The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion ) 0 ( R r   and a matrix ) (    r R being in perfect thermal contact at R r  is considered. The heat conduction in each region is described by the time-fractional heat conduction equation with the Caputo derivative of fractional order 2 0   and , 2 0    respectively. The Laplace trans...

We examine critically some of the existing descriptions of the envelope of a 1-parameter family of surfaces in 3-space. An old, natural, description is that the envelope is the union of the characteristic curves (defined as the “limit intersection curves” of surfaces from the family). This description fell in disrepute during the 20th century. We claim that this relegation of the limit intersec...

Because of their similarities, but mainly because of their differences, it is a matter of interest to determine the relationship between the Hardy space H(R) and the space of integrable functions L(R). The purpose of this paper is to address some unanswered questions concerning the family of spaces Xs(R ) that lie between H and L, and thus gain a better understanding of the gap that separates t...

Using the method introduced by Grisaru et al., boundary S matrices for the physical excitations of the open Hubbard chain with boundary fields are studied. In contrast to the open supersymmetric t-J model, the boundary S matrix for the charge excitations depend on the boundary fields though the boundary fields do not break the spin-SU(2) symmetry. E-mail address: [email protected]

We discuss the possibility that fermionic condensates arise from the dominance of scalar exchange forces over vector gluon exchange. When a scalar in the adjoint representation is exchanged in the reaction A + A → A+A, the usual most attractive channel (MAC) rule is reversed in sign, with the consequence that the formation of a condensate with the largest possible Casimir is favored. More gener...

We prove that the probability PN for a real random Gaussian N ×N ×2 tensor to be of real rank N is PN = (Γ((N + 1)/2))N/G(N + 1), where Γ(x), G(x) denote the gamma and Barnes G-functions respectively. This is a rational number for N odd and a rational number multiplied by πN/2 for N even. The probability to be of rank N + 1 is 1− PN . The proof makes use of recent results on the probability of ...

Abstract: Motivated by statistical mechanics contexts, we study the properties of the q-Laplace transform, which is an extension of the well-known Laplace transform. In many circumstances, the kernel function to evaluate certain integral forms has been studied. In this article, we establish relationships between q-exponential and other well-known functional forms, such as Mittag–Leffler functio...