Transfer function identification from impulse response via a new set of orthogonal hybrid functions (HF)

The present work proposes a new set of hybrid functions (HF) which evolved from the synthesis of sample-and-hold functions (SHF) and triangular functions (TF). Traditional block pulse functions (BPF) still continue to be attractive to many researchers in the arena of control theory. Block pulse functions also gave birth to a few useful variants. Two such variants are SHF and TF. The former is efficient for analyzing sample-and-hold control systems, while triangular functions established their superiority in obtaining piecewise linear solution of various control problems. After developing the basic theory of HF, a few square integrable functions are approximated via this set in a piecewise linear manner. For such approximation, it is shown, the mean integral square error (MISE) is much less than block pulse function based approximation. The operational matrices for integration in HF domain are also derived. Finally, this new set is employed for solving identification problem from impulse response data. The results are compared with the solutions obtained via BPF, SHF, TF, etc. and many illustrations are presented.     

On Haar wavelet operational matrix of general order and its application for the numerical solution of fractional Bagley Torvik equation

In the present analysis, the motion of an immersed plate in a Newtonian fluid described by Torvik and Bagley’s fractional differential equation [1] has been considered. This Bagley Torvik equation has been solved by operational matrix of Haar wavelet method. The obtained result is compared with analytical solution suggested by Podlubny [2]. Haar wavelet method is used because its computation is simple as it converts the problem into algebraic matrix equation.     

Three-level parallel J-Jacobi algorithms for Hermitian matrices

The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal load balancing between all available processors/cores is obtained. A similar blocking technique can be used to exploit local cache memory of each processor to further speed up the process. Due to diversity of modern computer architectures, each of the algorithms described here may be the method of choice for a particular hardware and a given matrix size. All proposed block algorithms compute the eigenvalues with relative accuracy similar to the original non-blocked Jacobi algorithm.     

Logarithms of iteration matrices, and proof of a conjecture by Shadrin and Zvonkine

A proof of a conjecture by Shadrin and Zvonkine, relating the entries of a matrix arising in the study of Hurwitz numbers to a certain sequence of rational numbers, is given. The main tools used are iteration matrices of formal power series and their (matrix) logarithms.     

Linear relations of refined enumerations of alternating sign matrices

In recent papers we have studied refined enumerations of alternating sign matrices with respect to a fixed set of top and bottom rows. The present paper is a first step towards extending these considerations to alternating sign matrices where in addition some left and right columns are fixed. The main result is a simple linear relation between the number of n×n alternating sign matrices where the top row as well as the left and the right column is fixed and the number of n×n alternating sign matrices where the two top rows and the bottom row are fixed. This may be seen as a first indication for the fact that the refined enumerations of alternating sign matrices with respect to a fixed set of top and bottom rows as well as left and right columns can possibly be reduced to the refined enumerations where only some top and bottom rows are fixed. For the latter numbers we provide a system of linear equations that conjecturally determines them uniquely.     

Combining stir-bar sorptive extraction and large volume injection-gas chromatography-mass spectrometry for the determination of benzotriazole UV stabilizers in wastewater matrices

Stir‐bar sorptive extraction and liquid desorption followed by large volume injection‐gas chromatography coupled to mass spectrometry under selected ion monitoring mode acquisition (SBSE‐LD/LVI‐GC‐MS(SIM)) was applied for the determination of six benzotriazole UV stabilizers (Tinuvin P, Allyl‐bzt, Tinuvin 320, Tinuvin 326, Tinuvin 327 and Tinuvin 328) in wastewater matrices. Parameters affecting the performance of extraction and desorption steps were thoroughly evaluated using uni‐ and multivariate optimization strategies, based on the use of experimental factorial designs. Assays performed with stir bars, coated with 24 μL of polydimethylsiloxane, on 25 mL of ultra‐pure water samples spiked at the 0.5 ng/mL level, yielded recoveries ranging from 47.9±1.4% (Tinuvin P) to 103.1±3.6% (Tinuvin 326), under optimized experimental conditions. When applied to complex matrices (e.g. wastewater), the methodology showed also excellent linear dynamic ranges (0.02–10.00 ng/mL) for the six benzotriazole UV stabilizers studied with correlation coefficients higher than 0.9970, limits of quantification in between 0.004 and 0.015 ng/mL, suitable repeatability (RSD<12.7%) and reproducibility (RSD<4.5%). The application of the proposed methodology to urban sewage waters from Spain and Portugal wastewater plants revealed the presence of low contents of some benzotriazole UV stabilizers.     

Linear matrix differential dynamical systems with fuzzy matrices

In this paper, we investigate linear first-order fuzzy matrix differential dynamical systems where the coefficients matrix is described by a fuzzy matrix. We show some properties of the matrix differential dynamical systems, and their phase portraits are described by means of examples.     

Some properties of the vertical structure operators for hydrostatic atmospheric models

Hydrostatic atmospheric models in a generalized vertical coordinate are considered. The governing equations are linearized with respect to a general basic state including arbitrary vertical variation of the reference temperature profile. Vertical structure equations are derived and studied for both continuous and discretized models. Some properties of vertical normal modes are defined and a comparison between continuous and discrete cases is made.     

Four Mutually Orthogonal Latin Squares of Order 14

The paper gives example of orthogonal array OA(6, 14) obtained from a difference matrix . The construction is equivalent to four mutually orthogonal Latin squares (MOLS) of order 14. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 363–367, 2012     

Intersection Matrices Revisited

Several intersection matrices of s‐subsets versus k‐subsets of a v‐set are introduced in the literature. We study these matrices systematically through counting arguments and generating function techniques. A number of new or known identities appear as natural consequences of this viewpoint; especially, use of the derivative operator and some related operators reveals some connections between intersection matrices and the “combinatorics of creation‐annihilation.” As application, the eigenvalues of several intersection matrices including some generalizations of the adjacency matrices of the Johnson scheme are derived; two new bases for the Bose–Mesner algebra of the Johnson scheme are introduced and the associated intersection numbers are obtained as well. Finally, we determine the rank of some intersection matrices. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 383–397, 2012