the rent should then be shared equally. Agree on how much you can each afford and how you will split the cost of living before signing on the dotted line. Being in love doesn't mean you can or should put yourself in a stressful financial situation.
Both partners share the emotional risk of combining lives by living together, but sometimes the financial risk is skewed in one direction. Creating some sort of cohabitation agreement can help neutralize this risk. If you were to break up, who would move out? How would the finances be handled during that process? These may not be fun questions to ask, but if you don't discuss it up front you may be dealing with financial stress on top of emotional stress if the relationship comes to an end.
While you need a strategy for paying various bills, combining accounts is not a good solution. Signing up for a joint checking account or credit card is a big decision, and not one that makes sense for couples who are cohabitating. If your partner goes on a shopping spree, you could be on the line for 100% of the cost. Be smart — keep your accounts separate for now.
Set aside time for fun — whether that means cooking dinner together or going to see a movie, make sure you're still enjoying your partner after moving in together. While you're at it, make a date to talk about your finances too. Communicating about bills or any other money-related topics should be intentional. If some sort of tension does arise, it'll be easier to bring it up within the context of a planned meeting rather than out of the blue.
Disclaimer: The links and mentions on this site may be affiliate links. But they do not affect the actual opinions and recommendations of the authors.
Wise Bread is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to amazon.com.
These are great tips! I'm moving in with my significant other in a few months. I'll keep some of these in mind.
Great tips. I like the idea of easy discussions first that lead to harder discussions of money. Better to have all expectations on the table. Less awkward in the long run.


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CostX Version 3.21 Released
Exactal is pleased to announce the release of version 3.21 for its CostX® range of products. The 3.21 release is a general release for all customers and includes a number of significant speed improvements when dealing with drawings and especially when using large BIM models. Multi-user support has also been enhanced when multiple users are measuring from the same drawing at the same time.
Exactal continues to enhance the CostX® range with each new release and version 3.21 is recommended for all customers under maintenance as a free upgrade.
Customers with maintenance may download version 3.21 through Exactal's dedicated support site TechWeb at http://techweb.exactal.com/downloads/search.php?product=P_5&rec_int=4. As soon as the type of product has been selected and your valid serial number entered the product may downloaded. Users may retrieve their serial number by copying the text from the about box for CostX®
PLEASE NOTE: This upgrade is only valid for users under maintenance. Users who are not under maintenance but who would like to upgrade should contact Exactal Sales & Marketing Manager, Ms Chris Reilly, at email@example.com

subset: commoncrawl


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Research on Nanomaterials
Manufactured nanomaterials are in more than 1,300 commercial products including medical equipment, textiles, fuel additives, cosmetics, plastics and more. EPA scientists research the most prevalent nanomaterials that may have human and environmental health implications. The research is developing a scientific foundation to better understand, predict and manage the challenges of nanomaterials.
- Why is EPA studying nanomaterials?
EPA researchers are studying the unique chemical and physical features of nanomaterials (such as size, shape, chemical composition, stability, etc) to help develop predictive models to determine which nanomaterials may pose a higher probability of risk and those expected to have little impact.
- What are the unique characteristics of nanomaterials?
Due to the rapid and diverse growth of engineered nanomaterials, it is a challenge for regulators and risk assessors to understand the potential for exposure and whether methods used for assessing conventional chemicals can be used for nanomaterials. EPA researchers are identifying and characterizing the unique chemical and physical features of nanomaterials, such as
- size,
- shape,
- chemical composition,
- stability, etc.
This allows the researchers to develop predictive models to determine which nanomaterials may pose a higher probability of risk and those expected to have little impact.
- What nanomaterials is EPA studying?
- Nano Silver: Because silver nanomaterials have antibacterial, antifungal and antiviral properties, they are used in medical equipment, textiles and cosmetics, fabrics, plastics and other consumer products. EPA is researching the fate and transport of nanosilver and how they interact with the environment. EPA is developing methods to measure nanosilver concentration and characteristics such as size, shape, surface charge, and surface chemistry to better understand the role of these physical and chemical properties.
- Carbon Nanotubes: These nanomaterials are one of the most abundant classes of nanomaterials, and come in a variety of shapes and sizes. Carbon materials have a wide range of uses, including composites for vehicles or sports equipment, coatings, textiles, polymers, plastics and integrated circuits for electronic components. The interactions between carbon nanotubes and natural organic matter strongly affect their transport, transformation and exposure in aquatic environments. EPA research evaluates the physical and chemical properties of carbon nanotubes to determine which ones influence their behavior in the environment and in biological systems.
- Cerium dioxide: Nanoscale cerium dioxide is used in electronics, plastics, biomedical supplies, energy, fuel additives, and other consumer products. One application of cerium dioxide nanomaterials leads to dispersion in the environment, which is the use as a fuel-borne catalyst in diesel engines. There is ongoing research to evaluate exposure to cerium dioxide from diesel emissions and the potential for environmental and public health impacts.
- Titanium dioxide: Nano titanium dioxide is used in many products. It can be found in sunscreens, cosmetics, paints and coatings, and electronic devices. Titanium dioxide may be activated by ultraviolet radiation, a normal component of sunlight, to catalyze reactions that can be toxic to fish and other aquatic species under certain conditions. EPA is researching the potential for titanium dioxide nanomaterials to be released from consumer products and enter the environment, be transformed in the environment, and to become toxic to sensitive environmental species or to humans.
- Iron: One important use of nano zero-valent iron particles is to catalyze the breakdown of chlorinated hydrocarbon compounds that are among the most common toxic contaminants found in hazardous waste sites. The injection of zerovalent iron into such sites is a relatively inexpensive and rapid way to reduce the presence of these hazardous environmental pollutants. EPA research is being conducted to assure that this beneficial use of nanomaterials is not associated with unwanted or unexpected adverse side effects on human health or the environment.
- Micronized Copper: Micro and nanometer sized copper particles are used as preservatives in pressure treated lumber and in some paints and coatings. Treated woods are produced by injecting finely ground copper carbonate -- or "micronized" particles -- into wood. EPA is working with the Consumer Product Safety Commission to evaluate the potential for release of copper particles or copper ions from such products under normal use and wear. Widespread use of copper-treated lumber has increased the potential for human and environmental exposure to these nanomaterials. This has created a need to better understand their fate and behavior. A team of EPA scientists measured how much micronized copper leaches from the copper-treated wood as it weathers and ages. The results were used to gage potential exposures from direct contact with the treated wood and its runoff. Another team of EPA scientists studied what happens to the copper particles when treated wood fragments are ingested. Sawdust from three copper-treated wood products were tested in a simulated digestion system consisting of an artificial stomach and intestinal fluid. Study results indicated that the copper escapes as copper ions when digested. This suggests that copper is highly bioaccessible at low pH and may pose a potential human exposure risk when ingested.
US EPA (2014) "Release of Micronized Copper Particles from Pressure-treated Wood Products." (PDF) (56 pp, 1.3 M) Publication No. 600/R-14/365.
- How will EPA use this research?
EPA will use this research to develop research protocols for characterizing engineered nanomaterials (ENMs) and for evaluating exposure and toxicity in complex biological or environmental systems. This research will allow EPA scientists to evaluate the relationships between the physical and chemical properties of ENMs and their fate, transport, and effects which could lead to safer and more sustainable ENMs.
EPA develops scientific methods to study and evaluate the unique properties of nanomaterials, how they behave during manufacturing, product use, and end of life disposal. To better protect human health and the environment, EPA and others use the research to inform policy and regulatory decisions about chemicals.
Learn about our work to control nanoscale materials under the Toxic Substances Control Act
Nanomaterials Research
- Mapping environmental fate of nanomaterials
- Nanomaterial effects on ecosystems and wildlife health
- Developing sustainable nanomaterials
Mapping environmental fate of nanomaterials
The environmental fate of chemicals describes the processes by which chemicals move and change in the environment. Due to the uncertainty about the unique characteristics of nanomaterials and their potential uses and effects, it is important to map the environmental fate of nanomaterials. EPA is developing information to describe the relationships between key properties of nanomaterials and their
- environmental fate,
- transport,
- transformation,
- bio-distribution,
- exposure, and
- toxicity to humans and other species.
- Estimating Nanomaterial Transport in Soils
Quantifying how nanomaterials move from point of release to human or ecological systems is essential for assessing environmental exposures. Studies to quantify transport are time-consuming, labor-intensive, and can only be conducted on a small number of nanomaterials at a time.
EPA scientists evaluate the use of using an automated screening technology to help quantify transport. This technique can rapidly screen the mobility of nanomaterials. It also generates parameters for soil/sediments retaining nanomaterials and how nanomaterials are transported in soil/sediments. This methodology is useful to both regulators and the regulated community for the preparation of pre-manufactured notices that EPA requires.
- Innovative Nanomaterial Characterization Techniques
Measuring the concentration and size distribution of nanomaterials is critical for studying their environmental behavior. EPA researchers developed a unique technique to assess nanomaterials. The method combines a size separation technique with an elemental concentration detector to provide better assessments. The technique provides information simultaneously on nanomaterial size, number and metallic composition which was not possible with the older technique.
Using this technique, scientists can distinguish natural minerals or metal with natural organic matter from low concentrations of nanomaterials. This is critical for measuring nanomaterials in environmental samples such as drinking water and stream samples. This technique can be used by companies that produce nanomaterials to support premanufacture notice requirements. It is also useful to EPA's Office of Water our regional offices around the nations to monitor engineered nanomaterials in surface and ground water.
- Case Study: The Impact of Silver Nanoparticles on Municipal Solid Waste
EPA evaluated the possible environmental impacts of using polyvinylpyrrolidone (PVP) coated silver nanoparticles (PVP-AgNPs) for composting municipal solid waste. The analysis suggests that microbial activity can be impacted within hours of AgNPs exposure, although at low AgNPs concentrations activity can be relatively stable.
Data from this and other studies show that toxicity might be different when dealing with complex microbial communities. This suggests that data from pure culture studies may be inaccurate in predicting the impact of AgNPs on microbial communities.
It is unclear whether the bacterial response is caused by bacterial populations resistant to AgNPs, the decrease in Ag+ release, transformation of AgNPs, or reduction in bioavailability. More research is needed to identify which concentrations of silver nanoparticles begin to have a toxicological effect on waste management systems.
Nanomaterial Effects on Ecosystems and Wildlife Health
Nanomaterials have become widely used in products ranging from clothing (which incorporates bacteria-fighting nano Silver) to sunscreen. Nanomaterials are very useful, but there is insufficient information about how nanomaterials affect ecosystem health.
Since nanomaterials are much smaller than normal (about 100,000 times smaller than the width of a human hair), they are absorbed more easily by animal's lungs and skin. EPA is in the process of researching how nanomaterials interact with biological processes important to the health of ecosystems and wildlife species that live in these ecosystems.
- Studying Nanomaterials in Ecosystems and the Environment
EPA is in the process of researching how nanomaterials interact with biological processes important to the health of ecosystems and wildlife species that live in these ecosystems. Evaluating the potential toxicity of nanomaterials is difficult because they have unique chemical properties, high reactivity, and do not dissolve in liquid media. Testing for potential impacts on ecological systems is especially challenging because they enter the environment through multiple exposure routes, transform over time, and food-chain transfers occur.
Existing test protocols for soluble chemicals may not work to test the safety of nanomaterials. EPA researchers conduct laboratory analyses to evaluate new approaches and procedures for studying the impacts of specific nanomaterials in freshwater, marine and terrestrial ecosystems. The results from the lab studies provide guidance about how to properly evaluate nanomaterials and how to characterize them in key organisms and different ecosystems.
- Using New Chemical Data to Classify Nanomaterials
EPA scientists are using new high-throughput screening and zebrafish assays (from the ToxCast chemical prioritization research) to determine if they can be used to screen nanomaterials for potential effects to human health and the environment. Researchers used these to test over 50 samples. Metal nanoparticles show strong cellular stress responses across many different cell types. Most other nanomaterials are not significantly cytotoxic.
Nano forms of Cerium (Ce), Titanium Dioxide (TiO2), Silicon Dioxide (SiO2) and Carbon Nanotubes (CNT) are active in various primary human cell systems for a variety of endpoints, generally at concentrations above 1 g /ml. The methods demonstrate the feasibility of using these assays to evaluate a range of nanomaterials, but much refinement is needed before using them to identify any potential adverse health and environmental effects.
Developing Sustainable Nanomaterials
EPA scientists are researching more sustainable ways to produce and apply nonmaterials, in order to minimize their potential environmental and human health impacts.
- Green production of nanomaterials to promote sustainable nanotechnologies
EPA scientists evaluate the production of sustainable nanomaterials in a medium in which they are to be used. The approach EPA is evaluating can be used to replace hazardous chemicals with naturally occurring antioxidants that reduce the metal salts and contain the nanomaterials that are formed. Several protocols have been developed to show that the benign antioxidants present in agricultural wastes (e.g., grape must from wineries, beet juice, simple sugars, tea and coffee extracts) are good alternative starting materials to produce nanomaterials in water or by using nontoxic byproducts such as glycerol, which comes from the biofuel industry.
This research could provide safer methods to produce nanoparticles used for the growing nanotechnology industry. The impact of nanomaterials on health and the environment is further minimized by developing sustainable nanomaterials.
- Nano-encapsulated Membranes
Lack of safe drinking water is the primary cause of many diseases in the world today. Every day, tens of thousands of people die from causes directly related to contaminated water. The scarcity and contamination of worldwide drinking water requires the development of highly efficient water purification techniques such as membrane filtration. Membrane assisted water purification is found to be a solution for the water crisis. For instance, membrane purification technologies such as a Reverse Osmosis (RO), Membrane Distillation (MD) and recently Forward Osmosis (FO) are widely used to produce water from ground water, surface water, waste water, and water extracted from saline sources such as brackish ground water and seawater.
Nano composite membranes and materials are the backbone of various modern technologies for a variety of sustainable applications. EPA researchers are developing and evaluating a method to employ bio-renewable materials such as cellulose to develop nano-encapsulated membranes for future water purification purposes. EPA is developing novel methods for preparing cellulosic and nanomaterial incorporated cellulosic membranes for sustainable applications. The nano-encapsulated membranes currently being developed and tested by EPA researchers can be useful for a number of applications in water or solvent purification.
Collaborative Research on Nanomaterials
- Extramural Nanotechnology Research
- Duke University — Center for Environmental Implications of NanoTechnology
- University of California — Center for Environmental Implications of Nanotechnology (UC—CEIN)
- EPA and NSF Lifecycle and Molecular Design Grant Awards: Four groups of researchers hope to make the world safer via one-time sustainability science awards that the National Science Foundation (NSF) and the Environmental Protection Agency (EPA)
- EPA Partners for Nanomaterial Research
- Small Business Innovation Research (SBIR) Grants Awarded for Nanotechnology Projects
- National Nanotechnology Initiative (Nano.gov)
- Nanotechnology and Nanomaterials Fact Sheet (PDF) (2 pp, 269 K, About PDF)
- Nanomaterial Case Studies
- Nanomaterials Research Publications
EPA Technical Contact
- Rosemary Keane (email@example.com)


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Cardigan – 6%DOKIDOKI
Skirt – N/A
Shoes – N/A
Cardigan – 6%DOKIDOKI – JPY 6,000
Tights – Hanjiro (shop) – JPY 500 | Legwarmers – N/A – JPY 1,000 | Shoes – N/A – JPY 2,000
Hair – LOOP – JPY 5,000
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See all the people we photographed at the 7th Harajuku Fashion Walk
Inspired by the stunningly creative street fashion that exploded on the streets of Tokyo and Osaka in the late 1990's, photo-journalist Kjeld Duits launched JAPANESE STREETS in 2002. This makes JS one of the first fashion blogs on the net, and the very first to cover Japanese street fashion.
Recent photos by Kjeld Duits:
The second part of this two part series focuses on the people at Design Festa 8 comments
The first part of this two part series focuses on the art at Design Festa 4 comments
Dorothy Vacance—one of Tokyo's hidden gems—is offering really cute embroidered patches featuring traditional images of Japan 0 comments
One of Tokyo's most important fashion and design exhibitions, rooms, took place again this week. JAPANESE STREETS picked a few favorites 3 comments
Last year, Israel's famous Tikotin Museum of Japanese Art exhibited over 100 of JAPANESE STREETS photographs 6 comments


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Police say the X-rays don't lie: A man who tried to flee from a New Hampshire jewelry store with a diamond ring worth $3,200 swallowed it.
Employees at Bellman's Jewelers in Manchester say Ronald Perley came in Thursday pretending to shop for an engagement ring. Police say the 52-year-old Perley picked up a ring and ran toward the door.
Workers confronted him, saying they saw Perley put his hand to his mouth and swallow. He denied swallowing the ring. Police got a search warrant and brought him to Elliot Hospital, where X-rays showed the 14-karat white-gold ring with princess-cut diamonds inside him.
Perley was arraigned on charges of theft and falsifying physical evidence. It wasn't immediately clear whether he had a lawyer. His $50,000 bail includes the ring's


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China's virtual vigilantes: Civic action or cyber mobs?
Concerned citizens are targeting anyone from accused pedophiles to activists with 'human flesh search engines' that post people's personal information online.
| Beijing
Some call it a weapon in the hands of a righteous army, forged so that wrongdoers might be smitten. Others say it simply allows a mob of vigilantes to publicly vilify and humiliate anyone they choose to pick on through grotesque invasions of privacy.
Either way, the peculiarly Chinese Internet phenomenon known as the "human flesh search engine," a citizen-driven, blog-based hunt for alleged undesirables, claimed a fresh victim this month when a mid-ranking government official lost his job.
Accused of accosting a young girl, Lin Jiaxiang found his name, address, phone number, and workplace plastered all over Chinese cyberspace for 250 million Internet users to see, and his alleged crime the subject of hundreds of insulting blog postings.
Mr. Lin might be thought to have gotten his just deserts, especially since the police refused to prosecute him because he'd been drunk. Grace Wang, however, a Chinese student at Duke University, was outraged when netizens back home, offended by her efforts to mediate a campus dispute between pro-Tibetan and Chinese students last March, tracked down her parents' address and emptied a bucket of feces by their front door.
Once the actions of Ms. Wang and Lin had attracted attention in Internet chat rooms, both were quickly identified by people who recognized the photos of them posted on the Web.
It was not long before others who knew them had created an ad hoc human flesh search engine, and began posting many other personal details about the two.
With more Internet users than anywhere else in the world, there is no shortage of amateur detectives ready to join the hunt. And with chat rooms the only public space where Chinese citizens can express themselves anonymously and with any real freedom, they have become forums for strong opinions on many issues.
"It is a tradition in China," says Yu Hai, a sociologist at Shanghai's Fudan University. "People here like to moralize. And since traditional media are government mouthpieces, the Internet has become a very convenient channel for ordinary people to vent their feelings."
They can do so pretty much however they like, not only because they can disguise their identities, but also because there is no privacy law in China yet. "There is no practicable, feasible, and concrete legal instrument" to regulate Internet use, says Li Xu, deputy head of Tsinghua University's Institute for Internet Behavior.
One man who found himself the quarry of a human flesh search, Wang Fei, is testing the law by bringing China's first suit against websites that he says carried defamatory statements about him.
Mr. Wang drew the ire of fellow Internauts after his wife committed suicide last year. Her diary, posted posthumously by her sister, voiced suspicions that Wang had an affair with a colleague. The blogosphere blamed Wang for his wife's death, and turned on him with a vengeance.
"You will fall into the endless darkness and abyss of misery hated by billions" read one post, labeling Wang a "beast" and "scum."
The virtual insults spilled over into real life. Someone painted "blood for blood" on Wang's front door, his lawyer said. He and his relatives were bombarded with furious telephone calls, and he was fired from his job at an advertising agency, along with his alleged mistress.
"Those websites published insulting, defamatory, and untrue information about Wang that damaged his reputation ... and violated his privacy," argues his lawyer, Zhang Yanfeng. "He is suing them for damages, for mental distress, and lost earnings."
The case has already taken nine months and will probably not come to judgment until next spring, says Mr. Zhang, because of "a great many disagreements" among the judges and the expert witnesses.
Among the issues the court must resolve, in the absence of any clear legislation, is whether information such as a cellphone number, an ID card number, or an address can be said to be private. The judges must also consider how far website managers are responsible and legally liable for posts on their sites, and weigh the competing interests of free speech and privacy protection.
A poll published earlier this year in the China Youth Daily found that nearly 80 percent of respondents thought that human-flesh search engines should be regulated, and 65 percent thought they invaded people's privacy.
The dilemma, says Dr. Li, is that "allowing arbitrary speech with no regulation ... violates privacy rights. But if you over-regulate citizens' ability to express themselves, the Internet will lose its very nature and its attraction."
Drawing too heavy a cloak around personal privacy, moreover, would protect abusive officials from the public pillorying they deserve, argues Liu Deliang, head of the Asia-Pacific Institute for Cyberlaw Studies.
"Ordinary people have no enforceable right to supervise government officials' behavior or to control the corruption they see everywhere," he says. "So they use the Internet to do that."
"Human-flesh searches are a neutral technology that can be used for good or ill," says Dr. Liu. "But they must strike a balance between public and private interests."


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High School Mathematics Extensions/Primes/Modular Arithmetic
|Modular Arithmetic
|Problems & Projects
|Problem Set
|Exercise Solutions
|Problem Set Solutions
|Definition Sheet
|Full Version
|PDF Version
Modular Arithmetic
Modular arithmetic connects with primes in an interesting way.
Modular arithmetic is a system in which all numbers up to some positive integer, n say, are used. So if you were to start counting you would go 0, 1, 2, 3, ... , n - 1 but instead of counting n you would start over at 0. And what would have been n + 1 would be 1 and what would have been n + 2 would be 2. Once 2n has been reached the number is reset to 0 again, and so on. Modular arithmetic is also called clock-arithmetic because we only use 12 numbers to tell standard time. On clocks we start at 1 instead of 0, continue to 12, and then start at 1 again. Hence the name clock-arithmetic.
The sequence also continues into what would be the negative numbers. What would have been -1 is now n - 1. For example, consider modulo 7 arithmetic, it's just like ordinary arithmetic except the only numbers we use are 0, 1, 2, 3, 4, 5 and 6. If we see a number outside of this range we add 7 to (or subtract 7 from) it, until it lies within that range.
As mentioned above, modular arithmetic is not that different to ordinary arithmetic. For example in modulo 7 arithmetic, we have
We have done some calculation with negative numbers. Consider 5 × -6. Since -6 does not lie in the range 0 to 6, we need to add 7 to it until it does. And -6 + 7 = 1. So in modular 7 arithmetic, -6 = 1. In the above example we showed that 5 × -6 = -30 = 5, but 5 × 1 = 5. So we didn't do ourselves any harm by using -6 instead of 1. Why?
Note - Negatives: The preferred representation of -3 is 4, as -3 + 7 = 4, but using either -3 and 4 in a calculation will give us the same answer as long as we convert the final answer to a number between 0 and 6 (inclusive).
Find in modulo 11
- -1 × -5
- 3 × 7
3. Compute the first 10 the powers of 2
- 21, 22, 23, ... , 210
What do you notice?
Using the powers of 2 find
- 61, 62, 63, ... , 610
What do you notice again?
i.e. find, by trial and error (or otherwise), all numbers x such that x2 = 4 (mod 11). There are two solutions, find both .
i.e. find all numbers x such that x2 = 9 (mod 11). There are two solutions, find both.
Consider a number n, the inverse of n is the number that when multiplied by n gives 1. For example, if we were to solve the following equation
the (mod 7) is used to make it clear that we are doing arithemetic modulo 7. We want to get rid of the 5 somehow. Multiplying it by something to turn it into a 1 would do the job. Notice that
because 3 multiplied by 5 gives 1, we say 3 is the inverse of 5 in modulo 7. Now we multiply both sides by 3
So x = 2 modulo 7 is the required solution.
Definition (Inverse)
- The inverse of (a number) x is a number y such that xy = 1. We denote the inverse of x by x-1 or 1/x.
Inverse is unique
From above, we know the inverse of 5 is 3, but does 5 have another inverse? The answer is no. In fact, in any reasonable number system, a number can have one and only one inverse. We can see that from the following proof
Suppose n has two inverses b and c
From the above argument, all inverses of n must be equal. As a result, if the number n has an inverse, the inverse must be unique.
An interesting property of any modulo n arithmetic is that the number n - 1 has itself as an inverse. That is, (n - 1) × (n - 1) = 1 (mod n), or we can write (n - 1)2 = (-1)2 = 1 (mod n). The proof is left as an exercise at the end of the section.
Existence of inverse
Not every number has an inverse in every modulo arithmetic. For example, 3 doesn't have an inverse mod 6, i.e., we can't find a number x such that 3x = 1 mod 6 (the reader can easily check).
Consider modulo 15 arithmetic and note that 15 is composite. We know the inverse of 1 is 1 and of 14 is 14. But what about 3, 6, 9, 12, 5 and 10? None of them has an inverse! Note that each of them shares a common factor with 15!
As an example, we show that 3 does not have an inverse modulo 15. Suppose 3 has an inverse x, then we have
We make the jump from modular arithemetic into rational number arithmetic. If 3x = 1 in modulo 15 arithmetic, then
for some integer k. Now we divide both sides by 3, we get
But this cannot be true, because we know that x is an integer, not a fraction. Therefore 3 doesn't have an inverse in mod 15 arithmetic. To show that 10 doesn't have an inverse is harder and is left as an exercise.
We will now state the theorem regarding the existence of inverses in modular arithmetic.
- If n is prime then every number (except 0) has an inverse in modulo n arithmetic.
- If n is composite then every number that doesn't share a common factor with n has an inverse.
It is interesting to note that division is closely related to the concept of inverses. Consider the following expression
the conventional way to calculate the above would be to find the inverse of 3 (being 5). So
We write the inverse of 3 as 1/3, so we think of multiplying 3-1 as dividing by 3, we get
Notice that we got the same answer! In fact, the division method will always work if the inverse exists.
However, the expression in a different modulo system will produce the wrong answer, for example
we don't get 2, as 3-1 does not exist in modulo 9, so we can't use the division method.
1. Does 8 have an inverse in mod 16 arithemetic? If not, why not?
2. Find x mod 7 if x exists:
3. Calculate x in two ways, finding inverse and division
4. (Trick) Find x
Find all inverses mod n (n ≤ 19)
Coprime and greatest common divisor
Two numbers are said to be coprimes if their greatest common divisor (gcd) is 1. E.g. 21 and 55 are both composite, but they are coprime as their greatest common divisor is 1. In other words, they do not share a common divisor other than 1.
There is a quick and elegant way to compute the gcd of two numbers, called Euclid's algorithm. Let's illustrate with a few examples:
Example 1:
- Find the gcd of 21 and 49.
We set up a two-column table where the larger of the two numbers is on the right hand side as follows
We now compute 49 (mod 21) which is 7 and put it in the second row smaller column, and put 21 into the larger column.
Perform the same action on the second row to produce the third row.
Whenever we see the number 0 appear on the smaller column, we know the corresponding larger number is the gcd of the two numbers we started with, i.e. 7 is the gcd of 21 and 49. This algorithm is called Euclid's algorithm.
Example 2
- Find the gcd of 31 and 101
Example 3
- Find the gcd of 132 and 200
Important to note
- The gcd need not be a prime number.
- The gcd of two different primes is 1. In other words, two different primes are always coprime.
1. Determine whether the following sets of numbers are coprimes
- 5050 5051
- 59 78
- 111 369
- 2021 4032
2. Find the gcd of the numbers 15, 510 and 375
info -- Algorithm
An algorithm is a step-by-step description of a series of actions when performed correctly can accomplish a task. There are algorithms for finding primes, deciding whether 2 numbers are coprimes, finding inverses and many other purposes.
You'll learn how to implement some of the algorithms we have seen using a computer in the chapter [[../../../Mathematical Programming/]].
Finding Inverses
Let's look at the idea of inverse again, but from a different angle. In fact we will provide a sure-fire method to find the inverse of any number. Let's consider:
- 5x = 1 (mod 7)
We know x is the inverse of 5 and we can work out it is 3 reasonably quickly. But x = 10 is also a solution, so is x = 17, 24, 31, ... 7n + 3. So there are infinitely many solutions; therefore we say 3 is equivalent to 10, 17, 24, 31 and so on. This is a crucial observation.
Now let's consider
A new notation is introduced here, it is the equal sign with three strokes instead of two. It is the "equivalent" sign; the above statement should read "216x is EQUIVALENT to 1" instead of "216x is EQUAL to 1". From now on, we will use the equivalent sign for modulo arithmetic and the equal sign for ordinary arithmetic.
Back to the example, we know that x exists, as gcd(811,216) = 1. The problem with the above question is that there is no quick way to decide the value of x! The best way we know is to multiply 216 by 1, 2, 3, 4... until we get the answer, there are at most 811 calculations, way too tedious for humans. But there is a better way, and we have touched on it quite a few times!
We notice that we could make the jump just like before into rational mathematics:
We jump into rational maths again
We jump once more
Now the pattern is clear, we shall start from the beginning so that the process is not broken:
Now all we have to do is choose a value for f and substitute it back to find a! Remember a is the inverse of 216 mod 811. We choose f = 0, therefore e = 1, d = 13, c = 40, b = 53 and finally a = 199! If f is chosen to be 1 we will get a different value for a.
The very perceptive reader should have noticed that this is just Euclid's gcd algorithm in reverse.
Here are a few more examples of this ingenious method in action:
Example 1
Find the smallest positive value of a:
Choose d = 0, therefore a = 49.
Example 2 Find the smallest positive value of a:
Choose e = 0, therefore a = -152 = 669
Example 3 Find the smallest positive value of a:
Set i = 0, then a = -21 = 34. Why is this so slow for two numbers that are so small? What can you say about the coefficients?
Example 4 Find the smallest positive value of a:
Now d is not an integer, therefore 21 does not have an inverse mod 102.
What we have discussed so far is the method of finding integer solutions to equations of the form:
- ax + by = 1
where x and y are the unknowns and a and b are two given constants, these equations are called linear Diophantine equations. It is interesting to note that sometimes there is no solution, but if a solution exists, it implies that infinitely many solutions exist.
Diophantine equation
In the Modular Arithmetic section, we stated a theorem that says if gcd(a,m) = 1 then a-1 (the inverse of a) exists in mod m. It is not difficult to see that if p is prime then gcd(b,p) = 1 for all b less than p, therefore we can say that in mod p, every number except 0 has an inverse.
We also showed a way to find the inverse of any element mod p. In fact, finding the inverse of a number in modular arithmetic amounts to solving a type of equations called Diophantine equations. A Diophantine equation is an equation of the form
- ax + by = d
where x and y are unknown.
As an example, we should try to find the inverse of 216 in mod 811. Let the inverse of 216 be x, we can write
we can rewrite the above in every day arithmetic
which is in the form of a Diophantine equation.
Now we are going to do the inelegant method of solving the above problem, and then the elegant method (using Magic Tables).
Both methods mentioned above uses the Euclid's algorithm for finding the gcd of two numbers. In fact, the gcd is closely related to the idea of an inverse. Let's apply the Euclid's algorithm on the two numbers 216 and 811. This time, however, we should store more details; more specifically, we want to set up an additional column called PQ which stands for partial quotient. The partial quotient is just a technical term for "how many n goes into m" e.g. The partial quotient of 3 and 19 is 6, the partial quotient of 4 and 21 is 5 and one last example the partial quotient of 7 and 49 is 7.
The tables says three 216s goes into 811 with remainder 163, or symbollically:
- 811 = 3×216 + 163.
Let's continue:
Reading off the table, we can form the following expressions
- 811 = 3× 216 + 163
- 216 = 1× 163 + 53
- 163 = 3× 53 + 4
- 53 =13× 4 + 1
Now that we can work out the inverse of 216 by working the results backwards
- 1 = 53 - 13×4
- 1 = 53 - 13×(163 - 3×53)
- 1 = 40×53 - 13×163
- 1 = 40×(216 - 163) - 13×163
- 1 = 40×216 - 53×163
- 1 = 40×216 - 53×(811 - 3×216)
- 1 = 199×216 - 53×811
Now look at the equation mod 811, we will see the inverse of 216 is 199.
Magic Table
The Magic Table is a more elegant way to do the above calculations, let us use the table we form from Euclid's algorithm
Now we set up the so-called "magic table" which looks like this initially
Now we write the partial quotient on the first row:
We produce the table according to the following rule:
- Multiply a partial quotient one space to the left of it in a different row, add the product to the number two space to the left on the same row and put the sum in the corresponding row.
It sounds more complicated then it should. Let's illustrate by producing a column:
We put a 3 in the second row because 3 = 3×1 + 0. We put a 1 in the third row because 1 = 3×0 + 1.
We shall now produce the whole table without disruption:
We can check that
- |199×216 - 811×53| = 1
In fact, if the magic table is contructed properly, and we cross multiplied and subtracted the last two column correctly, then we will always get 1 or -1, provided the two numbers we started with were coprimes. The magic table is just a cleaner way of doing the mathematics.
1. Find the smallest positive x:
2. Find the smallest positive x:
(a) Produce the magic table for 33a = 1 (mod 101)
(b) Evaluate and express in the form p/q
What do you notice?
(a) Produce the magic table for 17a = 1 (mod 317)
(b) Evaluate and express in the form p/q
What do you notice?
Chinese remainder theorem
The Chinese remainder theorem is known in China as Han Xing Dian Bing, which in its most naive translation means Han Xing counts his soldiers. The original problem goes like this:
- There exists a number x, when divided by 3 leaves remainder 2, when divided by 5 leaves remainder 3 and when divided by 7 leaves remainder 2. Find the smallest x.
We translate the question into symbolic form:
How do we go about finding such a x? We shall use a familiar method and it is best illustrated by example:
Looking at x = 2 (mod 3), we make the jump into ordinary mathematics
Now we look at the equation modulo 5
Substitute into (1) to get the following
Now look at the above modulo 7
we get
We choose b = 1 to minimize x, therefore x = 23. And a simple check (to be performed by the reader) should confirm that x = 23 is a solution. A good question to ask is what is the next smallest x that satisfies the three congruences? The answer is x = 128, and the next is 233 and the next is 338, and they differ by 105, the product of 3, 5 and 7.
We will illustrate the method of solving a system of congruences further by the following examples:
Example 1 Find the smallest x that satisfies:
now substitute back into the first equation, we get
we obtain
again substituting back
Therefore 52 is the smallest x that satisfies the congruences.
Example 2
Find the smallest x that satisfies:
substituting back
now solve for b
again, substitue back
Therefore 269 is the smallest x that satisfies the congruences.
1. Solve for x
2. Solve for x
*Existence of a solution*
The exercises above all have a solution. So does there exist a system of congruences such that no solution could be found? It certainly is possible, consider:
- x ≡ 5 (mod 15)
- x ≡ 10 (mod 21)
a cheekier example is:
- x ≡ 1 (mod 2)
- x ≡ 0 (mod 2)
but we won't consider silly examples like that.
Back to the first example, we can try to solve it by doing:
the above equation has no solution because 3 does not have an inverse modulo 21!
One may be quick to conclude that if two modulo systems share a common factor then there is no solution. But this is not true! Consider:
we can find a solution
we now multiply both sides by the inverse of 5 (which is 17), we obtain
obviously, k = 3 is a solution, and the two modulo systems are the same as the first example (i.e. 15 and 21).
So what determines whether a system of congruences has a solution or not? Let's consider the general case:
we have
essentially, the problem asks us to find k and l such that the above equations are satisfied.
We can approach the problem as follows
now suppose m and n have gcd(m,n) = d, and m = dmo, n = dno. We have
if (a - b)/d is an integer then we can read the equation mod mo, we have:
Again, the above only makes sense if (a - b)/d is integeral. Also if (a - b)/d is an integer, then there is a solution, as mo and no are coprimes!
In summary: for a system of two congruent equations
there is a solution if and only if
- d = gcd(m,n) divides (a - b)
And the above generalises well into more than 2 congruences. For a system of n congruences:
- ...
for a solution to exist, we require that if i ≠ j
- gcd(mi,mj) divides (ai - aj)
Decide whether a solution exists for each of the congruences. Explain why.
- x ≡ 7 (mod 25)
- x ≡ 22 (mod 45)
- x ≡ 7 (mod 23)
- x ≡ 3 (mod 11)
- x ≡ 3 (mod 13)
- x ≡ 7 (mod 25)
- x ≡ 22 (mod 45)
- x ≡ 7 (mod 11)
- x ≡ 4 (mod 28)
- x ≡ 28 (mod 52)
- x ≡ 24 (mod 32)
To go further
This chapter has been a gentle introduction to number theory, a profoundly beautiful branch of mathematics. It is gentle in the sense that it is mathematically light and overall quite easy. If you enjoyed the material in this chapter, you would also enjoy Further Modular Arithmetic, which is a harder and more rigorous treatment of the subject.
Also, if you feel like a challenge you may like to try out the Problem Set we have prepared for you. On the other hand, the project asks you to take a more investigative approach to work through some of the finer implications of the Chinese Remainder Theorem.
Acknowledgement: This chapter of the textbook owes much of its inspiration to Terry Gagen, Emeritus Associate Professor of Mathematics at the University of Sydney, and his lecture notes on "Number Theory and Algebra". Terry is a much loved figure among his students and is renowned for his entertaining style of teaching.
1. The Largest Known Primes--A Summary
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Mark Hamill
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|Mark Hamill
|25 September, 1951
|IMDB profile
|Wikipedia has information unrelated to Futurama
|Category of characters voiced by Mark Hamill
Mark Richard Hamill is an American actor, voice actor, producer, director, and writer. He is best known for his portrayal of Luke Skywalker in the Star Wars original trilogy, although he has played the character in other works, the Joker in the DC animated universe, and Skips in Cartoon Network's Regular Show. Hamill sang "This Toyshop's Goin' to War" as the Chanukah Zombie in Bender's Big Score.


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Song in Tosca or Turandot for example crossword clue was seen on Crosswords with Friends September 28 2022 . There's a leaderboard which turns on the rivalry. You can challenge your friends daily and see who solved the daily crossword faster. The game won't leave you empty-handed. If you're good enough, you can collect rewards and even earn badges. It's great when your progress is appreciated, and Crosswords with Friends does just that.
Song in Tosca or Turandot for example
Find other clues of Crosswords with Friends September 28 2022.


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'Winter's Bone' director: Be a respectful observer
Debra Granik '85 returns to Brandeis for screening, Q&A
Not confined to the age, gender or circumstances he or she was born into, a filmmaker can lead more than one life.
To Debra Granik '85, co-writer and director of the Oscar-nominated film "Winter's Bone," that's one of her craft's greatest joys.
"Winter's Bone" took Granik into the stark world of the rural, poverty-stricken Ozark region of Southern Missouri. The protagonist is Ree Dolly, a 17-year-old girl, whose mother is disabled by depression and whose drug-addicted father is missing. While she tries to care for her younger siblings, she searches for her dad, knowing the family will lose their home if she doesn't find him.
|From left: Debra Granik '85, Film Studies Program Chair Alice Kelikian, Brandeis President Fred Lawrence
"I want to make people understand and have an interest and some compassion and some attraction to a person they thought they never would or could or should," said Granik, who returned to Brandeis for a screening and Q&A on May 2. "And I feel like, gosh, so many times there really is a reason for it. The pulse in someone else's life and what they care about and what they need is just inherently interesting to each of us."
But inhabiting and portraying others' lives comes with great responsibility. Unfamiliar with environment and culture of the Ozarks, Granik -- a college educated woman living in New York City -- knew every decision she made in her portrayal of the community had meaning.
"As an outsider, I have these choices, but I don't have the lived experience to tell me sometimes which way to go, what to feature, what's important," she said. "All I knew, really, is what I admired, and I was very aware of what I didn't know."
Granik recalls reading a comment on a blog that took her to task because the only scenes in which Ree and her siblings are able to scrounge up food are when they hunt squirrel. That is, in fact, still done in the Ozarks, but it's not an exclusive source of sustenance.
"This blog must have been a couple weeks after I had taken out a scene where Ree and her best friend actually buy food in a grocery store, and that was very sobering because I realized in that one instant, by this woman's very astute comment, that everything you put in a portrait or take out of a portrait has such weight," she said. "That's kind of a weird, uncomfortable power, because omission or exaggeration or canting anything – it's a very delicate balance of what people feel they are going to learn about a region."
Granik suggested that since college affords students the privilege of having designated space and time to think and communicate with others about whatever subjects they are interested in or passionate about, they should use the time to "be a curious and respectful observer of everything."
"No one can make you do that, you can't buy that, but you can cultivate that," she said. "Don't feel that you know best. [Be] very porous to other people who are thinking as hard as you are."
Categories: Alumni, Arts, Humanities and Social Sciences


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I married Harriet the Furniture Seller in Brightwall Village. We lived there very happily until she started complaining about our house. I moved her to the nicest house in Brightwall, and still she complained. So I set her up in a nice little house in the Bowerstone Old Quarter. It even had an indoor staircase! Harriet the Furniture Seller seemed very happy there.
Then, we destroyed the Old Quarter en route to my becoming Queen. Harriet the Furniture Seller's and my house was not spared from the fiery destruction. But I'm playing through the game as a good guy, so I paid Reaver Industries to repair the Old Quarter. Our house was rebuilt complete with its little plaque with the heart on it, but I can't find Harriet the Furniture Seller anywhere. She's not hanging out in the house, in Bowerstone Market where I usually find her, or anywhere on the streets of the Old Quarter. She's not back in Brightwall. I moved our household to a new house in Bowerstone Market to see if that would free her from some glitch, but she's still nowhere to be found.
Where, oh where, has my poor Harriet the Furniture Seller gone?
Update: Louise the Housewife and I are set up very happily in Bowerstone Castle, but not a day goes by that I don't think fondly of my Harriet the Furniture Seller, and miss her dearly.


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Gas City, Indiana…….Jon Stanbrough of Avon, Indiana is no stranger to winning in the AMSOIL National Sprint Car competition, and on Friday night he kicked off "Indiana Sprintweek" in style by capturing his 30th career win with the series, this one coming at Gas City I-69 Speedway. The win was the first for his Amati Racing team.
The most recent winner with the series, Chad Boespflug, led the field to green and paced a hammer-down race through the first half. Stanbrough, who started alongside, actually slid back to the third spot as Bryan Clauson became the biggest threat to Boespflug's lead. As the first half wound on, Shane Cottle joined the lead pack and made it a four-car tussle.
Stanbrough jumped to the top on lap 12 and soon had a line carved in around the outside, circling Boespflug for the lead on lap 16. Just a lap later, the only caution of the race flew when Casey Shuman slowed to a stop.
After the restart, Stanbrough raced to a comfortable advantage, only giving up some ground late in the going as he encountered slower cars. At the finish, it was a .860-second win for Stanbrough in the Marion Underground Construction – Shane Wade Enterprises #66 DRC/Dynotech.
"(Crew chief) Daryl (Tate) and I never lost communication with each other, and his hard work and Shane Wade giving us the chance to do this, and those guys believing in me put this all together. We've just kept at it when we've been so close to winning races lately. Jeff Peterson did a great job on bleeders tonight, and we really made gains there. I never met Shane Wade before this came together, and hopefully now that we got him one, we can get some more this week," Stanbrough said.
Cottle held on for second, as he inched away from everyone else and actually reeled in the leader on the bottom in the Epperson Painting – Leer Racing #2 Spike/Claxton.
"I had Jon passed at one point, but I just had to get a way by Chad (Boespflug). He got us back and I just blew the corner a few too many times before I settled down. I think we were as fast as he was once I got going, but hopefully this is the turn we needed after all the bad luck we've had lately to get one in the win column soon," Cottle said.
Hunter Schuerenberg made a huge surge on the cushion, as he picked up the "Hard Charger" award from ProSource and made himself an early favorite for the week-long B&W Auto Mart "Josh Burton Hard Charger Award" after climbing from 4th to finish third in the MyLocalFordStore.com – Fatheadz Eyewear #35 Mach-1/Rider
"We knew the track would be heavy, so we took a chance and tried to keep it free to be good early. It worked out pretty well for us. We've gotten back to stuff we used to do, and I'm feeling really comfortable. We have done so little to the car, people probably wouldn't believe us. I've got a lot of confidence in it right now to just go out and drive the crap out of it," Schuerenberg said.
Clauson held on for fourth despite a flattening right-rear tire on the Tony Stewart/Curb-Agajanian Racing – Chevy Performance, while Dave Darland rounded out the top-five in the Phillips Motorsports – Racer's Advantage #71P DRC/Foxco. Darland also picked up the night's ProSource "Fast Time Award."
AMSOIL USAC SPRINT CAR NATIONAL CHAMPIONSHIP RACE RESULTS: July 12, 2013 – Gas City, Indiana – Gas City I-69 Speedway – "Indiana Sprintweek"
QUALIFYING: 1. Dave Darland, 71p, Phillips-12.295; 2. Shane Cottle, 2, Epperson-12.466; 3. Chase Stockon, 32, 32/TBI-12.609; 4. Bryan Clauson, 20, Stewart/Curb-Agajanian-12.619; 5. Brady Bacon, 69, Dynamics-12.620; 6. C.J. Leary, 30, Leary-12.625; 7. Jon Stanbrough, 66, Wade-12.712; 8. Mark Smith, 1m, Smith-12.740; 9. Justin Grant, 27a, Elson-12.838; 10. Chad Boespflug, 57, Hazen-12.917; 11. Dakota Jackson, 3, Jackson-12.973; 12. Christopher Bell, 67, Kunz/Curb-Agajanian-12.997;13. Richard Vander Weerd, 10, Vander Weerd-13.145; 14. Nick Drake, 55, Cline-13.288; 15. Chris Windom, 11, Walker-13.354; 16. Jace Vander Weerd, 88, Vander Weerd-13.385; 17. Hunter Schuerenberg, 35, Byram-13.414; 18. Wes McIntyre, 83, McIntyre-13.462; 19. Brady Short, 11p, Pottorff-13.472; 20. Kyle Robbins, 17R, Robbins-13.487; 21. Ryan Pace, 44, Pace-13.493; 22. Tracy Hines, 4, Hines-13.530; 23. Tyler Courtney, 23c, Courtney/Anderson-13.558; 24. Gary Taylor, 40, Hery-13.585; 25. Kevin Thomas Jr., 17RW, Dutcher/RW/Tri-Star-13.601; 26. Todd Keen, 18k, Keen-13.629; 27. Chad Shields, 81, Shields-13.644; 28. Casey Shuman, 21k, Krockenberger-13.686; 29. Kyle Cummins, 3c, Cummins-13.729; 30. Brett Burdette, 17B, Burdette-13.767; 31. Bradley Sterrett, 90, Leer-13.782; 32. Kevin Studley, 57x, Studley-13.825; 33. Chris Gurley, 12G, Team Automotive-13.831; 34. Max McGhee, 17, McGhee-13.853; 35. Ryan Bernal, 73, Ford-13.875; 36. Nathan Moore, 48, Moore-13.899; 37. Tyler Hewitt, 97x, Hewitt-13.901; 38. A.J. Hopkins, 14H, Hopkins-13.914; 39. Jerry Coons Jr., 10E, Edison-14.008; 40. Scotty Weir, 18, Keen-14.008; 41. Ted Hines, 12, Hines-14.073; 42. Kent Schmidt, 5k, Schmidt-14.114; 43. Todd Gnat, 51G, Gnat-14.155; 44. Conner Donelson, 3W, Sweat-14.236; 45. Brian Hayden, 77, Wingo-14.256; 46. Robert Ballou, 21x, Pollock-14.268; 47. Travis Welpott, 18x, Welpott-14.326; 48. Logan Jarrett, 29, Jarrett-14.420; 49. Mike Terry Jr., 85, Terry-14.697; 50. Dalten Gabbard, 77x, Arizona Heat-14.754; 51. Caleb Armstrong, 11J, Yeley-14.809; 52. Daylan Chambers, 4c, Chambers-14.900; 53. Dusty Shriver, 73x, Shriver-15.477.
QUALIFYING RACE #1: (8 laps) 1. Gurley, 2. Bernal, 3. Coons, 4. Hewitt, 5. Terry, 6. Ted Hines, 7. Hayden, 8. Shriver, 9. Gnat, 10. Welpott, 11. Armstrong. NT
QUALIFYING RACE #2: (8 laps) 1. McGhee, 2. Hopkins, 3. Weir, 4. Ballou, 5. Jarrett, 6. Gabbard, 7. Donelson, 8. Schmidt, 9. Chambers, 10. Moore. NT
FIRST HEAT: (10 laps) 1. Schuerenberg, 2. Darland, 3. Weir, 4. R.Vander Weerd, 5. Pace, 6. Thomas, 7. Bacon, 8. Grant, 9. Cummins, 10. McGhee. NT
SECOND HEAT: (10 laps) 1. Tracy Hines, 2. Cottle, 3. McIntyre, 4. Boespflug, 5. Drake, 6. Keen, 7. Leary, 8. Hopkins, 9. Burdette, 10. Ballou. 2:04.46
THIRD HEAT: (10 laps) 1. Stanbrough, 2. Short, 3. Courtney, 4. Stockon, 5. Coons, 6. Windom, 7. Gurley, 8. Jackson, 9. Sterrett, 10. Shields. 2:10.44
FOURTH HEAT: (10 laps) 1. Clauson, 2. Bell, 3. Taylor, 4. Shuman, 5. Bernal, 6. J.Vander Weerd, 7. Hewitt, 8. Smith, 9. Studley, 10. Robbins. NT
SEMI: (12 laps) 1. Bacon, 2. Grant, 3. Leary, 4. Smith, 5. Thomas, 6. Windom, 7. Cummins, 8. Pace, 9. Coons, 10. Hopkins, 11. Gurley, 12. Hewitt, 13. B+allou, 14. Burdette, 15. Sterrett, 16. Drake, 17. Jackson, 18. Bernal, 19. Robbins, 20. J.Vander Weerd, 21. Keen, 22. Shields. NT
FEATURE: (30 laps) 1. Jon Stanbrough, 2. Shane Cottle, 3. Hunter Schuerenberg, 4. Bryan Clauson, 5. Dave Darland, 6. Chad Boespflug, 7. Christopher Bell, 8. Chase Stockon, 9. Kevin Thomas Jr., 10. Chris Windom, 11. Tyler Courtney, 12. Brady Bacon, 13. Richard Vander Weerd, 14. Justin Grant, 15. Brady Short, 16. Jerry Coons Jr., 17. Gary Taylor, 18. Ryan Bernal, 19. Wes McIntyre, 20. Tracy Hines, 21. C.J. Leary, 22. Mark Smith, 23. Casey Shuman, 24. Scotty Weir. NT
FEATURE LAP LEADERS: Laps 1-15 Boespflug, Laps 16-30 Stanbrough.
NEW AMSOIL NATIONAL SPRINT POINTS: 1-Darland-865, 2-Clauson-831, 3-Stockon-792, 4-Thomas-791, 5-Schuerenberg-790, 6-Bacon -774, 7-Hines-728, 8-Ballou-682, 9-Cottle-534, 10-Courtney-525.
NEW INDIANA SPRINT WEEK POINTS: 1-Cottle-69; 2-Stanbrough-68; 3-Schuerenberg-62; 4-Clauson-62; 5-Darland-61; 6-Boespflug-50; 7-Bell-49; 8-Stockon-48; 9-Thomas-37; 10-Courtney-37.
NEXT AMSOIL NATIONAL SPRINT RACE: July 13 – Kokomo, Indiana – Kokomo Speedway – "Indiana Sprintweek"


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I have tried looking and cannot find it.
If I have an array like this
How do I eliminate the number 23 from the array.
I have tried looking and cannot find it.
If I have an array like this
How do I eliminate the number 23 from the array.
What I mean specifically is to delete the element within the array … totally… not leave it blank or null.
If you know that the value is the third one in the array:
$tt = array(10, 2, 23, 14);
If you want to remove every element with the value 23:
$tt = array(10, 2, 23, 14);
foreach($tt as $key=>$value) {
if($value == 23) {
That loop might be a bit inefficient/slow – the unset can also cause set fragmentation slowing later iterations. This actually sucks a bit more RAM while running, but releases itself quickly enough:
$tt = array(10, 2, 23, 14);
Since array_diff returns all elements in the first array that don't match elements in the second array.
Another approach would be to use array_search to find the matching key instead of iterating it.
if ($key=array_search('23',$tt)) unset($tt[$key]);
Assuming there's only one. to check for multiple instances, I'd just use "while" instead of "if".
An approach using array_filter may also be worth looking at.
Or just… not putting the 23 in the array in the first place… what input are you getting, and why do you need to remove one?
Do the keys have to retain their original values or not?
Today's entry of the PHP thread of the day series is relevant to this question.
First, this won't work - $value isn't bound to the source value array (To do this use "foreach ($array as $key => &$value)" and note the ampersand which causes the value to be passed by reference). Second, if you did receive the $value by reference, deleting a value on an object or array under iteration can cause undefined behavior by PHP.
LOOK CLOSER. He's calling $tt (the parent) by key for the unset, NOT $value. As such you don't have to pull $value by reference! Not sure where you were going with that, but… no, you're WAY off the money there.
unset inside foreach works just fine. First, foreach does the same thing as an array_walk, which is a pointer based operation using internal pointers… so the pointer to 'next' should still be valid even with the unset…
Which is why his code runs just FINE!
Oh, and array_filter and it's kine are problematic since you can't pass values to the user function and frankly heavy on the overhead (with the nested userland function call) is the slowest of them too… after mentioning it above I gave it a whirl, NOT worth the effort.
Should and is aren't always the same with PHP and you should know that by now.
From the docs of [fphp]array_walk[/fphp]
I've seen PHP do bizarre things if you unset an element - particularly the element that will be next - in a foreach. Now granted, this behavior may have be fixed, but I long ago made it a point to avoid calling unset on the object I'm iterating on (I still do it when I absolutely need to, but that code gets extra heavy testing as a result).
It was slice I was looking for. It was just confusing because there are about thirty array functions.
No, there's about 80 (or there was about 3 years ago when I counted them all).
And don't you just love that most array functions have arguments in the order (needle, haystack) and most string functions work in (haystack, needle) order?? heh heh - Love PHP, but I don't love it's inconsistencies.
foreach is different, though:
Since the
foreach is looping through a copy of the array, changing the original array will not alter the array which is being looped through, and thus, no conflict should occur.
In other words, this:
$array = array(1, 2, 1, 4, 1, 6, 1, 8, 1, 10);
$needle = 1;
foreach($array as $key=>$value) {
if($value == $needle) {
should be functionally identical to this:
$array = array(1, 2, 1, 4, 1, 6, 1, 8, 1, 10);
$needle = 1;
for($i = 0, $array_copy = $array, $length = count($array_copy); $i < $length; $i++) {
if($array_copy[$i] == $needle) {
but not this:
$array = array(1, 2, 1, 4, 1, 6, 1, 8, 1, 10);
$needle = 1;
for($i = 0, $length = count($array); $i < $length; $i++) {
if($array[$i] == $needle) {
At least they're consistent within those two, completely unrelated, groups of functions. I never understood how folks get hung up on this particular setup; maybe we shouldn't have used the term "needle" and "haystack" for both groups.
No, it isn't consistent. [fphp]str_replace[/fphp] and [fphp]str_ireplace[/fphp] is (needle, replace, haystack)
I still feel the defining feature of PHP 6 should be shunting all existing functions to a legacy namespace. With a php.ini setting enabled the legacy namespace is imported to the root namespace. Otherwise the whole function library should be redone in an object oriented manner. All arrays would be array objects with the array methods tied to them, same with strings. This would be an enormous change and unlikely to ever occur, but it would be the perfect time to address these problems while using the ini flag to maintain BC.
Fine, mostly consistent. Way to pick on the minor things.
That does rank amongst my pet peeves about PHP – namespace and parameter orders. It literally feels like they just rolled a D6 on the order of parameters in functions… maybe it's the machine language/assembly coder in me, but come on… pick one, AT&T (dest, value) or Intel (target, value)… don't mix and match willy-nilly.
But it's like function, class and method names… camelcase, don't camelcase, underscores, don't underscore… PICK ONE!
This is only partly an excuse, but PHP does have coding standards for naming. The other side of the coin is that much of PHP is based on the names of the C functions being called behind-the-scenes.


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LF-270-4PS High Capacity
In support of various states Low Lead laws, Leonard is pleased to offer the new ECO-MIX™ line of thermostatic mixing valves. These valves have all been certified as meeting the lead free requirements. Note: Lead Free is defined as "not more than a weighted average of 0.25 percent when used with respect to the wetted surfaces of pipes and pipe fittings, plumbing fittings, and fixtures". In addition, these valves are all listed to the stringent performance requirements of their pertinent ASSE Standard. Leonard's valve models give plumbing engineers "integrated control" for water tempering design and installation needs, and offer efficient response time to temperature and pressure fluctuations, ensuring optimal temperature control and performance for domestic hot water systems.


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Interesting article! One of my friends is carrying quite a bit of debt (credit cards & student loans). She said that her parents argue over money, and it has shaped the way she views her own finances.
She didn't have a lot growing up...so when she got older, she bought everything she wanted without giving a second thought to whether or not she could afford it. The problem now is that she's deep in debt.
People don't realize how much they'll pay over time when they go into debt. There's nothing more important than safeguarding your financial well-being. There's a really nifty calculator by Bills.com that shows you how much your debt is really costing you. (http://www.bills.com/debt-consolidation-calculator/) It can be a real eye-opener.


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If you are thinking about tweeting about clouds, pork, exercise or even Mexico, think again. Doing so may result in a closer look by the U.S. Department of Homeland Security.
In a story appearing earlier today on the U.K's Daily Mail website, it was reported that the DHS has been forced to release a list of keywords and phrases it uses to monitor various social networking sites. The list provides a glimpse into what DHS describes as "signs of terrorist or other threats against the U.S."
The list was posted by the Electronic Privacy Information Center who filed a request under the Freedom of Information Act, before suing to obtain the release of the documents. The documents were part of the department's 2011 'Analyst's Desktop Binder' used by workers at their National Operations Center which instructs workers to identify 'media reports that reflect adversely on DHS and response activities'.
The information sheds new light on how government analysts are instructed to patrol the internet searching for domestic and external threats. The Daily Mail's article noted the Electronic Privacy Information Center wrote a letter to the House Homeland Security Subcommittee on Counter-terrorism and Intelligence, describing it's choice of words as 'broad, vague and ambiguous'.
What wasn't disclosed is how the agency actually gains access to the various search engines and social networks to monitor the specified keywords. My guess is the DHS has a "special arrangement" with companies like
I would love to learn more about the technologies used to accomplish this type of social / web monitoring. The applications for monitoring trends and social statics are fascinating when applied to other industry sectors. Given the extent of the monitoring, I'm sure this post itself is now coming up on the DHS radar, so please feel free to leave a comment with any insights.
(Update 1: Reading through the Desktop Binder, I discovered the DHS Twitter account is @dhsnocmmc1 and DHS appears to be using tweetdeck to monitor the various keywords. See Page 38 -- Also interesting to note they seem to be using a Mac Mini as a server, and no password vaults. All Passwords appear to be shared in a plain text word document.)
(Update 2: On page 37, DHS instructs analysts to accept invalid SSL certificates forever without verification. Although invalid SSL warnings often appear in benign situations, they can also signal a man-in-the-middle attack. Not a good practice for the security conscious. Thanks to @obraon twitter for the tip.)
Find Reuven on Twitter @rUv | Linkedin | Google+ | Facebook | Podcast
Full List of Keywords & Search Terms continued on next page.
The complete DHS Analyst's Desktop Binder is available here.
You can read the original article at the DailyMail.co.uk
Find Reuven on Twitter @rUv | Linkedin | Google+


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General Information
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Downloading images from Magnum Photos Pro are only available for professional licensing users. If you would like more information about prints, posters, books and other merchandise for personal use, please visit the Magnum Shop at shop.magnumphotos.com


text: In 1910 Gaumont demonstrated his Chronophone system, which synchronised sound and film, at the Gaumont Palace in Paris. The compressed-air amplifier, which he called the Eglephone, was just a part of the whole system. The volume was enough for an audience of 4000. Initially the longest moving picture that could be made with synchronised sound was only 200ft, due to the limited playing time of the Gramophone record. (Projection was at 16 frames per second) Gaumont surmounted this problem by having two gramophone platters; a deft operator could switch between them to give a more or less continuous soundtrack.