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Search results for: MORSE HOMOLOGY, P-LAPLACIAN
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A note on the Morse homology for a class of functionals in Banach spaces involving the 2p-area functional
PublicationIn this paper we show how to construct Morse homology for an explicit class of functionals involving the 2p-area functional. The natural domain of definition of such functionals is the Banach space W_0^{1,2p}(\Omega), where p > n/2 and \Omega \subet R^n is a bounded domain with sufficiently smooth boundary. As W_0^{1,2p}(\Omega) is not isomorphic to its dual space,critical points of such functionals cannot be non-degenerate...
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Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
PublicationIn this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain...
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Connection matrix theory for discrete dynamical systems
PublicationIn [C] and [F1] the connection matrix theory for Morse decomposition is developedin the case of continuous dynamical systems. Our purpose is to study the case of discrete timedynamical systems.
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Positive solutions for three-point one-dimensional p-Laplacian boundary value problems with advanced arguments [online]
PublicationPraca dotyczy problemów istnienia dodatnich rozwiązań dla trzy-punktowych zagadnień brzegowych z wyprzedzonymi argumentami. Zastosowano twierdzenie Avery-Petersona o punkcie stałym aby uzyskać warunki dostateczne na istnienie conajmniej trzech dodatnich rozwiązań.
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Positive solutions of one-dimensional p-Laplacian boundary value problems for fourth-order differential equations with deviating arguments
PublicationPraca dotyczy istnienia dodatnich rozwiązań dla równań różniczkowych rzędu czwartego z warunkami brzegowymi z odchylonymi argumentami. Stosując twierdzenie o punkcie stałym dla stożków podano warunki dostateczne na istnienia takich rozwiązań.
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Positive solutions to third-order impulsive Sturm-Liouville boundary value problems with deviated arguments and one-dimensional p-Laplacian
PublicationBadane są równania różniczkowe z impulsami trzeciego rzędu z odchylonymi argumentami przy zadanych warunkach brzegowych typu Sturma-Liouvilla. Podano warunki dostateczne na istnienie dodatnich rozwiązań takich problemów stosując twierdzienie o punkcie stałym dla stożków.
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Index filtrations and Morse decomposition for discrete dynamical systems
PublicationOn a Morse decomposition of an isolated invariant set of a homeomorphism(discrete dynamical system) there are partial orderings defined by the homeomorphism.These are called admissible orderings of the...
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Unlocking the Secrets of River Pollution: Analyzing Organic Pollutants in Sediments—Experimental Study
PublicationUntreated wastewater released into rivers can result in water pollution, the spread of waterborne diseases, harm to ecosystems, contamination of soil and groundwater, as well as air pollution and respiratory problems for nearby humans and animals due to the release of greenhouse gases. The current study aims to investigate the recent input of anthropogenic loads into the rivers using linear alkylbenzene (LAB), which is one of the...
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Molecular and structural basis of inner core lipopolysaccharide alterations in Escherichia coli: incorporation of glucuronic acid and phosphoethanolamine in the heptose region.
PublicationIt is well established that lipopolysaccharide (LPS) often carries nonstoichiometric substitutions in lipid A and in the inner core. In this work, the molecular basis of inner core alterations and their physiological significance are addressed. A new inner core modification of LPS is described, which arises due to the addition of glucuronic acid on the third heptose with a concomitant loss of phosphate on the second heptose. This...
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Structural features responsible for control of the eukaryotic GlcN-6-P synthase activity
PublicationGlucosamine-6-phosphate (GlcN-6-P) synthase is responsible for catalysis of the first and practically irreversible step in hexosamine metabolism. As UDP-GlcNAc, the final product of the hexosamine path, constitutes one of the essential substrates for assembly of bacterial and fungal cell walls, the enzyme is an interesting target for antimicrobial therapy.The structure of E. coli enzyme, known since 2001, forms a dimer of two identical...
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Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
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A New Boson with a Mass of 125 GeV Observed with the CMS Experiment at the Large Hadron Collider
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