Based on a q-deformation of the kinematical algebra C 1 (S 1) +Vect(S 1) a q-analog to the Borel quantization on S 1 is constructed. The resulting momentum operator is given in terms of q-derivatives. Via a generalized version of the Ehrenfest theorem it leads, together with the position operator, to a nonlinear q-diierence equation on the N-point discretization S 1 N of S 1. In the limit q ! 1...

4 Phenomenologi al Equation Closure. 7 4 1 Examples 8 Example: River Flow 8 Quasi-equilibrium approximation 8 Example: TraÆ Flow 9 Example: Heat Condu tion 10 Fi k's Law 10 Thermal ondu tivity, difusivity, heat equation 10 Example: Granular Flow 11 Example: Invis id Fluid Flow 12 In ompressible Euler Equations 12 In ompressible Navier-Stokes Equations 12 Gas Dynami s 13 Equation of State 13 Ise...

[This document is http://www.math.umn.edu/ ̃garrett/m/complex/notes 2014-15/09c Riemann and zeta.pdf] 1. Riemann’s explicit formula 2. Analytic continuation and functional equation of ζ(s) 3. Appendix: Perron identity [Riemann 1859] exhibited a precise relationship between primes and zeros of ζ(s). A similar idea applies to any zeta or L-function with analytic continuation, functional equation, ...

We discuss magnetoexcitons dispersion in single and coupled GaAs − (Ga,Al)As quantum wells using the Bethe-Salpeter (B-S) formalism. The B-S formalism in the case of quantum wells provides an equation for the exciton wave function which depends on two space variables plus the time variable, i.e. the B-S equation is 2 + 1-dimensional equation. We compare the results for magnetoexcitons dispersio...

where  < λ < n,  < β + λ < n, and p,q, r ≥  satisfying p + q + r = (n – λ – β)/λ. Recently, there has been tremendous interest in studying integral systems. Because the integral equation(s) not only formulate abstractly many laws and relations in science, engineering, economics, and other fields of applied science, but also they provide a special technique to investigate the global propert...

in the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(p,q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}a_{l}xb_{l}+overset{v} ‎{underset{s=1}{sum}}c_{s}widetilde{x}d_{s}=f$‎. ‎by this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎when the‎ ‎matrix equation is consistent over...

in this paper, an iterative method is proposed for solving large general sylvester matrix equation $axb+cxd = e$, where $a in r^{ntimes n}$ , $c in r^{ntimes n}$ , $b in r^{stimes s}$ and  $d in r^{stimes s}$ are given matrices and $x in r^{stimes s}$  is the unknown matrix. we present a global conjugate gradient (gl-cg) algo- rithm for solving linear system of equations with multiple right-han...

ABSTRACT. With S a linearly ordered set with the least upper bound property, with g a nonincreasing real-valued function on S, and with A a densely denned dissipative linear operator, an evolution system M is developed to solve the modified Stieljes integral equation M(s, i)x = x + A((L)[sdgM(-, t)x). An affine version of this equation is also considered. Under the hypothesis that the evolufion...

Oscillation properties of solutions of the forced second order linear difference equation ∆(rk∆xk) + ckxk+1 = hk are investigated. The authors show that if the forcing term h does not oscillate, in some sense, too rapidly, then the oscillation of the unforced equation implies oscillation of the forced equation. Some results illustrating this statement and extensions to the more general half-lin...

We establish the local well-posedness in H(S) with any s > 72 for a modified Camassa-Holm equation derived as the EPDiff equation with respect to the H(S) metric, and obtain the global existence of the weak solution in H(S) under some sign assumption on the initial values and prove the convergence of the corresponding finite particle approximation method.