Synchrotrons which are useful for cutting edge research are large machines, costing tens or hundreds of millions of dollars to construct, and each beamline (there may be 20 to 50 at a large synchrotron) costs another two or three million dollars on average. These installations are mostly built by the science funding agencies of governments of developed countries, or by collaborations between several countries in a region, and operated as infrastructure facilities available to scientists from universities and research organisations throughout the country, region, or world. More compact models, however, have been developed, such as the Compact Light Source.
Brave (2012 movie)
Brave is a 2012 American animated adventure movie which stars Billy Connolly and Emma Thompson. The movie was released on June 22, 2012, by Walt Disney Studios Motion Pictures and distributed by Walt Disney Pictures. Pixar was the studio that worked on this movie. It received positive responses from critics and won an Oscar.
The movie is set in Scotland during the Medieval period. 16-year-old Princess causes chaos in the kingdom of DunBroch by not wanting to marry.
It took six years to make.
Bunkyū
France at the Olympics
France has taken part in every Olympic Games with the possible exception of the 1904 Games. In 1904, different sources list Albert Corey as taking place in the games for either the United States or France.
The International Olympic Committee's official abbreviation for France is FRA.
France has hosted the Games 5 time:
French athletes have won 671 medals at the Summer Olympic Games. Fencing and cycling are their best sports. France has won 94 medals at the Winter Olympic Games. Most of these are in alpine skiing.
Leading in that sport
Enryaku
Jean-Honoré Fragonard
Jean-Honoré Fragonard (5 April 1732 in Grasse - 22 August 1806 in Paris) was a French artist. He is remembered as one of the most important French painters of the rococo style. He was a pupil of François Boucher, and developed Boucher's style further. At first he did historical paintings, but soon gave up on these.
He then painted things that were light-hearted, gay, and slightly erotic. His works include "The Swing", "A Young Girl Reading", and "The Secret Meeting". Together with Boucher and Antoine Watteau, he is one of the principal painters of French Rococo. He lost his wealth during the French Revolution. After the revolution, the painting style was different, because he had trouble adapting, he died a poor man.
System of linear equations
In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
Mathematicians show the relationship between different factors in the form of equations. "Linear equations" mean the variable appears only once in each equation without being raised to a power. A "system" of linear equations means that all of the equations are true at the same time. So, the person solving the system of equations is looking for the values of each variable that will make all of the equations true at the same time. If no such values can satisfy all of the equations in the system, then the equations are called "inconsistent."
For example,
is a system of three equations in the three variables formula_2, formula_3, formula_4. A "solution" to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by
since it makes all three equations valid:
In mathematics, the theory of linear systems is a branch of linear algebra, a subject which is fundamental to modern mathematics. Computer algorithms for finding the solutions are an important part of numerical linear algebra, and such methods play a prominent role in engineering, physics, chemistry, computer science, and economics. A system of non-linear equations can often be approximated by a linear system (see linearization), a helpful technique when making a mathematical model, computer model, or computer simulation of a relatively complex system. For complex systems, there are many equations and many variables, not just two or three. In many cases, the number of equations and variables in the system are the same. In some cases, there are more variables than equations, and the solution will be a range of different values rather than one exact solution.
The simplest kind of linear system involves two equations and two variables:
One method for solving such a system is as follows. First, solve the top equation for formula_2 in terms of formula_3:
Now substitute this expression for "x" into the bottom equation:
This results in a single equation involving only the variable formula_3. Solving gives formula_13, and substituting this back into the equation for formula_2 yields formula_15:
This method generalizes to systems with additional variables.
Very often, all the coefficients are written in the form of a matrix A, which is called a coefficient matrix.
In much the same way, the variables can be written in the form of a vector:
This makes it possible to write
Mathematically, the vector defined above is a 1-by-n matrix. The system of equations can then be solved using the multiplication operation defined on matrices. A, x and b are all part of the same algebraic field.
There a three cases when looking for solutions to a system of linear equations:
There are two categories of methods for solving a system of linear equations. Iterative methods use many steps to get a solution, direct methods only need one step:
Examples for iterative methods are:
There are examples such as geodesy where there many more measurements than unknowns. Such a system is almost always overdetermined and has no exact solution. Each measurement is usually inaccurate and includes some amount of error. Since the measurements are not exact, it is not possible to obtain an exact solution to the system of linear equations; methods such as Least squares can be used to compute a solution that best fits the overdetermined system. This least squares solution can often be used as a stand-in for an exact solution.
Solving a system of linear equations has a complexity of at most O (n). At least n operations are needed to solve a general system of n linear equations. The best algorithm known to date was developed by Don Coppersmith and Shmuel Winograd and dates from 1990. It has a complexity of n Unfortunately, it is of little practical use.
Using computers to solve systems of linear equations is used every day. For example, it is used in weather forecasting models. Hot dog factories use it to make small changes in the receipe as food ingredient prices change. College cafeterias use it to figure out how much food to cook based on past experience when the cafeteria gives students the choice between multiple entrees.
François Boucher
François Boucher (29 September 1703 in Paris - 30 May 1770) was a French painter, mostly known as one of the main artists of the French rococo movement. He painted several portraits of his patroness, Madame de Pompadour. He is also known for his open-minded voluptuous paintings.
Valdivia expedition
The Valdivia expedition was a scientific exedition to explore the Deep sea. It was a German expedition, done in 1898 and 1899. A ship was bought from "Hamburg-Amerikanischen Packetfahrt-Actien-Gesellschaft" HAPAG and given instruments to be able to perform scientific measurements. The ship left Hamburg on 31st July 1898 and returned on 1st May 1899. The ship had travelled over 32.000 nautical miles. The expedition was very successful. The results were published in 24 volumes; publishing them took until 1940.
Spain at the Olympics
Spain first took part in the Olympic Games in 1900. It has sent athletes to compete in most Summer Olympic Games since 1920. Spain has taken part in every Winter Olympic Games since 1936.