A prime geodesic theorem for regular geodesics in a higher rank locally symmetric space is proved. An application to class numbers is given. The proof relies on a Lefschetz formula for higher rank torus actions.

In this paper, we present an abstract framework which describes algebraically the derivation of order conditions independently of the nature of differential equations considered or the type of integrators used to solve them. Our structure includes a Hopf algebra of functions, whose properties are used to answer several questions of prime interest in numerical analysis. In particular, we show th...

Let M be a 2 and 3-torsion free prime Γ-ring, d a nonzero derivation on M and U a nonzero Lie ideal of M . In this paper it is proved that U is a central Lie ideal of M if d satisfies one of the following (i) d(U) ⊂ Z, (ii) d(U) ⊂ U and d(U) = 0, (iii) d(U) ⊂ U , d(U) ⊂ Z.

The prime geodesic theorem for regular geodesics in a higher rank locally symmetric space is proved. An application to class numbers is given. The proof relies on a Lefschetz formula that is based on work of Andreas Juhl.

the aim of this paper is to show that under some mild conditions a functional equation of multiplicative (; )-derivation is superstable on standard operator algebras. furthermore, we prove that this generalized derivation can be a continuous and an inner (; )- derivation.

The celebrated Weil bound for character sums says that for any low-degree polynomial P and any additive character χ, either χ(P ) is a constant function or it is distributed close to uniform. The goal of higher-order Fourier analysis is to understand the connection between the algebraic and analytic properties of polynomials (and functions, generally) at a more detailed level. For instance, wha...

Model checking of recursion schemes, known as higher-order model checking, has actively been studied recently and is becoming a basis for verification of higher-order programs. Some practical model checking algorithms have been developed based on the reduction from model checking to intersection type inference, but they are not completely satisfactory. We propose a novel approach to developing ...

We extend an existing first-order typing system for strictness analysis to the fully higher-order case, covering both the derivation system and the inference algorithm. The resulting strictness typing system has expressive capabilities far beyond that of traditional strictness analysis systems. This extension is developed with the explicit aim of formally proving soundness of higher-order stric...

A procedure for loading particle velocities from a relativistic kappa distribution in particle-in-cell (PIC) and Monte Carlo simulations is presented. It based on the rejection method beta prime distribution. The part extends earlier Maxwell-Juttner distribution, then acceptance rate reaches ~95%. Utilizing generalized distributions, we successfully reproduce including power-law tail. derivatio...