Eigenvalues and Eigenfunctions

The increasing number of Islamic followers in worldwide context and positive tourism trends boost up the demand for and supply of Islamic hospitality services. It is assumed that the emergence of Islamic financing is one of the driving factors of Syariah Compliant hotels besides the increasing number of Arab and Muslim travellers and their high purchasing power. However, specific guidelines need to be introduced in constructing this concept since there are many different opinions and inconsistencies in understanding such practices among the Syariah scholars and hotel operators. Corpus of past literatures affirmed that currently there is no standardization being introduced and most of the hotel operators came out with their own interpretation of compliant strategies. Therefore, this study empirically investigates the customers' awareness on Syariah Compliant concept and practices. Self-reported questionnaires were used to gather the data from the customers using convenience sampling. Result shows the more customers aware of Syariah Compliant concept and practices, the more they will accept it. However, it could be said that customers in general are not really comprehend about Syariah Compliant hence hotel operators are responsible to educate the customers.

The application of a trigonometric polynomial and an exponential fitting approach is compared for a three-point formula for second-order derivatives, for Simpson's quadrature rule and for Numerov's scheme for second-order differential equations. The expressions for the occurring parameters are constructed in both the approaches and the behaviour of these parameters with respect to the introduced frequency is studied. The errors for specific problems obtained in both the approaches as a function of the frequency are compared.

The effect of non-sphericity of the quantum dot on the eigenvalues and eigenfunctions has been investigated for the case when the barrier height at the surface is finite. The ground and excited state energies have been calculated variationally for prolate and oblate spheroids as a function of eccentricity of the spheroid. Analytic wavefunctions giving the admixture of higher angular momentum states have been obtained as a function of eccentricity.

This paper used the integer linear programming algorithm to solve the optimal phasor measurement unit (PMU) placement problem for full system observability. As the integer linear programming method leads to various optimal solutions, the multiple solution sets are generated, and a method is suggested to find the best set of PMU placement among the multiple solution sets for assessing the dynamic stability. In this method, two indices are used to assess dynamic stability. One is based on the real part of dominant eigenvalues of the system and the other one is based on MSE (Mean Squared Error) of system response. Different PMU placements with full observability property are ranked based on these indices. The suggested method is tested on the IEEE 39-bus test system and the results are shown in this paper.

We study basisness of root functions of Sturm–Liouville problems with a boundary condition depending quadratically on the spectral parameter. We determine the explicit form of the biorthogonal system. Using this we prove that the system of root functions, with arbitrary two functions removed, form a minimal system in L2, except some cases where this system is neither complete nor minimal. For the basisness in we prove that the part of the root space is quadratically close to systems of sines and cosines. We also consider these basis properties in the context of general L_p

It is well known that the harmonic oscillator potential can be solved by using raising and lowering operators. This operator method can be generalized with the help of supersymmetry and the concept of ``shape-invariant'' potentials. This generalization allows one to calculate the energy eigenvalues and eigenfunctions of essentially all known exactly solvable potentials in a simple and elegant manner.

This work presents a comparative study of two different control strategies for a flexible single-link manipulator. The dynamic model of the flexible manipulator involves modeling the rotational base and the flexible link as rigid bodies using the Euler Lagrange's method. The resulting system has one Degree-Of-Freedom (one DOF) and it provide freedom to increase the degree as well. Two types of regulators are studied, the State-Regulator using Pole Placement, and the Linear-Quadratic regulator (LQR). The LQR is obtained by resolving the Ricatti equation, in this work, we apply and compare two strategies to control the tip of the flexible link: state-feedback and linear quadratic regulator. These regulators are designed to reduce tip vibrations and increase system stability due to the flexibility of the arm.

This paper present our experience in the design of a permanent magnet generator. The generator has a long translator and a permanent magnet mover as magnetic field source. It generates a three phase electrical current. The generator is proposed to be operated using a dual chamber free piston internal combustion linear engine. The finished product is to be placed in a hybrid electric vehicle to generate electricity to run the motors and to charge the batteries [1],[2]. The machine design is performed using a 2D finite element analysis. The generator produces a three phase voltage and the power output is 7 kW. This paper also presents the fabrication of the prototype. © 2006 IEEE.

http://ieeexplore.ieee.org/ielx5/4107286/4107287/04107367.pdf?tp=&arnumber=4107367&isnumber=4107287

An introduction to Dirac delta function$ and its salient properties are presented. The experience of having taught  subjects in physics such as quantum mechanics, electromagnetism, optics, mathematical physics for the past three decades, the presentation in this communication is distinct and different. Many situations wherein Dirac delta function plays important roles are listed and discussed. It is hoped that this pedagogical paper will help the beginners to understand and appreciate this important singular function.
$ P. A. M. Dirac, “The Principles of Quantum mechanics”, Oxford Science Publications, 1970.

Laminar pulsating flows through rectangular channels, driven by an oscillatory pressure gradient, are common in microfluidic devices such as actuators and mixers. In channels with high width to height aspect ratio, the flow becomes 2D within a short distance from the entrance and an exact solution of the Navier-Stokes equations can be derived.
After formulating the problem in dimensionless form (Sec.1 and Sec.2), these notes derive the analytic solution using two methods: the Eigenfunction Expansion (Sec.3) and the asymptotic complex solution (Sec.4). These solutions are used to analyze the impact of the governing dimensionless parameters on the shape of the velocity profile (Sec.5.1), the flow rate per unit
width (Sec.5.2), and the wall shear stress (Sec.5.3).
These notes are also designed with a didactic purpose, providing a simple case study to practice with fundamental concepts such as nondimensionalization, transfer functions, and function decompositions. At the scope, all the Matlab files used are listed and described, and three complementary appendices are included: Sec.A discusses the link between different dimensionless formulations; Sec.B presents a tutorial on projections for discrete and continuous datasets; Sec.C lists additional Matlab files to compute a Finite Element (FE) solution of the problem using the pdep routine.

Quantized contact transformations are Toeplitz operators over a contact manifold $(X,\alpha)$ of the form $U_{\chi} = \Pi A \chi \Pi$, where $\Pi : H^2(X) \to L^2(X)$ is a Szego projector, where $\chi$ is a contact transformation and where $A$ is a pseudodifferential operator over $X$. They provide a flexible alternative to the Kahler quantization of symplectic maps, and encompass many of the examples in the physics literature, e.g. quantized cat maps and kicked rotors. The index problem is to determine $ind(U_{\chi})$ when the principal symbol is unitary, or equivalently to determine whether $A$ can be chosen so that $U_{\chi}$ is unitary. We show that the answer is yes in the case of quantized symplectic torus automorphisms $g$---by showing that $U_g$ duplicates the classical transformation laws on theta functions. Using the Cauchy-Szego kernel on the Heisenberg group, we calculate the traces on theta functions of each degree N. We also study the quantum dynamics generated by a general q.c.t. $U_{\chi}$, i.e. the quasi-classical asymptotics of the eigenvalues and eigenfunctions under various ergodicity and mixing hypotheses on $\chi.$ Our principal results are proofs of equidistribution of eigenfunctions $\phi_{Nj}$ and weak mixing properties of matrix elements $(B\phi_{Ni}, \phi_{Nj})$ for quantizations of mixing symplectic maps.

Brushless Doubly Fed Induction Generator (BDFIG) has been recently proposed to be used in variable speed wind turbines. This paper intends to investigate the influence of certain model simplifications to obtain a reduced-order model of a wind turbine with BDFIG suitable for transient studies. To achieve this goal, small signal analysis is performed for a recently manufactured 250 kVA BDFIG to obtain system modes and their participation factors. Identifying highly damped modes, influences of neglecting dynamics of their participated states are studied through time-domain simulation in MATLAB/Simulink.

In this article, the causes of drift in the velocity and the displacement time history are investigated. It is found that, in addition to numerical error, drift is caused by overdeterminacy in the constants of integration. Because there are six independent prescribed at-rest conditions (three initial and three terminal), the eigenfunctions from an eigenvalue problem, which is described by a sixth-order ordinary differential equation satisfying the six initial and terminal at-rest conditions, are chosen as a basis of expansion. The eigenfunctions form a dense and complete set and span a vector space. The eigenfunctions are used to expand an accelerogram. Drift-free consistent velocity and displacement time histories are then obtained, also in terms of the eigen-functions, without direct integration and baseline correction. A method is also proposed to modify a real recorded accelerogram using the eigenfunctions to generate time histories compatible with the target response spectra without drift.

We address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform and to the Seiberg-Witten map we construct an isomorphism between the operator and the phase space representations of the extended Heisenberg algebra. This map provides a systematic approach to derive the entire structure of noncommutative quantum mechanics in phase space. We construct the extended starproduct, Moyal bracket and propose a general definition of noncommutative states. We study the dynamical and eigenvalue equations of the theory and prove that the entire formalism is independent of the particular choice of Seiberg-Witten map. Our approach unifies and generalizes all the previous proposals for the phase space formulation of noncommutative quantum mechanics.

A control reinforced beam and four reinforced concrete beams with various extent of defects in the form of voids and load-induced cracking were analyzed. Local flexural stiffness at each coordinate point was derived by substituting the regressed data at that point and using the centered-finite-divided-difference formula. The results of the first derivative of the local flexular stiffness for the reinforced concrete beams with voids were compared with those obtained from a similar beam with cracks in the middle. The results were also compared with a similar beam with cracks on the right side of the beam.

sem-proceedings.com/19i/sem.org-IMAC-XIX-193603-Detection-Defects-Reinforced-Concrete-Beams-Using-Modal-Data.pdf

The eigenvalue equation of a band or a block tridiagonal matrix, the tight binding model for a crystal, a molecule, or a particle in a lattice with random potential or hopping amplitudes: these and other problems lead to three-term recursive relations for (multicomponent) amplitudes. Amplitudes n steps apart are linearly related by a transfer matrix, which is the product of n matrices. Its exponents describe the decay lengths of the amplitudes. A formula is obtained for the counting function of the exponents, based on a duality relation and the Argument Principle for the zeros of analytic functions. It involves the corner blocks of the inverse of the associated Hamiltonian matrix. As an illustration, numerical evaluations of the counting function of quasi 1D Anderson model are shown.

In functional linear regression, the slope "parameter" is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an ill-posed problem and has points of contact with a range of methodologies, including statistical smoothing and deconvolution. The standard approach to estimating the slope function is based explicitly on functional principal components analysis and, consequently, on spectral decomposition in terms of eigenvalues and eigenfunctions. We discuss this approach in detail and show that in certain circumstances, optimal convergence rates are achieved by the PCA technique. An alternative approach based on quadratic regularisation is suggested and shown to have advantages from some points of view.

We report quasiparticle calculations of the newly observed wurtzite polymorph of InAs and GaAs. The calculations are performed in the GW approximation ͑based on a model dielectric function͒ using plane waves and pseudopotentials. For comparison we also report the study of the zinc-blende phase within the same approximations. In the InAs compound the In 4d electrons play a very important role: whether they are frozen in the core or not leads either to a correct or a wrong band ordering ͑negative gap͒ within the local-density appproximation ͑LDA͒. We have calculated the GW band structure in both cases. In the first approach, we have estimated the correction to the pd repulsion calculated within the LDA and included this effect in the calculation of the GW corrections to the LDA spectrum. In the second case, we circumvent the negative gap problem by first using the screened exchange approximation and then calculating the GW corrections starting from the so obtained eigenvalues and eigenfunctions. This approach, that can be thought of as a step towards self-consistency, leads to a more realistic band structure and was also used for GaAs. For both InAs and GaAs in the wurtzite phase we predict an increase of the quasiparticle gap with respect to the zinc-blende polytype.

We propose a stable and efficient divide-and-conquer algorithm for computing the eigendecomposition of a symmetric tri-block-diagonal matrix. The matrix can be derived from discretizing Laplace operator eigenvalue in some two-dimensional graphs. All numerical results show that our algorithm is competitive with other methods, such as e.g QR algorithm, Cuppen's divide-and-conquer algorithm. We also show how to improve our algorithm by Fast Multipole Method.

For reconstruction of low-rank matrices from undersampled measurements, we develop an iterative algorithm based on least-squares estimation. While the algorithm can be used for any low-rank matrix, it is also capable of exploiting a-priori knowledge of matrix structure. In particular, we consider linearly structured matrices, such as Hankel and Toeplitz, as well as positive semidefinite matrices. The performance of the algorithm, referred to as alternating least-squares (ALS), is evaluated by simulations and compared to the Cramér-Rao bounds.

We present a procedure to construct a configuration-interaction expansion containing arbitrary excitations from an underlying full-configuration-interaction-type wave function defined for a very large active space. Our procedure is based on the density-matrix renormalization group (DMRG) algorithm that provides the necessary information in terms of the eigenstates of the reduced density matrices to calculate the coefficient of any basis state in the many-particle Hilbert space. Since the dimension of the Hilbert space scales binomially with the size of the active space, a sophisticated Monte Carlo sampling routine is employed. This sampling algorithm can also construct such configurationinteraction-type wave functions from any other type of tensor network states. The configurationinteraction information obtained serves several purposes. It yields a qualitatively correct description of the molecule's electronic structure, it allows us to analyze DMRG wave functions converged for the same molecular system but with different parameter sets (e.g., different numbers of active-system (block) states), and it can be considered a balanced reference for the application of a subsequent standard multi-reference configuration-interaction method.

This work introduces a link-analysis procedure for discovering relationships in a relational database or a graph, generalizing both simple and multiple correspondence analysis. It is based on a random-walk model through the database defining a Markov chain having as many states as elements in the database. Suppose we are interested in analyzing the relationships between some elements (or records) contained in two different tables of the relational database. To this end, in a first step, a reduced, much smaller, Markov chain containing only the elements of interest and preserving the main characteristics of the initial chain, is extracted by stochastic complementation . This reduced chain is then analyzed by projecting jointly the elements of interest in the diffusion-map subspace [42] and visualizing the results. This two-step procedure reduces to simple correspondence analysis when only two tables are defined and to multiple correspondence analysis when the database takes the form of a simple starschema. On the other hand, a kernel version of the diffusion-map distance, generalizing the basic diffusion-map distance to directed graphs, is also introduced and the links with spectral clustering are discussed. Several datasets are analyzed by using the proposed methodology, showing the usefulness of the technique for extracting relationships in relational databases or graphs.

The set of eigenvalues of a graph together with their multiplicities is called the spectrum of . The knowledge of spectrum can be used to obtain various topological properties of graphs like connectedness, toughness and many more. In this paper we use MATLAB to completely describe the spectrum of Sierpiński graphs and Sierpiński triangles, thus adding to the classes of graphs whose spectrum is known.

In a recent study by Kornath et al. [J. Chem. Phys. 118, 6957 (2003)], the Lin clusters with n = 2, 4 and 8 have been isolated in argon matrices at 15 K and characterized by Raman spectroscopy. This has prompted us to carry out a theoretical study on such clusters up to n = 10, using Hartree-Fock theory, plus low-order Møller-Plesset perturbation corrections. To check against the above study of Kornath et al., as a by-product we have made the same approximations for n = 6 and 8 as we have for n = 10. This has led us to emphasize trends with n through the Lin clusters for (i) ground-state energy, (ii) HOMO-LUMO energy gap, (iii) dissociation energy, and (iv) Hartree-Fock eigenvalue sum. The role of electron correlation in distinguishing between low-lying isomers is plainly crucial, and will need a combination of experiment and theory to obtain decisive results such as that of Kornath et al. for Li8. In particular, it is shown that Hartree-Fock theory plus bond order correlations does account for the experimentally observed symmetry T d symmetry for Li8. I. BACKGROUND AND OUTLINE

A detailed study of the axicon-based Bessel-Gauss resonator with concave output coupler is presented. We employ a technique to convert the Huygens-Fresnel integral self-consistency equation into a matrix equation and then find the eigenvalues and the eigenfields of the resonator at one time. A paraxial ray analysis is performed to find the self-consistency condition to have stable periodic ray trajectories after one or two round trips. The fast-Fourier-transform-based Fox and Li algorithm is applied to describe the three-dimensional intracavity field distribution. Special attention was directed to the dependence of the output transverse profiles, the losses, and the modal-frequency changes on the curvature of the output coupler and the cavity length. The propagation of the output beam is discussed. . Numerical propagation of the output beam of the ABGR for (a) plane and (b) spherical R ϭ 10L output couplers.

Gaussian wavepackets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an extended potential formulation. We develop Gaussian semiquantal dynamics to provide a phase space formalism and construct a propagator with desirable qualities. We qualitatively evaluate the behaviour of these semiquantal equations, and show that they reproduce the quantal behavior better than the standard Gaussian semiclassical dynamics. We also show that these semiclassical equations arise as truncations to semiquantal dynamics non-self-consistent inh. This enables us to introduce an extended semiclassical dynamics that retains the power of the Hamiltonian phase space formulation. Finally, we show how to obtain approximate eigenvalues and eigenfunctions in this formalism, and demonstrate with an example that this works well even for a classically strongly chaotic Hamiltonian.

The use of 3D models for progressive transmission and broadcasting applications is an interesting challenge due to the nature and complexity of such content. In this paper, a new image format for the representation of 3D progressive model is proposed. The powerful spectral analysis is combined with the state of art Geometry Image(GI) to encode static 3D models into spectral geometry images(SGI) for robust 3D shape representation. Based on the 3D model's surface characteristics, SGI separated the geometrical image into low and high frequency layers to achieve effective Level of Details(LOD) modeling. For SGI, the connectivity data of the model is implicitly encoded in the image, thus removing the need for additional channel bits allocated for its protection during transmission. We demonstrated that by coupling SGI together with an efficient channel allocation scheme, an image based method for 3D representation suitable for adoption in conventional broadcasting standard is proposed. The proposed framework is effective in ensuring the smooth degradation of progressive 3D models across varying channel bandwidths and packet loss conditions.

In this paper we obtain the continuity of attractors for semilinear parabolic problems with Neumann boundary conditions relatively to perturbations of the domain. We show that, if the perturbations on the domain are such that the convergence of eigenvalues and eigenfunctions of the Neumann Laplacian is granted then, we obtain the upper semicontinuity of the attractors. If, moreover, every equilibrium of the unperturbed problem is hyperbolic we also obtain the continuity of attractors. We also give necessary and sufficient conditions for the spectral convergence of Neumann problems under perturbations of the domain. r

In this work, we solve the Klein-Gordon (KG) equation for the general deformed Morse potential with equal scalar and vector potentials by using the Nikiforov-Uvarov (NU) method, which is based on the solutions of general second-order linear differential equation with special functions. The energy eigenvalues and corresponding normalized eigenfunctions are obtained. It is found that the eigenfunctions can be expressed by the Laguerre polynomials. Our solutions have a good agreement with earlier study.

We make use of recent results from random matrix theory to identify a derived threshold, for isolating noise from image features. The procedure assumes the existence of a set of noisy images, where denoising can be carried out on individual rows or columns independently. The fact that these are guaranteed to be correlated makes the correlation matrix an ideal tool for isolating noise. The random matrix result provides lowest and highest eigenvalues for the Gaussian random noise for which case, the eigenvalue distribution function is analytically known. This provides an ideal threshold for removing Gaussian random noise and thereby separating the universal noisy features from the non-universal components belonging to the specific image under consideration.

We study the transmission and conductance in poly{G}(T) N poly{G} strand, where G refers to Guanine and T refers to Thymine. We show that T plays a role as a barrier and the transmission decreases exponentially with the increasing number of Ts. We also investigate the transmission and conductance through superlattices poly{GGTT} and poly{GT}. Minibands are observed in these structures. The effect of coupling between DNA molecule and metal contacts is also explored.

ABSTRACT Localized surface plasmon resonances (LSPRs) in metallic nanoparticles (NPs) are calculated by a boundary integral equation (BIE) method. The response to the incident electromagnetic field and the NP polarizability are shown to depend on eigenvalues and eigenfunctions of the integral operator associated with BIE. The NP polarizability is conveniently expressed as an eigenmode sum of analytic terms when the Drude model of metals is used. The proposed polarizability decomposition is proven to offer an analytical tool for the design of plasmonic nanostructures.

According to recent experiments, magnetically confined fusion plasmas with "drift wave-zonal flow turbulence" ͑DW-ZF͒ give rise to broadband electromagnetic waves. Sharapov et al. ͓Europhysics .071͔ reported an abrupt change in the magnetic turbulence during L-H transitions in Joint European Torus ͓P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 ͑1987͔͒ plasmas. A broad spectrum of Alfvénic-like ͑electromagnetic͒ fluctuations appears from E ϫ B flow driven turbulence in experiments on the large plasma device ͑LAPD͒ ͓W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 ͑1991͔͒ facility at UCLA. Evidence of the existence of magnetic fluctuations in the shear flow region in the experiments is shown. We present one possible theoretical explanation of the generation of electromagnetic fluctuations in DW-ZF systems for an example of LAPD experiments.

We examine the evolution of an N-point signal produced and sensed at finite arrays of points transverse to a planar waveguide, within the framework of the finite quantization of geometric optics. In contradistinction to the common mechanical Hamiltonians (kinetic plus potential energy terms) the classical waveguide Hamiltonian is the square root of a difference of squares of the refractive index profile minus the optical momentum. The finitely quantized model requires the solution of the square eigenvalue and eigenfunction problem which leads to a step-two difference equation that contains two solutions and two signs of energy. We find the proper linear combinations to fit the Kravchuk functions of the finite oscillator model.

This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition H † ϭH on the Hamiltonian, where † represents the mathematical operation of complex conjugation and matrix transposition. This conventional Hermiticity condition is sufficient to ensure that the Hamiltonian H has a real spectrum. However, replacing this mathematical condition by the weaker and more physical requirement H ‡ ϭH, where ‡ represents combined parity reflection and time reversal PT, one obtains new classes of complex Hamiltonians whose spectra are still real and positive. This generalization of Hermiticity is investigated using a complex deformation Hϭ p 2 ϩx 2 (ix) ⑀ of the harmonic oscillator Hamiltonian, where ⑀ is a real parameter. The system exhibits two phases: When ⑀у0, the energy spectrum of H is real and positive as a consequence of PT symmetry. However, when Ϫ1Ͻ⑀Ͻ0, the spectrum contains an infinite number of complex eigenvalues and a finite number of real, positive eigenvalues because PT symmetry is spontaneously broken. The phase transition that occurs at ⑀ϭ0 manifests itself in both the quantum-mechanical system and the underlying classical system. Similar qualitative features are exhibited by complex deformations of other standard real Hamiltonians Hϭp 2 ϩx 2N (ix) ⑀ with N integer and ⑀ϾϪN; each of these complex Hamiltonians exhibits a phase transition at ⑀ϭ0. These PTsymmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space.

The effect of non-sphericity of the quantum dot on the eigenvalues and eigenfunctions has been investigated for the case of both the finite and infinite barrier. The ground and excited state energies have been calculated for prolate and oblate spheroids as a function of eccentricity of the spheroid. The analytic wavefunctions giving the admixture of higher angular momentum states have been obtained as a function of eccentricity.

We report the results of a study on the spectral properties of Laplace and Stokes operators modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, η, tends to zero. The eigenvalues and eigenfunctions are determined either analytically or numerically as functions of η, both in the continuous case and after applying Fourier or finite difference discretization schemes. For fixed η, we find that only the part of the spectrum corresponding to eigenvalues λ≲η−1 approaches Dirichlet boundary conditions, while the remainder of the spectrum is made of uncontrolled, spurious wall modes. The penalization error for the controlled eigenfunctions is estimated as a function of η and λ. Surprisingly, in the Stokes case, we show that the eigenfunctions approximately satisfy, with a precision O(η), Navier slip boundary conditions with slip length equal to √η. Moreover, for a given discretization, we show that there exists a value of η, corresponding to a balance between penalization and discretization errors, below which no further gain in precision is achieved. These results shed light on the behavior of volume penalization schemes when solving the Navier–Stokes equations, outline the limitations of the method, and give indications on how to choose the penalization parameter in practical cases.

We present non-quadratic Hessian-based regularization methods that can be effectively used for image-restoration problems, in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second-order differential operators. Specifically, we derive second-order regularizers that involve matrix norms of the Hessian operator. The definition of these functionals is based on an alternative interpretation of TV that relies on mixed norms of directional derivatives. We show that the resulting regularizers retain some of the most favorable properties of TV, namely, convexity, homogeneity, rotation, and translation invariance, while dealing effectively with the staircase effect. We further develop an efficient minimization scheme for the corresponding objective functions. The proposed algorithm is of the iterative-reweighted-least-squares (IRLS) type and results from a majorization-minimization approach. It relies on a problemspecific preconditioned conjugate-gradient method (PCG) which makes the overall minimization scheme very attractive, since it can be effectively applied to large images in a reasonable computational time. We validate the overall proposed regularization framework through deblurring experiments under additive Gaussian noise on standard and biomedical images.

Many perception problems in robotics such as object recognition, scene understanding, and mapping are tackled using scale-invariant interest points extracted from intensity images. Since interest points describe only local portions of objects and scenes, they offer robustness to clutter, occlusions, and intra-class variation.

Communication networks provide a larger flexibility with respect to the control design of large-scale interconnected systems by allowing the information exchange between the local controllers of the subsystems. The use of communication networks comes, however, at the price of non ideal signal transmission such as time delay which is a source of instability and deteriorates the control performance. This paper introduces an approach for the design of the communication topology for the distributed control of large-scale interconnected systems in order to optimize the whole system's performance in the presence of constant time delay. First, a decentralized control law that stabilizes the overall interconnected system is designed. Then the performance is improved by designing the distributed control law, i.e. allowing the controller of the subsystems to exchange information, by considering the time delay in the networks. As a novelty in this paper, the design of the communication topology between the controllers is also considered. The problem is formulated as a mixed-integer optimization problem. Furthermore, a method based on matrix perturbation theory is discussed to design the topology which also captures the relation between the time delay, controller gain and performance of the overall system. In addition, it is shown that the proposed strategy also guarantees the stability of the overall system under the permanent communication link failure. The results are validated through a numerical example.

We propose a stable and efficient divide-and-conquer algorithm for computing the eigendecomposition of a symmetric tri-block-diagonal matrix. The matrix can be derived from discretizing Laplace operator eigenvalue in some two-dimensional graphs. All numerical results show that our algorithm is competitive with other methods, such as e.g QR algorithm, Cuppen's divide-and-conquer algorithm. We also show how to improve our algorithm by Fast Multipole Method.

Two computer programs (FGHEVEN and FGHFFT) for solving the one-dimensional Schrodinger equation for bound-state eigenvalues and eigenfunctions are presented. Both computer programs are based on the Fourier grid Hamiltonian method (J. Chem. Phys. 91(1989) 3571). The method is exceptionally simple and robust. It relies on using the momentum representation for the kinetic energy operator and the coordinate representation for the potential energy. The first computer program (FGHEVEN) is based on an explicit (very simple) expression for the Hamiltonian matrix. The eigenvalues of this matrix give the required bound-state energies and the eigenvectors yield directly the eigenfunctions evaluated on the regularly spaced grid points. In this paper the theory has been slightly extended to encompass the situation where an even number of grid points is used. The second program (FGHFFT) is based on a complimentary theory which makes use of the discrete fast Fourier transform technique to evaluate the Hamiltonian matrix. The programs are self-contained and include subroutines to find the eigenvalues and eigenvectors needed.