Related papers: Simplifying matrix differential equations with gen…

Let g be a (say, sufficiently differentiable) function on the reals. One knows how to apply g to Hermitian elements A of a C* algebra. Yet the question of differentiability of the mapping A to g(A) is not trivial, since in general "A and dA…

The analysis of many physical phenomena can be reduced to the study of solutions of differential equations with polynomial coefficients. In the present work, we establish the necessary and sufficient conditions for the existence of…

By analyzing an optimization problem over orthogonal matrices, we prove a generalization of the Hardy-Littlewood-P\'olya rearrangement inequality to positive definite matrices. The inequality is then extended to rectangular matrices. Using…

The method of parameter variation for linear differential equations is extended to classes of second order nonlinear differential equations. This allows to reduce the latter to first order differential equations. Known classical equations…

Using purely Hamiltonian methods we derive a simple differential equation for the generator of the most general local symmetry transformation of a Lagrangian. The restrictions on the gauge parameters found by earlier approaches are easily…

In this paper we extent the previously published DALI-approximation for likelihoods to cases in which the parameter dependency is in the covariance matrix. The approximation recovers non-Gaussian likelihoods, and reduces to the Fisher…

We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations. With this we are able to reprove Hoelder's Theorem that the Gamma function satisfies no…

We extend A.B. Mingarelli's method for constructing generalized factorials. Our extension uses a pair of arithmetic functions $(x, y)$, where $x$ is superadditive. When $x$ is the identity function, our generalized factorial reduces to…

We compute the parametrized post-Newtonian parameter $\gamma$ in the case of a static point source for multiscalar-tensor gravity with completely general nonderivative couplings and potential in the Jordan frame. Similarly to the single…

Using the auxiliary field representation of the simplicial chiral models on a (d-1)-dimensional simplex, the simplicial chiral models are generalized through replacing the term Tr$(AA^{\d})$ in the Lagrangian of these models by an arbitrary…

We show that the strongly minimal second Painlev\'e equation (y" = 2y^3+ty+\alpha) is geometrically trivial, that is we show that if y_1,...,y_n are distinct solutions such that y_1,y_1',y_2,y_2',...,y_n,y_n' are algebraically dependent…

This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by a linear combination of polynomials, trigonometrical and…

We review and pursue further the study of constrained realisations of affine Gaudin models, which form a large class of two-dimensional integrable field theories with gauge symmetries. In particular, we develop a systematic gauging…

We will examine a particular mathematical derivation in a paper by P. Falkensteiner and H. Grosse (F&G) [1]. In [1] a quantity "delta(A)" is defined. This quantity is generated when the normal ordered generalized charge operator undergoes a…

Many key invariants in the representation theory of classical groups (symmetric groups $S_n$, matrix groups $GL_n$, $O_n$, $Sp_{2n}$) are polynomials in $n$ (e.g., dimensions of irreducible representations). This allowed Deligne to extend…

Given a function on diagonal matrices, there is a unique way to extend this to an invariant (by conjugation) function on symmetric matrices. We show that the extension preserves regularity -- that is, if the original function is k times…

Dyson's integration theorem is widely used in the computation of eigenvalue correlation functions in Random Matrix Theory. Here we focus on the variant of the theorem for determinants, relevant for the unitary ensembles with Dyson index…

This paper develops one of the methods for study of nonlinear Partial Differential equations. We generalize Sato equation and represent the algorithm for construction of some classes of nonlinear Partial Differential Equations (PDE)…

Matrix differential-difference Lax pairs play an essential role in the theory of integrable nonlinear differential-difference equations. We present sufficient conditions which allow one to simplify such a Lax pair by matrix gauge…

An alternative parameterization of R-matrix theory is presented which is mathematically equivalent to the standard approach, but possesses features which simplify the fitting of experimental data. In particular there are no level shifts and…