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Search results for: LERAY–SCHAUDER DEGREE
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Conley index in Hilbert spaces and the Leray-Schauder degree
PublicationZdefiniowane są liczby Bettiego i charakterystyka Eulera LS-indeksu dla potoków generowanych przez pole zwarte w przestrzeni Hilberta. Główna teza pracy to wzór typu Poincare-Hopfa łączący wspomnianą chatrakterystykę Eulera ze stopniem Leray-Schaudera.
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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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A NEW MASTER'S DEGREE PROGRAM IN GEODESY
PublicationFaculty of Civil and Environmental Engineering (WILiS) at Gdansk University of Technology (GUT) offers studies in the fields of Geodesy and Cartography. The bachelor program (7 semesters) was started ten years ago in 2009. It provides the student with the basic skills and knowledge in the fields of surveying, geodesy and more generally geomatics and cartography. It is strongly related to expertise knowledge of civil building (geodetic...
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Degree product formula in the case of a finite group action
PublicationLet V, W be finite dimensional orthogonal representations of a finite group G. The equivariant degree with values in the Burnside ring of G has been studied extensively by many authors. We present a short proof of the degree product formula for local equivariant maps on V and W.
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Seiberg-Witten invariants the topological degree and wall crossing formula
PublicationFollowing S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.
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Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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Quantum mechanical which-way experiment with an internal degree of freedom
PublicationFor a particle travelling through an interferometer, the trade-off between the available which-way information and the interference visibility provides a lucid manifestation of the quantum mechanical wave-particle duality. Here we analyse this relation for a particle possessing an internal degree of freedom such as spin. We quantify the trade-off with a general inequality that paints an unexpectedly intricate picture of wave-particle...
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Effects of the Origin and Deacetylation Degree of Chitosan on Properties of Its Coatings on Titanium
PublicationThe properties of chitosan coatings on titanium surfaces may be influenced by a variety of factors, including their chemical characteristics and the deposition method. The aim of this research was to determine the influence of a chitosan’s origin (a type of shrimp) and deacetylation degree (DD), when deposited on a very smooth titanium surface, on adhesion and biological behavior. The tests were performed using chitosan of a degree...
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On the dervative of the Legendre function of the first kind with respect to its degree [Corrigendum]
PublicationSkorygowano błąd matematyczny w pracy: R. Szmytkowski, On the derivative of the Legendre function of the first kind with respect to its degree, J. Phys. A: Math. Gen. Vol. 39(2006) s. 15147-15172 [744014]
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The computational complexity of the backbone coloring problem for bounded-degree graphs with connected backbones
PublicationGiven a graph G, a spanning subgraph H of G and an integer λ>=2, a λ-backbone coloring of G with backbone H is a vertex coloring of G using colors 1, 2, ..., in which the color difference between vertices adjacent in H is greater than or equal to lambda. The backbone coloring problem is to find such a coloring with maximum color that does not exceed a given limit k. In this paper, we study the backbone coloring problem for bounded-degree...
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Topological degree for equivariant gradient perturbations of an unbounded self-adjoint operator in Hilbert space
PublicationWe present a version of the equivariant gradient degree defined for equivariant gradient perturbations of an equivariant unbounded self-adjoint operator with purely discrete spectrum in Hilbert space. Two possible applications are discussed.
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“Space & Satellite Technologies" intercollegiate master-degree courses of study in Tri-City (Poland)
PublicationSince summer semester of the academic year 2016/2017, two faculties of Gdansk University of Technology GUT (Faculty of Mechanical Engineering and Faculty of Electronics, Telecommunications and Informatics) together with the Gdynia Maritime University (Faculty of Electronics) and the Polish Naval Academy in Gdynia (Faculty of Command and Naval Operations) have opened intercollegiate master -...
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A novel degree-hour method for rational design loading
PublicationCooling degree-hours (CDH) received the broadest application in evaluation of the ambient air cooling efficiency in power engineering (engine intake air cooling systems) and air conditioning. The current CDH numbers are defined as a drop in air temperature multiplied by associated time duration of performance and their summarized annual number is used to estimate the annual effect achieved due to sucked air cooling in power plants...
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Engineering and Management of Space Systems - an International Joint Master's Double-Degree Programme
PublicationDynamic development of the European space sector results in a necessity for suitable Higher Education Institution graduates. Current study programs of Aerospace Technology are focused on the field of mechanical engineering. Although engineering methods for design, construction and assembly of mechanical systems are covered, interdisciplinarity and life cycle aspects are not considered in a sufficient degree. Due to the increasing...
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From hobbies, straightforward analysis to serious research – the road to phd degree
PublicationThe illustration of the main articles goal is an example of author's academic career course, the aim of which is to obtain a doctoral degree in the field of geodesy and cartography. Today, the most important thing for the young scientist is the devotion to research in certain field of science, which is interested for the large community of scientists. From a psychological point of view, a unity of interest and experiments must...
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A selectively reduced degree basis for efficient mixed nonlinear isogeometric beam formulations with extensible directors
PublicationThe effect of higher order continuity in the solution field by using NURBS basis function in isogeometric analysis (IGA) is investigated for an efficient mixed finite element formulation for elastostatic beams. It is based on the Hu–Washizu variational principle considering geometrical and material nonlinearities. Here we present a reduced degree of basis functions for the additional fields of the stress resultants and strains...
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Degree of monopoly and market power vs. price flexibility in Polish economy: empirical analysis based on COICOP classification
PublicationResearch background: The issue of price flexibility is crucial in the economy both in the aspect of company theory and its macroeconomic consequences. In a number of publications, the sources of variable price flexibility are linked to the market power of enterprises as well as the market structure that has developed in a given branch. It is difficult to indicate empirical studies that would state clearly whether price flexibility...
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Characterization of carbon deposit with controlled carburization degree
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Sum Coloring of Bipartite Graphs with Bounded Degree
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Degree of T-equivariant maps in R^n
PublicationW pracy przedstawiona jest konstrukcja niezmienniczego stopnia topologicznego dla odwzorowań z symetriami działających na przestrzeni euklidesowej z inwolucją. Udowodnione jest twierdzenie, że dwa dopuszczalne i gradientowe odwzorowania niezmiennicze są niezmienniczo homotopijne wtedy i tylko wtedy, gdy są one homotopijne niezmienniczo i gradientowo.
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Sum coloring of bipartite graphs with bounded degree.
PublicationArtykuł poświęcony jest złożoności obliczeniowej zagadnienia sumacyjnego kolorowania grafów dwudzielnych o ograniczonym stopniu. Zawiera dowód tego, że sumacyjne kolorowanie grafów dwudzielnych stopnia mniejszego równego 5 jest NP-zupełne oraz opis wielomianowego algorytmu, który optymalnie sumacyjnie koloruje grafy dwudzielne podkubiczne.
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CPTU test - a tool for consolidation degree estimation.
PublicationW artykule przedstawiono metody oceny stopnia konsolidacji podłoża gruntowego z wykorzystaniem nowoczesnych technik sondowania statycznego metodą CPTU.
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Engineering and Management of Space Systems (EMSS) - an international joint Master's double-degree program
PublicationDynamic development of the space sector of European, and especially of Polish and German economies results in a necessity for suitable Higher Education Institution graduates. The increasing digitization, distribution and networking of technical systems leads to the necessity of a degree programme teaching “the systems view” and “interdisciplinarity” methods and skills. Furthermore, it is necessary to consider the entire life cycle...
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The complexity of the T-coloring problem for graphs with small degree
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Type D personality and the degree of control of bronchial asthma
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Assessment of the Degree of Factors Impact on Employment in Ukraine’s Agriculture
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Packing [1,Delta]-factors in graphs of small degree
PublicationRozważano problem znalezienia w grafie zadanej liczby k krawędziowo rozłącznych [1,Delta]-faktorów, gdzie Delta oznacza stopień grafu. Problem ten można rozwiązać w czasie liniowym dla k=2, jest on jednak NP-trudny dla każdego k>=3. Pokazano, że wariant minimalizacjny problemu dla k=2 jest NP-trudny dla grafów planarnych podkubicznych, jednak w ogólności istnieje algorytm (42 Delta - 30) / (35 Delta - 21) - aproksymacyjny.
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The complexity of the T-coloring problem for graphs with small degree.
PublicationW pracy ustalono złożoność obliczeniową problemu optymalnego kolorowania grafów o ustalonym stopniu.
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On the derivative of the Legendre function of the first kind with respect to its degree
PublicationPokazano, że pochodna po indeksie funkcji Legendre'a pierwszego rodzaju, obliczona dla całkowitej wartości indeksu, może być wyrażona przez funkcje elementarne. Skonstruowano kilka jawnych reprezentacji tej pochodnej. Zaprezentowano przykłady zastosowań otrzymanych wzorów.
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Equivariant degree of convex-valued applied to set-valued BVP
PublicationW pracy określono stopień ekwiwariantny dla odwzorowań o wartościach zwartych i wypukłych. Zastosowano go do dowodu twierdzenia o istnieniu wielunietrywialnych rozwiązań problemu brzegowego typu Dirichleta dla inkluzji różniczkowych z warunkami wzrostu typu Bernsteina-Nagumo, z dodatkowymi symetriami
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Evaluation of Inoculated Waste Biological Stabilization Degree by Olfactometric Methods
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Dynamic mechanical properties and flexing fatigue resistance of tire sidewall rubber as function of waste tire rubber reclaiming degree
PublicationA stepwise downsizing method of gel particles in reclaimed rubber to a micro-nano scale and its excellent dynamic performance in tire sidewall were introduced by this work. The results showed that the size of gel particles decreased from several micrometers to micro-nanometers with the increase of reclaiming degree, accompanied by reduced molecular weight and widened molecular weight distribution of sol fraction. The addition of...
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On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order).
PublicationWyprowadzono szereg zamkniętych wyrażeń dla pochodnych stowarzyszonej funkcji Legendre'a pierwszego rodzaju względem jej dolnego indeksu w przypadku, gdy górny indeks jest liczbą całkowitą. Wyniki zastosowano do znalezienia pewnych nowych reprezentacji (w tym typu Rodriguesa) stowarzyszonych funkcji Legendre'a drugiego rodzaju o indeksach całkowitych.
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On the derivative of associated Le.gendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
PublicationW pracy podano szereg zamkniętych wyrażeń dla pochodnej stowarzyszonej funkcji Legendre'a o stopniu (dolnym indeksie) całkowitym względem jej rzędu (górnego indeksu). Wyniki zastosowano do wyprowadzenia kilku nowych reprezentacji, w tym typu Rodriguesa, stowarzyszonych funkcji Legendre'a drugiego rodzaju z całkowityni indeksani.
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Chaotic invariant sets of vibro-impact systems with one degree of freedom
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Addendum to ''On the derivative of the Legendre function of the first kind with respect to its degree''
PublicationPraca stanowi uzupełnienie wcześniejszej publikacji autora [J. Phys. A: Math. Gen. 39(2006) 15147-15172]. Przedstawiono w niej nowe wyrażenia dla pochodnej funkcji Legendre'a względem jej indeksu i zastosowano je do konstrukcji dwóch nowych reprezentacji funkcji Legendre'a drugiego rodzaju z całkowitym indeksem.
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Method of determining the degree of liquid aeration in a variable capacity displacement pump
PublicationThe Author concludes, that there is a possibility of determining a concrete value of the liquid aeration coefficient during the pump operation by finding such value of coefficient with which the increase of torque of mechanical losses is proportional to the indicated torque determined with a fixed value of increase of pressure in the pump working chambers. The fixed value of increase of pressure assumed in searching the liquid...
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Equivariant degree of convex-valued maps applied to set-valued BVP
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Modelling and testing of a hydrodynamic clutch filled with electrorheological fluid in varying degree
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Degree Days as a Method to Estimate the Optimum Harvest Date of ‘Conference’ Pears
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Degree Days as a Method to Estimate the Optimal Harvest Date of ‘Conference’ Pears
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Effect of cross-linking degree on selected properties of retrograded starch adipate
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Degree of entaglement as a physically ill-posted problem: The case of entaglement with vacuum
PublicationAnalizujemy przypadek fotonu w superpozycji różnych modów i zadajemy pytanie o stopień ich splątania z próżnią. Problem okazuje się być źle postawiony, gdyż nie wiemy którą reprezentację algebry CCR wybrać dla kwantowania pola. Gdy dokonamy wyboru jednoznacznie możemy rozwiązać zagadnienie splątania. Tak więc trudność nie leży w matematyce lecz w fizyce problemu.
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Modeling of Composite Shells in 6-Parameter Nonlinear Theory with Drilling Degree of Freedom
PublicationWithin the framework of a 6-parameter nonlinear shell theory, with strain measures of Cosserat type, constitutive relations are proposed for thin elastic composite shells. The material law is expressed in terms of five engineering constants of classical anisotropic continuum plus an additional parameter accounting for drilling stiffness. The theory allows for unlimited displacements and rotations. A number of examples are presented...
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Grazing bifurcation and chaotic oscillations of vibro-impact systems with one degree of freedom
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Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: II
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Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: I
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Effect of preparation method on the properties of potato starch acetates with an equal degree of substitution
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A review of recent advances in the single- and multi-degree-of-freedom ultrasonic piezoelectric motors
PublicationIn this paper a comprehensive review of recent studies on the ultrasonic piezoelectric motors is presented. The analytical, numerical and experimental analysis. In further sections, classification methods of piezoelectric motors, survey criteria and three main groups of ultrasonic piezoelectric motors with examples have been presented and described. Finally, the conclusions and future research perspectives have been proposed.