相关论文: Remark on Shape Invariant Potential
Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…
In its most general form, the recognition problem in Riemannian geometry asks for the identification of an unknown Riemannian manifold via measurements of metric invariants on the manifold. We introduce a new infinite sequence of…
There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various…
We estimate from above and below the dimension of invariant measure for contracting-on-average iterated function systems in $\R^d$.
The space rotation invariance hypothesis is examined. The basic space-time properties and the physical object description from this point of view are considered. An $\omega$-invariance as an approximation of the space rotation invariance…
A relation between the deformed Hulth\'en potential and the Eckart one is used to write the bound-state wavefunctions of the former in terms of Jacobi polynomials and to calculate their normalization coefficients. The shape invariance…
The goal of this contribution is to discuss various resonance expansions that have been proposed in the literature.
In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.
We provide a variational derivation of the limit shape of minimal difference partitions and discuss the link with exclusion statistics. Also see arXiv:0707.2312 for a related paper.
We discuss various phenomena of tangency in projective and convex geometry.
Some observations on the Wu-Sprung potential.
We generalize the index polynomial invariant to the case of virtual tangles. Three polynomial invariants result from this generalization; we give a brief overview of their definition and some basic properties.
`Shape dynamics' is meant here in the sense of a type of conformogeometrical reformulation of GR, some of which have of late been considered as generalizations of or alternatives to GR. This note concerns in particular cases based on the…
This is a concise overview of the definitions and properties of the linking number and its higher-order generalization, Milnor invariants.
We express the Partial regularities and $a^*$-invariants of a Borel type ideal in terms of its irredundant irreducible decomposition. In addition we consider the behaviours of those invariants under intersections and sums.
We explore the notion of sectional number of a group homomorphism, leading to a generalization of the covering number of a group, and present several characterizations when the sectional number is finite, providing estimates for computing…
In this note we outline the history of q-deformations; indicate their physical shortcomings; suggest their apparent resolution via an invariant formulation based on a new mathematics of genotopic type; and point out their expected physical…
The support of wavelet transform associated with square integrable irreducible representation of a homogeneous space is shown to have infinite measure. Pointwise homogeneous approximation property for wavelet transform has been…
We introduce the concept of protometric and present some properties of protometrics.
Manifestly invariant renormalization scheme for supersymmetric gauge theories is proposed. This scheme is applied to supersymmetric quantum electrodynamics.