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A linear congruence equation ax=b (mod m) (1) is solvable iff the congruence b=0 (mod d) (2) with d=GCD(a,m) is the greatest common divisor is solvable. Let one solution to ...

The n functions f_1(x), f_2(x), ..., f_n(x) are linearly dependent if, for some c_1, c_2, ..., c_n in R not all zero, sum_(i=1)^nc_if_i(x)=0 (1) for all x in some interval I. ...

States that for a nondissipative Hamiltonian system, phase space density (the area between phase space contours) is constant. This requires that, given a small time increment ...

The term "lobster" is used to refer either to a particular polyiamond or to a class of tree called a lobster graph. When referring to polyiamonds, the lobster is the ...

By analogy with the log sine function, define the log cosine function by C_n=int_0^(pi/2)[ln(cosx)]^ndx. (1) The first few cases are given by C_1 = -1/2piln2 (2) C_2 = ...

The continuous distribution with parameters m and b>0 having probability and distribution functions P(x) = (e^(-(x-m)/b))/(b[1+e^(-(x-m)/b)]^2) (1) D(x) = 1/(1+e^(-(x-m)/b)) ...

The term "loop" has a number of meanings in mathematics. Most simply, a loop is a closed curve whose initial and final points coincide in a fixed point p known as the ...

The Lorentzian function is the singly peaked function given by L(x)=1/pi(1/2Gamma)/((x-x_0)^2+(1/2Gamma)^2), (1) where x_0 is the center and Gamma is a parameter specifying ...

The radical circle of the Lucas circles is the circumcircle of the Lucas tangents triangle. Its center has trilinear center function alpha_(1151)=2cosA+sinA (1) corresponding ...

A Lucas polynomial sequence is a pair of generalized polynomials which generalize the Lucas sequence to polynomials is given by W_n^k(x) = ...