Search Results for ""

The system of partial differential equations U_t = [V,W] (1) V_t = [W,U] (2) W_t = [U,V], (3) where [A,B] denotes the commutator.

For b>a>0, 1/b<(lnb-lna)/(b-a)<1/a.

The integral transform defined by (Kphi)(x)=int_0^inftyG_(pq)^(mn)(xt|(a_p); (b_q))phi(t)dt, where G_(pq)^(mn) is a Meijer G-function. Note the lower limit of 0, not -infty ...

The natural domain of a function is the maximal chain of domains on which it can be analytically continued to a single-valued function.

The "natural exponential function" is the name sometimes given in elementary contexts to the function f(x)=e^x, where e =2.718... is the base of the natural logarithm. While ...

Let rho(x)dx be the fraction of time a typical dynamical map orbit spends in the interval [x,x+dx], and let rho(x) be normalized such that int_0^inftyrho(x)dx=1 over the ...

The general equation of fluid flow (lambda+2mu)del (del ·u)-mudel x(del xu)=rho(partial^2u)/(partialt^2), where mu and lambda are coefficients of viscosity, u is the velocity ...

The series which arises in the binomial theorem for negative integer -n, (x+a)^(-n) = sum_(k=0)^(infty)(-n; k)x^ka^(-n-k) (1) = sum_(k=0)^(infty)(-1)^k(n+k-1; k)x^ka^(-n-k) ...

Let f:R->R, then the negative part of f is the function f^-:R->R defined by f^-(x)=max(-f(x),0). Note that the negative part is itself a nonnegative function. The negative ...

The negative real axis is the portion of the real axis with x<0.