Sparse block-Jacobi matrices with arbitrarily accurate Hausdorff dimension

We show that the Hausdorff dimension of the spectral measure of a class of deterministic, i.e. nonrandom, block-Jacobi matrices may be determined with any degree of precision, improving a result of Zlatos [Andrej Zlatos,. Sparse potentials with fractional Hausdorff dimension, J. Funct. Anal. 207 (2004) 216-252]. (C) 2010 Elsevier Inc. All rights reserved.

Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices

B.M. Brown, M. Marletta, S. Naboko, I. Wood: Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices, J. London Math. Soc., June 2008; 77: 700-718. The full text of this article will be made available in this repository in June 2009 Sponsorship: EPSRC,INTAS

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

∗ Partially supported by Grant MM-428/94 of MESC.

Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices

000 Mathematics Subject Classification: Primary 16R50, Secondary 16W55.

Tradeoff between PAPR reduction and decoding complexity in transformed OFDM systems

It is known that in an OFDM system using Hadamard transform or phase alteration before the IDFT operation can reduce the Peak-to-Average Power Ratio (PAPR). Both these techniques can be viewed as constellation precoding for PAPR reduction. In general, using non-diagonal transforms, like Hadamard transform, increases the ML decoding complexity. In this paper we propose the use of block-IDFT matrices and show that appropriate block-IDFT matrices give lower PAPR as well as lower decoding complexity compared to using Hadamard transform. Moreover, we present a detailed study of the tradeoff between PAPR reduction and the ML decoding complexity when using block-IDFT matrices with various sizes of the blocks.

Exploring isospectral spring-mass systems with firefly algorithm

This paper investigates in-line spring-mass systems (An), fixed at one end and free at the other, with n-degrees of freedom (d.f.). The objective is to find feasible in-line systems (B(n)) that are isospectral to a given system. The spring-mass systems, A(n) and B(n), are represented by Jacobi matrices. An error function is developed with the help of the Jacobi matrices A(n) and B(n). The problem of finding the isospectral systems is posed as an optimization problem with the aim of minimizing the error function. The approach for creating isospectral systems uses the fact that the trace of two isospectral Jacobi matrices A(n) and B(n) should be identical. A modification is made to the diagonal elements of the given Jacobi matrix (A(n)), to create the isospectral systems. The optimization problem is solved using the firefly algorithm augmented by a local search procedure. Numerical results are obtained and resulting isospectral systems are shown for 4 d.f. and 10 d.f. systems.

Implementation and application of basis set superposition error-correction schemes to the theoretical modeling of weak intermolecular interactions

This thesis deals with the so-called Basis Set Superposition Error (BSSE) from both a methodological and a practical point of view. The purpose of the present thesis is twofold: (a) to contribute step ahead in the correct characterization of weakly bound complexes and, (b) to shed light the understanding of the actual implications of the basis set extension effects in the ab intio calculations and contribute to the BSSE debate. The existing BSSE-correction procedures are deeply analyzed, compared, validated and, if necessary, improved. A new interpretation of the counterpoise (CP) method is used in order to define counterpoise-corrected descriptions of the molecular complexes. This novel point of view allows for a study of the BSSE-effects not only in the interaction energy but also on the potential energy surface and, in general, in any property derived from the molecular energy and its derivatives A program has been developed for the calculation of CP-corrected geometry optimizations and vibrational frequencies, also using several counterpoise schemes for the case of molecular clusters. The method has also been implemented in Gaussian98 revA10 package. The Chemical Hamiltonian Approach (CHA) methodology has been also implemented at the RHF and UHF levels of theory for an arbitrary number interacting systems using an algorithm based on block-diagonal matrices. Along with the methodological development, the effects of the BSSE on the properties of molecular complexes have been discussed in detail. The CP and CHA methodologies are used for the determination of BSSE-corrected molecular complexes properties related to the Potential Energy Surfaces and molecular wavefunction, respectively. First, the behaviour of both BSSE-correction schemes are systematically compared at different levels of theory and basis sets for a number of hydrogen-bonded complexes. The Complete Basis Set (CBS) limit of both uncorrected and CP-corrected molecular properties like stabilization energies and intermolecular distances has also been determined, showing the capital importance of the BSSE correction. Several controversial topics of the BSSE correction are addressed as well. The application of the counterpoise method is applied to internal rotational barriers. The importance of the nuclear relaxation term is also pointed out. The viability of the CP method for dealing with charged complexes and the BSSE effects on the double-well PES blue-shifted hydrogen bonds is also studied in detail. In the case of the molecular clusters the effect of high-order BSSE effects introduced with the hierarchical counterpoise scheme is also determined. The effect of the BSSE on the electron density-related properties is also addressed. The first-order electron density obtained with the CHA/F and CHA/DFT methodologies was used to assess, both graphically and numerically, the redistribution of the charge density upon BSSE-correction. Several tools like the Atoms in Molecules topologycal analysis, density difference maps, Quantum Molecular Similarity, and Chemical Energy Component Analysis were used to deeply analyze, for the first time, the BSSE effects on the electron density of several hydrogen bonded complexes of increasing size. The indirect effect of the BSSE on intermolecular perturbation theory results is also pointed out It is shown that for a BSSE-free SAPT study of hydrogen fluoride clusters, the use of a counterpoise-corrected PES is essential in order to determine the proper molecular geometry to perform the SAPT analysis.

Representation theorems for indefinite quadratic forms and applications

Diese Arbeit widmet sich den Darstellungssätzen für symmetrische indefinite (das heißt nicht-halbbeschränkte) Sesquilinearformen und deren Anwendungen. Insbesondere betrachten wir den Fall, dass der zur Form assoziierte Operator keine Spektrallücke um Null besitzt. Desweiteren untersuchen wir die Beziehung zwischen reduzierenden Graphräumen, Lösungen von Operator-Riccati-Gleichungen und der Block-Diagonalisierung für diagonaldominante Block-Operator-Matrizen. Mit Hilfe der Darstellungssätze wird eine entsprechende Beziehung zwischen Operatoren, die zu indefiniten Formen assoziiert sind, und Form-Riccati-Gleichungen erreicht. In diesem Rahmen wird eine explizite Block-Diagonalisierung und eine Spektralzerlegung für den Stokes Operator sowie eine Darstellung für dessen Kern erreicht. Wir wenden die Darstellungssätze auf durch (grad u, h() grad v) gegebene Formen an, wobei Vorzeichen-indefinite Koeffzienten-Matrizen h() zugelassen sind. Als ein Resultat werden selbstadjungierte indefinite Differentialoperatoren div h() grad mit homogenen Dirichlet oder Neumann Randbedingungen konstruiert. Beispiele solcher Art sind Operatoren die in der Modellierung von optischen Metamaterialien auftauchen und links-indefinite Sturm-Liouville Operatoren.

Computing the Hessenberg matrix associated with a self-similar measure

We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calculate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures. We apply this method to approximate the Hessenberg matrix associated with a self-similar measure and compare it with the result obtained by a former method for self-similar measures which uses a fixed point theorem for moment matrices. Results are given for a series of classical examples of self-similar measures. Finally, we also apply the method introduced in this paper to some examples of sums of (not self-similar) measures obtaining the exact value of the sections of the Hessenberg matrix.

Burst error correction using partial fourier matrices and block sparse representation

There is a strong relation between sparse signal recovery and error control coding. It is known that burst errors are block sparse in nature. So, here we attempt to solve burst error correction problem using block sparse signal recovery methods. We construct partial Fourier based encoding and decoding matrices using results on difference sets. These constructions offer guaranteed and efficient error correction when used in conjunction with reconstruction algorithms which exploit block sparsity.

On diagonal-Schur complements of block diagonally dominant matrices

It is known that the diagonal-Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices [J.Z. Liu, Y.Q. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365-380], and the same is true for nonsingular H-matrices [J.Z. Liu, J.C. Li, Z.T. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Algebra Appl. 428 (2008) 1009-1030]. In this paper, we research the properties on diagonal-Schur complements of block diagonally dominant matrices and prove that the diagonal-Schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices, and the same holds for generalized block strictly diagonally dominant matrices. (C) 2010 Elsevier Inc. All rights reserved.

Evaluation of APD and SiPM Matrices as Sensors for Monolithic PET Detector Block

Gamma detectors based on monolithic scintillator blocks coupled to APDs matrices have proved to be a good alternative to pixelated ones for PET scanners. They provide comparable spatial resolution, improve the sensitivity and make easier the mechanical design of the system. In this study we evaluate by means of Geant4-based simulations the possibility of replacing the APDs by SiPMs. Several commercial matrices of light sensors coupled to LYSO:Ce monolithic blocks have been simulated and compared. Regarding the spatial resolution and linearity of the detector, SiPMs with high photo detection efficiency could become an advantageous replacement for the APDs