Search results for: Riesz basis

Authors: Mehdi Rashidi-Kouchi, Asghar Rahimi

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Sun introduced a generalization of frames and showed that this includes more other cases of generalizations of frame concept and proved that many basic properties can be derived within this more general context. Another generalization of frames is frames in Hilbert C*-module. It has been proved that every g-frame in Hilbert space H respect to Hilbert space K is a frame for B(H;K) as Hilbert C*-module. We show that every g-Riesz basis for Hilbert space H respect to K by add a condition is a Riesz basis for Hilbert B(K)-module B(H;K). Also, we investigate similar result for g-orthonormal and orthogonal bases.

Keywords: frame, g-frame, Riesz basis, g-Riesz basis, Hilbert C*-module

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Authors: Mouna Zitouni, Mariem Tounsi

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This research introduces an application of the Riesz mixture model for medical image segmentation for accurate diagnosis and treatment of brain tumors. We propose a pixel classification technique based on the Riesz distribution, derived from an extended Bartlett decomposition. To our knowledge, this is the first study addressing this approach. The Expectation-Maximization algorithm is implemented for parameter estimation. A comparative analysis, using both synthetic and real brain images, demonstrates the superiority of the Riesz model over a recent method based on the Wishart distribution.

Keywords: EM algorithm, segmentation, Riesz probability distribution, Wishart probability distribution

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Authors: Ti-Jun Xiao, Zhe Xu

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Controllability is one of the fundamental issues in control systems. In this paper, we study the controllability of second order evolutional control systems in Hilbert spaces with memory and boundary controls, which model dynamic behaviors of some viscoelastic materials. Transferring the control problem into a moment problem and showing the Riesz property of a family of functions related to Cauchy problems for some integrodifferential equations, we obtain a general boundary controllability theorem for these second order evolutional control systems. This controllability theorem is applicable to various concrete 1D viscoelastic systems and recovers some previous related results. It is worth noting that Riesz sequences can be used for numerical computations of the control functions and the identification of new Riesz sequence is of independent interest for the basis-function theory. Moreover, using the Riesz sequences, we obtain the existence and uniqueness of (weak) solutions to these second order evolutional control systems in Hilbert spaces. Finally, we derive the exact boundary controllability of a viscoelastic beam equation, as an application of our abstract theorem.

Keywords: evolutional control system, controllability, boundary control, existence and uniqueness

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

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Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization

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Authors: M. M. M. Jaradat

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For a given graph G, the set Ԑ of all subsets of E(G) forms an |E(G)| dimensional vector space over Z2 with vector addition X⊕Y = (X\Y ) [ (Y \X) and scalar multiplication 1.X = X and 0.X = Ø for all X, Yϵ Ԑ. The cycle space, C(G), of a graph G is the vector subspace of (E; ⊕; .) spanned by the cycles of G. Traditionally there have been two notions of minimality among bases of C(G). First, a basis B of G is called a d-fold if each edge of G occurs in at most d cycles of the basis B. The basis number, b(G), of G is the least non-negative integer d such that C(G) has a d-fold basis; a required basis of C(G) is a basis for which each edge of G belongs to at most b(G) elements of B. Second, a basis B is called a minimum cycle basis (MCB) if its total length Σ BϵB |B| is minimum among all bases of C(G). The lexicographic product GρH has the vertex set V (GρH) = V (G) x V (H) and the edge set E(GρH) = {(u1, v1)(u2, v2)|u1 = u2 and v1 v2 ϵ E(H); or u1u2 ϵ E(G) and there is α ϵ Aut(H) such that α (v1) = v2}. In this work, a construction of a minimum cycle basis for the wreath product of wheels with paths is presented. Also, the length of the longest cycle of a minimum cycle basis is determined. Moreover, the basis number for the wreath product of the same is investigated.

Keywords: cycle space, minimum cycle basis, basis number, wreath product

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Authors: Manal Azzidani

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This research consideres the extension of special functions called Positive Linear Operators. the bounded linear operator which defined from normed space to Banach space will extend to the closure of the its domain, And extend identified linear functional on a vector subspace by Hana-Banach theorem which could be generalized to the positive linear operators.

Keywords: extension, positive operator, Riesz space, sublinear function

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Authors: Dimitris Varsamis, Nicholas Karampetakis

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It is well known that any interpolating polynomial P(x,y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis etc. The aim of this paper is twofold: a) to present transformations between the coordinates of the polynomial P(x,y) in the aforementioned basis and b) to present transformations between these bases.

Keywords: bivariate interpolation polynomial, polynomial basis, transformations, interpolating polynomial

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Authors: Haohao Wang

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The purpose of this paper is to find elimination ideals via Grobner basis. We first introduce the concept of Grobner bases, and then, we provide computational algorithms to applications for curves and surfaces.

Keywords: curves, surfaces, Grobner basis, elimination

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Authors: Abdelhamid Zerroug, Mlle Ismahene Sehili

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Spectral methods are usually applied to solve uni-dimensional boundary value problems. With the advantage of the creation of multidimensional basis, we propose a new spectral method for bi-dimensional problems. In this article, we start by creating bi-spectral basis by different ways, we developed also a new relations to determine the expressions of spectral coefficients in different partial derivatives expansions. Finally, we propose the principle of a new bi-spectral method for the bi-dimensional problems.

Keywords: boundary value problems, bi-spectral methods, bi-dimensional Legendre basis, spectral method

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Authors: Sebastian Andersen, Peter N. Poulsen

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The use of basis projection in the structural dynamic analysis is frequently applied. The purpose of the method is to improve the computational efficiency, while maintaining a high solution accuracy, by projection the governing equations onto a small set of carefully selected basis vectors. The present work considers basis projection in kinematic nonlinear systems with a focus on two widely used basis vectors; the system mode shapes and their modal derivatives. Particularly the latter basis vectors are given special attention since only approximate modal derivatives have been used until now. In the present work the complete modal derivatives, derived from perturbation methods, are presented and compared to the previously applied approximate modal derivatives. The correctness of the complete modal derivatives is illustrated by use of an example of a harmonically loaded kinematic nonlinear structure modeled by beam elements.

Keywords: basis projection, finite element method, kinematic nonlinearities, modal derivatives

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Authors: Adil Al-Rammahi

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Image or document encryption is needed through e- government data base. Really in this paper we introduce two matrices images, one is the public, and the second is the secret (original). The analyses of each matrix is achieved using the transformation of singular values decomposition. So each matrix is transformed or analyzed to three matrices say row orthogonal basis, column orthogonal basis, and spectral diagonal basis. Product of the two row basis is calculated. Similarly the product of the two column basis is achieved. Finally we transform or save the files of public, row product and column product. In decryption stage, the original image is deduced by mutual method of the three public files.

Keywords: image cryptography, singular values decomposition

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Authors: Mengjun Yang, Zhulin Zong, Jie Gao

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In this paper, a new and robust algorithm is proposed to achieve high resolution for inverse synthetic aperture radar (ISAR) imaging in the compressive sensing (CS) framework. Traditional CS based methods have to assume that unknown scatters exactly lie on the pre-divided grids; otherwise, their reconstruction performance dropped significantly. In this processing algorithm, several basis shifts are utilized to achieve the same effect as grid refinement does. The detailed implementation of the basis shift algorithm is presented in this paper. From the simulation we can see that using the basis shift algorithm, imaging precision can be improved. The effectiveness and feasibility of the proposed method are investigated by the simulation results.

Keywords: ISAR imaging, sparse reconstruction, off-grid, basis shift

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Authors: Zsolt Lipcsey, Sampson Marshal Imeh

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We investigate a certain characterisation for rank of a semigroup by Howie and Ribeiro (1999), to ascertain the relevance of the concept of independence. There are cases where the concept of independence fails to be useful for this purpose. One would expect the basic element to be the maximal independent subset of a given semigroup. However, we construct examples for semigroups where finite basis exist and the basis is larger than the number of independent elements.

Keywords: generating sets, independent set, rank, cyclic semigroup, basis, commutative

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Authors: Ying Li, Yan Li

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A new algorithm for single hidden layer feedforward neural networks (SLFN), Orthogonal Basis Extreme Learning (OBEL) algorithm, is proposed and the algorithm derivation is given in the paper. The algorithm can decide both the NNs parameters and the neuron number of hidden layer(s) during training while providing extreme fast learning speed. It will provide a practical way to develop NNs. The simulation results of function approximation showed that the algorithm is effective and feasible with good accuracy and adaptability.

Keywords: neural network, orthogonal basis extreme learning, function approximation

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Authors: Fahimeh Hooshyar, Seyyed Mojtaba Abtahi

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Democracy which is, in its greek roots, consisted of “Demo” (People) and “Kratic” (people) is referring to governing of the people or governing by the people. in its widest definition it refers to a common lifestyle in which all the people has the equal potentials for social participating. But in political perspective, democracy is looking for the equal participation right of the citizens in political decision-making process. in this viewpoint, the democracy is solely a political construct or a social-political style in which all the values are relative. In this definition of the democracy emphasis is on equality of the people based on the governing rule and the natural social and political rights of every member of humankind. This notion of democracy by no means is a self reliant idea and the need of an ideological basis for approaching to this idea is inevitable. In this paper we are trying to define the inter-relations of democracy and its philosophical basis to Islamic fundamental ideas. Our approach to this topic would be a philosophical ideological one.

Keywords: Islam, democracy, democracy’s philosophical basis, secularism, fundamentalism

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Authors: Kumar Ashwini, Nayak C. Vinod

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Sudden unexpected death in epilepsy (SUDEP) is a rarity. Each year, about one in 150 epileptics, whose seizures are not controlled, may die of SUDEP. It is a leading cause of death in young adults with uncontrolled seizures. Understanding the genetic basis for SUDEP, is crucial given that the rate of sudden death in epilepsy patients is 20 fold that of the general population. We encountered one such case of a young male, a known epileptic, who was brought dead after a sudden collapse. We hereby present a poster discussing the autopsy findings of this case and also highlighting the importance of understanding the genetic basis of SUDEP.

Keywords: sudden death, epilepsy, genetic, autopsy

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Authors: C. Pislaru, A. Shebani

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This paper uses the radial basis function neural network (RBFNN) for system identification of nonlinear systems. Five nonlinear systems are used to examine the activity of RBFNN in system modeling of nonlinear systems; the five nonlinear systems are dual tank system, single tank system, DC motor system, and two academic models. The feed forward method is considered in this work for modelling the non-linear dynamic models, where the K-Means clustering algorithm used in this paper to select the centers of radial basis function network, because it is reliable, offers fast convergence and can handle large data sets. The least mean square method is used to adjust the weights to the output layer, and Euclidean distance method used to measure the width of the Gaussian function.

Keywords: system identification, nonlinear systems, neural networks, radial basis function, K-means clustering algorithm

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Authors: Kasif Khan, Azlan Allahwala, Moiz Ali, Hasan Lodhi, Umer Amjad

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The number of runs scored by batsmen and wickets taken by bowlers serves as a natural way of quantifying the performance of a cricketer. Traditionally the batsmen and bowlers are rated on their batting or bowling average respectively. However, in a game like Cricket, it is not sufficient to evaluate performance on the basis of average. The biasness in selecting batsman and bowler on the basis of their past performance. The objective is to predict the best player and comparing their performance on the basis of venue, opponent, weather, and particular position. On the basis of predictions and analysis, and comparison the best team is selected for next upcoming series of Pakistan. The system is based and will be built to aid analyst in finding best possible team combination of Pakistan for a particular match and by providing them with advisories so that they can select the best possible team combination. This will also help the team management in identifying a perfect batting order and the bowling order for each match.

Keywords: data analysis, Pakistan cricket players, quantifying individual performance, cricket

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Authors: A. Ejah Umraeni Salam, M. Tola, M. Selintung, F. Maricar

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Clean water is an essential and fundamental human need. Therefore, its supply must be assured by maintaining the quality, quantity and water pressure. However the fact is, on its distribution system, leakage happens and becomes a common world issue. One of the technical causes of the leakage is a leaking pipe. The purpose of the research is how to use the Radial Basis Function Neural (RBFNN) model to detect the location and the magnitude of the pipeline leakage rapidly and efficiently. In this study the RBFNN are trained and tested on data from EPANET hydraulic modeling system. Method of Radial Basis Function Neural Network is proved capable to detect location and magnitude of pipeline leakage with of the accuracy of the prediction results based on the value of RMSE (Root Meant Square Error), comparison prediction and actual measurement approaches 0.000049 for the whole pipeline system.

Keywords: radial basis function neural network, leakage pipeline, EPANET, RMSE

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Authors: Xuan Zhou, Litian Zhang, Shuixiang Li

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Mesh deformation using radial basis function interpolation method has been demonstrated to produce quality meshes with relatively little computational cost using a concise algorithm. However, it still suffers from the limited deformation ability, especially in large deformation. In this paper, a pre-displacement improvement is proposed to improve the problem that illegal meshes always appear near the moving inner boundaries owing to the large relative displacement of the nodes near inner boundaries. In this improvement, nodes near the inner boundaries are first associated to the near boundary nodes, and a pre-displacement based on the displacements of associated boundary nodes is added to the nodes near boundaries in order to make the displacement closer to the boundary deformation and improve the deformation capability. Several 2D and 3D numerical simulation cases have shown that the pre-displacement improvement for radial basis function (RBF) method significantly improves the mesh quality near inner boundaries and deformation capability, with little computational burden increasement.

Keywords: mesh deformation, mesh quality, background mesh, radial basis function

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Authors: Ahmed Elrewainy

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Mixing in the hyperspectral imaging occurs due to the low spatial resolutions of the used cameras. The existing pure materials “endmembers” in the scene share the spectra pixels with different amounts called “abundances”. Unmixing of the data cube is an important task to know the present endmembers in the cube for the analysis of these images. Unsupervised unmixing is done with no information about the given data cube. Sparsity is one of the recent approaches used in the source recovery or unmixing techniques. The l₁-norm optimization problem “basis pursuit” could be used as a sparsity-based approach to solve this unmixing problem where the endmembers is assumed to be sparse in an appropriate domain known as dictionary. This optimization problem is solved using proximal method “iterative thresholding”. The l₁-norm basis pursuit optimization problem as a sparsity-based unmixing technique was used to unmix real and synthetic hyperspectral data cubes.

Keywords: basis pursuit, blind source separation, hyperspectral imaging, spectral unmixing, wavelets

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Authors: Maryamosadat Ghasemi, Reza Amrollahi

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Plasma equilibrium geometry has a great influence on the confinement and magnetohydrodynamic stability in tokamaks. The poloidal field (PF) system of a tokamak should be able to support this plasma equilibrium geometry. In this work the prepared numerical code based on radial basis functions are presented and used to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibrium of tokamak plasma. The radial basis functions (RBFs) which is a kind of numerical meshfree method (MFM) for solving partial differential equations (PDEs) has appeared in the last decade and is developing significantly in the last few years. This technique is applied in this study to obtain the equilibrium configuration for Alborz Tokamak. The behavior of numerical solution convergences show the validation of this calculations.

Keywords: equilibrium, grad–shafranov, radial basis functions, Alborz Tokamak

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Authors: T. Bryan , V. Kepuska, I. Kostnaic

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A method of data compression and denoising is introduced that is based on atomic decomposition of audio data using “basis vectors” that are learned from the audio data itself. The basis vectors are shown to have higher data compression and better signal-to-noise enhancement than the Gabor and gammatone “seed atoms” that were used to generate them. The basis vectors are the input weights of a Sparse AutoEncoder (SAE) that is trained using “envelope samples” of windowed segments of the audio data. The envelope samples are extracted from the audio data by performing atomic decomposition with Gabor or gammatone seed atoms. This process identifies segments of audio data that are locally coherent with the seed atoms. Envelope samples are extracted by identifying locally coherent audio data segments with Gabor or gammatone seed atoms, found by matching pursuit. The envelope samples are formed by taking the kronecker products of the atomic envelopes with the locally coherent data segments. Oracle signal-to-noise ratio (SNR) verses data compression curves are generated for the seed atoms as well as the basis vectors learned from Gabor and gammatone seed atoms. SNR data compression curves are generated for speech signals as well as early American music recordings. The basis vectors are shown to have higher denoising capability for data compression rates ranging from 90% to 99.84% for speech as well as music. Envelope samples are displayed as images by folding the time series into column vectors. This display method is used to compare of the output of the SAE with the envelope samples that produced them. The basis vectors are also displayed as images. Sparsity is shown to play an important role in producing the highest denoising basis vectors.

Keywords: sparse dictionary learning, autoencoder, sparse autoencoder, basis vectors, atomic decomposition, envelope sampling, envelope samples, Gabor, gammatone, matching pursuit

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Authors: Boukari Nassim

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This paper describes the use of odd pair autoregressive coefficients (Yule _Walker and Burg) for the feature extraction of electroencephalogram (EEG) signals. In the classification: the radial basis function neural network neural network (RBFNN) is employed. The RBFNN is described by his architecture and his characteristics: as the RBF is defined by the spread which is modified for improving the results of the classification. Five types of EEG signals are defined for this work: Set A, Set B for normal signals, Set C, Set D for interictal signals, set E for ictal signal (we can found that in Bonn university). In outputs, two classes are given (AC, AD, AE, BC, BD, BE, CE, DE), the best accuracy is calculated at 99% for the combined odd pair autoregressive coefficients. Our method is very effective for the diagnosis of epileptic EEG signals.

Keywords: epilepsy, EEG signals classification, combined odd pair autoregressive coefficients, radial basis function neural network

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Authors: J. B. Akshataeva, G. T. Aigarinova, A. Amankulova, D. S. Kalkanova

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This article examines some aspects of the insurance of agricultural activities, strategic documents on deepening investment opportunities. Insurance market development is before the society and the state. It also examines problems of agricultural insurance development in the market economy of Kazakhstan as the basis for food security.

Keywords: agriculture, food safety, insurance, privacy issues

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Authors: Kyu Chul Lee, Sung Hyun Yoo, Choon Ki Ahn, Myo Taeg Lim

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Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended Kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore, the number of centers will be considered since it affects the performance of approximation.

Keywords: extended Kalman filter, classification problem, radial basis function networks (RBFN), finite impulse response (FIR) filter

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Authors: Xi Zuo

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Against the background of the aging population and changing family structure in China, community canteens have become an important vehicle for community-based home care services and a new space for social interaction. In this paper, we review past studies and the actual construction situation in China, firstly sort out the social interaction of the elderly and the types of places, and on this basis, we find that there is an obvious disconnection between the current construction and the academic research, and the contradiction between social benefit and cost-effectiveness, and therefore we put forward the relevant construction planning and thinking, in order to provide a disciplinary basis and academic support for the construction of community canteens and the construction of elderly-friendly cities. In order to provide disciplinary basis and academic support for the construction of community canteens and the construction of senior-friendly cities.

Keywords: urban and rural planning, community canteens, elderly people, senior-friendly

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Authors: Wei Yan, Wei Dong

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Facing the understanding problem of update and preservation of urban history space under background of rapid Chinese urbanization, so at first there is a need to dig the philosophic principles of “antithesis” and “unification” which are contained in the traditional Chinese literature known as “antithesis” and do the job of planning translation by personal understanding in order to form understanding and value systems of dialectical urban history space under the foundation of “antithesis”. Then we could put forward a “context” concept for urban history space under the foregoing basis. After that, we will take the update and preservation of Ningbo Tianyi Pavilion’s historical district as an example to discuss problems related to understanding of urban history area under the basis of Chinese tradition culture, improvement of value system, construction of urban trait space and Chinese “localization” of planning theory.

Keywords: antithesis, traditional values, city renewal and conservation, the “context” of city history space

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Authors: Janaína F. Guidolini, Jean P. H. B. Ometto, Angélica Giarolla, Peter M. Toledo, Carlos A. Valera

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The water crisis, a major problem of the 21^st century, occurs mainly due to poor management. The central issue that should govern the management is the integration of the various aspects that interfere with the use of water resources and their protection, supported by legal basis. A watershed is a unit of water interacting with the physical, biotic, social, economic and cultural variables. The Brazilian law recognized river basin as the territorial management unit. Based on the diagnosis of the current situation of the water resources of the Rio Grande Basin, a discussion informed in the Brazilian legal basis was made to propose measures to fight or mitigate damages and environmental degradation in the Basin. To manage water resources more efficiently, conserve water and optimize their multiple uses, the integration of acquired scientific knowledge and management is essential. Moreover, it is necessary to monitor compliance with environmental legislation.

Keywords: conservation of soil and water, environmental laws, river basin, sustainability

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Authors: Yilmaz Simsek

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In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values.

Keywords: generating functions, Bernstein basis functions, Bernstein polynomials, Bezier curves, differential equations

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