The purpose of this article is threefold First it provides the reader with a few useful and e cient tools which should enable her him to evaluate nontrivial de terminants for the case such a determinant should appear in her his research Second it lists a number of such determinants that have been already evaluated together with explanations which tell in which contexts they have appeared Third ...

Myelin encephalitogenic or basic protein (BP) 1 accounts for 30% of the protein in central nervous system (CNS) myelin (1), where BP is postulated to serve a structural role. BP is unique to myelin, and a similar, if not identical, protein designated P1 (2) is present in peripheral nervous system (PNS) myelin (2-4). BP has a monomeric mol wt of 18,500 daltons and is comprised of 169 amino acids...

where Sn (also known as the symmetric group on n elements) is the set of all permutations of {1, 2, . . . , n}, i.e., all the ways of pairing up the n rows of the matrix with the n columns, and I(π) is the inversion number of π, the minimal number of transpositions of adjacent columns needed to turn π into the identity permutation. This formula [1] is practical for some simple matrices such as ...

Indian Ocean is known as a source of moisture for southeast of Iran due to summer precipitation. In this study, in order to investigate the role of SST of Indian Ocean, and the convergence and divergence fields in the precipitation of southeast of Iran, precipitation data of five synoptic stations were used during 2000-2010, including Iranshahr, Khash, ChahBahar, Zabul, and Saravan. To investig...

The path-integral of the fermionic oscillator with a time-dependent frequency is analyzed. We give the exact relation between the boundary condition to define the domain in which the path-integral is performed and the transition amplitude that the path-integral calculates. According to this relation, the amplitude suppressed by a zero mode does not indicate any special dynamics, unlike the anal...

Interpolation theory suggests a generalization of the usual Vandermonde determinant to numbers with multiplicities. We prove a discriminant formula for this generalized Vandermonde determinant and give an application to the Hermite interpolation problem.

The determinant for complex matrices cannot be extended to quaternionic matrices. Instead, the Study determinant and the closely related q-determinant are widely used. We show that the Study determinant can be characterized as the unique functional which extends the absolute value of the complex determinant and discuss its spectral and linear algebraic aspects. 1. Introduction. Quaternionic lin...

Let H be a Hilbert space with an inner product that is conjugate linear in the first variable. We do not presume unless we say so that H is separable. We denote by B(H) the set of bounded linear operators H → H. For any A ∈ B(H), A∗A is positive and one proves that it has a unique positive square root |A| ∈ B(H). We call |A| the absolute value of A. We say that U ∈ B(H) is a partial isometry if...

I propose a large class of stochastic Markov processes associated with probability distributions analogous to that of lattice gauge theory with dynamical fermions. The construction incorporates the idea of approximate spectral split of the determinant through local loop action, and the idea of treating the infrared part of the split through explicit diagonalizations. I suggest that exact algori...