In the present paper we start the systematic explicit construction of invariant differential operators by giving explicit description of one of the main ingredients the cuspidal parabolic subalgebras. We explicate also the maximal parabolic subalgebras, since these are also important even when they are not cuspidal. Our approach is easily generalised to the supersymmetric and quantum group sett...

Recently, findings of lowered serum testosterone levels and other hypogonadal symptoms have been reported in endurance trained males",2. The mechanisms of these changes have been proposed to be similar to those put forth for females experiencing athletic amenorrhoea, a disruption of the hypothalamic-pituitary-gonadal axis. In preliminary findings, we have found a relationship between changes in...

We characterize certain maximal curves over finite fields whose plane models are of Hurwitz type, namely xy +y +x = 0. We also consider maximal hyperelliptic curves of maximal genus. Finally, we discuss maximal curves of type y + y = x via Class Field Theory.

The theory of (Muckenhoupt) weights arises in many areas of analysis, for example in connection with bounds for singular integrals and maximal functions on weighted spaces. We prove that a certain averaging process gives a method for constructing Ap weights from a measurably varying family of dyadic Ap weights. This averaging process is suggested by the relationship between the Ap weight class ...

In this paper, we investigate the relationship between comonotonicity and stoploss order. We prove our main results by using a characterization of stop-loss order within the framework of Yaari’s (1987) dual theory of choice under risk. Wang and Dhaene (1997) explore related problems in the case of bivariate random variables. We extend their work to an arbitrary sum of random variables and prese...

We study some topological properties of maximal ideal spaces of certain algebras of almost periodic functions. Our main result is that such spaces are contractible. We present several analytic corollaries of this result. MSC: 42A75; 46J10

We study two-dimensional triangular systems of Newton equations (acceleration = velocity-independent force) admitting three functionally independent quadratic integrals of motion. The main idea is to exploit the fact that the first component M1(q1) of a triangular force depends on one variable only. By using the existence of extra integrals of motion we reduce the problem to solving a simultane...

We propose a method by modulus of curve families to identify extremal quasiconformal mappings in the Heisenberg group. This approach allows to study minimizers not only for the maximal distortion but also for a mean distortion functional, where the candidate for the extremal map is not required to have constant distortion. As a counterpart of a classical Euclidean extremal problem, we consider ...

For a family of weight functions, hκ, invariant under a finite reflection group on R, analysis related to the Dunkl transform is carried out for the weighted L spaces. Making use of the generalized translation operator and the weighted convolution, we study the summability of the inverse Dunkl transform, including as examples the Poisson integrals and the Bochner-Riesz means. We also define a m...

Weighted L for p ∈ 1,∞ and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. Al...