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The purpose of hydraulic fracturing is to change the flow pattern in the reservoir from one that converges radially on the well bore Figure 2 with flow resistance concentrated near the wellbore, to one where flow in the reservoir is linear to a highly conductive fracture that conducts fluid to the wellbore with minimal flow resistance Figure 3. The success of this operation depends upon the conductivity of the hydraulic fracture and how successfully this conductivity can be retained following the treatment. These, in turn, depend largely upon the design and execution of the fracturing treatment. A hydraulic fracture is created in a subsurface formation when a fluid is pumped into that formation at a rate faster than the formation can accept the fluid through its matrix permeability. For example, Figure 4 illustrates the pressure versus time behavior at the surface of a well that is being fractured. As fluid is pumped into the target formation at a rate sufficient to fracture the well, the pressure at the formation face builds up rapidly to the point that the formation fails and a fracture is developed. Continued injection at high rate causes the fracture to extend from the wellbore, and this growth in fracture length is accompanied by an increase in fracture width at the wellbore and proportionately throughout the fracture. Leak-off through the face of the fracture reduces the amount of fluid retained in the fracture. Only that fluid retained within the fracture is effective in extending the fracture.

## Your Life in Weeks

What do anti-MMR vaccination groups think? Those who are against the MMR immunization voice their opinions through online blogs, forums and groups and are mainly parents of autistic children searching for an environmental cause of autism. These parents often cite the Wakefield study, as well as governmental reports to prove the link, or at least a possible connection, to Autism and the MMR immunization. One report by the FDA in is often cited by anti-MMR groups as governmental evidence that demonstrates the link between vaccine dangers and developmental disorders.

This study, sponsored by the FDA Modernization Act, reviewed all mercury containing food and drugs as a general assessment. The concerns about the neurological effects of mercury on infant health, although only researched through the effects of methyl-mercury, worried much of the population who were increasingly aware of the dangers of lead http:

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I recently watched a video where a man, with a gun in a holster on his hip, explained his guide to women using what he likes to call the hot crazy matrix. The chart looks like the basic graph that would be shown in an economics class: The crazy axis starts at a four because all women are at least somewhat crazy. She should be between a five to seven crazy and above an eight hot.

The has a pulse axis is simply from 0 to 1. Either a man has one or he does not. The key then is for women to find a man who is both alive and relatively low on the asshole scale.

## 8 Useful Databases to Dig for Data (and 100 more)

Page 5 Question 21 What is the flow balance in a maximum flow problem? The flow balance refers to the concept that objects cannot get stuck at any of the nodes. Flow balance means that objects must move back and forth between each pair of nodes. Flow balance refers to the decision where we are trying to maximize the number of objects we move between two points, where there are many different ways to get from one point to the other. Flow balance means that the number of objects reaching the destination must be balanced by the number of objects that return to the origin point.

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Jinxed, a vintage edgematching puzzle by Tryne. There are 24 triangular tiles, the edges of which are colored with a dot in one of four colors red, yellow, white, and green. The tiles are to be arranged into a hexagon such that all touching edges match and the border is all red. It is possible to solve the puzzle with other border constraints, too. MacMahon shows the possible tile sets for 1, 2, and 4 colors in Figure 2, and gives a solution for the 4-color set.

Kadon’s Multimatch III is essentially the same puzzle. Similar to Jinxed a vintage edgematching puzzle from Tryne. There are nine discs on pegs, arranged in a 3×3 grid of holes in a baseboard. Each disc has four diamonds arranged pointing north, south, east, and west. Each diamond is one of eight colors: The discs must be arranged such that no color appears more than once in each of the three rows and three columns of six diamonds.

In this case, not every color appears in every row or column. There is a second constraint – when a pair of colors is placed adjacent horizontally, then that same pair cannot be placed adjacent again in that direction – likewise for the vertical. I have a loose copy but it was also included in the F.

## Simulation

Both made a square of months, which is the size that fits best into a comic pane. Mozart and Einstein are obvious references when talking about early accomplishments. Everything else about the two is different. But I can definitely see why you would think we had. NepaGirl Still reeling in my shoes. This has shifted the paradigm I was ignorantly, and wastefully living my life on.

Sometimes I feel like Neo in Matrix, it goes on and on, there is no end. Levels of Game. This graph I did one night at 2am. I couldn’t sleep, opened excel and did it. Dan is World’s best Dating coach. Inventor of Direct and Natural Game.

I also like charts. I think these boil down to two factors: Stability is related to job security, maturity, and mental health. Hotness is clearly related to how generally attractive you find them. Both are just as important. When you meet for a drink you realize he looks nothing like his photos. You charge through the date and part ways, only to find that this man is stalking you hard months later. This goes on for years, probably ending in someone dying.

## Analyze, graph and present scientific data faster than ever with Prism 7!

The Archimedean spiral , studied by Archimedes as a method to trisect an angle and square the circle. Analytic geometry allowed curves, such as the Folium of Descartes , to be defined using equations instead of geometrical construction. A fundamental advance in the theory of curves was the advent of analytic geometry in the seventeenth century.

When it comes to graphing and comparing functions, the TI graphing calculator is the end-all device for math and science students. But one of the most entertaining aspects of Texas Instruments’ powerful algebraic and trigonometric calculator is not the equations themselves, but rather the art that can be “equated” on them—just think of them as the mathematical equivalent of the Etch A Sketch.

Show Solution In this part the interest is compounded quarterly and that means it is compounded 4 times a year. It is important to not do too much rounding in intermediate steps with these problems. Show Solution Here we are compounding monthly and so that means we are compounding 12 times a year. So, how many decimal places should we keep in these? Well, unfortunately the answer is that it depends. The larger the initial amount the more decimal places we will need to keep around.

As a general rule of thumb, set your calculator to the maximum number of decimal places it can handle and take all of them until the final answer and then round at that point. This means that we are going to have to solve an exponential equation to get at the answer. In that section we saw that we need to get the exponential on one side by itself with a coefficient of 1 and then take the natural logarithm of both sides.

The work will be a little messier, but for the most part it will be the same. Short term population growth is often modeled by the exponential growth equation and the decay of a radioactive element is governed the exponential decay equation.

## Mathematics

I find it unnecessarily complicated. This shows up when trying to read about Markov Chain Monte Carlo methods. Markov chain Monte Carlo MCMC is a technique for estimating by simulation the expectation of a statistic in a complex model.

The graph Laplacian matrix is a real symmetric matrix, thus diagonalizable, and can be decomposed into a set of eigen- values λ={λ e } e=1,,´n and a set of orthogonal eigenvectors.

Browse the full archives below The Margin Matrix: If you knew you were going to face that bet times and you made it every time, you would come pretty close to doubling your money per the law of large numbers. A few interesting points worth highlighting: Quantitative vs Qualitative Value of Outcomes The player in this poker game making the correct decision is going to be wrong the majority of the time. However, by outcome, he will double his money.

Assuming the player was correct every time, If we were to redraw the matrix and weight the quadrants according to quantitative vs qualitative, it would look like this: Qualitative Value of Outcomes -Matrix redrawn so each square is sized as a percent of net winnings. Quantitative Value of Outcomes — Matrix redrawn so each square is sized as percent of decisions: Even though he loses nine times out of 10, he still doubles his money.

## How Good Are Those Young-Earth Arguments?

A mathematician won’t find much in here that’s helpful, but it would make a really good textbook for a nontechnical math class–the sort of ‘shotgun’ math class lots of liberal arts students take instead of calculus. The general setup for a chapter is: Introduce a classic problem, define some basic graph theory terms that would be helpful, prove a couple theorems, give a couple of examples.

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Optimizations The library works relatively quickly for several reasons. First, I changed the data structure in the priority queue in such a way that the priority update of any element of the queue takes O lg n time. This is achieved by the fact that each element monitors its position in the heap during rebuilding the queue. Secondly, during the stress tests, I noticed that garbage collection takes considerable time.

This is not surprising, since the algorithm creates many small objects when it walks the graph. A problem is solved with the garbage collector using the object pool. This is a data structure that allows you to reuse objects when they are no longer needed. To admit, I think that this is not the limit of perfection. It is likely, if you use a hierarchical approach, described by Boris will be able to speed up the time for even larger graphs.

How does the demo work? Creating a library is, of course, very interesting. But I think the demo project deserves a separate description. I learned a few lessons, and I would like to share with you, in the hope that it will be useful. It is easiest to present each intersection with a node of the graph.