45 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
Role of Stearoyl-CoA desaturase-1 (SCD1) in the activation of epidermal growth factor receptor (EGFR) in lung cancer cells
No full textCancer cells activate lipogenic enzymes, including StearoylCoA Desaturase-1 (SCD1), the key enzyme that converts saturated fatty acids (SFA) into monounsaturated fatty acids (MUFA). Previously, we established that SCD1 regulates lipogenesis, cell proliferation and invasiveness in lung cancer cells, as well as tumor formation in mice. We recently reported that SCD1 modulates the PI3K/Akt pathway, a central signaling cascade, along with ERK, which are involved in the regulation of lipid biosynthesis, growth and survival of mammalian cells. Growth factor-activated tyrosine kinase receptors, such as epidermal growth factor (EGF) receptors (EGFR), are main activators of Akt and ERK signals, two cascades that are most often deranged in cancer. A hallmark of cancer is the metabolic shift towards macromolecular synthesis to support cell replication. SCD1 expression increases in cancer cells. The molecular mechanisms by which SCD1 regulates the biological phenotype of cancer cells is still unknown. The poor prognosis and ineffective treatments of some cancers, such as lung cancer, calls for better understanding of their mechanisms and for finding novel targets that, like SCD1, modulate the Akt and ERK pathways. Here we provide evidence that SCD1 activity controls the activation of EGFR and its downstream signaling targets, Akt and ERK. Using H460 human lung cancer cells, we observed that the activating phosphorylation of Tyr1068 and Tyr1086 residues in EGFR upon EGF stimulation was markedly impaired when SCD1 activity was blocked with CVT-11127, a novel small molecule SCD inhibitor. In addition, supplementation with oleic acid, the product of SCD1, restored EGF-induced phosphorylation of EGFR but not the full phosphorylation of Akt. Finally, abrogation of SCD1 dramatically altered distribution of rafts and non-raft domains, suggesting that the regulation of EGFR function by SCD1 may involve the alteration of membrane lipid domains. All results are representative of 3 separate experiments. In conclusion, our data indicate that SCD1 may coordinate the regulation of lipid biosynthesis and the transduction signals that control cancer cell metabolism, proliferation, survival and tumorigenesis by modulating EGFR activation, which subsequently modifies the Akt and ERK signaling platforms. Our findings also suggest SCD1 is a potential target for novel pharmacological interventions in lung cancer.M.S.Includes bibliographical referencesby Mary Nashe
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
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