and Applied Analysis 3 Equation (3) has a unique positive equilibrium given by y = 1 + p − z + √(1 + p − z) 2 + 4r (q + 1) 2 (q + 1) . (19) The linearized equation associated with (3) about the equilibrium is given by

In this paper, we use the Mellin-Barnes-Watson method to relate solutions of a certain type $q$-difference equations at $Q=0$ and $Q=\infty$. We consider two special cases; first is equation $K$-theoretic $I$-function quintic, which degree 25; Adams' find extra 20 $Q=0$. The second case fuchsian case, confluent differential cohomological quintic. compute connection matrix study confluence struc...

Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is n...

Exact solutions of the Nizhnik-Novikov-Veselov equation by Li [New kink-shaped solutions and periodic wave solutions for the (2+1)-dimensional Sine-Gordon equation, Appl. Math. Comput. 215 (2009). 3777-3781 ] are analyzed. We have observed that fourteen solutions by Li from thirty do not satisfy the equation. The other sixteen exact solutions by Li can be found from the general solutions of the...

1. Poisson Equation 1 2. Outline of Topics 3 2.1. Finite Difference Method 3 2.2. Finite Element Method 3 2.3. Finite Volume Method 3 2.4. Sobolev Spaces and Theory on Elliptic Equations 3 2.5. Iterative Methods: Conjugate Gradient and Multigrid Methods 3 2.6. Nonlinear Elliptic Equations 3 2.7. Fast Multiple Method 3 3. Physical Examples 4 3.1. Gauss’ law and Newtonian gravity 4 3.2. Electrost...

1. January 3rd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. Example 1: The Ohsawa–Takegoshi Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. Example 2: The Hörmander(-Skoda) Theorem . . . . . . ...