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Search results for: DESCRIPTIVE ANALYSIS METHODS
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A Comprehensive Approach to Azo Dichlorotriazine Dye Treatment: Assessing the Impact of Physical, Chemical, and Biological Treatment Methods through Statistical Analysis of Experimental Data
PublicationThis exploration investigates integrated treatment systems combining advanced oxidation processes (Fenton and photo-Fenton) with biological methods for the effective elimination of stubborn organic compounds in simulated textile wastewater composed of azo Dichlorotriazine dye. A comprehensive optimization of key process factors including catalyst dosage, hydrogen peroxide quantity, irradiation duration, etc. was systematically...
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Analysis of server-side and client-side Web-GIS data processing methods on the example of JTS and JSTS using open data from OSM and geoportal
PublicationThe last decade has seen a rapid evolution of processing, analysis and visualization of freely available geographic data using Open Source Web-GIS. In the beginning, Web-based Geographic Information Systems employed a thick-client approach which required installation of platform-specific browser plugins. Later on, research focus shifted to platform-independent thin client solutions in which data processing and analysis was performed...
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Izolacja lotnych związków organicznych z próbek wody. Metody i aparatura. Analysis of volatile organic compounds (VOCs) in water samples. Methods and apparatus.
PublicationOmówiono techniki wykorzystywane do przygotowania próbek wody do oznaczeń analitów z grupy lotnych związków organicznych (VOCs) za pomocą chromatografii gazowej. Opisano wady i zalety takich technik jak: bezpośrednie dozowanie próbki wody do kolumny chromatograficznej, ekstrakcja rozpuszczalnikiem, ekstrakcja do fazy stałej lub stacjonarnej, ekstrakcja membranowa oraz analiza fazy nadpowierzchniowej. Omówiono także nowe rozwiązania...
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Exploring Modelling Methods in Systems Analysis and Design
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Qualitative data analysis methods
e-Learning CoursesThis is the continuation of Qualitatative Data Analysis Methods course provided online
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International Conference on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (Conference on Analysis of Algorithms)
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Methods of quantitative analysis (team project)
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Qualitative Data Analysis Methods -Summer 2022
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Scientific methods of computer data analysis and presentation
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Analysis of antibiotic resistance in Escherichia coli isolated from the Reda River and the Oliwski Stream using basic statistical methods = Zastosowanie metod ststystycznych do analizy antybiotykoodporności bakterii wskaźnikowych pochodzących z rzeki Redy i Potoku Oliwskiego
PublicationIn this study distribution of antimicrobial resistance patterns among fecal indicator bacteria (Escherichia coli and Enterococcus spp.) was examined in two watercourses. The susceptibility analyses were carried out against the antimicrobial agents, important in treating human E. coli and enterococcal infection. Water samples were obtained from the Oliwski Stream and from the Reda River. On each watercourse the five representative...
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METHODS OF QUANTITATIVE ANALYSIS (TEAM PROJECT) (2022/2023)
e-Learning CoursesMETHODS OF QUANTITATIVE ANALYSIS (TEAM PROJECT) - Economic Analytics, Lecture and Lab, Winter Semester 2022/2022. Teacher: dr Piotr Paradowski
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Qualitative Data Analysis Methods -Summer 22/23
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[AEiE, ITiT] Scientific methods of computer data analysis and presentation - 2022/2023
e-Learning Courses{mlang pl} Dyscyplina: AEiE, ITiT Zajęcia obowiązkowe dla doktorantów II roku Prowadzący: Tomasz Berezowski Liczba godzin: 30 Forma zajęć: wykład/projekt/seminarium {mlang} {mlang en} Discipline: AEiE, ITiT Obligatory course for 2nd-year PhD students Academic teacher: Tomasz Berezowski Total hours of training: 30 teaching hours Course type: Lecture/project/seminar {mlang}
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[AEEiTK, ITiT] Scientific methods of computer data analysis and presentation - 2023/2024
e-Learning Courses{mlang pl} Dyscyplina: AEiE, ITiT Zajęcia obowiązkowe dla doktorantów II roku Prowadzący: Tomasz Berezowski Liczba godzin: 30 Forma zajęć: wykład/projekt/seminarium {mlang} {mlang en} Discipline: AEiE, ITiT Obligatory course for 2nd-year PhD students Academic teacher: Tomasz Berezowski Total hours of training: 30 teaching hours Course type: Lecture/project/seminar {mlang}
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[AEEiTK, ITiT] Scientific methods of computer data analysis and presentation 2024/2025
e-Learning Courses{mlang pl} Dyscyplina: AEiE, ITiT Zajęcia obowiązkowe dla doktorantów II roku Prowadzący: Tomasz Berezowski Liczba godzin: 30 Forma zajęć: wykład/projekt/seminarium {mlang} {mlang en} Discipline: AEiE, ITiT Obligatory course for 2nd-year PhD students Academic teacher: Tomasz Berezowski Total hours of training: 30 teaching hours Course type: Lecture/project/seminar {mlang}
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Weak forms of shadowing in topological dynamics
PublicationWe consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomor- phisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing)...
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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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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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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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Almost homoclinic solutions for the second order Hamiltonian systems
PublicationW niniejszej pracy badam istnienie rozwiązań prawie homoklinicznych (almost homoclinic) dla układu Hamiltona rzędu drugiego (układu Newtona): ü(t) + V_{u}(t,u) = f(t), gdzie t є R, u є R^{n}, V(t,u) = -K(t,u) + W(t,u), K,W: R x R^{n} → R są klasy C^{1}, K spełnia warunek ''pinching'', W_{u}(t,u)=o(|u|), gdy |u| → 0 jednostajnie względem t, f: R → R^{n} jest funkcją ciągłą, niezerową i odpowiednio małą w L^{2}(R,R^{n}). Przy tych...
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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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On the theorem of Tverberg
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Borsuk-Ulam type theorems on product spaces II
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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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Fixed point index for $G$-equivariant multivalued maps
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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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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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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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Selections and approximations of convex-valued equivariant mappings
PublicationUdowodniono szereg twierdzeń o współzmienniczych selekcjach i aproksymacjach ciągłych, mierzalnych i typu Caratheodory'ego dla odwzorowań G-współzmienniczych o wartościach wypukłych, gdzie G jest grupą zwartą Liego. Tw. typu Michaela, Celliny, Browdera, Kuratowskiego-Ryll-Nardzewskiego, Castaing itd.
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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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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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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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The relative cup-length in local Morse cohomology
PublicationLocal Morse cohomology associates cohomology groups to isolating neighborhoods of gradient flows of Morse functions on (generally non-compact) Riemannian manifolds M. We show that local Morse cohomology is a module over the cohomology of the isolating neighborhood, which allows us to define a cup-length relative to the cohomology of the isolating neighborhood that gives a lower bound on the number of critical points of functions...
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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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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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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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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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Fixed orbit index for equivariant maps
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Fourier transform symmetry and invariance for neurocontrol of NARMA models
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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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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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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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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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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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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.