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Search results for: MORSE HOMOLOGY, P-LAPLACIAN
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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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Analysis of blood vessel topology by cubical homology
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Morse cohomology in a Hilbert space via the Conley index
PublicationThe main theorem of this paper states that Morse cohomology groups in a Hilbert space are isomorphic to the cohomological Conley index. It is also shown that calculating the cohomological Conley index does not require finite-dimensional approximations of the vector field. Further directions are discussed.
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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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ASCOT – More than a horse race!
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Computation of cubical homology, cohomology, and (co)homological operations via chain contraction
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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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Directed laplacian kernels for link analysis
PublicationPrzedstawiono zastosowanie algorytmów opartych o funkcje jądra do problemu analizy linków i cytowań. Zaproponowano nowe funkcje jądra zbudowane na operatorze Laplace'a dla grafów skierowanych. Odzwierciedlają one powiązanie pomiędzy węzłami grafu jako funkcję długości łączących je ścieżek oraz istotności odwiedzanych po drodze węzłów. Eksperymenty z nowymi funkcjami jądra przeprowadzono na zbiorze cytowań pobranych z publikacji...
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Bernstein-type theorem for ϕ-Laplacian
PublicationIn this paper we obtain a solution to the second-order boundary value problem of the form \frac{d}{dt}\varPhi'(\dot{u})=f(t,u,\dot{u}), t\in [0,1], u\colon \mathbb {R}\to \mathbb {R} with Sturm–Liouville boundary conditions, where \varPhi\colon \mathbb {R}\to \mathbb {R} is a strictly convex, differentiable function and f\colon[0,1]\times \mathbb {R}\times \mathbb {R}\to \mathbb {R} is continuous and satisfies a suitable growth...
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P and T
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Equivariant Morse equation
PublicationThe paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.
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Inducing a map on homology from a correspondence
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Homology algorithm based on acyclic subspace
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Hart's E and P
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Graph Approach to the Computation of the Homology of Continuous Maps
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Synthesis of compounds with C-P-P and C=P-P bond systems based on the phospha-Wittig reaction
PublicationA reactivity study of a β-diketiminate titanium(III) phosphanylphosphido complex [MeNacNacTi(Cl){η2-P(SiMe3)-PtBu2}] (1) towards ketones such as benzophenone, 9-fluorenone, acetophenone, cyclopentanone, cyclohexanone and cycloheptanone is reported. The reactions of 1 with aromatic ketones (without α-protons) directly lead to the Ti(III) complex [MeNacNacTi(μ2-Cl)(OSiMe3)] (5) as well as Ti(IV) complexes with the pinacol condensation...
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Morse inequalities via Conley index theory
PublicationThe relation known as the Morse inequalities can be extended to a more general setting of flows on a locally compact metric spaces (Conley index) as well as dynamical systems on Hilbert spaces (LS-index). This paper is a discourse around this extension. Except the part concerning the LS-index the material is self-contained and has a character of a survey.
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Persistent homology as a new method of the assessment of heart rate variability
PublicationHeart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent...
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Morze możliwości
PublicationZ Karolem Moszykiem, Kierownikiem ds. Rozwoju Operacyjnego/ Lean Six Sigma Black Belt, DCT Gdańsk SA i prelegentem pierwszego Gdańskiego Manager Clubu - o ciągłbym doskonaleniu w głębokowodnym terminalu kontenerowym - rozmawiał Łukasz Rogatka
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Nase More
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Characteristics of the topology of the Internet
PublicationRozdział dotyczy charakterystyki topologii Internetu. Ukazuje zagrożenia wynikające z bezskalowego charakteru sieci. Opisuje naturę ataku - destrukcyjnego działania mającego na celu wyeliminowanie ważnego elementu sieci. Przedstawia reguły doboru tras, pozwalające ustanawiać ścieżki realizacji połączeń omijające określone węzły sieci, narażone na atak.
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Index filtrations and Morse decompositions for discrete dynamical systems
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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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<p>Immunochemotherapy for Richter syndrome: current insights</p>
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Eye-mouse for disabled
PublicationW pracy przedstawiono projekt urządzenia umożliwiającego komunikację z komputerem za pomocą ruchów gałki ocznej osobom niepełnosprawnym
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TOPOLOGY AND ITS APPLICATIONS
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Homology Homotopy and Applications
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Current protocols in mouse biology
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Scanning networks with cactus topology
PublicationThe family of Pursuit and Evasion problems is widelystudied because of its numerous practical applications,ranging from communication protocols to cybernetic andphysical security. Calculating the search number of a graphis one of most commonly analyzed members of this problemfamily. The search number is the smallest number of mobileagents required to capture an invisible and arbitrarily fastfugitive, for instance piece of malicious...
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Decision Support in Selecting a Reliable Strategy for Sustainable Urban Transport Based on Laplacian Energy of T-Spherical Fuzzy Graphs
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Targeting of p53 and its homolog p73 by protoporphyrin IX
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<p>Experience of Polish Patients with Obesity in Contacts with Medical Professionals</p>
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Gdynia otwarta na morze
PublicationTradycję przestrzenną Gdyni stworzyły lata międzywojenne. To one ukształtowały ją w sensie urbanistycznym i architektonicznym oraz wykreowały główną ideę przestrzenną, którą jest otwarcie miasta na morze. Idea ta jest w pewnym sensie oczywista, gdyż nadmorskie położenie Gdyni wyraźnie do tego predestynowało. Dzięki konsekwentnej działalności zarówno projektanta portu - inżyniera Tadeusza Wendy, jak i głównego projektanta miasta...
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"Obraz do wnętrza/morze"
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Activation of the C=P bond in phosphanylphosphaalkenes C=P–P bond system) in the reaction with nucleophilic reagents: MeLi, nBuLi and tBuLi
PublicationThree reactions of phosphanylphosphaalkene (1) with nucleophiles were performed to activate the diphosphorus monomer. We observed similar results in the reactions with MeLi and nBuLi, in which the P–P bond is cleavaged and triphosphorus systems [P(Me)2–CH(biph)–CH(biph)–P–(PtBu 2)]- (1a'') and [P(nBu)2–CH(biph)–CH(biph)–P–(PtBu 2)]- (1b''), respectively, are formed depending on the nucleophilic reagent (biph ¼ biphenyl). In the...
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Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition
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PHONOLOGY
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TOPOLOGY
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<p>Analysis of toxicity and anticancer activity of micelles of sodium alginate-curcumin</p>
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<p>Experience of Patients with Obesity in Contacts with Medical Professionals [Response to Letter]</p>
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From phosphanylphosphaalkenes to coordination copper and silver polymers containing P–P bonds
PublicationThis study was focused on the activation of the C[double bond, length as m-dash]P bond via reactions of Ph2C[double bond, length as m-dash]P-PtBu2 (1) with 1,6-hexanediol and selected dithiols (1,4-butanedithiol, 1,4-benzenedithiol and 1,4-benzenedimethanethiol). These reactions proceed according to a 1,2-addition mechanism, providing new compounds with formulas {(Ph)2(H)C-P-PtBu2}{μ2-(O-(CH2)6-O)}{tBu2P-P-C(H)(Ph)2} (2), {(Ph)2(H)C-P-PtBu2}{μ2-(S-(CH2)4-S)}{tBu2P-P-C(H)(Ph)2}...
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On the topology of spaces of partial and local maps
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Biochemical properties of the HtrA homolog from bacterium Stenotrophomonas maltophilia
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Syntheses and structures of the first terminal phosphanylphosphido complex of hafnium [cp2hf(cl){η1-(me3si)p-p(net2)2}] and the firstzirconocene-phosphanylphosphinidene dimer [cp2zr{μ2-p-p(net2)2}2zrcp2]
PublicationReactions of (Et2N)2P-P(SiMe3)Li with [Cp2MCl2] (M= Zr, Hf) in toluene or pentane yield the related terminal phosphanylphosphido complexes [Cp2M(Cl){η1-(Me3Si)P-P(NEt2)2}]. The solid statestructure of [Cp2Hf(Cl){η1-(Me3Si)P-P(NEt2)2}] was established by single crystal X-ray diffraction. The reaction of (Et2N)2P-P(SiMe3)Li with [Cp2ZrCl2] in THF or DME solutions leads to the formationof deep red crystals of the first neutral diamagnetic...
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Reactions of R<sub>2</sub>P-P(SiMe<sub>3</sub>)Li with [(R'<sub>3</sub>P)<sub>2</sub>PtCl<sub>2</sub>]. A General and Efficient Entrance to Phosphanylphosphinidene Complexes of Platinum. Syntheses and Structures of [(η<sub>2</sub>-P=P<sup>i</sup>Pr<sub>2</sub>)Pt(p-Tol<sub>3</sub>P)<sub>2</sub>], [(η<sub>2</sub>-P=P<sup>t</sup>Bu<sub>2</sub>)Pt(p-Tol<sub>3</sub>P)<sub>2</sub>], [{η<sub>2</sub>-P=P(N<sup>i</sup>Pr<sub>2</sub>)2}Pt(p-Tol<sub>3</sub>P)<sub>2</sub>] and [{(Et<sub>2</sub>PhP)<sub>2</sub>Pt}<sub>2</sub>P<sub>2</sub>].
PublicationReakcje pochodnych litowych difosfanów R2P-P(SiMe3)Li z (R'3P)2PtCl2 zachodzą łatwo i prowadzą do wytworzenia bocznie (side-on) związanych fosfanofosfinidenowych kompleksów platyny [(η2-P=PR2)Pt(PR'3)2] (dla R=tBu, iPr, Et2N, iPr2N). Reakcja Ph2P-P(SiMe3)Li...
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Identity verification based on mouse movements
PublicationW pracy przedstawiono ideę systemu zabezpieczeń biometrycznych opartego na sposobie poruszania myszą. Pomiary odczytywane z myszy są przykładem cech behawioralnych, które w przeciwieństwie do fizjologicznych są bardzo niestabilne. Opisano zbiór cech, które można wydobyć z danych pochodzących z myszy. Przeprowadzono eksperymenty dla danych zebranych od trzynastu użytkowników. Zaprezentowano wyniki uwierzytelniania za pomocą metody...
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Cardinal regenerative features of the MRL mouse
PublicationIn this review, we discuss recent studies relating to major features of adult MRL mouse biology that contribute to the regenerative responses seen. These include an increased inflammatory cell profile, a unique glycolytic metabolic state typically found during embryogenesis, and a cell cycle phenotype of DNA damage and G2/M arrest. These traits have been found in other mammalian and non-mammalian regenerative systems. How these...
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On-line P-coloring of graphs
PublicationFor a given induced hereditary property P, a P-coloring of a graph G is an assignment of one color to each vertex such that the subgraphs induced by each of the color classes have property P. We consider the effectiveness of on-line P-coloring algorithms and give the generalizations and extensions of selected results known for on-line proper coloring algorithms. We prove a linear lower bound for the performance guarantee function...