C.-S. Liu, "Exponential function rational expansion method for nonlinear differential-difference equa- tions," Chaos, Solitons and Fractals, vol. 40, no. 2, pp. 708-716, 2009.C.-S. Liu, "Exponential function rational expansion method for nonlinear differential-difference equations," Chaos, ...
When [mu][lambda] < 0, the exponential function solution of system (44) can be expressed as Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the (G'/[G.sup.2])-Expansion Method Among these four models for the road shoulder, the exponential function can...
The Exponential Function 2 GRUNK Never Forgive!Theorem 1 For matrices A,B∈Mn the Taylor expansion of the function t↦eA+tB,t∈R is ∑k=0∞tkAk(1) where A0(s)=esA and Ak(s)=∫0sdt1∫0t1dt2⋯∫0tk−1dtk⋅e(s−t1)A⋅Be(t2−t1)A⋅B⋯BetkA for s∈R. ...
exponential function expansion and homogeneous balance principle method are used to solve the Burgers-BBM equation.Together with transformation skill and Maple symbolic mathematical software,the traveling wave solutions,solitary wave solutions and periodic solutions of trigonometric function of the Burgers-BBM...
By setting up the linear recursion for five expansion coefficients and solving the matrix exponential function exp(i|v→|M5) one arrives at the following quasi-analytical formula for an SU(5) matrix U=exp(iλ→⋅v→)=∑j=15exp(izj|v→|)5zj4−3zj2−2ζzj−ξ{(zj...
From the above pictures, it appears reasonable to assume that a horizontal stretch (either compression or expansion) produces yet another exponential function. To take a concrete example, lets go back to our old friend . This graph can be horizontally compressed by replacingxwith 2x. These two ...
Suppose that we have the exponential integral function3 (12.78) Ei(x)=∫−∞xeuudu, which we find more convenient to write in the form (12.79)− Ei(−x)=∫x∞e−uudu=E1(x), to be evaluated for large values of x. This function has a series expansion that converges for...
So we just need to proof n\|\bm{X}_n-\bm{Y}_n\|\to 0. The power series expansion of exponential function yields \bm{X}_n=\bm{I}+\frac{\bm{A}+\bm{B}}{n}+\frac{1}{2}\bigg(\frac{\bm{A}+\bm{B}}{n}\bigg)^2+\cdots\\ and...
2015a A size expansion analysis using a toy model based on the equivalence between Bondi K-factor and expo nential function. J. Fac. Agr., ... Shimojo,Masataka - 《Journal of the Faculty of Agriculture Kyushu University》 被引量: 0发表: 2015年 Lemaitre-Tolman-Bondi model and accelera...
The value distribution of the Hurwitz zeta function with an irrational shift 51:58 Theta-finite pro-Hermitian vector bundles from loop groups elements 51:02 Torsion points and concurrent lines on Del Pezzo surfaces of degree one 58:59 Applications of optimal transportation in causal inference ...