Related papers: Remark on Shape Invariant Potential

The "potentials" being considered are analogues of classical Riesz potentials of order 1, and the idea is to look at how they might map L^p spaces into Sobolev spaces in various settings.

We discuss some new invariants of quark mixing and show their usefulness with a simple example. We also present some other new tools for analyzing quark mixing.

This is a survey of the inverse spectral problem on (mainly compact) Riemannian manifolds, with or without boundary. The emphasis is on wave invariants: on how wave invariants have been calculated and how they have been applied to concrete…

A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.

Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…

Receptive field profiles registered by cell recordings have shown that mammalian vision has developed receptive fields tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time.…

Some inequalities for different types of convexity are established.

In this article, we propose the notion of the general $p$-affine capacity and prove some basic properties for the general $p$-affine capacity, such as affine invariance and monotonicity. The newly proposed general $p$-affine capacity is…

In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of $N=2$ supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we…

We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.

In this paper, we observe a fixed number of unknown $2\pi$-periodic functions differing from each other by both phases and amplitude. This semiparametric model appears in literature under the name "shape invariant model." While the common…

In shape analysis, the concept of shape spaces has always been vague, requiring a case-by-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes in a manifold. This notion…

We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.

We prove that multiple-recurrence and polynomial-recurrence of invertible infinite measure preserving transformations are both properties which pass to extensions.

The procedure proposed recently by J.Bougie, A.Gangopadhyaya and J.V.Mallow to study the general form of shape invariant potentials in one-dimensional Supersymmetric Quantum Mechanics (SUSY QM) is generalized to the case of Higher Order…

In this paper we propose a theory of contact invariants and open string invariants, which are generalizations of the relative invariants. We introduce two moduli spaces $\bar{\mathcal{M}}_{A}(M^{+},C,g,m+\nu,{\bf y},{\bf…

The paper introduces cycles cross ratio, which extends the classic cross ratio of four points to various settings: conformal geometry, Lie spheres geometry, etc. Just like its classic counterpart cycles cross ratio is a measure of…

It is understood now that all projective (and conformal) invariants of Riemannian metrics can be found by a transparent construction based on representation theory. So this article with a partial and quite cumbersome construction of…

In this position paper we suggest a possible metric approach to shape comparison that is based on a mathematical formalization of the concept of observer, seen as a collection of suitable operators acting on a metric space of functions.…

We address the problem of rational extensions of six examples of shape-invariant potentials having finitely many discrete eigenstates. The overshoot eigenfunctions are proposed as candidates unique in this group for the virtual state…