Two-Link Flexible Manipulator Control Using Sliding Mode Control Based Linear Matrix Inequality

Science.gov (United States)

Zulfatman; Marzuki, Mohammad; Alif Mardiyah, Nur

2017-04-01

Two-link flexible manipulator is a manipulator robot which at least one of its arms is made of lightweight material and not rigid. Flexible robot manipulator has some advantages over the rigid robot manipulator, such as lighter, requires less power and costs, and to result greater payload. However, suitable control algorithm to maintain the two-link flexible robot manipulator in accurate positioning is very challenging. In this study, sliding mode control (SMC) was employed as robust control algorithm due to its insensitivity on the system parameter variations and the presence of disturbances when the system states are sliding on a sliding surface. SMC algorithm was combined with linear matrix inequality (LMI), which aims to reduce the effects of chattering coming from the oscillation of the state during sliding on the sliding surface. Stability of the control algorithm is guaranteed by Lyapunov function candidate. Based on simulation works, SMC based LMI resulted in better performance improvements despite the disturbances with significant chattering reduction. This was evident from the decline of the sum of squared tracking error (SSTE) and the sum of squared of control input (SSCI) indexes respectively 25.4% and 19.4%.

Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays

International Nuclear Information System (INIS)

Balasubramaniam, P.; Kalpana, M.; Rakkiyappan, R.

2012-01-01

Fuzzy cellular neural networks (FCNNs) are special kinds of cellular neural networks (CNNs). Each cell in an FCNN contains fuzzy operating abilities. The entire network is governed by cellular computing laws. The design of FCNNs is based on fuzzy local rules. In this paper, a linear matrix inequality (LMI) approach for synchronization control of FCNNs with mixed delays is investigated. Mixed delays include discrete time-varying delays and unbounded distributed delays. A dynamic control scheme is proposed to achieve the synchronization between a drive network and a response network. By constructing the Lyapunov—Krasovskii functional which contains a triple-integral term and the free-weighting matrices method an improved delay-dependent stability criterion is derived in terms of LMIs. The controller can be easily obtained by solving the derived LMIs. A numerical example and its simulations are presented to illustrate the effectiveness of the proposed method. (interdisciplinary physics and related areas of science and technology)

Linear inequalities and overlap bounds: a novel use of an operator inequality

International Nuclear Information System (INIS)

Cohen, M.; Leopold, J.G.

1976-01-01

Bounds to overlap integrals are obtained by an operator inequality technique. The formulation involves a set of linear inequalities with several overlap integrals as unknowns. The 'solution' of this set of inequalities leads to bound expressions which complement those of other workers. (author)

Useful tools for non-linear systems: Several non-linear integral inequalities

Czech Academy of Sciences Publication Activity Database

Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.

2013-01-01

Roč. 49, č. 1 (2013), s. 73-80 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf

Matrix inequalities for the difference between arithmetic mean and harmonic mean

OpenAIRE

Liao, Wenshi; Wu, Junliang

2015-01-01

Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between arithmetic mean and harmonic mean. In addition, relevant inequalities for the Hilbert-Schmidt norm and determinant are established.

On an Optimal -Control Problem in Coefficients for Linear Elliptic Variational Inequality

Directory of Open Access Journals (Sweden)

Olha P. Kupenko

2013-01-01

Full Text Available We consider optimal control problems for linear degenerate elliptic variational inequalities with homogeneous Dirichlet boundary conditions. We take the matrix-valued coefficients in the main part of the elliptic operator as controls in . Since the eigenvalues of such matrices may vanish and be unbounded in , it leads to the “noncoercivity trouble.” Using the concept of convergence in variable spaces and following the direct method in the calculus of variations, we establish the solvability of the optimal control problem in the class of the so-called -admissible solutions.

Solving linear inequalities in a least squares sense

Energy Technology Data Exchange (ETDEWEB)

Bramley, R.; Winnicka, B. [Indiana Univ., Bloomington, IN (United States)

1994-12-31

Let A {element_of} {Re}{sup mxn} be an arbitrary real matrix, and let b {element_of} {Re}{sup m} a given vector. A familiar problem in computational linear algebra is to solve the system Ax = b in a least squares sense; that is, to find an x* minimizing {parallel}Ax {minus} b{parallel}, where {parallel} {center_dot} {parallel} refers to the vector two-norm. Such an x* solves the normal equations A{sup T}(Ax {minus} b) = 0, and the optimal residual r* = b {minus} Ax* is unique (although x* need not be). The least squares problem is usually interpreted as corresponding to multiple observations, represented by the rows of A and b, on a vector of data x. The observations may be inconsistent, and in this case a solution is sought that minimizes the norm of the residuals. A less familiar problem to numerical linear algebraists is the solution of systems of linear inequalities Ax {le} b in a least squares sense, but the motivation is similar: if a set of observations places upper or lower bounds on linear combinations of variables, the authors want to find x* minimizing {parallel} (Ax {minus} b){sub +} {parallel}, where the i{sup th} component of the vector v{sub +} is the maximum of zero and the i{sup th} component of v.

Analysis of junior high school students' attempt to solve a linear inequality problem

Science.gov (United States)

Taqiyuddin, Muhammad; Sumiaty, Encum; Jupri, Al

2017-08-01

Linear inequality is one of fundamental subjects within junior high school mathematics curricula. Several studies have been conducted to asses students' perform on linear inequality. However, it can hardly be found that linear inequality problems are in the form of "ax + b condition leads to the research questions concerning students' attempt on solving a simple linear inequality problem in this form. In order to do so, the written test was administered to 58 students from two schools in Bandung followed by interviews. The other sources of the data are from teachers' interview and mathematics books used by students. After that, the constant comparative method was used to analyse the data. The result shows that the majority approached the question by doing algebraic operations. Interestingly, most of them did it incorrectly. In contrast, algebraic operations were correctly used by some of them. Moreover, the others performed expected-numbers solution, rewriting the question, translating the inequality into words, and blank answer. Furthermore, we found that there is no one who was conscious of the existence of all-numbers solution. It was found that this condition is reasonably due to how little the learning components concern about why a procedure of solving a linear inequality works and possibilities of linear inequality solution.

The Golden-Thompson inequality: Historical aspects and random matrix applications

International Nuclear Information System (INIS)

Forrester, Peter J.; Thompson, Colin J.

2014-01-01

The Golden-Thompson inequality, Tr (e A+B ) ⩽ Tr (e A e B ) for A, B Hermitian matrices, appeared in independent works by Golden and Thompson published in 1965. Both of these were motivated by considerations in statistical mechanics. In recent years the Golden-Thompson inequality has found applications to random matrix theory. In this article, we detail some historical aspects relating to Thompson's work, giving in particular a hitherto unpublished proof due to Dyson, and correspondence with Pólya. We show too how the 2 × 2 case relates to hyperbolic geometry, and how the original inequality holds true with the trace operation replaced by any unitarily invariant norm. In relation to the random matrix applications, we review its use in the derivation of concentration type lemmas for sums of random matrices due to Ahlswede-Winter, and Oliveira, generalizing various classical results

Robust Stability and H∞ Control of Uncertain Piecewise Linear Switched Systems with Filippov Solutions

DEFF Research Database (Denmark)

Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal

2012-01-01

This paper addresses the robust stability and control problem of uncertain piecewise linear switched systems where, instead of the conventional Carathe ́odory solutions, we allow for Filippov solutions. In other words, in contrast to the previous studies, solutions with infinite switching in fini...... algorithm is proposed to surmount the aforementioned matrix inequality conditions....... time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, based on earlier results, the stability problem of piecewise linear systems with Filippov solutions is translated into a number of linear matrix inequality feasibility tests. Subsequently, a set of matrix...... inequalities are brought forward, which determines the asymptotic stability of the Filippov solutions of a given uncertain piecewise linear system. Afterwards, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H∞ per- formance are formulated. Finally, a V-K iteration...

New robust stable MPC using linear matrix inequalities

Directory of Open Access Journals (Sweden)

M.A. Rodrigues

2000-03-01

Full Text Available This paper addresses the stability of Model Predictive Control (MPC with output feedback. The proposed controller uses a new state-space formulation of the system, and the control problem is presented as an LMI optimization problem. The stability condition for the closed loop is included as a Lyapunov inequality. The resulting optimization problem becomes nonlinear with the inclusion of the stabilizing condition. A suboptimal solution is developed and the problem reduces to a pair of coupled LMI problems. An iterative solution that converges to a stable output feedback gain is proposed. A polytopic set of process models can be considered. A simulation example is included in the paper and shows that the proposed strategy eliminates the usual practice of enforcing robustness by detuning the MP controller.

Radii of Solvability and Unsolvability of Linear Systems

Czech Academy of Sciences Publication Activity Database

Hladík, M.; Rohn, Jiří

2016-01-01

Roč. 503, 15 August (2016), s. 120-134 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * linear equations * linear inequalities * matrix norm Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016

Matrix algebra for linear models

CERN Document Server

Gruber, Marvin H J

2013-01-01

Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. Matrix Algebra for Linear Models offers readers a unique, unified view of matrix analysis theory (where and when necessary), methods, and their applications. Written f

Matrix Tricks for Linear Statistical Models

CERN Document Server

Puntanen, Simo; Styan, George PH

2011-01-01

In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple "tricks" which simplify and clarify the treatment of a problem - both for the student and

Hardy inequality on time scales and its application to half-linear dynamic equations

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Řehák Pavel

2005-01-01

Full Text Available A time-scale version of the Hardy inequality is presented, which unifies and extends well-known Hardy inequalities in the continuous and in the discrete setting. An application in the oscillation theory of half-linear dynamic equations is given.

Finite-Time Stability Analysis of Discrete-Time Linear Singular Systems

Directory of Open Access Journals (Sweden)

Songlin Wo

2014-01-01

Full Text Available The finite-time stability (FTS problem of discrete-time linear singular systems (DTLSS is considered in this paper. A necessary and sufficient condition for FTS is obtained, which can be expressed in terms of matrix inequalities. Then, another form of the necessary and sufficient condition for FTS is also given by using matrix-null space technology. In order to solve the stability problem expediently, a sufficient condition for FTS is given via linear matrix inequality (LMI approach; this condition can be expressed in terms of LMIs. Finally, an illustrating example is also given to show the effectiveness of the proposed method.

Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems

DEFF Research Database (Denmark)

Adegas, Fabiano Daher; Stoustrup, Jakob

2015-01-01

the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems......SUMMARY Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between....... The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyright © 2014 John Wiley & Sons, Ltd....

Applied linear algebra and matrix analysis

CERN Document Server

Shores, Thomas S

2018-01-01

In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems. The second edition’s revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google’s PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces. Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and M...

New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit

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Xu Guanlei

2009-01-01

Full Text Available The uncertainty principle plays an important role in mathematics, physics, signal processing, and so on. Firstly, based on definition of the linear canonical transform (LCT and the traditional Pitt's inequality, one novel Pitt's inequality in the LCT domains is obtained, which is connected with the LCT parameters a and b. Then one novel logarithmic uncertainty principle is derived from this novel Pitt's inequality in the LCT domains, which is associated with parameters of the two LCTs. Secondly, from the relation between the original function and LCT, one entropic uncertainty principle and one Heisenberg's uncertainty principle in the LCT domains are derived, which are associated with the LCT parameters a and b. The reason why the three lower bounds are only associated with LCT parameters a and b and independent of c and d is presented. The results show it is possible that the bounds tend to zeros.

Growth and inequality in India : analysis of an extended social accounting matrix

NARCIS (Netherlands)

Pieters, Janneke

Based on an extended Social Accounting Matrix (SAM) for 2002-03. this study shows how sectoral growth in India affects Inequality A breakdown of the wage,account into three educational levels and 10 sectors of employment improves the link between sectoral expansion and household income in the SAM

Typical Werner states satisfying all linear Bell inequalities with dichotomic measurements

Science.gov (United States)

Luo, Ming-Xing

2018-04-01

Quantum entanglement as a special resource inspires various distinct applications in quantum information processing. Unfortunately, it is NP-hard to detect general quantum entanglement using Bell testing. Our goal is to investigate quantum entanglement with white noises that appear frequently in experiment and quantum simulations. Surprisingly, for almost all multipartite generalized Greenberger-Horne-Zeilinger states there are entangled noisy states that satisfy all linear Bell inequalities consisting of full correlations with dichotomic inputs and outputs of each local observer. This result shows generic undetectability of mixed entangled states in contrast to Gisin's theorem of pure bipartite entangled states in terms of Bell nonlocality. We further provide an accessible method to show a nontrivial set of noisy entanglement with small number of parties satisfying all general linear Bell inequalities. These results imply typical incompleteness of special Bell theory in explaining entanglement.

Some Results on facets for linear inequality in 0-1 variables

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D. Sashi Bhusan

2010-03-01

Full Text Available The facet of Knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. Such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. Strong covers for facets of Knapsack ploytope has been developed in the first part of the present paper. Generating family of valid cutting planes that satisfy inequality with 0-1 variables through algorithms are the attraction of this paper.

Generating Nice Linear Systems for Matrix Gaussian Elimination

Science.gov (United States)

Homewood, L. James

2004-01-01

In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

Science.gov (United States)

Acikmese, Ahmet Behcet; Corless, Martin

2004-01-01

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

A one-layer recurrent neural network for non-smooth convex optimization subject to linear inequality constraints

International Nuclear Information System (INIS)

Liu, Xiaolan; Zhou, Mi

2016-01-01

In this paper, a one-layer recurrent network is proposed for solving a non-smooth convex optimization subject to linear inequality constraints. Compared with the existing neural networks for optimization, the proposed neural network is capable of solving more general convex optimization with linear inequality constraints. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed as long as the designed parameters in the model are larger than the derived lower bounds.

H2 Control for the Continuous-Time Markovian Jump Linear Uncertain Systems with Partly Known Transition Rates and Input Quantization

Directory of Open Access Journals (Sweden)

Xin-Gang Zhao

2013-01-01

Full Text Available For a class of continuous-time Markovian jump linear uncertain systems with partly known transition rates and input quantization, the H2 state-feedback control design is considered. The elements in the transition rates matrix include completely known, boundary known, and completely unknown ones. First, an H2 cost index for Markovian jump linear uncertain systems is introduced; then by introducing a new matrix inequality condition, sufficient conditions are formulated in terms of linear matrix inequalities (LMIs for the H2 control of the Markovian jump linear uncertain systems. Less conservativeness is achieved than the result obtained with the existing technique. Finally, a numerical example is given to verify the validity of the theoretical results.

Oracle Inequalities for Convex Loss Functions with Non-Linear Targets

DEFF Research Database (Denmark)

Caner, Mehmet; Kock, Anders Bredahl

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target...... of the same order as that of the oracle. If the target is linear we give sufficient conditions for consistency of the estimated parameter vector. Next, we briefly discuss how a thresholded version of our estimator can be used to perform consistent variable selection. We give two examples of loss functions...

Further results on "Robust MPC using Linear Matrix Inequalities"

NARCIS (Netherlands)

Lazar, M.; Heemels, W.P.M.H.; Munoz de la Pena, D.; Alamo, T.

2008-01-01

This paper presents a novel method for designing the terminal cost and the auxiliary control law (ACL) for robust MPC of uncertain linear systems, such that ISS is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is

Matrix model and time-like linear dila ton matter

International Nuclear Information System (INIS)

Takayanagi, Tadashi

2004-01-01

We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple Fermi surface. Indeed, after a Lorentz transformation, the corresponding 2d spacetime is a conventional linear dila ton background with a time-dependent tachyon field. We show that the tree level scattering amplitudes in the matrix model perfectly agree with those computed in the world-sheet theory. The classical trajectories of fermions correspond to the decaying D-boranes in the time-like linear dilaton CFT. We also discuss the ground ring structure. Furthermore, we study the properties of the time-like Liouville theory by applying this matrix model description. We find that its ground ring structure is very similar to that of the minimal string. (author)

The linear parameters and the decoupling matrix for linearly coupled motion in 6 dimensional phase space

International Nuclear Information System (INIS)

Parzen, G.

1997-01-01

It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system, where the motion is uncoupled, by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6 x 6 matrix, R. It will be shown that of the 36 elements of the 6 x 6 decoupling matrix R, only 12 elements are independent. A set of equations is given from which the 12 elements of R can be computed form the one period transfer matrix. This set of equations also allows the linear parameters, the β i , α i , i = 1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix

Finite-time H∞ control for linear continuous system with norm-bounded disturbance

Science.gov (United States)

Meng, Qingyi; Shen, Yanjun

2009-04-01

In this paper, the definition of finite-time H∞ control is presented. The system under consideration is subject to time-varying norm-bounded exogenous disturbance. The main aim of this paper is focused on the design a state feedback controller which ensures that the closed-loop system is finite-time bounded (FTB) and reduces the effect of the disturbance input on the controlled output to a prescribed level. A sufficient condition is presented for the solvability of this problem, which can be reduced to a feasibility problem involving linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems

Czech Academy of Sciences Publication Activity Database

Hilscher, R.; Řehák, Pavel

2003-01-01

Roč. 12, č. 1 (2003), s. 171-189 ISSN 1056-2176 R&D Projects: GA ČR GA201/01/0079; GA ČR GP201/01/P041 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : linear Hamiltonian dynamic systems * disconjugacy * Riccati inequality Subject RIV: BA - General Mathematics Impact factor: 0.256, year: 2002

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

Science.gov (United States)

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Linear matrix differential equations of higher-order and applications

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Mustapha Rachidi

2008-07-01

Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.

The use of Lyapunov differential inequalities for estimating the transients of mechanical systems

Science.gov (United States)

Alyshev, A. S.; Dudarenko, N. A.; Melnikov, V. G.; Melnikov, G. I.

2018-05-01

In this paper we consider an autonomous mechanical system in a finite neighborhood of the zero of the phase space of states. The system is given as a matrix differential equation in the Cauchy form with the right-hand side of the polynomial structure. We propose a method for constructing a sequence of linear inhomogeneous differential inequalities for Lyapunov functions. As a result, we obtain estimates of transient processes in the form of functional inequalities.

A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

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Zhijun Luo

2014-01-01

Full Text Available A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

Matrix analysis

CERN Document Server

Bhatia, Rajendra

1997-01-01

A good part of matrix theory is functional analytic in spirit. This statement can be turned around. There are many problems in operator theory, where most of the complexities and subtleties are present in the finite-dimensional case. My purpose in writing this book is to present a systematic treatment of methods that are useful in the study of such problems. This book is intended for use as a text for upper division and gradu­ ate courses. Courses based on parts of the material have been given by me at the Indian Statistical Institute and at the University of Toronto (in collaboration with Chandler Davis). The book should also be useful as a reference for research workers in linear algebra, operator theory, mathe­ matical physics and numerical analysis. A possible subtitle of this book could be Matrix Inequalities. A reader who works through the book should expect to become proficient in the art of deriving such inequalities. Other authors have compared this art to that of cutting diamonds. One first has to...

Synchronization and Control of Linearly Coupled Singular Systems

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Fang Qingxiang

2013-01-01

Full Text Available The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI, indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.

Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations

DEFF Research Database (Denmark)

Garde, Henrik

2018-01-01

. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method...

Using spectral element method to solve variational inequalities with applications in finance

International Nuclear Information System (INIS)

Moradipour, M.; Yousefi, S.A.

2015-01-01

Under the Black–Scholes model, the value of an American option solves a time dependent variational inequality problem (VIP). In this paper, first we discretize the variational inequality of American option in temporal direction by applying the Rannacher time stepping and achieve a sequence of elliptic variational inequalities. Second we discretize the spatial domain of variational inequalities by using spectral element methods with high order Lagrangian polynomials introduced on Gauss–Legendre–Lobatto points. Also by computing integrals by the Gauss–Legendre–Lobatto quadrature rule we derive a sequence of the linear complementarity problems (LCPs) having a positive definite sparse coefficient matrix. To find the unique solutions of the LCPs, we use the projected successive over-relaxation (PSOR) algorithm. Furthermore we present some existence and uniqueness theorems for the variational inequalities and LCPs. Finally, theoretical results are verified on the relevant numerical examples.

A neural network method for solving a system of linear variational inequalities

International Nuclear Information System (INIS)

Lan Hengyou; Cui Yishun

2009-01-01

In this paper, we transmute the solution for a new system of linear variational inequalities to an equilibrium point of neural networks, and by using analytic technique, some sufficient conditions are presented. Further, the estimation of the exponential convergence rates of the neural networks is investigated. The new and useful results obtained in this paper generalize and improve the corresponding results of recent works.

H 2 guaranteed cost control of discrete linear systems

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Colmenares W.

2000-01-01

Full Text Available This paper presents necessary and sufficient conditions for the existence of a quadratically stabilizing output feedback controller which also assures H 2 guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.

Jensen's operator inequality and its converses

DEFF Research Database (Denmark)

Hansen, Frank; Pecaric, Josip; Peric, Ivan

2007-01-01

We give a general formulation of Jensen's operator inequality for unital fields of positive linear mappings, and we consider different types of converse inequalities......We give a general formulation of Jensen's operator inequality for unital fields of positive linear mappings, and we consider different types of converse inequalities...

Reducing Data Size Inequality during Finite Element Model Separation into Superelements

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Yu. V. Berchun

2015-01-01

Full Text Available The work considers two methods of automatic separation of final element model into super-elements to decrease computing resource demand when solving the linearly - elastic problems of solid mechanics. The first method represents an algorithm to separate a final element grid into simply connected sub-regions according to the set specific number of nodes in the super-element. The second method is based on the generation of a super-element with the set specific data size of the coefficient matrix of the system of equations of the internal nodes balance, which are eliminated during super-element transformation. Both methods are based on the theory of graphs. The data size of a matrix of coefficients is assessed on the assumption that the further solution of a task will use Holetsky’s method. Before assessment of data size, a KatkhillaMackey's (Cuthill-McKee algorithm renumbers the internal nodes of a super-element both to decrease a profile width of the appropriate matrix of the system of equations of balance and to reduce the number of nonzero elements. Test examples show work results of abovementioned methods compared in terms of inequality of generated super-element separation according to the number of nodes and data size of the coefficient matrix of the system of equations of the internal nodes balance. It is shown that the offered approach provides smaller inequality of data size of super-element matrixes, with slightly increasing inequality by the number of tops.

Robustness of Linear Systems towards Multi-Dissipative Pertubations

DEFF Research Database (Denmark)

Thygesen, Uffe Høgsbro; Poulsen, Niels Kjølstad

1997-01-01

We consider the question of robust stability of a linear time invariant plant subject to dynamic perturbations, which are dissipative in the sense of Willems with respect to several quadratic supply rates. For instance, parasitic dynamics are often both small gain and passive. We reduce several...... robustness analysis questions to linear matrix inequalities: robust stability, robust H2 performance and robust performance in presence of disturbances with finite signal-to-noise ratios...

Structured Control of Affine Linear Parameter Varying Systems

DEFF Research Database (Denmark)

Adegas, Fabiano Daher; Stoustrup, Jakob

2011-01-01

This paper presents a new procedure to design structured controllers for discrete-time affine linear parametervarying systems (A LPV). The class of control structures includes decentralized of any order, fixed order output feedback, simultaneous plant-control design, among others. A parametervarying...... non-convex condition for an upper bound on the induced L2-norm performance is solved by an iterative linear matrix inequalities (LMI) optimization algorithm. Numerical examples demostrate the effectiveness of the proposed approach....

Chosen interval methods for solving linear interval systems with special type of matrix

Science.gov (United States)

Szyszka, Barbara

2013-10-01

The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

A Spreadsheet-Based, Matrix Formulation Linear Programming Lesson

DEFF Research Database (Denmark)

Harrod, Steven

2009-01-01

The article focuses on the spreadsheet-based, matrix formulation linear programming lesson. According to the article, it makes a higher level of theoretical mathematics approachable by a wide spectrum of students wherein many may not be decision sciences or quantitative methods majors. Moreover...

Strong practical stability and stabilization of uncertain discrete linear repetitive processes

Czech Academy of Sciences Publication Activity Database

Dabkowski, Pavel; Galkowski, K.; Bachelier, O.; Rogers, E.; Kummert, A.; Lam, J.

2013-01-01

Roč. 20, č. 2 (2013), s. 220-233 ISSN 1070-5325 R&D Projects: GA MŠk(CZ) 1M0567 Institutional research plan: CEZ:AV0Z10750506 Institutional support: RVO:67985556 Keywords : strong practical stability * stabilization * uncertain discrete linear repetitive processes * linear matrix inequality Subject RIV: BC - Control Systems Theory Impact factor: 1.424, year: 2013 http://onlinelibrary.wiley.com/doi/10.1002/nla.812/abstract

Pre-Service Teachers' Linear and Quadratic Inequalities Understandings

Science.gov (United States)

Bicer, Ali; Capraro, Robert M.; Capraro, Mary M.

2014-01-01

The National Council of Teachers of Mathematics [NCTM] noted that middle and high school students are expected to be able to both explain inequalities by using mathematical symbols and understand meanings by interpreting the solutions of inequalities. Unfortunately, research has revealed that not only do middle and high school students hold…

Fuzzy attitude control of solar sail via linear matrix inequalities

Science.gov (United States)

Baculi, Joshua; Ayoubi, Mohammad A.

2017-09-01

This study presents a fuzzy tracking controller based on the Takagi-Sugeno (T-S) fuzzy model of the solar sail. First, the T-S fuzzy model is constructed by linearizing the existing nonlinear equations of motion of the solar sail. Then, the T-S fuzzy model is used to derive the state feedback controller gains for the Twin Parallel Distributed Compensation (TPDC) technique. The TPDC tracks and stabilizes the attitude of the solar sail to any desired state in the presence of parameter uncertainties and external disturbances while satisfying actuator constraints. The performance of the TPDC is compared to a PID controller that is tuned using the Ziegler-Nichols method. Numerical simulation shows the TPDC outperforms the PID controller when stabilizing the solar sail to a desired state.

Matrix preconditioning: a robust operation for optical linear algebra processors.

Science.gov (United States)

Ghosh, A; Paparao, P

1987-07-15

Analog electrooptical processors are best suited for applications demanding high computational throughput with tolerance for inaccuracies. Matrix preconditioning is one such application. Matrix preconditioning is a preprocessing step for reducing the condition number of a matrix and is used extensively with gradient algorithms for increasing the rate of convergence and improving the accuracy of the solution. In this paper, we describe a simple parallel algorithm for matrix preconditioning, which can be implemented efficiently on a pipelined optical linear algebra processor. From the results of our numerical experiments we show that the efficacy of the preconditioning algorithm is affected very little by the errors of the optical system.

Minimal solution of linear formed fuzzy matrix equations

Directory of Open Access Journals (Sweden)

Maryam Mosleh

2012-10-01

Full Text Available In this paper according to the structured element method, the $mimes n$ inconsistent fuzzy matrix equation $Ailde{X}=ilde{B},$ which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method.

A simplified density matrix minimization for linear scaling self-consistent field theory

International Nuclear Information System (INIS)

Challacombe, M.

1999-01-01

A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tuma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree - Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. copyright 1999 American Institute of Physics

Fourier transform inequalities for phylogenetic trees.

Science.gov (United States)

Matsen, Frederick A

2009-01-01

Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity requirement implies non-trivial constraints on the site-pattern frequency vectors. We call these additional constraints "edge-parameter inequalities". In this paper, we first motivate the edge-parameter inequalities by considering a pathological site-pattern frequency vector corresponding to a quartet tree with a negative internal edge. This site-pattern frequency vector nevertheless satisfies all of the constraints described up to now in the literature. We next describe two complete sets of edge-parameter inequalities for the group-based models; these constraints are square-free monomial inequalities in the Fourier transformed coordinates. These inequalities, along with the phylogenetic invariants, form a complete description of the set of site-pattern frequency vectors corresponding to bona fide trees. Said in mathematical language, this paper explicitly presents two finite lists of inequalities in Fourier coordinates of the form "monomial < or = 1", each list characterizing the phylogenetically relevant semialgebraic subsets of the phylogenetic varieties.

KEELE, Minimization of Nonlinear Function with Linear Constraints, Variable Metric Method

International Nuclear Information System (INIS)

Westley, G.W.

1975-01-01

1 - Description of problem or function: KEELE is a linearly constrained nonlinear programming algorithm for locating a local minimum of a function of n variables with the variables subject to linear equality and/or inequality constraints. 2 - Method of solution: A variable metric procedure is used where the direction of search at each iteration is obtained by multiplying the negative of the gradient vector by a positive definite matrix which approximates the inverse of the matrix of second partial derivatives associated with the function. 3 - Restrictions on the complexity of the problem: Array dimensions limit the number of variables to 20 and the number of constraints to 50. These can be changed by the user

Weighted H∞ Filtering for a Class of Switched Linear Systems with Additive Time-Varying Delays

Directory of Open Access Journals (Sweden)

Li-li Li

2015-01-01

Full Text Available This paper is concerned with the problem of weighted H∞ filtering for a class of switched linear systems with two additive time-varying delays, which represent a general class of switched time-delay systems with strong practical background. Combining average dwell time (ADT technique with piecewise Lyapunov functionals, sufficient conditions are established to guarantee the exponential stability and weighted H∞ performance for the filtering error systems. The parameters of the designed switched filters are obtained by solving linear matrix inequalities (LMIs. A modification of Jensen integral inequality is exploited to derive results with less theoretical conservatism and computational complexity. Finally, two examples are given to demonstrate the effectiveness of the proposed method.

Generalization of Samuelson's inequality and location of eigenvalues

Indian Academy of Sciences (India)

Department of Mathematics, H. P. University, Shimla 171 005, India ... Refinements, extensions and applications of such inequalities have been studied ..... Samuelson inequality with extensions and applications in statistics and matrix theory,.

Product spaces and Nelson's inequality

International Nuclear Information System (INIS)

Faris, W.G.

1976-01-01

Certain inequalities for unbounded linear operators in L 2 extend to product spaces. This product space property is used to give a new proof that Gross's inequality for matrices implies Nelson's inequality for ordinary differential operators, and that this in turn implies Nelson's inequality for partial differential operators in infinitely many dimensions. A new proof of Gross's inequality is given. There is also a discussion of the physical meaning of Nelson's inequality in quantum field theory. The article may serve as an introduction for non-specialists to some of the recent mathematical work in this subject. (Auth.)

LMI-based gain scheduled controller synthesis for a class of linear parameter varying systems

DEFF Research Database (Denmark)

Bendtsen, Jan Dimon; Anderson, Brian; Lanzon, Alexander

2006-01-01

This paper presents a novel method for constructing controllers for a class of single-input multiple-output (SIMO) linear parameter varying (LPV) systems. This class of systems encompasses many physical systems, in particular systems where individual components vary with time, and is therefore...... of significant practical relevance to control designers. The control design presented in this paper has the properties that the system matrix of the closed loop is multi-affine in the various scalar parameters, and that the resulting controller ensures a certain degree of stability for the closed loop even when...... as a standard linear time-invariant (LTI) design combined with a set of linear matrix inequalities, which can be solved efficiently with software tools. The design procedure is illustrated by a numerical example....

Linear models in matrix form a hands-on approach for the behavioral sciences

CERN Document Server

Brown, Jonathon D

2014-01-01

This textbook is an approachable introduction to statistical analysis using matrix algebra. Prior knowledge of matrix algebra is not necessary. Advanced topics are easy to follow through analyses that were performed on an open-source spreadsheet using a few built-in functions. These topics include ordinary linear regression, as well as maximum likelihood estimation, matrix decompositions, nonparametric smoothers and penalized cubic splines. Each data set (1) contains a limited number of observations to encourage readers to do the calculations themselves, and (2) tells a coherent story based on statistical significance and confidence intervals. In this way, students will learn how the numbers were generated and how they can be used to make cogent arguments about everyday matters. This textbook is designed for use in upper level undergraduate courses or first year graduate courses. The first chapter introduces students to linear equations, then covers matrix algebra, focusing on three essential operations: sum ...

TOEPLITZ, Solution of Linear Equation System with Toeplitz or Circulant Matrix

International Nuclear Information System (INIS)

Garbow, B.

1984-01-01

Description of program or function: TOEPLITZ is a collection of FORTRAN subroutines for solving linear systems Ax=b, where A is a Toeplitz matrix, a Circulant matrix, or has one or several block structures based on Toeplitz or Circulant matrices. Such systems arise in problems of electrodynamics, acoustics, mathematical statistics, algebra, in the numerical solution of integral equations with a difference kernel, and in the theory of stationary time series and signals

Holographic entropy inequalities and gapped phases of matter

Energy Technology Data Exchange (ETDEWEB)

Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Cao, ChunJun [Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Walter, Michael [Stanford Institute for Theoretical Physics,Stanford University, Stanford, CA 94305 (United States); Wang, Zitao [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States)

2015-09-29

We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.

Holographic entropy inequalities and gapped phases of matter

International Nuclear Information System (INIS)

Bao, Ning; Cao, ChunJun; Walter, Michael; Wang, Zitao

2015-01-01

We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.

Robust output feedback H-infinity control and filtering for uncertain linear systems

CERN Document Server

Chang, Xiao-Heng

2014-01-01

"Robust Output Feedback H-infinity Control and Filtering for Uncertain Linear Systems" discusses new and meaningful findings on robust output feedback H-infinity control and filtering for uncertain linear systems, presenting a number of useful and less conservative design results based on the linear matrix inequality (LMI) technique. Though primarily intended for graduate students in control and filtering, the book can also serve as a valuable reference work for researchers wishing to explore the area of robust H-infinity control and filtering of uncertain systems. Dr. Xiao-Heng Chang is a Professor at the College of Engineering, Bohai University, China.

Modern linear control design a time-domain approach

CERN Document Server

Caravani, Paolo

2013-01-01

This book offers a compact introduction to modern linear control design.  The simplified overview presented of linear time-domain methodology paves the road for the study of more advanced non-linear techniques. Only rudimentary knowledge of linear systems theory is assumed - no use of Laplace transforms or frequency design tools is required. Emphasis is placed on assumptions and logical implications, rather than abstract completeness; on interpretation and physical meaning, rather than theoretical formalism; on results and solutions, rather than derivation or solvability.  The topics covered include transient performance and stabilization via state or output feedback; disturbance attenuation and robust control; regional eigenvalue assignment and constraints on input or output variables; asymptotic regulation and disturbance rejection. Lyapunov theory and Linear Matrix Inequalities (LMI) are discussed as key design methods. All methods are demonstrated with MATLAB to promote practical use and comprehension. ...

Variance estimation for complex indicators of poverty and inequality using linearization techniques

Directory of Open Access Journals (Sweden)

Guillaume Osier

2009-12-01

Full Text Available The paper presents the Eurostat experience in calculating measures of precision, including standard errors, confidence intervals and design effect coefficients - the ratio of the variance of a statistic with the actual sample design to the variance of that statistic with a simple random sample of same size - for the "Laeken" indicators, that is, a set of complex indicators of poverty and inequality which had been set out in the framework of the EU-SILC project (European Statistics on Income and Living Conditions. The Taylor linearization method (Tepping, 1968; Woodruff, 1971; Wolter, 1985; Tille, 2000 is actually a well-established method to obtain variance estimators for nonlinear statistics such as ratios, correlation or regression coefficients. It consists of approximating a nonlinear statistic with a linear function of the observations by using first-order Taylor Series expansions. Then, an easily found variance estimator of the linear approximation is used as an estimator of the variance of the nonlinear statistic. Although the Taylor linearization method handles all the nonlinear statistics which can be expressed as a smooth function of estimated totals, the approach fails to encompass the "Laeken" indicators since the latter are having more complex mathematical expressions. Consequently, a generalized linearization method (Deville, 1999, which relies on the concept of influence function (Hampel, Ronchetti, Rousseeuw and Stahel, 1986, has been implemented. After presenting the EU-SILC instrument and the main target indicators for which variance estimates are needed, the paper elaborates on the main features of the linearization approach based on influence functions. Ultimately, estimated standard errors, confidence intervals and design effect coefficients obtained from this approach are presented and discussed.

Multivariate Bonferroni-type inequalities theory and applications

CERN Document Server

Chen, John

2014-01-01

Multivariate Bonferroni-Type Inequalities: Theory and Applications presents a systematic account of research discoveries on multivariate Bonferroni-type inequalities published in the past decade. The emergence of new bounding approaches pushes the conventional definitions of optimal inequalities and demands new insights into linear and Fréchet optimality. The book explores these advances in bounding techniques with corresponding innovative applications. It presents the method of linear programming for multivariate bounds, multivariate hybrid bounds, sub-Markovian bounds, and bounds using Hamil

Nature beyond Linearity: Meteorological Variability and Jensen's Inequality Can Explain Mast Seeding Behavior

Directory of Open Access Journals (Sweden)

Marcos Fernández-Martínez

2017-11-01

Full Text Available Mast seeding, the extremely variable and synchronized production of fruits, is a common reproductive behavior in plants. Weather is centrally involved in driving masting. Yet, it is often claimed that it cannot be the sole proximate cause of masting because weather is less variable than fruit production and because the shape of their distributions differ. We used computer simulations to demonstrate that the assumption that weather cannot be the main driver of masting was only valid for linear relationships between weather and fruit production. Non-linear relationships between interannual variability in weather and crop size, however, can account for the differences in their variability and the shape of their distributions because of Jensen's inequality. Exponential relationships with weather can increase the variability of fruit production, and sigmoidal relationships can produce bimodal distributions. These results challenge the idea that meteorological variability cannot be the main proximate driver of mast seeding, returning meteorological variability to the forefront of masting research.

A survey of matrix theory and matrix inequalities

CERN Document Server

Marcus, Marvin

2010-01-01

Written for advanced undergraduate students, this highly regarded book presents an enormous amount of information in a concise and accessible format. Beginning with the assumption that the reader has never seen a matrix before, the authors go on to provide a survey of a substantial part of the field, including many areas of modern research interest.Part One of the book covers not only the standard ideas of matrix theory, but ones, as the authors state, ""that reflect our own prejudices,"" among them Kronecker products, compound and induced matrices, quadratic relations, permanents, incidence

Parameter-dependent PWQ Lyapunov function stability criteria for uncertain piecewise linear systems

Directory of Open Access Journals (Sweden)

Morten Hovd

2018-01-01

Full Text Available The calculation of piecewise quadratic (PWQ Lyapunov functions is addressed in view of stability analysis of uncertain piecewise linear dynamics. As main contribution, the linear matrix inequality (LMI approach proposed in (Johansson and Rantzer, 1998 for the stability analysis of PWL and PWA dynamics is extended to account for parametric uncertainty based on a improved relaxation technique. The results are applied for the analysis of a Phase Locked Loop (PLL benchmark and the ability to guarantee a stability region in the parameter space well beyond the state of the art is demonstrated.

New computational method for non-LTE, the linear response matrix

International Nuclear Information System (INIS)

Fournier, K.B.; Grasiani, F.R.; Harte, J.A.; Libby, S.B.; More, R.M.; Zimmerman, G.B.

1998-01-01

My coauthors have done extensive theoretical and computational calculations that lay the ground work for a linear response matrix method to calculate non-LTE (local thermodynamic equilibrium) opacities. I will give briefly review some of their work and list references. Then I will describe what has been done to utilize this theory to create a computational package to rapidly calculate mild non-LTE emission and absorption opacities suitable for use in hydrodynamic calculations. The opacities are obtained by performing table look-ups on data that has been generated with a non-LTE package. This scheme is currently under development. We can see that it offers a significant computational speed advantage. It is suitable for mild non-LTE, quasi-steady conditions. And it offers a new insertion path for high-quality non-LTE data. Currently, the linear response matrix data file is created using XSN. These data files could be generated by more detailed and rigorous calculations without changing any part of the implementation in the hydro code. The scheme is running in Lasnex and is being tested and developed

FUNDAMENTAL MATRIX OF LINEAR CONTINUOUS SYSTEM IN THE PROBLEM OF ESTIMATING ITS TRANSPORT DELAY

Directory of Open Access Journals (Sweden)

N. A. Dudarenko

2014-09-01

Full Text Available The paper deals with the problem of quantitative estimation for transport delay of linear continuous systems. The main result is received by means of fundamental matrix of linear differential equations solutions specified in the normal Cauchy form for the cases of SISO and MIMO systems. Fundamental matrix has the dual property. It means that the weight function of the system can be formed as a free motion of systems. Last one is generated by the vector of initial system conditions, which coincides with the matrix input of the system being researched. Thus, using the properties of the system- solving for fundamental matrix has given the possibility to solve the problem of estimating transport linear continuous system delay without the use of derivation procedure in hardware environment and without formation of exogenous Dirac delta function. The paper is illustrated by examples. The obtained results make it possible to solve the problem of modeling the pure delay links using consecutive chain of aperiodic links of the first order with the equal time constants. Modeling results have proved the correctness of obtained computations. Knowledge of transport delay can be used when configuring multi- component technological complexes and in the diagnosis of their possible functional degeneration.

On Functional Inequalities Originating from Module Jordan Left Derivations

OpenAIRE

Kang Sheon-Young; Chang Ick-Soon; Kim Hark-Mahn

2008-01-01

Abstract We first examine the generalized Hyers-Ulam stability of functional inequality associated with module Jordan left derivation (resp., module Jordan derivation). Secondly, we study the functional inequality with linear Jordan left derivation (resp., linear Jordan derivation) mapping into the Jacobson radical.

Homogenization of variational inequalities for obstacle problems

International Nuclear Information System (INIS)

Sandrakov, G V

2005-01-01

Results on the convergence of solutions of variational inequalities for obstacle problems are proved. The variational inequalities are defined by a non-linear monotone operator of the second order with periodic rapidly oscillating coefficients and a sequence of functions characterizing the obstacles. Two-scale and macroscale (homogenized) limiting variational inequalities are obtained. Derivation methods for such inequalities are presented. Connections between the limiting variational inequalities and two-scale and macroscale minimization problems are established in the case of potential operators.

Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers

CERN Document Server

Li, Deng-Feng

2016-01-01

This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .

On Functional Inequalities Originating from Module Jordan Left Derivations

Directory of Open Access Journals (Sweden)

Kang Sheon-Young

2008-01-01

Full Text Available Abstract We first examine the generalized Hyers-Ulam stability of functional inequality associated with module Jordan left derivation (resp., module Jordan derivation. Secondly, we study the functional inequality with linear Jordan left derivation (resp., linear Jordan derivation mapping into the Jacobson radical.

The detection of influential subsets in linear regression using an influence matrix

OpenAIRE

Peña, Daniel; Yohai, Víctor J.

1991-01-01

This paper presents a new method to identify influential subsets in linear regression problems. The procedure uses the eigenstructure of an influence matrix which is defined as the matrix of uncentered covariance of the effect on the whole data set of deleting each observation, normalized to include the univariate Cook's statistics in the diagonal. It is shown that points in an influential subset will appear with large weight in at least one of the eigenvector linked to the largest eigenvalue...

Event-Triggered Output-Feedback Control for Disturbed Linear Systems

Directory of Open Access Journals (Sweden)

Hao Jiang

2018-01-01

Full Text Available In the last few decades, event-triggered control received considerable attention, because of advantages in reducing the resource utilization, such as communication load and processor. In this paper, we propose an event-triggered output-feedback controller for disturbed linear systems, in order to achieve both better resource utilization and disturbance attenuation properties at the same time. Based on our prior work on state-feedback H∞ control for disturbed systems, we propose an approach to design an output-feedback H∞ controller for the system whose states are not completely observable, and a sufficient condition guaranteeing the asymptotic stability and robustness of the system is given in the form of LMIs (Linear Matrix Inequalities.

Operator Arithmetic-Harmonic Mean Inequality on Krein Spaces

Directory of Open Access Journals (Sweden)

M. Dehghani

2014-03-01

Full Text Available We prove an operator arithmetic-harmonic mean type inequality in Krein space setting, by using some block matrix techniques of indefinite type. We also give an example which shows that the operator arithmetic-geometric-harmonic mean inequality for two invertible selfadjoint operators on Krein spaces is not valid, in general.

Classification of the linear canonical transformation and its associated real symplectic matrix

NARCIS (Netherlands)

Bastiaans, M.J.; Alieva, T.

2007-01-01

Based on the eigenvalues of the real symplectic ABCD-matrix that characterizes the linear canonical integral transformation, a classification of this transformation and the associated ABCD-system is proposed and some nuclei (i.e. elementary members) in each class are described. In the

Weighted inequalities for fractional integral operators and linear commutators in the Morrey-type spaces

Directory of Open Access Journals (Sweden)

Hua Wang

2017-01-01

Full Text Available Abstract In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators I α $I_{\\alpha}$ in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutators [ b , I α ] $[b,I_{\\alpha}]$ formed by b and I α $I_{\\alpha}$ are established. Also we study related problems about two-weight, weak type inequalities for I α $I_{\\alpha}$ and [ b , I α ] $[b,I_{\\alpha}]$ in the Morrey-type spaces and give partial results.

New Delay-Dependent Robust Exponential Stability Criteria of LPD Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

Directory of Open Access Journals (Sweden)

Sirada Pinjai

2013-01-01

Full Text Available This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

Finite-Time Robust H∞ Control for Uncertain Linear Continuous-Time Singular Systems with Exogenous Disturbances

Directory of Open Access Journals (Sweden)

Songlin Wo

2018-01-01

Full Text Available Singular systems arise in a great deal of domains of engineering and can be used to solve problems which are more difficult and more extensive than regular systems to solve. Therefore, in this paper, the definition of finite-time robust H∞ control for uncertain linear continuous-time singular systems is presented. The problem we address is to design a robust state feedback controller which can deal with the singular system with time-varying norm-bounded exogenous disturbance, such that the singular system is finite-time robust bounded (FTRB with disturbance attenuation γ. Sufficient conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs. When these LMIs are feasible, the desired robust controller is given. A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

Some means inequalities for positive operators in Hilbert spaces

Directory of Open Access Journals (Sweden)

Jin Liang

2017-01-01

Full Text Available Abstract In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and show that the weighted multivariate operator geometric mean possess several attractive properties and means inequalities.

Local hyperspectral data multisharpening based on linear/linear-quadratic nonnegative matrix factorization by integrating lidar data

Science.gov (United States)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2015-10-01

In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods.

Semidefinite linear complementarity problems

International Nuclear Information System (INIS)

Eckhardt, U.

1978-04-01

Semidefinite linear complementarity problems arise by discretization of variational inequalities describing e.g. elastic contact problems, free boundary value problems etc. In the present paper linear complementarity problems are introduced and the theory as well as the numerical treatment of them are described. In the special case of semidefinite linear complementarity problems a numerical method is presented which combines the advantages of elimination and iteration methods without suffering from their drawbacks. This new method has very attractive properties since it has a high degree of invariance with respect to the representation of the set of all feasible solutions of a linear complementarity problem by linear inequalities. By means of some practical applications the properties of the new method are demonstrated. (orig.) [de

Transportation and concentration inequalities for bifurcating Markov chains

DEFF Research Database (Denmark)

Penda, S. Valère Bitseki; Escobar-Bach, Mikael; Guillin, Arnaud

2017-01-01

We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two offsprings, we use transportation inequalities to provide useful...... concentration inequalities.We also study deviation inequalities for the empirical means under relaxed assumptions on the Wasserstein contraction for the Markov kernels. Applications to bifurcating nonlinear autoregressive processes are considered for point-wise estimates of the non-linear autoregressive...

Classifying 50 years of Bell inequalities

International Nuclear Information System (INIS)

Rosset, Denis; Gisin, Nicolas; Bancal, Jean-Daniel

2014-01-01

Since John S Bell demonstrated the interest of studying linear combinations of probabilities in relation with the EPR paradox in 1964, Bell inequalities have lead to numerous developments. Unfortunately, the description of Bell inequalities is subject to several degeneracies, which make any exchange of information about them unnecessarily hard. Here, we analyze these degeneracies and propose a decomposition for Bell-like inequalities based on a set of reference expressions which is not affected by them. These reference expressions set a common ground for comparing Bell inequalities. We provide algorithms based on finite group theory to compute this decomposition. Implementing these algorithms allows us to set up a compendium of reference Bell-like inequalities, available online at www.faacets.com. This website constitutes a platform where registered Bell-like inequalities can be explored, new inequalities can be compared to previously-known ones and relevant information on Bell inequalities can be added in a collaborative manner. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’. (paper)

Classifying 50 years of Bell inequalities

Science.gov (United States)

Rosset, Denis; Bancal, Jean-Daniel; Gisin, Nicolas

2014-10-01

Since John S Bell demonstrated the interest of studying linear combinations of probabilities in relation with the EPR paradox in 1964, Bell inequalities have lead to numerous developments. Unfortunately, the description of Bell inequalities is subject to several degeneracies, which make any exchange of information about them unnecessarily hard. Here, we analyze these degeneracies and propose a decomposition for Bell-like inequalities based on a set of reference expressions which is not affected by them. These reference expressions set a common ground for comparing Bell inequalities. We provide algorithms based on finite group theory to compute this decomposition. Implementing these algorithms allows us to set up a compendium of reference Bell-like inequalities, available online at www.faacets.com. This website constitutes a platform where registered Bell-like inequalities can be explored, new inequalities can be compared to previously-known ones and relevant information on Bell inequalities can be added in a collaborative manner. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

Science.gov (United States)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control

International Nuclear Information System (INIS)

Wang Jun-Wei; Ma Qing-Hua; Zeng Li

2011-01-01

Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua's circuits connected in a drive-response configuration. In particular, in the mixed-synchronization regime, different state variables of the response system can evolve into complete synchronization, anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix. Using Lyapunov stability theory, we derive some sufficient criteria for achieving global mixed-synchronization. It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities (LMIs). Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach. (general)

Homogenization of variational inequalities and equations defined by pseudomonotone operators

International Nuclear Information System (INIS)

Sandrakov, G V

2008-01-01

Results on the convergence of sequences of solutions of non-linear equations and variational inequalities for obstacle problems are proved. The variational inequalities and equations are defined by a non-linear, pseudomonotone operator of the second order with periodic, rapidly oscillating coefficients and by sequences of functions characterizing the obstacles and the boundary conditions. Two-scale and macroscale (homogenized) limiting problems for such variational inequalities and equations are obtained. Results on the relationship between solutions of these limiting problems are established and sufficient conditions for the uniqueness of solutions are presented. Bibliography: 25 titles

Linearly constrained minimax optimization

DEFF Research Database (Denmark)

Madsen, Kaj; Schjær-Jacobsen, Hans

1978-01-01

We present an algorithm for nonlinear minimax optimization subject to linear equality and inequality constraints which requires first order partial derivatives. The algorithm is based on successive linear approximations to the functions defining the problem. The resulting linear subproblems...

Automatic Offline Formulation of Robust Model Predictive Control Based on Linear Matrix Inequalities Method

Directory of Open Access Journals (Sweden)

Longge Zhang

2013-01-01

Full Text Available Two automatic robust model predictive control strategies are presented for uncertain polytopic linear plants with input and output constraints. A sequence of nested geometric proportion asymptotically stable ellipsoids and controllers is constructed offline first. Then the feedback controllers are automatically selected with the receding horizon online in the first strategy. Finally, a modified automatic offline robust MPC approach is constructed to improve the closed system's performance. The new proposed strategies not only reduce the conservatism but also decrease the online computation. Numerical examples are given to illustrate their effectiveness.

Advanced topics in linear algebra weaving matrix problems through the Weyr form

CERN Document Server

O'Meara, Kevin; Vinsonhaler, Charles

2011-01-01

The Weyr matrix canonical form is a largely unknown cousin of the Jordan canonical form. Discovered by Eduard Weyr in 1885, the Weyr form outperforms the Jordan form in a number of mathematical situations, yet it remains somewhat of a mystery, even to many who are skilled in linear algebra. Written in an engaging style, this book presents various advanced topics in linear algebra linked through the Weyr form. Kevin O'Meara, John Clark, and Charles Vinsonhaler develop the Weyr form from scratch and include an algorithm for computing it. A fascinating duality exists between the Weyr form and the

Dynamics of Multi-Scale Intra-Provincial Regional Inequality in Zhejiang, China

Directory of Open Access Journals (Sweden)

Wenze Yue

2014-08-01

Full Text Available This paper investigates regional inequality in a multi-scale framework, using Exploratory Spatial Data Analysis, based on the per capita Gross Domestic Product (GDP of counties and municipalities within the Zhejiang province in China between the years of 1990 and 2010. A Spatial Markov Chain is used to identify the dynamics of regional wealth disparity in Zhejiang. The results show that the regional inequality of Zhejiang is sensitive to the geographic scale of the analysis. In addition, the inter-county inequality shows an inverted-U shape pattern. At the same time, the inter-municipality inequality displays a more consistently upward trend, and the evolution of the interregional inequality is relatively stable over time. The regional inequality is more significant at finer (larger spatial scales. The decomposition of the Theil Index shows that the contribution of the inequalities between Northeast Zhejiang and Southwest Zhejiang increased. The increasingly larger values of the Global Moran’s I show that there is an intensifying spatial aggregation of economic development. The comparison of the traditional Markov transition matrix and the Spatial Markov transition matrix illustrates how the relative wealth or poverty of neighboring counties make a significance difference in wealth in a given county as measured using domestic GDP per capita in Zhejiang province. This space-time analysis is valuable for policy making towards sustainable economic development in China given the soaring spatial inequality.

Linear programming model for solution of matrix game with payoffs trapezoidal intuitionistic fuzzy number

Directory of Open Access Journals (Sweden)

Darunee Hunwisai

2017-01-01

Full Text Available In this work, we considered two-person zero-sum games with fuzzy payoffs and matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers (TrIFNs. The concepts of TrIFNs and their arithmetic operations were used. The cut-set based method for matrix game with payoffs of TrIFNs was also considered. Compute the interval-type value of any alfa-constrategies by simplex method for linear programming. The proposed method is illustrated with a numerical example.

The structure of solutions of the matrix linear unilateral polynomial equation with two variables

Directory of Open Access Journals (Sweden)

N. S. Dzhaliuk

2017-07-01

Full Text Available We investigate the structure of solutions of the matrix linear polynomial equation $A(\\lambdaX(\\lambda+B(\\lambdaY(\\lambda=C(\\lambda,$ in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices $A (\\lambda, B(\\lambda$ \\ and \\ $C(\\lambda$ are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients $A(\\lambda$ and $B(\\lambda.$ 

Fundamental Matrix for a Class of Point Delay Linear Systems

International Nuclear Information System (INIS)

Sen, M. de la; Alastruey, C. F.

1998-01-01

It is difficult to establish explicit analytic forms for fundamental matrices of delayed linear systems. In this paper, an explicit form of exponential type is given for such a matrix in the case of punctual delays. The existence of real and complex fundamental matrices, for the case of real parameterizations of the differential system, is studied and discussed. Some additional commutativity properties involving the matrices parameters and the fundamental matrices as well as explicit expressions for the solution of the delayed differential system are also given. (Author)

Comparison of Damage Models for Predicting the Non-Linear Response of Laminates Under Matrix Dominated Loading Conditions

Science.gov (United States)

Schuecker, Clara; Davila, Carlos G.; Rose, Cheryl A.

2010-01-01

Five models for matrix damage in fiber reinforced laminates are evaluated for matrix-dominated loading conditions under plane stress and are compared both qualitatively and quantitatively. The emphasis of this study is on a comparison of the response of embedded plies subjected to a homogeneous stress state. Three of the models are specifically designed for modeling the non-linear response due to distributed matrix cracking under homogeneous loading, and also account for non-linear (shear) behavior prior to the onset of cracking. The remaining two models are localized damage models intended for predicting local failure at stress concentrations. The modeling approaches of distributed vs. localized cracking as well as the different formulations of damage initiation and damage progression are compared and discussed.

Batched Triangular Dense Linear Algebra Kernels for Very Small Matrix Sizes on GPUs

KAUST Repository

Charara, Ali; Keyes, David E.; Ltaief, Hatem

2017-01-01

Batched dense linear algebra kernels are becoming ubiquitous in scientific applications, ranging from tensor contractions in deep learning to data compression in hierarchical low-rank matrix approximation. Within a single API call, these kernels are capable of simultaneously launching up to thousands of similar matrix computations, removing the expensive overhead of multiple API calls while increasing the occupancy of the underlying hardware. A challenge is that for the existing hardware landscape (x86, GPUs, etc.), only a subset of the required batched operations is implemented by the vendors, with limited support for very small problem sizes. We describe the design and performance of a new class of batched triangular dense linear algebra kernels on very small data sizes using single and multiple GPUs. By deploying two-sided recursive formulations, stressing the register usage, maintaining data locality, reducing threads synchronization and fusing successive kernel calls, the new batched kernels outperform existing state-of-the-art implementations.

Batched Triangular Dense Linear Algebra Kernels for Very Small Matrix Sizes on GPUs

KAUST Repository

Charara, Ali

2017-03-06

Batched dense linear algebra kernels are becoming ubiquitous in scientific applications, ranging from tensor contractions in deep learning to data compression in hierarchical low-rank matrix approximation. Within a single API call, these kernels are capable of simultaneously launching up to thousands of similar matrix computations, removing the expensive overhead of multiple API calls while increasing the occupancy of the underlying hardware. A challenge is that for the existing hardware landscape (x86, GPUs, etc.), only a subset of the required batched operations is implemented by the vendors, with limited support for very small problem sizes. We describe the design and performance of a new class of batched triangular dense linear algebra kernels on very small data sizes using single and multiple GPUs. By deploying two-sided recursive formulations, stressing the register usage, maintaining data locality, reducing threads synchronization and fusing successive kernel calls, the new batched kernels outperform existing state-of-the-art implementations.

New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation

Science.gov (United States)

Liu, Jianzhou; Wang, Li; Zhang, Juan

2017-11-01

The discrete coupled algebraic Riccati equation (DCARE) has wide applications in control theory and linear system. In general, for the DCARE, one discusses every term of the coupled term, respectively. In this paper, we consider the coupled term as a whole, which is different from the recent results. When applying eigenvalue inequalities to discuss the coupled term, our method has less error. In terms of the properties of special matrices and eigenvalue inequalities, we propose several upper and lower matrix bounds for the solution of DCARE. Further, we discuss the iterative algorithms for the solution of the DCARE. In the fixed point iterative algorithms, the scope of Lipschitz factor is wider than the recent results. Finally, we offer corresponding numerical examples to illustrate the effectiveness of the derived results.

Income inequality and child maltreatment in the United States.

Science.gov (United States)

Eckenrode, John; Smith, Elliott G; McCarthy, Margaret E; Dineen, Michael

2014-03-01

To examine the relation between county-level income inequality and rates of child maltreatment. Data on substantiated reports of child abuse and neglect from 2005 to 2009 were obtained from the National Child Abuse and Neglect Data System. County-level data on income inequality and children in poverty were obtained from the American Community Survey. Data for additional control variables were obtained from the American Community Survey and the Health Resources and Services Administration Area Resource File. The Gini coefficient was used as the measure of income inequality. Generalized additive models were estimated to explore linear and nonlinear relations among income inequality, poverty, and child maltreatment. In all models, state was included as a fixed effect to control for state-level differences in victim rates. Considerable variation in income inequality and child maltreatment rates was found across the 3142 US counties. Income inequality, as well as child poverty rate, was positively and significantly correlated with child maltreatment rates at the county level. Controlling for child poverty, demographic and economic control variables, and state-level variation in maltreatment rates, there was a significant linear effect of inequality on child maltreatment rates (P income inequality across US counties was significantly associated with higher county-level rates of child maltreatment. The findings contribute to the growing literature linking greater income inequality to a range of poor health and well-being outcomes in infants and children.

Experimental violation of entropic inequalities

International Nuclear Information System (INIS)

Bovino, F.A.; Castagnoli, G.; Ekert, A.; Horodecki, P.; Alves, C.M.; Sergienko, A.V.

2005-01-01

Full text: We report the experimental evidence that polarization entangled photons violate the inequality based on Renyi entropy. Our experimental method is based on four-photon coincidences in photon bunching and antibunching effects. We introduce an additional 'phase marking' technique, which allow observing the violation of the inequalities even with non-deterministic sources of entangled photons. Our method can be applied to measure selected non-linear properties of bipartite quantum states, such as purity or entanglement. (author)

T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols

International Nuclear Information System (INIS)

Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2013-01-01

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders. -- Highlights: ► New superposition T-matrix code is applied to soot aerosols. ► Quasi-Rayleigh side-scattering peak in linear depolarization (LD) is explained. ► LD measurements can be used for morphological characterization of soot aerosols

A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems.

Science.gov (United States)

Liu, Tao; Huang, Jie

2017-04-17

This paper presents a discrete-time recurrent neural network approach to solving systems of linear equations with two features. First, the system of linear equations may not have a unique solution. Second, the system matrix is not known precisely, but a sequence of matrices that converges to the unknown system matrix exponentially is known. The problem is motivated from solving the output regulation problem for linear systems. Thus, an application of our main result leads to an online solution to the output regulation problem for linear systems.

Aging linear viscoelasticity of matrix-inclusion composite materials featuring ellipsoidal inclusions

OpenAIRE

LAVERGNE, Francis; SAB, Karam; SANAHUJA, Julien; BORNERT, Michel; TOULEMONDE, Charles

2016-01-01

A multi-scale homogenization scheme is proposed to estimate the time-dependent strains of fiber-reinforced concrete. This material is modeled as an aging linear viscoelastic composite material featuring ellipsoidal inclusions embedded in a viscoelastic cementitious matrix characterized by a time-dependent Poisson's ratio. To this end, the homogenization scheme proposed in Lavergne et al. [1] is adapted to the case of a time-dependent Poisson's ratio and it is successfully validated on a non-a...

Reduction of Under-Determined Linear Systems by Sparce Block Matrix Technique

DEFF Research Database (Denmark)

Tarp-Johansen, Niels Jacob; Poulsen, Peter Noe; Damkilde, Lars

1996-01-01

numerical stability of the aforementioned reduction. Moreover the coefficient matrix for the equilibrium equations is typically very sparse. The objective is to deal efficiently with the full pivoting reduction of sparse rectangular matrices using a dynamic storage scheme based on the block matrix concept.......Under-determined linear equation systems occur in different engineering applications. In structural engineering they typically appear when applying the force method. As an example one could mention limit load analysis based on The Lower Bound Theorem. In this application there is a set of under......-determined equilibrium equation restrictions in an LP-problem. A significant reduction of computer time spent on solving the LP-problem is achieved if the equilib rium equations are reduced before going into the optimization procedure. Experience has shown that for some structures one must apply full pivoting to ensure...

Integral and discrete inequalities and their applications

CERN Document Server

Qin, Yuming

2016-01-01

This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics. The present volume is part 1 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.

Matrix theory selected topics and useful results

CERN Document Server

Mehta, Madan Lal

1989-01-01

Matrices and operations on matrices ; determinants ; elementary operations on matrices (continued) ; eigenvalues and eigenvectors, diagonalization of normal matrices ; functions of a matrix ; positive definiteness, various polar forms of a matrix ; special matrices ; matrices with quaternion elements ; inequalities ; generalised inverse of a matrix ; domain of values of a matrix, location and dispersion of eigenvalues ; symmetric functions ; integration over matrix variables ; permanents of doubly stochastic matrices ; infinite matrices ; Alexander matrices, knot polynomials, torsion numbers.

On P-weight and P-distance inequalities

DEFF Research Database (Denmark)

Britz, Thomas Johann

2006-01-01

Jang and Park asked in [On a MacWilliams type identity and a perfectness for a binary linear (n, n - 1, j)-poset code, Discrete Math. 265 (2003) 85-104] whether, for each poset P = {l...., n}, the P-weights and P-distances satisfy the inequalities w(P)(x) - w(P)(y)......Jang and Park asked in [On a MacWilliams type identity and a perfectness for a binary linear (n, n - 1, j)-poset code, Discrete Math. 265 (2003) 85-104] whether, for each poset P = {l...., n}, the P-weights and P-distances satisfy the inequalities w(P)(x) - w(P)(y)...

Exact solution of some linear matrix equations using algebraic methods

Science.gov (United States)

Djaferis, T. E.; Mitter, S. K.

1977-01-01

A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

Matrix completion by deep matrix factorization.

Science.gov (United States)

Fan, Jicong; Cheng, Jieyu

2018-02-01

Conventional methods of matrix completion are linear methods that are not effective in handling data of nonlinear structures. Recently a few researchers attempted to incorporate nonlinear techniques into matrix completion but there still exists considerable limitations. In this paper, a novel method called deep matrix factorization (DMF) is proposed for nonlinear matrix completion. Different from conventional matrix completion methods that are based on linear latent variable models, DMF is on the basis of a nonlinear latent variable model. DMF is formulated as a deep-structure neural network, in which the inputs are the low-dimensional unknown latent variables and the outputs are the partially observed variables. In DMF, the inputs and the parameters of the multilayer neural network are simultaneously optimized to minimize the reconstruction errors for the observed entries. Then the missing entries can be readily recovered by propagating the latent variables to the output layer. DMF is compared with state-of-the-art methods of linear and nonlinear matrix completion in the tasks of toy matrix completion, image inpainting and collaborative filtering. The experimental results verify that DMF is able to provide higher matrix completion accuracy than existing methods do and DMF is applicable to large matrices. Copyright © 2017 Elsevier Ltd. All rights reserved.

State control of discrete-time linear systems to be bound in state variables by equality constraints

International Nuclear Information System (INIS)

Filasová, Anna; Krokavec, Dušan; Serbák, Vladimír

2014-01-01

The paper is concerned with the problem of designing the discrete-time equivalent PI controller to control the discrete-time linear systems in such a way that the closed-loop state variables satisfy the prescribed equality constraints. Since the problem is generally singular, using standard form of the Lyapunov function and a symmetric positive definite slack matrix, the design conditions are proposed in the form of the enhanced Lyapunov inequality. The results, offering the conditions of the control existence and the optimal performance with respect to the prescribed equality constraints for square discrete-time linear systems, are illustrated with the numerical example to note effectiveness and applicability of the considered approach

Steffensen's Integral Inequality on Time Scales

Directory of Open Access Journals (Sweden)

Ozkan Umut Mutlu

2007-01-01

Full Text Available We establish generalizations of Steffensen's integral inequality on time scales via the diamond- dynamic integral, which is defined as a linear combination of the delta and nabla integrals.

Generalization of Samuelson's inequality and location of eigenvalues

Indian Academy of Sciences (India)

We prove a generalization of Samuelson's inequality for higher order central moments. Bounds for the eigenvalues are obtained when a given complex × matrix has real eigenvalues. Likewise, we discuss bounds for the roots of polynomial equations.

Separability of quantum states and the violation of Bell-type inequalities

International Nuclear Information System (INIS)

Loubenets, Elena R.

2004-01-01

In contrast to the widespread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where separable quantum state does not satisfy the original Bell inequality although the latter inequality, in its perfect correlation form, is valid for all joint classical measurements. In a very general setting, we discuss inequalities for joint experiments upon a bipartite quantum system. For any separable quantum state, we derive quantum analogs of the original Bell inequality and specify the conditions sufficient for a separable state to satisfy the original Bell inequality. We introduce the extended Clauser-Horne-Shimony-Holt inequality and prove that, for any separable quantum state, this inequality holds for a variety of linear combinations

Robust stability of bidirectional associative memory neural networks with time delays

Science.gov (United States)

Park, Ju H.

2006-01-01

Based on the Lyapunov Krasovskii functionals combined with linear matrix inequality approach, a novel stability criterion is proposed for asymptotic stability of bidirectional associative memory neural networks with time delays. A novel delay-dependent stability criterion is given in terms of linear matrix inequalities, which can be solved easily by various optimization algorithms.

Robust stability of bidirectional associative memory neural networks with time delays

International Nuclear Information System (INIS)

Park, Ju H.

2006-01-01

Based on the Lyapunov-Krasovskii functionals combined with linear matrix inequality approach, a novel stability criterion is proposed for asymptotic stability of bidirectional associative memory neural networks with time delays. A novel delay-dependent stability criterion is given in terms of linear matrix inequalities, which can be solved easily by various optimization algorithms

Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P-matrix --- The full report.

OpenAIRE

Ben Gharbia , Ibtihel; Gilbert , Jean Charles

2012-01-01

The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) 0 ≤ x ⊥ (Mx+q) ≥ 0 can be viewed as a nonsmooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x,Mx+q)=0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge in at most n iterations. We show in this paper that this result no longer holds when M is a P-matrix of order ≥ 3, since then the algorithm may...

From Static Output Feedback to Structured Robust Static Output Feedback: A Survey

OpenAIRE

Sadabadi , Mahdieh ,; Peaucelle , Dimitri

2016-01-01

This paper reviews the vast literature on static output feedback design for linear time-invariant systems including classical results and recent developments. In particular, we focus on static output feedback synthesis with performance specifications, structured static output feedback, and robustness. The paper provides a comprehensive review on existing design approaches including iterative linear matrix inequalities heuristics, linear matrix inequalities with rank constraints, methods with ...

Inequalities for differential and integral equations

CERN Document Server

Ames, William F

1997-01-01

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course.Key Features* Covers a variety of linear and nonlinear inequalities which find widespread applications in the theory of various classes of differential and integral equations* Contains many inequalities which have only recently appeared in literature and cannot yet be found in other books* Provides a valuable reference to engineers and graduate students

Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

Science.gov (United States)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2017-04-01

This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

H∞ state estimation of generalised neural networks with interval time-varying delays

Science.gov (United States)

Saravanakumar, R.; Syed Ali, M.; Cao, Jinde; Huang, He

2016-12-01

This paper focuses on studying the H∞ state estimation of generalised neural networks with interval time-varying delays. The integral terms in the time derivative of the Lyapunov-Krasovskii functional are handled by the Jensen's inequality, reciprocally convex combination approach and a new Wirtinger-based double integral inequality. A delay-dependent criterion is derived under which the estimation error system is globally asymptotically stable with H∞ performance. The proposed conditions are represented by linear matrix inequalities. Optimal H∞ norm bounds are obtained easily by solving convex problems in terms of linear matrix inequalities. The advantage of employing the proposed inequalities is illustrated by numerical examples.

ORACLE INEQUALITIES FOR THE LASSO IN THE COX MODEL.

Science.gov (United States)

Huang, Jian; Sun, Tingni; Ying, Zhiliang; Yu, Yi; Zhang, Cun-Hui

2013-06-01

We study the absolute penalized maximum partial likelihood estimator in sparse, high-dimensional Cox proportional hazards regression models where the number of time-dependent covariates can be larger than the sample size. We establish oracle inequalities based on natural extensions of the compatibility and cone invertibility factors of the Hessian matrix at the true regression coefficients. Similar results based on an extension of the restricted eigenvalue can be also proved by our method. However, the presented oracle inequalities are sharper since the compatibility and cone invertibility factors are always greater than the corresponding restricted eigenvalue. In the Cox regression model, the Hessian matrix is based on time-dependent covariates in censored risk sets, so that the compatibility and cone invertibility factors, and the restricted eigenvalue as well, are random variables even when they are evaluated for the Hessian at the true regression coefficients. Under mild conditions, we prove that these quantities are bounded from below by positive constants for time-dependent covariates, including cases where the number of covariates is of greater order than the sample size. Consequently, the compatibility and cone invertibility factors can be treated as positive constants in our oracle inequalities.

Optimal Taxation, Inequality and Top Incomes

OpenAIRE

Andrienko, Yuri; Apps, Patricia; Rees, Ray

2014-01-01

In a number of high-income countries over the past few decades there has been a large growth in income inequality and at the same time a shift in the burden of taxation from the top to the middle of the income distribution. This paper applies the theory of optimal piecewise linear taxation to the issue of the taxation of top incomes. Our results suggest that an appropriate response to rising inequality is a shift towards a more progressive multi-bracket income tax system, with a more differen...

Lasso and probabilistic inequalities for multivariate point processes

OpenAIRE

Hansen, Niels Richard; Reynaud-Bouret, Patricia; Rivoirard, Vincent

2012-01-01

Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated by linear combinations of a fixed dictionary. To select coefficients, we propose an adaptive $\\ell_{1}$-penalization methodology, where data-driven weights of the penalty are derived from new Bernstein type inequalities for martingales. Oracle inequalities...

The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

Science.gov (United States)

Pang, Haotian; Liu, Han; Vanderbei, Robert

2014-02-01

We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

Individual and Collective Analyses of the Genesis of Student Reasoning Regarding the Invertible Matrix Theorem in Linear Algebra

Science.gov (United States)

Wawro, Megan Jean

2011-01-01

In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

Linear algebra

CERN Document Server

Liesen, Jörg

2015-01-01

This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

Stability Analysis of Wireless Measurement and Control System Based on Dynamic Matrix

Directory of Open Access Journals (Sweden)

Yongxian SONG

2014-01-01

Full Text Available Focus on data packet loss and time delay problems in wireless greenhouse measurement and control system, and temperature and humidity were taken as the research objects, the model of temperature and humidity information transmission was set up by decoupling technology according to the characteristics of wireless greenhouse measurement and control system. According to related theory of exponential stability in network control system, the stability conditions judgment of temperature and humidity control model was established, the linear matrix inequality that time delay and packet loss should satisfy was obtained when wireless measurement and control system was stable operation. The feasibility analysis of linear matrix inequality (LMI was implemented Using LMI toolbox in MATLAB, and the critical values of time delay and packet loss rate were obtained when the system was stable operation. The wireless sensor network control system simulation model with time delay and packet loss was set up using TrueTime toolbox. The simulation results have shown that the system was in a stable state when time delay and packet loss rate obtained were less than the critical values in wireless greenhouse sensor network measurement and control system; With the increase of time delay and packet loss rate, and stable performance drops; When time delay and packet loss rate obtained were more than the critical values, the measurement and control system would be in a state of flux, and when it was serious, even can lead to collapse of the whole system. As a result, the critical values determination of time delay and packet loss rate provided a theoretical basis for establishing stable greenhouse wireless sensor network (WSN measurement and control system in practical application.

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

Science.gov (United States)

Zhang, Langwen; Xie, Wei; Wang, Jingcheng

2017-11-01

In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min-max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.

Spin observables in p-barp → ΛΛ and density-matrix constraints

International Nuclear Information System (INIS)

Elchikh, Mokhtar; Richard, Jean-Marc

2005-01-01

The positivity conditions of the spin density matrix constrain the spin observables of the reaction p-barp → Λ-barΛ, leading to model-independent, non-trivial inequalities. The formalism is briefly presented and examples of inequalities are provided

To what extent does immigration affect inequality?

Science.gov (United States)

Berman, Yonatan; Aste, Tomaso

2016-11-01

The current surge in income and wealth inequality in most western countries, along with the continuous immigration to those countries demand a quantitative analysis of the effect immigration has on economic inequality. This paper presents a quantitative analysis framework providing a way to calculate this effect. It shows that in most cases, the effect of immigration on wealth and income inequality is limited, mainly due to the relative small scale of immigration waves. For a large scale flow of immigrants, such as the immigration to the US, the UK and Australia in the past few decades, we estimate that 10 % ÷ 15 % of the wealth and income inequality increase can be attributed to immigration. The results demonstrate that immigration could possibly decrease inequality substantially, if the characteristics of the immigrants resemble the characteristics of the destination middle class population in terms of wealth or income. We empirically found that the simple linear relation ΔS = 0.18 ρ roughly describes the increase in the wealth share of the top 10 % due to immigration of a fraction ρ of the population.

Adaptive tracking control of leader-following linear multi-agent systems with external disturbances

Science.gov (United States)

Lin, Hanquan; Wei, Qinglai; Liu, Derong; Ma, Hongwen

2016-10-01

In this paper, the consensus problem for leader-following linear multi-agent systems with external disturbances is investigated. Brownian motions are used to describe exogenous disturbances. A distributed tracking controller based on Riccati inequalities with an adaptive law for adjusting coupling weights between neighbouring agents is designed for leader-following multi-agent systems under fixed and switching topologies. In traditional distributed static controllers, the coupling weights depend on the communication graph. However, coupling weights associated with the feedback gain matrix in our method are updated by state errors between neighbouring agents. We further present the stability analysis of leader-following multi-agent systems with stochastic disturbances under switching topology. Most traditional literature requires the graph to be connected all the time, while the communication graph is only assumed to be jointly connected in this paper. The design technique is based on Riccati inequalities and algebraic graph theory. Finally, simulations are given to show the validity of our method.

Multiplicative algorithms for constrained non-negative matrix factorization

KAUST Repository

Peng, Chengbin

2012-12-01

Non-negative matrix factorization (NMF) provides the advantage of parts-based data representation through additive only combinations. It has been widely adopted in areas like item recommending, text mining, data clustering, speech denoising, etc. In this paper, we provide an algorithm that allows the factorization to have linear or approximatly linear constraints with respect to each factor. We prove that if the constraint function is linear, algorithms within our multiplicative framework will converge. This theory supports a large variety of equality and inequality constraints, and can facilitate application of NMF to a much larger domain. Taking the recommender system as an example, we demonstrate how a specialized weighted and constrained NMF algorithm can be developed to fit exactly for the problem, and the tests justify that our constraints improve the performance for both weighted and unweighted NMF algorithms under several different metrics. In particular, on the Movielens data with 94% of items, the Constrained NMF improves recall rate 3% compared to SVD50 and 45% compared to SVD150, which were reported as the best two in the top-N metric. © 2012 IEEE.

Some New Inequalities of Opial's Type on Time Scales

Directory of Open Access Journals (Sweden)

Samir H. Saker

2012-01-01

Full Text Available We will prove some new dynamic inequalities of Opial's type on time scales. The results not only extend some results in the literature but also improve some of them. Some continuous and discrete inequalities are derived from the main results as special cases. The results can be applied on the study of distribution of generalized zeros of half-linear dynamic equations on time scales.

Solutions to variational inequalities of parabolic type

Science.gov (United States)

Zhu, Yuanguo

2006-09-01

The existence of strong solutions to a kind of variational inequality of parabolic type is investigated by the theory of semigroups of linear operators. As an application, an abstract semi permeable media problem is studied.

Parallelism in matrix computations

CERN Document Server

Gallopoulos, Efstratios; Sameh, Ahmed H

2016-01-01

This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of pa...

Some determinantal inequalities for Hadamard and Fan products of matrices

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Xiaohui Fu

2016-10-01

Full Text Available Abstract In this note, we generalize some determinantal inequalities which are due to Lynn (Proc. Camb. Philos. 60:425-431, 1964, Chen (Linear Algebra Appl. 368:99-106, 2003 and Ando (Linear Multilinear Algebra 8:291-316, 1980.

A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate

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Min Sun

2014-01-01

Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.

Memory State Feedback RMPC for Multiple Time-Delayed Uncertain Linear Systems with Input Constraints

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Wei-Wei Qin

2014-01-01

Full Text Available This paper focuses on the problem of asymptotic stabilization for a class of discrete-time multiple time-delayed uncertain linear systems with input constraints. Then, based on the predictive control principle of receding horizon optimization, a delayed state dependent quadratic function is considered for incorporating MPC problem formulation. By developing a memory state feedback controller, the information of the delayed plant states can be taken into full consideration. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. Then, based on the Lyapunov-Krasovskii function, a delay-dependent sufficient condition in terms of linear matrix inequality (LMI can be derived to design a robust MPC algorithm. Finally, the digital simulation results prove availability of the proposed method.

Inequalities Theory of Majorization and Its Applications

CERN Document Server

Marshall, Albert W; Arnold, Barry

2011-01-01

This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. … This work is a valuable resource!” (Mathematical Reviews). “The authors … present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of … Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded...

Spin observables in antiproton-proton to AntiLambda-Lambda and density-matrix constraints

OpenAIRE

Elchikh, Mokhtar; Richard, Jean-Marc

2005-01-01

The positivity conditions of the spin density matrix constrain the spin observables of the reaction antiproton-proton to AntiLambda-Lambda, leading to model-independent, non-trivial inequalities. The formalism is briefly presented and examples of inequalities are provided.

An algorithm for the solution of dynamic linear programs

Science.gov (United States)

Psiaki, Mark L.

1989-01-01

The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation

Advanced linear algebra for engineers with Matlab

CERN Document Server

Dianat, Sohail A

2009-01-01

Matrices, Matrix Algebra, and Elementary Matrix OperationsBasic Concepts and NotationMatrix AlgebraElementary Row OperationsSolution of System of Linear EquationsMatrix PartitionsBlock MultiplicationInner, Outer, and Kronecker ProductsDeterminants, Matrix Inversion and Solutions to Systems of Linear EquationsDeterminant of a MatrixMatrix InversionSolution of Simultaneous Linear EquationsApplications: Circuit AnalysisHomogeneous Coordinates SystemRank, Nu

L∞-error estimate for a system of elliptic quasivariational inequalities

Directory of Open Access Journals (Sweden)

M. Boulbrachene

2003-01-01

Full Text Available We deal with the numerical analysis of a system of elliptic quasivariational inequalities (QVIs. Under W2,p(Ω-regularity of the continuous solution, a quasi-optimal L∞-convergence of a piecewise linear finite element method is established, involving a monotone algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs.

On the Cauchy Functional Inequality in Banach Modules

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Park Choonkil

2008-01-01

Full Text Available Abstract We investigate the following functional inequality: in Banach modules over a -algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a -algebra.

Quantum nonlocality, Bell inequalities, and the memory loophole

International Nuclear Information System (INIS)

Barrett, Jonathan; Collins, Daniel; Popescu, Sandu; Hardy, Lucien; Kent, Adrian

2002-01-01

In the analysis of experiments designed to reveal violation of Bell-type inequalities, it is usually assumed that any hidden variables associated with the nth particle pair would be independent of measurement choices and outcomes for the first (n-1) pairs. Models which violate this assumption exploit what we call the memory loophole. We focus on the strongest type of violation, which uses the two-sided memory loophole, in which the hidden variables for pair n can depend on the previous measurement choices and outcomes in both wings of the experiment. We show that the two-sided memory loophole allows a systematic violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality when the data are analyzed in the standard way, but cannot produce a violation if a CHSH expression depending linearly on the data is used. In the first case, the maximal CHSH violation becomes small as the number of particle pairs tested becomes large. Hence, although in principle the memory loophole implies a slight flaw in the existing analyses of Bell experiments, the data still strongly confirm quantum mechanics against local hidden variables. We consider also a related loophole, the simultaneous measurement loophole, which applies if all measurements on each side are carried out simultaneously. We show that this can increase the probability of violating the linearized CHSH inequality as well as other Bell-type inequalities

Minimum error discrimination for an ensemble of linearly independent pure states

International Nuclear Information System (INIS)

Singal, Tanmay; Ghosh, Sibasish

2016-01-01

Inspired by the work done by Belavkin (1975 Stochastics 1 315) and independently by Mochon, (2006 Phys. Rev. A 73 032328), we formulate the problem of minimum error discrimination (MED) of any ensemble of n linearly independent pure states by stripping the problem of its rotational covariance and retaining only the rotationally invariant aspect of the problem. This is done by embedding the optimal conditions in a matrix equality as well as matrix inequality. Employing the implicit function theorem in these conditions we get a set of first-order coupled ordinary nonlinear differential equations which can be used to drag the solution from an initial point (where solution is known) to another point (whose solution is sought). This way of obtaining the solution can be done through a simple Taylor series expansion and analytic continuation when required. Thus, we complete the work done by Belavkin and Mochon by ultimately leading their theory to a solution for the MED problem of linearly independent pure state ensembles. We also compare the computational complexity of our technique with the barrier-type interior point method of SDP and show that our technique is computationally as efficient as (actually, a bit more than) the SDP algorithm, with the added advantage of being much simpler to implement. (paper)

An efficient method for minimizing a convex separable logarithmic function subject to a convex inequality constraint or linear equality constraint

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available We consider the problem of minimizing a convex separable logarithmic function over a region defined by a convex inequality constraint or linear equality constraint, and two-sided bounds on the variables (box constraints. Such problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems as well as in various practical problems such as problems of production planning and scheduling, allocation of resources, decision making, facility location problems, and so forth. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.

Some Schrödinger-type inequalities for stabilization of discrete linear systems associated with the stationary Schrödinger operator

Directory of Open Access Journals (Sweden)

Zongcai Jiang

2016-10-01

Full Text Available Abstract By applying some Schrödinger-type inequalities developed by Huang (Int. J. Math. 27(2:1650009, 2016, we are concerned with stabilization of discrete linear systems associated with the Schrödinger operator. Our first aim is to prove a state-dependent switching law associated with the Schrödinger operator, which is based on a convex combination. Next, we derive sufficient conditions associated with the Schrödinger operator that guarantee the uniform exponential stability of the system. Finally, we propose a necessary and sufficient condition for the stability of a system with two Schrödinger subsystems.

Simultaneous Robust Fault and State Estimation for Linear Discrete-Time Uncertain Systems

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Feten Gannouni

2017-01-01

Full Text Available We consider the problem of robust simultaneous fault and state estimation for linear uncertain discrete-time systems with unknown faults which affect both the state and the observation matrices. Using transformation of the original system, a new robust proportional integral filter (RPIF having an error variance with an optimized guaranteed upper bound for any allowed uncertainty is proposed to improve robust estimation of unknown time-varying faults and to improve robustness against uncertainties. In this study, the minimization problem of the upper bound of the estimation error variance is formulated as a convex optimization problem subject to linear matrix inequalities (LMI for all admissible uncertainties. The proportional and the integral gains are optimally chosen by solving the convex optimization problem. Simulation results are given in order to illustrate the performance of the proposed filter, in particular to solve the problem of joint fault and state estimation.

Income inequality and obesity prevalence among OECD countries.

Science.gov (United States)

Su, Dejun; Esqueda, Omar A; Li, Lifeng; Pagán, José A

2012-07-01

Using recent pooled data from the World Health Organization Global Infobase and the World Factbook compiled by the Central Intelligence Agency of the United States, this study assesses the relation between income inequality and obesity prevalence among 31 OECD countries through a series of bivariate and multivariate linear regressions. The United States and Mexico well lead OECD countries in both obesity prevalence and income inequality. A sensitivity analysis suggests that the inclusion or exclusion of these two extreme cases can fundamentally change the findings. When the two countries are included, the results reveal a positive correlation between income inequality and obesity prevalence. This correlation is more salient among females than among males. Income inequality alone is associated with 16% and 35% of the variations in male and female obesity rates, respectively, across OECD countries in 2010. Higher levels of income inequality in the 2005-2010 period were associated with a more rapid increase in obesity prevalence from 2002 to 2010. These associations, however, virtually disappear when the US and Mexico have been excluded from the analysis. Findings from this study underscore the importance of assessing the impact of extreme cases on the relation between income inequality and health outcomes. The potential pathways from income inequality to the alarmingly high rates of obesity in the cases of the US and Mexico warrant further research.

Reduced Order Extended Luenberger Observer Based Sensorless Vector Control Fed by Matrix Converter with Non-linearity Modeling

DEFF Research Database (Denmark)

Lee, Kyo-Beum; Blaabjerg, Frede

2004-01-01

This paper presents a new sensorless vector control system for high performance induction motor drives fed by a matrix converter with non-linearity compensation. The nonlinear voltage distortion that is caused by commutation delay and on-state voltage drop in switching device is corrected by a new...

vSmartMOM: A vector matrix operator method-based radiative transfer model linearized with respect to aerosol properties

International Nuclear Information System (INIS)

Sanghavi, Suniti; Davis, Anthony B.; Eldering, Annmarie

2014-01-01

In this paper, we build up on the scalar model smartMOM to arrive at a formalism for linearized vector radiative transfer based on the matrix operator method (vSmartMOM). Improvements have been made with respect to smartMOM in that a novel method of computing intensities for the exact viewing geometry (direct raytracing) without interpolation between quadrature points has been implemented. Also, the truncation method employed for dealing with highly peaked phase functions has been changed to a vector adaptation of Wiscombe's delta-m method. These changes enable speedier and more accurate radiative transfer computations by eliminating the need for a large number of quadrature points and coefficients for generalized spherical functions. We verify our forward model against the benchmarking results of Kokhanovsky et al. (2010) [22]. All non-zero Stokes vector elements are found to show agreement up to mostly the seventh significant digit for the Rayleigh atmosphere. Intensity computations for aerosol and cloud show an agreement of well below 0.03% and 0.05% at all viewing angles except around the solar zenith angle (60°), where most radiative models demonstrate larger variances due to the strongly forward-peaked phase function. We have for the first time linearized vector radiative transfer based on the matrix operator method with respect to aerosol optical and microphysical parameters. We demonstrate this linearization by computing Jacobian matrices for all Stokes vector elements for a multi-angular and multispectral measurement setup. We use these Jacobians to compare the aerosol information content of measurements using only the total intensity component against those using the idealized measurements of full Stokes vector [I,Q,U,V] as well as the more practical use of only [I,Q,U]. As expected, we find for the considered example that the accuracy of the retrieved parameters improves when the full Stokes vector is used. The information content for the full Stokes

Uniqueness theorems in linear elasticity

CERN Document Server

Knops, Robin John

1971-01-01

The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...

Reconciling consumption inequality with income inequality

NARCIS (Netherlands)

Lepetyuk, V.; Stoltenberg, C.A.

2012-01-01

The rise in consumption inequality in response to the increase in income inequality over the last three decades in the U.S. is puzzling to expected-utility-based incomplete market models. The two-sided lack of commitment models exhibit too little consumption inequality while the standard incomplete

Reconciling consumption inequality with income inequality

NARCIS (Netherlands)

Lepetyuk, V.; Stoltenberg, C.A.

2013-01-01

The rise in within-group consumption inequality in response to the increase in within-group income inequality over the last three decades in the U.S. is puzzling to expected-utility-based incomplete market models. The two-sided lack of commitment models exhibit too little consumption inequality

Limit theorems for linear spectrum statistics of orthogonal polynomial ensembles and their applications in random matrix theory

Science.gov (United States)

Pan, Guangming; Wang, Shaochen; Zhou, Wang

2017-10-01

In this paper, we consider the asymptotic behavior of Xfn (n )≔∑i=1 nfn(xi ) , where xi,i =1 ,…,n form orthogonal polynomial ensembles and fn is a real-valued, bounded measurable function. Under the condition that Var Xfn (n )→∞ , the Berry-Esseen (BE) bound and Cramér type moderate deviation principle (MDP) for Xfn (n ) are obtained by using the method of cumulants. As two applications, we establish the BE bound and Cramér type MDP for linear spectrum statistics of Wigner matrix and sample covariance matrix in the complex cases. These results show that in the edge case (which means fn has a particular form f (x ) I (x ≥θn ) where θn is close to the right edge of equilibrium measure and f is a smooth function), Xfn (n ) behaves like the eigenvalues counting function of the corresponding Wigner matrix and sample covariance matrix, respectively.

A Hierarchical Linear Model for Estimating Gender-Based Earnings Differentials.

Science.gov (United States)

Haberfield, Yitchak; Semyonov, Moshe; Addi, Audrey

1998-01-01

Estimates of gender earnings inequality in data from 116,431 Jewish workers were compared using a hierarchical linear model (HLM) and ordinary least squares model. The HLM allows estimation of the extent to which earnings inequality depends on occupational characteristics. (SK)

Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

KAUST Repository

Angela Mihai, L.

2013-03-01

Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.

Violating Bell inequalities maximally for two d-dimensional systems

International Nuclear Information System (INIS)

Chen Jingling; Wu Chunfeng; Oh, C. H.; Kwek, L. C.; Ge Molin

2006-01-01

We show the maximal violation of Bell inequalities for two d-dimensional systems by using the method of the Bell operator. The maximal violation corresponds to the maximal eigenvalue of the Bell operator matrix. The eigenvectors corresponding to these eigenvalues are described by asymmetric entangled states. We estimate the maximum value of the eigenvalue for large dimension. A family of elegant entangled states |Ψ> app that violate Bell inequality more strongly than the maximally entangled state but are somewhat close to these eigenvectors is presented. These approximate states can potentially be useful for quantum cryptography as well as many other important fields of quantum information

Impact of Income Inequality on the Nation's Health.

Science.gov (United States)

López, Diego B; Loehrer, Andrew P; Chang, David C

2016-10-01

Income inequality in the United States has been increasing in recent decades. It is unclear whether income inequality has an independent effect on health outcomes, or whether it simply correlates with increasing levels of poverty. The goal of this study was to evaluate whether income inequality is significantly associated with US county health care expenditures and health care use. Cross-sectional analysis of county health expenditure data from the Health Resources and Services Administration's Area Resources File, county income inequality measures (Gini coefficient) from the Census' American Community Survey, and estimates of potentially preventable admissions and potentially discretionary procedures from the Nationwide Inpatient Sample (1998 to 2011). Datasets were linked via county Federal Information Processing Standard codes. Multivariable linear and Poisson regression analyses were performed at the county level adjusting for county characteristics. A total of 1,237 counties (of 3,144) were included. Income inequality was associated with higher health care expenditures, with each 1 percentage-point increase in county Gini coefficient associated with a US$40,008 increase in annual county Medicare cost (p = 0.003), and an increase of 174.7 total county Medicare inpatient days per year (p inequality had higher potentially preventable admission (eg 4.86 rate ratio for low-birth-weight hospital admissions in the top income inequality quartile compared with bottom quartile; p income inequality quartile compared with bottom quartile; p Income inequality is independently associated with higher health care expenditures and more health care use, with increases in both potentially discretionary procedures and in potentially preventable admissions. Copyright © 2016 American College of Surgeons. Published by Elsevier Inc. All rights reserved.

Time trends in absolute and relative socioeconomic inequalities in leisure time physical inactivity in northern Sweden.

Science.gov (United States)

Szilcz, Máté; Mosquera, Paola A; Sebastián, Miguel San; Gustafsson, Per E

2018-02-01

The aim was to investigate the time trends in educational, occupational, and income-related inequalities in leisure time physical inactivity in 2006, 2010, and 2014 in northern Swedish women and men. This study was based on data obtained from the repeated cross-sectional Health on Equal Terms survey of 2006, 2010, and 2014. The analytical sample consisted of 20,667 (2006), 31,787 (2010), and 21,613 (2014) individuals, aged 16-84. Logistic regressions were used to model the probability of physical inactivity given a set of explanatory variables. Slope index of inequality (SII) and relative index of inequality (RII) were used as summary measures of the social gradient in physical inactivity. The linear trend in inequalities and difference between gender and years were estimated by interaction analyses. The year 2010 displayed the highest physical inactivity inequalities for all socioeconomic position indicators, but educational and occupational inequalities decreased in 2014. However, significant positive linear trends were found in absolute and relative income inequalities. Moreover, women had significantly higher RII of education in physical inactivity in 2014 and significantly higher SII and RII of income in physical inactivity in 2010, than did men in the same years. The recent reduction in educational and occupational inequalities following the high inequalities around the time of the great recession in 2010 suggests that the current policies might be fairly effective. However, to eventually alleviate inequities in physical inactivity, the focus of the researchers and policymakers should be directed toward the widening trends of income inequalities in physical inactivity.

Linear algebra

CERN Document Server

Shilov, Georgi E

1977-01-01

Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

Inequality in health versus inequality in lifestyle choices

Directory of Open Access Journals (Sweden)

Arnstein Øvrum

2015-10-01

Full Text Available Repeated Norwegian cross-sectional data for the period 2005 to 2011 are used to compare sources of inequality in health, as represented by self-assessed health and obesity, with sources of inequality in lifestyles that are central to the production of health, as represented by physical activity, cigarette smoking and dietary behavior. Sources of overall inequality and socioeconomic inequality in these lifestyle and health indicators are compared by estimating probit models, and by decomposing the explained part of the associated Gini and concentration indices with respect to education and income. As potential sources of inequality, we consider education, income, occupation, age, gender, marital status, psychological traits and childhood circumstances. Our results suggest that sources of inequality in health are not necessarily representative of sources of inequality in underlying lifestyles. While education is generally an important source of overall inequality in both lifestyles and health, income is unimportant in all lifestyle indicators except physical activity. In several cases, education and income are clearly outranked by other factors in terms of explaining overall inequality, such as gender in eating fruits and vegetables and age in fish consumption. These results suggest that it is important to decompose both overall inequality and socioeconomic inequality in different lifestyle and health indicators. In indicators where other factors than education and income are clearly most important, policy makers should consider to target these factors to efficiently improve overall population health.

An approach for solving linear fractional programming problems ...

African Journals Online (AJOL)

The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebraically using the concept of duality ...

Best linear unbiased prediction of genomic breeding values using a trait-specific marker-derived relationship matrix.

Directory of Open Access Journals (Sweden)

Zhe Zhang

2010-09-01

Full Text Available With the availability of high density whole-genome single nucleotide polymorphism chips, genomic selection has become a promising method to estimate genetic merit with potentially high accuracy for animal, plant and aquaculture species of economic importance. With markers covering the entire genome, genetic merit of genotyped individuals can be predicted directly within the framework of mixed model equations, by using a matrix of relationships among individuals that is derived from the markers. Here we extend that approach by deriving a marker-based relationship matrix specifically for the trait of interest.In the framework of mixed model equations, a new best linear unbiased prediction (BLUP method including a trait-specific relationship matrix (TA was presented and termed TABLUP. The TA matrix was constructed on the basis of marker genotypes and their weights in relation to the trait of interest. A simulation study with 1,000 individuals as the training population and five successive generations as candidate population was carried out to validate the proposed method. The proposed TABLUP method outperformed the ridge regression BLUP (RRBLUP and BLUP with realized relationship matrix (GBLUP. It performed slightly worse than BayesB with an accuracy of 0.79 in the standard scenario.The proposed TABLUP method is an improvement of the RRBLUP and GBLUP method. It might be equivalent to the BayesB method but it has additional benefits like the calculation of accuracies for individual breeding values. The results also showed that the TA-matrix performs better in predicting ability than the classical numerator relationship matrix and the realized relationship matrix which are derived solely from pedigree or markers without regard to the trait. This is because the TA-matrix not only accounts for the Mendelian sampling term, but also puts the greater emphasis on those markers that explain more of the genetic variance in the trait.

Multivariate Matrix-Exponential Distributions

DEFF Research Database (Denmark)

Bladt, Mogens; Nielsen, Bo Friis

2010-01-01

be written as linear combinations of the elements in the exponential of a matrix. For this reason we shall refer to multivariate distributions with rational Laplace transform as multivariate matrix-exponential distributions (MVME). The marginal distributions of an MVME are univariate matrix......-exponential distributions. We prove a characterization that states that a distribution is an MVME distribution if and only if all non-negative, non-null linear combinations of the coordinates have a univariate matrix-exponential distribution. This theorem is analog to a well-known characterization theorem...

Global Inequality

DEFF Research Database (Denmark)

Niño-Zarazúa, Miguel; Roope, Laurence; Tarp, Finn

2017-01-01

This paper measures trends in global interpersonal inequality during 1975–2010 using data from the most recent version of the World Income Inequality Database (WIID). The picture that emerges using ‘absolute,’ and even ‘centrist’ measures of inequality, is very different from the results obtained...... using standard ‘relative’ inequality measures such as the Gini coefficient or Coefficient of Variation. Relative global inequality has declined substantially over the decades. In contrast, ‘absolute’ inequality, as captured by the Standard Deviation and Absolute Gini, has increased considerably...... and unabated. Like these ‘absolute’ measures, our ‘centrist’ inequality indicators, the Krtscha measure and an intermediate Gini, also register a pronounced increase in global inequality, albeit, in the case of the latter, with a decline during 2005 to 2010. A critical question posed by our findings is whether...

Income Distribution across Ethnic Groups in Malaysia : Results from a New Social Accounting Matrix

NARCIS (Netherlands)

Saari, M. Yusof; Dietzenbacher, Erik; Los, Bart

A new social accounting matrix is constructed for Malaysia for the year 2000 to analyze sources of income inequality among ethnic groups in Malaysia. The analysis reveals that income inequality can be decomposed into the interaction of: (i) hourly wages; (ii) working hours per week; and (iii) number

Does a Rise in Income Inequality Lead to Rises in Transportation Inequality and Mobility Practice Inequality?

Directory of Open Access Journals (Sweden)

Joko Purwanto

2016-06-01

Full Text Available Social and economic inequalities have sharpened in the late 20th century. During this period, Europe has witnessed a rising unemployment rate, a declining wages for the least qualified workers, a slowing of income growth, and an increasing gap between the richest and the poorest. Based on the hypothesis of the relation between socio-economic condition and mobility behaviour, it is necessary to ask how these socio-economic inequalities manifest themselves in transportation: does a rise in income inequality lead to a rise in transportation inequality and mobility practice inequality? This question is particularly relevant today as some European countries are facing high socio-economic inequalities following the financial crisis that started in 2008. Using results from transport, car ownership and mobility surveys as well as household surveys from the Paris (Île-de-France region between eighties and late nineties, this paper tries to answer this question. The results show how inequalities in transportation and mobility practice have decreased during the period in spite of an increase in income inequalities. We find that the evolution of socio-economic inequality, most specifically income inequality was simply one of the determining factors of the evolution of inequalities in transportation and mobility practice. In fact, the most important role in that evolution is not played by the evolution of income inequality but by the evolution of elasticity between transportation and income. Reducing the effects of this elasticity should be the main target of transport policies to diminish inequality in transportation and mobility practice.

European health inequality through the 'Great Recession': social policy matters.

Science.gov (United States)

van der Wel, Kjetil A; Saltkjel, Therese; Chen, Wen-Hao; Dahl, Espen; Halvorsen, Knut

2018-05-01

This paper investigates the association between the Great Recession and educational inequalities in self-rated general health in 25 European countries. We investigate four different indicators related to economic recession: GDP; unemployment; austerity and a 'crisis' indicator signifying severe simultaneous drops in GDP and welfare generosity. We also assess the extent to which health inequality changes can be attributed to changes in the economic conditions and social capital in the European populations. The paper uses data from the European Social Survey (2002-2014). The analyses include both cross-sectional and lagged associations using multilevel linear regression models with country fixed effects. This approach allows us to identify health inequality changes net of all time-invariant differences between countries. GDP drops and increasing unemployment were associated with decreasing health inequalities. Austerity, however, was related to increasing health inequalities, an association that grew stronger with time. The strongest increase in health inequality was found for the more robust 'crisis' indicator. Changes in trust, social relationships and in the experience of economic hardship of the populations accounted for much of the increase in health inequality. The paper concludes that social policy has an important role in the development of health inequalities, particularly during times of economic crisis. © 2018 The Authors. Sociology of Health & Illness published by John Wiley & Sons Ltd on behalf of Foundation for SHIL.

Matrix Mathematics Theory, Facts, and Formulas (Second Edition)

CERN Document Server

Bernstein, Dennis S

2011-01-01

When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminat

Global Inequality

DEFF Research Database (Denmark)

Niño-Zarazúa, Miguel; Roope, Laurence; Tarp, Finn

2017-01-01

This paper measures trends in global interpersonal inequality during 1975–2010 using data from the most recent version of the World Income Inequality Database (WIID). The picture that emerges using ‘absolute,’ and even ‘centrist’ measures of inequality, is very different from the results obtained...... by centrist measures such as the Krtscha, could return to 1975 levels, at today's domestic and global per capita income levels, but this would require quite dramatic structural reforms to reduce domestic inequality levels in most countries....... using standard ‘relative’ inequality measures such as the Gini coefficient or Coefficient of Variation. Relative global inequality has declined substantially over the decades. In contrast, ‘absolute’ inequality, as captured by the Standard Deviation and Absolute Gini, has increased considerably...

Income inequality and high blood pressure in Colombia: a multilevel analysis.

Science.gov (United States)

Lucumi, Diego I; Schulz, Amy J; Roux, Ana V Diez; Grogan-Kaylor, Andrew

2017-11-21

The objective of this research was to examine the association between income inequality and high blood pressure in Colombia. Using a nationally representative Colombian sample of adults, and data from departments and municipalities, we fit sex-stratified linear and logistic multilevel models with blood pressure as a continuous and binary variable, respectively. In adjusted models, women living in departments with the highest quintile of income inequality in 1997 had higher systolic blood pressure than their counterparts living in the lowest quintile of income inequality (mean difference 4.42mmHg; 95%CI: 1.46, 7.39). Women living in departments that were at the fourth and fifth quintile of income inequality in 1994 were more likely to have hypertension than those living in departments at the first quintile in the same year (OR: 1.56 and 1.48, respectively). For men, no associations of income inequality with either systolic blood pressure or hypertension were observed. Our findings are consistent with the hypothesis that income inequality is associated with increased risk of high blood pressure for women. Future studies to analyze pathways linking income inequality to high blood pressure in Colombia are needed.

Linearization of Euclidean Norm Dependent Inequalities Applied to Multibeam Satellites Design

OpenAIRE

Camino , Jean-Thomas; Artigues , Christian; Houssin , Laurent; Mourgues , Stéphane

2016-01-01

Euclidean norm computations over continuous variables appear naturally in the constraints or in the objective of many problems in the optimization literature, possibly defining non-convex feasible regions or cost functions. When some other variables have discrete domains, it positions the problem in the challenging Mixed Integer Nonlinear Programming (MINLP) class. For any MINLP where the nonlinearity is only present in the form of inequality constraints involving the Euclidean norm, we propo...

Rising U.S. income inequality, gender and individual self-rated health, 1972-2004.

Science.gov (United States)

Zheng, Hui

2009-11-01

The effect of income inequality on health has been a contested topic among social scientists. Most previous research is based on cross-sectional comparisons rather than temporal comparisons. Using data from the General Social Survey and the U.S. Census Bureau, this study examines how rising income inequality affects individual self-rated health in the U.S. from 1972 to 2004. Data are analyzed using hierarchical generalized linear models. The findings suggest a significant association between income inequality and individual self-rated health. The dramatic increase in income inequality from 1972 to 2004 increases the odds of worse self-rated health by 9.4 percent. These findings hold for three measures of income inequality: the Gini coefficient, the Atkinson Index, and the Theil entropy index. Results also suggest that overall income inequality and gender-specific income inequality harm men's, but not women's, self-rated health. These findings also hold for the three measures of income inequality. These findings suggest that inattention to gender composition may explain apparent discrepancies across previous studies.

Matrix effect study in the determination of linear alkylbenzene sulfonates in sewage sludge samples.

Science.gov (United States)

Cantarero, Samuel; Zafra-Gómez, Alberto; Ballesteros, Oscar; Navalón, Alberto; Vílchez, José L; Verge, Coral; De Ferrer, Juan A

2011-04-01

We propose a study of the matrix effect in the determination of linear alkylbenzene sulfonates (LAS) in sewage sludge samples. First, a rapid, selective and sensitive method is proposed. The method involves two stages: the extraction of the compound from the samples and analysis by liquid chromatography with fluorescence detection (LC-FLD). Three different techniques of extraction (microwave-assisted extraction, Soxhlet, and ultrasounds) were compared, and microwave-assisted extraction was selected as the best suited for our purpose. Microwave-assisted extraction allows reducing the extraction time (25 min compared with 12 h for conventional Soxhlet extraction) and solvent waste (25 ml of methanol compared with 200 ml for Soxhlet or more than 50 ml for the ultrasonic procedure). Absence of matrix effect was evaluated with two standards (2ØC(8:0) and 2ØC(16:0) ) that are not commercial; therefore, neither of them was detected in sewage sludge samples and they showed similar environmental behavior (adsorption and precipitation) to LAS (C(11:0) -C(13.0) ), which allow us to evaluate the matrix effect. Validation was carried out by a recovery assay, and the method was applied to samples from different sources; therefore, they had different compositions. Copyright © 2011 SETAC.

Experimental demonstration of H∞ filter performance for dynamic compensation of rhodium neutron detectors

International Nuclear Information System (INIS)

Park, Moon-Ghu; Choi, Yu-Sun; Lee, Kwang-Dae

2008-01-01

This paper describes the experimental demonstration of the theoretical result of the previous work on LMI (linear matrix inequality) based H ∞ filter for time-delay compensation of self-powered neutron detectors. The filter gains are optimized in the sense of noise attenuation level of H ∞ setting. By introducing bounded real lemma, the conventional algebraic Riccati inequalities are converted into linear matrix inequalities (LMIs). Finally, the filter design problem is solved via the convex optimization framework using LMIs. The experimental measurements of rhodium detector signal from a research reactor show that the predicted theoretical filter performance is verified by showing successful reconstruction of the reference power signal

T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols

Science.gov (United States)

Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2013-07-01

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.

Educational Inequality and Income Inequality: An Empirical Study on China

Science.gov (United States)

Yang, Jun; Huang, Xiao; Li, Xiaoyu

2009-01-01

Based on the endogenous growth theory, this paper uses the Gini coefficient to measure educational inequality and studies the empirical relationship between educational inequality and income inequality through a simultaneous equation model. The results show that: (1) Income inequality leads to educational inequality while the reduction of…

Linear algebra

CERN Document Server

Said-Houari, Belkacem

2017-01-01

This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...

Robust Model Predictive Control of Networked Control Systems under Input Constraints and Packet Dropouts

Directory of Open Access Journals (Sweden)

Deyin Yao

2014-01-01

Full Text Available This paper deals with the problem of robust model predictive control (RMPC for a class of linear time-varying systems with constraints and data losses. We take the polytopic uncertainties into account to describe the uncertain systems. First, we design a robust state observer by using the linear matrix inequality (LMI constraints so that the original system state can be tracked. Second, the MPC gain is calculated by minimizing the upper bound of infinite horizon robust performance objective in terms of linear matrix inequality conditions. The method of robust MPC and state observer design is illustrated by a numerical example.

Computation of a Reference Model for Robust Fault Detection and Isolation Residual Generation

Directory of Open Access Journals (Sweden)

Emmanuel Mazars

2008-01-01

Full Text Available This paper considers matrix inequality procedures to address the robust fault detection and isolation (FDI problem for linear time-invariant systems subject to disturbances, faults, and polytopic or norm-bounded uncertainties. We propose a design procedure for an FDI filter that aims to minimize a weighted combination of the sensitivity of the residual signal to disturbances and modeling errors, and the deviation of the faults to residual dynamics from a fault to residual reference model, using the ℋ∞-norm as a measure. A key step in our procedure is the design of an optimal fault reference model. We show that the optimal design requires the solution of a quadratic matrix inequality (QMI optimization problem. Since the solution of the optimal problem is intractable, we propose a linearization technique to derive a numerically tractable suboptimal design procedure that requires the solution of a linear matrix inequality (LMI optimization. A jet engine example is employed to demonstrate the effectiveness of the proposed approach.

H∞ control for uncertain linear system over networks with Bernoulli data dropout and actuator saturation.

Science.gov (United States)

Yu, Jimin; Yang, Chenchen; Tang, Xiaoming; Wang, Ping

2018-03-01

This paper investigates the H ∞ control problems for uncertain linear system over networks with random communication data dropout and actuator saturation. The random data dropout process is modeled by a Bernoulli distributed white sequence with a known conditional probability distribution and the actuator saturation is confined in a convex hull by introducing a group of auxiliary matrices. By constructing a quadratic Lyapunov function, effective conditions for the state feedback-based H ∞ controller and the observer-based H ∞ controller are proposed in the form of non-convex matrix inequalities to take the random data dropout and actuator saturation into consideration simultaneously, and the problem of non-convex feasibility is solved by applying cone complementarity linearization (CCL) procedure. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed new design techniques. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Socioeconomic hierarchy and health gradient in Europe: the role of income inequality and of social origins.

Science.gov (United States)

Chauvel, Louis; Leist, Anja K

2015-11-14

Health inequalities reflect multidimensional inequality (income, education, and other indicators of socioeconomic position) and vary across countries and welfare regimes. To which extent there is intergenerational transmission of health via parental socioeconomic status has rarely been investigated in comparative perspective. The study sought to explore if different measures of stratification produce the same health gradient and to which extent health gradients of income and of social origins vary with level of living and income inequality. A total of 299,770 observations were available from 18 countries assessed in EU-SILC 2005 and 2011 data, which contain information on social origins. Income inequality (Gini) and level of living were calculated from EU-SILC. Logit rank transformation provided normalized inequalities and distributions of income and social origins up to the extremes of the distribution and was used to investigate net comparable health gradients in detail. Multilevel random-slope models were run to post-estimate best linear unbiased predictors (BLUPs) and related standard deviations of residual intercepts (median health) and slopes (income-health gradients) per country and survey year. Health gradients varied across different measures of stratification, with origins and income producing significant slopes after controls. Income inequality was associated with worse average health, but income inequality and steepness of the health gradient were only marginally associated. Linear health gradients suggest gains in health per rank of income and of origins even at the very extremes of the distribution. Intergenerational transmission of status gains in importance in countries with higher income inequality. Countries differ in the association of income inequality and income-related health gradient, and low income inequality may mask health problems of vulnerable individuals with low status. Not only income inequality, but other country characteristics such

Soffer's inequality

International Nuclear Information System (INIS)

Goldstein, G.R.; Jaffe, R.L.; Ji, X.

1995-01-01

Various issues surrounding a recently proposed inequality among twist-two quark distributions in the nucleon are discussed. We provide a rigorous derivation of the inequality in QCD, including radiative corrections and scale dependence. We also give a more heuristic, but more physical derivation, from which we show that a similar inequality does not exist among twist-three quark distributions. We demonstrate that the inequality does not constrain the nucleon's tensor charge. Finally we explore physical mechanisms for saturating the inequality, arguing it is unlikely to occur in nature

Welfare family policies and gender earnings inequality: A cross-national comparative analysis

OpenAIRE

Mandel, Hadas; Semyonov, Moshe

2003-01-01

The present study examines whether and to what extent welfare-family policies are likely to affect earnings inequality between economically active men and women. Using hierarchical linear models, we combine individual-level variables (obtained from the Luxembourg Income Study) with country level data (obtained from secondary sources) to evaluate the net effects of welfare family policies on gender earnings inequality across 20 industrialized countries. The analysis reveals that net of individ...

A Novel Finite-Sum Inequality-Based Method for Robust H∞ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays.

Science.gov (United States)

Zhang, Xian-Ming; Han, Qing-Long; Ge, Xiaohua

2017-09-22

This paper is concerned with the problem of robust H∞ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust H∞ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.

Early-life income inequality and adolescent health and well-being.

Science.gov (United States)

Elgar, Frank J; Gariépy, Geneviève; Torsheim, Torbjørn; Currie, Candace

2017-02-01

A prevailing hypothesis about the association between income inequality and poor health is that inequality intensifies social hierarchies, increases stress, erodes social and material resources that support health, and subsequently harms health. However, the evidence in support of this hypothesis is limited by cross-sectional, ecological studies and a scarcity of developmental studies. To address this limitation, we used pooled, multilevel data from the Health Behaviour in School-aged Children study to examine lagged, cumulative, and trajectory associations between early-life income inequality and adolescent health and well-being. Psychosomatic symptoms and life satisfaction were assessed in surveys of 11- to 15-year-olds in 40 countries between 1994 and 2014. We linked these data to national Gini indices of income inequality for every life year from 1979 to 2014. The results showed that exposure to income inequality from 0 to 4 years predicted psychosomatic symptoms and lower life satisfaction in females after controlling lifetime mean income inequality, national per capita income, family affluence, age, and cohort and period effects. The cumulative income inequality exposure in infancy and childhood (i.e., average Gini index from birth to age 10) related to lower life satisfaction in female adolescents but not to symptoms. Finally, individual trajectories in early-life inequality (i.e., linear slopes in Gini indices from birth to 10 years) related to fewer symptoms and higher life satisfaction in females, indicating that earlier exposures mattered more to predicting health and wellbeing. No such associations with early-life income inequality were found in males. These results help to establish the antecedent-consequence conditions in the association between income inequality and health and suggest that both the magnitude and timing of income inequality in early life have developmental consequences that manifest in reduced health and well-being in adolescent girls

Picone-type inequalities for nonlinear elliptic equations and their applications

Directory of Open Access Journals (Sweden)

Takaŝi Kusano

2001-01-01

Full Text Available Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are also obtained.

Additive Functional Inequalities in Banach Modules

Directory of Open Access Journals (Sweden)

An JongSu

2008-01-01

Full Text Available Abstract We investigate the following functional inequality in Banach modules over a -algebra and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a -algebra in the spirit of the Th. M. Rassias stability approach. Moreover, these results are applied to investigate homomorphisms in complex Banach algebras and prove the generalized Hyers-Ulam stability of homomorphisms in complex Banach algebras.

Income Inequality, Income, and Internet Searches for Status Goods: A Cross-National Study of the Association Between Inequality and Well-Being.

Science.gov (United States)

Walasek, Lukasz; Brown, Gordon D A

Is there a positive association between a nation's income inequality and concerns with status competition within that nation? Here we use Google Correlate and Google Trends to examine frequency of internet search terms and find that people in countries in which income inequality is high search relatively more frequently for positional brand names such as Prada, Louis Vuitton, or Chanel. This tendency is stronger among well-developed countries. We find no evidence that income alone is associated with searches for positional goods. We also present evidence that the concern with positional goods does not reflect non-linear effects of income on consumer spending, either across nations or (extending previous findings that people who live in unequal US States search more for positional goods) within the USA. It is concluded that income inequality is associated with greater concerns with positional goods, and that this concern is reflected in internet searching behaviour.

Matrices and linear transformations

CERN Document Server

Cullen, Charles G

1990-01-01

""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first

Factorizable S-matrix for SO(D)/SO(2) circle times SO(D - 2) non-linear σ models with fermions

International Nuclear Information System (INIS)

Abdalla, E.; Lima-Santos, A.

1988-01-01

The authors compute the exact S matrix for the non-linear sigma model with symmetry SO(D)/SO(2) circle times SO(D-2) coupled to fermions in a minimal or supersymmetric way. The model has some relevance in string theory with non-zero external curvature

Inequality

DEFF Research Database (Denmark)

Addison, Tony; Pirttilä, Jukka; Tarp, Finn

2017-01-01

Many low‐ and middle‐income countries are achieving good rates of economic growth, while high inequality remains a priority concern. Some countries meanwhile have low growth, high inequality, and pervasive poverty—often linked to their fragility. There is now active debate on how countries should...... set themselves goals for achieving both absolute poverty reduction and lower inequality. But policy action needs to be better served by analysis and data....

An Approach for Solving Linear Fractional Programming Problems

OpenAIRE

Andrew Oyakhobo Odior

2012-01-01

Linear fractional programming problems are useful tools in production planning, financial and corporate planning, health care and hospital planning and as such have attracted considerable research interest. The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebr...

Robust Adaptive Exponential Synchronization of Stochastic Perturbed Chaotic Delayed Neural Networks with Parametric Uncertainties

Directory of Open Access Journals (Sweden)

Yang Fang

2014-01-01

Full Text Available This paper investigates the robust adaptive exponential synchronization in mean square of stochastic perturbed chaotic delayed neural networks with nonidentical parametric uncertainties. A robust adaptive feedback controller is proposed based on Gronwally’s inequality, drive-response concept, and adaptive feedback control technique with the update laws of nonidentical parametric uncertainties as well as linear matrix inequality (LMI approach. The sufficient conditions for robust adaptive exponential synchronization in mean square of uncoupled uncertain stochastic chaotic delayed neural networks are derived in terms of linear matrix inequalities (LMIs. The effect of nonidentical uncertain parameter uncertainties is suppressed by the designed robust adaptive feedback controller rapidly. A numerical example is provided to validate the effectiveness of the proposed method.

Synchronization approach for chaotic time-varying delay system based on Wirtinger inequality

Directory of Open Access Journals (Sweden)

Zhanshan Zhao

2017-01-01

Full Text Available A novel control approach based on Wirtinger inequality is designed for nonlinear chaos synchronization time delay system. In order to reduce the conservatism for the stability criterion, a Lyapunov–Krasovskii functional with triple-integral term is constructed. The improved Wirtinger inequality is used to reduce the conservative which is caused by Jensen inequality, and a stability criterion is proposed by reciprocally convex method. Furthermore, a state feedback controller is designed to synchronize the master-slave systems based on the proposed criteria through cone complementary linearization approach. Finally, a simulation for Lorenz chaos time delay system is given to prove the validity based on the proposed synchronization control approach.

Income inequality within urban settings and depressive symptoms among adolescents.

Science.gov (United States)

Pabayo, Roman; Dunn, Erin C; Gilman, Stephen E; Kawachi, Ichiro; Molnar, Beth E

2016-10-01

Although recent evidence has shown that area-level income inequality is related to increased risk for depression among adults, few studies have tested this association among adolescents. We analysed the cross-sectional data from a sample of 1878 adolescents living in 38 neighbourhoods participating in the 2008 Boston Youth Survey. Using multilevel linear regression modelling, we: (1) estimated the association between neighbourhood income inequality and depressive symptoms, (2) tested for cross-level interactions between sex and neighbourhood income inequality and (3) examined neighbourhood social cohesion as a mediator of the relationship between income inequality and depressive symptoms. The association between neighbourhood income inequality and depressive symptoms varied significantly by sex, with girls in higher income inequality neighbourhood reporting higher depressive symptom scores, but not boys. Among girls, a unit increase in Gini Z-score was associated with more depressive symptoms (β=0.38, 95% CI 0.28 to 0.47, p=0.01) adjusting for nativity, neighbourhood income, social cohesion, crime and social disorder. There was no evidence that the association between income inequality and depressive symptoms was due to neighbourhood-level differences in social cohesion. The distribution of incomes within an urban area adversely affects adolescent girls' mental health; future work is needed to understand why, as well as to examine in greater depth the potential consequences of inequality for males, which may have been difficult to detect here. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

Improvement of Aczél's Inequality and Popoviciu's Inequality

Directory of Open Access Journals (Sweden)

Shanhe Wu

2007-06-01

Full Text Available We generalize and sharpen Aczél's inequality and Popoviciu's inequality by means of two classical inequalities, a unified improvement of Aczél's inequality and Popoviciu's inequality is given. As application, an integral inequality of Aczél-Popoviciu type is established.

Mixed H∞ and passive control for linear switched systems via hybrid control approach

Science.gov (United States)

Zheng, Qunxian; Ling, Youzhu; Wei, Lisheng; Zhang, Hongbin

2018-03-01

This paper investigates the mixed H∞ and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weighted H∞ and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixed H∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given.

Linear Algebraic Method for Non-Linear Map Analysis

International Nuclear Information System (INIS)

Yu, L.; Nash, B.

2009-01-01

We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.

ITMETH, Iterative Routines for Linear System

International Nuclear Information System (INIS)

Greenbaum, A.

1989-01-01

1 - Description of program or function: ITMETH is a collection of iterative routines for solving large, sparse linear systems. 2 - Method of solution: ITMETH solves general linear systems of the form AX=B using a variety of methods: Jacobi iteration; Gauss-Seidel iteration; incomplete LU decomposition or matrix splitting with iterative refinement; diagonal scaling, matrix splitting, or incomplete LU decomposition with the conjugate gradient method for the problem AA'Y=B, X=A'Y; bi-conjugate gradient method with diagonal scaling, matrix splitting, or incomplete LU decomposition; and ortho-min method with diagonal scaling, matrix splitting, or incomplete LU decomposition. ITMETH also solves symmetric positive definite linear systems AX=B using the conjugate gradient method with diagonal scaling or matrix splitting, or the incomplete Cholesky conjugate gradient method

Is income inequality related to childhood dental caries in rich countries?

Science.gov (United States)

Bernabé, Eduardo; Hobdell, Martin H

2010-02-01

The aim of this study was to assess the correlates of income and income inequality with dental caries in a sample of all countries, as well as in rich countries alone. In this ecological study, the authors analyzed national data on income, income inequality and dental caries from 48 countries. Of them, 22 were rich countries (according to World Bank criteria). The authors determined income by gross national income (GNI) per capita (formerly known as gross national product) and income inequality by the Gini coefficient (a measure of income inequality on a scale between 0 and 1). They assessed dental caries according to the decayed, missing, filled teeth (dmft) index in 5- to 6-year-old children. The authors used Pearson and partial correlation coefficients to examine the linear associations of income and income inequality with dental caries. GNI per capita, but not the Gini coefficient, was inversely correlated with the dmft index in the 48 countries. However, the results showed an opposite pattern when analyses were restricted to rich countries (that is, the dmft index was significantly correlated with the Gini coefficient but not with GNI per capita). These findings support the income inequality hypothesis that beyond a certain level of national income, the relationship between income and the population's health is weak. Income inequality was correlated more strongly with dental caries than was income in rich countries. Among rich countries, income inequality is a stronger determinant of childhood dental caries than is absolute income.

The Optimization on Ranks and Inertias of a Quadratic Hermitian Matrix Function and Its Applications

Directory of Open Access Journals (Sweden)

Yirong Yao

2013-01-01

Full Text Available We solve optimization problems on the ranks and inertias of the quadratic Hermitian matrix function subject to a consistent system of matrix equations and . As applications, we derive necessary and sufficient conditions for the solvability to the systems of matrix equations and matrix inequalities , and in the Löwner partial ordering to be feasible, respectively. The findings of this paper widely extend the known results in the literature.

Patterned Inequalities and the Inequality Regime of a Swedish Housing Company

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Kristina Boréus

2015-12-01

Full Text Available In this article, the authors analyze inequalities between different groups of employees at a housing company in a larger Swedish city. The concept of inequality regime is taken as a point of departure. The purposes of the article are three: first, to add to knowledge of how inequality is generated at an organizational level at specific workplaces; second, to contribute to the understanding of how different practices, processes, and meanings of inequality regimes may interact to create and reinforce inequalities between natives and immigrants; and, third, to contribute to the empirical usefulness of the concept of inequality regime by demonstrating how it can be operationalized and combined with other concepts in the analysis. The study shows how the practices, processes, and meanings at the given workplace generated and reproduced different kinds of inequalities: unequal wages, an ethnic division of labor, unequal influence and job security, and unequal opportunities to capitalize on useful skills (i.e., language competence. Important conclusions are that different kinds of inequalities may reinforce each other by creating vicious circles, and subtler forms of inequality may partly explain explicit wage inequalities.

Structural interaction between gender and race inequality in Brazil

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José Alcides Figueiredo Santos

2010-01-01

Full Text Available This paper is guided by the theoretical notion that social divisions generate effects derived from its structural interaction. Having in mind this theoretical motivation, it estimates the gender earnings gap among white e non white (black and mixed color groups in Brazil. All the eight Generalized Linear Models estimated, whose variables are successively included, show that the gender gap is big across both racial groups but it is bigger among whites. The investigation explores the role of the underlying context of class inequality, as well as others factors, on understanding the racial variation of the gender inequality. The study considers that the characteristics of the racial inequality in Brazil, as well as the intersection between class and race, explain the bigger gender advantage for the white man. The racial hierarchy establishes limits of variation on the gender hierarchy for the non white.

Ground states of linear rotor chains via the density matrix renormalization group

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Iouchtchenko, Dmitri; Roy, Pierre-Nicholas

2018-04-01

In recent years, experimental techniques have enabled the creation of ultracold optical lattices of molecules and endofullerene peapod nanomolecular assemblies. It was previously suggested that the rotor model resulting from the placement of dipolar linear rotors in one-dimensional lattices at low temperature has a transition between ordered and disordered phases. We use the density matrix renormalization group (DMRG) to compute ground states of chains of up to 100 rotors and provide further evidence of the phase transition in the form of a diverging entanglement entropy. We also propose two methods and present some first steps toward rotational spectra of such molecular assemblies using DMRG. The present work showcases the power of DMRG in this new context of interacting molecular rotors and opens the door to the study of fundamental questions regarding criticality in systems with continuous degrees of freedom.

A relevant two qubit Bell inequality inequivalent to the CHSH inequality

International Nuclear Information System (INIS)

Collins, Daniel; Gisin, Nicolas

2004-01-01

We computationally investigate the complete polytope of Bell inequalities for two particles with small numbers of possible measurements and outcomes. Our approach is limited by Pitowsky's connection of this problem to the computationally hard NP problem. Despite this, we find that there are very few relevant inequivalent inequalities for small numbers. For example, in the case with three possible 2-outcome measurements on each particle, there is just one new inequality. We describe mixed 2-qubit states which violate this inequality but not the CHSH. The new inequality also illustrates a sharing of bi-partite non-locality between three qubits: something not seen using the CHSH inequality. It also inspires us to discover a class of Bell inequalities with m possible n-outcome measurements on each particle

Green's matrix for a second-order self-adjoint matrix differential operator

International Nuclear Information System (INIS)

Sisman, Tahsin Cagri; Tekin, Bayram

2010-01-01

A systematic construction of the Green's matrix for a second-order self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first-order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.

Positive maps, majorization, entropic inequalities and detection of entanglement

International Nuclear Information System (INIS)

Augusiak, R; Stasinska, J

2009-01-01

In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that any positive map Λ:M d (C)→M d (C) can be written as the difference between two completely positive maps Λ=Λ 1 -Λ 2 , we propose a possible way to generalize the Nielsen-Kempe majorization criterion. Then, we present two methods of derivation of some general classes of entropic inequalities useful for the detection of entanglement. While the first one follows from the aforementioned generalized majorization relation and the concept of Schur-concave decreasing functions, the second is based on some functional inequalities. What is important is that, contrary to the Nielsen-Kempe majorization criterion and entropic inequalities, our criteria allow for the detection of entangled states with positive partial transposition when using indecomposable positive maps. We also point out that if a state with at least one maximally mixed subsystem is detected by some necessary criterion based on the positive map Λ, then there exist entropic inequalities derived from Λ (by both procedures) that also detect this state. In this sense, they are equivalent to the necessary criterion [IxΛ](rhov AB )≥0. Moreover, our inequalities provide a way of constructing multi-copy entanglement witnesses and therefore are promising from the experimental point of view. Finally, we discuss some of the derived inequalities in the context of the recently introduced protocol of state merging and the possibility of approximating the mean value of a linear entanglement witness.

Fighting status inequalities

DEFF Research Database (Denmark)

Nielsen, Morten Ebbe Juul; Landes, Xavier

2016-01-01

Status inequalities seem to play a fairly big role in creating inequalities in health. This article assumes that there can be good reasons to fight status inequalities in order to reduce inequalities in health. It examines whether the neorepublican ideal of non-dominance does a better job as a th...

LINPACK, Subroutine Library for Linear Equation System Solution and Matrix Calculation

International Nuclear Information System (INIS)

Dongarra, J.J.

1979-01-01

1 - Description of problem or function: LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE: General, GB: General band, PO: Positive definite, PP: Positive definite packed, PB: Positive definite band, SI: Symmetric indefinite, SP: Symmetric indefinite packed, HI: Hermitian indefinite, HP: Hermitian indefinite packed, TR: Triangular, GT: General tridiagonal, PT: Positive definite tridiagonal, CH: Cholesky decomposition, QR: Orthogonal-triangular decomposition, SV: Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA: Factor, CO: Factor and estimate condition, SL: Solve, DI: Determinant and/or inverse and/or inertia, DC: Decompose, UD: Update, DD: Down-date, EX Exchange. The following chart shows all the LINPACK subroutines. The initial 'S' in the names may be replaced by D, C or Z and the initial 'C' in the complex-only names may be replaced by a Z. SGE: FA, CO, SL, DI; SGB: FA, CO, SL, DI; SPO: FA, CO, SL, DI; SPP: FA, CO, SL, DI; SPB: FA, CO, SL, DI; SSI: FA, CO, SL, DI; SSP: FA, CO, SL, DI; CHI: FA, CO, SL, DI; CHP: FA, CO, SL, DI; STR

Transfer matrix method for dynamics modeling and independent modal space vibration control design of linear hybrid multibody system

Science.gov (United States)

Rong, Bao; Rui, Xiaoting; Lu, Kun; Tao, Ling; Wang, Guoping; Ni, Xiaojun

2018-05-01

In this paper, an efficient method of dynamics modeling and vibration control design of a linear hybrid multibody system (MS) is studied based on the transfer matrix method. The natural vibration characteristics of a linear hybrid MS are solved by using low-order transfer equations. Then, by constructing the brand-new body dynamics equation, augmented operator and augmented eigenvector, the orthogonality of augmented eigenvector of a linear hybrid MS is satisfied, and its state space model expressed in each independent model space is obtained easily. According to this dynamics model, a robust independent modal space-fuzzy controller is designed for vibration control of a general MS, and the genetic optimization of some critical control parameters of fuzzy tuners is also presented. Two illustrative examples are performed, which results show that this method is computationally efficient and with perfect control performance.

The Relationship between Income Inequality and Inequality in Schooling

Science.gov (United States)

Mayer, Susan E.

2010-01-01

Children of affluent parents get more schooling than children of poor parents, which seems to imply that reducing income inequality would reduce inequality in schooling. Similarly, one of the best predictors of an individual's income is his educational attainment, which seems to imply that reducing inequality in schooling will reduce income…

Dynamic inequalities on time scales

CERN Document Server

Agarwal, Ravi; Saker, Samir

2014-01-01

This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics. In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Čebyšv's inequality. Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail.

THE DAMASCUS INEQUALITY

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F. M. Dannan

2016-12-01

Full Text Available In 2016 Prof. Fozi M. Dannan from Damascus, Syria, proposed an interesting inequality for three positive numbers with unit product. It became widely known but was not proved yet in spite of elementary formulation. In this paper we prove this inequality together with similar ones, its proof occurred to be rather complicated. We propose some proofs based on different ideas: Lagrange multipliers method, geometrical considerations, Klamkin–type inequalities for symmetric functions, usage of symmetric reduction functions of computer packages. Also some corollaries and generalizations are considered, they include cycle inequalities, triangle geometric inequalities, inequalities for arbitrary number of values and special forms of restrictions on numbers, applications to cubic equations and symmetric functions.

Stability Criterion of Linear Stochastic Systems Subject to Mixed H2/Passivity Performance

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Cheung-Chieh Ku

2015-01-01

Full Text Available The H2 control scheme and passivity theory are applied to investigate the stability criterion of continuous-time linear stochastic system subject to mixed performance. Based on the stochastic differential equation, the stochastic behaviors can be described as multiplicative noise terms. For the considered system, the H2 control scheme is applied to deal with the problem on minimizing output energy. And the asymptotical stability of the system can be guaranteed under desired initial conditions. Besides, the passivity theory is employed to constrain the effect of external disturbance on the system. Moreover, the Itô formula and Lyapunov function are used to derive the sufficient conditions which are converted into linear matrix inequality (LMI form for applying convex optimization algorithm. Via solving the sufficient conditions, the state feedback controller can be established such that the asymptotical stability and mixed performance of the system are achieved in the mean square. Finally, the synchronous generator system is used to verify the effectiveness and applicability of the proposed design method.

Introduction to computational linear algebra

CERN Document Server

Nassif, Nabil; Erhel, Jocelyne

2015-01-01

Introduction to Computational Linear Algebra introduces the reader with a background in basic mathematics and computer programming to the fundamentals of dense and sparse matrix computations with illustrating examples. The textbook is a synthesis of conceptual and practical topics in ""Matrix Computations."" The book's learning outcomes are twofold: to understand state-of-the-art computational tools to solve matrix computations problems (BLAS primitives, MATLAB® programming) as well as essential mathematical concepts needed to master the topics of numerical linear algebra. It is suitable for s

Matrix with Prescribed Eigenvectors

Science.gov (United States)

Ahmad, Faiz

2011-01-01

It is a routine matter for undergraduates to find eigenvalues and eigenvectors of a given matrix. But the converse problem of finding a matrix with prescribed eigenvalues and eigenvectors is rarely discussed in elementary texts on linear algebra. This problem is related to the "spectral" decomposition of a matrix and has important technical…

Assessing environmental inequalities in ambient air pollution across urban Australia.

Science.gov (United States)

Knibbs, Luke D; Barnett, Adrian G

2015-04-01

Identifying inequalities in air pollution levels across population groups can help address environmental justice concerns. We were interested in assessing these inequalities across major urban areas in Australia. We used a land-use regression model to predict ambient nitrogen dioxide (NO2) levels and sought the best socio-economic and population predictor variables. We used a generalised least squares model that accounted for spatial correlation in NO2 levels to examine the associations between the variables. We found that the best model included the index of economic resources (IER) score as a non-linear variable and the percentage of non-Indigenous persons as a linear variable. NO2 levels decreased with increasing IER scores (higher scores indicate less disadvantage) in almost all major urban areas, and NO2 also decreased slightly as the percentage of non-Indigenous persons increased. However, the magnitude of differences in NO2 levels was small and may not translate into substantive differences in health. Copyright © 2015 Elsevier Ltd. All rights reserved.

The Ginibre inequality

International Nuclear Information System (INIS)

Sylvester, G.S.

1980-01-01

In the Ising-type models of statistical mechanics and the related quantum field theories, an inequality of Ginibre implies useful positivity and monotonicity properties: the Griffiths correlation inequalities. Essentially, the Ginibre inequality states that certain functions on the cycle group of a graph are positive definite. This has been proved for arbitrary graphs when the spin dimensions is 1 or 2 (classical Ising or plane rotator models). We give a counterexample to show that these spin dimensions are the only ones for which the Ginibre inequality is generally true: there are graphs for which it never holds when the spin dimension is at least 3. On the other hand, we show that for any graph the inequality holds for the apparent leading term in the large-spin-dimension limit. (The leading term vanishes in the graph of the counterexample.) Based on these results, one expects the Ginibre inequality to be true in most instances, with infrequent exceptions. A numerical survey supports this. The surprising failure of the Ginibre inequality in higher dimensions need not necessarily mean the Griffiths inequalities fail as well, but a different approach to them is required. (orig.)

Inequality and development

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Jovanović-Gavrilović Biljana D.

2003-01-01

Full Text Available Inequality can be analyzed from various aspects. In this paper our attention is drawn to economic inequality, most frequently manifested through income and wealth. The measurement of economic inequality is a complex task. The Lorenz curve and a number of numerical indices are applied, and let us mention the following ones: the Gini coefficient, the coefficient of variation, the Theil index and the Atkinson measure. These indices do satisfy the criteria (principles presenting, according to general consent an appropriate measure of economic inequality: anonymity (symmetry principle, population principle, relative income principle and the Dalton principle of transfer. In recent times, the problem of inequality has been attracting a lot of attention. The explanation should be sought in the widening of income differences (within individual countries and between them and also in new knowledge about the relationship between inequality and development. The attitude to inequality being determined mainly by the economic development level (as presented in the Kuznets hypothesis is gradually being replaced by the attitude to inequality being the determinant of income and its growth. Contrary to previous beliefs about the stronger income inequalities being favorable to the economic growth, more recent research has pointed to the fact that a more equal distribution of income through various channels, can possibly act as an efficient stimulus of growth.

Stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters

International Nuclear Information System (INIS)

Wang Linshan; Zhang Zhe; Wang Yangfan

2008-01-01

Some criteria for the global stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters are presented. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish some easy-to-test criteria of global exponential stability in the mean square for the stochastic neural networks. The criteria are computationally efficient, since they are in the forms of some linear matrix inequalities

Functional inequalities

CERN Document Server

Ghoussoub, Nassif

2013-01-01

The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of...

Efficient Brownian Dynamics of rigid colloids in linear flow fields based on the grand mobility matrix

Science.gov (United States)

Palanisamy, Duraivelan; den Otter, Wouter K.

2018-05-01

We present an efficient general method to simulate in the Stokesian limit the coupled translational and rotational dynamics of arbitrarily shaped colloids subject to external potential forces and torques, linear flow fields, and Brownian motion. The colloid's surface is represented by a collection of spherical primary particles. The hydrodynamic interactions between these particles, here approximated at the Rotne-Prager-Yamakawa level, are evaluated only once to generate the body's (11 × 11) grand mobility matrix. The constancy of this matrix in the body frame, combined with the convenient properties of quaternions in rotational Brownian Dynamics, enables an efficient simulation of the body's motion. Simulations in quiescent fluids yield correct translational and rotational diffusion behaviour and sample Boltzmann's equilibrium distribution. Simulations of ellipsoids and spherical caps under shear, in the absence of thermal fluctuations, yield periodic orbits in excellent agreement with the theories by Jeffery and Dorrepaal. The time-varying stress tensors provide the Einstein coefficient and viscosity of dilute suspensions of these bodies.

Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules.

Science.gov (United States)

Marrero-Ponce, Yovani; Martínez-Albelo, Eugenio R; Casañola-Martín, Gerardo M; Castillo-Garit, Juan A; Echevería-Díaz, Yunaimy; Zaldivar, Vicente Romero; Tygat, Jan; Borges, José E Rodriguez; García-Domenech, Ramón; Torrens, Francisco; Pérez-Giménez, Facundo

2010-11-01

Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E(k)) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES(k), is here proposed as a new molecular representation easily calculated from E(k). Then, the kth stochastic bond linear indices are calculated using ES(k) as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity

Approximate Solution of LR Fuzzy Sylvester Matrix Equations

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Xiaobin Guo

2013-01-01

Full Text Available The fuzzy Sylvester matrix equation AX~+X~B=C~ in which A,B are m×m and n×n crisp matrices, respectively, and C~ is an m×n LR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.

Correlations in star networks: from Bell inequalities to network inequalities

International Nuclear Information System (INIS)

Tavakoli, Armin; Renou, Marc Olivier; Gisin, Nicolas; Brunner, Nicolas

2017-01-01

The problem of characterizing classical and quantum correlations in networks is considered. Contrary to the usual Bell scenario, where distant observers share a physical system emitted by one common source, a network features several independent sources, each distributing a physical system to a subset of observers. In the quantum setting, the observers can perform joint measurements on initially independent systems, which may lead to strong correlations across the whole network. In this work, we introduce a technique to systematically map a Bell inequality to a family of Bell-type inequalities bounding classical correlations on networks in a star-configuration. Also, we show that whenever a given Bell inequality can be violated by some entangled state ρ , then all the corresponding network inequalities can be violated by considering many copies of ρ distributed in the star network. The relevance of these ideas is illustrated by applying our method to a specific multi-setting Bell inequality. We derive the corresponding network inequalities, and study their quantum violations. (paper)

Leggett–Garg inequalities

International Nuclear Information System (INIS)

Emary, Clive; Lambert, Neill; Nori, Franco

2014-01-01

In contrast to the spatial Bell's inequalities which probe entanglement between spatially separated systems, the Leggett–Garg inequalities test the correlations of a single system measured at different times. Violation of a genuine Leggett–Garg test implies either the absence of a realistic description of the system or the impossibility of measuring the system without disturbing it. Quantum mechanics violates the inequalities on both accounts and the original motivation for these inequalities was as a test for quantum coherence in macroscopic systems. The last few years has seen a number of experimental tests and violations of these inequalities in a variety of microscopic systems such as superconducting qubits, nuclear spins, and photons. In this article, we provide an introduction to the Leggett–Garg inequalities and review these latest experimental developments. We discuss important topics such as the significance of the non-invasive measurability assumption, the clumsiness loophole, and the role of weak measurements. Also covered are some recent theoretical proposals for the application of Leggett–Garg inequalities in quantum transport, quantum biology and nano-mechanical systems. (review article)

Distributed Leader-Following Finite-Time Consensus Control for Linear Multiagent Systems under Switching Topology

Science.gov (United States)

Xu, Xiaole; Chen, Shengyong

2014-01-01

This paper investigates the finite-time consensus problem of leader-following multiagent systems. The dynamical models for all following agents and the leader are assumed the same general form of linear system, and the interconnection topology among the agents is assumed to be switching and undirected. We mostly consider the continuous-time case. By assuming that the states of neighbouring agents are known to each agent, a sufficient condition is established for finite-time consensus via a neighbor-based state feedback protocol. While the states of neighbouring agents cannot be available and only the outputs of neighbouring agents can be accessed, the distributed observer-based consensus protocol is proposed for each following agent. A sufficient condition is provided in terms of linear matrix inequalities to design the observer-based consensus protocol, which makes the multiagent systems achieve finite-time consensus under switching topologies. Then, we discuss the counterparts for discrete-time case. Finally, we provide an illustrative example to show the effectiveness of the design approach. PMID:24883367

Numerical linear algebra theory and applications

CERN Document Server

Beilina, Larisa; Karchevskii, Mikhail

2017-01-01

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

Robust Sensor Faults Reconstruction for a Class of Uncertain Linear Systems Using a Sliding Mode Observer: An LMI Approach

International Nuclear Information System (INIS)

Iskander, Boulaabi; Faycal, Ben Hmida; Moncef, Gossa; Anis, Sellami

2009-01-01

This paper presents a design method of a Sliding Mode Observer (SMO) for robust sensor faults reconstruction of systems with matched uncertainty. This class of uncertainty requires a known upper bound. The basic idea is to use the H ∞ concept to design the observer, which minimizes the effect of the uncertainty on the reconstruction of the sensor faults. Specifically, we applied the equivalent output error injection concept from previous work in Fault Detection and Isolation (FDI) scheme. Then, these two problems of design and reconstruction can be expressed and numerically formulate via Linear Matrix Inequalities (LMIs) optimization. Finally, a numerical example is given to illustrate the validity and the applicability of the proposed approach.

Immigration and income inequality

DEFF Research Database (Denmark)

Deding, Mette; Hussain, Azhar; Jakobsen, Vibeke

2010-01-01

During the last two decades most Western countries have experienced increased net immigration as well as increased income inequality. This article analyzes the effects on income inequality of an increased number of immigrants in Denmark and Germany for the 20- year period 1984-2003 and how...... the impact of the increased number of immigrants differs between the two countries. We find higher inequality for immigrants than natives in Denmark but vice versa for Germany. Over the period 1984-2003, this particular inequality gap has narrowed in both countries. At the same time, the contribution...... of immigrants to overall inequality has increased, primarily caused by increased between-group inequality. The share of immigrants in the population is more important for the change in overall inequality in Denmark than in Germany, while the opposite is the case for inequality among immigrants....

Peripherality, income inequality, and life expectancy: revisiting the income inequality hypothesis.

Science.gov (United States)

Moore, Spencer

2006-06-01

Recent criticisms of the income inequality and health hypothesis have stressed the lack of consistent significant evidence for the stronger effects of income inequality among rich countries. Despite such criticisms, little attention has been devoted to the income-based criteria underlying the stratification of countries into rich/poor groups and whether trade patterns and world-system role provide an alternative means of stratifying groups. To compare income-based and trade-based criteria, 107 countries were grouped into four typologies: (I) high/low income, (II) OECD membership/non-membership, (III) core/non-core, and (IV) non-periphery/periphery. Each typology was tested separately for significant differences in the effects of income inequality between groups. Separate group comparison tests and regression analyses were conducted for each typology using Rodgers (1979) specification of income, income inequality, and life expectancy. Interaction terms were introduced into Rodgers specification to test whether group classification moderated the effects of income inequality on health. Results show that the effects of income inequality are stronger in the periphery than non-periphery (IV) (-0.76 vs -0.23; P income inequality and population health have assumed (i) income differences between countries best capture global stratification and (ii) the negative effects of income inequality are stronger in high-income countries. However, present findings emphasize (i) the importance of measuring global stratification according to trading patterns and (ii) the strong, negative effects of income inequality on life expectancy among peripheral populations.

From general discrimination to segmented inequality: Migration and inequality in urban China.

Science.gov (United States)

Lu, Yao; Wang, Feng

2013-11-01

Internal migration in China during the last three decades, the largest in human history, offers a rare opportunity to understand inequalities in the making. Using data spanning 10years from China's largest metropolis, Shanghai, this study assesses how enduring state institutions interplay with the spread of market forces to shape income inequality between migrants and native urban workers. Though the wages of both Chinese migrants and urban workers rose considerably, economic restructuring during the decade under study resulted in diminished privileges for urbanites and subsequently increased collision between migrants and urban workers in the private sectors. These shifts, rather than substantially reducing inequality, have led to an evolving form of inequality, from an initial general blatant discrimination against migrants across the board, to a new and more subtle form of inequality characterized by substantial segmented discrimination against migrants within economic sectors, with the degree of inequality varying from sector to sector. We discuss how this changing inequality reflects complementary rather than competing roles of the state and market institutions in inequality creation and maintenance. Copyright © 2013 Elsevier Inc. All rights reserved.

Why reduce health inequalities?

Science.gov (United States)

Woodward, A; Kawachi, I

2000-12-01

It is well known that social, cultural and economic factors cause substantial inequalities in health. Should we strive to achieve a more even share of good health, beyond improving the average health status of the population? We examine four arguments for the reduction of health inequalities.1 Inequalities are unfair. Inequalities in health are undesirable to the extent that they are unfair, or unjust. Distinguishing between health inequalities and health inequities can be contentious. Our view is that inequalities become "unfair" when poor health is itself the consequence of an unjust distribution of the underlying social determinants of health (for example, unequal opportunities in education or employment).2 Inequalities affect everyone. Conditions that lead to marked health disparities are detrimental to all members of society. Some types of health inequalities have obvious spillover effects on the rest of society, for example, the spread of infectious diseases, the consequences of alcohol and drug misuse, or the occurrence of violence and crime.3 Inequalities are avoidable. Disparities in health are avoidable to the extent that they stem from identifiable policy options exercised by governments, such as tax policy, regulation of business and labour, welfare benefits and health care funding. It follows that health inequalities are, in principle, amenable to policy interventions. A government that cares about improving the health of the population ought therefore to incorporate considerations of the health impact of alternative options in its policy setting process.3 Interventions to reduce health inequalities are cost effective. Public health programmes that reduce health inequalities can also be cost effective. The case can be made to give priority to such programmes (for example, improving access to cervical cancer screening in low income women) on efficiency grounds. On the other hand, few programmes designed to reduce health inequalities have been formally

Discriminative Elastic-Net Regularized Linear Regression.

Science.gov (United States)

Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen

2017-03-01

In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

A linear programming manual

Science.gov (United States)

Tuey, R. C.

1972-01-01

Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

Triangularization of a Matrix

Indian Academy of Sciences (India)

Much of linear algebra is devoted to reducing a matrix (via similarity or unitary similarity) to another that has lots of zeros. The simplest such theorem is the Schur triangularization theorem. This says that every matrix is unitarily similar to an upper triangular matrix. Our aim here is to show that though it is very easy to prove it ...

Inequalities with applications to engineering

CERN Document Server

Cloud, Michael J; Lebedev, Leonid P

2014-01-01

This book offers a concise introduction to mathematical inequalities for graduate students and researchers in the fields of engineering and applied mathematics. It begins by reviewing essential facts from algebra and calculus and proceeds with a presentation of the central inequalities of applied analysis, illustrating a wide variety of practical applications. The text provides a gentle introduction to abstract spaces, such as metric, normed, and inner product spaces. It also provides full coverage of the central inequalities of applied analysis, such as Young's inequality, the inequality of the means, Hölder's inequality, Minkowski's inequality, the Cauchy–Schwarz inequality, Chebyshev's inequality, Jensen's inequality, and the triangle inequality. The second edition features extended coverage of applications, including continuum mechanics and interval analysis. It also includes many additional examples and exercises with hints and full solutions that may appeal to upper-level undergraduate and graduate...

Impact of income and income inequality on infant health outcomes in the United States.

Science.gov (United States)

Olson, Maren E; Diekema, Douglas; Elliott, Barbara A; Renier, Colleen M

2010-12-01

The goal was to investigate the relationships of income and income inequality with neonatal and infant health outcomes in the United States. The 2000-2004 state data were extracted from the Kids Count Data Center. Health indicators included proportion of preterm births (PTBs), proportion of infants with low birth weight (LBW), proportion of infants with very low birth weight (VLBW), and infant mortality rate (IMR). Income was evaluated on the basis of median family income and proportion of federal poverty levels; income inequality was measured by using the Gini coefficient. Pearson correlations evaluated associations between the proportion of children living in poverty and the health indicators. Linear regression evaluated predictive relationships between median household income, proportion of children living in poverty, and income inequality for the 4 health indicators. Median family income was negatively correlated with all birth outcomes (PTB, r = -0.481; LBW, r = -0.295; VLBW, r = -0.133; IMR, r = -0.432), and the Gini coefficient was positively correlated (PTB, r = 0.339; LBW, r = 0.398; VLBW, r = 0.460; IMR, r = 0.114). The Gini coefficient explained a significant proportion of the variance in rate for each outcome in linear regression models with median family income. Among children living in poverty, the role of income decreased as the degree of poverty decreased, whereas the role of income inequality increased. Both income and income inequality affect infant health outcomes in the United States. The health of the poorest infants was affected more by absolute wealth than relative wealth.

Hardy type inequalities on time scales

CERN Document Server

Agarwal, Ravi P; Saker, Samir H

2016-01-01

The book is devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T. In particular, the book contains the time scale versions of classical Hardy type inequalities, Hardy and Littlewood type inequalities, Hardy-Knopp type inequalities via convexity, Copson type inequalities, Copson-Beesack type inequalities, Liendeler type inequalities, Levinson type inequalities and Pachpatte type inequalities, Bennett type inequalities, Chan type inequalities, and Hardy type inequalities with two different weight functions. These dynamic inequalities contain the classical continuous and discrete inequalities as special cases when T = R and T = N and can be extended to different types of inequalities on different time scales such as T = hN, h > 0, T = qN for q > 1, etc.In this book the authors followed the history and development of these inequalities. Each section in self-contained and one can see the relationship between the time scale versions of the inequalities and...

Migration and regional inequality

DEFF Research Database (Denmark)

Peng, Lianqing; Swider, Sarah

2017-01-01

Scholars studying economic inequality in China have maintained that regional inequality and economic divergence across provinces have steadily increased over the past 30 years. New studies have shown that this trend is a statistical aberration; calculations show that instead of quickly and sharply...... rising, regional inequality has actually decreased, and most recently, remained stable. Our study suggests that China’s unique migratory regime is crucial to understanding these findings. We conduct a counterfactual simulation to demonstrate how migration and remittances have mitigated income inequality...... across provinces in order to show that without these processes, we would have seen more of a rise in interprovincial income inequality. We conclude by arguing that inequality in China is still increasing, but it is changing and becoming less place-based. As regional inequality decreases, there are signs...

Horizontal Inequity in Health Care Utilization among the Middle-Aged and Elderly in China.

Science.gov (United States)

Li, Chaofan; Dou, Lei; Wang, Haipeng; Jing, Shanshan; Yin, Aitian

2017-07-26

Equitable utilization of health care is a primary goal of the Chinese health system. This study aimed to examine horizontal inequity in health care utilization and identify the factors resulting in inequity among the middle-aged and elderly in China. The data were obtained from the China Health and Retirement Longitudinal Study (CHARLS). We employed the concentration index (CI) and horizontal inequity (HI) to measure inequity in health care utilization. Non-linear regression models were used to decompose the CI into the contribution of each factor. The CIs for the probability of and total number of outpatient visits were 0.0642 and 0.0780, respectively, and those for inpatient visits were 0.1418 and 0.1471, respectively. The HIs were also significantly positive. Living standard was the most important contributor. The contribution of health insurance varied between plans. This study supported the presence of pro-rich inequity in health care utilization for both probability and frequency among the middle-aged and elderly in China. Narrowing the living standard gap and improving the health insurance benefit package for the elderly should help to resolve these inequities.

From the Triangle Inequality to the Isoperimetric Inequality

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 2. From the Triangle Inequality to the Isoperimetric Inequality. S Kesavan. General Article Volume 19 Issue 2 February 2014 pp 135-148. Fulltext. Click here to view fulltext PDF. Permanent link:

Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes

International Nuclear Information System (INIS)

Liolios, A.A.; Boglou, A.K.

2003-01-01

The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-θ method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-convex linear complementarity problem is solved with a reduced number of unknowns

Global income related health inequalities

Directory of Open Access Journals (Sweden)

Jalil Safaei

2007-01-01

Full Text Available Income related health inequalities have been estimated for various groups of individuals at local, state, or national levels. Almost all of theses estimates are based on individual data from sample surveys. Lack of consistent individual data worldwide has prevented estimates of international income related health inequalities. This paper uses the (population weighted aggregate data available from many countries around the world to estimate worldwide income related health inequalities. Since the intra-country inequalities are subdued by the aggregate nature of the data, the estimates would be those of the inter-country or international health inequalities. As well, the study estimates the contribution of major socioeconomic variables to the overall health inequalities. The findings of the study strongly support the existence of worldwide income related health inequalities that favor the higher income countries. Decompositions of health inequalities identify inequalities in both the level and distribution of income as the main source of health inequality along with inequalities in education and degree of urbanization as other contributing determinants. Since income related health inequalities are preventable, policies to reduce the income gaps between the poor and rich nations could greatly improve the health of hundreds of millions of people and promote global justice. Keywords: global, income, health inequality, socioeconomic determinants of health

Measuring socioeconomic inequality in health, health care and health financing by means of rank-dependent indices: a recipe for good practice.

Science.gov (United States)

Erreygers, Guido; Van Ourti, Tom

2011-07-01

The tools to be used and other choices to be made when measuring socioeconomic inequalities with rank-dependent inequality indices have recently been debated in this journal. This paper adds to this debate by stressing the importance of the measurement scale, by providing formal proofs of several issues in the debate, and by lifting the curtain on the confusing debate between adherents of absolute versus relative health differences. We end this paper with a 'matrix' that provides guidelines on the usefulness of several rank-dependent inequality indices under varying circumstances. Copyright © 2011 Elsevier B.V. All rights reserved.

Strong Convergence Theorems for Variational Inequalities and Split Equality Problem

Directory of Open Access Journals (Sweden)

Yu Jing Wu

2013-01-01

Full Text Available Let H1, H2, and H3 be real Hilbert spaces, let C⊆H1, Q⊆H2 be two nonempty closed convex sets, and let A:H1→H3, B:H2→H3 be two bounded linear operators. The split equality problem (SEP is to find x∈C, y∈Q such that Ax=By. Let H=H1×H2; consider f:H→H a contraction with coefficient 00, and M:H→H is a β-inverse strongly monotone mapping. Let 0<γ<γ̅/α, S=C×Q and G:H→H3 be defined by restricting to H1 is A and restricting to H2 is -B, that is, G has the matrix form G=[A,-B]. It is proved that the sequence {wn}={(xn,yn}⊆H generated by the iterative method wn+1=PS[αnγf(wn+(I-αnTPS(I-γnG*GPS(wn-λnMwn] converges strongly to w̃ which solves the SEP and the following variational inequality: 〈(T-λfw̃,w-w̃〉≥0 and 〈Mw̃,w-w̃〉≥0 for all w∈S. Moreover, if we take M=G*G:H→H,  γn=0, then M is a β-inverse strongly monotone mapping, and the sequence {wn} generated by the iterative method wn+1=αnγf(wn+(I-αnTPS(wn-λnG*Gwn converges strongly to w̃ which solves the SEP and the following variational inequality: 〈(T-λfw̃,w-w̃〉≥0 for all w∈S.

A tour of inequality

Science.gov (United States)

Eliazar, Iddo

2018-02-01

This paper presents a concise and up-to-date tour to the realm of inequality indices. Originally devised for socioeconomic applications, inequality indices gauge the divergence of wealth distributions in human societies from the socioeconomic 'ground state' of perfect equality, i.e. pure communism. Inequality indices are quantitative scores that take values in the unit interval, with the zero score characterizing perfect equality. In effect, inequality indices are applicable in the context of general distributions of sizes - non-negative quantities such as count, length, area, volume, mass, energy, and duration. For general size distributions, which are omnipresent in science and engineering, inequality indices provide multi-dimensional and infinite-dimensional quantifications of the inherent inequality - i.e., the statistical heterogeneity, the non-determinism, the randomness. This paper compactly describes the insights and the practical implementation of inequality indices.

Imaging linear and circular polarization features in leaves with complete Mueller matrix polarimetry.

Science.gov (United States)

Patty, C H Lucas; Luo, David A; Snik, Frans; Ariese, Freek; Buma, Wybren Jan; Ten Kate, Inge Loes; van Spanning, Rob J M; Sparks, William B; Germer, Thomas A; Garab, Győző; Kudenov, Michael W

2018-06-01

Spectropolarimetry of intact plant leaves allows to probe the molecular architecture of vegetation photosynthesis in a non-invasive and non-destructive way and, as such, can offer a wealth of physiological information. In addition to the molecular signals due to the photosynthetic machinery, the cell structure and its arrangement within a leaf can create and modify polarization signals. Using Mueller matrix polarimetry with rotating retarder modulation, we have visualized spatial variations in polarization in transmission around the chlorophyll a absorbance band from 650 nm to 710 nm. We show linear and circular polarization measurements of maple leaves and cultivated maize leaves and discuss the corresponding Mueller matrices and the Mueller matrix decompositions, which show distinct features in diattenuation, polarizance, retardance and depolarization. Importantly, while normal leaf tissue shows a typical split signal with both a negative and a positive peak in the induced fractional circular polarization and circular dichroism, the signals close to the veins only display a negative band. The results are similar to the negative band as reported earlier for single macrodomains. We discuss the possible role of the chloroplast orientation around the veins as a cause of this phenomenon. Systematic artefacts are ruled out as three independent measurements by different instruments gave similar results. These results provide better insight into circular polarization measurements on whole leaves and options for vegetation remote sensing using circular polarization. Copyright © 2018 The Author(s). Published by Elsevier B.V. All rights reserved.

Distributed Event-Triggered Control of Multiagent Systems with Time-Varying Topology

Directory of Open Access Journals (Sweden)

Jingwei Ma

2014-01-01

Full Text Available This paper studies the consensus of first-order discrete-time multiagent systems, where the interaction topology is time-varying. The event-triggered control is used to update the control input of each agent, and the event-triggering condition is designed based on the combination of the relative states of each agent to its neighbors. By applying the common Lyapunov function method, a sufficient condition for consensus, which is expressed as a group of linear matrix inequalities, is obtained and the feasibility of these linear matrix inequalities is further analyzed. Simulation examples are provided to explain the effectiveness of the theoretical results.

New stability and stabilization for switched neutral control systems

International Nuclear Information System (INIS)

Xiong Lianglin; Zhong Shouming; Ye Mao; Wu Shiliang

2009-01-01

This paper concerns stability and stabilization issues for switched neutral systems and presents new classes of piecewise Lyapunov functionals and multiple Lyapunov functionals, based on which, two new switching rules are introduced to stabilize the neutral systems. One switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. The other is based on the determination of average dwell time computed from a new class of linear matrix inequalities (LMIs). And then, state-feedback control is derived for the switched neutral control system mainly based on the state switching rules. Finally, three examples are given to demonstrate the effectiveness of the proposed method.

Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays.

Science.gov (United States)

Huang, Haiying; Du, Qiaosheng; Kang, Xibing

2013-11-01

In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results. © 2013 ISA. Published by ISA. All rights reserved.

The linearization method in hydrodynamical stability theory

CERN Document Server

Yudovich, V I

1989-01-01

This book presents the theory of the linearization method as applied to the problem of steady-state and periodic motions of continuous media. The author proves infinite-dimensional analogues of Lyapunov's theorems on stability, instability, and conditional stability for a large class of continuous media. In addition, semigroup properties for the linearized Navier-Stokes equations in the case of an incompressible fluid are studied, and coercivity inequalities and completeness of a system of small oscillations are proved.

Porting of the DBCSR library for Sparse Matrix-Matrix Multiplications to Intel Xeon Phi systems

OpenAIRE

Bethune, Iain; Gloess, Andeas; Hutter, Juerg; Lazzaro, Alfio; Pabst, Hans; Reid, Fiona

2017-01-01

Multiplication of two sparse matrices is a key operation in the simulation of the electronic structure of systems containing thousands of atoms and electrons. The highly optimized sparse linear algebra library DBCSR (Distributed Block Compressed Sparse Row) has been specifically designed to efficiently perform such sparse matrix-matrix multiplications. This library is the basic building block for linear scaling electronic structure theory and low scaling correlated methods in CP2K. It is para...

Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

OpenAIRE

Zuidwijk, Rob

2005-01-01

textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an optimal solution are investigated, and the optimal solution is studied on a so-called critical range of the initial data, in which certain properties such as the optimal basis in linear programming are ...

Inequality, Tolerance, and Growth

DEFF Research Database (Denmark)

Bjørnskov, Christian

This paper argues for the importance of individuals' tolerance of inequality for economic growth. By using the political ideology of governments as a measure of revealed tolerance of inequality, the paper shows that controlling for ideology improves the accuracy with which the effects of inequality...... are measured. Results show that inequality reduces growth but more so in societies where people perceive it as being relatively unfair. Further results indicate that legal quality and social trust are likely transmission channels for the effects of inequality....

Inequality, Tolerance, and Growth

DEFF Research Database (Denmark)

Bjørnskov, Christian

2004-01-01

This paper argues for the importance of individuals' tolerance of inequality for economic growth. By using the political ideology of governments as a measure of revealed tolerance of inequality, the paper shows that controlling for ideology improves the accuracy with which the effects of inequality...... are measured. Results show that inequality reduces growth but more so in societies where people perceive it as being relatively unfair. Further results indicate that legal quality and social trust are likely transmission channels for the effects of inequality....

The different worlds of inequality: Psychological determinants and implications of economic inequality

OpenAIRE

Steiniger, Tim

2015-01-01

Social and economic inequalities have been a concern in human societies throughout history. In recent years especially wealth and income inequality have been the focus of controversial public, political, and scientific debates. The present thesis seeks to contribute to the ongoing inequality debate by regarding economic inequality from a psychological point of view. Together with Detlef Fetchenhauer, Thomas Schlösser, and Daniel Ehlebracht, I experimentally investigated the psychological dete...

ARMA Cholesky Factor Models for the Covariance Matrix of Linear Models.

Science.gov (United States)

Lee, Keunbaik; Baek, Changryong; Daniels, Michael J

2017-11-01

In longitudinal studies, serial dependence of repeated outcomes must be taken into account to make correct inferences on covariate effects. As such, care must be taken in modeling the covariance matrix. However, estimation of the covariance matrix is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcomes these limitations, two Cholesky decomposition approaches have been proposed: modified Cholesky decomposition for autoregressive (AR) structure and moving average Cholesky decomposition for moving average (MA) structure, respectively. However, the correlations of repeated outcomes are often not captured parsimoniously using either approach separately. In this paper, we propose a class of flexible, nonstationary, heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the covariance matrix that we denote as ARMACD. We analyze a recent lung cancer study to illustrate the power of our proposed methods.

A companion matrix for 2-D polynomials

International Nuclear Information System (INIS)

Boudellioua, M.S.

1995-08-01

In this paper, a matrix form analogous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials. These polynomials arise in the context of 2-D linear systems theory. Necessary and sufficient conditions are also presented under which a matrix is equivalent to this companion form. (author). 6 refs

Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

Science.gov (United States)

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

Educational inequality in the occurrence of abdominal obesity:Pró-Saúde Study

Directory of Open Access Journals (Sweden)

Ronaldo Fernandes Santos Alves

2015-01-01

Full Text Available OBJECTIVE To estimate the degree of educational inequality in the occurrence of abdominal obesity in a population of non-faculty civil servants at university campi.METHODS In this cross-sectional study, we used data from 3,117 subjects of both genders aged 24 to 65-years old, regarding the baseline ofPró-Saúde Study, 1999-2001. Abdominal obesity was defined according to abdominal circumference thresholds of 88 cm for women and 102 cm for men. A multi-dimensional, self-administered questionnaire was used to evaluate education levels and demographic variables. Slope and relative indices of inequality, and Chi-squared test for linear trend were used in the data analysis. All analyses were stratified by genders, and the indices of inequality were standardized by age.RESULTS Abdominal obesity was the most prevalent among women (43.5%; 95%CI 41.2;45.9, as compared to men (24.3%; 95%CI 22.1;26.7, in all educational strata and age ranges. The association between education levels and abdominal obesity was an inverse one among women (p < 0.001; it was not statistically significant among men (p = 0.436. The educational inequality regarding abdominal obesity in the female population, in absolute terms (slope index of inequality, was 24.0% (95%CI 15.5;32.6. In relative terms (relative index of inequality, it was 2.8 (95%CI 1.9;4.1, after the age adjustment.CONCLUSIONS Gender inequality in the prevalence of abdominal obesity increases with older age and lower education. The slope and relative indices of inequality summarize the strictly monotonous trend between education levels and abdominal obesity, and it described educational inequality regarding abdominal obesity among women. Such indices provide relevant quantitative estimates for monitoring abdominal obesity and dealing with health inequalities.

Handbook of linear algebra

CERN Document Server

Hogben, Leslie

2013-01-01

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.New to the Second EditionSeparate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of

Several applications of Cartwright-Field's inequality

OpenAIRE

Minculete, Nicuşor; Furuichi, Shigeru

2011-01-01

In this paper we present several applications of Cartwright-Field's inequality. Among these we found Young's inequality, Bernoulli's inequality, the inequality between the weighted power means, H\\"{o}lder's inequality and Cauchy's inequality. We give also two applications related to arithmetic functions and to operator inequalities.

Bell's inequalities for quantum mechanics

International Nuclear Information System (INIS)

Andaas, H.E.

1991-10-01

Inequalities corresponding to the generalized Bell's inequalities of local realism are derived for the quantum case. The extremal values permitted by these inequalities exceed those allowed by the generalized Bell's inequalities. Quantum predictions for systems of two spin-1/2 particles prepared as mixtures do not violate Bell's inequalities. 15 refs

Income Inequality and Education

Directory of Open Access Journals (Sweden)

Richard Breen

2015-08-01

Full Text Available Many commentators have seen the growing gap in earnings and income between those with a college education and those without as a major cause of increasing inequality in the United States and elsewhere. In this article we investigate the extent to which increasing the educational attainment of the US population might ameliorate inequality. We use data from NLSY79 and carry out a three-level decomposition of total inequality into within-person, between-person and between-education parts. We find that the between-education contribution to inequality is small, even when we consider only adjusted inequality that omits the within-person component. We carry out a number of simulations to gauge the likely impact on inequality of changes in the distribution of education and of a narrowing of the differences in average incomes between those with different levels of education. We find that any feasible educational policy is likely to have only a minor impact on income inequality.

Linear data mining the Wichita clinical matrix suggests sleep and allostatic load involvement in chronic fatigue syndrome.

Science.gov (United States)

Gurbaxani, Brian M; Jones, James F; Goertzel, Benjamin N; Maloney, Elizabeth M

2006-04-01

To provide a mathematical introduction to the Wichita (KS, USA) clinical dataset, which is all of the nongenetic data (no microarray or single nucleotide polymorphism data) from the 2-day clinical evaluation, and show the preliminary findings and limitations, of popular, matrix algebra-based data mining techniques. An initial matrix of 440 variables by 227 human subjects was reduced to 183 variables by 164 subjects. Variables were excluded that strongly correlated with chronic fatigue syndrome (CFS) case classification by design (for example, the multidimensional fatigue inventory [MFI] data), that were otherwise self reporting in nature and also tended to correlate strongly with CFS classification, or were sparse or nonvarying between case and control. Subjects were excluded if they did not clearly fall into well-defined CFS classifications, had comorbid depression with melancholic features, or other medical or psychiatric exclusions. The popular data mining techniques, principle components analysis (PCA) and linear discriminant analysis (LDA), were used to determine how well the data separated into groups. Two different feature selection methods helped identify the most discriminating parameters. Although purely biological features (variables) were found to separate CFS cases from controls, including many allostatic load and sleep-related variables, most parameters were not statistically significant individually. However, biological correlates of CFS, such as heart rate and heart rate variability, require further investigation. Feature selection of a limited number of variables from the purely biological dataset produced better separation between groups than a PCA of the entire dataset. Feature selection highlighted the importance of many of the allostatic load variables studied in more detail by Maloney and colleagues in this issue [1] , as well as some sleep-related variables. Nonetheless, matrix linear algebra-based data mining approaches appeared to be of

Socioeconomic Status and Health: A New Approach to the Measurement of Bivariate Inequality.

Science.gov (United States)

Erreygers, Guido; Kessels, Roselinde

2017-06-23

We suggest an alternative way to construct a family of indices of socioeconomic inequality of health. Our indices belong to the broad category of linear indices. In contrast to rank-dependent indices, which are defined in terms of the ranks of the socioeconomic variable and the levels of the health variable, our indices are based on the levels of both the socioeconomic and the health variable. We also indicate how the indices can be modified in order to introduce sensitivity to inequality in the socioeconomic distribution and to inequality in the health distribution. As an empirical illustration, we make a comparative study of the relation between income and well-being in 16 European countries using data from the Survey of Health, Ageing and Retirement in Europe (SHARE) Wave 4.

Socioeconomic Status and Health: A New Approach to the Measurement of Bivariate Inequality

Science.gov (United States)

Kessels, Roselinde

2017-01-01

We suggest an alternative way to construct a family of indices of socioeconomic inequality of health. Our indices belong to the broad category of linear indices. In contrast to rank-dependent indices, which are defined in terms of the ranks of the socioeconomic variable and the levels of the health variable, our indices are based on the levels of both the socioeconomic and the health variable. We also indicate how the indices can be modified in order to introduce sensitivity to inequality in the socioeconomic distribution and to inequality in the health distribution. As an empirical illustration, we make a comparative study of the relation between income and well-being in 16 European countries using data from the Survey of Health, Ageing and Retirement in Europe (SHARE) Wave 4. PMID:28644405

From the Triangle Inequality to the Isoperimetric Inequality

Indian Academy of Sciences (India)

IAS Admin

Calculus of variations, shape optimization, isoperimetric prob- lems. Figure 1. Starting from the triangle inequality, we will dis- cuss a series of shape optimization problems us- ing elementary geometry and ultimately derive the classical isoperimetric inequality in the plane. One of the important results we learn in plane geom ...

All inequality is not equal: children correct inequalities using resource value

Science.gov (United States)

Shaw, Alex; Olson, Kristina R.

2013-01-01

Fairness concerns guide children's judgments about how to share resources with others. However, it is unclear from past research if children take extant inequalities or the value of resources involved in an inequality into account when sharing with others; these questions are the focus of the current studies. In all experiments, children saw an inequality between two recipients—one had two more resources than another. What varied between conditions was the value of the resources that the child could subsequently distribute. When the resources were equal in value to those involved in the original inequality, children corrected the previous inequality by giving two resources to the child with fewer resources (Experiment 1). However, as the value of the resources increased relative to those initially shared by the experimenter, children were more likely to distribute the two high value resources equally between the two recipients, presumably to minimize the overall inequality in value (Experiments 1 and 2). We found that children specifically use value, not just size, when trying to equalize outcomes (Experiment 3) and further found that children focus on the relative rather than absolute value of the resources they share—when the experimenter had unequally distributed the same high value resource that the child would later share, children corrected the previous inequality by giving two high value resources to the person who had received fewer high value resources. These results illustrate that children attempt to correct past inequalities and try to maintain equality not just in the count of resources but also by using the value of resources. PMID:23882227

The Feedback Control Strategy of the Takagi-Sugeno Fuzzy Car-Following Model with Two Delays

Directory of Open Access Journals (Sweden)

Cong Zhai

2016-01-01

Full Text Available Considering the driver’s sensing the headway and velocity the different time-varying delays exist, respectively, and the sensitivity of drivers changes with headway and speed. Introducing the fuzzy control theory, a new fuzzy car-following model with two delays is presented, and the feedback control strategy of the new fuzzy car-following model is studied. Based on the Lyapunov function theory and linear matrix inequality (LMI approach, the sufficient condition that the existence of the fuzzy controller is given making the closed-loop system is asymptotic, stable; namely, traffic congestion phenomenon can effectively be suppressed, and the controller gain matrix can be obtained via solving linear matrix inequality. Finally, the simulation examples verify that the method which suppresses traffic congestion and reduces fuel consumption and exhaust emissions is effective.

Inequality in CO2 emissions across countries and its relationship with income inequality: A distributive approach

International Nuclear Information System (INIS)

Padilla, Emilio; Serrano, Alfredo

2006-01-01

This paper analyzes the inequality in CO 2 emissions across countries (and groups of countries) and the relationship of this inequality with income inequality across countries for the period (1971-1999). The research employs the tools that are usually applied in income distribution analysis. The methodology used here gives qualitative and quantitative information on some of the features of the inequalities across countries that are considered most relevant for the design and discussion of policies aimed at mitigating climate change. The paper studies the relationship between CO 2 emissions and GDP and shows that income inequality across countries has been followed by an important inequality in the distribution of emissions. This inequality has diminished mildly, although the inequality in emissions across countries ordered in the increasing value of income (inequality between rich and poor countries) has diminished less than the 'simple' inequality in emissions. Lastly, the paper shows that the inequality in CO 2 emissions is mostly explained by the inequality between groups with different per capita income level. The importance of the inequality within groups of similar per capita income is much lower and has diminished during the period, especially in the low middle income group

Mini-lecture course: Introduction into hierarchical matrix technique

KAUST Repository

Litvinenko, Alexander

2017-12-14

The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations (mesh points). The H-matrix technique allows us to work with general class of matrices (not only structured or Toeplits or sparse). H-matrices can keep the H-matrix data format during linear algebra operations (inverse, update, Schur complement).

Linear Models

CERN Document Server

Searle, Shayle R

2012-01-01

This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.

Inequalities an approach through problems

CERN Document Server

Venkatachala, B J

2018-01-01

This book discusses about the basic topics on inequalities and their applications. These include the arithmetic mean–geometric mean inequality, Cauchy–Schwarz inequality, Chebyshev inequality, rearrangement inequality, convex and concave functions and Muirhead's theorem. The book contains over 400 problems with their solutions. A chapter on geometric inequalities is a special feature of this book. Most of these problems are from International Mathematical Olympiads and from many national mathematical Olympiads. The book is intended to help students who are preparing for various mathematical competitions. It is also a good source book for graduate students who are consolidating their knowledge of inequalities and their applications. .

Bell inequalities stronger than the Clauser-Horne-Shimony-Holt inequality for three-level isotropic states

International Nuclear Information System (INIS)

Ito, Tsuyoshi; Imai, Hiroshi; Avis, David

2006-01-01

We show that some two-party Bell inequalities with two-valued observables are stronger than the CHSH inequality for 3x3 isotropic states in the sense that they are violated by some isotropic states in the 3x3 system that do not violate the CHSH inequality. These Bell inequalities are obtained by applying triangular elimination to the list of known facet inequalities of the cut polytope on nine points. This gives a partial solution to an open problem posed by Collins and Gisin. The results of numerical optimization suggest that they are candidates for being stronger than the I 3322 Bell inequality for 3x3 isotropic states. On the other hand, we found no Bell inequalities stronger than the CHSH inequality for 2x2 isotropic states. In addition, we illustrate an inclusion relation among some Bell inequalities derived by triangular elimination

Energy conserving, linear scaling Born-Oppenheimer molecular dynamics.

Science.gov (United States)

Cawkwell, M J; Niklasson, Anders M N

2012-10-07

Born-Oppenheimer molecular dynamics simulations with long-term conservation of the total energy and a computational cost that scales linearly with system size have been obtained simultaneously. Linear scaling with a low pre-factor is achieved using density matrix purification with sparse matrix algebra and a numerical threshold on matrix elements. The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] yields microcanonical trajectories with the approximate forces obtained from the linear scaling method that exhibit no systematic drift over hundreds of picoseconds and which are indistinguishable from trajectories computed using exact forces.

Violation of a Bell-like inequality by a combination of Rayleigh scattering with a Mach–Zehnder setup

International Nuclear Information System (INIS)

Rother, Tom

2016-01-01

In this paper I propose a classical optics experiment that results in a maximum violation of a Bell-like inequality. The first part is concerned with the Bell-like inequality (the so-called CHSH-inequality) itself. Its importance and its maximum violation in Quantum Mechanics (QM) are discussed in detail by employing an abstract probability state concept in a 4-dim. but classical event space. A T-matrix that represents the integral part of a corresponding Green's function as well as a statistical operator that contains a negative quasi-probability can be related to the corresponding quantum mechanical experiment. It is demonstrated that the derivation and usage of the T-matrix and the Green's function is equivalent to what is known from classical scattering theory. It is shown moreover that the negative quasi-probability of the statistical operator may be interpreted as a sink of probabilities related to two single events of the considered 4-dim. event space. A necessary condition for the violation of the CHSH-inequality is derived and discussed afterwards. In the second part of this paper I discuss a modification of the 4-dim. event space considered in the first part. It is shown that a combination of conventional Rayleigh scattering with a Mach–Zehnder setup would be able to put this modification into practice. Thus it becomes possible to achieve a maximum violation of the CHSH-inequality, if formulated in terms of intensities, on a pure classical way. The combination of classical light scattering with correlation experiments such as proposed in this paper may open new ways to study and to use the violation of Bell-like inequalities in modern optics. - Highlights: • Consistent Green's function formulation of the quantum mechanical Bell's experiment and its classical counterpart. This description is closely related to what is known from electromagnetic wave scattering. This is achieved by introducing an abstract probability state concept. • Discussion of a

Determinants of income inequality

OpenAIRE

Afandi, Akhsyim; Rantung, Vebryna Permatasari; Marashdeh, Hazem

2017-01-01

This study examines whether changing economic structure, social conditions, and financialization are responsible for increased income inequality in Indonesia. By employing panel data of 32 provinces in Indonesia that spans from 2007 to 2013, it finds that structural change affects income inequality, increased share of finance reduces inequality, which is against the financialization hypothesis, and social conditions have expected effects on income inequality. While an increased share of both ...

Incorporating concepts of inequality and inequity into health benefits analysis

Directory of Open Access Journals (Sweden)

Tuchmann Jessica L

2006-03-01

Full Text Available Abstract Background Although environmental policy decisions are often based in part on both risk assessment information and environmental justice concerns, formalized approaches for addressing inequality or inequity when estimating the health benefits of pollution control have been lacking. Inequality indicators that fulfill basic axioms and agree with relevant definitions and concepts in health benefits analysis and environmental justice analysis can allow for quantitative examination of efficiency-equality tradeoffs in pollution control policies. Methods To develop appropriate inequality indicators for health benefits analysis, we provide relevant definitions from the fields of risk assessment and environmental justice and consider the implications. We evaluate axioms proposed in past studies of inequality indicators and develop additional axioms relevant to this context. We survey the literature on previous applications of inequality indicators and evaluate five candidate indicators in reference to our proposed axioms. We present an illustrative pollution control example to determine whether our selected indicators provide interpretable information. Results and Conclusions We conclude that an inequality indicator for health benefits analysis should not decrease when risk is transferred from a low-risk to high-risk person, and that it should decrease when risk is transferred from a high-risk to low-risk person (Pigou-Dalton transfer principle, and that it should be able to have total inequality divided into its constituent parts (subgroup decomposability. We additionally propose that an ideal indicator should avoid value judgments about the relative importance of transfers at different percentiles of the risk distribution, incorporate health risk with evidence about differential susceptibility, include baseline distributions of risk, use appropriate geographic resolution and scope, and consider multiple competing policy alternatives. Given

Inequalities in Science

OpenAIRE

Xie, Y.

2014-01-01

Inequalities in scientists’ contributions to science and their rewards have always been very high. There are good reasons to propose that inequalities in science across research institutions and across individual scientists have increased in recent years. In the meantime, however, globalization and internet technology have narrowed inequalities in science across nations and facilitated the expansion of science and rapid production of scientific discoveries through international collaborative ...

The inequality footprints of nations: a novel approach to quantitative accounting of income inequality.

Directory of Open Access Journals (Sweden)

Ali Alsamawi

Full Text Available In this study we use economic input-output analysis to calculate the inequality footprint of nations. An inequality footprint shows the link that each country's domestic economic activity has to income distribution elsewhere in the world. To this end we use employment and household income accounts for 187 countries and an historical time series dating back to 1990. Our results show that in 2010, most developed countries had an inequality footprint that was higher than their within-country inequality, meaning that in order to support domestic lifestyles, these countries source imports from more unequal economies. Amongst exceptions are the United States and United Kingdom, which placed them on a par with many developing countries. Russia has a high within-country inequality nevertheless it has the lowest inequality footprint in the world, which is because of its trade connections with the Commonwealth of Independent States and Europe. Our findings show that the commodities that are inequality-intensive, such as electronic components, chemicals, fertilizers, minerals, and agricultural products often originate in developing countries characterized by high levels of inequality. Consumption of these commodities may implicate within-country inequality in both developing and developed countries.

The inequality footprints of nations: a novel approach to quantitative accounting of income inequality.

Science.gov (United States)

Alsamawi, Ali; Murray, Joy; Lenzen, Manfred; Moran, Daniel; Kanemoto, Keiichiro

2014-01-01

In this study we use economic input-output analysis to calculate the inequality footprint of nations. An inequality footprint shows the link that each country's domestic economic activity has to income distribution elsewhere in the world. To this end we use employment and household income accounts for 187 countries and an historical time series dating back to 1990. Our results show that in 2010, most developed countries had an inequality footprint that was higher than their within-country inequality, meaning that in order to support domestic lifestyles, these countries source imports from more unequal economies. Amongst exceptions are the United States and United Kingdom, which placed them on a par with many developing countries. Russia has a high within-country inequality nevertheless it has the lowest inequality footprint in the world, which is because of its trade connections with the Commonwealth of Independent States and Europe. Our findings show that the commodities that are inequality-intensive, such as electronic components, chemicals, fertilizers, minerals, and agricultural products often originate in developing countries characterized by high levels of inequality. Consumption of these commodities may implicate within-country inequality in both developing and developed countries.

Global Inequality: An Introduction

Directory of Open Access Journals (Sweden)

Michelle Bata

2015-08-01

Full Text Available Global inequality has been little analyzed by sociologists despite their claim to be the scienti?c experts most in charge of the study of human inequalities and social strati?cation. Most undergraduate courses on social inequalities study race, class and gender without ever acknowledging that the greatest inequalities are between those individuals and households that live in developed versus less developed societies. The amount of international inequality has vastly outweighed within country inequalities since at least the 1870s when a wave of economic globalization under the Pax Britannica increased average wages in the core while leaving most of the periphery and the semiperiphery at subsistence levels. Increasing inequality was one of the most important consequences of nineteenth century globalization, and this fact is pregnant with importance for those who seek to understand what the consequences of twentieth century globalization may be. Resistance to global capitalism and attacks on symbols of power are likely to increase, just as they did in the decades following the great expansion of trade and investment in the last decades of the nineteenth century. Research into the causes of increasing inequalities is thus extremely important for social scientists, policy makers and global citizens who need to understand how the world-system works in order to change it.

A Generalized Affine Isoperimetric Inequality

OpenAIRE

Chen, Wenxiong; Howard, Ralph; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong

2004-01-01

A purely analytic proof is given for an inequality that has as a direct consequence the two most important affine isoperimetric inequalities of plane convex geometry: The Blaschke-Santalo inequality and the affine isoperimetric inequality of affine differential geometry.

Impacts of generalized uncertainty principle on black hole thermodynamics and Salecker-Wigner inequalities

International Nuclear Information System (INIS)

Tawfik, A.

2013-01-01

We investigate the impacts of Generalized Uncertainty Principle (GUP) proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity on black hole thermodynamics and Salecker-Wigner inequalities. Utilizing Heisenberg uncertainty principle, the Hawking temperature, Bekenstein entropy, specific heat, emission rate and decay time are calculated. As the evaporation entirely eats up the black hole mass, the specific heat vanishes and the temperature approaches infinity with an infinite radiation rate. It is found that the GUP approach prevents the black hole from the entire evaporation. It implies the existence of remnants at which the specific heat vanishes. The same role is played by the Heisenberg uncertainty principle in constructing the hydrogen atom. We discuss how the linear GUP approach solves the entire-evaporation-problem. Furthermore, the black hole lifetime can be estimated using another approach; the Salecker-Wigner inequalities. Assuming that the quantum position uncertainty is limited to the minimum wavelength of measuring signal, Wigner second inequality can be obtained. If the spread of quantum clock is limited to some minimum value, then the modified black hole lifetime can be deduced. Based on linear GUP approach, the resulting lifetime difference depends on black hole relative mass and the difference between black hole mass with and without GUP is not negligible

Inequalities in Science

Science.gov (United States)

Xie, Y.

2014-01-01

Inequalities in scientists’ contributions to science and their rewards have always been very high. There are good reasons to propose that inequalities in science across research institutions and across individual scientists have increased in recent years. In the meantime, however, globalization and internet technology have narrowed inequalities in science across nations and facilitated the expansion of science and rapid production of scientific discoveries through international collaborative networks. PMID:24855244

Economic inequality increases risk taking.

Science.gov (United States)

Payne, B Keith; Brown-Iannuzzi, Jazmin L; Hannay, Jason W

2017-05-02

Rising income inequality is a global trend. Increased income inequality has been associated with higher rates of crime, greater consumer debt, and poorer health outcomes. The mechanisms linking inequality to poor outcomes among individuals are poorly understood. This research tested a behavioral account linking inequality to individual decision making. In three experiments ( n = 811), we found that higher inequality in the outcomes of an economic game led participants to take greater risks to try to achieve higher outcomes. This effect of unequal distributions on risk taking was driven by upward social comparisons. Next, we estimated economic risk taking in daily life using large-scale data from internet searches. Risk taking was higher in states with greater income inequality, an effect driven by inequality at the upper end of the income distribution. Results suggest that inequality may promote poor outcomes, in part, by increasing risky behavior.

Impact of income inequality on life expectancy in a highly unequal developing country: the case of Brazil.

Science.gov (United States)

Rasella, Davide; Aquino, Rosana; Barreto, Mauricio Lima

2013-08-01

Few studies have analysed the effects of income inequality on health in developing countries, particularly during economic growth, reduction of social disparities and reinforcement of the welfare and healthcare system. We evaluated the association between income inequality and life expectancy in Brazil, including the effect of social and health interventions, in the period 2000-2009. A panel dataset was created for the 27 Brazilian states over the referred time period. Multivariable linear regressions were performed using fixed-effects estimation with heteroscedasticity and serial correlation robust SEs. Models were fitted for life expectancy as a dependent variable, using the Gini index or a percentile income dispersion ratio as the main independent variable, and for demographic, socioeconomic and healthcare-related determinants as covariates. The Gini index, as the other measure of income inequality, was negatively associated with life expectancy (pincome inequality, contributing-together with PHC-to decreasing death rates in the population. Reducing income inequality may represent an important step towards improving health and increasing life expectancy, particularly in developing countries where inequalities are high.

Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

Directory of Open Access Journals (Sweden)

Minsong Zhang

2014-01-01

Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Covariance Bell inequalities

Science.gov (United States)

Pozsgay, Victor; Hirsch, Flavien; Branciard, Cyril; Brunner, Nicolas

2017-12-01

We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities is their nonlinearity; this has nontrivial consequences for the derivation of their local bound, which is not reached by deterministic local correlations. For our simplest inequality, we derive analytically tight bounds for both local and quantum correlations. An interesting application of covariance Bell inequalities is that they can act as "shared randomness witnesses": specifically, the value of the Bell expression gives device-independent lower bounds on both the dimension and the entropy of the shared random variable in a local model.

Inequality of Opportunity and Income Inequality in Nine Chinese Provinces, 1989-2006

DEFF Research Database (Denmark)

Eriksson, Tor Viking; Zhang, Yingqiang

2010-01-01

's own choices (''effort''). What is the relationship between income inequality and inequality of opportunity? For this purpose we use data from the China Health and Nutrition Survey collected from nine provinces during the period 1989 to 2006. The CHNS has detailed information about incomes and other...... factors enabling us to construct a host of circumstance and effort variables for the offspring. We find that China has a substantial degree of inequality of opportunity. Parental income and parents' type of employer explain about two thirds of the total inequality of opportunity. Notably, parental...

Linear reversible second-order cellular automata and their first-order matrix equivalents

International Nuclear Information System (INIS)

Macfarlane, A J

2004-01-01

Linear or one-dimensional reversible second-order cellular automata, exemplified by three cases named as RCA1-3, are introduced. Displays of their evolution in discrete time steps, t=0, 1, 2, ..., from their simplest initial states and on the basis of updating rules in modulo 2 arithmetic, are presented. In these, shaded and unshaded squares denote cells whose cell variables are equal to one and zero respectively. This paper is devoted to finding general formulas for, and explicit numerical evaluations of, the weights N(t) of the states or configurations of RCA1-3, i.e. the total number of shaded cells in tth line of their displays. This is achieved by means of the replacement of RCA1-3 by the equivalent linear first-order matrix automata MCA1-3, for which the cell variables are 2x2 matrices, instead of just numbers (element of Z 2 ) as for RCA1-3. MCA1-3 are tractable because it has been possible to generalize to them the heavy duty methods already well-developed for ordinary first-order cellular automata like those of Wolfram's Rules 90 and 150. While the automata MCA1-3 are thought to be of genuine interest in their own right, with untapped further mathematical potential, their treatment has been applied here to expediting derivation of a large body of general and explicit results for N(t) for RCA1-3. Amongst explicit results obtained are formulas also for each of RCA1-3 for the total weight of the configurations of the first 2 M times, M=0, 1, 2, ..

Legal Quality, Inequality, and Tolerance

DEFF Research Database (Denmark)

Bjørnskov, Christian

Previous findings suggest that income inequality leads to lower legal quality. This paper argues that voters' tolerance of inequality exerts an additional influence. Empirical findings suggest that inequality leads to lower legal quality due to its effect on trust while the tolerance of inequality...

Legal Quality, Inequality, and Tolerance

DEFF Research Database (Denmark)

Bjørnskov, Christian

2004-01-01

Previous findings suggest that income inequality leads to lower legal quality. This paper argues that voters' tolerance of inequality exerts an additional influence. Empirical findings suggest that inequality leads to lower legal quality due to its effect on trust while the tolerance of inequality...

Regional income inequality model based on theil index decomposition and weighted variance coeficient

Science.gov (United States)

Sitepu, H. R.; Darnius, O.; Tambunan, W. N.

2018-03-01

Regional income inequality is an important issue in the study on economic development of a certain region. Rapid economic development may not in accordance with people’s per capita income. The method of measuring the regional income inequality has been suggested by many experts. This research used Theil index and weighted variance coefficient in order to measure the regional income inequality. Regional income decomposition which becomes the productivity of work force and their participation in regional income inequality, based on Theil index, can be presented in linear relation. When the economic assumption in j sector, sectoral income value, and the rate of work force are used, the work force productivity imbalance can be decomposed to become the component in sectors and in intra-sectors. Next, weighted variation coefficient is defined in the revenue and productivity of the work force. From the quadrate of the weighted variation coefficient result, it was found that decomposition of regional revenue imbalance could be analyzed by finding out how far each component contribute to regional imbalance which, in this research, was analyzed in nine sectors of economic business.

A new look at the robust control of discrete-time Markov jump linear systems

Science.gov (United States)

Todorov, M. G.; Fragoso, M. D.

2016-03-01

In this paper, we make a foray in the role played by a set of four operators on the study of robust H2 and mixed H2/H∞ control problems for discrete-time Markov jump linear systems. These operators appear in the study of mean square stability for this class of systems. By means of new linear matrix inequality (LMI) characterisations of controllers, which include slack variables that, to some extent, separate the robustness and performance objectives, we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of H2 performance. Since each operator provides a different degree of conservatism, the results are unified in the form of an iterative LMI technique for designing robust H2 controllers, whose convergence is attained in a finite number of steps. The method yields a new way of computing mixed H2/H∞ controllers, whose conservatism decreases with iteration. Two numerical examples illustrate the applicability of the proposed results for the control of a small unmanned aerial vehicle, and for an underactuated robotic arm.

Passivity analysis for uncertain BAM neural networks with time delays and reaction-diffusions

Science.gov (United States)

Zhou, Jianping; Xu, Shengyuan; Shen, Hao; Zhang, Baoyong

2013-08-01

This article deals with the problem of passivity analysis for delayed reaction-diffusion bidirectional associative memory (BAM) neural networks with weight uncertainties. By using a new integral inequality, we first present a passivity condition for the nominal networks, and then extend the result to the case with linear fractional weight uncertainties. The proposed conditions are expressed in terms of linear matrix inequalities, and thus can be checked easily. Examples are provided to demonstrate the effectiveness of the proposed results.

Stabilization of discrete-time LTI positive systems

Directory of Open Access Journals (Sweden)

Krokavec Dušan

2017-12-01

Full Text Available The paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the state-feedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.

The impact of increasing income inequalities on educational inequalities in mortality - An analysis of six European countries.

Science.gov (United States)

Hoffmann, Rasmus; Hu, Yannan; de Gelder, Rianne; Menvielle, Gwenn; Bopp, Matthias; Mackenbach, Johan P

2016-07-08

Over the past decades, both health inequalities and income inequalities have been increasing in many European countries, but it is unknown whether and how these trends are related. We test the hypothesis that trends in health inequalities and trends in income inequalities are related, i.e. that countries with a stronger increase in income inequalities have also experienced a stronger increase in health inequalities. We collected trend data on all-cause and cause-specific mortality, as well as on the household income of people aged 35-79, for Belgium, Denmark, England & Wales, France, Slovenia, and Switzerland. We calculated absolute and relative differences in mortality and income between low- and high-educated people for several time points in the 1990s and 2000s. We used fixed-effects panel regression models to see if changes in income inequality predicted changes in mortality inequality. The general trend in income inequality between high- and low-educated people in the six countries is increasing, while the mortality differences between educational groups show diverse trends, with absolute differences mostly decreasing and relative differences increasing in some countries but not in others. We found no association between trends in income inequalities and trends in inequalities in all-cause mortality, and trends in mortality inequalities did not improve when adjusted for rising income inequalities. This result held for absolute as well as for relative inequalities. A cause-specific analysis revealed some association between income inequality and mortality inequality for deaths from external causes, and to some extent also from cardiovascular diseases, but without statistical significance. We find no support for the hypothesis that increasing income inequality explains increasing health inequalities. Possible explanations are that other factors are more important mediators of the effect of education on health, or more simply that income is not an important

Particles geometry influence in the thermal stress level in an SiC reinforced aluminum matrix composite considering the material non-linear behavior

International Nuclear Information System (INIS)

Miranda, Carlos A. de J.; Libardi, Rosani M.P.; Boari, Zoroastro de M.

2009-01-01

An analytical methodology was developed to predict the thermal stress level that occurs in a metallic matrix composite reinforced with SiC particles, when the temperature decreases from 600 deg C to 20 deg C during the fabrication process. This analytical development is based on the Eshelby method, dislocation mechanisms, and the Maxwell-Boltzmann distribution model. The material was assumed to have a linear elastic behavior. The analytical results from this formulation were verified against numerical linear analyses that were performed over a set of random non-uniform distribution of particles that covers a wide range of volumetric ratios. To stick with the analytical hypothesis, particles with round geometry were used. Each stress distribution, represented by the isostress curves at ΔT=-580 deg C, was analyzed with an image analyzer. A statistical procedure was applied to obtain the most probable thermal stress level. Analytical and numerical results compared very well. Plastic deformation as well as particle geometry can alter significantly the stress field in the material. To account for these effects, in this work, several numerical analyses were performed considering the non-linear behavior for the aluminum matrix and distinct particle geometries. Two distinct sets of data with were used. To allow a direct comparison, the first set has the same models (particle form, size and distribution) as used previously. The second set analyze quadrilateral particles and present very tight range of volumetric ratio, closer to what is found in actual SiC composites. A simple and fast algorithm was developed to analyze the new results. The comparison of these results with the previous ones shows, as expected, the strong influence of the elastic-plastic behavior of the aluminum matrix on the composite thermal stress distribution due to its manufacturing process and shows, also, a small influence of the particles geometry and volumetric ratio. (author)

Inequality of Opportunity in Egypt

OpenAIRE

Hassine, Nadia Belhaj

2012-01-01

The article evaluates the contribution of inequality of opportunity to earnings inequality in Egypt and analyzes its evolution across three time periods and different population groups. It provides parametric and nonparametric estimates of a lower bound for the degree of inequality of opportunity for wage and salary workers. On average, the contribution of opportunity-shaping circumstances to earnings inequality declined from 22 percent in 1988 to 15 percent in 2006. Levels of inequality of o...

The Comparative Organizational Inequality Network: Toward an Economic Sociology of Inequality

OpenAIRE

Tomaskovic-Devey , Donald; Godechot, Olivier

2017-01-01

The international Comparative Organizational Inequality Network (COIN) asks: • What factors drive overall income inequality within and between workplaces? • How do workplaces exacerbate or mitigate the impact of individual distinctions, such as education level, gender, or immigrant status? • How do inequality-generating mechanisms vary as a function of institutional context? List of authors: Donald Tomaskovic-Devey with Nina Bandelj, Irene Boeckmann, István Boza, David Co...

Lorentz-invariant Bell's inequality

International Nuclear Information System (INIS)

Kim, Won Tae; Son, Edwin J.

2005-01-01

We study Bell's inequality in relation to the Einstein-Podolsky-Rosen paradox in the relativistic regime. For this purpose, a relativistically covariant analysis is used in the calculation of the Bell's inequality, which results in the maximally violated Bell's inequality in any reference frame

The Impact of Educational and Gender Inequality on Income Inequality in South Asia

OpenAIRE

Kanwal, Ayesha; Munir, Kashif

2015-01-01

This paper examines the impact of educational and gender inequality in education on income inequality in South Asian countries for the time period of 1980 to 2010. Random effect model (REM) and fixed effect model (FEM) are used for estimation. Using the concept of education Gini the study find that there exist a positive relationship between educational and income inequality. The results also indicate that gender inequality in education at primary and tertiary level has positive and significa...

Deriving Einstein-Podolsky-Rosen steering inequalities from the few-body Abner Shimony inequalities

Science.gov (United States)

Zhou, Jie; Meng, Hui-Xian; Jiang, Shu-Han; Xu, Zhen-Peng; Ren, Changliang; Su, Hong-Yi; Chen, Jing-Ling

2018-04-01

For the Abner Shimony (AS) inequalities, the simplest unified forms of directions attaining the maximum quantum violation are investigated. Based on these directions, a family of Einstein-Podolsky-Rosen (EPR) steering inequalities is derived from the AS inequalities in a systematic manner. For these inequalities, the local hidden state (LHS) bounds are strictly less than the local hidden variable (LHV) bounds. This means that the EPR steering is a form of quantum nonlocality strictly weaker than Bell nonlocality.

Two linearization methods for atmospheric remote sensing

International Nuclear Information System (INIS)

Doicu, A.; Trautmann, T.

2009-01-01

We present two linearization methods for a pseudo-spherical atmosphere and general viewing geometries. The first approach is based on an analytical linearization of the discrete ordinate method with matrix exponential and incorporates two models for matrix exponential calculation: the matrix eigenvalue method and the Pade approximation. The second method referred to as the forward-adjoint approach is based on the adjoint radiative transfer for a pseudo-spherical atmosphere. We provide a compact description of the proposed methods as well as a numerical analysis of their accuracy and efficiency.

Looking for symmetric Bell inequalities

OpenAIRE

Bancal, Jean-Daniel; Gisin, Nicolas; Pironio, Stefano

2010-01-01

Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell e...

Three Interpretations of the Matrix Equation Ax = b

Science.gov (United States)

Larson, Christine; Zandieh, Michelle

2013-01-01

Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…

Global Inequalities in Cervical Cancer Incidence and Mortality are Linked to Deprivation, Low Socioeconomic Status, and Human Development

OpenAIRE

Gopal K. Singh, PhD; Romuladus E. Azuine, DrPH, RN; Mohammad Siahpush, PhD

2012-01-01

Objectives This study examined global inequalities in cervical cancer incidence and mortality rates as a function of cross-national variations in the Human Development Index (HDI), socioeconomic factors, Gender Inequality Index (GII), and healthcare expenditure. Methods Age-adjusted incidence and mortality rates were calculated for women in 184 countries using the 2008 GLOBOCAN database, and incidence and mortality trends were analyzed using the WHO cancer mortality database. Log-linear regre...

Protein structure estimation from NMR data by matrix completion.

Science.gov (United States)

Li, Zhicheng; Li, Yang; Lei, Qiang; Zhao, Qing

2017-09-01

Knowledge of protein structures is very important to understand their corresponding physical and chemical properties. Nuclear Magnetic Resonance (NMR) spectroscopy is one of the main methods to measure protein structure. In this paper, we propose a two-stage approach to calculate the structure of a protein from a highly incomplete distance matrix, where most data are obtained from NMR. We first randomly "guess" a small part of unobservable distances by utilizing the triangle inequality, which is crucial for the second stage. Then we use matrix completion to calculate the protein structure from the obtained incomplete distance matrix. We apply the accelerated proximal gradient algorithm to solve the corresponding optimization problem. Furthermore, the recovery error of our method is analyzed, and its efficiency is demonstrated by several practical examples.

Health inequalities in Ethiopia: modeling inequalities in length of life within and between population groups.

Science.gov (United States)

Tranvåg, Eirik Joakim; Ali, Merima; Norheim, Ole Frithjof

2013-07-11

Most studies on health inequalities use average measures, but describing the distribution of health can also provide valuable knowledge. In this paper, we estimate and compare within-group and between-group inequalities in length of life for population groups in Ethiopia in 2000 and 2011. We used data from the 2011 and 2000 Ethiopia Demographic and Health Survey and the Global Burden of Disease study 2010, and the MODMATCH modified logit life table system developed by the World Health Organization to model mortality rates, life expectancy, and length of life for Ethiopian population groups stratified by wealth quintiles, gender and residence. We then estimated and compared within-group and between-group inequality in length of life using the Gini index and absolute length of life inequality. Length of life inequality has decreased and life expectancy has increased for all population groups between 2000 and 2011. Length of life inequality within wealth quintiles is about three times larger than the between-group inequality of 9 years. Total length of life inequality in Ethiopia was 27.6 years in 2011. Longevity has increased and the distribution of health in Ethiopia is more equal in 2011 than 2000, with length of life inequality reduced for all population groups. Still there is considerable potential for further improvement. In the Ethiopian context with a poor and highly rural population, inequality in length of life within wealth quintiles is considerably larger than between them. This suggests that other factors than wealth substantially contribute to total health inequality in Ethiopia and that identification and quantification of these factors will be important for identifying proper measures to further reduce length of life inequality.

No association between gender inequality and peak HIV prevalence in developing countries - an ecological study.

Science.gov (United States)

Kenyon, Chris R; Buyze, Jozefien

2015-01-01

The prevalence of both gender inequality and HIV prevalence vary considerably both within all developing countries and within those in sub-Saharan Africa. We test the hypothesis that the extent of gender inequality is associated with national peak HIV prevalence. Linear regression was used to test the association between national peak HIV prevalence and three markers of gender equality - the gender-related development index (GDI), the gender empowerment measure (GEM), and the gender inequality index (GII). No evidence was found of a positive relationship between gender inequality and HIV prevalence, either in the analyses of all developing countries or those limited to Africa. In the bivariate analyses limited to Africa, there was a positive association between the two measures of gender "equality" and peak HIV prevalence (GDI: coefficient 28, 95% confidence interval (CI) 9.1-46.8; GEM: coefficient 54.8, 95% CI 20.5-89.1). There was also a negative association between the marker of gender "inequality" and peak HIV prevalence (GII: coefficient -66.9, 95% CI -112.8 to -21.0). These associations all disappeared on multivariate analyses. We could not find any evidence to support the hypothesis that variations in the extent of gender inequality explain variations in HIV prevalence in developing countries.

Characterization of a high-intensity three-qubit GHZ state using state tomography and Gisin's inequality

Energy Technology Data Exchange (ETDEWEB)

Lu Huaixin, E-mail: huaixinlu@wfu.edu.c [Department of Physics and Electronic Science, Weifang University, Weifang, Shandong 261061 (China); Zhao Jiaqiang; Wang Xiaoqin [Department of Physics and Electronic Science, Weifang University, Weifang, Shandong 261061 (China)

2011-05-02

We experimentally characterized a high-intensity optical three-qubit Greenberger-Horne-Zeilinger (GHZ) states with a count of {approx}25/s by using the method of over-complete state tomography. Furthermore, based on the state, a convincing, 3.5 standard deviations, violation of Gisin's inequality has been measured, thus confirming the validity of Gisin's inequality for three-qubit GHZ states. From the data, we verified the good agreement of the experimental violation with the value predicted by quantum mechanics given the reconstructed density matrix. This result represents the first step towards the experimental implementation of Gisin's theorem. - Highlights: We have characterized a high-intensity three-qubit GHZ states. We have achieved convincing results of the violation of Gisin's inequalities. We verified the agreement of the experimental violation with theoretical value.

Volume Inequalities for Isotropic Measures

OpenAIRE

Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong

2006-01-01

A direct approach to Ball's simplex inequality is presented. This approach, which does not use the Brascamp-Lieb inequality, also gives Barthe's characterization of the simplex for Ball's inequality and extends it from discrete to arbitrary measures. It also yields the dual inequality, along with equality conditions, and it does both for arbitrary measures.

The Geography of Gender Inequality.

Science.gov (United States)

Fisher, Brendan; Naidoo, Robin

2016-01-01

Reducing gender inequality is a major policy concern worldwide, and one of the Sustainable Development Goals. However, our understanding of the magnitude and spatial distribution of gender inequality results either from limited-scale case studies or from national-level statistics. Here, we produce the first high resolution map of gender inequality by analyzing over 689,000 households in 47 countries. Across these countries, we find that male-headed households have, on average, 13% more asset wealth and 303% more land for agriculture than do female-headed households. However, this aggregate global result masks a high degree of spatial heterogeneity, with bands of both high inequality and high equality apparent in countries and regions of the world. Further, areas where inequality is highest when measured by land ownership generally are not the same areas that have high inequality as measured by asset wealth. Our metrics of gender inequality in land and wealth are not strongly correlated with existing metrics of poverty, development, and income inequality, and therefore provide new information to increase the understanding of one critical dimension of poverty across the globe.

The Interplay between socioeconomic inequalities and clinical oral health.

Science.gov (United States)

Steele, J; Shen, J; Tsakos, G; Fuller, E; Morris, S; Watt, R; Guarnizo-Herreño, C; Wildman, J

2015-01-01

Oral health inequalities associated with socioeconomic status are widely observed but may depend on the way that both oral health and socioeconomic status are measured. Our aim was to investigate inequalities using diverse indicators of oral health and 4 socioeconomic determinants, in the context of age and cohort. Multiple linear or logistic regressions were estimated for 7 oral health measures representing very different outcomes (2 caries prevalence measures, decayed/missing/filled teeth, 6-mm pockets, number of teeth, anterior spaces, and excellent oral health) against 4 socioeconomic measures (income, education, Index of Multiple Deprivation, and occupational social class) for adults aged ≥21 y in the 2009 UK Adult Dental Health Survey data set. Confounders were adjusted and marginal effects calculated. The results showed highly variable relationships for the different combinations of variables and that age group was critical, with different relationships at different ages. There were significant income inequalities in caries prevalence in the youngest age group, marginal effects of 0.10 to 0.18, representing a 10- to 18-percentage point increase in the probability of caries between the wealthiest and every other quintile, but there was not a clear gradient across the quintiles. With number of teeth as an outcome, there were significant income gradients after adjustment in older groups, up to 4.5 teeth (95% confidence interval, 2.2-6.8) between richest and poorest but none for the younger groups. For periodontal disease, income inequalities were mediated by other socioeconomic variables and smoking, while for anterior spaces, the relationships were age dependent and complex. In conclusion, oral health inequalities manifest in different ways in different age groups, representing age and cohort effects. Income sometimes has an independent relationship, but education and area of residence are also contributory. Appropriate choices of measures in relation to age

Immigration and income inequality

DEFF Research Database (Denmark)

Deding, Mette; Jakobsen, Vibeke; Azhar, Hussain

Four income inequality measures (Gini-coefficient, 90/10-decile ratio, and two generalized entropy indices) are applied to analyse immigrants’ income position relative to natives in a comparative perspective. Administrative data is used for Denmark, while survey data is used for Germany. We find...... higher inequality among immigrants than natives in Denmark, but vice versa for Germany. Over the period 1984-2003, this inequality gap has narrowed in both countries. At the same time, the contribution of immigrants to overall inequality has increased systematically, primarily caused by the increased...... share of immigrants in the population....

Graphing Inequalities, Connecting Meaning

Science.gov (United States)

Switzer, J. Matt

2014-01-01

Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…

The Growth-Inequality Association:

DEFF Research Database (Denmark)

Bjørnskov, Christian

2008-01-01

This note suggests that the association between income inequality and economic growth rates might arguably depend on the political ideology of incumbent governments. Estimates indicate that under leftwing governments, inequality is negatively associated with growth while the association is positive...... under rightwing governments. This may provide a qualification to recent studies of inequality....

Decomposing the Gini Inequality Index: An Expanded Solution with Survey Data Applied to Analyze Gender Income Inequality

Science.gov (United States)

Larraz, Beatriz

2015-01-01

The aim of this article is to propose a new breakdown of the Gini inequality ratio into three components ("within-group" inequality, "between-group" inequality, and intensity of "transvariation" between groups to the total inequality index). The between-group inequality concept computes all the differences in salaries…

Sparsity Prevention Pivoting Method for Linear Programming

DEFF Research Database (Denmark)

Li, Peiqiang; Li, Qiyuan; Li, Canbing

2018-01-01

When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper....... The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

Sparsity Prevention Pivoting Method for Linear Programming

DEFF Research Database (Denmark)

Li, Peiqiang; Li, Qiyuan; Li, Canbing

2018-01-01

. The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following......When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

Robust performance results for discrete-time systems

Directory of Open Access Journals (Sweden)

Mahmoud Magdi S.

1997-01-01

Full Text Available The problems of robust performance and feedback control synthesis for a class of linear discrete-time systems with time-varying parametric uncertainties are addressed in this paper. The uncertainties are bound and have a linear matrix fractional form. Based on the concept of strongly robust H ∞ -performance criterion, results of robust stability and performance are developed and expressed in easily computable linear matrix inequalities. Synthesis of robust feedback controllers is carried out for several system models of interest.

The sociogeometry of inequality: Part I

Science.gov (United States)

Eliazar, Iddo

2015-05-01

The study of socioeconomic inequality is of prime economic and social importance, and the key quantitative gauges of socioeconomic inequality are Lorenz curves and inequality indices-the most notable of the latter being the popular Gini index. In this series of papers we present a sociogeometric framework to the study of socioeconomic inequality. In this part we shift from the notion of Lorenz curves to the notion of Lorenz sets, define inequality indices in terms of Lorenz sets, and introduce and explore a collection of distance-based and width-based inequality indices stemming from the geometry of Lorenz sets. In particular, three principle diameters of Lorenz sets are established as meaningful quantitative gauges of socioeconomic inequality-thus indeed providing a geometric quantification of socioeconomic inequality.

Handbook of functional equations functional inequalities

CERN Document Server

2014-01-01

As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the  Riemann–Stieltjes integral, means and related functional inequalities, Weighted G...

Firming Up Inequality

OpenAIRE

Jae Song; David J. Price; Fatih Guvenen; Nicholas Bloom; Till von Wachter

2015-01-01

Earnings inequality in the United States has increased rapidly over the last three decades, but little is known about the role of firms in this trend. For example, how much of the rise in earnings inequality can be attributed to rising dispersion between firms in the average wages they pay, and how much is due to rising wage dispersion among workers within firms? Similarly, how did rising inequality affect the wage earnings of different types of workers working for the same employer—men vs. w...

Baby Booming Inequality? Demographic Change and Inequality in Norway, 1967{2004.

OpenAIRE

Almås, Ingvild; Havnes, Tarjei; Mogstad, Magne

2011-01-01

We demonstrate how age-adjusted inequality measures can be used to evaluate whether changes in inequality over time are because of changes in the age structure. In particular, we explore the hypothesis that the substantial rise in earnings inequality since the early 1980s is driven by the large baby boom cohorts approaching the peak of the age-earnings profile. Using administrative data on earnings for every Norwegian male over the period 1967-2004, we find that the impact of age ...

Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes

CERN Document Server

Liolios, A

2003-01-01

The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-theta method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-c...

Globalization and inequality

NARCIS (Netherlands)

Mills, Melinda

Globalization is increasingly linked to inequality, but with often divergent and polarized findings. Some researchers show that globalization accentuates inequality both within and between countries. Others maintain that these claims are patently incorrect, arguing that globalization has

Globalization, Inequality & International Economic Law

Directory of Open Access Journals (Sweden)

Frank J. Garcia

2017-04-01

Full Text Available International law in general, and international economic law in particular, to the extent that either has focused on the issue of inequality, has done so in terms of inequality between states. Largely overlooked has been the topic of inequality within states and how international law has influenced that reality. From the perspective of international economic law, the inequality issue is closely entwined with the topics of colonialism and post-colonialism, the proper meaning of development, and globalization. While international economic law has undoubtedly contributed to the rise of inequality, it is now vital that the subject of international economic law be examined for how it may contribute to the lessening of inequality. To do so will require a shift in the way that we think, in order to address inequality as a problem of an emerging global market society, and how best to regulate that society and its institutions.

The Geography of Gender Inequality.

Directory of Open Access Journals (Sweden)

Brendan Fisher

Full Text Available Reducing gender inequality is a major policy concern worldwide, and one of the Sustainable Development Goals. However, our understanding of the magnitude and spatial distribution of gender inequality results either from limited-scale case studies or from national-level statistics. Here, we produce the first high resolution map of gender inequality by analyzing over 689,000 households in 47 countries. Across these countries, we find that male-headed households have, on average, 13% more asset wealth and 303% more land for agriculture than do female-headed households. However, this aggregate global result masks a high degree of spatial heterogeneity, with bands of both high inequality and high equality apparent in countries and regions of the world. Further, areas where inequality is highest when measured by land ownership generally are not the same areas that have high inequality as measured by asset wealth. Our metrics of gender inequality in land and wealth are not strongly correlated with existing metrics of poverty, development, and income inequality, and therefore provide new information to increase the understanding of one critical dimension of poverty across the globe.

Global interpersonal inequality: Trends and measurement

DEFF Research Database (Denmark)

Niño-Zarazúa, Miguel; Roope, Laurence; Tarp, Finn

This paper discusses different approaches to the measurement of global interpersonal in equality. Trends in global interpersonal inequality during 1975-2005 are measured using data from UNU-WIDER’s World Income Inequality Database. In order to better understand the trends, global interpersonal...... inequality is decomposed into within-country and between-country inequality. The paper illustrates that the relationship between global interpersonal inequality and these constituent components is a complex one. In particular, we demonstrate that the changes in China’s and India’s income distributions over...... the past 30 years have simultaneously caused inequality to rise domestically in those countries, while tending to reduce global inter-personal inequality. In light of these findings, we reflect on the meaning and policy relevance of global vis-à-vis domestic inequality measures...

(Mis)perceptions of inequality.

Science.gov (United States)

Hauser, Oliver P; Norton, Michael I

2017-12-01

Laypeople's beliefs about the current distribution of outcomes such as income and wealth in their country influence their attitudes toward issues ranging from taxation to healthcare - but how accurate are these beliefs? We review the burgeoning literature on (mis)perceptions of inequality. First, we show that people on average misperceive current levels of inequality, typically underestimating the extent of inequality in their country. Second, we delineate potential causes of these misperceptions, including people's overreliance on cues from their local environment, leading to their erroneous beliefs about both the overall distributions of wealth and income and their place in those distributions. Third, we document that these (mis)perceptions of inequality - but not actual levels of inequality - drive behavior and preferences for redistribution. More promisingly, we review research suggesting that correcting misperceptions influences preferences and policy outcomes. Copyright © 2017 Elsevier Ltd. All rights reserved.

Matrix transformations and sequence spaces

International Nuclear Information System (INIS)

Nanda, S.

1983-06-01

In most cases the most general linear operator from one sequence space into another is actually given by an infinite matrix and therefore the theory of matrix transformations has always been of great interest in the study of sequence spaces. The study of general theory of matrix transformations was motivated by the special results in summability theory. This paper is a review article which gives almost all known results on matrix transformations. This also suggests a number of open problems for further study and will be very useful for research workers. (author)

Handling of computational in vitro/in vivo correlation problems by Microsoft Excel: IV. Generalized matrix analysis of linear compartment systems.

Science.gov (United States)

Langenbucher, Frieder

2005-01-01

A linear system comprising n compartments is completely defined by the rate constants between any of the compartments and the initial condition in which compartment(s) the drug is present at the beginning. The generalized solution is the time profiles of drug amount in each compartment, described by polyexponential equations. Based on standard matrix operations, an Excel worksheet computes the rate constants and the coefficients, finally the full time profiles for a specified range of time values.

Wringing out better Bell inequalities

International Nuclear Information System (INIS)

Braunstein, S.L.; Caves, C.M.

1989-01-01

Local realism implies constraints on the statistics of two physically separated systems. These constraints, known collectively as Bell inequalities, can be violated by quantum mechanics. We generalize the standard Bell inequalities in two ways: first, by 'chaining' the Clauser-Horne-Shimony-Holt Bell inequality for two-state systems and, second, by formulating information-theoretic Bell inequalities that apply to any pair of systems. (orig.)

Looking for symmetric Bell inequalities

Energy Technology Data Exchange (ETDEWEB)

Bancal, Jean-Daniel; Gisin, Nicolas [Group of Applied Physics, University of Geneva, 20 rue de l' Ecole-de Medecine, CH-1211 Geneva 4 (Switzerland); Pironio, Stefano, E-mail: jean-daniel.bancal@unige.c [Laboratoire d' Information Quantique, Universite Libre de Bruxelles (Belgium)

2010-09-24

Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins-Gisin-Linden-Massar-Popescu type.

Looking for symmetric Bell inequalities

International Nuclear Information System (INIS)

Bancal, Jean-Daniel; Gisin, Nicolas; Pironio, Stefano

2010-01-01

Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins-Gisin-Linden-Massar-Popescu type.

Health inequality - determinants and policies

DEFF Research Database (Denmark)

Diderichsen, Finn; Andersen, Ingelise; Manual, Celie

2012-01-01

The review ”Health inequality – determinants and policies” identifies key-areas to be addressed with the aim to reduce the social inequality in health. The general life expectancy has steadily been increasing, but the data reveals marked social inequalities in health as well as life expectancy....... The review seeks to identify the causes of this social inequality. The analysis finds 12 areas of great importance for the inequality in health. This is i.e. early child development, schooling and education, the health behavior of the population, and the role of the health system. Within each of the 12 areas...

Post-1500 Population Flows and the Long Run Determinants of Economic Growth and Inequality.

Science.gov (United States)

Putterman, Louis; Weil, David N

2010-01-01

We construct a matrix showing the share of the year 2000 population in every country that is descended from people in different source countries in the year 1500. Using the matrix to adjust indicators of early development so they reflect the history of a population's ancestors rather than the history of the place they live today greatly improves the ability of those indicators to predict current GDP. The variance of early development history of a country's inhabitants is a good predictor for current inequality, with ethnic groups originating in regions having longer histories of organized states tending to be at the upper end of a country's income distribution.

Non-commutative Nash inequalities

International Nuclear Information System (INIS)

Kastoryano, Michael; Temme, Kristan

2016-01-01

A set of functional inequalities—called Nash inequalities—are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative L p spaces, where their relationship to Poincaré and log-Sobolev inequalities is fleshed out. We prove Nash inequalities for a number of unital reversible semigroups

adapta~k>n -11 of the surrogate memods for linear programming ...

African Journals Online (AJOL)

2005-08-02

Aug 2, 2005 ... inequality problem is made uj~ of the primal and dual optimal solutions for the given primal ... KEYWORDS: Linear Programming, Duality Theory, Surrogate Methods. ..... replaces x and the process IS repeated with the new x.

Two-step algorithm of generalized PAPA method applied to linear programming solution of dynamic matrix control

International Nuclear Information System (INIS)

Shimizu, Yoshiaki

1991-01-01

In recent complicated nuclear systems, there are increasing demands for developing highly advanced procedures for various problems-solvings. Among them keen interests have been paid on man-machine communications to improve both safety and economy factors. Many optimization methods have been good enough to elaborate on these points. In this preliminary note, we will concern with application of linear programming (LP) for this purpose. First we will present a new superior version of the generalized PAPA method (GEPAPA) to solve LP problems. We will then examine its effectiveness when applied to derive dynamic matrix control (DMC) as the LP solution. The approach is to aim at the above goal through a quality control of process that will appear in the system. (author)

Socioeconomic status and health : A new approach to the measurement of bivariate inequality

NARCIS (Netherlands)

Erreygers, G.; Kessels, R.

2017-01-01

We suggest an alternative way to construct a family of indices of socioeconomic inequality of health. Our indices belong to the broad category of linear indices. In contrast to rank-dependent indices, which are defined in terms of the ranks of the socioeconomic variable and the levels of the health

Social inequality: philosophical and sociological reflection

Directory of Open Access Journals (Sweden)

A. Sh. Victorov

2014-01-01

Full Text Available Social inequality is the phenomena that is hypothetically the base for first human communities genesis. Modern model for capitalist society as market relations form fails to satisfy the needs of society’s social development, and strongly requires to create new social knowledge structure and new approach for inequality sociology theory development. Our study conceptual logic comprises routine, philosophic and ideological reflexions analysis to create new social inequality definition in the context of new sociologic knowledge structure. Social inequality is the one of key problems in global sociology; the need is obvious to extract social inequality into separate discipline. Inequality sociology target is the decision of theoretical and practical problems in the formation of comprehensive knowledge about inequality phenomena in modern community, and in the development of common and specialized theoretical-methodological base for inequality study.

Matrix groups for undergraduates

CERN Document Server

Tapp, Kristopher

2005-01-01

Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.

Quantum mechanics and Bell's inequalities

International Nuclear Information System (INIS)

Jones, R.T.; Adelberger, E.G.

1994-01-01

Santos argues that, if one interprets probabilities as ratios of detected events to copies of the physical system initially prepared, the quantum mechanical predictions for the classic tests of Bell's inequalities do not violate the inequalities. Furthermore, he suggests that quantum mechanical states which do violate the inequalities are not physically realizable. We discuss a physically realizable experiment, meeting his requirements, where quantum mechanics does violate the inequalities

Global chaos synchronization of coupled parametrically excited ...

Indian Academy of Sciences (India)

In this paper, we study the synchronization behaviour of two linearly coupled parametrically excited chaotic pendula. The stability of the synchronized state is examined using Lyapunov stability theory and linear matrix inequality (LMI); and some sufficient criteria for global asymptotic synchronization are derived from which ...

Finite-time stability of neutral-type neural networks with random time-varying delays

Science.gov (United States)

Ali, M. Syed; Saravanan, S.; Zhu, Quanxin

2017-11-01

This paper is devoted to the finite-time stability analysis of neutral-type neural networks with random time-varying delays. The randomly time-varying delays are characterised by Bernoulli stochastic variable. This result can be extended to analysis and design for neutral-type neural networks with random time-varying delays. On the basis of this paper, we constructed suitable Lyapunov-Krasovskii functional together and established a set of sufficient linear matrix inequalities approach to guarantee the finite-time stability of the system concerned. By employing the Jensen's inequality, free-weighting matrix method and Wirtinger's double integral inequality, the proposed conditions are derived and two numerical examples are addressed for the effectiveness of the developed techniques.

International Conference on Matrix Analysis and its Applications 2015

CERN Document Server

2017-01-01

This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas. With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on Matrix Analysis and its Applications 2015, held in Coimbra, Portugal, was the sixth in a series of conferences. Applied and Computational Matrix Analysis will appeal to graduate students and researchers in theoretical and applied mathematics, physics and engineering who are seeking an overview of recent problems and methods in matrix analysis.

The Oxford handbook of economic inequality

NARCIS (Netherlands)

Salverda, W.; Nolan, B.; Smeeding, T.M.

2009-01-01

The essential guide for students and researchers interested in economic inequality Contains 27 original research contributions from the top names in economic inequality. The Oxford Handbook of Economic Inequality presents a new and challenging analysis of economic inequality, focusing primarily on

Robust decentralised PI based LFC design for time delay power systems

International Nuclear Information System (INIS)

Bevrani, Hassan; Hiyama, Takashi

2008-01-01

In this paper, two robust decentralised proportional integral (PI) control designs are proposed for load frequency control (LFC) with communication delays. In both methodologies, the PI based LFC problem is reduced to a static output feedback (SOF) control synthesis for a multiple delay system. The first one is based on the optimal H ∞ control design using a linear matrix inequalities (LMI) technique. The second control design gives a suboptimal solution using a developed iterative linear matrix inequalities (ILMI) algorithm via the mixed H 2 /H ∞ control technique. The control strategies are suitable for LFC applications that usually employ PI control. The proposed control strategies are applied to a three control area power system with time delays and load disturbance to demonstrate their robustness

Income-related inequality and inequity in the use of dental services in Finland after a major subsidization reform.

Science.gov (United States)

Raittio, Eero; Kiiskinen, Urpo; Helminen, Sari; Aromaa, Arpo; Suominen, Anna Liisa

2015-06-01

In Finland, a major oral healthcare reform (OHCR), implemented during 2001-2002, opened the public dental services (PDS) and extended subsidies for private dental services to entire adult population. Before the reform, adults born earlier than 1956 were not entitled to use PDS nor did they receive any reimbursements for their private dental costs. We aimed to examine changes in the income-related inequality and inequity in the use of dental services among the adult Finns after the reform. Representative data from Finnish adults born in 1970 or earlier were gathered from three identical postal surveys concerning the use of dental services and subjective perceptions of oral health. Those surveys were conducted before the OHCR in 2001 (n = 1907) and after the OHCR in 2004 (n = 1629) and 2007 (n = 1509). We used concentration index and its decomposition to analyse income-related inequality and inequity in the use of dental services and factors associated with them. Results showed that pro-rich inequality and inequity in the overall use of dental services narrowed from 2001 to 2004. However, between 2004 and 2007, pro-rich inequality and inequity widened, so it returned to a rather similar level in 2007 as it had been in 2001. Most of the pro-rich inequality and inequity were related to regular dental visiting habit and income level. While there was pro-poor inequality and inequity in the use of PDS, there was pro-rich inequality and inequity in the use of private dental services throughout the study years. It seems that income-related inequality and inequity in the use of dental services narrowed only temporarily after the reform. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Functional Bell inequalities can serve as a stronger entanglement witness than conventional Bell inequalities

International Nuclear Information System (INIS)

Sen, Aditi; Sen, Ujjwal; Zukowski, Marek

2002-01-01

We consider a Bell inequality for a continuous range of settings of the apparatus at each site. This 'functional' Bell inequality gives a better range of violation for generalized Greenberger, Horne, and Zeilinger states. Also a family of N-qubit bound entangled states violate this inequality for N>5

Linear methods in band theory

DEFF Research Database (Denmark)

Andersen, O. Krogh

1975-01-01

of Korringa-Kohn-Rostoker, linear-combination-of-atomic-orbitals, and cellular methods; the secular matrix is linear in energy, the overlap integrals factorize as potential parameters and structure constants, the latter are canonical in the sense that they neither depend on the energy nor the cell volume...

[Inequalities in health in Italy].

Science.gov (United States)

Caiazzo, Antonio; Cardano, Mario; Cois, Ester; Costa, Giuseppe; Marinacci, Chiara; Spadea, Teresa; Vannoni, Francesca; Venturini, Lorenzo

2004-01-01

Socioeconomic inequality and its impact on health is a growing concern in the European public health debate. In many countries, the issue is moving away from description towards the identification of the determinants of inequalities and the development of policies explicitly aimed at reducing inequalities in health. In Italy, ten years after the publication of the first report on inequalities in health, this topic is seldom present on the agenda of public policy makers. The purpose of this report is to update the Italian profile of social variation in health and health care in order to stimulate the debate on ways to tackle inequalities in health that are preventable. In the first section of this book, the threefold objective is to describe the principal mechanisms involved in the generation of social inequalities in health (Introduction); to report Italian data on the distribution and magnitude of this phenomenon in the last decade; and to evaluate policies and interventions in both the social (chapter 1.9, Section I) and the health sector (chapter 2.3, Section I), which are potentially useful to reduce health inequalities. It is intended for anyone who is in a position to contribute t o decision-making that will benefit the health of communities. For this reason, chapters are organized by specific determinants of inequalities on which interentions may have an impact. The methodological approach in the second section focuses on the best methods to monitor social inequalities including recommendations on social indicators, sources of information and study models, based on European guidelines revised for the Italian situation. According to data from national and local studies, mortality increases linearly with social disadvantage for a wide range of indicators at both the individual (education, social class, income, quality of housing) and the geographical level (deprivation indexes computed at different levels of aggregation). This positive correlation is evident

Investigating the impact of the English health inequalities strategy: time trend analysis.

Science.gov (United States)

Barr, Ben; Higgerson, James; Whitehead, Margaret

2017-07-26

Objective  To investigate whether the English health inequalities strategy was associated with a decline in geographical health inequalities, compared with trends before and after the strategy. Design  Time trend analysis. Setting  Two groups of lower tier local authorities in England. The most deprived, bottom fifth and the rest of England. Intervention  The English health inequalities strategy-a cross government strategy implemented between 1997 and 2010 to reduce health inequalities in England. Trends in geographical health inequalities were assessed before (1983-2003), during (2004-12), and after (2013-15) the strategy using segmented linear regression. Main outcome measure  Geographical health inequalities measured as the relative and absolute differences in male and female life expectancy at birth between the most deprived local authorities in England and the rest of the country. Results  Before the strategy the gap in male and female life expectancy between the most deprived local authorities in England and the rest of the country increased at a rate of 0.57 months each year (95% confidence interval 0.40 to 0.74 months) and 0.30 months each year (0.12 to 0.48 months). During the strategy period this trend reversed and the gap in life expectancy for men reduced by 0.91 months each year (0.54 to 1.27 months) and for women by 0.50 months each year (0.15 to 0.86 months). Since the end of the strategy period the inequality gap has increased again at a rate of 0.68 months each year (-0.20 to 1.56 months) for men and 0.31 months each year (-0.26 to 0.88) for women. By 2012 the gap in male life expectancy was 1.2 years smaller (95% confidence interval 0.8 to 1.5 years smaller) and the gap in female life expectancy was 0.6 years smaller (0.3 to 1.0 years smaller) than it would have been if the trends in inequalities before the strategy had continued. Conclusion  The English health inequalities strategy was associated with a decline in geographical inequalities

Performance evaluation of matrix gradient coils.

Science.gov (United States)

Jia, Feng; Schultz, Gerrit; Testud, Frederik; Welz, Anna Masako; Weber, Hans; Littin, Sebastian; Yu, Huijun; Hennig, Jürgen; Zaitsev, Maxim

2016-02-01

In this paper, we present a new performance measure of a matrix coil (also known as multi-coil) from the perspective of efficient, local, non-linear encoding without explicitly considering target encoding fields. An optimization problem based on a joint optimization for the non-linear encoding fields is formulated. Based on the derived objective function, a figure of merit of a matrix coil is defined, which is a generalization of a previously known resistive figure of merit for traditional gradient coils. A cylindrical matrix coil design with a high number of elements is used to illustrate the proposed performance measure. The results are analyzed to reveal novel features of matrix coil designs, which allowed us to optimize coil parameters, such as number of coil elements. A comparison to a scaled, existing multi-coil is also provided to demonstrate the use of the proposed performance parameter. The assessment of a matrix gradient coil profits from using a single performance parameter that takes the local encoding performance of the coil into account in relation to the dissipated power.

Generalised Assignment Matrix Methodology in Linear Programming

Science.gov (United States)

Jerome, Lawrence

2012-01-01

Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

Income inequality, disinvestment in health care and use of dental services.

Science.gov (United States)

Bhandari, Bishal; Newton, Jonathan T; Bernabé, Eduardo

2015-01-01

To explore the interrelationships between income inequality, disinvestment in health care, and use of dental services at country level. This study pooled national estimates for use of dental services among adults aged 18 years or older from the 70 countries that participated in the World Health Survey from 2002 to 2004, together with aggregate data on national income (GDP per capita), income inequality (Gini coefficient), and disinvestment in health care (total health expenditure and dentist-to-population ratio) from various international sources. Use of dental services was defined as having had dental problems in the last 12 months and having received any treatment to address those needs. Associations between variables were explored using Pearson correlation coefficients and linear regression. Data from 63 countries representing the six WHO regions were analyzed. Use of dental services was negatively correlated with Gini coefficient (Pearson correlation coefficient -0.48, P dental services was attenuated but remained significant after adjustments for GDP per capita, total health expenditure, and dentist-to-population ratio (regression coefficient -0.36; 95% CI -0.57, -0.15). This study shows an inverse relationship between income inequality and use of dental services. Of the two indicators of disinvestment in health care assessed, only dentist-to-population ratio was associated with income inequality and use of dental services. © 2014 American Association of Public Health Dentistry.

Doubling inequalities for anisotropic plate equations and applications to size estimates of inclusions

International Nuclear Information System (INIS)

Di Cristo, M; Lin, C-L; Morassi, A; Rosset, E; Vessella, S; Wang, J-N

2013-01-01

We prove the upper and lower estimates of the area of an unknown elastic inclusion in a thin plate by one boundary measurement. The plate is made of non-homogeneous linearly elastic material belonging to a general class of anisotropy and the domain of the inclusion is a measurable subset of the plate. The size estimates are expressed in terms of the work exerted by a couple field applied at the boundary and of the induced transversal displacement and its normal derivative taken at the boundary of the plate. The main new mathematical tool is a doubling inequality for solutions to fourth-order elliptic equations whose principal part P(x, D) is the product of two second-order elliptic operators P 1 (x, D), P 2 (x, D) such that P 1 (0, D) = P 2 (0, D). The proof of the doubling inequality is based on the Carleman method, a sharp three-spheres inequality and a bootstrapping argument. (paper)

Exploring linear algebra labs and projects with Mathematica

CERN Document Server

Arangala, Crista

2014-01-01

Matrix Operations Lab 0: An Introduction to Mathematica Lab 1: Matrix Basics and Operations Lab 2: A Matrix Representation of Linear Systems Lab 3: Powers, Inverses, and Special Matrices Lab 4: Graph Theory and Adjacency Matrices Lab 5: Permutations and Determinants Lab 6: 4 x 4 Determinants and Beyond Project Set 1 Invertibility Lab 7: Singular or Nonsingular? Why Singularity Matters Lab 8: Mod It Out, Matrices with Entries in ZpLab 9: It's a Complex World Lab 10: Declaring Independence: Is It Linear? Project Set 2 Vector Spaces Lab 11: Vector Spaces and SubspacesLab 12: Basing It All on Just a Few Vectors Lab 13: Linear Transformations Lab 14: Eigenvalues and Eigenspaces Lab 15: Markov Chains, An Application of Eigenvalues Project Set 3 Orthogonality Lab 16: Inner Product Spaces Lab 17: The Geometry of Vector and Inner Product SpacesLab 18: Orthogonal Matrices, QR Decomposition, and Least Squares Regression Lab 19: Symmetric Matrices and Quadratic Forms Project Set 4 Matrix Decomposition with Applications L...

Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks

International Nuclear Information System (INIS)

Mathiyalagan, K.; Sakthivel, R.; Marshal Anthoni, S.

2012-01-01

This Letter addresses the stability analysis problem for a class of uncertain discrete-time stochastic fuzzy neural networks (DSFNNs) with time-varying delays. By constructing a new Lyapunov–Krasovskii functional combined with the free weighting matrix technique, a new set of delay-dependent sufficient conditions for the robust exponential stability of the considered DSFNNs is established in terms of Linear Matrix Inequalities (LMIs). Finally, numerical examples with simulation results are provided to illustrate the applicability and usefulness of the obtained theory. -- Highlights: ► Applications of neural networks require the knowledge of dynamic behaviors. ► Exponential stability of discrete-time stochastic fuzzy neural networks is studied. ► Linear matrix inequality optimization approach is used to obtain the result. ► Delay-dependent stability criterion is established in terms of LMIs. ► Examples with simulation are provided to show the effectiveness of the result.

Optimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions

KAUST Repository

Muhamadiev, È rgash; Nazarov, Murtazo

2015-01-01

© 2014 Elsevier Inc. In this paper the interpolation inequality of Szepessy [12, Lemma 4.2] is revisited. The lower bound in the above reference is proven to be proportional to p^-2, where p is a polynomial degree, that goes fast to zero

Brokerage in Cross-Border Mobility: Social Mechanisms and the (ReProduction of Social Inequalities

Directory of Open Access Journals (Sweden)

Thomas Faist

2014-12-01

Full Text Available Brokerage is an essential yet understudied function in social life. In one of the classics in the field of sociology, Georg Simmel differentiated three types of the “third” which help to analyse brokerage: the disinterested mediator or arbitrator, tertius gaudens and divide et impera. Studies that conceptualise traffickers and smugglers as brokers are extremely rare. Scholars lack a typology which can serve as a basis for comparative research. To advance scholarship on brokerage this article seeks to develop a conceptual-typological matrix by setting out to explore three questions: Why does brokerage exist? What kind of social mechanism is brokerage? What are the implications of brokerage for social inequalities and equalities? The analysis concludes with the consequences of different types of brokerage for the (reproduction of social inequalities.

Inequality in OECD countries.

Science.gov (United States)

Thévenot, Celine

2017-08-01

This article recalls the state of play of inequality levels and trends in OECD countries, with a special focus on Nordic countries. It sheds light on explaining the drivers of the rise in inequality and its economic consequences. It addresses in particular the issue of redistribution through taxes and transfers. It concludes with an overview of policy packages that should be considered to address the issue of rising inequalities.

An Explicit Consistent Geometric Stiffness Matrix for the DKT Element

Directory of Open Access Journals (Sweden)

Eliseu Lucena Neto

Full Text Available Abstract A large number of references dealing with the geometric stiffness matrix of the DKT finite element exist in the literature, where nearly all of them adopt an inconsistent form. While such a matrix may be part of the element to treat nonlinear problems in general, it is of crucial importance for linearized buckling analysis. The present work seems to be the first to obtain an explicit expression for this matrix in a consistent way. Numerical results on linear buckling of plates assess the element performance either with the proposed explicit consistent matrix, or with the most commonly used inconsistent matrix.

Globally exponential synchronization in an array of asymmetric coupled neural networks

International Nuclear Information System (INIS)

Lu Jianquan; Ho, Daniel W.C.; Liu Ming

2007-01-01

In this Letter, we study the globally exponential synchronization in an array of linearly coupled neural networks with delayed coupling. The coupling configuration matrix is assumed to be asymmetric, which is more coincident with the real-world network. The difficulty arising from the asymmetry of the coupling matrix has been overcame in this work. Some synchronization criteria are given in terms of strict linear matrix inequalities (LMIs), which can be efficiently solved by using interior point algorithm. Some previous synchronization results are generalized. Numerical simulation is also given to verify our theoretical analysis

Income Inequality: Impact of Inequality Measures on Crimes An Analysis of the State of New Jersey

Directory of Open Access Journals (Sweden)

Bertram C. Ifeanyi OKPOKWASILI

2016-05-01

Full Text Available This research used time-series data for the 50 year period of 1964 to 2014 to investigate the relationship between income inequalities and crimes in the state of New Jersey, United States of America. It found that income inequality had a significant relationship to all four types of crime measured – murder, forcible rape, aggravated assault and property crimes. Statistical significance would seem to depend on the model and inequality measure used. A log-log relationship existed between inequalities and all the crimes. Different inequality measures enabled different measures of significance. It also found that it was possible to come to different conclusions with respect to the relationships by using different inequality measures- the Gini and the 20/20 measures in our case.

Fast and scalable inequality joins

KAUST Repository

Khayyat, Zuhair

2016-09-07

Inequality joins, which is to join relations with inequality conditions, are used in various applications. Optimizing joins has been the subject of intensive research ranging from efficient join algorithms such as sort-merge join, to the use of efficient indices such as (Formula presented.)-tree, (Formula presented.)-tree and Bitmap. However, inequality joins have received little attention and queries containing such joins are notably very slow. In this paper, we introduce fast inequality join algorithms based on sorted arrays and space-efficient bit-arrays. We further introduce a simple method to estimate the selectivity of inequality joins which is then used to optimize multiple predicate queries and multi-way joins. Moreover, we study an incremental inequality join algorithm to handle scenarios where data keeps changing. We have implemented a centralized version of these algorithms on top of PostgreSQL, a distributed version on top of Spark SQL, and an existing data cleaning system, Nadeef. By comparing our algorithms against well-known optimization techniques for inequality joins, we show our solution is more scalable and several orders of magnitude faster. © 2016 Springer-Verlag Berlin Heidelberg

Health Inequalities in Global Context

Science.gov (United States)

Beckfield, Jason; Olafsdottir, Sigrun

2017-01-01

The existence of social inequalities in health is well established. One strand of research focuses on inequalities in health within a single country. A separate and newer strand of research focuses on the relationship between inequality and average population health across countries. Despite the theorization of (presumably variable) social conditions as “fundamental causes” of disease and health, the cross-national literature has focused on average, aggregate population health as the central outcome. Controversies currently surround macro-structural determinants of overall population health such as income inequality. We advance and redirect these debates by conceptualizing inequalities in health as cross-national variables that are sensitive to social conditions. Using data from 48 World Values Survey countries, representing 74% of the world’s population, we examine cross-national variation in inequalities in health. The results reveal substantial variation in health inequalities according to income, education, sex, and migrant status. While higher socioeconomic position is associated with better self-rated health around the globe, the size of the association varies across institutional context, and across dimensions of stratification. There is some evidence that education and income are more strongly associated with self-rated health than sex or migrant status. PMID:29104292

New Sufficient LMI Conditions for Static Output Stabilization

DEFF Research Database (Denmark)

Adegas, Fabiano Daher

2014-01-01

This paper presents new linear matrix inequality conditions to the static output feedback stabilization problem. Although the conditions are only sufficient, numerical experiments show excellent success rates in finding a stabilizing controller....

Inequalities in global health inequalities research: A 50-year bibliometric analysis (1966-2015)

Science.gov (United States)

Pericàs, Juan M.; Benach, Joan

2018-01-01

Background Increasing evidence shows that health inequalities exist between and within countries, and emphasis has been placed on strengthening the production and use of the global health inequalities research, so as to improve capacities to act. Yet, a comprehensive overview of this evidence base is still needed, to determine what is known about the global and historical scientific production on health inequalities to date, how is it distributed in terms of country income groups and world regions, how has it changed over time, and what international collaboration dynamics exist. Methods A comprehensive bibliometric analysis of the global scientific production on health inequalities, from 1966 to 2015, was conducted using Scopus database. The historical and global evolution of the study of health inequalities was considered, and through joinpoint regression analysis and visualisation network maps, the preceding questions were examined. Findings 159 countries (via authorship affiliation) contributed to this scientific production, three times as many countries than previously found. Scientific output on health inequalities has exponentially grown over the last five decades, with several marked shift points, and a visible country-income group affiliation gradient in the initiation and consistent publication frequency. Higher income countries, especially Anglo-Saxon and European countries, disproportionately dominate first and co-authorship, and are at the core of the global collaborative research networks, with the Global South on the periphery. However, several country anomalies exist that suggest that the causes of these research inequalities, and potential underlying dependencies, run deeper than simply differences in country income and language. Conclusions Whilst the global evidence base has expanded, Global North-South research gaps exist, persist and, in some cases, are widening. Greater understanding of the structural determinants of these research

Isoperimetric inequalities for minimal graphs

International Nuclear Information System (INIS)

Pacelli Bessa, G.; Montenegro, J.F.

2007-09-01

Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal graphs in N x R. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fundamental form. (author)

Gender Inequality and Trade

OpenAIRE

Busse, Matthias; Spielmann, Christian

2004-01-01

The paper empirically explores the international linkages between gender inequality and trade flows of a sample of 92 developed and developing countries. The focus is on comparative advantage in labour-intensive manufactured goods. The results indicate that gender wage inequality is positively associated with comparative advantage in labour-intensive goods, that is, countries with a larger gender wage gap have higher exports of these goods. Also, gender inequality in labour force activity rat...

A convex optimization approach for solving large scale linear systems

Directory of Open Access Journals (Sweden)

Debora Cores

2017-01-01

Full Text Available The well-known Conjugate Gradient (CG method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.

Discrimination, perceived social inequity, and mental health among rural-to-urban migrants in China.

Science.gov (United States)

Lin, Danhua; Li, Xiaoming; Wang, Bo; Hong, Yan; Fang, Xiaoyi; Qin, Xiong; Stanton, Bonita

2011-04-01

Status-based discrimination and inequity have been associated with the process of migration, especially with economics-driven internal migration. However, their association with mental health among economy-driven internal migrants in developing countries is rarely assessed. This study examines discriminatory experiences and perceived social inequity in relation to mental health status among rural-to-urban migrants in China. Cross-sectional data were collected from 1,006 rural-to-urban migrants in 2004-2005 in Beijing, China. Participants reported their perceptions and experiences of being discriminated in daily life in urban destination and perceived social inequity. Mental health was measured using the symptom checklist-90 (SCL-90). Multivariate analyses using general linear model were performed to test the effect of discriminatory experience and perceived social inequity on mental health. Experience of discrimination was positively associated with male gender, being married at least once, poorer health status, shorter duration of migration, and middle range of personal income. Likewise, perceived social inequity was associated with poorer health status, higher education attainment, and lower personal income. Multivariate analyses indicate that both experience of discrimination and perceived social inequity were strongly associated with mental health problems of rural-to-urban migrants. Experience of discrimination in daily life and perceived social inequity have a significant influence on mental health among rural-to-urban migrants. The findings underscore the needs to reduce public or societal discrimination against rural-to-urban migrants, to eliminate structural barriers (i.e., dual household registrations) for migrants to fully benefit from the urban economic development, and to create a positive atmosphere to improve migrant's psychological well-being.

On T-solutions of degenerate anisotropic elliptic variational inequalities with L1-data

International Nuclear Information System (INIS)

Kovalevsky, Alexander A; Gorban, Yuliya S

2011-01-01

We introduce the notions of T-solutions and shift T-solutions of variational inequalities corresponding to a non-linear degenerate anisotropic elliptic operator, a constraint set in a sufficiently large class, and an L 1 -right-hand side. We prove theorems on the existence and uniqueness of such solutions and describe their properties. While the notion of T-solution is defined only when the constraint set contains at least one bounded function, the notion of shift T-solution does not require this condition. We describe the relation between these notions and prove that these types of solutions of a variational inequality coincide with ordinary solutions whenever the right-hand side is sufficiently regular.

Conference on Inequalities and Applications

CERN Document Server

Losonczi, László; Gilányi, Attila; Páles, Zsolt; Plum, Michael

2009-01-01

Inequalities continue to play an essential role in mathematics. Perhaps, they form the last field comprehended and used by mathematicians in all areas of the discipline. Since the seminal work Inequalities (1934) by Hardy, Littlewood and Pólya, mathematicians have laboured to extend and sharpen their classical inequalities. New inequalities are discovered every year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. The study of inequalities reflects the many and various aspects of mathematics. On one hand, there is the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand, the subject is the source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are numerous applications in a wide variety of fields, from mathematical physics to biology and economics. This volume contains the contributions of the participants of th...

The sociogeometry of inequality: Part II

Science.gov (United States)

Eliazar, Iddo

2015-05-01

The study of socioeconomic inequality is of prime economic and social importance, and the key quantitative gauges of socioeconomic inequality are Lorenz curves and inequality indices - the most notable of the latter being the popular Gini index. In this series of papers we present a sociogeometric framework to the study of socioeconomic inequality. In this part we focus on the gap between the rich and the poor, which is quantified by gauges termed disparity curves. We shift from disparity curves to disparity sets, define inequality indices in terms of disparity sets, and introduce and explore a collection of distance-based and width-based inequality indices stemming from the geometry of disparity sets. We conclude with mean-absolute-deviation (MAD) representations of the inequality indices established in this series of papers, and with a comparison of these indices to the popular Gini index.

Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

NARCIS (Netherlands)

R.A. Zuidwijk (Rob)

2005-01-01

textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an

More on operator Bellman inequality | Mirzapour | Quaestiones ...

African Journals Online (AJOL)

We present a Bellman inequality involving operator means for operators acting on a Hilbert space. We also give some Bellman inequalities concerning sesquilinear forms. Finally, we re ne the Jensen's operator inequality and use it for obtaining a re nement of the Bellman operator inequality. Keywords: Bellman inequality ...

Socioeconomic Inequalities in Health and Perceived Unmet Needs for Healthcare among the Elderly in Germany

Directory of Open Access Journals (Sweden)

Jens Hoebel

2017-09-01

Full Text Available Research into health inequalities in the elderly population of Germany is relatively scarce. This study examines socioeconomic inequalities in health and perceived unmet needs for healthcare and explores the dynamics of health inequalities with age among elderly people in Germany. Data were derived from the Robert Koch Institute’s cross-sectional German Health Update study. The sample was restricted to participants aged 50–85 years (n = 11,811. Socioeconomic status (SES was measured based on education, (former occupation, and income. Odds ratios and prevalence differences were estimated using logistic regression and linear probability models, respectively. Our results show that self-reported health problems were more prevalent among men and women with lower SES. The extent of SES-related health inequalities decreased at older ages, predominantly among men. Although the prevalence of perceived unmet needs for healthcare was low overall, low SES was associated with higher perceptions of unmet needs in both sexes and for several kinds of health services. In conclusion, socioeconomic inequalities in health exist in a late working age and early retirement but may narrow at older ages, particularly among men. Socially disadvantaged elderly people perceive greater barriers to accessing healthcare services than those who are better off.

An MCMC method for the evaluation of the Fisher information matrix for non-linear mixed effect models.

Science.gov (United States)

Riviere, Marie-Karelle; Ueckert, Sebastian; Mentré, France

2016-10-01

Non-linear mixed effect models (NLMEMs) are widely used for the analysis of longitudinal data. To design these studies, optimal design based on the expected Fisher information matrix (FIM) can be used instead of performing time-consuming clinical trial simulations. In recent years, estimation algorithms for NLMEMs have transitioned from linearization toward more exact higher-order methods. Optimal design, on the other hand, has mainly relied on first-order (FO) linearization to calculate the FIM. Although efficient in general, FO cannot be applied to complex non-linear models and with difficulty in studies with discrete data. We propose an approach to evaluate the expected FIM in NLMEMs for both discrete and continuous outcomes. We used Markov Chain Monte Carlo (MCMC) to integrate the derivatives of the log-likelihood over the random effects, and Monte Carlo to evaluate its expectation w.r.t. the observations. Our method was implemented in R using Stan, which efficiently draws MCMC samples and calculates partial derivatives of the log-likelihood. Evaluated on several examples, our approach showed good performance with relative standard errors (RSEs) close to those obtained by simulations. We studied the influence of the number of MC and MCMC samples and computed the uncertainty of the FIM evaluation. We also compared our approach to Adaptive Gaussian Quadrature, Laplace approximation, and FO. Our method is available in R-package MIXFIM and can be used to evaluate the FIM, its determinant with confidence intervals (CIs), and RSEs with CIs. © The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Three experimental tests of Bell's inequalities by measurement of polarization correlation of photons

International Nuclear Information System (INIS)

Aspect, A.

1983-02-01

We have performed three experimental tests of Bell's inequalities by measuring the linear-polarization correlation of photons emitted by pairs in the 4p 2 1 S 0 → 4s4p 1 P 1 → 4s 2 1 S 0 radiative cascade of calcium. The first part of this dissertation reminds the theoretical background (Bell's theorem), and the experimental situation (previous experiments). We then describe our apparatus: the source (calcium atomic beam selectively excited by two-photon absorption), the optics, the photon coincidence-counting system. Our first experiment, analogous to previous ones (but more precise) involves one-channel polarizers. Our second experiment, based on a conceptually simpler scheme, uses two-channel polarizers. The third experiment involves acousto-optical switches followed by two linear polarizers: these devices act as time-varying polarizers, the orientation of which is changed during the time of flight of photons. In the three experiments, the results are in good agreement with the Quantum mechanical predictions, and they distinctly violate the relevant Bell's inequalities [fr

Trends in Global Gender Inequality

Science.gov (United States)

Dorius, Shawn F.; Firebaugh, Glenn

2010-01-01

This study investigates trends in gender inequality throughout the world. Using data encompassing a large majority of the world's population, we examine trends in recent decades for key indicators of gender inequality in education, mortality, political representation and economic activity. We find that gender inequality is declining in virtually…

Happiness Inequality: How Much Is Reasonable?

Science.gov (United States)

Gandelman, Nestor; Porzecanski, Rafael

2013-01-01

We compute the Gini indexes for income, happiness and various simulated utility levels. Due to decreasing marginal utility of income, happiness inequality should be lower than income inequality. We find that happiness inequality is about half that of income inequality. To compute the utility levels we need to assume values for a key parameter that…

How education determine wage inequality

Directory of Open Access Journals (Sweden)

PhD. Student Ionuț Constantin

2009-12-01

Full Text Available One of the problems the economy of the past 50 years has been generated by the increase to differences in income between workers with a level of preparedness higher compared to those with a poor level of training. There is a view that education can lead to greater inequality of income. Analyzing the current situation of increasing inequalities in most developed societies in which there is a high level of education, with schools that are financed by public funds, we can reach the conclusion that a labor force educated young will be associated with an increase in inequality of income, so education does not reduce social inequality, reducing inequality is necessary for the education of the active population is high but one uniform

Some Nonlinear Dynamic Inequalities on Time Scales

Indian Academy of Sciences (India)

The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential ...

Relative index of inequality and slope index of inequality: a structured regression framework for estimation

NARCIS (Netherlands)

Moreno-Betancur, Margarita; Latouche, Aurélien; Menvielle, Gwenn; Kunst, Anton E.; Rey, Grégoire

2015-01-01

The relative index of inequality and the slope index of inequality are the two major indices used in epidemiologic studies for the measurement of socioeconomic inequalities in health. Yet the current definitions of these indices are not adapted to their main purpose, which is to provide summary

ORACLS: A system for linear-quadratic-Gaussian control law design

Science.gov (United States)

Armstrong, E. S.

1978-01-01

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Globalisation, Inequality and Populism

OpenAIRE

Nolan, Brian

2017-01-01

read before the Society, 20 April 2017; Symposium 2016-2017: Globalisation, Inequality and the Rise of Populism Inequality in the distribution of income and wealth among individuals has now come to the fore as a core concern across the industrialised world. In 2013 then President of the United States Barack Obama identified rising income inequality as ?the defining challenge of our times?. The Managing Director of the International Monetary Fund Christine Lagarde has stated that ?reducing ...

What's in a country average? Wealth, gender, and regional inequalities in immunization in India.

Science.gov (United States)

Pande, Rohini P; Yazbeck, Abdo S

2003-12-01

Recent attention to Millennium Development Goals by the international development community has led to the formation of targets to measure country-level achievements, including achievements on health status indicators such as childhood immunization. Using the example of immunization in India, this paper demonstrates the importance of disaggregating national averages for a better understanding of social disparities in health. Specifically, the paper uses data from the India National Family Health Survey 1992-93 to analyze socioeconomic, gender, urban-rural and regional inequalities in immunization in India for each of the 17 largest states. Results show that, on average, southern states have better immunization levels and lower immunization inequalities than many northern states. Wealth and regional inequalities are correlated with overall levels of immunization in a non-linear fashion. Gender inequalities persist in most states, including in the south, and seem unrelated to overall immunization or the levels of other inequalities measured here. This suggests that the gender differentials reflect deep-seated societal factors rather than health system issues per se. The disaggregated information and analysis used in this paper allows for setting more meaningful targets than country averages. Additionally, it helps policy makers and planners to understand programmatic constraints and needs by identifying disparities between sub-groups of the population, including strong and weak performers at the state and regional levels.

The Growing Importance of Linear Algebra in Undergraduate Mathematics.

Science.gov (United States)

Tucker, Alan

1993-01-01

Discusses the theoretical and practical importance of linear algebra. Presents a brief history of linear algebra and matrix theory and describes the place of linear algebra in the undergraduate curriculum. (MDH)

Socioeconomic Inequality in Childhood Obesity.

Science.gov (United States)

Moradi, Ghobad; Mostafavi, Farideh; Azadi, Namamali; Esmaeilnasab, Nader; Ghaderi, Ebrahim

2017-08-15

The aim of this study was to assess the socioeconomic inequalities in obesity and overweight in children aged 10 to 12 yr old. A cross-sectional study. This study was conducted on 2506 children aged 10 to 12 yr old in the city of Sanandaj, western Iran in 2015. Body mass index (BMI) was calculated. Considering household situation and assets, socioeconomic status (SES) of the subjects was determined using Principal Component Analysis (PCA). Concentration Index was used to measure inequality and Oaxaca decomposition was used to determine the share of different determinants of inequality. The prevalence of overweight was 24.1% (95% CI: 22.4, 25.7). 11.5% (95% CI: 10.0, 12.0) were obese. The concentration index for overweight and obesity, respectively, was 0.10 (95% CI: 0.05, 0.15), and 0.07 (95% CI:0.00, 0.14) which indicated inequality and a higher prevalence of obesity and overweight in higher SES. The results of Oaxaca decomposition suggested that socioeconomic factors accounted for 75.8% of existing inequalities. Residential area and mother education were the most important causes of inequality. To reduce inequalities in childhood obesity, mother education must be promoted and special attention must be paid to residential areas and children gender.

Linear-control-based synchronization of coexisting attractor networks with time delays

International Nuclear Information System (INIS)

Yun-Zhong, Song

2010-01-01

This paper introduces the concept of linear-control-based synchronization of coexisting attractor networks with time delays. Within the new framework, closed loop control for each dynamic node is realized through linear state feedback around its own arena in a decentralized way, where the feedback matrix is determined through consideration of the coordination of the node dynamics, the inner connected matrix and the outer connected matrix. Unlike previously existing results, the feedback gain matrix here is decoupled from the inner matrix; this not only guarantees the flexible choice of the gain matrix, but also leaves much space for inner matrix configuration. Synchronization of coexisting attractor networks with time delays is made possible in virtue of local interaction, which works in a distributed way between individual neighbours, and the linear feedback control for each node. Provided that the network is connected and balanced, synchronization will come true naturally, where theoretical proof is given via a Lyapunov function. For completeness, several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme. (general)

Inequality in CO2 emissions across countries and its relationship with income inequality : a distributive approach

OpenAIRE

Padilla, Emilio

2006-01-01

This paper analyses the inequality in CO2 emissions across countries (and groups of countries) and the relationship of this inequality with income inequality across countries for the period (1971-1999). The research employs the tools that are usually applied in income distribution analysis. The methodology used here gives qualitative and quantitative information on some of the features of the inequalities across countries that are considered most relevant for the design and discussion of poli...

Inequality in CO2 emissions across countries and its relationship with income inequality: a distributive approach

OpenAIRE

Emilio Padilla; Alfredo Serrano

2005-01-01

This paper analyses the inequality in CO2 emissions across countries (and groups of countries) and the relationship of this inequality with income inequality across countries for the period (1971-1999). The research employs the tools that are usually applied in income distribution analysis. The methodology used here gives qualitative and quantitative information on some of the features of the inequalities across countries that are considered most relevant for the design and discussion of poli...

Linear Water Waves

Science.gov (United States)

Kuznetsov, N.; Maz'ya, V.; Vainberg, B.

2002-08-01

This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'

Social inequalities in 'sickness'

DEFF Research Database (Denmark)

Wel, Kjetil A. van der; Dahl, Espen; Thielen, Karsten

2011-01-01

The aim of this paper is to examine educational inequalities in the risk of non-employment among people with illnesses and how they vary between European countries with different welfare state characteristics. In doing so, the paper adds to the growing literature on welfare states and social...... from Eurostat and OECD that include spending on active labour market policies, benefit generosity, income inequality, and employment protection. Using multilevel techniques we find that comprehensive welfare states have lower absolute and relative social inequalities in sickness, as well as more...... inequalities in health by studying the often overlooked ‘sickness’-dimension of health, namely employment behaviour among people with illnesses. We use European Union Statistics on Income and Living Conditions (EU-SILC) data from 2005 covering 26 European countries linked to country characteristics derived...

Extensions of Heinz–Kato–Furuta inequality, II

Directory of Open Access Journals (Sweden)

Nakamoto Ritsuo

1999-01-01

Full Text Available In our preceding note, we discussed a generalized Schwarz inequality, an improvement of the Heinz–Kato–Furuta inequality and an inequality related to the Furuta inequality. In succession, we give further discussions on them from the viewpoint of the covariance–variance inequality and the chaotic order. Finally, we consider a relation between our improvement and Wielandt's theorem.

Elementary matrix algebra

CERN Document Server

Hohn, Franz E

2012-01-01

This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations - homogeneous or nonhomogeneous - and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology.Other subjects include the complete treatment of the structur

On weighted dyadic Carleson's inequalities

Directory of Open Access Journals (Sweden)

Tachizawa K

2001-01-01

Full Text Available We give an alternate proof of weighted dyadic Carleson's inequalities which are essentially proved by Sawyer and Wheeden. We use the Bellman function approach of Nazarov and Treil. As an application we give an alternate proof of weighted inequalities for dyadic fractional maximal operators. A result on weighted inequalities for fractional integral operators is given.

Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

Directory of Open Access Journals (Sweden)

Wen-Jer Chang

2014-01-01

Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

Competitive Pressure on China: Income Inequality

OpenAIRE

Ten Raa, T.; Pan, H.

2001-01-01

In the preceding paper we have seen that the top types of labor are relatively scarce in China and this raises the issue of income inequality under competition.Our main finding is that inequality would multiply indeed. Subsidiary, the nature of inequality would shift from the rural-urban divide to differences between social classes.The existing negative relationship between development and inequality would be dissolved by competition.

Random linear codes in steganography

Directory of Open Access Journals (Sweden)

Kamil Kaczyński

2016-12-01

Full Text Available Syndrome coding using linear codes is a technique that allows improvement in the steganographic algorithms parameters. The use of random linear codes gives a great flexibility in choosing the parameters of the linear code. In parallel, it offers easy generation of parity check matrix. In this paper, the modification of LSB algorithm is presented. A random linear code [8, 2] was used as a base for algorithm modification. The implementation of the proposed algorithm, along with practical evaluation of algorithms’ parameters based on the test images was made.[b]Keywords:[/b] steganography, random linear codes, RLC, LSB

Stability theory for dynamic equations on time scales

CERN Document Server

Martynyuk, Anatoly A

2016-01-01

This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems. In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Ma...

Quantum correlations and Nash equilibria of a bi-matrix game

International Nuclear Information System (INIS)

Iqbal, Azhar

2004-01-01

Playing a symmetric bi-matrix game is usually physical implemented by sharing pairs of 'objects' between two players. A new setting is proposed that explicitly shows effects of quantum correlations between the pairs on the structure of payoff relations and the 'solutions' of the game. The setting allows a re-expression of the game such that the players play the classical game when their moves are performed on pairs of objects having correlations that satisfy Bell's inequalities. If players receive pairs having quantum correlations the resulting game cannot be considered another classical symmetric bi-matrix game. Also the Nash equilibria of the game are found to be decided by the nature of the correlations. (letter to the editor)

Multipartite omnidirectional generalized Bell inequality

Energy Technology Data Exchange (ETDEWEB)

Nagata, Koji [Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701 (Korea, Republic of)

2007-10-26

We derive a multipartite generalized Bell inequality which involves the entire range of settings for each of the local observers. Especially, it is applied to show non-local behavior of a six-qubit mixture of Greenberger-Horne-Zeilinger correlations stronger than previous Bell inequalities. For certain noise admixture to the correlations an explicit local realistic model exists in the case of a standard Bell experiment. Bell experiments with many local settings reveal the non-locality of the state. It turns out that the new inequality is more stringent than many other Bell inequalities in the specific quantum state.

Geometric inequalities for black holes

International Nuclear Information System (INIS)

Dain, Sergio

2013-01-01

Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)

Multipartite omnidirectional generalized Bell inequality

International Nuclear Information System (INIS)

Nagata, Koji

2007-01-01

We derive a multipartite generalized Bell inequality which involves the entire range of settings for each of the local observers. Especially, it is applied to show non-local behavior of a six-qubit mixture of Greenberger-Horne-Zeilinger correlations stronger than previous Bell inequalities. For certain noise admixture to the correlations an explicit local realistic model exists in the case of a standard Bell experiment. Bell experiments with many local settings reveal the non-locality of the state. It turns out that the new inequality is more stringent than many other Bell inequalities in the specific quantum state

Geometric inequalities for black holes

Energy Technology Data Exchange (ETDEWEB)

Dain, Sergio [Universidad Nacional de Cordoba (Argentina)

2013-07-01

Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)

Some thoughts on Harker-Kasper inequalities

International Nuclear Information System (INIS)

Woolfson, M.M.

1988-01-01

The approach by Harker and Kasper which led to the first inequality relationships between structure factors has not previously been applied to the space group P1 and there seems to have been a view that it could not give useful results for that space group. The idea has also been advanced that Harker-Kasper inequalities are contained within the complete set of determinantal inequalities derived by Karle and Hauptman. It is shown that the Harker-Kasper approach can be applied in space group P1 and gives inequality relationships which are distinct, at least in form, from those derived from determinants. Indeed, in some cases, a simple Harker-Kasper inequality can be more effective than an equally simple determinantal inequality in restricting the allowed values of three-phase invariants. (orig.)

Income inequality in the developing world.

Science.gov (United States)

Ravallion, Martin

2014-05-23

Should income inequality be of concern in developing countries? New data reveal less income inequality in the developing world than 30 years ago. However, this is due to falling inequality between countries. Average inequality within developing countries has been slowly rising, though staying fairly flat since 2000. As a rule, higher rates of growth in average incomes have not put upward pressure on inequality within countries. Growth has generally helped reduce the incidence of absolute poverty, but less so in more unequal countries. High inequality also threatens to stall future progress against poverty by attenuating growth prospects. Perceptions of rising absolute gaps in living standards between the rich and the poor in growing economies are also consistent with the evidence. Copyright © 2014, American Association for the Advancement of Science.

Educational inequality in cardiovascular disease depends on diagnosis

DEFF Research Database (Denmark)

Christensen, Anne V; Koch, Mette B; Davidsen, Michael

2016-01-01

BACKGROUND: Social inequality is present in the morbidity as well as the mortality of cardiovascular diseases. This paper aims to quantify and compare the level of educational inequality across different cardiovascular diagnoses. DESIGN: Register based study. METHODS: Comparison of the extent...... index of inequality: -29 (-35.1; -21.9) to -1 (-4.8; -3.8)). CONCLUSION: The degree of educational inequality in cardiovascular diseases depends on the diagnosis, with the highest inequality in ischaemic heart disease, acute myocardial infarction, heart failure and stroke. Small differences were found...... of inequality across different cardiovascular diagnoses requires a measure of inequality which is comparable across subgroups with different educational distributions. The slope index of inequality and the relative index of inequality were applied for measuring inequalities in incidence of six cardiovascular...

Global Oral Health Inequalities

Science.gov (United States)

Garcia, I.; Tabak, L.A.

2011-01-01

Despite impressive worldwide improvements in oral health, inequalities in oral health status among and within countries remain a daunting public health challenge. Oral health inequalities arise from a complex web of health determinants, including social, behavioral, economic, genetic, environmental, and health system factors. Eliminating these inequalities cannot be accomplished in isolation of oral health from overall health, or without recognizing that oral health is influenced at multiple individual, family, community, and health systems levels. For several reasons, this is an opportune time for global efforts targeted at reducing oral health inequalities. Global health is increasingly viewed not just as a humanitarian obligation, but also as a vehicle for health diplomacy and part of the broader mission to reduce poverty, build stronger economies, and strengthen global security. Despite the global economic recession, there are trends that portend well for support of global health efforts: increased globalization of research and development, growing investment from private philanthropy, an absolute growth of spending in research and innovation, and an enhanced interest in global health among young people. More systematic and far-reaching efforts will be required to address oral health inequalities through the engagement of oral health funders and sponsors of research, with partners from multiple public and private sectors. The oral health community must be “at the table” with other health disciplines and create opportunities for eliminating inequalities through collaborations that can harness both the intellectual and financial resources of multiple sectors and institutions. PMID:21490232

On some fractional order hardy inequalities

Directory of Open Access Journals (Sweden)

Kufner Alois

1997-01-01

Full Text Available Weighted inequalities for fractional derivatives ( fractional order Hardy-type inequalities have recently been proved in [4] and [1]. In this paper, new inequalities of this type are proved and applied. In particular, the general mixed norm case and a general twodimensional weight are considered. Moreover, an Orlicz norm version and a multidimensional fractional order Hardy inequality are proved. The connections to related results are pointed out.

Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

Science.gov (United States)

Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

2018-02-01

In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Dilna, N.; Rontó, András

2010-01-01

Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

Science.gov (United States)

Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

2018-04-01

In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

The analysis and geometry of Hardy's inequality

CERN Document Server

Balinsky, Alexander A; Lewis, Roger T

2015-01-01

This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality.   The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.

Bipartite Bell Inequality and Maximal Violation

International Nuclear Information System (INIS)

Li Ming; Fei Shaoming; Li-Jost Xian-Qing

2011-01-01

We present new bell inequalities for arbitrary dimensional bipartite quantum systems. The maximal violation of the inequalities is computed. The Bell inequality is capable of detecting quantum entanglement of both pure and mixed quantum states more effectively. (general)

Speed-Sensorless DTC-SVM for Matrix Converter Drives With Simple Non-Linearity Compensation

DEFF Research Database (Denmark)

Lee, Kyo-Beum; Blaabjerg, Frede; Yoon, Tae-Woong

2005-01-01

This paper presents a new method to improve sensorless performance of matrix converter drives using a parameter estimation scheme. To improve low-speed sensorless performance, the non-Iinearities of a matrix converter drive such as commutation delays, turn-on and turn-off times of switching devic...... method is applied for high performance induction motor drives using a 3 kW matrix converter system without a speed sensor. Experimental results are shown to illustrate the feasibility of the proposed strategy....

Dual affine isoperimetric inequalities

Directory of Open Access Journals (Sweden)

Bin Xiong

2006-01-01

Full Text Available We establish some inequalities for the dual -centroid bodies which are the dual forms of the results by Lutwak, Yang, and Zhang. Further, we establish a Brunn-Minkowski-type inequality for the polar of dual -centroid bodies.

Reinterpreting between-group inequality

NARCIS (Netherlands)

Elbers, C.T.M.; Lanjouw, P.F.; Mistiaen, J.; Özler, B

2008-01-01

We evaluate observed inequality between population groups against a benchmark of the maximum between-group inequality attainable given the number and relative sizes of those groups under examination. Because our measure is normalized by these parameters, drawing comparisons across different settings

Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations

DEFF Research Database (Denmark)

Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.

2004-01-01

of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water non-linearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into the numerical behaviour of this rather complicated system of non-linear PDEs....