We report, for the f irst time to our knowledge, comparisons of light-scattering computations for large, randomly oriented, moderately absorbing spheroids based on the geometric-optics approximation and the exact T-matrix method. We show that in most cases the geometric-optics approximation is (much) more accurate for spheroids than for surface-equivalent spheres and can be used in phase functi...

If A is an nxn complex matrix and λ is an eigenvalue of A with geometric multiplicity k, then λ is in at least k of the Geršgorin discs Di of A. Let k, r, t be positive integers with k ≤ r ≤ t . Then there is a t x t complex matrix A and an eigenvalue λ of A such that λ has geometric multiplicity k and algebraic multiplicity t, and λ is in precisely r Geršgorin Discs of A. Some examples and rel...

By minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. This new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. Since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. In fac...

I n this paper, we present a novel algorithmic approach, the hybrid matrix geometric/invariant subspace method, f o r finding the stationary probability distribut ion of the f inite QBD process which arises in performance analysis of computer and communication systems. Assuming that the QBD state space i s defined in two dimensions with m phases and K f 1 levels, the solution Vector for level k...

We use a Riemannian (or pseudo-Riemannian) geometric framework to formulate the theory of the classical r-matrix for integrable systems. In this picture the r-matrix is related to a fourth rank tensor, named the r-tensor, on the configuration space. The r-matrix itself carries one connection type index and three tensorial indices. Being defined on the configuration space it has no momentum depe...

We present an independent component analysis (ICA) algorithm based on geometric considerations [10] [11] to decompose a linear mixture of more sources than sensor signals. Bofill and Zibulevsky [2] recently proposed a two-step approach for the separation: first learn the mixing matrix, then recover the sources using a maximum-likelihood approach. We present an efficient method for the matrix-re...

In this paper, we give a proof of the equivalence of N = 1 SO/Sp gauge theories deformed from N = 2 by the superpotential of adjoint field Φ and the dual type IIB supersting theory on CY threefold geometries with fluxes and orientifold action after geometric transition. Furthermore, by relating the geometric picture to the matrix model, we show the equivalence among the field theory and the cor...

In this paper we introduce a general class of level dependent Quasi-Birth-and-Death (QBD) processes and their stationary solution. We obtain the complete characterization of their fundamental matrices in terms of minimal non-negative solution of number of matrix quadratic equations. Our results will provide mixed-geometric solution for the stationary solution of level dependent chains. Applicat...

This paper discusses a new class of matrix nearness problems that measure approximation error using a directed distance measure called a Bregman divergence. Bregman divergences offer an important generalization of the squared Frobenius norm and relative entropy, and they all share fundamental geometric properties. In addition, these divergences are intimately connected with exponential families...

Card shuffling is an interesting topic to explore because of its complexity. Initially, card shuffling seems simple because it is ubitquitous. The majority of people know how to shuffle a deck of cards but few consider the math behind it. However, when it comes to analyzing the elements of card shuffling, it incorporates linear algebra, group theory, probability theory, and Markov Chains. When ...