To investigate and understand basic properties of non-radial solar p-modes with high wave numbers l, it is sufficient to consider only the outer layers of the sun. As an atmosphere, the upper part of the convection zone may be approximated by a plane layer with constant gravity. A simple standard model is a polytropic convection zone with an overlying isothermal atmosphere. In this case, the ad...

Remarkably simple closed-form expressions for the elements of the groups SU(n), SL(n,R), and SL(n,C) with n = 2, 3, and 4 are obtained using linear functions of biquaternions instead of n × n matrices. These representations do not directly generalize to SU(n > 4). However, the quaternion methods used are sufficiently general to find applications in quantum chromodynamics and other problems whic...

In the present paper, we first prove the logarithmic convexity of the elementary function b x −a x x , where x 6= 0 and b > a > 0. Basing on this, we then provide a simple proof for Schur-convex properties of the extended mean values, and, finally, discover some convexity related to the extended mean values.

In the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(S) is the dual of a function algebra.

This article describes the first cycle of a multiyear research project aimed at establishing a common ground between educationally relevant psychological research and educational practice. We translated a theoretically motivated, carefully crafted, and laboratory-based instructional procedure of proven effectiveness into a classroom intervention, making minimal modifications to the instructiona...

In a diffusion model of risk, we focus on the initial capital needed to make the probability of ruin within finite time equal to a prescribed value. It is defined as a solution of a nonlinear equation. The endeavor to write down and to investigate analytically this solution as a function of the premium rate seems not technically feasible. Instead, we obtain informative bounds for this capital i...

An extension of the ideas of the Prelle-Singer procedure to second order differential equations is proposed. As in the original PS procedure, this version of our method deals with differential equations of the form y ′′ = M (x, y, y ′)/N (x, y, y ′), where M and N are polynomials with coefficients in the field of complex numbers C. The key to our approach is to focus not on the final solution b...

We consider predicative type-abstraction disciplines based on type quantification with finitely stratified levels. The main technical result is that the functions representable in the finitely stratified polymorphic A-calculus are precisely the super-elementary functions, i.e. the class £4 in Grzegorczyk's subrecursive hierarchy. This implies that there is no super-elementary bound on the lengt...

In this paper we give some background theory on the concept of fractional calculus, in particular the Riemann-Liouville operators. We then investigate the Taylor-Riemann series using Osler’s theorem and obtain certain double infinite series expansions of some elementary functions. In the process of this we give a proof of the convergence of an alternative form of Heaviside’s series. A Semi-Tayl...