Related papers: On the relation between Dyer-Lashof algebra and th…
Existence and spatio-temporal symmetric patterns of periodic solutions to second order reversible equivariant non-autonomous periodic systems with multiple delays are studied under the Hartman-Nagumo growth conditions. The method is based…
We solve the Killing-Yano equation on manifolds with a $G$-structure for $G=SO(n), U(n), SU(n), Sp(n)\cdot Sp(1), Sp(n), G_2$ and $Spin(7)$. Solutions include nearly-K\"ahler, weak holonomy $G_2$, balanced SU(n) and holonomy $G$ manifolds.…
After a review of the arrows of time, we describe the possibilities of a time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is time-symmetric, the rigged Hilbert space formulation, which arose from Dirac's bra-ket…
We develop a general scheme to construct integrable systems starting from realizations in symmetric coboundary dynamical Lie algebroids and symmetric coboundary Poisson groupoids. The method is based on the successive use of Dirac reduction…
We classify the existent Birkhoff-type theorems into four classes: First, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement…
For $\Gamma$ a cocompact or cofinite Fuchsian group, we study the hyperbolic lattice point problem in conjugacy classes, which is a modification of the classical hyperbolic lattice point problem. We use large sieve inequalities for the…
We present a novel approach to establish the Birkhoff's theorem validity in the so-called quadratic Poincar\'e Gauge theories of gravity. By obtaining the field equations via the Palatini formalism, we find paradigmatic scenarios where the…
Current searches for signals of departures from the fundamental symmetries of General Relativity using gravitational waves are largely dominated by propagation effects like dispersion and birefringence from highly dynamic sources such as…
This work outlines a time-domain numerical integration technique for linear hyperbolic partial differential equations sourced by distributions (Dirac $\delta$-functions and their derivatives). Such problems arise when studying binary black…
The properties of zero modes in particle-hole symmetric systems are analyzed in the presence of strong random scattering by a disordered environment. The study is based on the calculation of the time-averaged density distribution on a…
The aim of this paper is to continue the research of JMP 46, 042501 (2005) of regular static spherically symmetric spacetimes in Einstein-Born-Infeld theories from the point of view of the spacetime geometry and the electromagnetic…
We initiate the study of the spherically symmetric Einstein-Klein-Gordon system in the presence of a negative cosmological constant, a model appearing frequently in the context of high-energy physics. Due to the lack of global hyperbolicity…
The description of symmetry breaking proposed by K. Symanzik within the framework of renormalizable theories is generalized from the geometrical point of view. For an arbitrary compact Lie group, a soft breaking of arbitrary covariance, and…
The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…
The relevance of parity and time reversal (PT)-symmetric structures in optical systems is known for sometime with the correspondence existing between the Schrodinger equation and the paraxial equation of diffraction where the time parameter…
We study the spontaneous temporal symmetry breaking instability in a coherently-driven passive optical Kerr resonator observed experimentally by Xu and Coen in Opt.~Lett.~{\bf 39}, 3492 (2014). We perform a detailed stability analysis of…
The stationary Schr\"odinger equation can be cast in the form $H \rho = E \rho$, where $H$ is the system's Hamiltonian and $\rho$ is the system's density matrix. We explore the merits of this form of the stationary Schr\"odinger equation,…
Assuming SO(3)-spherical symmetry, the 4-dimensional Einstein equation reduces to an equation conformally related to the field equation for 2-dimensional gravity following from the Lagrangian L = R^(1/3). Solutions for 2-dimensional gravity…
It is frequently the case that a white-noise-driven parabolic and/or hyperbolic stochastic partial differential equation (SPDE) can have random-field solutions only in spatial dimension one. Here we show that in many cases, where the…
The hyperbolic model (HM) time integration scheme tackles parabolic problems by adding a small artificial second order time derivative term. Described by Samarskii in his 1971 book, the scheme reappeared as the generalized Du Fort-Frankel…