Of special interest are those Lamé equations with finite monodromy group, having therefore algebraic solutions, studied by Baldassarri, Beukers and van der Waall, Chudnovsky and Chudnovsky, Dwork and many others (cf. [2], [4], [8] just to mention some papers). Lamé equations also occur in the context of Grothendieck’s p-curvature conjecture (cf. [8, p. 15]). This conjecture says that if the p-c...

let h be an infinite--dimensional hilbert space and k(h) be the set of all compact operators on h. we will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher jordan derivation on k(h) associated with the following cauchy-jencen type functional equation 2f(frac{t+s}{2}+r)=f(t)+f(s)+2f(r) for all t,s,rin k(h).

The aim of this note is to offer hyperstability results for linear functional equations of the form f(s) + f(t) = 1 n n ∑ i=1 f(sφi(t)) (s, t ∈ S), where S is a semigroup and where φ1, . . . , φn : S → S are pairwise distinct automorphisms of S such that the set {φ1, . . . , φn} is a group equipped with the composition as the group operation. The main results state that if f satisfies a stabili...

‎the object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎at first we prove that a quasi-conformally flat spacetime is einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎einstein's field equation with cosmological constant is covariant constant‎. ‎next‎, ‎we prove that if the perfect...

The purpose of this paper is twofold. First we derive theoretically, using appropriate transformation on x(n), the closed-form solution of the nonlinear difference equation x(n+1) = 1/(±1 + x(n)), n ∈ N_0. The form of solution of this equation, however, was first obtained in [10] but through induction principle. Then, with the solution of the above equation at hand, we prove a case ...

We construct multiplicative Green?s (or +Green?s) function for *Sturm-Liouville (*SL) equation. The basic properties of *Green?s are given. Then, *SL equation is evaluated by using function. Effectiveness in *case will thus be seen some examples.

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

Associated to a newform f (z) is a Dirichlet series L f (s) with functional equation and Euler product. Hecke showed that if the Dirichlet series F (s) has a functional equation of the appropriate form, then F (s) = L f (s) for some holomorphic newform f (z) on Γ(1). Weil extended this result to Γ 0 (N) under an assumption on the twists of F (s) by Dirichlet characters. We show that, at least f...

Exponentially localized solutions of the Klein-Gordon equation for two and three space variables are presented. The solutions depend on four free parameters. For some relations between the parameters, the solutions describe wave packets filled with oscillations whose amplitudes decrease in the Gaussian way with distance from a point running with group velocity along a straight line. The solutio...