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Wyniki wyszukiwania dla: applied mathematics
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Homoclinic orbits for a class of singular second order Hamiltonian systems in R3
PublikacjaW niniejszym artykule rozważamy autonomiczny układ Hamiltonowski w 3-wymiarowej przestrzeni euklidesowej, z potencjałem osiągającym maksimum globalne właściwe równe zero w początku układu współrzędnych i mającym za zbiór punktów osobliwych prostą, która nie przechodzi przez początek układu. Przy założeniu, że potencjał spełnia pewien warunek zwartości w nieskończoności i warunek Gordona w otoczeniu prostej punktów osobliwych, stosując...
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The shadowing chain lemma for singular Hamiltonian systems involving strong forces
PublikacjaW niniejszym artykule rozważamy autonomiczny układ Hamiltonowski na płaszczyźnie z potencjałem, który ma punkt osobliwy (studnię nieskończonej głębokości) i maksimum globalne właściwe równe zero przyjmowane w dwóch różnych punktach płaszczyzny. Przy założeniu, że w otoczeniu punktu osobliwego potencjał spełnia warunek Gordona(gradient tego potencjału w otoczeniu punktu osobliwego jest tzw. silną siłą, ang. a strong force) dowodzimy...
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Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers
PublikacjaLet f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math....
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Equivariant Morse equation
PublikacjaThe paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.
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Seiberg-Witten invariants the topological degree and wall crossing formula
PublikacjaFollowing 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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Existence and uniqueness of solutions for single-population McKendrick-von Foerster models with renewal
PublikacjaWe study a McKendrick-von Foerster type equation with renewal. This model is represented by a single equation which describes one species which produces young individuals. The renewal condition is linear but takes into account some history of the population. This model addresses nonlocal interactions between individuals structured by age. The vast majority of size-structured models are also treatable. Our model generalizes a number...
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Equitable coloring of corona products of graphs
PublikacjaIn this paper we consider an equitable coloring of some corona products of graphs G and H in symbols, G o H). In particular, we show that deciding the colorability of G o H is NP-complete even if G is 4-regular and H is K_2. Next, we prove exact values or upper bounds on the equitable chromatic number of G o H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a path, a cycle or a complete graph.
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Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3
PublikacjaWe consider a conservative second order Hamiltonian system \ddot{q}+ ∇V(q)=0 in R3 with a potential V having a global maximum at the origin and a line l ∩ {0} = ∅ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
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The Hopf theorem for gradient local vector fields on manifolds
PublikacjaWe prove the Hopf theorem for gradient local vector fields on manifolds, i.e., we show that there is a natural bijection between the set of gradient otopy classes of gradient local vector fields and the integers if the manifold is connected Riemannian without boundary.
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublikacjaWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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Relativity of arithmetic as a fundamental symmetry of physics
PublikacjaArithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters ‘plus’ or ‘times’ one has certain freedom of interpreting this operation. This leads to some freedom in definitions of derivatives, integrals and, thus, practically all equations occurring in...
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Degree product formula in the case of a finite group action
PublikacjaLet 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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THE REPRESENTATION PROBLEM FOR A DIFFUSION EQUATION AND FRACTAL R-L LADDER NETWORKS
PublikacjaThe representation problem is to prove that a discretization in space of the Fourier transform of a diffusion equation with a constant diffusion coefficient can be realized explicitly by an infinite fractal R-L ladder networks. We prove a rigidity theorem: a solution to the representation problem exists if and only if the space discretization is a geometric space scale and the fractal ladder networks is a Oustaloup one. In this...
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Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point.
PublikacjaW niniejszej pracy badamy problem istnienia bifurkacji w zbiorze rozwiązań równania F(x,p)=0, gdzie F jest odwzorowaniem klasy C^2z iloczynu kartezjańskiego X i R^k do Y, X i Y są przestrzeniami Banacha takimi, że X jest podprzestrzenią liniową Y. Co więcej, dany jest iloczyn skalarny w Y, ciągły względem norm w X i Y. Pokazujemy, że pod pewnymi warunkami (0,p) jest punktem bifurkacji i opisujemyzbiór rozwiązań równania F(x,p)=0...
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On the doubly connected domination number of a graph
PublikacjaW pracy została zdefiniowana liczba dominowania podwójnie spójnego i przedstawiono jej podstawowe własności.
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Asymptotic error expansions for Schoenberg type operators.
PublikacjaW pracy wyprowadzono rozwinięcie asymptotyczne dla błędu w L2 operatorówSchoenberga.
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Tomasz Wąsowicz dr hab.
OsobyAbsolwent Technikum Elektrycznego w Słupsku (1997 rok) oraz Wydziału Matematyki, Fizyki i Informatyki Uniwersytetu Gdańskiego (2002 rok). W 2006 roku obronił dysertację doktorską z fizyki na WMFiI UG. Pracując już w PG, w 2018 roku uzyskał habilitację. W pierwszym okresie prace badawcze Tomasza Wąsowicza miały związek ze spektroskopią atomową wysokiej zdolności rozdzielczej i koncentrowały się na pomiarze i analizie prawdopodobieństw...
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Tomasz Klimczuk prof. dr hab. inż.
OsobyStopnie naukowe i zawodowe dr hab. (2008) Wydz. FTiMS PG dr (2001) Wydz. FTiMS PG inż. (1997) Wydz. ZiE PG mgr inż. (1995 )Wydz. FTiMS PG Zatrudnienie grudzień 2013 – do chwili obcecnejprofesor nadzwyczajny na Wydziale Fizyki Technicznej i Matematyki Stosowanej Politechniki Gdańskiej wrzesień 2012 – grudzień 2013 adiunkt na Wydziale Fizyki Technicznej i Matematyki Stosowanej Politechniki Gdańskiej wrzesień 2009 – sierpień 2012grant-holder...
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Grażyna Jarosz dr hab. inż.
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Marcin Byczuk mgr inż.
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Hybrid Obfuscation Technique for Reverse Engineering Problems
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Human-Computer Interface Based on Visual Lip Movement and Gesture Recognition
PublikacjaThe multimodal human-computer interface (HCI) called LipMouse is presented, allowing a user to work on a computer using movements and gestures made with his/her mouth only. Algorithms for lip movement tracking and lip gesture recognition are presented in details. User face images are captured with a standard webcam. Face detection is based on a cascade of boosted classifiers using Haar-like features. A mouth region is located in...
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The symmetrization method and limit cycles of vibro-impact systems
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Structural stability of invariant sets of vibro-impact systems
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On the regularity of the displacement sequence of an orientation preserving circle homeomorphism
PublikacjaWe investigate the regularity properties of the displacemnet sequence of an orientation preserving circle homeomorphism. is rational, then ηn(z) is asymptotically periodic with semi-period q. This
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Paired domination subdivision and multisubdivision numbers of graphs
PublikacjaThe paired domination subdivision number sdpr(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the paired domination number of G. We prove that the decision problem of the paired domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the paired domination muttisubdivision number of a nonempty graph...
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A space-efficient algorithm for computing the minimum cycle mean in a directed graph
PublikacjaAn algorithm is introduced for computing the minimum cycle mean in a strongly connected directed graph with n vertices and m arcs that requires O(n) working space. This is a considerable improvement for sparse graphs in comparison to the classical algorithms that require O(n^2) working space. The time complexity of the algorithm is still O(nm). An implementation in C++ is made publicly available at http://www.pawelpilarczyk.com/cymealg/.
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On the connected and weakly convex domination numbers
PublikacjaIn this paper we study relations between connected and weakly convex domination numbers. We show that in general the difference between these numbers can be arbitrarily large and we focus on the graphs for which a weakly convex domination number equals a connected domination number. We also study the influence of the edge removing on the weakly convex domination number, in particular we show that a weakly convex domination number...
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On-line ranking of split graphs
PublikacjaA vertex ranking of a graph G is an assignment of positive integers (colors) to the vertices of G such that each path connecting two vertices of the same color contains a vertex of a higher color. Our main goal is to find a vertex ranking using as few colors as possible. Considering on-line algorithms for vertex ranking of split graphs, we prove that the worst case ratio of the number of colors used by any on-line ranking algorithm...
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On the ratio between 2-domination and total outer-independent domination numbers of trees
PublikacjaA 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)D has a at least two neighbors in D. A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The 2-domination (total outer-independent domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (total...
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On trees with double domination number equal to 2-outer-independent domination number plus one
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G=(V,E), a subset D subseteq V(G) is a 2-dominating set if every vertex of V(G)D has at least two neighbors...
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Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
PublikacjaWe consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is...
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Tomasz Sobczyk
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Józef Eugeniusz Sienkiewicz prof. dr hab.
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Positive solutions to Sturm–Liouville problems with non-local boundary conditions
PublikacjaIn this paper, the existence of at least three non-negative solutions to non-local boundary-value problems for second-order differential equations with deviating arguments α and ζ is investigated. Sufficient conditions, which guarantee the existence of positive solutions, are obtained using the Avery–Peterson theorem. We discuss our problem for both advanced and delayed arguments. An example is added to illustrate the results.
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Orken Mamyrbayev Professor
Osoby1. Education: Higher. In 2001, graduated from the Abay Almaty State University (now Abay Kazakh National Pedagogical University), in the specialty: Computer science and computerization manager. 2. Academic degree: Ph.D. in the specialty "6D070300-Information systems". The dissertation was defended in 2014 on the topic: "Kazakh soileulerin tanudyn kupmodaldy zhuyesin kuru". Under my supervision, 16 masters, 1 dissertation...
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Agent-based social network as a simulation of a market behaviour
PublikacjaRecent years and the outbreak of world's economic crisis in 2008 proved the crucial importance of reliable analysis of market dynamics. However, werarely apply models of proper detail level (the global prosperity forecast of 2007 can be seen as a grim proof). The behaviour of individuals and companies is far from being ideal and rational. Many claims that the economic paradigm of rational expectations (coming from J. Muth and R....
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A Measurable Selector in Kadison’s Carpenter’s Theorem
PublikacjaWe show the existence of a measurable selector in Carpenter’s Theorem due to Kadison. This solves a problem posed by Jasper and the first author in an earlier work. As an application we obtain a characterization of all possible spectral functions of shift-invariant subspaces of L 2 (R d ) and Carpenter’s Theorem for type I ∞ von Neumann algebras.
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Properties of sensorless control systems based on multiscalar models of the induction motor
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Slot harmonics in cage motors due to saturation of a main magnetic circuit
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Computer simulation of induction heating system with series inverter
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The stand for determining of thermal‐electrical material properties of induction heated charge
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The optimisation of induction heating system based on multiquadric function approximation
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Induction heating in estimation of thermal properties of conductive materials
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Properties of sensorless control systems based on multiscalar models of the induction motors
PublikacjaCelem artykułu jest opracowanie ogólnych postaci multiskalarnych modeli silnika indukcyjnego i zaprezentowanie właściwości bezczujnikowych układów regulacji opartych na takich modelach. Poprzednio prezentowane modele multiskalarne silnika indukcyjnego oparte na wykorzystaniu wektorów prądu stojana i strumienia wirnika zostły uogólnione jako model typu 1. Nowy model typu 2 zdefiniowany został dla wektora prądu stojana i innego wektora...
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Implementation of power transformer controlled switching algorithm
PublikacjaThe article presents two new algorithms of controlled switching the power transformer. The main aim of the paper is to obtain formulas that determine the moments of closing of the circuit breaker poles. The study contains projects of control systems for both algorithms. Mathematical formulas for the time instants of the breaker poles closing were developed on the basis of electric circuit theory and magnetic circuit theory. The...
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Magnetic and infrared thermography methods in detection of antipersonnel landmines
PublikacjaIn this paper the two alternative methods of antipersonnel landmine detection are shown: the magnetic method and the active infrared thermography. The experimental results of the detection of selected, plastic mines using both methods are also presented.
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Research of leakage magnetic field in deenergized transformer
PublikacjaThe article deals with the issue of the numerical analysis of the magnetic field occurring around the transformer after it has been powered down. The main goal of this analysis was to examine if it is possible to identify the residual fluxes in the transformer legs based on this fields’ measurements. It was also intended to determine the type and the location of magnetic sensors. Numerical analysis of the magnetic field was performed....
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Representation of magnetic hysteresis in a circuit model of a single-phase transformer
PublikacjaThe paper presents a mathematical model for the hysteresis phenomenon in a multi-winding single-phase core type transformer. The set of loop differential equations was developed for K-th winding transformer model where the flux linkages of each winding includes a flux common Φ to all windings as function of magneto motive force Θ of all windings. The first purpose of this paper is to determine a hysteresis nonlinearity involved...
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State and control system variables sensitivity to rotor asymmetry in the induction motor drive
PublikacjaThe aim of this paper is to undertake analysis and comparison of the closed-loop and sensorless control systems sensitivity to the broken rotor for diagnostic purposes. For the same vector control system induction motor drive analysis concerning operation with the asymmetric motor, broken rotor fault handling and operation were investigated. Reliability, range of stable operation, fault symptoms and application of diagnosis methods...