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Search results for: orlicz-sobolev spaces
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Anisotropic Orlicz–Sobolev spaces of vector valued functions and Lagrange equations
PublicationIn this paper we study some properties of anisotropic Orlicz and Orlicz–Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give conditions which ensure that the principal part of variational functional is finitely defined and continuously differentiable on Orlicz–Sobolev space.
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Regularity of weak solutions for aclass of elliptic PDEs in Orlicz-Sobolev spaces
PublicationWe consider the elliptic partial differential equation in the divergence form $$-\div(\nabla G(\nabla u(x))) t + F_u (x, u(x)) = 0,$$ where $G$ is a convex, anisotropic function satisfying certain growth and ellipticity conditions We prove that weak solutions in $W^{1,G}$ are in fact of class $W^{2,2}_{loc}\cap W^{1,\infty}_{loc}$.
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Minimization of integral functionals in Sobolev spaces
PublicationPraca ma charakter przeglądowy i jest skierowana do młodych matematyków i doktorantów. Dotyczy problematyki omawianej przeze mnie na Zimowej Szkole Centrum Badań Nieliniowych im. J.P. Schaudera w Toruniu w roku 2009. Zawarłam w niej wybrane, znane wyniki dotyczące problemu minimalizacji funkcjonałów całkowych w przestrzeniach Sobolewa funkcji jednej zmiennej.
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Quasilinear elliptic problem in anisotropic Orlicz–Sobolev space on unbounded domain
PublicationWe study a quasilinear elliptic problem $-\text{div} (\nabla \Phi(\nabla u))+V(x)N'(u)=f(u)$ with anisotropic convex function $\Phi$ on the whole $\R^n$. To prove existence of a nontrivial weak solution we use the mountain pass theorem for a functional defined on anisotropic Orlicz-Sobolev space $\WLPhispace(\R^n)$. As the domain is unbounded we need to use Lions type lemma formulated for Young functions. Our assumptions broaden...
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Mountain pass type periodic solutions for Euler–Lagrange equations in anisotropic Orlicz–Sobolev space
PublicationUsing the Mountain Pass Theorem, we establish the existence of periodic solution for Euler–Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part and a forcing term. We consider two situations: G satisfying at infinity and globally. We give conditions on the growth of the potential near zero for both situations.
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On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces
PublicationIn this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function c(x, A) = |A[x]2 |. We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular generated by G is twice differentiable...
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A Generalized Version of the Lions-Type Lemma
PublicationIn this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz–Sobolev spaces. What matters here is the behavior of the integral, not the space
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Periodic solutions of Lagrangian systems under small perturbations
PublicationIn this paper we prove the existence of mountain pass periodic solutions of a certain class of generalized Lagrangian systems under small perturbations. We show that the found periodic solutions converge to a periodic solution of the unperturbed system if the perturbation tends to 0. The proof requires to work in a rather unusual (mixed) Orlicz–Sobolev space setting, which bears several challenges.
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Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator
PublicationUsing the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\Lcal_v(t,u(t),\dot u(t))=\Lcal_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[a,b]\\ u(a)=u(b)=0 \end{cases} \end{equation*} has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian $\Lcal=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$ with growth conditions determined by anisotropic G-function and some geometric conditions...
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Existence of Two Periodic Solutions to General Anisotropic Euler-Lagrange Equations
PublicationAbstract. This paper is concerned with the following Euler-Lagrange system d/dtLv(t,u(t), ̇u(t)) =Lx(t,u(t), ̇u(t)) for a.e.t∈[−T,T], u(−T) =u(T), Lv(−T,u(−T), ̇u(−T)) =Lv(T,u(T), ̇u(T)), where Lagrangian is given by L=F(t,x,v) +V(t,x) +〈f(t),x〉, growth conditions aredetermined by an anisotropic G-function and some geometric conditions at infinity.We consider two cases: with and without forcing termf. Using a general version...
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Homoclinics for singular strong force Lagrangian systems in R^N
PublicationWe will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove...
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Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity
PublicationIn this paper we consider existence and uniqueness of the three-dimensional static boundary-value problems in the framework of so-called gradient-incomplete strain-gradient elasticity. We call the strain-gradient elasticity model gradient-incomplete such model where the considered strain energy density depends on displacements and only on some specific partial derivatives of displacements of first- and second-order. Such models...
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On weak solutions of boundary value problems within the surface elasticity of Nth order
PublicationA study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining...
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Public Spaces - Coexistence and Participation
PublicationThe paper is an attempt to answer two questions: (1) how to develop positive social relations and citizenship among residents of cities in Poland and (2) howsuitable shaping of public space affects the activation and integration of local residents.The specificity of the post-war process of urbanization in Poland - a country traditionally agricultural - was its political dimension (forced 'nationalisation' of agriculture and industrialization...
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Generalized Dobrushin Coefficients on Banach Spaces
PublicationThe asymptotic behavior of iterates of bounded linear operators (not necessarily positive), acting on Banach spaces, is studied. Through the Dobrushin ergodicity coefficient, we generalize some ergodic theorems obtained earlier for classical Markov semigroups acting on L1 (or positive operators on abstract state spaces).
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Investigating Feature Spaces for Isolated Word Recognition
PublicationMuch attention is given by researchers to the speech processing task in automatic speech recognition (ASR) over the past decades. The study addresses the issue related to the investigation of the appropriateness of a two-dimensional representation of speech feature spaces for speech recognition tasks based on deep learning techniques. The approach combines Convolutional Neural Networks (CNNs) and timefrequency signal representation...
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Investigating Feature Spaces for Isolated Word Recognition
PublicationThe study addresses the issues related to the appropriateness of a two-dimensional representation of speech signal for speech recognition tasks based on deep learning techniques. The approach combines Convolutional Neural Networks (CNNs) and time-frequency signal representation converted to the investigated feature spaces. In particular, waveforms and fractal dimension features of the signal were chosen for the time domain, and...
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Architecture of ecumenical spaces in public buildings in the 21st century: Links among the architecture of multi-faith spaces, their names, and the functions they serve in Polish airports
PublicationThis study explores the architecture and arrangement of prayer spaces in public buildings. It examines whether Polish airports have prayers spaces and whether a correlation exists between the name (e.g., “multi-faith space,” “place of prayer,” and “place of focus”) and design. The study is supported by analyses of ecumenical spaces, which have recently been brought into service andwhere a visible symbiosis exists between their...
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Contemporary Spaces of Memory - Towards Transdisciplinarity in Architecture
PublicationThe paper explores new phenomena in the contemporary practice of commemoration implemented through architecture. Architectural objects related to memory can be a place where new trends and phenomena appear earlier than in other architectural objects. The text is an attempt to prove that these new spaces of memory are a kind of laboratory where new ideas taking place in architecture and related disciplines are being tested. Research...
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The Changing Nature of In‐Between Spaces in the Transformation Process of Cities
PublicationIn the in‐between spaces of cities, there are many problems of various nature and scale: functional, spatial, economic, environmental, visual, and social. There are also some hidden potentials that can be activated. The aim of the article is to explore the possibilities of solving existing problems and to show the possibilities of using the potentials of in‐between spaces with regard to the changing nature of a city. The article,...
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Application of Mazur-Orlicz`s theorem in AMISE calculation
PublicationW pracy podano nowe wyprowadzenie formuły asymptotycznej błędu aproksymacji dla operatorów całkowych w przestrzeniach niezmienniczych na przesunięcia. Obliczono asymptotykę błędu średniokwakratowego dla estymatora gęstości.
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Ad hoc prayer spaces – a challenge of the architecture of the 21th century
PublicationThis article considers the problem of arranging places of prayer in the vicinity of universities and dormitories. A survey was conducted among students living in the dormitories of the Gdańsk University of Technology in order to determine if there was a real need to arrange such spaces. Subsequently, examples of temporary chapels designed in the last 20 years in Western European countries were presented. Analysis of the selected...
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Planning the City Against Barriers. Enhancing the Role of Public Spaces
PublicationContemporary cities are being fragmented by growing number of technical barriers like roads, railways, infrastructural objects, that generate variety of problems of different nature. The aim of the research is to present the issues connected with such barriers in the city and the ways of solving them. Main problems are e.g.: the destruction of the complexity of urban fabric, functional disadvantages, environmental and landscape...
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Evolution of Edges and Porosity of Urban Blue Spaces: A Case Study of Gdańsk
PublicationCurrent waterfront studies focus mainly on a land-based perspective, failing to include the water side. Water is, however, not just a resource for port and industrial purposes and an edge to the waterfront; it is also a feature of the waterfront and the complex relation between water and city. Thus, the article suggests that water-land edges need to be re-contextualised, taking into consideration also their shape, functionality,...
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Public spaces connecting cities. Green and Blue Infrastructures potential.
PublicationA city fragmentation causes a lot of negative effects in urban environment such as: disconnecting the environmental, functional and compositional relations, a loss of urban compactness, chaotic development, visual chaos, a domination of technical landscape, reduction of security. This is why one of main challenges for urban planners is to connect the fragmented structures by creating friendly, attractive and safe public space....
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Mazur-Orlicz theorem and asymptotic formula for the error in supreme norm.
PublicationObliczono formułę asymptotyczną błędu interpolacji dla normy supremum.
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Permeability of Waterfronts—Contemporary Approach in Designing Urban Blue Spaces
PublicationThe constant struggle with rising sea levels and flood hazards has resulted in the change of the paradigm in shaping urban waterfronts towards increasing their permeability and creation of urban blue spaces. The aim of the paper was to indicate a new approach in designing public spaces at the sea–land interface by presenting a comparative study of the design solutions used in case of the four selected case studies: the Sea Organs...
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Designing of Parking Spaces on Parking Taking into Account the Parameters of Design Vehicles
PublicationNowadays, in all cities, there is an acute problem of a lack of parking spaces. The number of vehicles is constantly increasing not only in big cities and megacities, but also in small towns of the country, and there are not enough parking places—the pace of solving the problem is several times slower than the growth rate of transport among citizens. The paper is dedicated to the determination of an optimal size of a parking place...
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Recovery and Management of Postindustrial Spaces in the City on Selected Examples od European Implementations
PublicationUndeveloped, neglected and then abandoned post-industrial areas often located in a short distance from city centers have become, on one hand a major problem for city stewards due to the formation of dead urban tissue disturbing the continuity and cohesion of urbanized areas, on the other hand are spaces with high potential for a good location. The article aims to formulate, from the architectural and urban perspective, an answer...
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DESIGNING OF PARKING SPACES TAKING INTO ACCOUNT THE PARAMETERS OF DESIGN VEHICLES IN RUSSIA
PublicationNowadays, in all the cities, there is an acute problem of a lack of parking spaces. The number of vehicles are becoming more and more larger, not only in megacities, but in small cities of the country, as well and there are no more parking places - the pace of solving the problem is several times slower than the rate of the transport growth among the citizens. The article is dedicated to the determination of the optimum sizes parking...
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The evolution of education spaces - from plan as generator to regenerative architecture, virtual rooms and green campuses
PublicationThe study programmes are often considered the main formative factors in the process of educating future architects. Another highly influential component is the architectural characteristics of learning spaces, and consequently the impact of the physical built environment on the quality of education has been widely discussed. However, not often do we realise that the characteristics of education spaces correlate with the organisational...
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Contemporary bottom-up tools for public spaces activation. Współczesne oddolne narzędzia aktywizacji przestrzeni publicznych
PublicationThis article attempts to figure out the current understanding of public spaces and the contemporary tools for bottom-up activation of public spaces to make them more friendly and functional. The paper investigates contemporary public spaces' challenges and what tools can be used to improve them. In this research, the main issue will be the question: what kind of tools and actions can be offered to maintain the quality of public...
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A Study of Cross-Linguistic Speech Emotion Recognition Based on 2D Feature Spaces
PublicationIn this research, a study of cross-linguistic speech emotion recognition is performed. For this purpose, emotional data of different languages (English, Lithuanian, German, Spanish, Serbian, and Polish) are collected, resulting in a cross-linguistic speech emotion dataset with the size of more than 10.000 emotional utterances. Despite the bi-modal character of the databases gathered, our focus is on the acoustic representation...
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Analysis of 2D Feature Spaces for Deep Learning-based Speech Recognition
Publicationconvolutional neural network (CNN) which is a class of deep, feed-forward artificial neural network. We decided to analyze audio signal feature maps, namely spectrograms, linear and Mel-scale cepstrograms, and chromagrams. The choice was made upon the fact that CNN performs well in 2D data-oriented processing contexts. Feature maps were employed in the Lithuanian word recognition task. The spectral analysis led to the highest word...
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Cost-efficient multi-objective design optimization of antennas in highly-dimensional parameter spaces
PublicationMulti-objective optimization of antenna structures in highly-dimensional parameter spaces is investigated. For expedited design, variable-fidelity EM simulations and domain patching algorithm are utilized. The results obtained for a monopole antenna with 13 geometry parameters are compared with surrogate-assisted optimization involving response surface approximation modeling.
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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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Acoustical Standards Used in Design of School Spaces = Standardy akustyczne używane w projektowaniu przestrzeni szkoły
PublicationArtykuł prezentuje wytyczne projektowania akustyki wnętrz w pomieszczeniach szkolnych zawarte w europejskich i amerykańskich standardach technicznych. Opisane są także aktualne polskie przepisy odnoszące się do akustyki wnętrza. We wnioskach zaprezentowano wytyczne dla poprawy komfortu akustycznego w szkołach. // Design guidelines for interior acoustics in learning spaces included in European and American technical standards and...
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On the topology of spaces of partial and local maps
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Shopping Centres - a Threat to Public Spaces?
PublicationObszary wewnętrznych przestrzeni pieszych w centrach handlowych stają się substytutami śródmiejskich przestrzeni publicznych miast. Mimo ich stylizacji architektonicznej na ulice handlowe nie spełniają takiej samej funkcji jak przestrzenie tradycyjne. Powoduje to zagrożenia związane ze wzrostem znaczenia konsumpcjonizmu i tworzenia zamkniętych przestrzeni prywatnych niedostępnych dla całego społeczeństwa. Mimo to mogą one być elementami...
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MEDIA ARCHITECTURE AND INTERACTIVE ART INSTALLATIONS STIMULATING HUMAN INVOLVEMENT AND ACTIVITIES IN PUBLIC SPACES
PublicationThis paper examines the potential for media architecture and interactive art installations to stimulate human involvement and activities in public spaces. On the basis of theoretical approaches, case studies and interdisciplinary surveys, the paper provides insight into how screens projecting media and interactive installations in city spaces can inspire people to become active on many levels. The research is focused, both on temporary...
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Indoor air quality of everyday use spaces dedicated to specific purposes—a review
PublicationAccording to literature data, some of the main factors which significantly affect the quality of the indoor environment in residential households or apartments are human activities such as cooking, smoking, cleaning, and indoor exercising. The paper presents a literature overview related to air quality in everyday use spaces dedicated to specific purposes which are integral parts of residential buildings, such as kitchens, basements,...
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Changing by light - how the lighting of intelligent spaces can influence the urban image
PublicationIn the article light will be presented as a tool in the process of transforming the urban space. The reason for this use of light is the commercial aspect of space that forces it to be still competitive and profitable. Such a need gives rise to many innovative solutions in the city space, which allow transmitting information in order to attract human attention, and sometimes make it even possible to involve the user in the interaction...
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Expedited EM-driven multi-objective antenna design in highly-dimensional parameter spaces
PublicationA technique for low-cost multi-objective optimization of antennas in highly-dimensional parameter spaces is presented. The optimization procedure is expedited by exploiting fast surrogate models, including coarse-discretization EM antenna simulations and response surface approximations (RSA). The latter is utilized to yield an initial set of Pareto non-dominated designs which are further refined using response correction methods....
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Evaluation of working spaces' technical condition of marine diesel engine on the basis of operation research
PublicationThe paper presents the method of evaluation of the technical state of working spaces of a marine diesel engine at the reduced control susceptibility. The method foresees making diagnosis on the basis of the measurements of exhaust gas pressure in the channels connecting engine cylinders with turbocharger's turbine. In the beginning of the article the research objects are characterized i.e. ZVIEZDA main engine of M401 type and the...
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Energy of the City in High Quality Public Spaces in the Presence of Water.The Role of Water in Contemporary Public Spaces in Paris
PublicationW artykule zwrócono uwagę na jeden z aspektów energii miasta - jakość przestrzeni publicznych. Wykazano istotną rolę wody w kształtowaniu przestrzeni publicznych wysokiej jakości w obrębie przekształconych obszarów poprzemysłowych Paryża. Odpowiednie wykorzystanie nadwodnego położenia, bądź wprowadzenie elementów z obecnością wody, pozwoliło stworzyć najbardziej atrakcyjne i niepowtarzalne miejsca.
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Evolution of magnetic and transport properties in (Cr1−xMnx)2AlC MAX-phase synthesized by arc melting technique
PublicationHerein we initiate a comeback to the arc melting technique to produce MAX-phase solid solutions. Bulk samples of (Cr1−xMnx)2AlC MAX-phase with X = 0, 0.025, 0.05 and 0.1 were synthesized and studied by means of X-ray diffractometry, scanning electron microscopy in combination with energy-dispersive X-ray spectroscopy. Samples were established to be homogeneous with an incorporation of Cr7C3, AlCr2 and Al2O3 secondary phases which...
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On the Conley index in Hilbert spaces –- a multivalued case
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On the homotopy equivalence of the spaces of proper and local maps
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On the Conley index in Hilbert spaces - a multivalued case
PublicationW pracy podano definicję niezmiennika topologicznego wykrywającego zbiory niezmiennicze dla wielowartościowych układów dynamicznych generowanych przez inkluzje różniczkowe semiliniowe w przestrzeni Hilberta. Naszkicowano możliwość zastosowania do badania rozwiązań okresowych inkluzji hamiltonowskich.
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On the Conley index in Hilbert spaces in the absence of uniqueness
PublicationW artykule podana jest konstrukcja indeksu Conley`a w przestrzeniach nieskończonego wymiaru dla równań różniczkowych bez jednoznaczności rozwiązań. Celem pracy jest przygotowanie właściwej teorii do badań ilościowych i jakościowych pewnych typów nieliniowych układów eliptycznych.