Expansions Of Matrix Research Articles

Bayes synthesis of multidimensional stochastic system with high availability by wavelet canonical expansions

Paper in devoted to methodological and instrumental software synthesis support for multidimensional stochastic systems with high availability (StSHA). For modeling of nonstationary stochastic processes (StP) it is supposed to implement wavelet canonical expansions (WLCE), based on coefficients of canonical expansions of covariance matrix using two dimensional orthonormal wavelet basis with compact carrier. Vector StSHA input and output are nonlinear on vector of random parameters with known probability density and Gaussian (normal) noise. Noises do not depend upon random parameters. Functional Bayes criterion (FBC) is presented by linear functional. Optimal system is synthesized using conditional risk criterion. General StSHA synthesis method and algorithm contains 4 steps and 7 positions. FBC optimal estimate is calculated by WLCE method. Special software is developed for scalar nonlinear StSHA. Results of computer experiments are given and discussed. His shown that high efficiency of method at 8 WLCE items. Directions of future investigations are presented.

THE EFFECT OF INTRA-ABDOMINAL PRESSURE EXPERIMENTAL CHANGES ON THE ULTRASTRUCTURE OF THE RAT'S LEVATOR ANI MUSCLE

In clinical practice, it is well known that an increase in intra-abdominal pressure can lead to disorders in the functioning of internal organs, cause the development of multiple organ failure and the formation of pelvic organ prolapse. Despite the fact that the pelvic bottom along with the muscles of the anterior abdominal wall and the diaphragm, takes an active part in the formation of intra-abdominal pressure, so far there are practically no morphological studies of the muscles of the pelvic diaphragm and their reactive changes that occur in response to an increase in intra-abdominal pressure. The aim of the study was to study the ultrastructural rearrangements of the levator ani muscle in response to experimentally formed states of increase and decrease in intra-abdominal pressure. The work was performed on 21 male outbred adult white laboratory rats. It has been established that after damage to the myofibrillar apparatus of the muscle fibers of the levator ani muscle in response to an increase in intra-abdominal pressure, the processes of sarcoplasmic adaptation and activation of the synthetic apparatus begin in them, which leads to a gradual restoration of their structure to its initial state. These changes are subject to certain time dynamics. 4 weeks after the increase in intra-abdominal pressure, a slight atrophy of the myofibrillar apparatus is observed and expansions of the intermyofibrillar cytoplasmic matrix appear. In mitochondria distinctly expressed irreversible changes in mitochondria occur, many mitochondria die. Subsequently, a significant amount of glycogen granules appears between the myofibrils, the structure of the myons is restored. Eight weeks after the start of the experiment, the structure of most muscle fibers is restored almost completely. The structure of the levator ani muscle did not change during the simulation of reduced intra-abdominal pressure in comparison with the control group at all periods of observation. In general, the study shows that the levator ani muscle skeletal muscle tissue has a high mechanic-dependent plasticity, which manifests itself in compensatory rearrangements of the ultrastructure of its fibers in response to changes in intra-abdominal pressure.

An improved response function based stochastic meshless method for problems in elasto-statics

The current study proposes an improved response function (IRF) based stochastic element free Galerkin method (SEFGM) for the analysis of problems in elasto-statics, wherein Young’s modulus is modelled as a homogeneous random field with symmetric distribution characteristics. The proposed SEFGM approximates displacement as the sum of a deterministic part and a stochastic part. The stochastic part is modelled with the help of an IRF, which is a function of discretized set of random variables. Moving least square shape functions are employed to discretize the random field. Utilizing Taylor series expansions of stiffness matrix and force vector and IRF approximation of displacement, explicit expressions for system responses in terms of random variables are derived. Stochastic informations of system responses are evaluated by employing Monte Carlo Simulation (MCS) on the response function, which eliminates the need of construction and simulation of system matrices at each set of sample generation. 1D and 2D numerical examples in elasto-statics are solved using proposed method. Results are validated with those obtained by direct simulation of system of equations using MCS and also compared with other methods like second order perturbation and ad-hoc response function based SEFGM. Normalized computational times required for all the methods are also compared. It is found that the proposed method is computationally efficient and can produce accurate results even for higher coefficient of variation of input random fields.

Numerical investigation on the repeated low-velocity impact behavior of composite laminates

The dynamic mechanical responses and damage development of cross-ply composite laminates under repeated low-velocity impact are investigated through finite element simulations with ABAQUS/Explicit. A progressive damage model for laminates, consisting of the continuum damage model, the 3D Hashin failure criterion and the damage evolution model based on equivalent displacement, is integrated with the bilinear traction-separation relationship cohesive model to simulate the damage initiation, evolution and propagation behavior of different damage modes in composite laminates. Compared with the experimental results, the established finite element model was validated through the global mechanical response and damage distribution contous. Besides, a mesh refinement study was performed by using three different element sizes. The validated model was adopted to investigate the repeated impact behaviors of composite laminates under three different energies. The qualitative conclusions about the effects of repeated impact on global mechanical response were summarized by the changes of impact force, displacement, contact time and energy absorption. Moreover, the effects of repeated impact on the damage characteristics and expansions of matrix and delamination were discussed in detail.

Freestanding and flexible composites of magnetocaloric Gd5(Si,Ge)4 microparticles embedded in thermoplastic poly(methyl methacrylate) matrix

The implementation of processed magnetic materials onto thermoplastics can be an approach for practical use of brittle intermetallic materials on device development with the advantage of enlarging the range of applications. In this paper, we present the evaluation on the effect of blending magnetocaloric Gd5Si2.4Ge1.6 3.4 μm particles with in different weight fractions onto a flexible, transparent and non-magnetic poly(methyl methacrylate) (PMMA). A close to homogeneous grain distribution along the polymer surface were achieved by using a simple solvent casting method for their magnetocaloric properties studies. From XRD analysis, it was found a unit cell volume shrinkage by increasing the powder concentration followed by a reduction on the amount of secondary monoclinic phase as a result of interfacial interactions. As a consequence, a weakening of secondary phases effect on the composite magnetocaloric behavior is observed as a result of the effective hydrostatic pressure from the difference between thermal expansions of matrix and filler.

An efficient spectral method for numerical time-dependent perturbation theory.

We develop the Fourier-Laplace Inversion of the Perturbation Theory (FLIPT), a novel numerically exact "black box" method to compute perturbative expansions of the density matrix with rigorous convergence conditions. Specifically, the FLIPT method is extremely well-suited to simulate multiphoton pulsed laser experiments with complex pulse shapes. The n-dimensional frequency integrals of the nth order perturbative expansion are evaluated numerically using tensor products. The N-point discretized integrals are computed in O(N2) operations, a significant improvement over the O(Nn) scaling of standard quadrature methods.

Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix II. Only one designated value

ABSTRACTThis paper is a sequel to ‘Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values’, where a ‘bivalent’ Belnap-Dunn semantics is provided for all the expansions referred to in its title. The aim of the present paper is to carry out a parallel investigation for all natural implicative expansions of Kleene's strong 3-valued matrix now with only one designated value.

Microstructure and thermal expansion behavior of a novel Cf-SiCNWs/AZ91D composite with dual interface

Abstract In this study, a novel composite with dual interface, namely T-700 carbon fibers grafted with SiCNWs reinforced AZ91D (Cf-SiCNWs/AZ91D), was designed. The microstructure of the Cf-SiCNWs/AZ91D composite was fully characterized and its thermal expansion behaviors from 25 to 450 °C investigated. The results show that the Cf-SiCNWs/AZ91D has dual interface of Cf/AZ91D and SiCNWs/AZ91D. In the alloy matrix, the nanowires are uniformly distributed without any agglomerates and showing a good bond with the matrix. Near the interface of SiCNWs/AZ91D, considerable dislocations were observed, which can be attributed to the different thermal expansions of SiCNWs and AZ91D matrix. It was found that the thermal expansion behavior of the Cf-SiCNWs/AZ91D composite was significantly influenced by its interfacial configuration, which can reduce the coefficients of thermal expansion and improve the stability of the composite.

Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values

ABSTRACTA conditional is natural if it fulfils the three following conditions. (1) It coincides with the classical conditional when restricted to the classical values T and F; (2) it satisfies the Modus Ponens; and (3) it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two designated elements. (We understand the notion ‘natural conditional’ according to N. Tomova, ‘A lattice of implicative extensions of regular Kleene's logics’, Reports on Mathematical Logic, 47, 173–182, 2012.)

Influence of Particle Attributes on Residual Stresses in Particulate Ceramic Composites

The contribution deals with the issue of residual stresses in particulate ceramic composites used in microelectronics. Residual stresses are developed in the composite due to cooling during manufacturing process. Different coefficients of thermal expansions of particles and matrix cause important residual stresses in the composite influencing their mechanical behaviour. The main aim of the paper is to determine influence of particle properties on magnitude and distribution of residual stresses in the composite matrix. Three dimensional numerical model was developed and finite element method (FEM) was used for numerical simulations. Results obtained contribute to a better understanding of residual stresses distribution and fracture processes in the studied type of composite.

Hybrid space–angle adaptivity for whole-core particle transport calculations

Adaptive refinement is a powerful method for efficiently solving physical problems. In this paper we present a new coupled space–angle adaptive algorithm for neutron transport calculations. The scheme is specifically employed for the solution of the integral form of transport equation based on the collision probability–response matrix method. The adaptive algorithm is started by first applying angular adaptivity and then projecting the solution to the spatial mesh refinement. A posteriori error estimate is derived by utilizing the flux gradient approach based on the net current leakage of nodes. A new approach is used to apply continuity of flux in the interface between nodes by escalating the order of spherical harmonics expansions of entrance response matrix to the same order of spherical harmonics expansions of outgoing angular flux at the neighboring node. Using an integral transport method within the node and refined space and angle variables, a new method for whole-core transport calculations is introduced. The validity of the developed adaptive strategy is assessed by a series of numerical experiments. Comparisons indicate that the space–angle adaptivity framework is capable of resulting acceptable solution with less number of the degrees of freedom (DOFs).

Effect of fire exposure on cracking, spalling and residual strength of fly ash geopolymer concrete

Fly ash based geopolymer is an emerging alternative binder to cement for making concrete. The cracking, spalling and residual strength behaviours of geopolymer concrete were studied in order to understand its fire endurance, which is essential for its use as a building material. Fly ash based geopolymer and ordinary portland cement (OPC) concrete cylinder specimens were exposed to fires at different temperatures up to 1000°C, with a heating rate of that given in the International Standards Organization (ISO) 834 standard. Compressive strength of the concretes varied in the range of 39–58MPa. After the fire exposures, the geopolymer concrete specimens were found to suffer less damage in terms of cracking than the OPC concrete specimens. The OPC concrete cylinders suffered severe spalling for 800 and 1000°C exposures, while there was no spalling in the geopolymer concrete specimens. The geopolymer concrete specimens generally retained higher strength than the OPC concrete specimens. The Scanning Electron Microscope (SEM) images of geopolymer concrete showed continued densification of the microstructure with the increase of fire temperature. The strength loss in the geopolymer concrete specimens was mainly because of the difference between the thermal expansions of geopolymer matrix and the aggregates.

CSR expansions of matrix powers in max algebra

We study the behavior of max-algebraic powers of a reducible nonnegative matrix A ∈ R + n × n A\in \mathbb {R}_+^{n\times n} . We show that for t ≥ 3 n 2 t\geq 3n^2 , the powers A t A^t can be expanded in max-algebraic sums of terms of the form C S t R CS^tR , where C C and R R are extracted from columns and rows of certain Kleene stars, and S S is diagonally similar to a Boolean matrix. We study the properties of individual terms and show that all terms, for a given t ≥ 3 n 2 t\geq 3n^2 , can be found in O ( n 4 log ⁡ n ) O(n^4\log n) operations. We show that the powers have a well-defined ultimate behavior, where certain terms are totally or partially suppressed, thus leading to ultimate C S t R CS^tR terms and the corresponding ultimate expansion. We apply this expansion to the question whether { A t y , t ≥ 0 } \{A^ty,\; t\geq 0\} is ultimately linear periodic for each starting vector y y , showing that this question can also be answered in O ( n 4 log ⁡ n ) O(n^4\log n) time. We give examples illustrating our main results.

Re-evaluation of neutrino mixing pattern according to latest T2K result

We re-evaluate neutrino mixing patterns according to the latest T2K result for a larger mixing angle θ 13, and find that the PMNS mixing matrix has larger deviations from bimaximal (BM) and tribimaximal (TB) mixing patterns than previously expected. We also find that several schemes connecting PMNS and CKM mixing matrices can accommodate the latest T2K result nicely. As necessary updates to former works, we make new triminimal expansions of PMNS mixing matrix based on BM and TB mixing patterns. We also propose a new mixing pattern with a self-complementary relation between the mixing angles θ 12 + θ 13 ⋍ 45°, and find such a new mixing pattern in leading order can provide a rather good description of the data.

Investigation of Coating Layer to Reduce Thermal Stresses in Steel Fiber Reinforced Aluminum Metal Matrix Composite

In this study, by using coating layers to reduce thermal stresses in the metal matrix composites with a mismatch in coefficients of thermal expansions of fiber and matrix is investigated. The thermoelastic solutions based on a three cylinder model are deformed. It is shown that the effectiveness of the layer can be defined by the product of its cofficients of thermal expansions and thickness and that a compensating layer with a sufficiently high coefficient of thermal expansions can reduce the thermal stresses in the metal matrix. . In order to verify the results were compared with the finite element method. In this solution, 224 nodes and 44 nine-node isoparametric elements are used. The study is based on a three cylinder model isolating one steel fiber with a coating layer and a aluminum matrix layer. Only monotonic cooling is studied and the variation of the material properties with temperatures is not considered. The results have been presented in graphics.

Taylor series expansions for airborne radar space-time adaptive processing

Space-time adaptive processing (STAP) for range-dependent clutter rejection in airborne radar is considered. Indeed, radar antenna architectures or configurations that are different from the conventional uniform linear antenna array (ULA) and side-looking (SL) configuration have consequences on the clutter properties. The authors here investigate the use of Taylor series expansions (TSEs) of the space–time covariance matrix in the classical sample matrix inversion (SMI) STAP method in order to mitigate the range non-stationarity of the clutter and they compare it to the derivative-based updating (DBU) already proposed in the literature. The authors also propose a new algorithm based on a TSE of the clutter plus noise subspace in conjunction with the eigencanceler-based (EC) STAP, which improves the performance in term of signal-to-interference plus noise ratio (SINR) loss, compared to the DBU method. In this study, the particular cases of a ULA and a uniform circularly curved antenna (UCCA) array in SL and non-SL monostatic configurations as well as a ULA in some bistatic configurations are considered for the test and the comparison of the presented algorithms.

Generalizations of two-index two-variable Hermite matrix polynomials

AbstractIn this paper, we introduce a new generalization of the Hermite matrix polynomials expansions of some relevant matrix functions appearing in the solution of differential systems. An explicit representation and an expansion of the matrix exponential in a series of these matrix polynomials is obtained. Properties of Hermite matrix polynomials such as the recurrence formula permit an efficient computations of matrix functions are established. A new expansions of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed.

Analytical Diagnosis and Tuning of Narrowband Multicoupled Resonator Filters

A novel analytical filter diagnosis technique based on the partial fraction expansions of admittance matrix is proposed in this paper. The technique is applicable to computer-aided filter tuning of a general Chebyshev filter. The key issue in the proposed technique is the extension of the realizability conditions to the asynchronously tuned filters for removing the phase-loading effect. Using this analytical diagnosis technique, the inherent dispersion effects of the resonators and coupling elements are compensated by removable stray couplings in the diagnosed filter models. The filter topology that can be handled by this technique is only limited by the availability of the exact filter synthesis technique with which the filter to be diagnosed is designed

Excited states in the multireference state-specific coupled-cluster theory with the complete active space reference

The recently proposed multireference state-specific coupled-cluster theory with the complete active space reference has been used to study electronically excited states with different spatial and spin symmetries. The algorithm for the method has been obtained using the computerized approach for automatic generation of coupled-cluster diagrams with an arbitrary level of the electronic excitation from a formal reference determinant. The formal reference is also used to generate the genuine reference state in the form of a linear combination of determinants contracted to a configuration with the spin and spatial symmetries of the target state. The natural-orbital expansions of the one-electron configuration inferaction density matrix allowed us to obtain the most compact orbital space for the expansion of the reference function. We applied our approach in the calculations of singlet and triplet states of different spatial symmetries of the water molecule. The comparisons of the results with values obtained using other many-particle methods and with the full configuration interaction results demonstrate good ability of the approach to deal with electronic excited states.

Quantum Dissipation in the Hydrodynamic Moment Hierarchy: A Semiclassical Truncation Strategy

In this paper we formulate the hydrodynamic moment and cumulant expansions of the density matrix for a quantum system in which the time evolution is described by an infinite hierarchy of coupled hydrodynamic moment equations. For the case where the system interacts with a complex environment, we develop a semiclassical closure that truncates the hierarchy. Our numerical approach for solving the truncated system of equations is intimately related to the de Broglie -Bohm interpretation of quantum mechanics, in that the time evolution of each cumulant is constructed over a discrete ensemble of hydrodynamic paths. We discuss the advantages and disadvantages of this scheme and apply the method to a model problem for a particle escaping from a metastable potential well while in contact with a thermal bath.