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New Proof (new + proof)
Selected AbstractsConstrained Kalman Filtering: Additional ResultsINTERNATIONAL STATISTICAL REVIEW, Issue 2 2010Adrian Pizzinga Summary This paper deals with linear state space modelling subject to general linear constraints on the state vector. The discussion concentrates on four topics: the constrained Kalman filtering versus the recursive restricted least squares estimator; a new proof of the constrained Kalman filtering under a conditional expectation framework; linear constraints under a reduced state space modelling; and state vector prediction under linear constraints. The techniques proposed are illustrated in two real problems. The first problem is related to investment analysis under a dynamic factor model, whereas the second is about making constrained predictions within a GDP benchmarking estimation. Résumé Cet article traite des modèles espace-état sujets aux restrictions linéaires générales sur le vecteur d'état. La discussion se concentre autour de quatre aspects: le filtrage de Kalman restreint versus l'estimateur de moindres carrés restreint recursive; une nouvelle preuve du filtrage de Kalman restreint sous le cadre de l'espérance conditionelle; restrictions linéaires aux modèles espace-état réduits; et la prédiction d'état sous restrictions linéaires. Les techniques proposées sont illustrées par deux problèmes réels. Le premier problème est concerné par l'analyse d'investissement sous un modèle à facteur dynamique, tandis que le second concerne les prédictions restreintes dans l'estimation de benchmarking. [source] Improved bounds for the chromatic number of a graphJOURNAL OF GRAPH THEORY, Issue 3 2004S. Louis Hakimi Abstract After giving a new proof of a well-known theorem of Dirac on critical graphs, we discuss the elegant upper bounds of Matula and Szekeres-Wilf which follow from it. In order to improve these bounds, we consider the following fundamental coloring problem: given an edge-cut (V1, V2) in a graph G, together with colorings of ,V1, and ,V2,, what is the least number of colors in a coloring of G which "respects" the colorings of ,V1, and ,V2, ? We give a constructive optimal solution of this problem, and use it to derive a new upper bound for the chromatic number of a graph. As easy corollaries, we obtain several interesting bounds which also appear to be new, as well as classical bounds of Dirac and Ore, and the above mentioned bounds of Matula and Szekeres-Wilf. We conclude by considering two algorithms suggested by our results. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 217,225, 2004 [source] A weak solution approach to a reaction,diffusion system modeling pattern formation on seashellsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2009Jan Kelkel Abstract We investigate a reaction,diffusion system proposed by H. Meinhardt as a model for pattern formation on seashells. We give a new proof for the existence of a local weak solution for general initial conditions and parameters upon using an iterative approach. Furthermore, the solution is shown to exist globally for suitable initial data. The behavior of the solution in time and space is illustrated through numerical simulations. Copyright © 2009 John Wiley & Sons, Ltd. [source] The strong partition relation on ,1 revisitedMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 1 2004Steve Jackson Abstract We give a new proof of the strong partition relation on ,1, assuming the axiom of determinacy, which uses only a general argument not involving the complete analysis of a measure on ,1. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] An optimal memory-reduced procedure for calculating adjoints of the instationary Navier-Stokes equationsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 1 2006Michael Hinze Abstract This paper discusses approximation schemes for adjoints in control of the instationary Navier,Stokes system. It tackles the storage problem arising in the numerical calculation of the appearing adjoint equations by proposing a low-storage approach which utilizes optimal checkpointing. For this purpose, a new proof of optimality is given. This new approach gives so far unknown properties of the optimal checkpointing strategies and thus provides new insights. The optimal checkpointing allows a remarkable memory reduction by accepting a slight increase in run-time caused by repeated forward integrations as illustrated by means of the Navier,Stokes equations. In particular, a memory reduction of two orders of magnitude causes only a slow down factor of 2,3 in run-time. Copyright © 2005 John Wiley & Sons, Ltd. [source] Granger's representation theorem: A closed-form expression for I(1) processesTHE ECONOMETRICS JOURNAL, Issue 1 2005Peter Reinhard Hansen Summary, The Granger representation theorem states that a cointegrated vector autoregressive process can be decomposed into four components: a random walk, a stationary process, a deterministic part, and a term that depends on the initial values. In this paper, we present a new proof of the theorem. This proof enables us to derive closed-form expressions of all terms of the representation and allows a unified treatment of models with different deterministic specifications. The applicability of our results is illustrated by examples. For example, the closed-form expressions are useful for impulse response analyses and facilitate the analysis of cointegration models with structural changes. [source] Optimal designs for parameter estimation of the Ornstein,Uhlenbeck processAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 5 2009Maroussa Zagoraiou Abstract This paper deals with optimal designs for Gaussian random fields with constant trend and exponential correlation structure, widely known as the Ornstein,Uhlenbeck process. Assuming the maximum likelihood approach, we study the optimal design problem for the estimation of the trend µ and the correlation parameter , using a criterion based on the Fisher information matrix. For the problem of trend estimation, we give a new proof of the optimality of the equispaced design for any sample size (see Statist. Probab. Lett. 2008; 78:1388,1396). We also show that for the estimation of the correlation parameter, an optimal design does not exist. Furthermore, we show that the optimal strategy for µ conflicts with the one for ,, since the equispaced design is the worst solution for estimating the correlation. Hence, when the inferential purpose concerns both the unknown parameters we propose the geometric progression design, namely a flexible class of procedures that allow the experimenter to choose a suitable compromise regarding the estimation's precision of the two unknown parameters guaranteeing, at the same time, high efficiency for both. Copyright © 2008 John Wiley & Sons, Ltd. [source] Throwing Some Light on the Vast Darkness that is Analysis: Niels Henrik Abel's Critical Revision and the Concept of Absolute ConvergenceCENTAURUS, Issue 1 2010Henrik Kragh Sørensen During the first half of the nineteenth century, mathematical analysis underwent a transition from a predominantly formula-centred practice to a more concept-centred one. Central to this development was the reorientation of analysis originating in Augustin- Louis Cauchy's (1789,1857) treatment of infinite series in his Cours d'analyse. In this work, Cauchy set out to rigorize analysis, thereby critically examining and reproving central analytical results. One of Cauchy's first and most ardent followers was the Norwegian Niels Henrik Abel (1802,1829) who vowed to shed some light on the vast darkness in analysis. This paper investigates some important aspects of Abel's contribution to the reorientation in analysis. In particular, it stresses the role for critical revision in the process of rigorization. By critically examining past practice, the new practice sought to explain the relative success of the previous,now outdated,approach. This is illustrated by discussing a number of issues related to Abel's new proof of the binomial theorem (1826) including his reactions to the exception that he encountered to one of the central theorems of Cauchy's theory. Following this discussion, the formation of new concepts as the result of critical revisions is illustrated by analysing the early history of the concept of absolute convergence. Thereby, it is shown how a new concept was distilled, investigated, put to use and eventually superseded. [source] The Mathematical Contributions of Francesco Maurolico to the Theory of Music of the 16th Century (The Problems of a Manuscript)CENTAURUS, Issue 3 2006Tito M. Tonietti Here, in part I, his main results are presented and also their differences compared with the classical tradition of the mathematical theory of music. These results are a new proof of the number of commas in the tone, the theory of ,ictus', and a new notation for the composition of proportions. This is followed, in part II, by an explanation of how the original corpus of these folios was put together. Finally, part III discusses the complex puzzle of the manuscripts (one still extant, another probably lost, ,) and of their possible connections with the 1575 edition of a part of the corpus. Possible scenarios of the story of the manuscripts and probable interventions of the Jesuits on this edition are described. [source] Guaranteed H, robustness bounds for Wiener filtering and predictionINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2002P. Bolzern Abstract The paper deals with special classes of H, estimation problems, where the signal to be estimated coincides with the uncorrupted measured output. Explicit bounds on the difference between nominal and actual H, performance are obtained by means of elementary algebraic manipulations. These bounds are new in continuous-time filtering and discrete-time one-step ahead prediction. As for discrete-time filtering, the paper provides new proofs that are alternative to existing derivations based on the Krein spaces formalism. In particular, some remarkable H, robustness properties of Kalman filters and predictors are highlighted. The usefulness of these results for improving the estimator design under a mixed H2/H, viewpoint is also discussed. The dualization of the analysis allows one to evaluate guaranteed H, robustness bounds for state-feedback regulators of systems affected by actuator disturbances. Copyright © 2001 John Wiley & Sons, Ltd. [source] | |||||||||||||