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Search results for: SOBOLEV SPACES
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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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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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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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Design Space Reduction for Expedited Multi-Objective Design Optimization of Antennas in Highly-Dimensional Spaces
PublicationA surrogate-based technique for efficient multi-objective antenna optimization is discussed. Our approach exploits response surface approximation (RSA) model constructed from low-fidelity antenna model data (here, obtained through coarse-discretization electromagnetic simulations). The RSA model enables fast determination of the best available trade-offs between conflicting design goals. The cost of RSA model construction for multi-parameter...
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Space & Form
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Move into the open space – what can we expect from moving artistic interventions to open urban spaces?
PublicationThe paper discuses the role of incorporating creative engagement into the processes of urban and social development using cultural means of action and expression and the potential of artistic interventions in public space. The block of initiatives within the People’s Smart Sculpture EU project, realized by Gdańsk City Gallery, has been named “Move Into The Open Space”. This paper will provide...
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High Efficiency Configuration Space Sampling -- probing the distribution of available states
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The outdoor market places in the public space of a modern city. - Vol. I
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<title>Estimation and control of discrete fractional order states-space systems</title>
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Governmental supported space internship programmes in new ESA member states - Polish perspective
PublicationOver last 10 years ve new countries - Czech Republic, Romania, Poland, Hungary and Estonia - have joined the European Space Agency. These countries are currently experiencing a considerable increase of space activities aiming to take part in the European and Global space market. New companies, start-ups and consortiums have been created alongside oces of foreign entities have opened their premises in these countries. All of them...
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Translation Spaces
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ADVANCES IN SPACE RESEARCH
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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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Space
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Alternative approach to the solution of the momentum-space Schrödinger equation for bound states of the N-dimensional Coulomb problem
PublicationW pracy rozważono zagadnienie Schrödingera-Coulomba w R^N, N>=2, w reprezentacji pędowej. Radialne równanie całkowe występujące w stowarzyszonym zagadnieniu sturmowskim rozwiązano, stosując podane przez Ossiciniego symetryczne rozwinięcie typu Poissona funkcji Legendre'a drugiego rodzaju w szereg iloczynów wielomianów Gegenbauera. Następnie wykorzystano relację pomiędzy rozwiązaniami zagadnienia sturmowskiego oraz zagadnienia własnego...
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The outdoor market places in the public spaces of a modern city = Miejsca handlu targowego w przestrzeni publicznej współczesnego miasta (vol.1)
PublicationNowadays the market in the public space has different meanings. One of the point of view concentrate on the market as a low attraction of the city, which make it more chaotic. Although there exist contrary point of view – to apply the outdoor markets and the fairs in the public space as a one of the main attraction dedicated for toursits and local people.
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Game about space or game in the space?
PublicationThe article analyzes various aspects of the actions taken by participants involved in the process of a spatial change. Such a process is described as a game about space or a game in the space. Different terminology is presented, in particular the meaning of: spatial order, regional studies, eco-development, sustainable development. Different forms of the game are analyzed: space as a theater, as a casino, as an area of conflict....
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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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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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A note on Banach space isomorphic to Hilbert space
PublicationW pracy charakteryzuje się przestrzenie Hilberta w terminach istnienia pewnych funkcji gładkich.
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Space syntax analysis - methodology of understanding the space
PublicationNowadays space is considered as a net of connections between different areas. The questions how to delineate its character and how it is possible to objectively compare two spaces is the matter under consideration. This was the reason for creating new theories about the structure of place. "Space syntax analysis" (SSA) or simply "Space Syntax" defines a number of theories and research areas devoted to the analysis of space configuration....
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Journal of Function Spaces
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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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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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Redifining the Space – The Impact of Art Instalation in the Public Space
PublicationThe article presents the outcomes of the ‘Art and design’ - interdisciplinary programme WIRE 2013, and the work of studio regarding the impact of art instalation in the public Space . The subject of the workshop was an ‘Architectural Installation’. The relationship between art and architecture remains a challenging issue today, first and foremost in the domain of architecture, and particularly in art and design schools. To address...
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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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On the Conley index in Hilbert spaces –- a multivalued case
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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.
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Rehabilitation Spaces – Architecture for Children with Multiple Disabilities
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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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Energy of change in commercial, innovative and inteligent spaces
PublicationW artykule miasto zostanie zakwalifikowane do przestrzeni komercyjnych, które charakteryzuje ciągłe dążenie do atrakcyjności. Napędza to wykorzystywanie rozwiązań innowacyjnych w zakresie kształtowania przestrzeni, będących nowym źródłem miejskiej energii. W artykule uwaga skupi się innowacyjności przestrzeni, wynikającej z udziału technologii informacyjnych, które na styku z architekturą i sztuką czynią tą przestrzeń inteligentną....
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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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Crystallization of space: Space-time fractals from fractal arithmetic
PublicationFractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated...
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Art of Space – Art in Space / The Role of Sound Art in Public
PublicationThe article presents a discussion of the crossroad between art and architecture. It sketches out the theoretical and practical aspects of space revitalisation and improving its quality in the context of multisensory dimension of public spaces. The unique manifestation of art and creativity in public space could be detected and stimulated using participatory architecture, for instance interactive installations, projects related...
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Journal of Space Weather and Space Climate
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Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions
Publicationwe address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E ; (iii) we prove that the set of placements for which the strain...
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Borsuk-Ulam type theorems on product spaces II
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On iterates of strong Feller operators on ordered phase spaces.
PublicationPraca dotyczy asymptotycznych własności iteracji operatorów Markowa. Udowodniono, że operatory Lasoty i ich wielowymiarowe uogólnienia są asymptotycznie stabilne. Wyniki mają zastosowanie w modelowaniu rozwoju komórki.
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Embracing silence: Creating inclusive spaces for autistic employees
PublicationI concur with Asselineau et al. (2024) that workplace silence profoundly impacts individual and organizational processes. Although they have detailed its significance across different contexts, a vital aspect merits deeper investigation. Namely, many autistic individuals exhibit hypersensitivity to sensory stimuli, such as noise. For this demographic, as well as for nonautistic individuals with sensory processing disorders, exposure...
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Understanding the containment of public spaces: upgrading public domain
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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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On homotopy Conley index for multivalued flows in Hilbert spaces
PublicationPodano aproksymacyjną definicję indeksu homotopijnego, otrzymując naturalne związki z podobnymi niezmiennikami. Zbadano własności tego niezmiennika i zastosowano do badania gradientowych potoków wykazując pewne geometryczne własności zbiorów niezmienniczych
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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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Space and Culture
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Space and Polity
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