Super W-Symmetries, Covariantly Constant Forms And Duality Transformations

On a supersymmetric sigma model the covariantly constant forms are related to the conserved currents that are generators of a super W-algebra extending the superconformal algebra. The existence of covariantly constant forms restricts the holonomy group of the manifold. Via duality transformation we get new covariantly constant forms, thus restricting the holonomy group of the new manifold.Comment: 10 pages, Late

Unit-sphere preserving mappings

We prove that if a one-to-one mapping f : (n ≥ 2) preserves the unit n - 1 spheres (Sn -1), then f is a linear isometry up to translation

Bessel's Differential Equation and Its Hyers-Ulam Stability

We solve the inhomogeneous Bessel differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Bessel differential equation

The Nonlinear Multiplet Revisited

Using a reformulation of the nonlinear multiplet as a gauge multiplet, we discuss its dynamics. We show that the nonlinear ``duality'' that appears to relate the model to a conventional $\sigma$-model introduces a new sector into the theory.Comment: 11 pages, ITP-SB-94-23, USITP-94-1

Complex Structures, Duality, and WZW-Models in Extended Superspace

We find the complex structure on the dual of a complex target space. For $N=(2,2)$ systems, we prove that the space orthogonal to the kernel of the commutator of the left and right complex structures is {\em always} integrable, and hence the kernel is parametrized by chiral and twisted chiral superfield coordinates. We then analyze the particular case of $SU(2)\times SU(2)$, and are led to a new $N=2$ superspace formulation of the $SU(2)\times U(1)$ WZW-model.Comment: Latex, 16 pages. In this revised manuscript, we add a section and an author, and alter one of the conclusions of the pape

MAPPINGS PRESERVING REGULAR HEXAHEDRONS

We will prove that if a one-to-one mapping f : R 3 → R 3 preserves regular hexahedrons, then f is a linear isometry up to translation

Simple Harmonic Oscillator Equation and Its Hyers-Ulam Stability

We solve the inhomogeneous simple harmonic oscillator equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the simple harmonic oscillator equation

Perturbation of One-Dimensional Time-Independent Schrödinger Equation with a Near-Hyperbolic Potential

The authors have recently investigated a type of Hyers–Ulam stability of one-dimensional time-independent Schrödinger equation with a symmetric parabolic potential wall. In this paper, we investigate a type of Hyers–Ulam stability of the Schrödinger equation with a near-hyperbolic potential

Perturbation of One-Dimensional Time-Independent Schrödinger Equation with a Near-Hyperbolic Potential

The authors have recently investigated a type of Hyers–Ulam stability of one-dimensional time-independent Schrödinger equation with a symmetric parabolic potential wall. In this paper, we investigate a type of Hyers–Ulam stability of the Schrödinger equation with a near-hyperbolic potential