We present a new oscillation criterion to determine whether the number of eigenvalues below the essential spectrum of a given Jacobi operator is finite or not. As an application we show that Kenser’s criterion for Jacobi operators follows as a special case.

Let x : M → Sn+1(1) be an n-dimensional compact hypersurface with constant scalar curvature n(n − 1)r, r ≥ 1, in a unit sphere Sn+1(1), n ≥ 5, and let Js be the Jacobi operator of M . In 2004, L. J. Aĺıas, A. Brasil and L. A. M. Sousa studied the first eigenvalue of Js of the hypersurface with constant scalar curvature n(n− 1) in Sn+1(1), n ≥ 3. In 2008, Q.-M. Cheng studied the first eigenvalue...

In general, the value function associated with an exit time problem is a discontin-uous function. We prove that the lower (upper) semicontinuous envelope of the value function is a supersolution (subsolution) of the Hamilton-Jacobi equation involving the proximal subdiierentials (superdiierentials) with subdiierential type (superdiierential type) mixed boundary condition. We also show that if t...

This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y 2 D dX C Z. We improve the doubling and addition steps in Miller’s algorithm to compute the Tate pairing. We use the birational equivalence between Jacobi quartic curves and Weierstrass curves, together with a specific point representation to obtain the best res...

| In a note at the end of his paper Recherches sur les fractions continues, Stieltjes gave a necessary and suucient condition when a continued fraction is represented by a meromorphic function. This result is related to the study of compact Jacobi matrices. We indicate how this notion was developped and used since Stieltjes, with special attention to the results by M. G. Krein. We also pay atte...

A lifting map from cuspidal automorphic representations of the Jacobi group G J to cuspidal auto-morphic representations of the group PGL(2) is constructed. The lifting also has a local deenition, and the local and global versions are compatible. The local lifts can be described in terms of equivalence classes of local representations. The main idea in the construction is to exploit the close r...