Search Results for ""

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called hyperbolic if the matrix Z=[A B; B C] (2) ...

The even impulse pair is the Fourier transform of cos(pik), AdjustmentBox[I, BoxMargins -> {{0.13913, -0.13913}, {-0.5, 0.5}}]I(x)=1/2delta(x+1/2)+1/2delta(x-1/2). (1) It ...

Given a function of two variables df = (partialf)/(partialx)dx+(partialf)/(partialy)dy (1) = udx+vdy, (2) change the differentials from dx and dy to du and dy with the ...

The Lie derivative of tensor T_(ab) with respect to the vector field X is defined by L_XT_(ab)=lim_(deltax->0)(T_(ab)^'(x^')-T_(ab)(x))/(deltax). (1) Explicitly, it is given ...

The log-series distribution, also sometimes called the logarithmic distribution (although this work reserves that term for a distinct distribution), is the distribution of ...

The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed ...

A triangular matrix L of the form L_(ij)={a_(ij) for i>=j; 0 for i<j. (1) Written explicitly, L=[a_(11) 0 ... 0; a_(21) a_(22) ... 0; | | ... 0; a_(n1) a_(n2) ... a_(nn)]. ...

Given a complete graph K_n which is two-colored, the number of forced monochromatic triangles is at least {1/3u(u-1)(u-2) for n=2u; 2/3u(u-1)(4u+1) for n=4u+1; ...

The natural parametric equations of a curve are parametric equations that represent the curve in terms of a coordinate-independent parameter, generally arc length s, instead ...

Every irrational number x can be expanded in a unique continued fraction expansion x=b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...)))=[b_0;e_1b_1,e_2b_2,e_3b_3,...] such that b_0 ...