Operads are a specific tool for encoding type of algebras. For instance there are operads encoding associative algebras, commutative and associative algebras, Lie algebras, pre-Lie algebras, dendriform algebras, Poisson algebras and so on. A usual way of describing a type of algebras is by giving the generating operations and the relations among them. For instance a Lie algebra L is a vector sp...

The problem of nonseparable space-time covariance functions is essential and difficult in spatiotemporal data analysis. Considering that a fully symmetric space-time covariance function is inappropriate for many spatiotemporal processes, this article provides a way to construct a non-fully symmetric nonseparable space-time correlation function from any given marginal spatial Matérn and marginal...

The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim σ-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F ⊃ G ⊃ H . We show that for every symmetric space F/G, the generalized sine-Gordon models can be derived from the G/H WZW action, p...

The famous Frobenius characteristic map is a bijection from the space of characters of a symmetric group S n to the space of homogeneous symmetric functions of degree n. In this note, we prove a formula for the inverse map. More precisely, we express the generating function for the values of an arbitrary virtual character of S n in terms of the symmetric function which is the Frobenius image of...

(i) An explicit description of the range D(X)̂where X is a Euclidean space or a symmetric space of the noncompact type ([2], [3]). Here (D = Cc ). In the first case, f̂ in (1.1) is integration over hyperplanes in X = Rn; in the latter case f̂ in (1.1) refers to integration over horocycles ξ in the symmetric space X. (ii) Medical application in X-ray reconstruction ([6], p.47). (iii) Existence theo...

The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from its Satake diagram, in a way that is suited for the use with computer algebra systems; an example implementation for Maple Version 10 can be fou...

A symmetric space analogue of Casselman’s criterion for square integrability of representations of a p-adic group is established. It is described in terms of exponents of Jacquet modules along parabolic subgroups associated to the symmetric space.

In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...

In this paper we will prove that if $L$ is a continuous symmetric n-linear form on a Hilbert space and $widehat{L}$ is the associated continuous n-homogeneous polynomial, then $||L||=||widehat{L}||$. For the proof we are using a classical generalized  inequality due to S. Bernstein for entire functions of exponential type. Furthermore we study the case that if X is a Banach space then we have t...

This paper studies axially symmetric vibrations of a liquid-filled poroelastic thin cylinder saturated with two immiscible liquids of infinite extent that is surrounded by an inviscid elastic liquid. By considering the stress free boundaries, the frequency equation is obtained. Particular case, namely, liquid-filled poroelastic cylinder saturated with single liquid is discussed.  When the waven...