332 research outputs found
On some problems of M.Z. Nashed on outer inverses
No full textAbstractWhile not every linear operator on a Banach space has a generalized inner inverse, the situation for outer inverses is different. Every operator on a Banach space has an outer inverse. That answers one problem posed by M.Z. Nashed
Average sampling in L-2
No full textIn this Note, we show that any localized average sampler could not be a stable sampler for L-2, but that there is a localized determining sampler for L-2. To cite this article: M.Z. Nashed et al., C R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved
Continuous-Time Dynamic Risk Measures By Backward Stochastic Volterra Integral Equations
No full textContinuous-time dynamic convex and coherent risk measures are introduced. To obtain existence of such risk measures, backward stochastic Volterra integral equations (BSVIEs, for short) are studied. For such equations, notion of adapted M-solution is introduced, well-posedness is established, duality principles and comparison theorems are presented. Then a class of dynamic convex and coherent risk measures are identified as a component of the adapted M-solutions to certain BSVIEs. †Dedicated to Professor M.Z. Nashed. © 2007, Taylor & Francis Group, LLC
Mixed Integer Estimation and Validation for Next Generation GNSS
No full textThe coming decade will bring a proliferation of Global Navigation Satellite Systems (GNSS) that are likely to revolutionize society in the same way as the mobile phone has done. The promise of a broader multi-frequency, multi-signal GNSS “system of systems” has the potential of enabling a much wider range of demanding applications compared to the current GPS-only situation. Inorder toachieve the highest accuracies one must exploit the unique properties of the received carrier signals.These properties include the multi-satellite system tracking, the mm-level measurement precision, the frequency diversity, and the integer ambiguities of the carrier phases. Successful exploitation of these properties results in an accuracy improvement of the estimated GNSS parameters of two orders of magnitude.The theory that underpins this ultra precise GNSS parameter estimation and validation is the theory of integer inference.This theory is the topic of the present chapter
A NEW APPROACH TO CLASSIFICATION AND REGULARIZATION OF ILL-POSED OPERATOR EQUATIONS11This research was partially supported by the United States Army Research Office under grant DAAG-29-83-K-0109.
No full textSupportably and weakly convex functionals with applications to approximation theory and nonlinear programming
No full textOn moment-discretization and least-squares solutions of linear integral equations of the first kind
No full textAbstractLet K(s, t) be a continuous function on [0, 1] × [0, 1], and let K be the linear integral operator induced by the kernel K(s, t) on the space L2[0, 1]. This note is concerned with moment-discretization of the problem of minimizing ‖Kx−y‖ in the L2-norm, where y is a given continuous function. This is contrasted with the problem of least-squares solutions of the moment-discretized equation: ∝01 K(si, t) x(t) dt = y(si), i = 1, 2,h., n. A simple commutativity result between the operations of “moment-discretization” and “least-squares” is established. This suggests a procedure for approximating K†y (where K† is the generalized inverse of K), without recourse to the normal equation K∗Kx = K∗y, that may be used in conjunction with simple numerical quadrature formulas plus collocation, or related numerical and regularization methods for least-squares solutions of linear integral equations of the first kind
GENERALIZED INVERSE MAPPING THEOREMS AND RELATED APPLICATIONS OF GENERALIZED INVERSES IN NONLINEAR ANALYSIS
No full textManual Hydraulic Structures
No full textThis manual is the result of group work and origins in Dutch lecture notes that have been used since long time. Amongst the employees of the Hydraulic Engineering Department that contributed to this work are dr.ir. S. van Baars, ir.K.G.Bezuijen, ir.G.P.Bourguignon, prof.ir.A.Glerum, dr.ir.P.A.Kolkman, ir. H.K.T. Kuijper, ir. H.G. Voortman and prof.drs.ir. J.K. Vrijling. The latest years, this manual has been clarified, revised and expanded by ir. W.F. Molenaar and ing. M.Z. Voorendt. We have received much feedback from students and got good input from our student-assistants, which is highly appreciated and has been taken taken into account for this new edition. In the 2016 edition, some minor corrections were made throughout the Manual, most noticeably the equation for the spring stiffness of a combined system in Section 29.2. Section 11.1 has been updated with more generic weir discharge equations. Furthermore, serviceability requirements have been added to the chapter on wave-overtopping (Chapter 17) and the Blum theory for laterally loaded piles has been better explained in Chapter 44. The largest change is the addition of Chapter 49, about the determination of the height of flood defences
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