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Search results for: DESCRIPTIVE ANALYSIS METHODS
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
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Computer assisted method for proving existence of periodic orbits
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Homoclinic solutions for a class of autonomous second order Hamiltonian systems with a superquadratic potential
PublicationW niniejszej pracy udowodniliśmy istnienie nietrywialnego rozwiązania homoklinicznego dla autonomicznych układów Hamiltona drugiego rzędu z nadkwadratowym potencjałem. Orbitę homokliniczną otrzymaliśmy jako słabą granicę ciągu punktów prawie krytycznych, stosując zasadę minimaks do odpowiedniego funkcjonału akcji oraz prosty argument typu ''concentration-compactness''.
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Minimal number of periodic points for smooth self-maps of two-holed 3-dimensional closed ball
PublicationDla ciągłego odwzorowania f przestrzeni określonej w tytule w siebie, które posiada rzeczywiste wartości własne na drugiej grupie homologii, wyznaczona została minimalna liczba punktów r-periodycznych w klasie wszystkich gładkich odwzorowań homotopijnych z f.
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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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An approximative scheme of finding almost homoclinic solutions for a class of Newtonian systems
PublicationW niniejszej pracy badamy istnienie rozwiązań prawie homoklinicznych (ang. almost homoclinic solutions) dla pewnej klasy układów Newtona. Rozwiązanie prawie homokliniczne otrzymujemy jako granicę ciągu rozwiązań okresowych dla pewnego ciągu równań różniczkowych.
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The Conley index and spectral sequences
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On the space of equivariant local maps
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Spectral sequences and detailed connection matrices
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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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Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublicationLet $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$-periodic points...
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
PublicationFor a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m 4, we provide an algorithm for estimating the values of the topological invariant D^m_r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing D^m_r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013),...
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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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Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator
PublicationWe consider a generalization of the Allen-Cahn type equation in divergence form $-\rm{div}(\nabla G(\nabla u(x,y)))+F_u(x,y,u(x,y))=0$. This is more general than the usual Laplace operator. We prove the existence and regularity of heteroclinic solutions under standard ellipticity and $m$-growth conditions.
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Fixed point indices of iterations of planar homeomorphisms.
PublicationW pracy bada się postać indeksów iteracji lokalnych homeomorfizmów płaszczyzny.
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Multiresolution analysis and adaptive estimation on a sphere using stereographic wavelets
PublicationWe construct an adaptive estimator of a density function on d dimensional unit sphere Sd (d ≥ 2), using a new type of spherical frames. The frames, or as we call them, stereografic wavelets are obtained by transforming a wavelet system, namely Daubechies, using some stereographic operators. We prove that our estimator achieves an optimal rate of convergence on some Besov type class of functions by adapting to unknown smoothness....
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The smoothness test for a density function
PublicationThe problem of testing hypothesis that a density function has no more than μ derivatives versus it has more than μ derivatives is considered. For a solution, the L2 norms of wavelet orthogonal projections on some orthogonal ‘‘differences’’ of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution,...
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On mixing in the class of quadratic stochastic operators
PublicationWe study different types of limit behavior of quadratic stochastic operators acting on ℓ^1 (or ℓ^1_d) spaces in both strong and uniform topologies. The main motif of the paper is to express the uniform and strong asymptotic stability of the quadratic stochastic operator in terms of convergence of the associated (linear) nonhomogeneous Markov chain. We also examine which type of uniform convergence of iterates of the quadratic...
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Nonnegative solutions to nonlocal boundary value problems for systems of second-order differential equations dependent on the first-order derivatives
PublicationStosując tw. Avery-Petersona o punkcie stałym, podano warunki dostateczne na istnienie nieujemnych rozwiązań dla układów równań różniczkowych rzędu drugiego z argumentami opóźnionymi i wyprzedzonymi oraz warunkami brzegowymi zawierającymi całki Stieltjesa. Praca zawiera wiele przykładów.
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublicationQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the ℓ1 space. It turns out that in principle most of the results can be carried over to the L1 space. However, due to topological properties of this space one has to restrict in some situations to kernel quadratic stochastic operators. In this article we study the uniform and strong asymptotic...
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Fixed orbit index for equivariant maps
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Boundary value problems with causal operators
PublicationPraca dotyczy istnienia rozwiązań dla równań różniczkowych z nieliniowymi dwu-punktowymi warunkami brzegowymi. Podano warunki dostateczne na istnienie rozwiązań takich zagadnień stosując metodę iteracji monotonicznych. Dyskutowano też nierówności różniczkowe rzędu pierwszego z dodatnimi operatorami liniowymi oraz problem rozwiązań ekstremalnych.
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Positive solutions for fourth-order differential equations with deviating arguments and integral boundary conditions
PublicationBadane są problemy brzegowe dla równań różniczkowych rzędu czwartego z odchylonymi argumentami i z warunkami brzegowymi typu całkowego. Sformułowano twierdzenie dotyczące istnienia dodatnich rozwiązań takich problemów. W dowodzie korzystano z tw. Avery-Petersona o punktach stałych dla stożków. Podano przykład ilustrujący otrzymane wyniki.
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Existence of solutions for second order impulsive differential equations with deviating arguments
PublicationPraca dotyczy równań różniczkowych z impulsami i odchylonymi argumentami. Badano problem istnienia rozwiązań stosując metodę iteracji monotonicznych opartą na dolnych i górnych rozwiązaniach. Praca uogólnia szereg znanych wyników.
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Fourier transform symmetry and invariance for neurocontrol of NARMA models
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Positive solutions for second order impulsive differential equations involving Stieltjes integral conditions
PublicationIn this paper we investigate integral boundary value problems for fourth order differentialequations with deviating arguments.Wediscuss our problem both for advanced or delayedarguments. We establish sufficient conditions under which such problems have positivesolutions. To obtain the existence of multiple (at least three) positive solutions, we use afixed point theorem due to Avery and Peterson. An example is also included to...
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The equivariant spectral flow and bifurcation of periodic solutions of Hamiltonian systems
PublicationWe define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This G-equivariant spectral flow shares all common properties of the integer valued classical spectral flow, and it can be non-trivial even if the classical spectral flow vanishes. Our main theorem uses the G-equivariant spectral flow...
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Clarke duality for Hamiltonian systems with nonstandard growth
PublicationWe consider the existence of periodic solutions to Hamiltonian systems with growth conditions involving G-function. We introduce the notion of symplectic G-function and provide relation for the growth of Hamiltonian in terms of certain constant CG associated to symplectic G-function G. We discuss an optimality of this constant for some special cases. We also provide applications to the Φ-laplacian type systems.
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Equivariant Conley index in Hilbert spaces and applications to strongly indefinite problems
PublicationW pracy zdefiniowano teorię indeksu Conley`a w przestrzeni Hilberta z działaniem zwartej grupy Liego. Została ona wykorzystana do szacowania z dołu ilości rozwiązań periodycznych w teorii nieliniowych autonomicznych układów Hamiltona.
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Comparision principles for parabolic differential - functional initial - value problems.
PublicationBadamy paraboliczne równania z zależnością funkcyjną i podajemy kryteria jednoznaczności przy warunkach porównawczych typu Perrona i Lipschitza dla nieliniowej prawej strony. W przypadku gdy zależność funkcyjna dotyczy również pochodnej funkcji niewiadomej, to stosujemy nierówności typu Henry'ego.
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Boundary value problems for first order differential equations of mixed type
PublicationPraca dotyczy równań różniczkowo-całkowych z nieliniowymi warunkami brzegowymi. Podano warunki dostateczne na istnienie jedynego rozwiązania oraz rozwiązań ekstremalnych takich problemów. Dyskutowane są nierówności różniczkowo-całkowe. Podano przykłady ilustrujące otrzymane wyniki teoretyczne.
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Between Descriptive Geometry and CAD 3D
PublicationDescriptive geometry provides methods to analyse three-dimensional space through two-dimensional drawings and prepares to create technical documentation. Geometric form of an engineering project is presented by the means of projection methods based on a 3D model, which is present in designer’s imagination. The forthcoming era of Building Information Modelling (BIM) brings changes in the way the engineer works, as the vision is...
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The Use of Photographs in the Teaching/Learning of Descriptive Geometry
PublicationThe article presents the concept of enriching the Descriptive Geometry course with photographs and several simplified real-life engineering tasks. The photographic images used for the exercises are tightly linked to engineering structures, the given specialization and the surrounding world. The photo image as a record of central projection of a real space can be useful for presentation and analysis of the properties of perspective....
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Examples of Original Descriptive Geometry Task Items
PublicationThe paper presents several descriptive geometry drawing tasks and a comprehensive approach to their evaluation. The results as the task profile include the most important features and enable interpretation of the tasks in the educational system.
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Mulimedia manuals for descriptive geometry and engineering graphics
PublicationThe article discusses issues connected with ICT (Information and Communication Technologies) implementation in Descriptive Geometry and Engineering Graphics Education. The presentation of the issues is supported by the author's multimedia manuals made in Multimedia Flash MX technology and published on the Gdańsk University of Technology net.
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Selection of descriptive geometry textbooks
PublicationW artykule przedstawiono koncepcję badania podręczników do geometrii wykreślnej bazującą na psycholingwistycznej teorii komunikatu. Zaprezentowane podejście umożliwia analizę podręczników na sześciu poziomach odnoszących się do głównych funkcji komunikacji międzyludzkiej. W artykule skupiono się na postrzeganiu językowej funkcji podręczników geometrii wykreślnej i w tym zakresie stwierdzono wiele cech zbieżnych.
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Descriptive Modelling of Virtual Transactions.
PublicationArtykuł prezentuje opisowy model transakcji detalicznych, w którym ich znaczenie (IOR) wyrażone przez strukturę sprzedaży i udział w rynku jest uwarunkowane funkcjonalnością (FUN), na którą wpływają w sposób zwrotny trzy grupy czynników : technologicznych, (TFG) ludzkich (HFG) oraz rynkowych (MFG).
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Preparation of Descriptive Geometry Course in English
PublicationW artykule przedstawiono wybrane różnice stosowane w zapisie konstrukcji geometrycznych w podręcznikach do geometrii wykreślnej w różnych krajach.
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Descriptive geometry tasks with computer aided design for geodesy and cartography
PublicationZasady rzutowania topograficznego i środkowego stanowią teoretyczną podstawę dla kluczowych przedmiotów zawodowych na kierunku Geodezja i Kartografia, dlatego dobór zarówno treści nauczania jak i konkretnych zadań ćwiczeniowo-projektowych w ramach geometrii wykreślnej jest szczególnie istotny. W artykule na przykładzie tematów zadań rysunkowych omówiono zakres tematyczny z perspektywy dla danego kierunku studiów oraz sposoby jego...
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GDAŃSK UNIVERSITY OF TECHNOLOGY - A CONTINUATOR OF THE LVIV SCHOOL OF ARCHITECTS' EDUCATION ON THE EXAMPLE OF DESCRIPTIVE GEOMETRY TEACHING
PublicationThe new theory at the time was descriptive geometry, quickly reached the Polish lands. Her first lecture was held at the Warsaw School of Artillery and Engineering in 1809-1812, by a French teacher Jan Joachim Livet (1809-12). The new discipline was quickly adopted in all major centers of Polish science at that time, which include university cities - Warsaw, Krakow, Vilnius and the Krzemienieckie High School, which represent high...
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Spiritual care competence and caring abilities among Polish nurses: a correlation descriptive study
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Agile approach in a transforming organization, a descriptive study of chosen Polish companies with rapid revenue growth
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Public Finance in Poland in a COVID Fog: A Look Through the Lens of Fiscal Transparency and Accountability
PublicationAbstract. Goal– The aim of the article is to identify dysfunctional phenomena (implementation of specific mechanisms/solutions and actions taken), generating increased opacity and limit the responsibility/accountability of public f inance in Poland, exacerbated by the COVID-19 crisis. Methods– descriptive analysis, comparative analysis and financial analysis methods were used. Results– fiscal transparency and accountability in...
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Impact of cross-section centers estimation on the accuracy of the Point cloud spatial expansion using robust M-estimation and Monte Carlo simulation
PublicationThe point cloud spatial expansion (PCSE) method creates an alternative form of representing the shape of symmetrical objects and introduces additional descriptive geometric parameters. An important element of the procedure is determining the course of the axis of symmetry of cylindrical objects based on cross-sections of point clouds. Outliers occurring in laser measurements are of great importance in this case. In this study,...
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Use of structural equation modeling in quantitative research in the field of management and economics: A bibliometric analysis in the systematic literature review
PublicationPURPOSE: This paper aims to provide a comprehensive review of scholarly research focusing on using quantitative methods and particularly structural equation modeling (SEM) in management and economics studies, as well as provide a bibliometric agenda including the time horizon of individual publications, the highest citation rate, geographic and industry areas, methodological context, and keywords. METHODOLOGY: A systematic literature...
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Family business succession – the practical or also theoretical problem. Bibliometric analysis
PublicationFamily businesses, in various forms, have existed since societies began to be created. However, family business research has a decidedly shorter tradition. In favorable conditions, family enterprises develop for many generations, and their fate is intertwined with the fate of the families. The topics of family businesses are raised by researchers around the world. Estimates regarding the number of family businesses are a frequent...
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Typology and comparative analysis of black tents built in tradition of iranian tribes
PublicationThis study focused on the habits and way of life of nomads in the Iranian Highlands, but their homes, called Black Tents, were of the main interest. The research explored the construction of the Black Tents and the way of shaping the space in which family life takes place. It concerned the architectural forms of tents, structures and materials from which they are erected, as well as interior furnishings and objects that determine...
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Implementation of International Standards of Fiscal and Monetary Transparency - Case of Poland
PublicationResearch background: Financial managers, investors, lenders, counterparties and citizens should have useful, reliable, timely, complete, comparable, readable information on fiscal and monetary policy. The actions taken and instruments used by fiscal and monetary authorities have an important impact on economic conditions. Purpose of the article: The aim of the article is to assess Poland's compliance with international standards...
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POLAND’S ENERGY DEPENDENCE AT THE TURN OF THE 21ST CENTURY
PublicationThe following article is an attempt to assess Poland's energy independence in the years 1993-2020. The main aim of the paper is to present Poland's dependence on raw materials from foreign partners - in the field of imports of electricity, natural gas, crude oil, non-renewable energy resources, i.e., hard coal and lignite, and the country's dynamics in the amount of imports. In addition, the aim of the work is to answer research...
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Conditions of Iranian international trade in terms of lifting the sanctions: A case study of Polish-Iranian trade perspectives
PublicationThe main aim of the paper is to identify the areas and determine the feasibility of trade between Polish and Iranian companies in relation to historical and cultural conditions. The authors describe the complexity of the issue of foreign trade, the determinants of relations between Poland and the Islamic Republic of Iran, and the Iranian economy – its features, strengths and weaknesses, and consequences of the recent UN, EU, and...