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Quadratic Forms (quadratic + form)
Selected AbstractsQuadratic form of stable sub-manifold for power systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9-10 2004Daizhan Cheng Abstract The stable sub-manifold of type-1 unstable equilibrium point is fundamental in determining the region of attraction of a stable working point for power systems, because such sub-manifolds form the boundary of the region (IEEE Trans. Automat. Control 1998; 33(1):16,27; IEEE Trans. Circuit Syst. 1988; 35(6):712,728). The quadratic approximation has been investigated in some recent literatures (Automatica 1997; 33(10):1877,1883; IEEE Trans. Power Syst. 1997; 12(2):797,802). First, the paper reports our recent result: a precise formula is obtained, which provides the unique quadratic approximation with the error of 0(,,x,,3). Then the result is applied to differential,algebraic systems. The real form of practical large scale power systems are of this type. A detailed algorithm is obtained for the quadratic approximation of the stable sub-manifold of type-1 unstable equilibrium points of such systems. Some examples are presented to illustrate the algorithm and the application of the approximation to stability analysis of power systems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Computing simplifications for non-additive genetic modelsJOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 6 2003L. R. Schaeffer Summary A limiting factor in the analysis of non-additive genetic models has been the ability to compute the inverses of non-additive genetic covariance matrices for large populations. Also, the order of the equations was equal to the number of animals times the number of non-additive genetic effects that were included in the model. This paper describes a computing algorithm that avoids the inverses of the non-additive genetic covariance matrices and keeps the size of the equations to be the same as any animal model with only additive genetic effects. Quadratic forms for the non-additive genetic variances could also be computed without the inverses of the non-additive genetic covariance matrices. Zusammenfassung In der Analyse von nicht additiven genetischen Modellen war der limitierende Faktor die Fähigkeit Inversen der Matrizen nicht additiver genetischer Kovarianzen in großen Populationen zu berechnen. Auch die Reihenfolge der Gleichungen war gleich zu der Anzahl der Tiere mal der Anzahl der nicht additiven genetischen Effekte, die im Model berücksichtigt wurden. Diese Veröffentlichung beschreibt einen Berechnungsalgorithmus, der die Umkehrung der Matrizen nicht additiver genetischer Kovarianzen umgeht und die Gleichungen auf der selben Größe hält wie ein Tiermodel mit additiven genetischen Effekten. Auch quadratische Formen für nicht additive genetische Kovarianzen können ohne die Umkehrung der Matrizen nicht additiver genetischer Kovarianzen berechnet werden. [source] Construction of Lyapunov function for power system based on solving linear matrix inequalityELECTRICAL ENGINEERING IN JAPAN, Issue 4 2007Atsushi Ishigame Abstract This paper presents construction of Lyapunov functions for power systems based on solving the Linear Matrix Inequality (LMI) derived from the Lyapunov stability theorem considering the dynamics of load characteristic and AVR control system. The proposed Lyapunov function is constructed as a quadratic form of state variables and an integral term which satisfies the curl equation and the sector condition. An induction machine and a synchronous machine are considered as load characteristics. One-machine one-load infinite bus system is considered taking into account the flux decay effects and AVR with one time constant of the generator. To verify the proposed Lyapunov function, the transient stability assessment is shown. The critical clearing times given by the proposed Lyapunov function are compared with those obtained by the numerical integration method, and they are shown to be practical. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 158(4): 42, 50, 2007; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/eej.20328 [source] Lower bound limit analysis of cohesive-frictional materials using second-order cone programmingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2006A. Makrodimopoulos Abstract The formulation of limit analysis by means of the finite element method leads to an optimization problem with a large number of variables and constraints. Here we present a method for obtaining strict lower bound solutions using second-order cone programming (SOCP), for which efficient primal-dual interior-point algorithms have recently been developed. Following a review of previous work, we provide a brief introduction to SOCP and describe how lower bound limit analysis can be formulated in this way. Some methods for exploiting the data structure of the problem are also described, including an efficient strategy for detecting and removing linearly dependent constraints at the assembly stage. The benefits of employing SOCP are then illustrated with numerical examples. Through the use of an effective algorithm/software, very large optimization problems with up to 700 000 variables are solved in minutes on a desktop machine. The numerical examples concern plane strain conditions and the Mohr,Coulomb criterion, however we show that SOCP can also be applied to any other problem of lower bound limit analysis involving a yield function with a conic quadratic form (notable examples being the Drucker,Prager criterion in 2D or 3D, and Nielsen's criterion for plates). Copyright © 2005 John Wiley & Sons, Ltd. [source] State-space time integration with energy control and fourth-order accuracy for linear dynamic systemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Steen Krenk Abstract A fourth-order accurate time integration algorithm with exact energy conservation for linear structural dynamics is presented. It is derived by integrating the phase-space representation and evaluating the resulting displacement and velocity integrals via integration by parts, substituting the time derivatives from the original differential equations. The resulting algorithm has an exact energy equation, in which the change of energy is equal to the work of the external forces minus a quadratic form of the damping matrix. This implies unconditional stability of the algorithm, and the relative phase error is of fourth-order. An optional high-frequency algorithmic damping is constructed by optimal combination of three different damping matrices, each proportional to either the mass or the stiffness matrix. This leads to a modified form of the undamped algorithm with scalar weights on some of the matrices introducing damping of fourth-order in the frequency. Thus, the low-frequency response is virtually undamped, and the algorithm remains third-order accurate even when algorithmic damping is included. The accuracy of the algorithm is illustrated by an application to pulse propagation in an elastic medium, where the algorithmic damping is used to reduce dispersion due to the spatial discretization, leading to a smooth solution with a clearly defined wave front. Copyright © 2005 John Wiley & Sons, Ltd. [source] A non-linear positive method to reconstruct the parent textures from the inherited textures in phase transformationJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 2 2000M. Humbert The orientation distribution function (ODF) of the parent phase is reconstructed from the inherited ODF of the transformed phase, provided that the lattice symmetry of the parent phase is higher than that of the inherited one and that the orientation relation between both phases is known. In the cases of experimental errors or variant selections, the positivity of the ODF of the parent phase is ensured by assuming that it is of quadratic form. [source] Asymmetric invariants for a class of strictly hyperbolic systems including the Timoshenko beamMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2007Clelia Marchionna Abstract We introduce a set of conserved quantities of energy-type for a strictly hyperbolic system of two coupled wave equations in one space dimension. The system is subject to mechanical boundary conditions. Some of these invariants are asymmetric in the sense that their defining quadratic form contains second order derivatives in only one of the unknowns. We study their independence with respect to the usual energies and characterize their sign. In many cases, our results provide sharp well-posedness and stability results. Finally, we apply some of our conservation laws to the study of a singular perturbation problem previously considered by J. Lagnese and J. L. Lions. Copyright © 2007 John Wiley & Sons, Ltd. [source] A Non-homothetic Globally Concave Flexible Cost Function and its Application to Panel DataTHE JAPANESE ECONOMIC REVIEW, Issue 2 2001Shinichiro Nakamura A new non-homothetic globally concave flexible cost function is introduced and applied to a panel of firms in the Japanese paper and pulp industry. This cost function is a mixture of the generalized McFadden form and the generalized Ozaki form due to Nakamura (1990). A generalized index of technical change is used in place of the standard quadratic form of time-trend. The estimated cost function satisfied global concavity, and the symmetry condition of the Slutsky matrix was not rejected. Homotheticity was strongly rejected. JEL Classification Numbers: C33, D24. [source] A Generalized Portmanteau Test For Independence Of Two Infinite-Order Vector Autoregressive SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2006Chafik Bouhaddioui Primary 62M10; secondary 62M15 Abstract., In many situations, we want to verify the existence of a relationship between multivariate time series. Here, we propose a semiparametric approach for testing the independence between two infinite-order vector autoregressive (VAR(,)) series, which is an extension of Hong's [Biometrika (1996c) vol. 83, 615,625] univariate results. We first filter each series by a finite-order autoregression and the test statistic is a standardized version of a weighted sum of quadratic forms in the residual cross-correlation matrices at all possible lags. The weights depend on a kernel function and on a truncation parameter. Using a result of Lewis and Reinsel [Journal of Multivariate Analysis (1985) Vol. 16, pp. 393,411], the asymptotic distribution of the test statistic is derived under the null hypothesis and its consistency is also established for a fixed alternative of serial cross-correlation of unknown form. Apart from standardization factors, the multivariate portmanteau statistic proposed by Bouhaddioui and Roy [Statistics and Probability Letters (2006) vol. 76, pp. 58,68] that takes into account a fixed number of lags can be viewed as a special case by using the truncated uniform kernel. However, many kernels lead to a greater power, as shown in an asymptotic power analysis and by a small simulation study in finite samples. A numerical example with real data is also presented. [source] Spectral Regression For Cointegrated Time Series With Long-Memory InnovationsJOURNAL OF TIME SERIES ANALYSIS, Issue 6 2000D. Marinucci Spectral regression is considered for cointegrated time series with long-memory innovations. The estimates we advocate are shown to be consistent when cointegrating relationships among stationary variables are investigated, while ordinary least squares are inconsistent due to correlation between the regressors and the cointegrating residuals; in the presence of unit roots, these estimates share the same asymptotic distribution as ordinary least squares. As a corollary of the main result, we provide a functional central limit theorem for quadratic forms in non-stationary fractionally integrated processes. [source] Annihilating polynomials for quadratic forms and Stirling numbers of the second kindMATHEMATISCHE NACHRICHTEN, Issue 11 2007Stefan De WannemackerArticle first published online: 9 JUL 200 Abstract We present a set of generators of the full annihilator ideal for the Witt ring of an arbitrary field of characteristic unequal to two satisfying a non-vanishing condition on the powers of the fundamental ideal in the torsion part of the Witt ring. This settles a conjecture of Ongenae and Van Geel. This result could only be proved by first obtaining a new lower bound on the 2-adic valuation of Stirling numbers of the second kind. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Random vectors satisfying Khinchine,Kahane type inequalities for linear and quadratic formsMATHEMATISCHE NACHRICHTEN, Issue 9 2005Jesús Bastero Abstract We study the behaviour of moments of order p (1 < p < ,) of affine and quadratic forms with respect to non log-concave measures and we obtain an extension of Khinchine,Kahane inequality for new families of random vectors by using Pisier's inequalities for martingales. As a consequence, we get some estimates for the moments of affine and quadratic forms with respect to a tail volume of the unit ball of lnq (0 < q < 1). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Signal-to-interference-plus-noise ratio estimation for wireless communication systems: Methods and analysisNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 5 2004Daniel R. Jeske Abstract The Signal-to-Interference-plus-Noise Ratio (SINR) is an important metric of wireless communication link quality. SINR estimates have several important applications. These include optimizing the transmit power level for a target quality of service, assisting with handoff decisions and dynamically adapting the data rate for wireless Internet applications. Accurate SINR estimation provides for both a more efficient system and a higher user-perceived quality of service. In this paper, we develop new SINR estimators and compare their mean squared error (MSE) performance. We show that our new estimators dominate estimators that have previously appeared in the literature with respect to MSE. The sequence of transmitted bits in wireless communication systems consists of both pilot bits (which are known both to the transmitter and receiver) and user bits (which are known only by the transmitter). The SINR estimators we consider alternatively depend exclusively on pilot bits, exclusively on user bits, or simultaneously use both pilot and user bits. In addition, we consider estimators that utilize smoothing and feedback mechanisms. Smoothed estimators are motivated by the fact that the interference component of the SINR changes relatively slowly with time, typically with the addition or departure of a user to the system. Feedback estimators are motivated by the fact that receivers typically decode bits correctly with a very high probability, and therefore user bits can be thought of as quasipilot bits. For each estimator discussed, we derive an exact or approximate formula for its MSE. Satterthwaite approximations, noncentral F distributions (singly and doubly) and distribution theory of quadratic forms are the key statistical tools used in developing the MSE formulas. In the case of approximate MSE formulas, we validate their accuracy using simulation techniques. The approximate MSE formulas, of interest in their own right for comparing the quality of the estimators, are also used for optimally combining estimators. In particular, we derive optimal weights for linearly combining an estimator based on pilot bits with an estimator based on user bits. The optimal weights depend on the MSE of the two estimators being combined, and thus the accurate approximate MSE formulas can conveniently be used. The optimal weights also depend on the unknown SINR, and therefore need to be estimated in order to construct a useable combined estimator. The impact on the MSE of the combined estimator due to estimating the weights is examined. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004 [source] A Class of Multiplicity Adjusted Tests for Spatial Clustering Based on Case,Control Point DataBIOMETRICS, Issue 1 2007Toshiro Tango Summary A class of tests with quadratic forms for detecting spatial clustering of health events based on case,control point data is proposed. It includes Cuzick and Edwards's test statistic (1990, Journal of theRoyal Statistical Society, Series B52, 73,104). Although they used the property of asymptotic normality of the test statistic, we show that such an approximation is generally poor for moderately large sample sizes. Instead, we suggest a central chi-square distribution as a better approximation to the asymptotic distribution of the test statistic. Furthermore, not only to estimate the optimal value of the unknown parameter on the scale of cluster but also to adjust for multiple testing due to repeating the procedure by changing the parameter value, we propose the minimum of the profile p-value of the test statistic for the parameter as an integrated test statistic. We also provide a statistic to estimate the areas or cases which make large contributions to significant clustering. The proposed methods are illustrated with a data set concerning the locations of cases of childhood leukemia and lymphoma and another on early medieval grave site locations consisting of affected and nonaffected grave sites. [source] | |||||||||||||