Eigenvalues and Eigenfunctions

Compressed sensing allows for a significant reduction of the number of measurements when the signal of interest is of a sparse nature. Most computationally efficient algorithms for signal recovery rely on some knowledge of the sparsity level, i.e., the number of non-zero elements. However, the sparsity level is often not known a priori and can even vary with time. In this contribution we show that it is possible to estimate the sparsity level directly in the compressed domain, provided that multiple independent observations are available. In fact, one can use classical model order selection algorithms for this purpose. Nevertheless, due to the influence of the measurement process they may not perform satisfactorily in the compressed sensing setup. To overcome this drawback, we propose an approach which exploits the empirical distributions of the noise eigenvalues. We demonstrate its superior performance compared to state-of-the-art model order estimation algorithms numerically.

The objective of this paper is to summarize the work that has been developed by the authors for the last several years, in order to demonstrate that the Theory of Characteristic Modes can be used to perform a systematic design of different types of antennas. Characteristic modes are real current modes that can be computed numerically for conducting bodies of arbitrary shape. Since characteristic modes form a set of orthogonal functions, they can be used to expand the total current on the surface of the body. However, this paper shows that what makes characteristic modes really attractive for antenna design is the physical insight they bring into the radiating phenomena taking place in the antenna. The resonance frequency of modes, as well as their radiating behavior, can be determined from the information provided by the eigenvalues associated with the characteristic modes. Moreover, by studying the current distribution of modes, an optimum feeding arrangement can be found in order to obtain the desired radiating behavior.

This work represents a first systematic attempt to create a common ground for semi-classical and time-frequency analysis. These two different areas combined together provide interesting outcomes in terms of Schrödinger type equations. Indeed, continuity results of both Schrödinger propagators and their asymptotic solutions are obtained on-dependent Banach spaces, the semiclassical version of the well-known modulation spaces. Moreover, their operator norm is controlled by a constant independent of the Planck's constant. The main tool in our investigation is the joint application of standard approximation techniques from semi-classical analysis and a generalized version of Gabor frames, dependent of the parameter. Continuity properties of more general Fourier integral operators (FIOs) and their sparsity are also investigated.

The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on R n ⊕ R n. In this paper we will show that the replacement of this structure by an arbitrary symplectic structure leads to a pseudo-differential calculus of operators acting on functions or distributions defined, not on R n but rather on R n ⊕ R n. These operators are intertwined with the standard Weyl pseudodifferential operators using an infinite family of partial isometries of L 2 (R n) −→ L 2 (R 2n) indexed by S(R n). This allows us obtain spectral and regularity results for our operators using Shubin's symbol classes and Feichtinger's modulation spaces.

Signal-to-interference ratio (SIR) experienced by users is the major quality and capacity indicator of CDMA systems. In this paper, we analyze the impact of diversity combining schemes-maximal-ratio combining (MRC) and equalgain combining (EGC)-on the SIRs achievable with diversityreception RAKE receivers over GWSSUS time-variant fading uplink DS-CDMA channels based on finite-dimensional generalized random spreading performance evaluation methodology. Through the results of random matrix theory on the nonasymptotic eigenvalue distributions of finite-size random matrices, SIR statistics with linear RAKE multiuser receivers with MRC and EGC are derived in terms of the key system parameters. It turns out that MRC that is much complex than EGC in terms of channel estimation and computational complexity slightly outperforms EGC at low diversity orders and low channel specularity; however the performance of EGC converges to that with MRC as the diversity order D→ ∞ and the channel specularity tends to 1 as well as at low SNRs.

We have modeled the optical properties of the ZnMgO/ZnO/ZnMgO system and correlated them to its transport properties by employing an effective mass equation method. By its construction our method was sensitive to the barrier thickness of the system. From our results we deduce that there are more states in the well than resonant tunneling peaks in the transport data. The ''missing'' states in the electrical characteristics are not seen because of their much lower localization in the well. However these states are responsible for the UV activity of the system. Reducing the barrier thickness changes dramatically the localization of the states in the well without affecting significantly the energy levels. Hence the electrical properties can be changed without changing significantly the optical properties.

1. Zobecněné vlastní vektory. V dalším budeme uvažovat linearní operátory α : V → V , kde V je vektorový prostor dimenze n nad tělesem C. Zatím jsme se zabývali většinou tzv. diagonalizovatelnými lineárními operátory, tj. operátory α, které mají bázi složenou z vlastních vektorů. Ne všechny lineární operátory jsou ovšem diagonalizovatelné. Příklad 1. Vezměme α : C→C, jehož matice A ve standardní bázi je dána A = 

We consider different stiff spectral problems with a small parameter for the Laplace operator in two different domains of the plane Ω and Ω ε , respectively. Here Ω ε = Ω ∪ ω ε ∪ Γ , where Ω is a fixed open bounded domain with boundary Γ , ω ε is a curvilinear strip of variable width O(ε), and Γ = Ω ∩ω ε. ε and δ ε are small parameters that converge towards zero. The first problem is a Wentzell spectral problem in the fixed domain Ω, with the parameter δ ε appearing on the boundary condition, multiplying the normal derivative on Γ. For the second problem, posed in Ω ε with a Neumann condition on the boundary of Ω ε , the density and stiffness constants are of order O(ε −t) in the strip ω ε , with t > 1, while they are of order O(1) in the fixed domain Ω. We provide asymptotic expansions for the eigenvalues and eigenfunctions of both problems and obtain bounds for convergence rates of these eigenelements as ε → 0. In addition, we seek out the connection between both problems, which have a common limiting eigenvalue problem (cf. (2.15)-(2.16)), and notice an asymptotic dissociation in two spectral problems on Ω and Γ. We also show that the Wentzell spectral problem can be considered as an alternative approach for the stiff problem in the perturbed domain Ω ε when δ ε = ε t−1 , as ε → 0.

This paper proposes a method of probabilistic analysis to investigate the impact of stochastic uncertainty of grid-connected wind generation on power system small-signal stability. The proposed method is "analytical" in contrast to the numerical method of Monte Carlo simulation which relies on large number of random computations. It can directly calculate the probabilistic density function (PDF) of critical eigenvalues of a large-scale power system from the PDF of grid-connected multiple sources of wind power generation, thus to determine the probabilistic small-signal stability of the power system as affected by the wind generation. In the paper, an example of 16-machine power system with 3 grid-connected wind farms is used to demonstrate the application of the proposed method. The results of probabilistic stability analysis of the example power system are confirmed by the Monte Carlo simulation. It is shown that the stochastic variation of grid-connected wind generation can cause the system to lose stability even though the system is stable deterministically. The higher the level of wind penetration is, the more the probability that the system becomes unstable could be. Hence indeed penetration of stochastically variable wind generation threats stable operation of power systems as far as system small-signal stability is concerned.

In this paper Model Based Networked Control Systems (MB-NCS) are considered and on-line identification of system parameters in state space representation is used to upgrade the model and the controller of the system. The updated model is used to control the real system when feedback information is unavailable. The Extended Kalman Filter (EKF) is analyzed in the context of parameter identification and implemented in the MB-NCS framework. Emphasis is placed on global asymptotic estimators for the case when sensors provide noiseless measurements of the state of a linear system; it can be shown that the identification of parameters in this case is a linear problem, in contrast to the nonlinear combined stateparameter estimation problem. We propose new estimation models that offer better convergence properties than the EKF in this case. This estimation strategy is also applied to the MB-NCS framework resulting in a better usage of the network by allowing longer intervals without need for a measurement update.

This paper proposes an alprithin for computing syinmetric eigenvalues and eigenvectors that uses a onesided Jacobi approach and is targeted to a multicomputer in which nodes can be arranged as a two-dimensional mesh with an arbitrary number of rows and columns. The algorithm is analysed through simple analytical inodels of execution time, which show that an adequate choice of the mesh configuration (number of rows and columns) can improve performance significantly, with respect to a onedimensional configuration, which is the most frequently considered scenario in current proposals. This improvement is especially noticeable in large systems. I

The communication cost plays a key role in the performance of many parallel algorithms. In the particular case of the one-sided Jacobi method for symmetric eigenvalue and eigenvector computation the communication cost of previously proposed algorithms is mainly determined by the particular ordering being used. In this paper we proposed two novel Jacobi orderings: the permuted-BR ordering and the degree-4 ordering, aimed at efficiently exploiting the multi-port capability of a hypercube. It is shown that the former is nearly optimal for some scenarios and the latter outperforms previously known orderings by a factor of two.

We study the problem of the homogenization of Dirichlet eigenvalue problems for the p-Laplace operator in a sequence of perforated domains with fine-grained boundary. Using the asymptotic expansion method, we derive the homogenized problem for the new equation with an additional term of capacity type. Moreover, we show that a sequence of eigenvalues for the problem in perforated domains converges to the corresponding critical levels of the homogenized problem.

We study the performance of various beamformers for estimating a current dipole source at a known location using electroencephalography (EEG) and magnetoencephalography (MEG). We present our beamformers in the form of the generalized sidelobe canceler (GSC). Under this structure, the beamformer can be solved by finding a filter that achieves the minimum mean-squared error (MMSE) between the mainbeam response and filtered observed signal. We express the MMSE as a function of the filter's rank and use it as a criterion to evaluate the performance of the beamformers. We do not make any assumptions on the rank of the interference-plus-noise covariance matrix. Instead, we treat it as low-rank and derive a general expression for the MMSE. We present numerical examples to compare the MSE performance of beamformers commonly studied in the literature: principal components (PCs), cross-spectral metrics (CSMs), and eigencanceler (EIG) beamformers. Our results show that good estimates of the dipole source signals can be achieved using reduced-rank beamformers even for low signal-to-noise ratio (SNR) values.

Biogeography deals with the study of the distribution of biodiversity over space and time and has been well studied by naturists and biologists for over the last five decades. Recently, the theory of biogeography has been applied to solve difficult engineering optimization problems in the form of a nature-inspired metaheuristic, known as biogeography-based optimization (BBO) algorithm. In this correspondence paper, we present an in-depth analysis of the linear time-invariant (LTI) system model of immigration and emigration of organisms in an island biogeography system that forms the basis of BBO. We find the bound of the eigenvalues of the general LTI system matrix using the Perron-Frobenius theorem from linear algebra. Based on the bounds of the eigenvalues, we further investigate four important properties of the LTI biogeography system, including the system reasonability with probability distribution vectors, stability, convergence, and nature of the equilibrium state. Our analysis gives a better insight into the dynamics of migration in actual biogeography systems and also helps in the understanding of the search mechanism of BBO on multimodal fitness landscapes.

Careful calculations are performed to obtain the radial density–density response function for the He and the Be series. This is also done along the adiabatic connection of the density functional theory (as the system evolves from the real, physical system to the Kohn–Sham one). In this process the electron density is kept constant, while the strength of the interaction between electrons changes. The response functions are analyzed in terms of their eigenvalues and eigenfunctions. The latter change only little along this process. The absolute value of the eigenvalues is in general reduced by the interaction: A screening effect is present. For the near-degenerate systems, we notice that the opposite effect can appear (antiscreening).

The quantum computation of electronic energies can break the curse of dimensionality that plagues manyparticle quantum mechanics. It is for this reason that a universal quantum computer has the potential to fundamentally change computational chemistry and materials science, areas in which strong electron correlations present severe hurdles for traditional electronic structure methods. Here we present a state-of-the-art analysis of accurate energy measurements on a quantum computer for computational catalysis, using improved quantum algorithms with more than an order of magnitude improvement over the best previous algorithms. As a prototypical example of local catalytic chemical reactivity we consider the case of a ruthenium catalyst that can bind, activate, and transform carbon dioxide to the high-value chemical methanol. We aim at accurate resource estimates for the quantum computing steps required for assessing the electronic energy of key intermediates and transition states of its catalytic cycle. In particular, we present quantum algorithms for double-factorized representations of the four-index integrals that can significantly reduce the computational cost over previous algorithms, and we discuss the challenges of increasing active space sizes to accurately deal with dynamical correlations. We address the requirements for future quantum hardware in order to make a universal quantum computer a successful and reliable tool for quantum computing enhanced computational materials science and chemistry, and identify open questions for further research.

In addition to legal matters involving the development of consumer protection system in Romania, the organization and functioning of a proper institutional framework is particularly important to ensure the practical effectiveness of any legislation adopted in this field.
This article provides an analysis of the activities undertaken between 2012 and 2019 by the National Authority for Consumer Protection (NACP), as the specialized body of central public
administration performing tasks to protect Romanian consumers,
with the focus on its national market surveillance actions. The
research is completed with the assessment made by Romanian
consumers particularly on the effectiveness of these activities, and
generally on the consumer protection system developed at national
level, compared to the European Union average. As a conclusion, the authors highlight the need for NACP to act openly and firmly to make its activity of direct but also indirect protection of the Romanian consumers more efficient, complementing market surveillance actions with information and education activities and strengthening their decision-making capacity.

We present a new Lie algebraic method to study the eigenvalues and eigenfunctions of quantum anharmonic oscillators. We consider the Hamiltonians for the simple harmonic and anharmonic oscillator as the two generators of a Lie algebra, whose other generators may be found exactly or up to any order of the parameter involved. Specifically, the closed commutator algebra for the quartic anharmonic oscillator is established in a perturbation sense. An element of this Lie group, turning out to be the four-photon operator, transforms the quartic anharmonic oscillator Hamiltonian to the harmonic one in a perturbation sense; thus, facilitating the calculation of the eigenvalues and eigenfunctions of the former.

Given a simple, undirected graph G, Budinich [Discrete Applied Mathematics, 127 (2003), 535-543] proposed a lower bound on the clique number of G by combining the quadratic programming formulation of the clique number due to Motzkin and Straus (1965) with the spectral decomposition of the adjacency matrix of G. This lower bound improves the previously known spectral lower bounds on the clique number that rely on the Motzkin-Straus formulation. In this paper, we give a simpler, alternative characterization of this lower bound. For regular graphs, this simpler characterization allows us to obtain a simple, closed-form expression of this lower bound as a function of the positive eigenvalues of the adjacency matrix. Our computational results shed light on the quality of this lower bound in comparison with the other spectral lower bounds on the clique number.

Perhaps the most powerful method for deriving the Newtonian gravitational interaction between two masses is the multipole expansion. Once inner multipoles are calculated for a particular shape this shape can be rotated, translated, and even converted to an outer multipole with well established methods. The most difficult stage of the multipole expansion is generating the initial inner multipole moments without resorting to three dimensional numerical integration of complex functions. Previous work has produced expressions for the low degree inner multipoles for certain elementary solids. This work goes further by presenting closed form expressions for all degrees and orders. A combination of these solids, combined with the aforementioned multipole transformations, can be used to model the complex structures often used in precision gravitation experiments.

We propose to directly process 3D+t image sequences with mathematical morphology operators, using a new classification of the 3D + t structuring elements. Several methods (filtering, tracking, segmentation) dedicated to the analysis of 3D +1 datasets of zebrafish embryogenesis are introduced and validated through a synthetic dataset. Then, we illustrate the application of these methods to the analysis of datasets of zebrafish early development acquired with various microscopy techniques. This processing paradigm produces spatio-temporal coherent results as it benefits from the intrinsic redundancy of the temporal dimension, and minimizes the needs for human intervention in semi-automatic algorithms. Index Terms-3D +t mathematical morphology, in-vivo light microscopy, spatio-temporal structuring elements, zebrafish embryogenesis. I. INTRODUCTION T HE ROLE OF automated image processing methods is crucial for the analysis of new biological data based on in-vivo imaging observations. Developmental biology is under revolution with the inclusion of new microscopy technologies [1] and automated processing methods [2]. In this context, image analysis is still an open challenge: new methodologies applied to in-vivo imaging should provide a set of tools able to deal with very different types of datasets [3]. The zebrafish a vertebrate which has phylogenetic proximity to Manuscript

The aim of this work is to investigate the problem of piezoelectric laminate placement. This problem is addressed in the case of modal identification and active control of plate like structures using piezoelectric laminates. The placement technique is based on the inspection of the controllability Grammian of the system expressed in a modal state-space coordinates. The controllability Grammian is able to quantify how structural modes are controllable with a set of predefined actuators. An initial finite element model or an experimental modal identification of the structure is required at the initial step. The procedure consists in making a selection of the smallest subset of actuators which gives a norm of the system transfer function as close as possible to the norm of the original full set. As the study context consists in noise reduction in buildings, the second part of this paper describes an application of this technique on a wooden shutter box in order to reduce the acoustic transmission towards the inner room.

Few works have been performed in the field of experimental modal analysis by means of piezoelectric distributed elements. Piezoelectric laminates, initially intended for the monitoring and the control of smart structures, could also be dedicated to the experimental modal identification of an open-loop structure. A pole-residue development of the open-loop piezo-structure shows that conventional algorithms and a piezoelectric pseudocollocated actuator/sensor may be used to estimate the mechanical modal parameters. When an initial mathematical model of the structure is available, the 'best' excitation position is determined by checking the H 2 norm of the transfer function of the fully observed system. The same methodology can be applied for the selection of the monitoring locations. In most cases, experimental testing with the selected sensors set, gives acceptable information to identify target modes. These data, coupled with electrical sensing at the piezoelectric element level, can then be used to perform the modal analysis of the piezo-structure. A light clamped-free plate instrumented with piezo-laminates is used to illustrate this experimental approach. 2 The dynamic analysis of piezostructures 2.1 Modal analysis of a conventional structure The resolution of the eigenvalues problem of a conventional linear structure :

The aim of this work is to investigate the problem of piezoelectric laminate placement. This problem is addressed in the case of modal identification and active control of plate like structures using piezoelectric laminates. The placement technique is based on the inspection of the controllability Grammian of the system expressed in a modal state-space coordinates. The controllability Grammian is able to quantify how structural modes are controllable with a set of predefined actuators. An initial finite element model or an experimental modal identification of the structure is required at the initial step. The procedure consists in making a selection of the smallest subset of actuators which gives a norm of the system transfer function as close as possible to the norm of the original full set. As the study context consists in noise reduction in buildings, the second part of this paper describes an application of this technique on a wooden shutter box in order to reduce the acoustic transmission towards the inner room.

Careful calculations are performed to obtain the radial density–density response function for the He and the Be series. This is also done along the adiabatic connection of the density functional theory (as the system evolves from the real, physical system to the Kohn–Sham one). In this process the electron density is kept constant, while the strength of the interaction between electrons changes. The response functions are analyzed in terms of their eigenvalues and eigenfunctions. The latter change only little along this process. The absolute value of the eigenvalues is in general reduced by the interaction: A screening effect is present. For the near-degenerate systems, we notice that the opposite effect can appear (antiscreening).

Fig. 1. Visualization of the ground deformation associated with a simulation of the June, 1992 Mw=7.3 Landers, CA earthquake. (a) new hybrid visualization of the displacement-gradient tensor field (α = 0.022, β = 0.8, iter = 800, m r = 10), (b) previous visualization using hyperstreamlines only, (c) a common visualization method used in earthquake deformation studies showing the displacement vector field only, (d) the expected deformation modes for a right-lateral fault. Note how the glyph packing in the complex domains (see the highlighted region) better conveys the elliptical deformation pattern than the previous methods (e.g. (b) and (c)).

Time-dependent and time-independent quantum scattering methods are used to investigate state-to-state inelastic and reactive collision dynamics for a three-dimensional (3D) atom+triatom model of Cl+H2O→HCl+OH. The results elucidate the role of (i) intramolecular vibrational energy transfer and (ii) vibrational nonadiabaticity on the time scale of a reactive encounter in systems with nearly degenerate stretching “local modes.” Adiabatic two-dimensional (2D) vibrational eigenfunctions [ψn(r1,r2,R)] and eigenvalues [En(R)] are first obtained in OH bond coordinates (r1,r2) as a function of Cl–H2O center-of-mass separation (R), which then provides the requisite adiabatic potential energy curves and nonadiabatic coupling matrix elements for full 3D quantum wave packet propagation. Inspection of these 2D vibrational eigenfunctions indicates that near degeneracy between H2O symmetric |01+〉 and antisymmetric |01−〉 states is systematically lifted as R decreases, causing vibrational energy to ...

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. The Laplacian (respectively, the signless Laplacian) energy of G is the sum of the absolute values of the differences between the eigenvalues of the Laplacian (respectively, signless Laplacian) matrix and the arithmetic mean of the vertex degrees of the graph. In this paper, among some results which relate these energies, we point out some bounds to them using the energy of the line graph of G. Most of these bounds are valid for both energies, Laplacian and signless Laplacian. However, we present two new upper bounds on the signless Laplacian which are not upper bounds for the Laplacian energy.

II. INTRODUCTION URING many decades the electrical power system stability had been recognized as a security problem. Most blackout scenarios worldwide have been caused by instability problems due to the growth of the power systems, increase of power systems interconnections, use of new technologies and power system controls. Also the power system management on congestion scenarios has given rise to new instability forms that appear as voltage instability and inter-area mode oscillations. This document presents the most relevant results of the research titled "Analysis of the dynamic behavior of the power systems-Application Colombian interconnection with neighbor countries" developed in the Center of Energy Studies of the Escuela Colombiana de Ingeniería "Julio Garavito" [8].

We give a general method to construct a complete set of linearly independent Casimir operators of a Lie algebra with rank N. For a Casimir operator of degree p, this will be provided by an explicit calculation of its symmetric coefficients g A1A2..Ap. It is seen that these coefficients can be described by some rational polinomials of rank N. These polinomials are also multilinear in Cartan sub-algebra indices taking values from the set I • ≡ {1, 2, .., N }. The crucial point here is that for each degree one needs, in general, more than one polinomial. This in fact is related with an observation that the whole set of symmetric coefficients g A1A2..Ap is decomposed into some subsets which are in one-to-one correspondence with these polinomials. We call these subsets clusters and introduce some indicators with which we specify different clusters. These indicators determine all the clusters whatever the numerical values of coefficients g A1A2..Ap are. For any degree p, the number of clusters is independent of rank N. This hence allows us to generalize our results to any value of rank N. To specify the general framework, explicit contructions of 4th and 5th order Casimir operators of A N Lie algebras are studied and all the polinomials which specify the numerical value of their coefficients are given explicitly.

We give a general method to construct a complete set of linearly independent Casimir operators of a Lie algebra with rank N. For a Casimir operator of degree p, this will be provided by an explicit calculation of its symmetric coefficients gA1,A2,…,Ap. It is seen that these coefficients can be described by some rational polynomials of rank N. These polynomials are also multilinear in Cartan sub-algebra indices taking values from the set I0≡{1,2,…,N}. The crucial point here is that for each degree one needs, in general, more than one polynomial. This in fact is related to an observation that the whole set of symmetric coefficients gA1,A2,…,Ap is decomposed into some sub-sets which are in one-to-one correspondence with these polynomials. We call these sub-sets clusters and introduce some indicators with which we specify different clusters. These indicators determine all the clusters whatever the numerical values of coefficients gA1,A2,…,Ap are. For any degree p, the number of clusters...

In applications of principal component analysis (PCA) it has often been observed that the eigenvector with the largest eigenvalue has only nonnegative entries when the vectors of the underlying stochastic process have only nonnegative values. This has been used to show that the coordinate vectors in PCA are all located in a cone. We prove that the nonnegativity of the first eigenvector follows from the Perron-Frobenius (and Krein-Rutman theory). Experiments show also that for stochastic processes with nonnegative signals the mean vector is often very similar to the first eigenvector. This is not true in general, but we first give a heuristical explanation why we can expect such a similarity. We then derive a connection between the dominance of the first eigenvalue and the similarity between the mean and the first eigenvector and show how to check the relative size of the first eigenvalue without actually computing it. In the last part of the paper we discuss the implication of theoretical results for multispectral color processing.

Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the Navier-Stokes equations. We construct a dynamical, 10 5-dimensional state-space representation of plane Couette flow at Re = 400 in a small, periodic cell and offer a new method of visualizing invariant manifolds embedded in such high dimensions. We compute a new equilibrium solution of plane Couette flow and the leading eigenvalues and eigenfunctions of known equilibria at this Re and cell size. What emerges from global continuations of their unstable manifolds is a surprisingly elegant dynamical-systems visualization of moderate-Re turbulence. The invariant manifolds tessellate the region of state space explored by transiently turbulent dynamics with a rigid web of continuous and discrete symmetry-induced heteroclinic connections.

In this article, a new second order sliding mode differentiator with a variable exponent is proposed. Inspired by the classical super twisting differentiator, the dedicated differentiator allows to give a solution for reducing the effect of variable noise of sensor output measurement. To achieve this objective, the parameter α that is fixed in a super twisting differentiator is made variable in the proposed differentiator. First of all, the proposed differentiator is presented in free noise case, after that the extension to the case with output noise is given in details. In both cases the practical convergences of the observation error are guaranteed. In the first the radius of the practical stability is depending on the considered unknown input while in the second case this radius depends also on the noise. Finally some simulation results are given in order to show the performances and the effectiveness of the proposed differentiator compared to existing one.

One key factor that hinders the widespread deployment of speaker verification technologies is the requirement of long enrollment utterances to guarantee low error rate during verification. To gain user acceptance of speaker verification technologies, adaptation algorithms that can enroll speakers with short utterances are highly essential. To this end, this paper applies kernel eigenspace-based MLLR (KEMLLR) for speaker enrollment and compares its performance against three state-of-the-art model adaptation techniques: maximum a posteriori (MAP), maximum-likelihood linear regression (MLLR), and reference speaker weighting (RSW). The techniques were compared under the NIST2001 SRE framework, with enrollment data vary from 2 to 32 seconds. Experimental results show that KEMLLR is most effective for short enrollment utterances (between 2 to 4 seconds) and that MAP performs better when long utterances (32 seconds) are available.

We present a novel semantic approach to modeling and simulation of nanoelectronic devices. The approach is based on a finite volume spatial discretization scheme. The scheme was adapted to accurately treat material anisotropy. It is thus capable of capturing orientation and strain effects both of which are prominent in the nanoscale regime. We also demonstrate the method's simplicity and power with a three-dimensional simulation study of a quantum dot using a six band k • p Hamiltonian for holes as model.

In this paper a spectral theory pertaining to Quasi-Birth±Death Processes (QBDs) is presented. The QBD, which is a generalization of the birth±death process, is a powerful tool that can be utilized in modeling many stochastic phenomena. Our theory is based on the application of a matrix polynomial method to obtain the steady-state probabilities in state-homogeneous ®nite-state QBDs. The method is based on ®nding the eigenvalue±eigenvector pairs that solve a matrix polynomial equation. Since the computational eort in the solution procedure is independent of the cardinality of the counting set, it has an immediate advantage over other solution procedures. We present and prove dierent properties relating the quantities that arise in the solution procedure. By also compiling and formalizing the previously known properties, we present a formal uni®ed theory on the spectral properties of QBDs, which furnishes a formal framework to embody much of the previous work. This framework carries the prospect of furthering our understanding of the behavior the modeled systems manifest.

Using the Nikiforov-Uvarov method, the bound state energy eigenvalues and eigenfunctions of the PT-/non-PT-symmetric and non-Hermitian generalized Woods-Saxon (WS) potential with the real and complex-valued energy levels are obtained in terms of the Jacobi polynomials. According to the PT-symmetric quantum mechanics, we exactly solved the time-independent Schrödinger equation with same potential for the s-states and also for any l-state as well. It is shown that the results are in good agreement with the ones obtained before.

An approximate solution of the Schrödinger equation for the generalized Hulthén potential with non-zero angular quantum number is solved. The bound state energy eigenvalues and eigenfunctions are obtained in terms of Jacobi polynomials. The Nikiforov-Uvarov method is used in the computations. We have considered the timeindependent Schrödinger equation with the associated form of Hulthén potential which simulate the effect of the centrifugal barrier for any l-state. The energy levels of the used Hulthén potential gives satisfactory values for the non-zero angular momentum as the generalized Hulthén effective potential.

We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of boundary mass concentration. We discuss the asymptotic behavior of the Neumann eigenvalues in a ball and we deduce that the Steklov eigenvalues minimize the Neumann eigenvalues. Moreover, we study the dependence of the eigenvalues of the Steklov problem upon perturbation of the mass density and show that the Steklov eigenvalues violates a maximum principle in spectral optimization problems.

To study the stability of a nominal cyclic steady state in power electronic converters, it is necessary to obtain a linearization around the periodic orbit. In many past studies, this was achieved by explicitly deriving the Poincaré map that describes the evolution of the state from one clock instant to the next and then locally linearizing the map at the fixed point. However, in many converters, the map cannot be derived in closed form, and therefore this approach cannot directly be applied. Alternatively, the orbital stability can be worked out by studying the evolution of perturbations about a nominal periodic orbit, and some studies along this line have also been reported. In this paper, we show that Filippov's method-which has commonly been applied to mechanical switching systems-can be used fruitfully in power electronic circuits to achieve the same end by describing the behavior of the system during the switchings. By combining this and the Floquet theory, it is possible to describe the stability of power electronic converters. We demonstrate the method using the example of a voltage-mode-controlled buck converter operating in continuous conduction mode. We find that the stability of a converter is strongly dependent upon the so-called saltation matrix-the state transition matrix relating the state just after the switching to that just before. We show that the Filippov approach, especially the structure of the saltation matrix, offers some additional insights on issues related to the stability of the orbit, like the recent observation that coupling with spurious signals coming from the environment causes intermittent subharmonic windows. Based on this approach, we also propose a new controller that can significantly extend the parameter range for nominal period-1 operation.