Related papers: Calculation of a weak nonleptonic matrix element u…
We consider a pentadiagonal matrix which will be described in the text. We demonstrate practical methods for obtaining weak coupling expressions for the lowest eigenvector in terms of the parameters in the matrix, v and w. It is found that…
Let $\gamma$ denote imaginary parts of complex zeros of the Riemann zeta-function $\zeta(s)$. Certain sums over the $\gamma$'s are evaluated, by using the function $G(s) = \sum_{\gamma>0}\gamma^{-s}$ and other techniques. Some integrals…
Let $R$ be an associative ring and $e,f$ idempotent elements of $R$. In this paper we introduce the notion of $(e,f)$-invertibility for an element of $R$ and use it to define inner actions of weak Hopf algebras. Given a weak Hopf algebra…
We propose an algorithm for calculating matrix elements of the non-linear Boltzmann equation collision integral in isotropic case. These matrix elements are used as starting ones in the recurrence procedure for calculating the matrix…
A model of symmetry violation is described for a system that can spontaneously choose the left-handed or right-handed character of weak currents. For the hierarchic structure of fermion mass spectra, such a mirror symmetry system allows…
Modular symmetries offer a dynamic approach to understanding the flavour structure of leptonic mixing. Using the modular $\mathcal{A}_4$ flavour symmetry integrated in a type-II seesaw, we propose a simple and minimalistic model that…
An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we…
Weighted singular value decomposition (WSVD) of a quaternion matrix and with its help determinantal representations of the quaternion weighted Moore-Penrose inverse have been derived recently by the author. In this paper, using these…
Vibrational spectra can be computed without storing full-dimensional vectors by using low-rank sum-of-products (SOP) basis functions. We introduce symmetry constraints in the SOP basis functions to make it possible to separately calculate…
In recent years weak values have been used to explore interesting quantum features in novel ways. In particular, the real part of the weak value of the momentum operator has been widely studied, mainly in connection with (nonlocal) Bohmian…
We offer a simple method Monte Carlo for computation of Volterra's and spherical type multiple integrals with weak (integrable) singularities. An elimination of infinity of variance is achieved by incorporating singularities in the density,…
We prove a weak error estimate for the approximation in space and time of a semilinear stochastic Volterra integro-differential equation driven by additive space-time Gaussian noise. We treat this equation in an abstract framework, in which…
We characterize a value of an observable by a `sum rule' for generally non-commuting observables and a `product rule' when restricted to a maximal commuting subalgebra of observables together with the requirement that the value is unity for…
We compute scalar products and norms of Bethe vectors in the massless sector of AdS_3 integrable superstring theories, by exploiting the general difference form of the S-matrix of massless excitations in the pure Ramond-Ramond case, and the…
In this paper we study the Rotor Model of Martins and Nienhuis. After introducing spectral parameters, a combined use of integrability, polynomiality of the ground state wave function and a mapping into the fully-packed O(1)-model allows us…
This paper considers a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form $\mathscr{X}(x,|\vec E(x)|^2)\vec E(x)$, $\mathscr{Y}(x,|\vec H(x)|^2)\vec H(x)$, such that $\mathscr{X}(x,s)$,…
We derive spectral sum rules for inverse powers of the eigenvalues of the Helmholtz equation on a $d$-sphere in the presence of an arbitrary density. By adopting a rigorous renormalization scheme, we remove the divergent contributions of…
Direct measurements of the the structure functions F_1^{nu p} and F_1^{nu n} at a neutrino factory would allow for an accurate extraction of alpha_s from the Q^2-dependence of the Bjorken sum rule, complementing that based on the…
We study weighted sum processes associated to elements in a Wiener chaos with fixed order. More precisely, we show H\"older estimates and a functional limit theorem for them. Main tools we use are the integration by parts formula in…
Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails,…