this paper presents an operational formulation of the tau method based upon orthogonal polynomials by using a reduced set of matrix operations for the numerical solution of nonlinear multi-order fractional differential equations(fdes). the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of non-linear algebraic equations....

In this paper we prove some characterizations of the matrix orthogonal polynomials whose derivatives are also orthogonal, which generalize other known ones in the scalar case. In particular, we prove that the corresponding orthogonality matrix functional is characterized by a Pearson-type equation with two matrix polynomials of degree not greater than 2 and 1. The proofs are given for a general...

A matrix-valued measure Θ reduces to measures of smaller size if there exists a constant invertible matrix M such that MΘM∗ is block diagonal. Equivalently, the real vector space A of all matrices T such that TΘ(X) = Θ(X)T ∗ for any Borel set X is nontrivial. If the subspace Ah of self-adjoints elements in the commutant algebra A of Θ is nontrivial, then Θ is reducible via a unitary matrix. In ...

We derive the necessary and sufficient conditions of and the expressions for the orthogonal solutions, the symmetric orthogonal solutions, and the skew-symmetric orthogonal solutions of the system of matrix equations AX B and XC D, respectively. When the matrix equations are not consistent, the least squares symmetric orthogonal solutions and the least squares skewsymmetric orthogonal solutions...

A module M is called square-free if it contains nonon-zero omorphic submodules and B with A∩B= 0. Dually, Mis dual-square-free has no proper M=A+B M/A∼=M/B. In this paper we show that M=⊕i∈I Mi, then iff each Mi Mj ⊕j=i∈I are orthogonal. M=⊕ni=1Mi, dual-square-free, 1⩽i⩽n, ⊕ni=jMi factor-orthogonal. Moreover, in the finite case, weshow M=⊕i∈ISi a direct sum of non-is simple modules, dual-square...

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

A frame multiresolution (FMRA for short) orthogonal wavelet is a single-function orthogonal wavelet such that the associated scaling space V0 admits a normalized tight frame (under translations). In this paper, we prove that for any expansive matrix A with integer entries, there exist A-dilation FMRA orthogonal wavelets. FMRA orthogonal wavelets for some other expansive matrix with non integer ...

∗ Author for correspondence. Abstract: In this paper we have analysed the aperiodic correlation properties and the average BER performance of a family of complex orthogonal sequences suitable for code spreading in an asynchronous BPSK DS-CDMA communication system. The proposed complex sequences form a complex orthogonal matrix with desirable equal odd and even aperiodic correlations. Concatenat...

We show that a Schur form of a real orthogonal matrix can be obtained from a full CS decomposition. Based on this fact a CS decomposition-based orthogonal eigenvalue method is developed. We also describe an algorithm for orthogonal similarity transformation of an orthogonal matrix to a condensed product form, and an algorithm for full CS decomposition. The latter uses mixed shifted and zero-shi...