A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly...

It is shown that central elements in G. Letzter’s quantum group analogs of symmetric pairs lead to solutions of the reflection equation. This clarifies the relation between Letzter’s approach to quantum symmetric pairs and the approach taken by M. Noumi, T. Sugitani, and M. Dijkhuizen. We develop general tools to show that a Noumi-Sugitani-Dijkhuizen type construction of quantum symmetric pairs...

Extension of the fractional diffusion equation to two or three dimensions is not as simple as extension of the second-order equation. This is revealed by the solutions of the equations: unlike the Gaussian, the most general stable vector cannot be generated with an atomistic measure on the coordinate axes. A random combination of maximally skewed stable variables on the unit sphere generates a ...

Symmetric teleparallel gravity theories, in which the gravitational interaction is attributed to nonmetricity of a flat, symmetric, but not metric-compatible affine connection, have been topic growing interest recent studies. Numerous works study cosmology symmetric assuming flat Friedmann-Lema\^itre-Robertson-Walker metric, while working so-called "coincident gauge", further that connection co...

We show that under particular circumstances a general relativistic spherically symmetric bounded distribution of matter could satisfy a nonlocal equation of state. This equation relates, at a given point, the components of the corresponding energy momentum tensor not only as function at that point, but as a functional throughout the enclosed configuration. We have found that these types of dyna...

In this paper, the general case of an anisotropic thermo-electro elastic body subjected to static biasing fields is considered. The biasing fields may be introduced by heat flux, body forces, external surface tractions, and electric fields. By introducing proper thermodynamic functions and employing variational principle for a thermo-electro elastic body, the nonlinear constitutive relations an...

We study odd parity perturbations of spherically symmetric black holes with time-dependent scalar hair in shift-symmetric higher-order scalar-tensor theories. The analysis is performed a general way without assuming the degeneracy conditions. Nevertheless, we end up second-order equations for single master variable, similarly to cosmological tensor modes. thus identify form quadratic Lagrangian...

The Lemaître-Tolman-Bondi (LTB) model represents an inhomogeneous spherically symmetric universefilledwithfreelyfallingdustlikematterwithoutpressure. First,wehaveconsideredaFinslerian anstaz of (LTB) and have found a Finslerian exact solution of vacuum field equation. We have obtained the R(t,r) and S(t,r) with considering establish a new solution of Rµν = 0. Moreover, we attempttouseFinslergeo...

This paper suggests a closed-form solution of particular case of an algebraic Riccati equation and its application example to optimal and smooth motion planning for a given linear quadratic performance index. Actually, the algebraic Riccati equation can be changed into Moser-Veselov equation by deriving both symmetric and skew-symmetric conditions from an algebraic Riccati equation itself. Also...