Displaying similar documents to “An abstract semilinear first order differential equation in the hyperbolic case”

An abstract nonlinear second order differential equation

Jan Bochenek (1991)

Annales Polonici Mathematici

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By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.

Distribution of lattice points on hyperbolic surfaces

Vsevolod F. Lev (1996)

Acta Arithmetica

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Let two lattices Λ ' , Λ ' ' ⊂ ℝ s have the same number of points on each hyperbolic surface | x ₁ . . . x s | = C . We investigate the case when Λ’, Λ” are sublattices of ℤ s of the same prime index and show that then Λ’ and Λ” must coincide up to renumbering the coordinate axes and changing their directions.

The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields

Hourong Qin (1995)

Acta Arithmetica

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1. Introduction. Let F be a number field and O F the ring of its integers. Many results are known about the group K ₂ O F , the tame kernel of F. In particular, many authors have investigated the 2-Sylow subgroup of K ₂ O F . As compared with real quadratic fields, the 2-Sylow subgroups of K ₂ O F for imaginary quadratic fields F are more difficult to deal with. The objective of this paper is to prove a few theorems on the structure of the 2-Sylow subgroups of K ₂ O F for imaginary quadratic fields F. In our Ph.D....

The Lucas congruence for Stirling numbers of the second kind

Roberto Sánchez-Peregrino (2000)

Acta Arithmetica

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0. Introduction. The numbers introduced by Stirling in 1730 in his Methodus differentialis [11], subsequently called “Stirling numbers” of the first and second kind, are of the greatest utility in the calculus of finite differences, in number theory, in the summation of series, in the theory of algorithms, in the calculation of the Bernstein polynomials [9]. In this study, we demonstrate some properties of Stirling numbers of the second kind similar to those satisfied by binomial coefficients;...