The main objective of this work is to provide a closed formula for the forward, backward and symmetric solution of the 2-D general singular model (GSM) given in (Kurek, 1985). Of fundamental importance in our approach is the relative forward and backward fundamental matrix. Copyright c 2005 IFAC. Keywords: 2-D general singular models, implicit 2-D systems, fundamental matrix, forward solution, ...

We propose a class of synthetic optical materials in which the refractive index satisfies n(−x) = −n∗(x). We term such systems antisymmetric parity-time (APT ) structures. Unlike PT -symmetric systems, which require balanced gain and loss, i.e., n(−x) = n∗(x), APT systems consist of balanced positiveand negative-index materials. Despite the seemingly PT -symmetric optical potential V (x) ≡ n(x)...

In the following, we cover some material from linear algebra. Proofs of those facts can be found in any text on linear algebra, for example [Leo98]. For a matrix A, let A T denote the transposed matrix. We remind the reader that for two matrices A and B, we have (AB) T = B T A T. Furthermore, for any three matrices A, B and C, we have (AB)C = A(BC). A matrix A ∈ IR n×n is symmetric if A T = A. ...

The replicator equation is a simple model of evolution that leads to stable form of Nash Equilibrium, Evolutionary Stable Strategy (ESS). No individuals get an incentive unilaterally deviating from the equilibrium. It has been studied in connection with Evolutionary Game Theory, a theory John Maynard Smith and George R. Price developed to predict biological reproductive success of populations. ...

A spin model (for link invariants) is a square matrix W with non-zero complex entries which satisfies certain axioms. Recently it was shown that tWW−1 is a permutation matrix (the order of this permutation matrix is called the “index” of W ), and a general form was given for spin models of index 2. Moreover, new spin models, called non-symmetric Hadamard models, were constructed. In the present...

In this paper, using a quantum superalgebra associated with the universal central extension of sl(2, 2)(1), we introduce new R-matrices having an extra parameter x. As x → 0, they become those associated with the symmetric and anti-symmetric tensor products of the copies of the vector representation of Uqsl(2, 2) (1).

In this paper, using a quantum superalgebra associated with the universal central extension of sl(2, 2)(1), we introduce new R-matrices having an extra parameter x. As x → 0, they become those associated with the symmetric and anti-symmetric tensor products of the copies of the vector representation of Uqsl(2, 2) (1).

In this work‎, ‎an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$‎ ‎and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$‎ ‎where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$‎, ‎$mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$‎, ‎$ma...

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...

Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs, and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of th...