creating a black hole using particle flow

... use a function from one program in another program? By using a variety of smaller programs and arranging the inputs and outputs as you like, you can make the system behave in any manner that amuses ... mean, let alone the symbols? Think of learning to use the command line as learning a language When learning a language, we start with simple words As we increase our vocabulary, we also learn ... the hardware and software, they can make their systems support many interesting features, such as hot−swappable memory and main boards AIX Another UNIX contender is IBM's AIX AIX's main claim...

Ngày tải lên: 26/10/2014, 19:57

... decompose all root subspaces for roots of a maximal ksplit toral subalgebra a as a sum of root subspaces of a maximal toral subalgebra containing a From the Γ -diagram corresponding to a reductive ... has been implemented in several symbolic computation packages, like LiE, Maple, GAP4, Chevie, and Magma These packages have become an indispensable tool for scientists in many areas of mathematics ... present and past I thank the late Dr Charles Lewis for the undergraduate scholarship in his name that I received I thank my committee, Dr Ernest Stitzinger, Dr Tom Lada, and Dr Amassa Fauntleroy,...

Ngày tải lên: 13/11/2014, 09:13

... Association of America), Chapters 2, 7, and 14 Ralston, A. , and Rabinowitz, P 1978, A First Course in Numerical Analysis, 2nd ed (New York: McGraw-Hill), Chapter Householder, A. S 1970, The Numerical ... beginning usually depends on analysis rather than numerics Carefully crafted initial estimates reward you not only with reduced computational effort, but also with understanding and increased self-esteem ... iteration method get outside of the best bracketing bounds obtained at any stage We will see below that some pedagogically important algorithms, such as secant method or Newton-Raphson, can violate...

Ngày tải lên: 07/11/2013, 19:15

... that an interval contains a root, several classical procedures are available to refine it These proceed with varying degrees of speed and sureness towards the answer Unfortunately, the methods that ... must decide what accuracy on the root is attainable: Convergence to within 10−6 in absolute value is reasonable when the root lies near 1, but certainly unachievable if the root lies near 1026 One ... interval becomes smaller than this tolerance in absolute units Usually you may wish to take the tolerance to be (|x1 | + |x2 |)/2 where is the machine precision and x1 and x2 are the initial brackets...

Ngày tải lên: 15/12/2013, 04:15

... in the answer approximately doubles with each two function evaluations Third, taking out the function’s “bend” via exponential (that is, ratio) factors, rather than via a polynomial technique ... #include #define MAXIT 30 Maximum allowed number of iterations float rtsec(float (*func)(float), float x1, float x2, float xacc) Using the secant method, find the root of a function func ... section, are almost always better choices Figure 9.2.3 shows the behavior of secant and false-position methods in a difficult situation #include #define MAXIT 30 Set to the maximum allowed...

Ngày tải lên: 15/12/2013, 04:15

... excellent algorithm that pays close attention to these matters was developed in the 1960s by van Wijngaarden, Dekker, and others at the Mathematical Center in Amsterdam, and later improved by Brent ... root estimates, inverse quadratic interpolation uses three prior points to fit an inverse quadratic function (x as a quadratic function of y) whose value at y = is taken as the next estimate of the ... http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) Yes We can keep track of whether a supposedly superlinear method is actually converging...

Ngày tải lên: 15/12/2013, 04:15

... cover 1/3 the area of the complex plane, but its boundary is highly irregular — in fact, fractal (A fractal, so called, has self-similar structure that repeats on all scales of magnification.) How ... REFERENCES AND FURTHER READING: Acton, F.S 1970, Numerical Methods That Work; 1990, corrected edition (Washington: Mathematical Association of America), Chapter Ralston, A. , and Rabinowitz, P 1978, A ... known in advance to be multiple, then special methods of attack are readily devised Problems arise when (as is generally the case) we not know in advance what pathology a root will display ...

Ngày tải lên: 15/12/2013, 04:15

... (North America only),or send email to trade@cup.cam.ac.uk (outside North America) The eigenvalues of a matrix A are the roots of the “characteristic polynomial” P (x) = det [A − xI] However, as we ... power xn and rewrite it as a polynomial in 1/x.) The algorithm for backward deflation is therefore virtually identical to that of forward deflation, except that the original coefficients are taken in ... Starting from these relations, the Laguerre formulas make what Acton [1] nicely calls a rather drastic set of assumptions”: The root x1 that we seek is assumed to be located some distance a...

Ngày tải lên: 15/12/2013, 04:15

... or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) The matrix of partial derivatives appearing in equation (9.6.3) is the Jacobian matrix ... provide the function values F and the Jacobian matrix J If J is difficult to compute analytically, you can try having usrfun call the routine fdjac of §9.7 to compute the partial derivatives by finite ... great dissatisfaction, that your function F has a great number of local minima In Figure 9.6.1, for example, there is likely to be a local minimum wherever the zero contours of f and g make a...

Ngày tải lên: 15/12/2013, 04:15

... *f-fold-alam*slope; rhs2=f2-fold-alam2*slope; a= (rhs1/(alam*alam)-rhs2/(alam2*alam2))/(alam-alam2); b=(-alam2*rhs1/(alam*alam)+alam*rhs2/(alam2*alam2))/(alam-alam2); if (a == 0.0) tmplam = -slope/(2.0*b); ... numerical derivatives Of course, you can always replace fdjac with a routine that calculates the Jacobian analytically if this is easy for you to #include #include "nrutil.h" #define MAXITS ... may move too far for the quadratic approximation to be valid All we are guaranteed is that initially f decreases as we move in the Newton direction So the goal is to move to a new point xnew along...

Ngày tải lên: 15/12/2013, 04:15

... streaming database and rich text database files that comprise a particular database are inseparable BETA MATERIALS FOR MICROSOFT CERTIFIED TRAINER PREPARATION PURPOSES ONLY Module 4: Creating and ... transactions A transaction is a series of modifications to a database that leaves the database in a consistent state These modifications are called operations An operation is the smallest change ... contains user data and a public store contains public folder (or shared) data Each store is a logical database that has an associated streaming store file containing native Internet content Each...

Ngày tải lên: 21/12/2013, 05:18

... Dioxide (Alkenes) Acetals Ketals (Alkynes) Halide X Alkyl Gem-dihalides Carbon trihalides Halides Gem- tetrachloride Acid Halides Nitrogen Amides Carbo- Nitriles** Imidines dimides Azides Sulfur Amines ... in carbon dioxide it is +4 From these few examples, one sees that carbon is very versatile in the oxidation states it can adopt Crudely separating reactivity into redox and acid/base character, ... clear that the conversion of methane to methanol cannot proceed by simply by acid/base reagents by requires redox character, specifically an oxidizing reagent Once the oxidation state of carbon...

Ngày tải lên: 22/03/2014, 14:20

... mínima invasión es fundamentado principalmente por la alta capacidad de de cicatrización pulpar en dientes permanentes jóvenes, la ausencia de desplazamiento entre los fragmentos de la fractura radicular, ... respuesta pulpar, solo algunas complicaciones periodontales menores en relación a la invasión del ancho biológico y una adecuado resultado funcional y estético PALABRAS CLAVE: Fractura corono radicular ... presented adequate signs of root fracture healing with partial pulp obliteration in apical fragment, a radiopaque image compatible with hard tissue barrier at site of partial pulpotomy and normality...

Ngày tải lên: 23/03/2014, 13:20

Ngày tải lên: 27/03/2014, 11:48

... the data of A 1 and A1 ∼ ∼ together with inverse equivalences E : A 1 → A1 and F : A1 → A 1 An sl2 categorification results in the additional data of q, a and X ∈ End(E) Z (A1 ) with X − a nilpotent ... Corollary 5.33, there are a finite dimensional k-algebra A, an sl2 -categorification on A = A- mod and a morphism of sl2 -categorifications R : A → A such that the terms of M are direct summands of R (A) ... between K0 (A) and the dual of K0 (A- proj) Remark 5.2 A crucial application will be A = A- mod, where A is a symmetric algebra In that case, the choice of an adjunction (E, F ) determines an adjunction...

Ngày tải lên: 29/03/2014, 07:20

... ˆ 3-by-3 matrix and   1  a a3 a2 where a =  a2  , a1  a ˆ =  a3 a2 a1 a3 then C = S + a , where S = det (A) A 1 S tA−1 and a = tAa Now, I claim that the condition that the Jacobi identity ... computing an integral was known as “quadrature” in the classical literature (a reference to the quadrangles appearing in what we now call Riemann sums), so it was said that (1) was “solvable by quadrature” ... 0 On the other hand, if a = 0, then by a suitable change of basis A, we see that we can assume that a1 = a2 = and that a3 = Any change of basis A which preserves this normalization is seen to...

Ngày tải lên: 31/03/2014, 16:15

... define a linear map AdA : g → g by the formula AdA(X) = AXA−1 We will let Ad denote the map A → AdA Proposition 3.20 Let G be a matrix Lie group, with Lie algebra g Then for each A ∈ G, AdA is an ... Lie algebra is a linear space Thus we can understand much about Lie algebras just by doing linear algebra On the other hand, the Lie algebra of a matrix Lie group contains much information about ... A( t) as a loop, and A( s, t) as a parameterized family of loops which shrinks A( t) to a point Condition 1) says that for each value of the parameter s, we have a loop; condition 2) says that when...

Ngày tải lên: 31/03/2014, 16:18

... 2.2 Lemma Let A = i Ai be a connected graded R-algebra (that is A0 = R) If A+ := i>0 Ai is nitely generated as an A- module, then A is nitely generated as an R-algebra Proof Let a1 : : : an A+ be ... complex case, the image of an algebraic variety under a polynomial map is again an algebraic variety, meaning it is described by polynomial equations only In the real case this is already disproved ... a representation (8) A G-action on M is called a ne if M is an a ne space, and every `g : M ; M is an a ne map ! (9) A G-action on M is called orthogonal if (M ) is a Euclidean vector space and...

Ngày tải lên: 31/03/2014, 16:18

Ngày tải lên: 31/03/2014, 16:18

... nontrivial valuations for the case K = Q The ordinary absolute value ( 1, is an archimedean valuation Also, each prime number p can be associated with a valuation I I,, which we call the p-adic valuation ... groups that a wealth of important material of particular interest to mathematicians in a variety of areas Preface to the Russian Edition Preface to the Russian Edition has been amassed Unfortunately, ... involution Let A be a finite-dimensional (associative) algebra over a field K and let L = Z (A) be the center of A By an involution of A we mean an arbitrary K-linear antiautomorphism T: A + A of order...

Ngày tải lên: 31/03/2014, 16:21