相关论文: Remark on Shape Invariant Potential

The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.

$P$-values have been the focus of considerable criticism based on various considerations. Still, the $P$-value represents one of the most commonly used statistical tools. When assessing the suitability of a single hypothesized distribution,…

This work is an extension of the incomplete probability theory from the simple case of monofractals previously studied to the more general case of multifractals which can occur in the phase space without equiprobable partition.

In gauge theories, the mass of a field has been regarded as a purely on-shell concept: the pole mass is gauge-invariant, but the off-shell propagator has had no gauge-invariant definition of mass. We show that renormalization defines a…

In this paper we define the bi-orthogonal sectional curvature and we present two modified Yamabe invariants for compact 4-dimensional manifolds. In particular we obtained a relationship between one of these invariants and a Hopf conjecture.

A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…

We concur with de Castro's observation that the gauge considerations of our approach are not valid. Nevertheless, except for an error that will be corrected, all of our findings are accurate independent of those considerations.

In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be an invariant submanifold.In this case, we…

We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…

We give a new formula for the values of an irreducible character of the symmetric group S_n indexed by a partition of rectangular shape. Some observations and a conjecture are given concerning a generalization to arbitrary shapes.

We extend the classical Copson's inequalities so that the values of parameters involved go beyond what is currently known.

We consider each of the three classes of representations of cyclic groups that arise in the study of rational sphere maps. We study the possible number of terms for invariant polynomials with non-negative coefficients that are constant on…

In this paper, we study multivariate vector sampling expansions on general finitely generated shift-invariant subspaces. Necessary and sufficient conditions for a multivariate vector sampling theorem to hold are given.

We formulate and study the set of coupled nonlinear differential equations which define a series of shape invariant potentials which repeats after a cycle of $p$ iterations. These cyclic shape invariant potentials enlarge the limited…

This brief survey of some singularity invariants related to Milnor fibers should serve as a quick guide to references. We attempt to place things into a wide geometric context while leaving technicalities aside. We focus on relations among…

A purely imaginary potential can provide a phenomenological description of creation and absorption of quantum mechanical particles. PT-invariance of such a potential ensures that the non-unitary phenomena occur in a balanced manner. In…

We introduce the concept of constructible ideal and we relate this concept with the notion of constructible simplicial complex. Several properties of constructible ideals are studied.

This paper introduces a notion of integrality that is suitable for non-commutative varieties. It is compatible with the usual notion of integrality for schemes. The function field and generic point of a non-commutative integral space are…

The relationship between various methods to calculate the physical degrees of freedom for gauge invariant systems of a general form is established. The set of hidden parameters caused for the superfluous degrees of freedom is revealed.

This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.