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Nine Chapters on the Mathematical Art
|Chinese Mathematics
|History Topics Index
The Jiuzhang suanshu or Nine Chapters on the Mathematical Art is a practical handbook of mathematics consisting of 246 problems intended to provide methods to be used to solve everyday problems of engineering, surveying, trade, and taxation. It has played a fundamental role in the development of mathematics in China, not dissimilar to the role of Euclid's Elements in the mathematics which developed from the foundations set up by the ancient Greeks. There is one major difference which we must examine right at the start of this article and this is the concept of proof.
It is well known what that Euclid, for example, gives rigorous proofs of his results. Failure to see similar rigorous proofs in Chinese works such as the Nine Chapters on the Mathematical Art led to historians believing that the Chinese gave formulas without justification. This however is simply an example of historians well versed in mathematics which is essentially derived from Greek mathematics, thinking that Chinese mathematics was inferior since it was different. Recent work has begun to correct this false impression and understand that there are different understandings of "proof". For example in [8] Chemla shows that Chinese mathematicians certainly understood how to give convincing arguments that their methodology for solving particular problems was correct.
Let us now give a short description of each of the nine chapters of the book.
Chapter 1: Land Surveying.
This consists of 38 problems on land surveying. It looks first at area problems, then looks at rules for the addition, subtraction, multiplication and division of fractions. The Euclidean algorithm method for finding the greatest common divisor of two numbers is given. It then proceeds to further area problems which do not use the material on fractions which appears somewhat misplaced. The types of shapes for which the area is calculated include triangles, rectangles, circles, trapeziums. In Problem 32 an accurate approximation is given for π. This is discussed in detail in Liu Hui's biography.
Chapter 2: Millet and Rice.
This chapter contains 46 problems concerning the exchange of goods, particularly the exchange rates among twenty different types of grains, beans, and seeds. The mathematics involves a study of proportion and percentages and introduces the rule of three for solving proportion problems. Many of the problems seem simple an excuse to give the reader practice at handling difficult calculations with fractions.
Chapter 3: Distribution by Proportion.
Here there are 20 problems which again involve proportion, many involving different sums given to or owed by officials of various different ranks. Direct proportion, inverse proportion and compound proportion are all studied. In particular arithmetic and geometric progressions are used in some of the problems.
Chapter 4: Short Width.
This chapter contains 24 problems and takes its name from the first eleven problems which ask what the length of a field will be if the width is increased but the area kept constant. These first eleven problems involve unit fractions are all of the following type, where n = 2, 3, 4, ..., 12:
Suppose a field has width 1+ 1/2 + 1/3 + ... + 1/n. What must its length be if its area is 1?Problems 12 to 18 involve the extraction of square roots, and the remaining problems involve the extraction of cube roots. Notions of limits and infinitesimals appear in this chapter. Liu Hui whose commentary of 263 AD has become part of the text attempts to find the volume of a sphere, gives an approximate formula which he shows to be incorrect, then charmingly writes:-
Let us leave the problem to whoever can tell the truth.Chapter 5: Civil Engineering.
Here there are 28 problems on the construction of canals, ditches, dykes, etc. Volumes of solids such as prisms, pyramids, tetrahedrons, wedges, cylinders and truncated cones are calculated. Liu Hui, in his commentary, discusses a "method of exhaustion" he has invented to find the correct formula for the volume of a pyramid.
Chapter 6: Fair Distribution of Goods.
This chapter contains 28 problems involving ratio and proportion. The problems are varied and concern problems about travelling, taxation, sharing etc. Problem 12 is a pursuit problem:-
A good runner can go 100 paces while a poor runner covers 60 paces. The poor runner has covered a distance of 100 paces before the good runner sets off in pursuit. How many paces does it take the good runner before he catches up the poor runner.Problem 26 has become a classic type still used today:-
[Answer: 250 paces]
A cistern is filled through five canals. Open the first canal and the cistern fills in 1/3 day; with the second, it fills in 1 day; with the third, in 21/2 days; with the fourth, in 3 days, and with the fifth in 5 days. If all the canals are opened, how long will it take to fill the cistern?Chapter 7: Excess and Deficit.
[Answer: 15/74 of a day]
The 20 problems give a rule of double false position. Essentially linear equations are solved by making two guesses at the solution, then computing the correct answer from the two errors. For example to solve
ax + b = cwe try x = i, and instead of c we get c + d. Then we try x = j, and instead of c we obtain c + e. Then the correct solution is
x = (jd - ie)/(d - e).The first problem essentially contains the "guesses" in its formulation:-
Certain items are purchased jointly. If each person pays 8 coins, the surplus is 3 coins, and if each person gives 7 coins, the deficiency is 4 coins. Find the number of people and the total cost of the items.Problem 18, although not formulated as a "guessing problem" is solved in that manner:-
[Answer: There are 7 people and the total cost of the items is 53 coins.]
There are two piles, one containing 9 gold coins and the other 11 silver coins. The two piles of coins weigh the same. One coin is taken from each pile and put into the other. It is now found that the pile of mainly gold coins weighs 13 units less than the pile of mainly silver coins. Find the weight of a silver coin and of a gold coin.Chapter 8: Calculation by Square Tables.
Here 18 problems which reduce to solving systems of simultaneous linear equations are given. However the method given is basically that of solving the system using the augmented matrix of coefficients. The problems involve up to six equations in six unknowns and the only difference with the modern method is that the coefficients are placed in columns rather than rows. The matrix is then reduced to triangular form, using elementary column operations as is done today in the method of Gaussian elimination, and the answer interpreted for the original problem. Negative numbers are used in the matrix and the chapter includes rules to compute with them.
Chapter 9: Right angled triangles.
In this final chapter there are 24 problems which are all based on right angled triangles. The first 13 problems are solved using an application of Pythagoras's theorem, which the Chinese knew as the Gougu rule. Two problems study what are now called Pythagorean triples, while the remainder use the theory of similar triangles. Here is an example of one using similar triangles; it is Problem 20:-
There is a square town of unknown dimensions. There is a gate in the middle of each side. Twenty paces outside the North Gate is a tree. If one leaves the town by the South Gate, walks 14 paces due south, then walks due west for 1775 paces, the tree will just come into view. What are the dimensions of the town.
In the diagram the North Gate is N, the South Gate is S, and the tree is A. Walking south from S 14 paces reaches B, turn west and walk 1775 paces to C. From C the tree at A is just visible so the line CA passes through the corner D of the square.
Now triangles AND and ABC are similar so
20/(x/2) = (20 + x + 14)/1775.
Then x2 + x(20 + 14) = 2 (20×1775), or
x2 + 34x = 71000.
[Answer: The side of the town is 250 paces]
Quadratic equations are considered for the first time in Chapter 9, are solved by an analogue of division using ideas from geometry, in fact from the Chinese square-root algorithm, rather than from algebra.
Having looked at the content of the work, let us think next about its date. Liu Hui wrote a commentary on the Nine Chapters on the Mathematical Art in 263 AD. He believed that the text which he was commentating on was originally written around 1000 BC but incorporated much material from later eras. He wrote in the Preface:-
In the past, the tyrant Qin burnt written documents, which led to the destruction of classical knowledge. Later, Zhang Cang, Marquis of Peiping and Geng Shouchang, Vice-President of the Ministry of Agriculture, both became famous through their talent for calculation. Because of the ancient texts had deteriorated, Zhang Cang and his team produced a new version removing the poor parts and filling in the missing parts. Thus, they revised some parts with the result that these were different from the old parts ...Let us give some dates for the events Liu Hui describes. The Qin dynasty preceded the Han dynasty and it was the Qin ruler Shih Huang Ti who tried to reform education by destroying all earlier learning. He ordered all books to be burnt in 213 BC and Zhang Cang, who Liu Hui refers to, did his reconstruction around 170 BC. Most historians, however, would not believe that the original text of the Nine Chapters on the Mathematical Art was nearly as old as Liu Hui believed. In fact most historians think that the text originated around 200 BC after the burning of the books by Shih Huang Ti. Others give dates between 100 BC and 50 AD.
What methods are used to try to date the material? Perhaps the most important is to examine the units of length, volume and weight which appear in the various problems. Standard decimal units of length were established in China around 200 BC and later further subdivisions occurred. That the basic units are used, but not the later subdivisions, leads to a date of shortly after 200 BC. In Liu Hui's commentary subdivisions introduced around 250 AD are used, which is in line with this commentary being written in 263 AD.
Of course, the dating using units of length is not conclusive. Consider the fact that Britain changed to a decimal currency in 1970. If you pick up a book with mathematics problems given in decimal currency then we could argue as above and say that the book was written after 1970. However new editions of popular textbooks were brought out when the currency changed, so many older books appeared in decimal editions. The Nine Chapters on the Mathematical Art was certainly an important text, so may have had its units of length brought up to date as it evolved.
Is there other evidence for dating parts of the Nine Chapters on the Mathematical Art other than units of measurement? Yes, there are. Problems contain references to taxes, methods of distributing goods, towns, and parks which all point to slightly different dates for different parts of the text but 206 BC to 50 AD covering these different dates.
In addition to Liu Hui's commentary of 263, there was another important later commentary, namely that of Li Chunfeng whose commentary was written around 640 when he headed a team asked to annotate The Ten Classics. Li Chunfeng corrected and clarified some of Liu Hui's comments, expanding on much of what had been pretty concisely written.
The Nine Chapters on the Mathematical Art [4]:-
... has dominated the history of Chinese mathematics. It served as a textbook not only in China but also in neighbouring countries and regions until western science was introduced from the Far East around 1600 AD.Now although European science does not appear to have reached China in sixteenth century, it has been pointed out that a number of mathematical formulas and rules which were widely used in Europe during that century are essentially identical to formulas written down in the Nine Chapters on the Mathematical Art. This leads to an interesting question which historians have as yet no convincing answer, namely were the European formulas taken directly from those of China.
Article by: J J O'Connor and E F Robertson


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Immigration Reform Will Lead Members to Your Door
CUs stand to benefit tremendously from an attainable path to citizenship.
Since the 2012 elections, discussion of U.S. immigration policy reform has ramped up significantly.
Much of the conversation is driven by different proposals regarding the "path to citizenship," which would establish an attainable process for transitioning undocumented immigrants to documented U.S. residents and citizens.
In late June, the U.S. Senate passed a comprehensive—albeit controversial—immigration reform bill. Whether the House follows suit remains to be seen, but the Senate move is viewed as historic and somewhat of a victory for those rooting for reform.
With an estimated 11 million undocumented immigrants currently living and working in the U.S., credit union leaders who think strategically about membership growth can't afford to ignore the important step many Americans are pushing their legislators to take.
Credit unions, like many American businesses and organizations, stand to benefit tremendously from an attainable path to citizenship. In the most basic sense, credit unions will find a completely new market for lending products.
The process of obtaining U.S. residency and then citizenship is likely to remain long and costly, and prospective members will be looking for ways to fund the many stages of the immigration naturalization process.
As a Mexican immigrant, I remember going through an arduous and expensive immigration and naturalization process with my family when I was around 10 years old.
While the result was overwhelmingly happy, the steps to get there weren't always pleasant. As the first one in my family to learn English, I had been my parents' trusted interpreter and advisor on everything from registering my siblings for school to calling our local telephone company to dispute extra charges on our bill.
In addition to extensive paperwork, my family had to travel to the local immigration office frequently, which created its own financial hardship. My parents saved money from their paychecks every week or borrowed from family or a circle of friends through a "tanda," an informal savings and borrowing network common in immigrant communities.
Today, the filing fee for the application to naturalization through the U.S. Citizenship and Immigration Service has reached $680 per person, and families often have several individuals going through the process at once.
But this can be the least of the all the necessary expenses, which may include filing fees for temporary residence, permanent residency, or legal fees. In fact, some families pay upwards of $10,000 when all is said and done for just one individual to adjust his or her immigration status.
Some credit unions have acted on this need, repackaging their existing consumer loans to help individuals pay for these immigration expenses. Other credit unions also go above and beyond, connecting the community with immigration attorneys, legal clinics, interpreters, and other local service providers to make this process easier.
The need for this will only increase with immigration reform.
The larger benefit, however, is the ability to introduce an entirely new segment of the American consumer market—no longer hindered by the lack of traditional identification and documentation—to the credit union difference.
For many immigrants, particularly Mexican immigrants (who represent 60% of the nation's 11 million undocumented immigrants), traditional financial institutions may represent something entirely different than they do to most Americans.
Whereas U.S.-born consumers may not think twice about using traditional financial institutions to save and borrow, a Hispanic immigrant may not think this is even an option. With check-cashers, money order providers, and friends or family fronting loans, credit unions and banks often are not even considered by Hispanic immigrants.
Several factors prevent many Hispanic immigrants from using traditional financial institutions, including the fear of rejection due to a lack of credit, the lack of a welcoming environment, and a perception of higher fees or hoops to run through. Credit unions can change this.
A critical first step is establishing trust. Credit unions must work within their local communities now to begin to build the relationships that will grow over time. Credit unions already working with Hispanic communities certainly have a leg up.
One of the best hands-on ways to start is with culturally relevant financial education that takes into account how Hispanic immigrants handle their money today and shows them better alternatives that help them achieve financial success.
If my parents had been able to engage with credit unions earlier, we could have prevented a lot of frustration and worry. Not only would our concerns about immigration expenses have been alleviated, we also would have received guidance on dealing with other financial emergencies that often came up when I was a child—car breakdowns, emergency medical visits, or requests from relatives in Mexico who had emergencies of their own.
Like many Hispanic families, we are very loyal to those who help us during times of need; those who respect us and are welcoming. From this perspective, an earlier relationship with a credit union would have been a win-win for our family and the cooperative, which we likely would have recommended to friends and family.
Grassroots community initiatives, like culturally relevant financial education and outreach, often yield a higher return than extensive media campaigns.
This is particularly true for credit unions looking to serve immigrant families who are not only going through the immigration and naturalization process, but who are simply going through the stages of life that require a sound financial partner.
It's this kind of outreach that ultimately allows credit unions to plant the seeds of trust that grow into loyal, life-long memberships.
MIRIAM DE DIOS is CEO of Coopera and a native of Jalisco, Mexico.


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School Strike 4 Climate protest Aberystwyth, Wales, UKAdd to Lightbox
Aberystwyth UK 15/03/2019.
Over 300 young teenage students, pupils at several local secondary schools, - and their supporters - took part in noisy ' Strike4Climate' protests outside the offices of the Ceredigion County Council and Welsh Government in Aberystwyth this afternoon. The protests have been happening all across the UK and are calling for climate justice and action to halt and reverse the impacts of climate change. Photo credit: Keith Morris
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Struggling to find the best buy-to-let mortgage in Newport? speak to one of our buy to let mortgage advisers today
The term 'buy to let' generally refers to either the practice of buying a property to be let for profit or to the type of mortgages used to purchase a property for such letting. Many countries, both in the western world and in the developing nations, have seen a surge in the growth of the buy to let property market in the last 2 decades and this has fuelled a growth in amateur landlords and the but to let mortgage providers who are keen to encourage and profit from them in turn. In addition, this growth has generated a lot of commerce in other related sectors such as buy to let insurance.
10 year fixed buy to let mortgage
Many countries, both in the western world and in the developing nations, have seen a surge in the growth of the buy to let property market in Newport the last 2 decades and this has fuelled a growth in amateur landlords looking for quality mortgage advice, this is why mortgage brokers in Newport who specialise in Buy-to-let are so important and the but to let mortgage providers who are keen to encourage and profit from them in turn. In addition, this growth has generated a lot of commerce in other related sectors such as buy to let insurance.
Newport Buy to let mortgages have been available in the UK since the mid-nineties and they are specifically designed for investors to borrow money to purchase property in the private rental sector. The amount that a prospective but to let investor can borrow is generally determined by the rental valuation of the property. The annual income for a rented property has to cover a certain percentage of the mortgage repayments, the Association of Residential Letting Agents (ARLA) states that landlords should seek to be able to obtain gross rent returns equivalent to between 130 per cent and 150 per cent of the rental property's mortgage repayments, this takes into account the surplus rent to cover costs of property maintenance and slack periods when the property may be vacant of tenants.
Newport Buy To Let Mortgages.
Some buy to let mortgage lenders in Newport will lend you a maximum sum based on a multiple of your salary (usually a multiple of three) plus a percentage of the forecast rental income on the property. So if your annual salary is said 30,000 Franks and the forecast rental income is 10,000 Franks they will lend you 95,000 Franks. Other mortgages, in addition to factoring in your salary, will include any existing loan commitments you have, and then apply what is known as the 'deduction rule'. This rule relates to the annual mortgage payments worked out at a pre-set level of interest.
Buy to let mortgage interest rates are generally fairly close to residential mortgage rates but will generally be slightly higher and typically charge higher fees. This is due to the fact that buy to let loans are considered by the financial sector to represent a greater risk than residential owner-occupier mortgages, and they generally are.
The Situation in the UK About Buy To Lets
The buy to let market literally 'exploded' in the Newport around the beginning of the millennium with rising property prices and the increasing availability of buy to let funding fueling a surge in would-be investors trying to cash in on the trend of the market. One reason for their popularity is the tax advantages that are available to the UK buy to let investors. Rental income is treated just like a salary by the Inland Revenue, and is therefore often taxed at 22% or even 40%. However, landlords are allowed to deduct costs from the taxable portion of their rental income, and these costs can include the interest of the buy to let mortgage repayments as well as maintenance costs on the property. These tax incentives made the buy to let market very attractive for both professional investors and amateurs looking to make the most out of their savings.
Would-Be Buy-to-let Investors
The market peaked around 2007 and now the market is saturated in many areas across the country with too many properties available to tenants. While buy to let is generally not a good idea for people who do not possess some extra budget there are a lot of remortgage deals which will fund a deposit for a home. If you are worried about losing money during void periods many companies will provide insurance which can deliver as much as six months mortgage payments in the event of a property in Newport remaining unoccupied.
You may still be lucky, and find a hotspot but you need to do your homework and the figures correctly. Buy to let trends differ from town to town and literally from street to street. Good advice for potential investors is to visit the local letting agents who should be able to tell you who is renting what at the moment so you can define your target audience. It could be students, young professionals or families, for example. Look for areas that do have a shortage of properties and for indicators that people will move there, such as new business developments.
Buy to let mortgage deals are still rife and the rates are almost as competitive as with conventional deals. The mantra with your buy-to-let must be 'don't expect to get rich quickly'. You need to look long-term: an absolute minimum of five years – but probably nearer to ten years.
It's Rob from Property Investments UK.
In today's video we're going to be looking at what is professional buy to let and howit maybe could be suitable for yourselves or what to kind of consider and how to tryto find those great professional buy to let property deals.
So professional buy to letis quite simple in terms of, I suppose, the methodology or the type of deals it is.
Sobuy to let effectively, is buying a property to let out or to rent out.
The professionalaspect doesn't mean in terms of how professional or professional you are in terms of lettingit.
It's more referring to the tenant type of profile, so there's lots of different tenantprofiles within property of residential and commercial.
Specifically within residential property you could consider investing your money into aproperty deal that then rents out to maybe a student tenant or to what's classed as housingbenefits or local housing allowance tenants, social housing, also professional tenants,which is what the kind of professional buy to let property deals are that we look atwithin our property investments website.
Now when it comes to professional buy to lets,what we do mean with that is somebody that's really earning an income, a wage, and thatjob is effectively going to pay for their rent in that property.
There's a whole rangein terms of scale, so it could be somebody that's on an income of 10, 15, 20,000 a yearor somebody that's on an income of 50,000 plus a year.
It's just a category.
Professionalbuy to let just refers effectivity to somebody that's currently earning their way with anincome and that's what they're going to be using to pay for their rent.
Now on our website we have a number of different property deals, a number of different categories,everything from HMOs through to service accommodations.
Specifically though, with professional buyto lets, I'll pop below this videos some links and some details on what available propertydeals we currently have.
Now, typically on our website we only usually show one videoor, sorry, one property per category, but we do have many other opportunities available.
So if that particular property, is it maybe in the wrong area or you want to look at somethingslightly different, but you like the idea of a professional buy to let, simply sendus a message.
Give me a call and we can run through the different opportunities that wecurrently have that fit that particular type of category or strategy.
So hopefully that helps.
Any questions, don't hesitate to ask.
We just wanted to give youa bit of an idea of what professional buy to let property and what a ready to go kindof deal might look like.
And I put all of those kind of listings, those available dealsbelow this video with some links for you.
Any questions don't hesitate to ask and Ilook forward to catching up with you on the next video.
All the best.
How To Find The Best Buy To Let Mortgage For Your Investment Property | Real Estate Investing Tips
How do you really start a buy to let propertyinvestment business in today's market? Let me give you the ten things I think you needto consider.
Hi there, my name's Tony Law from your Your First Four Houses.
My channel'sall about helping you get to investment property number four as quickly and as painlessly aspossible.
Let me give you these ten things, I feel, you need to have at the forefrontof your mind in order to be successful in this property investing world of ours.
Thevery first one is to, you need to understand your financial goals.
Let me give you a specificway you should do this.
You basically need to understand how much money you're spendingevery single month.
Download three months worth of bank statements,work out what you're actually spending every single month, and that is the target thatyou need to hit, essentially, to be financially free.
The sooner you hit that target, thesooner you can basically give up the day job, essentially, and focus far, far more of yourenergy on building your property portfolio.
When you know what that number actually is.
Now I run a paperless office, largely, but when you know what that number is I needyou to do something vert manual for me.
I need you to go and draw up one of these, it'seffectively the kind of thing that you'd see if you were trying to raise finance for aparticular project.
At the top of it, you're going to have thattarget, that number that you've just worked out.
Running up the side, you're going tohave integers at about, say, 500 pounds, little marks going up the side.
Whenever you do adeal that puts money in your pocket you need to colour that in.
It may sound primitivebut it's incredibly powerful.
I've recommended this to a lot of people that use it and theyfind it really, really helps them keep focused.
Moving on quickly to point number two, youneed to work out how much time you can give to this.
Really, if you're working full-time,that doesn't mean that you haven't got time to do this.
You've got your lunch times, you'vegot your evenings, and you've usually got your weekends.
How much time can you give to this? The moretime you can give, the better and faster results you're going to achieve.
Next number three,I need you to start building your education.
Now, there's a number of ways that you cando this.
You can look at podcasts, you can get books, webinars, you can employ a coach,mentor, you can look at some courses.
The sooner that you can build your knowledge,the sooner you're going to better achieve bigger and better deals.
One of the specificthings I'd like you to consider if maybe this is an area of weakness for you, is to maybeget some training on negotiation because this is a real key thing that will really helpyou when you're speaking to agents or when you're speaking specifically to seller.
Pleaselook into that.
Number four, the sooner that you can focuson picking your strategy, the sooner you're going to be successful.
Now, I like peopleto focus on maybe one or two core strategies.
Rather than having more of a shotgun approach,it's better to be more laser focused.
See if you can work out which one or two corestrategies would work really well for you and start focusing on those.
Number five,research the different areas and work out where you should be actually buying.
Now,I did a video recently on this that basically gives you a really detailed explanation onhow to work out supply and demand in any area within about 60 seconds.
You need to lookat other things.
In the area that you're actually looking at,what's the situation with regards to perhaps new employment? What about transport links?Are they being improved, specifically? What about population? Is there an increase ordecline that you've noticed? All of these things can really dictate the better areasto actually invest.
Point number six, go and see a mortgage broker.
You need to find outwhat kind of mortgages you can get.
Again, I did another video here on how to actuallyimprove your credit rating.
I would strongly suggest that you watch that.
That will giveyou some real key tips to improve your credit rating, which is going to mean you'll getbetter access to better mortgages at lower rates.
Number seven, you need to learn how to findgreat deals.
Now, I know that this is a massive topic and we can go into this in a lot moredetail.
Essentially, you do need to understand how to find better deals.
You need to learn,very specifically, what makes a good deal for you.
Honestly, this is a real key thing.
You may have no funds at all but if you can find and negotiate really good deals, honestly,you'll never have problem raising the funds.
I'll invest with you if you can find reallygood deals.
In essence, there's lots of people around you that will be delighted to put moneyinto the deals if you can find them.
Next, start building connexions.
When I say that,I'm talking about connexions with agents.
I'm talking about connexions with deal sources.
I'm talking about connexions with people who can help you fund your next deal.
The sooner you start building genuine, sincere,honest, full-on relationships, friendships with people, honestly, the sooner you're goingto actually be successful in this property world of ours.
Number nine is simply exitstrategy.
So many people I talk to have no clear exit strategy.
They don't really understandtheir exit strategy at all.
I always encourage people to consider two exit strategies.
Iwould love you to do the same.
Even before you buy that very first property, just consider,are you holding this for the long term? Is this a flip that you want to churn to getthe money out very, very quickly? If things don't work out, is there a second way outfor you? Number ten, this is the big one.
This is whereso many people stumble and that is, you have to take action.
Now I know that seems bleedinglyobvious but so many people, they build their knowledge, they learn, learn, learn, but theystop at the action taking point.
Frankly, I don't really understand this if I'm beingtruthful with you.
I think it's largely down to fear quite often.
Quite often, perhaps,having somebody behind you that's maybe got their hand in the small of your back and justpushing you forwards or just giving you a bit of a shove to actually take that actionmight be really beneficial for you.
Let me ask you a question.
How many properties haveyou actually been out to see this week or this month? If they answer is none, then you're not takingany action, I would respectfully suggest.
You need to take that action.
I really hopethat you found that helpful.
I just want people to be successful in this property world ofours and to get to that magical place where the income that's coming in surpasses themoney that's going out.
If this sort of stuff really helps you, I am absolutely over themoon.
My name is Tony Law from Your First Four Houses.
I really hope you found thisone helpful.
I look forward to seeing you in the next video.
Before I go, please ifyou can take a moment to subscribe to my YouTube channel, if you haven't already done so.
Thatwould be absolutely brilliant.
If Facebook's more of your kind of thing, please like myFacebook page.
Thanks ever so much.
I look forward to seeing you in the next video.


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Record-setting Olympic gold medalist Michael Phelps is scheduled to visit the Orioles' spring-training facility before Thursday's 1 p.m. intrasquad game at Ed Smith Stadium.
Phelps is in town with renowned golf coach Hank Haney promoting their new show on The Golf Channel titled "The Haney Project." The show focuses around Haney teaching the 22-time medalist the game of golf.
Phelps, the most decorated athlete in Olympic history, followed the Ravens during their run to the Super Bowl. After the team's AFC championship win in New England, Phelps and Orioles outfielder Adam Jones visited the Ravens' locker room for the postgame celebration.


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ALEXCIOUS is a global EC site that gathers Japan's finest products and is purchased from over 70 countries worldwide.
Tublock is a new shape assembly block, made by piping joint manufacture. Using those three function of PIPE FITTING " tie, bend and divide" with turn a head and a hand, you can make various things which are hard to express with the conventional block by a various combination. Not to mention a creature and a character, a building or a vehicle and in the lifeline of a house or the factory.
You can make anything you want with unique shapes. There are 2 types of size; S /M, so you can play various combinations in different combinations. Please enjoy making original works.
After connecting, you can also rotate the connecting part. You can use whatever you want like making its head tilt or make its arms rotate.
All the products handling in ALEXCIOUS are the genuine products from the original makers.
Orders can be made anytime.
An automated mail will be delivered from ALEXCIOUS after an order has been placed.
For products that may take up to more than the period of notation to dispatch, another mail will be sent to notify the approximate shipping date in 1-3 business days
A confirmation mail will be sent with the voucher number that indicates that the product has been shipped.
After the order has been delivered, we request that you kindly rate our product on the review page.
|Shipping Method
|Delivery within Japan: Sagawa Express, Delivery Overseas: Express Mail Service (EMS) via the Japan Post Service
|Estimated Delivery Date
|Ship from
|Shinagawa-ku, Tokyo
|Message card (+ 110JPY / texts can be personalized) and gift wrapping (+ 550JPY) options are available. (Gift wrapping materials may be different from the image due to the size or shape of the product.)
|Customers inside Japan
Square (no handling fees)
PayPal (no handling fees)
ATM (no handling fees)
Convenience stores (no handling fees)
Online banking (no handling fees)
Cash-on-delivery (COD)
(For domestic shipping and wristwatch purchases only)
|Customers outside Japan
Square (no handling fees)
PayPal (no handling fees)
|Kindly notes
|If you view our site in Japanese, you may choose any one of the payment methods above. If you view our site in other languages including English, you may only make your payment with Square or PayPal.


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Receive your first 30-day supply of ALPROLIX immediately with a valid prescription from your healthcare provider. You may also be eligible to receive free factor for a limited period of time, while Patient Services addresses your factor access issue.DOWNLOAD APPLICATION
Whether you're new to ALPROLIX or already on therapy, the copay program offers up to $12,000 of co-payment or co-insurance costs for your ALPROLIX prescription. Best of all, there are no income requirements or caps, so you can get started with your treatment right away.DOWNLOAD APPLICATION
Helps you access ALPROLIX even if your insurance coverage is interrupted—for example, you are between jobs or changing insurers.DOWNLOAD APPLICATION
*Those with federal and state government insurance, such as Medicare, Medicaid, or TRICARE® are not eligible. Other eligibility requirements may apply. Sanofi Genzyme reserves the right to modify or discontinue the programs at any time.
TRICARE is a registered trademark of the Department of Defense (DoD), DHA. All rights reserved.
Bluetooth® is a registered trademark of Bluetooth SIG, Inc.
All rights reserved.
indications and important facts about alprolix
What is the most important information i should know about ALPROLIX® [Coagulation Factor IX (Recombinant), Fc Fusion Protein]? You should not use ALPROLIX if you are allergic to ALPROLIX or any of the other ingredients in ALPROLIX. Tell your healthcare provider if you have had an allergic reaction to any Factor IX product prior to using ALPROLIX.
Allergic reactions may occur. Call your healthcare provider or get emergency treatment right away if you have any of the following symptoms: hives, chest tightness, wheezing, difficulty breathing, or swelling of the face.
ALPROLIX may increase the risk of forming abnormal blood clots in your body, especially if you have risk factors for developing blood clots. Call your healthcare provider or seek emergency care if you have symptoms of a possible abnormal blood clot, which may include: chest pain, difficulty breathing, unexpected swelling of an arm or leg with or without pain or tenderness.
Your body can also make antibodies called "inhibitors" against ALPROLIX, which may stop ALPROLIX from working properly. Your healthcare provider may need to test your blood for inhibitors from time to time.
THE MOST COMMON SIDE EFFECTS OF ALPROLIX INCLUDE: headache, abnormal sensation in the mouth, and pain in your side with blood in your urine, which may be a sign of clot formation in the urinary collecting system. These are not all the possible side effects of ALPROLIX. Talk to your healthcare provider for more information and about any side effect that bothers you or does not go away.
Tell your healthcare provider about all your health conditions, including if you:
If your bleeding is not controlled and you experience a lack of clinical response to Factor IX therapy, call your healthcare provider right away.
Medicines are sometimes prescribed for purposes other than those listed here. Do not use ALPROLIX for a condition for which it was not prescribed. Do not share ALPROLIX with other people, even if they have the same symptoms that you have.
ALPROLIX is an injectable medicine that is used to help control and prevent bleeding in people with hemophilia B. Hemophilia B is also called congenital Factor IX deficiency.
Your healthcare provider may give you ALPROLIX when you have surgery.
ALPROLIX should be administered as ordered by your healthcare provider. You should be trained on how to do infusions by your healthcare provider. Many people with hemophilia B learn to infuse ALPROLIX by themselves or with the help of a family member. See the booklet called "Instructions for Use" packaged in your ALPROLIX for directions on infusing ALPROLIX. If you are unsure of the procedure, please ask your healthcare provider.
Please read this information carefully before using ALPROLIX and each time you get a refill, as there may be new information. This information does not take the place of talking with your healthcare provider about your medical condition or your treatment.
The risk information provided here is not comprehensive. To learn more, talk about ALPROLIX with your healthcare provider or pharmacist.
The FDA-approved product labeling can be found at www.alprolix.com or 1-855-MyALPROLIX (692-5776).
You are encouraged to report negative side effects of prescription drugs to the FDA. Visit www.fda.gov/medwatch, or call 1-800-FDA-1088.
Bioverativ Therapeutics Inc.
Waltham, MA 02451 USA
U.S. License #2078
That's okay. We just had to let you know you're about to leave ALPROLIX.com. Thanks for stopping by.
See you again soon.


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Hi, i have an assignment where i have to do a histogram, that is i receive a text and must count the times each word in the text appears. This method receives a BufferReader and a BufferWritter, what i did so far is transform the buffer reader into a string and i tried some things already, but couldnt find a solution, and i would like to know if u have some ideas to help me.
public static void histogram( BufferedReader in, BufferedWriter out ) throws IOException{ String insert; StringBuilder sb= new StringBuilder(); String [] word= new String [1000]; int [] counter = new int [1000]; int k; while((insert=in.readLine())!=null){ sb.append(insert); sb.append("\n"); } insert = sb.toString(); // this was my first try k = 0; for(int i =0; i<insert.length(); i ++){ if(Character.isLetter(insert.charAt(i))) ; else{ for(k =0; k<words.length; k ++){ if(words [k] == insert.substring(begin , i)) counter[k]++; if(words [k] == null) words [k] = insert.substring(begin , i); } } } //this one was the second words = insert.split(" " , 1000); k = 0; for(int i =0; i<word.length; i++){ out.write(word[i] + ": " + Integer.toString(counter[i])); out.newLine(); } }
There is somethings missing that i dont know how i can do, in the first try i tried to seperate the text in words while the "for" was running the string and counting how many equal words appear; in the second i tried to seperate the full string in words and then count, but in this case there were too many words to the array.
Thank you for helping


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It's time for another Spring in to Adventure Giveaway! This week is SEA-TO-SUMMIT Week because almost the entire prize package is awesome gear from Sea to Summit! You can't go wrong! Check out the awesome list of what's included in the prize package below.
As you know, for the last couple months Wilderness Dave along with: My Life Outdoors, The Outdoor Adventure, A Little Campy, Hiking the Trail and Trail Sherpa have been working together with a whole bunch of popular outdoor companies to bring you guys more than a month of giveaways.
Just like last week we are offering you tons of ways to earn extra entries and if you entered last week you know how easy it is!
As a reminder, here's what's up for grabs:
Grand Prize:
Sea To Summit Ultra-Mesh Stuff Sack
Sea To Summit Ultra-Sil View Dry Sack
Sea To Summit Ultra-Sil Sink
Sea To Summit Ultra-Sil Bucket
Beyond Coastal Travel Kit
Buff USA Merino Wool Buff
Alpine Aire Food Kit
Second Place Prize:
Sea To Summit Ultra Nano Dry Sack


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Angular contact ball bearings
Angular contact ball bearings have inner and outer ring raceways that are displaced relative to each other in the direction of the bearing axis. This means that these bearings are designed to accommodate combined loads, i.e. simultaneously acting radial and axial loads.
The axial load carrying capacity of angular contact ball bearings increases as the contact angle increases. The contact angle is defined as the angle between the line joining the points of contact of the ball and the raceways in the radial plane, along which the combined load is transmitted from one raceway to another, and a line perpendicular to the bearing axis (fig. 1).
In addition to the bearings presented in this section, other angular contact ball bearings include:
Double row cam rollers
Refer to Cam rollers.
Fixed section angular contact ball bearings
These bearings have very thin rings and a constant cross-sectional height within a particular series, irrespective of the bearing size. They are characterized by a low weight and high stiffness. SKF fixed section bearings have inch sizes and are available open or sealed in up to eight different cross-sectional heights. The designs include:
Hub bearing units
Hub bearing units (HBU) for the automotive industry are based on double row angular contact ball bearings (fig. 7, fig. 8, fig. 9). They have made an appreciable contribution to the achievement of more compact weight-saving designs, simplified assembly and enhanced reliability.
Detailed information about these products and variants for industrial applications can be supplied on request.


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Campground fees rise $1 this year at concessionaire-operated U.S. Forest Service campgrounds in Colorado.
"The fees go up a buck, but that's not unusual," Mike Kenealy, recreation and special uses coordinator for the White River National Forest, the Summit Daily News, Frisco, reported.
A new concessionaire, White River Recreation Co., is in place for the forest, but Kenealy said that's not why fees are rising. He said the hike happens from time to time.
Most of the fee increases are at family-type campgrounds across the White River National Forest. In Summit County, the company primarily operates sites on the banks of the Dillon Reservoir — Lowry and Prospector on the Frisco Peninsula, Peak One and Windy Point, Pine Cove and Heaton Bay.
Site fees vary depending on services, ranging from $17 at Pine Cove Campground to $24 at Heaton Bay, for those hooking up to electric. On the flip side, day-use fees went down a few dollars to $5 from last year's $8.
Overnight guests will be charged a $5 extra vehicle fee for the second vehicle at a site. The previous concessionaire charged that fee for the third vehicle.
Other than fees, the public shouldn't see much change in campground operations.
"It's a different company, but they have a long history of good campground operations across the country," Kenealy said, adding that there's a special use agreement in place that the company must adhere to.
However, the company plans to add sites to the online advance reservations system, as well as extend the reservation window beyond one week in advance.
The new concessionaire may also extend some campground seasons, such as a handful around Dillon Reservoir, though they'll remain first-come, first-served before Memorial Day and after Labor Day, Kenealy said, but reservations are available between the holidays. Typically, the season is mid-May through mid-September, but campgrounds such as Heaton Bay could remain open until Oct. 31.
The Forest Service operates campsites at Green Mountain Reservoir, Kenealy said. No changes go into effect at those sites. The Blue River Campground is also being run by the Forest Service rather than a concessionaire, with mountain pine beetle destruction causing the agency to take it back for mitigation. It reopened last year after being closed.
Green Mountain Reservoir's popular Cow Creek South campground was closed last summer so deceleration lanes could be installed near the entrance. It will likely reopen before July 4, Dillon Ranger District recreation staff officer Ken Waugh said. A new boat ramp has gone through the National Environmental Protection Act rigor and now awaits a possible Great Outdoors Colorado grant, but that won't keep the campground from opening.
Some Green Mountain Reservoir sites — McDonald Flats, Prairie Point, Cataract Creek — and Blue River campground will open May 4. The opening of the rest will be dependent on weather and demand, but all will be open by Memorial day, Waugh said.


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Featured Projects
Featured Projects
A campaign redesign for Showtime TV Network
Category: Campain, Rebranding, Print, Web, Mobile Design, Social Media, Motion Graphics, Photography
A campaign redesign for the Exploratorium.
Category: Campain, Rebranding, Print, Web, Mobile Design, Social Media, Motion Graphics, Photography
Fleuri gives off an elegant and romantic aura as it is made up of curves and shapes found in nature.
Category: Typography, Print, Photography
These seven quotes were arranged to be visually appealing with the sole use of Univers.
Category: Typography, Print, Photography
Other Projects
Motion Graphics
Why, hello!
My name is Rainar (pronounced
Reyn-na) and I have a focus on visual and web design. By spring, I would be a graduate of the Academy of Art University with a BA in Web Design + New Media.
I basically had a sketch pad and a pencil in hand when I was born and since then I've always wanted to become an artist. Now that I'm older, that dream became a reality as I dedicate myself in design whether it be print, web, photography, motion graphics and more!
Email firstname.lastname@example.com
View My resume


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SELLARS v. BETO(1972)
On petition for writ of certiorari to the United States Court of Appeals for the Fifth Circuit. The motion of The National Prison Project of the American Civil Liberties Union et al. for leave to file a brief, as amici curiae, is granted. The petition for a writ of certiorari is denied.
Mr. Justice DOUGLAS, with whom Mr. Justice BRENNAN and Mr. Justice MARSHALL concur, dissenting.
I vote to hear this case because it raises substantial questions of law in the area of the Eighth and Fourteenth Amendments. Petitioners are inmates of the Texas Department of Corrections (T. D. C.). They brought a class action under 42 U.S.C.A. 1983, challenging the constitutionality of: (1) a T. D. C. regulation barring all inmate assistance in preparation of legal work. (2) the primitive conditions of the solitary confinement as administered by the T. D. C. The District Court denied relief, Novak v. Beto, 320 F.Supp. 1206 (SD Tex.1970). On appeal, the United States Court of Appeals for the Fifth Circuit unanimously reversed as to the prohibition on prisoners' legal assistance, holding the State had not met its burden of providing alternatives to assure access to the courts as required by Johnson v. Avery, 393 U.S. 483 (1969). A divided Court affirmed the constitutionality of the conditions of solitary confinement. Novak v. Beto, 453 F.2d 661 (CA5 1971). A motion for a rehearing and rehearing en banc was denied March 8, 1972, six judges dissenting. Novak v. Beto, 456 F.2d 1303 (CA5 1972). If we are to believe the facts as stated by petitioner, and for purposes of appeal we must, a prisoner placed in solitary confinement in Texas will find himself in a shockingly primitive condition. [409 U.S. 968 , 969] The cell is kept in complete darkness 24 hours a day. A barred iron gate backed up by a wooden door blocks all light and prevents any human contact with those in the hall. 1 Within this black interior is a combination toilet-water basin and a steel bunk. The bunk has no mattress although the prisoner is given a blanket. The cell is otherwise bare. The inmate is fed on a bread and water diet with one full meal every 72 hours. 2 He is clothed only by a cloth gown. Aside from those conditions, which were considered inhumane at the time of Charles Dickens, the prisoner has no opportunity to exercise; he is not permitted correspondence with family, friends or lawyer; no visits are allowed and he is allowed no reading material of any kind.
The prisoner is not seen by a psychologist, psychiatrist or counselor before, during or after confinement to solitary. And all deprivations of solitary confinement apply uniformly regardless of the individual's background or criminal record of offense for which he is being punished.
A prisoner can be kept so confined for 15 days and reconfined after a two-day respite. Such practices as above described exist in all of Texas' 14 correctional facilities. [409 U.S. 968 , 970] The petitioners do not question the right of the prison to isolate inmates on cause but do challenge these practices.
Weems v. United States, 217 U.S. 349 , was a landmark in the definition of the Cruel and Unusual Punishment Clause. Robinson v. California made the Eighth Amendment binding on the States through the Fourteenth Amendment. 370 U.S. 660, 669 d 758. We said that the 'dignity of man' was the overriding value preserved by that clause. Trop v. Dulles, 356 U.S. 86, 100 .
The fitness of punishment is to be judged by applying evolving standards, for the clause 'is not fastened to the obsolete but may acquire meaning as public opinion becomes enlightened by a humane justice.' 217 U. S. at 378. What those standards are is now tendered. The extent to which the prohibition against cruel and unusual punishment will apply in prison must also be determined. In Haines v. Kerner, 404 U.S. 519 (1972), we held that a bare allegation of onerous penal conditions is sufficient to require a hearing.
Lower courts have often dealt with the issue and have reached divergent results3 without guidance from us. See Morales v. Schmidt, 340 F. Supp. 544 (D.C.1972). [409 U.S. 968 , 971] Denial of their petition in my view constitutes a travesty of justice. As Judge Tuttle stated in his dissent:
I would grant this petition and put the case down for argument.
[ Footnote 1 ] On the 9th of June 1972 the TDC revised their regulations on the lighting and diet.
[ Footnote 2 ] '50.92333 Diet.
[ Footnote 3 ] Some lower courts have held that some conditions or imprisonment constitute cruel and unusual punishment. See Wright v. McMann, 387 F.2d 519 (CA2 1967), on remand 321 F.Supp. 127 (NDNY 1970), app'd 460 F.2d 126 ( CA2 1972). Hancock v. Avery, 301 F.Supp. 786 (MD Tenn.1969); Holt v. Sarver, 300 F.Supp. 825 (ED Ark. 1969); Barnes v. Hocker, No. R 2071 (Nev. Sept. 5, 1969); Jordan v. Fitzharris, 257 F.Supp. 674 (ND Cal.1966). Contra: Sostre v. McGinnis, 442 F.2d 178, 192 (CA2 1971); Courtney v. Bishop, 409 F.2d 1185 (CA8 1969); Ford v. Board of Managers, 407 F.2d 937 ( CA3 1967); Krist v. Smith, 309 F.Supp. 497 (SD Ga.1970), aff'd, 439 F.2d 146 (CA5 1971).
[ Footnote 4 ] As stated by Judge Kaufman in Wright v. McMann, 387 F.2d 519, 526:


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Wimberley Office:
Suite 1 - 13620 Ranch Road Wimberley, TX 78676
Austin Office:
1107 Lambie Street
Austin, TX 78702
NEW CONSTRUCTION! Set atop Robertson Hill with an iconic backdrop of Austin's skyline, enjoy the wonderful east downtown Austin. This PH8 residence features an expansive open-concept living/dining and floor-to-ceiling windows with views of our park-like courtyard from your own personal patio. Enjoy the convenience of essential resort-like amenities including a pool deck over-looking Austin, state-of-the-art gym, dog park, breezeway and more! Sales are currently by appointment only.
Sarah and Lydia M. Robertson's Subdivision
Club House, Fitness Center, Pool-Community, Assigned Parking, Bike Storage/Locker, Conference/Meeting Room, Concierge, Dog Park, Elevator, Grill
Electricity Available, Internet-Other/Unknown, Phone Available
Built-in Book Cases, Ceiling-High, Walk-In Closet, Elevator, See Agent, Lighting Recessed, Pocket Doors
Dishwasher, Disposal, Microwave Oven, Refrigerator, Single Oven, Cook Top Electric
Sidewalk, Balcony-Covered, Balcony-Private, Dog Run, Electric Car Plug-in, Security Lighting
Property Listed by: McWilliams/Ballard Inc.
The information being provided is for consumers' personal, non-commercial use and may not be used for any purpose other than to identify prospective properties consumers may be interested in purchasing.
Based on information from the Austin Board of REALTORS® (alternatively, from ACTRIS) from January 26th, 2020 at 11:15pm CST. Neither the Board nor ACTRIS guarantees or is in any way responsible for its accuracy. The Austin Board of REALTORS®, ACTRIS and their affiliates provide the MLS and all content therein "AS IS" and without any warranty, express or implied. Data maintained by the Board or ACTRIS may not reflect all real estate activity in the market.
All information provided is deemed reliable but is not guaranteed and should be independently verified.


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radfactory needed a new logo design and created a contest on 99designs.
A winner was selected from 233 designs submitted by 76 freelance designers.
Viral Motion is a startup that focuses on helping mainstream and online businesses effectively join the social-networking revolution whilst harnessing the power of viral promotion on the Internet.
Viral Motion
Desired Color Scheme:
color scheme is open, white background prefered
Desired Style:
professional, clean, trendy
Accepted File Formats:
Vector Formats (.eps, .pdf or .ai); Layered Formats (.psd or .tiff)
Looking for clean, professional and trendy logo.
We have no specific requirements for the logo design, although we prefer to have a white background.
Find out how a design contest works or learn more about our logo design services.


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Why? Because you can! And pickle, and jam, or otherwise celebrate the resurgence of the domestic arts our forebears held so dear. Put on your best apron and step into our kitchen, won't you?
Candied. Bacon. Jerky.
This isn't bacon that's been candied. It's candy made of bacon - and then it's turned into jerky. How could you go wrong?
Bonus: Includes a sure-fire test to self-analyze what type of person you are. :)


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Short, soulful Uplifting Trance project, which allows you to learn how to mix and master your song, how to make a nice trance melody, sounds, sidechain, efects etc. Don't worry about compatibility and CPU usage, this project include free & amazing Synth1 VST only (attached to the pack with instruction how to install it). I strongly recommend this project to beginner music producers.
Mp3 file incuded (320 kbps) – you can use it in your presentations, videos etc, and of course if you know FL Studio you can edit this track as you want. If you have ANY questions please feel free to contact me!!


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The hues you choose for your wedding day are instrumental when it comes conveying the mood and personality of the celebration. "Colour registers in the same part of our brains that signals our emotions. You actually receive a lot more information from a colour than you can verbalize so choosing the right colour for your wedding day is huge," says colour psychologist Janice Lindsay. "You can use colour as a way of breaking expectations and expressing your own unique point of view," she adds.
We asked Lindsay to weigh in on some of the most popular wedding colours and what they say about your big day. Then we gathered together some ideas to inspire you — everything from cakes and flowers to gowns and gifts for your bridesmaids and groomsmen.


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KIEV, Ukraine (AP) — Top Western diplomats headed to Kiev Tuesday to try to defuse a standoff between President Viktor Yanukovych's government and thousands of demonstrators, following a night in which police in riot gear dismantled protesters' encampments outside government buildings.
But a compromise appeared elusive, as dozens of pro-government activists blocked the entrance to the European Commission office in Kiev just hours before the arrival of EU foreign policy chief Catherine Ashton.
Riot police maintained a strong presence in downtown Kiev, which demonstrators have occupied for weeks to protest against Yanukovych's decision to back away from an agreement with the European Union and tilt toward Russia instead.
But the atmosphere in the opposition tent camp, in a central square known as the Maidan, appeared calm. Music blasted from a giant stage, activists lined up to receive food from field kitchens and black-robed Orthodox priests talked to activists to boost morale, careful not to slip on a thick crust of ice and snow that blanketed the Ukrainian capital.
"We are standing on the Maidan so that Yanukovych will be afraid and know that there is another Ukraine, a European one, which doesn't want to go to Russia," said protester Anton Ostriysko, 35, who was warming himself at a fire after a night shift at the camp.
U.S. Assistant Secretary of State Victoria Nuland met with top opposition leaders Tuesday and was also slated to meet with Yanukovych. Ashton was due to arrive later in the day.
Yanukovych also sat down with his three predecessors as part of so-called "nationwide roundtable" discussions aimed at defusing the crisis.
The opposition Svoboda party said some 10 protesters were injured in one of the confrontations overnight, in which police tore down small tent camps blocking access to government buildings. Authorities said two policemen were injured, adding they had received no other complaints.
But the incidents appeared to be less violent than the club-swinging police dispersals of demonstrators a week and a half ago. That violence outraged many and drove hundreds of thousands of people into the streets the past two Sundays, turnouts perhaps larger even than the mass protests of the 2004 Orange Revolution that forced a rerun of a fraudulent presidential election.
On Sunday protesters also toppled a landmark statue of Soviet leader Vladimir Lenin in a symbolic defiance of Russian influence.
Tensions grew Monday when armed security troops stormed the office of a key opposition party, confiscating computer servers and leaving broken glass and smashed doors behind them. The party, called Fatherland, is headed by imprisoned former Prime Minister Yulia Tymoshenko, a longstanding foe of Yanukovych.
Ukraine's political standoff has been aggravated by its rapidly deteriorating finances. The economy has been in recession for more than a year, and the government is in desperate need of foreign funding to avoid a default. As talks stalled with the International Monetary Fund, Yanukovych has sought a bailout loan from Russia.
Jim Heintz and Yuras Karmanau contributed to this report.
Follow Heintz on Twitter at https://twitter.com/jeheintz and Danilova at https://twitter.com/mashadanilova
Copyright 2013 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.


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FRANKFURT (Reuters) - German drugmaker Boehringer Ingelheim said on Thursday it is facing more than 2,000 lawsuits in the United States over claims its blockbuster drug Pradaxa, the first in a new class of stroke prevention pills, caused severe and fatal bleeding.
The unlisted company confirmed the number of cases reported on Thursday by German newspaper Handelsblatt, adding the risk of side effects was known and had to be weighed against the drug's life saving potential.
"We are certain that we can show in the legal cases that we have worked very carefully and responsibly in research, development and marketing of Pradaxa," the company said in a written statement.
Pradaxa was the first to market in a promising new class of medicines designed to replace decades-old warfarin to prevent strokes in patients suffering from atrial fibrillation, a form of irregular heartbeat common among the elderly.
Like other blood thinners, Pradaxa's benefit of cutting the rate of fatal or debilitating strokes in the elderly comes at the risk of internal bleeding, which can also cost lives.
Boehringer cited a recent study by the U.S. Food and Drug Administration as showing that Pradaxa users ran a lower risk of severe bleedings than patients on warfarin.
Sales of the pill - which competes with Bayer and Johnson & Johnson's Xarelto as well as Bristol Myers-Squibb and Pfizer's Eliquis - were 1.1 billion euros ($1.5 billion) in 2012, its second year of market approval.
Reporting by Frank Siebelt and Ludwig Burger, editing by David Evans


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Notwithstanding small ups and downs that accompany news stories like the killing of bin Laden or the unemployment figures of the day, the overall trend is that voters are steadily giving up on the Obama presidency. That is reflected in Scott Rasmussen's Approval Index, which compares the president's "strong approval" and "strong disapproval" numbers. What makes this particular index important is that it is one of the few that consistently sample likely voters rather than registered voters or whoever answers the telephone.
Currently, Obama's Approval Index stands at -22, which I believe equals his lowest ever. A solid plurality of voters, 42%, strongly disapprove of his performance:
Overall, only 43% of likely voters approve of Obama's performance, while 55% disapprove.
When a president runs for re-election, the campaign should be, and nearly always is, a referendum on his performance. If that is the case in 2012, the Republican will win. The Democrats can't defend Obama's record, and they know it. They will try desperately to make the race about the Republican nominee rather than Obama's performance; that strategy will fail if the GOP nominates a solid, mainstream candidate without obvious eccentricities or personal flaws. But it could well succeed if the GOP nominates someone who can be portrayed as eccentric or extreme, or who has personal flaws that come to light during the campaign.
As we have noted before, Scott and I disagree somewhat on the Republican presidential field. He thinks it is weak, while I think it is solidly representative of the party's leadership and includes several potentially strong candidates. It is vitally important, in my view, that the party nominate one of those strong–i.e., mainstream, or, if you will, generic–candidates, and not take a flyer on a candidate who would serve as a distraction from the real issue in 2012, President Obama's horrible record in office.


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Suppose that a rational generating function is given representing the function $f(x) = \sum_{i=0}^{2n}{c_i x^i}$ where $c_i \in \mathbb{N}$
The goal is to determine if the coefficient in the middle, $c_n$, is nonzero or not.
For example, we could be given $f(x) = \frac{1 - 10x^9 + 9x^{10}}{(x - 1)^2}$, which represents $1 + 2x + 3x^2 + \cdots + 9x^8$. We are interested, in this case, in the middle coefficient, which happens to be 5.
Original Formulation
The actual value can be determined by evaluating a contour integral. This is accomplished by first multiplying $f(x)$ by $x^{-n}$. Then, rewriting the variable $x$ as $x\cdot e^{i t}$ and finally evaluating the integral $\int_C{f(x)dt}$. The result of all of this is the coefficient in question.
The Goal
I seek to find alternative formulations to this problem. Let me give some examples.
Example 1 : "Tiling"
Start with the original formula $f(x)$. Make a copy, for example $f(y)$, by rewriting $x$ as $y$. Then we can subtract the second function from the first, eliminating the first coefficient. We repeat additions and subtractions (possibly infinitely many times) until all coefficients except for the middle one have been eliminated.
Example 2 : "Division"
We multiply $f(x)$ by a function $g(y)$, where $g(y) = \frac{1}{1-x^{2n+1}}$, essentially making the series repeat forever. We then divide this by $x^n\cdot g(y)$, and get the remainder. This remainder is the first half of the original series, and $c_n$ can be easily obtained from this.
What is desired / Motivations
I'd simply like to have alternative formulations for the solution. I'm using this for an algorithm, and I'd like to publish this with anyone who gives a formulation that provides a quick result.


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National Oceanic and
Atmospheric Administration
April 2003
National Weather Service
National Centers for
Environmental Prediction
Concerns of possible global ozone depletion (e.g., WMO/UNEP, 1994) have led to
major international programs to monitor and explain the observed ozone variations in the
stratosphere. In response to these, and other long-term climate concerns, NOAA has
established routine monitoring programs using both ground-based and satellite measurement
techniques (OFCM, 1988).
Selected indicators of stratospheric climate are presented in each Summary from
information contributed by NOAA personnel. A Summary for the Northern Hemisphere is issued
each April, and, for the Southern Hemisphere, each December. These Summaries are available
on the World-Wide-Web at the site:
Further information may be obtained from:
Melvyn E. Gelman
NOAA, Climate Prediction Center
5200 Auth Road
Camp Springs, MD 20746-4304
Telephone: (301) 763-8000 ext.7558
Fax: (301) 763-8125
E-mail: email@example.com
For the Northern Hemisphere winter of 2002-2003,
low total ozone values were again observed over the Arctic region. The Arctic area experiencing very low ozone was larger
than for the previous two years, but not as large as in the 1990s. During December, January , February and March, of
2002-2003, there were portions of the Arctic region where average values of total ozone were up to 45 percent lower
than comparable values during the early 1980s. At the same time, total ozone values over middle latitudes and portions of the
Arctic region had much higher than average values. Minimum temperatures observed in the lower stratosphere over the Arctic region in
December and early January were below minus 78 C, allowing the formation of polar stratospheric clouds which promote the chemical
destruction of ozone. Stratosphere temperatures in mid January rose dramatically, with significant warming throughout the Arctic
stratosphere, with a splitting in two of the stratospheric polar vortex, and associated circulation effects. These stratospheric
warming conditions were also associated with movement of high ozone into the Aleutian Arctic region during January, and a splitting
in two of the region of low total ozone values. From 1979 to the early 1990s, total ozone had generally decreased over the
middle latitudes of the Northern Hemisphere at the rate of 2 to 4 percent per decade, but the downward trend has not continued
in recent years. The amounts of chlorine and other ozone destroying chemicals in the stratosphere have been reported to have
reached peak values around 1997-98, and have remained at high levels. Much of the recent year-to-year differences in north polar
winter-spring stratospheric ozone destruction may be explained as being due to the varying conditions associated with interannual
meteorological variability. The low total ozone values in the Arctic region in the winter of 2002-2003 are attributed to meteorological
conditions which were favorable for ozone destruction, with the continued presence of ozone destroying chemicals in the stratosphere.
The data available are listed below. This combination of complementary
data, from different platforms and sensors, provides a strong capability to monitor global
ozone and temperature.
We have used total column ozone data from the NASA Nimbus-7 SBUV instrument from 1979 through
February1985; NOAA-9 SBUV/2 from March 1985 to December 1988; NOAA-11 SBUV/2 from January 1989
to December 1993; NOAA-9 SBUV/2 from January 1994 to December 1995; NOAA-14 SBUV/2 from January
1996 to June 1998; NOAA-11 SBUV/2 from July 1998 to September 2000; and NOAA-16 SBUV/2 from October
2000. Solar Backscatter Ultra-Violet (SBUV) instruments can produce data only for daylight-viewing
conditions, so SBUV/2 data are not available at polar latitudes during winter darkness. Increasing
loss of NOAA-11 data at sub-polar latitudes from 1989 to1993 was caused by satellite precession,
resulting in SBUV/2 viewing high latitudes only in darkness.
The maps in
Figure 1a and 1b show Northern Hemisphere monthly mean total ozone
amounts for December 2002 and March 2003. High ozone extends over northern latitudes in the western hemisphere,
while low total ozone values prevail over the eastern hemisphere Arctic region. Figure 2a
shows the monthly mean total ozone percent difference of the December 2002 monthly mean for eight December
monthly means, 1979-1986 (Nagatani et al., 1988). The 1979 to 1986 base period is chosen
because 1979-1986 average values are indicative of the early data record. For December 2002,
negative anomalies of greater than 30 percent are evident extending from North America to Europe,
but with positive anomalies of more than 45 percent centered over the Aleutian Arctic region.
The persistence and movement of areas of low and high total ozone anomaly are shown in the maps
for January (Figure 2b), February (Figure 2c)
and March 2003 (Figure 2d). Figure 3a, b, c, and d
show maps of temperature anomaly at the lower stratospheric level of 50 hPa for December 2002 to
March 2003, respectively. The areas of low and high ozone anomaly correspond quite closely with
the regions of low and high temperature anomaly.
Figure 4 shows
monthly mean temperature anomalies at 50 hPa for three latitude regions, 65N-90N, 25N-65N,
and 25S-25N. The temperature anomalies for middle and high latitudes for December 2002 and
January to March 2003 were slightly negative, but strongly below average for the equatorial
Extremely low temperatures
(lower than -78 C) over the Arctic region in the lower stratosphere are linked to depletion of ozone.
Temperatures in the lower stratosphere are closely coupled to ozone through dynamics and photochemistry.
Very low temperatures contribute to the presence of polar stratospheric clouds (PSCs). PSCs enhance the
production and lifetime of reactive chlorine, leading to ozone depletion in the presence of sunlight
(WMO, 1999). Daily minimum temperatures over the polar region, 65N to 90N at 50 hPa (approximately 19 km)
are shown in Figure 5 . During November, December and early January, daily
minimum temperatures were lower than -78 C. Temperatures increased markedly in association with stratospheric
warming in mid January and then again in February and March.
Figure 6 compares
the average 100 hPa temperature in the polar region for each March of the last 24 years with the date the
stratospheric polar vortex diminished below a specific threshold size. The size of the vortex was defined
by the maximum in the gradient of potential vorticity contours at the 450 K isentropic surface, based on the
NCEP/NCAR reanalyses. March 2003 was close to average in the temperatures and duration of the polar vortex.
Figure 7 shows the relationship between the persistence of the polar vortex and the persistence of high latitude
total ozone values of less than 300 DU. In the winter of 2002-2003 there was close to average persistence of
both the Arctic polar vortex and region of anomalously low ozone.
Figure 8 shows the average area,
during February and March for each year since 1979, of low ozone (lower than 300 DU). For 2003, the area of
anomalously low total ozone was greater than conditions in 4 out of the last 5 years. But not as great as
most of the years in the 1990s.
A time series, from December 2002 to
March 2003, of normalized height anomalies from 1000 to 30 hPa, for the north polar region 65-90N, is shown in
Figure 9. The strong positive anomaly in January, associated with strong stratospheric warming, appears to
propagate from the stratosphere downward to the surface, resulting in a negative Arctic Oscillation phase.
However, relatively weak positive or negative height anomalies in other periods do not propagate down to the
surface (Zhou et al., 2002 and Baldwin and Dunkerton, 1999).
Figure 10 shows monthly average
anomalies of zonal mean total ozone, as a function of latitude and time, from January 1979 to March 2003.
The percent anomalies are derived relative to each month's 1979-2003 average. SBUV/2 data (in this figure
only) have been adjusted for long term consistency (Miller et al., 2002). The largest anomalies occur in
winter and spring months for the polar region of the Southern Hemisphere. In the north polar region,
positive anomalies prevailed in 1979 and the early 1980s, but mostly negative anomalies predominated
in the 1990s. However, during the winter of 2002-2003, positive zonal mean total ozone anomalies are
shown over the Northern Hemisphere. The Scientific Assessment of Ozone: 1998 (WMO, 1999) reported that
total column ozone decreased at northern midlatitudes (25-60N) between 1979 and 1991, with estimated linear
trend downward of 4 percent per decade. However, since the recovery after 1993 from the 1991 Mt. Pinatubo
volcanic eruption, the downward trend of total ozone has not continued.
The NOAA Climate Monitoring and
Diagnostics Laboratory (CMDL) operates a 16-station global Dobson spectrophotometer network for total ozone
trend studies. Figure 11 shows the total ozone data for four mid-latitude U.S. stations from1979 through 2002.
The large annual variation is a result of ozone transport processes which cause a winter-spring maximum and
summer-fall minimum at northern mid-latitudes. Figure 12 shows the four-station average percent deviation
from their long-term monthly means. These anomalies, derived from ground-based measurements, are consistent
with the anomalies from SBUV/2 satellite ozone measurements, shown in Figure 10. Middle latitude total ozone
values in the years since 1993 have not continued to decline as they had declined from 1979 to 1993. However
ozone values have also not recovered to their higher 1980 values. The implication of these changes needs to be
examined in the context of changes in amounts of ozone depleting gases in the atmosphere and varying meteorological
In the winter of 2002-2003, negative
and positive anomalies of total ozone were prevalent in the high latitudes of the Northern Hemisphere. The low
and high anomalies in total ozone were associated with the meteorological conditions of low and high anomalies
of lower stratosphere temperature. Arctic temperatures were sufficiently low for the formation of polar stratospheric
clouds and consequent chemical ozone depletion within the polar vortex. Chlorine and other ozone destroying chemicals
in the lower stratosphere reached peak values around 1997-98, and have remained at high levels. As a consequence, lower
stratosphere ozone destruction is strong when meteorological conditions of a strong polar vortex and cold polar
temperatures prevail.
Total ozone declined over mid-latitudes
of the Northern Hemisphere at the rate of about 2 to 4 percent per decade from 1979 to 1993. In recent years the
strong rate of decline of Northern Hemisphere total ozone has not continued, but current stratospheric ozone amounts
continue to be below the amounts measured before the early 1980s. A full explanation of ozone and temperature anomalies
must include all aspects of ozone photochemistry and meteorological dynamics. Continued monitoring and measurements are
essential toward this end.
Baldwin, M.P., X. Cheng, and T.J. Dunkerton, 1994: Observed correlations
between winter-mean tropospheric and stratospheric circulation anomalies. Geophys Res.
Lett., 21, 1141-1144.
Miller, A.J., R.M. Nagatani, L.E. Flynn,
S. Kondragunta, E. Beach, R. Stolarsky, R. McPeters, P.K. Bhartia, M. Deland, C.H. Jackman, D.J.Wuebbles, K.O.Putten,
and R.P. Cebula., 2002, A cohesive total ozone data set from SBUV/(2) satellite system, press, J. Geophys. Res.,
107(0), doi:10.1029/200,D000853.
Nagatani, R.N., A.J. Miller, K.W. Johnson,
and M.E. Gelman, 1988: An eight year climatology of meteorological and SBUV ozone data, NOAA Technical Report NWS 40,
OFCM, 1988: National Plan for Stratospheric
Monitoring 1988-1997. FCM-P17-1988. Federal Coordinator for Meteorological Services and Supporting Research, U.S. Dept.
Commerce, 124pp.
WMO, 1999: Scientific assessment of ozone
depletion: 1998. World Meteorological Organization Global Ozone Research and Monitoring Project - Report No. 44.
Zhou, S., A.J. Miller, J. Wang, and J.K.
Angell, 2002: Downward-propagating temperature anomalies in the preconditioned polar stratosphere. J. Climate,
15, 781-792.


text:
Chester needed a new logo design and created a contest on 99designs.
A winner was selected from 76 designs submitted by 43 freelance designers.
The creditplus logo was initially design for non prime or subprime motor loans direct to the consumer. We now wish to provide motor loans to prime and subprime consumers therefore needing a more generic look that will attrack both sets of consumers
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text:
Proud DadSaturday, May 31st, 2008
We're all very excited and proud of Kaylee! She made the high school cheerleading team. Quite an accomplishment for someone her age. She just skipped right over the middle school team and headed right for the high school team. I am so thankful to have such beautiful, happy, and healthy children!
Things are very busy here in the bluegrass. Chickens are at their peak right now so it takes almost all our time just gathering the 10-11,000 eggs we are getting every day. Most days it's 5am to 7pm or maybe a little later. I've tried my best to keep labor to a minimum, but everyone is getting worn down. We are still kicking around building a second set and I'm looking for the right person or persons for it and to help here. So far it's mostly my mom and I with a couple folks part time. My friend John and his mom both help out. Bj helps when she can, but lately it seems there is always something that needs to be done involving the children and she's been attending to that. Garett's class went to Pigeon Forge TN on a field trip. They took in a show at The Black Bear Jamboree. He wanted one of us to go so BJ went with him. Summer is coming and I know they dread coming to the chickenhouse every day.
We have made time to get out and do things with the horses a couple times a week. I've finally got Thumper, the colt born here on the farm almost 2 years ago, green broke and gelded. I think he will make a fine horse. I've been riding him a little bit and Madison tried him some too. Madison is quite the little cowgirl. She took her first ride outside the fence this week. We just rode around on the farm, but it was a huge deal to her. She can't even reach the stirups, but she makes the horses do what she wants them to. Of course her horse is very broke. It's a hand me down from me. Johnny horse has been here on the farm for about 5 years now. He had some fire in him when we first bought him, but it didn't take long for him to figure out that wasn't going to work with me. Garett and Kaylee don't have much desire to do the horse things, but Madison and Katie do. Katie is now bugging me for her own horse. We'll see how long she stays interested before we buy another one.
I finally broke down and hired someone to build a tack room in the barn. I figured it was do it now or I'd wait until someone stole my saddles. Must be a sign that things are tough because there is more burglary than ever here. I've been lucky not to have much stolen from me in the past. What did go missing I knew who took it and took appropriate action. Some of it I got back and those folks know never to show their face here again.
This weeks project is going to have to be bird proofing the chicken houses and the well house. Can't have wild birds anywhere around these chickens. Their immunity is not that of a domestic chicken. Bj's cousin Jason has agreed to help me some with it and keeping the place mowed. We're still shopping for a truck. I geuss I'll put off buying as long as I can. Just can't stand to let go of the money it will take to buy what I want. I don't know why $30,000 in debt scares me when we are in as deep as we are with the chickenhouses. Kaylee is keeping her eyes open though. She points out trucks she likes pretty regularly.
Well as always lots to do and little time to do it in………………………….So I better get busy. Thanks for reading and be sure to check out all the pics I've added to the site.


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Diane Kaplan, Ph.D.
Half-Time Institute Faculty
B.S. Social Planning & Public Policy, Cornell University, 1983
M.S. Counseling Psychology, San Francisco State University, 1986
Ph.D. Clinical Psychology, The Wright Institute, 1994
Dr. Kaplan has been working in the field of community mental health since 1984. She has worked as the Clinical Manager of a partial hospitalization program and as the Clinical Director of an outpatient community mental health program. The people she works with have presented with a variety of difficulties, from normal life-cycle transitions to more serious emotional trauma, including those experiencing schizophrenia and other psychoses. She is interested in a contemporary relational and intersubjective approach to psychotherapy and supervision.
She graduated from the Wright Institute in 1994 after completing a predoctoral internship at the UC Davis Counseling Center. During her postdoctoral fellowship in the Coordination of Practicum Training at UC Davis, she organized a practicum training program and taught courses on Intercultural Relations and Supervision.
Dr. Kaplan has a special interest in unconscious communication in groups and the effective use of group process in learning. Other special areas of interest include: the supervisory relationship, intercultural relations, and the application of intersubjective and relational theory to clinical work with people with severe emotional disturbances. She is interested in the relationship between psyche and soma. In addition to her private practice in psychoanalytically oriented psychotherapy, she also maintains a practice in biofeedback training, treating individuals with a variety of somatic difficulties including hypertension, arrhythmias, headaches, chronic pain, and stress related to traumatic life events.
Dr. Kaplan is also the Wright Institute's Clinic Director, in which role she directs the day-to-day operation of the Clinic and is involved in teaching, supervision, and crisis on-call services.


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This forum is devoted to the topic of JABO, Inc. and the marbles they produced, particularly the collector runs they produced circa 2008-2010.
Great Thread!
Santa got his photos back up on his site recently since they have been down since the Photobucket hostage taking. He has great photos of the labelled classic run trays that are on display at JABO for those trying to ID some of their JABOs..
D.A.S. Memorial Day Run May 23rd 2017
SEE THEM ALL HERE: http://biblefreak.org/marbles/web/MibID/2017%20D.A.S.%20May%2023rd%20Memorial%20Day/
D.A.S. Phoenix Rising May 9th, 2017
I was a 1/4 Share investor with Christopher Norby. These are some killer Marbles.
See them all HERE http://biblefreak.org/marbles/web/MibID/2017%20D.A.S.%20Phoenix%20Rising%20May/index.html...
Here is the new Run. Some Nice Stuff! Dave McCullough does it again.
See all 66 Images full sized here
10 Families...
Here they are. Dave does it once again. There are some killers in the run.
See them all here:http://biblefreak.org/marbles/web/MibID/2017%20D.A.S.%20RDR%20III%2002252017/...
Jan 19th, 2017. Dave's Appalachian Swirls Buckeye Run. This is a killer run loaded with Cranberry, Oxblood, Lutz, and several unique types, including the "Oxblood Blue Egg Yolk AKA Superman Shredded" "Wonder Woman (Look for Gold Lassos)", Lemoncello, Pink Cranberries, Blue Cranberries, Oxblood Egg...
Check them out
Check this link:
Early this morning i received a phone call from Dave McCullogh. Dave ask me to post this statement from Dave for the marble community.
Myself with a heavy heart and regrets it is as follows.
Dave McCullogh no longer has any connection or ties to Jabo Inc. of Reno Ohio. Dave would like to express...
Ok, I'm wondering if anyone has any new new's regarding what may or may not be happening at the Jabo facility? There must be something in the works, perhaps a run of marbles for the upcoming Buckeye marbles collectors show in Canton. thanks in advance for any info you might...
Is there any new info on the status of the Jabo facility? Plans for the future regarding any marble runs? Marble run before the sistersville Marblefest? Just wondering.:102:
to all you jabo collectors...Jabo Land is having a poll.
(please check out the link below).
We are voting on what's your favorite Jabo Classic?
hi i'm new here but i really like collecting marbles. started in 1991 mostly for wrist rocket ammo. but luckily i realized what a mistake i was making and nowdays when i have marbles i don't want i give them to my grandkids or the neighbors kids:thumbsup:
i was bummed out when i heard about Jabo...
I was cleaning out a closet in a spare bedroom today and stumbled upon a case of marbles I bought from JABO back around 1993 or 1994. I now remember have another one buried somewhere at my office I had also forgotten about.
The case here is a 55 pound carton of 1" classics and the one at my...
Much thanks to Dave McCullough formerly of JABO Inc. the Original Joker Team, including Rick Hall, Jim King, and Burt Wilkins all of whom have sent marbles over the past two years to allow me to photograph and keep or sell so we can have these images for future generations.
To see larger images...
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Once upon a time, there was a darling little boy named Kamron...
...and a sweet, little girl named Megan.
Kamron and Megan grew. They grew until they were teenagers. Kamron was gawky and awkward, with pimples, a mullet and a car as long as a boat.
Teenage Megan was a wee bit rebellious and her mom would probably say that she had an attitude...
Miraculously- those two made it through those teenage years and went to college. One night they met in a bar and fell madly in love.
They were inseparable. They went on lots of dates...
...tried out some strange hairstyles...
...and had lots and lots of fun!
Megan pestered the bejeezus out of Kamron until he finally asked her to marry him. Lucky
him her!
Then they had a huge, beautiful wedding.
Somewhere along the way, they added three crazy rugrats to make them one great big
dysfunctional happy family!
And here they are now- celebrating eight wonderful, wild, and crazy years of marriage today.
Happy Eighth Anniversary, Kamron! There is no one else I'd rather go through the ups and downs, the trials and the triumphs with than you! Here's to 50 more years. I love you!
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