相关论文: On Timelike slant helices in $S_{1}^{2}$

In this paper, we investigate special curves on a strong r-helix submanifold in Euclidean n-space E n. Also, we give the important relations between strong r-helix submanifolds and the special curves such as line of curvature, geodesic and…

We give a sup $\times$ inf inequality for an elliptic equation.

Here we derive some results on so called quantitative Runge approximation in the case of the time-harmonic Maxwell equations. This provides a Runge approximation having more explicit quantitative information. We additionally derive some…

We show, how the Riemann-Hilbert approach to the elastodynamic equations, which have been suggested in our preceding papers, works in the half-plane case. We pay a special attention to the appearance of the Rayleigh waves within the scheme.

We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, one which acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian…

We attack the specific time-dependent Hamiltonian problem H=-{1/2} (t_o/t)^a \partial_{xx} + (1/2) \omega^2 (t/t_o)^b x^2. This corresponds to a time-dependent mass (TM) Schr\"odinger equation. We give the specific transformations to a…

We discuss the geometry of timelike surfaces (two-dimensional submanifolds) in a Lorentzian manifold and its interpretation in terms of general relativity. A classification of such surfaces is presented which distinguishes four cases of…

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…

We show that two non-isometric, smooth, globally hyperbolic Lorentzian metrics can have the same hyperbolic Dirichlet-to-Neumann map on an infinite cylinder with timelike boundary.

In this article, we study the local existence of solutions for a wave equation with a nonlocal in time nonlinearity. Moreover, a blow-up results are proved under some conditions on the dimensional space, the initial data and the nonlinear…

This is a note on \cite{LSU} and \cite{FS}. Using their work line by line, we prove the H\"older-continuity of solutions to linear parabolic equations of mixed type, assuming the coefficient of $\frac{\partial}{\partial t}$ has…

Parasupersymmetry of the one dimensional time-dependent Schr\"odinger equation is established. It is intimately connected with a chain of the time-dependent Darboux transformations. As an example a parasupersymmetric model of…

In this article we consider variable coefficient, time-dependent wave equations. Using phase space methods we construct outgoing parametrices and prove Strichartz-type estimates globally in time. This is done in the context of C^2 metrics…

A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…

I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent…

This series of works revisits the geometry, dynamics, and covariant phase space of spherically symmetric spacetimes with the aim of exploring the thermodynamics of spacetime from their dynamical properties. In this first paper, we examine…

In this paper, we define a new kind of slant helix called f-eikonal V_{n}-slant helix in Pseudo- Riemannian manifolds and give the definition of harmonic curvature functions related to the f-eikonal V_{n}-slant helix in Pseudo- Riemannian…

Consider a spherically symmetric spacelike slice through a spherically symmetric spacetime. One can derive a universal bound for the optical scalars on any such slice. The only requirement is that the matter sources satisfy the dominant…

Homoclinic and heteroclinic motions in dynamics equations on time scales is investigated. The utilized time scale is a specific one such that it is a union of disjoint compact intervals. A numerical example that supports the theoretical…

We study Lie point symmetry structure of generalized nonlinear wave equations in the $(n+1)$-dimensional space-time.