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Search results for: history of mathematic
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Critical Case Stochastic Phylogenetic Tree Model via the Laplace Transform
PublicationBirth–and–death models are now a common mathematical tool to describe branching patterns observed in real–world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth–and–death model that is compatible with phylogenetic trees of both influenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the...
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Geometrical versus analytical approach in problem solving- an exploatory study
PublicationAbstract. In this study we analyse the geometrical visualization as a part of the process of solution. In total 263 students in the first year of study at three different universities in three different countries (Poland, Slovakia and Spain) were asked to solve four mathematical problems. The analysis of the results of all students showed that geometrical visualization for problems where there is a possibility to choose different ways...
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Path components of the space of gradient vector fields on the two dimensional disc
PublicationWe present a short proof that if two gradient maps on the twodimensional disc have the same degree, then they are gradient homotopic.
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Difference functional inequalities and applications.
PublicationThe paper deals with the difference inequalities generated by initial boundary value problems for hyperbolic nonlinear differential functional systems. We apply this result to investigate the stability of constructed difference schemes. The proof of the convergence of the difference method is based on the comparison technique, and the result for difference functional inequalities is used. Numerical examples are presented.
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On trees with equal domination and total outer-independent domination numbers
PublicationFor a graph G=(V,E), a subset D subseteq V(G) is a dominating set if every vertex of V(G)D has a neighbor in D, while it is a total outer-independent dominating set if every vertex of G has a neighbor in D, and the set V(G)D is independent. The domination (total outer-independent domination, respectively) number of G is the minimum cardinality of a dominating (total outer-independent dominating, respectively) set of G. We characterize...
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Double bondage in graphs
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G=(V,E) 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, denoted by gamma_d(G), is the minimum cardinality of a double dominating set of G. The double bondage number of G, denoted by b_d(G), is the minimum cardinality among all sets...
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Hat problem on a graph
PublicationThe topic of our paper is the hat problem. In that problem, each of n people is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color looking at the hat colors of the other people. The team wins if at least one person guesses his hat color correctly and no one guesses his hat color wrong, otherwise the team loses. The aim is to maximize the probability of win. In this version every...
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An upper bound on the total outer-independent domination number of a tree
PublicationA total outer-independent dominating set of a graph G=(V(G),E(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 total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n >= 4, with l leaves and s support vertices we have...
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A lower bound on the double outer-independent domination number of a tree
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent 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, and the set V(G)D is independent. The double outer-independent domination number of a graph G, denoted by gamma_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We...
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On the hat problem on a graph
PublicationThe topic of this paper is the hat problem in which each of n players is uniformly and independently fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of winning....
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Remarks on the convergence of an iterative method of solution of generalized least squares problem
PublicationW pracy przedstawiona jest metoda iteracyjna znajdowania regularyzowanego (w sensie Tichonowa) rozwiązania układu równań Ax=b z dowolną macierzą A. Dla danej liczby alfa i wektora g daje ona ciąg przybliżeń zbieżny do rozwiązania (w sensie najmniejszych kwadratów) tego układu. Rozwiązanie to minimalizuje odległość zbioru wszystkich rozwiązań średniokwadratowych układu Ax=b od wektora g. Podane zostało również oszacowanie szybkości...
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A NOTE ON ON-LINE RAMSEY NUMBERS FOR QUADRILATERALS
PublicationWe consider on-line Ramsey numbers defined by a game played between two players, Builder and Painter. In each round Builder draws an the edge and Painter colors it either red or blue, as it appears. Builder’s goal is to force Painter to create a monochromatic copy of a fixed graph H in as few rounds as possible. The minimum number of rounds (assuming both players play perfectly) is the on-line Ramsey number \widetilde{r}(H) of...
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Minimum order of graphs with given coloring parameters
PublicationA complete k-coloring of a graph G=(V,E) is an assignment F: V -> {1,...,k} of colors to the vertices such that no two vertices of the same color are adjacent, and the union of any two color classes contains at least one edge. Three extensively investigated graph invariants related to complete colorings are the minimum and maximum number of colors in a complete coloring (chromatic number χ(G) and achromatic number ψ(G), respectively),...
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Turán numbers for odd wheels
PublicationThe Turán number ex(n,G) is the maximum number of edges in any n-vertex graph that does not contain a subgraph isomorphic to G. A wheel W_n is a graph on n vertices obtained from a C_{n−1} by adding one vertex w and making w adjacent to all vertices of the C_{n−1}. We obtain two exact values for small wheels: ex(n,W_5)=\lfloor n^2/4+n/2\rfloor, ex(n,W_7)=\lfloor n^2/4+n/2+1 \rfloor. Given that ex(n,W_6) is already known, this...
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On domination multisubdivision number of unicyclic graphs
PublicationThe paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622–628], we constructively characterize all connected unicyclic graphs with...
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Decontaminating Arbitrary Graphs by Mobile Agents: a Survey
PublicationA team of mobile agents starting from homebases need to visit and clean all nodes of the network. The goal is to find a strategy, which would be optimal in the sense of the number of needed entities, the number of moves performed by them or the completion time of the strategy. Currently, the field of distributed graph searching by a team of mobile agents is rapidly expanding and many new approaches and models are being presented...
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Mixed graph edge coloring
PublicationW pracy rozważany jest problem kolorowania krawędzi grafu mieszanego, tj. grafu zawierającego zawiero skierowane, jak i nieskierowane krawędzie. Motywację do badań stanowią zagadnienia komunikacyjne z zakresu szeregowania zadań.
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Independence in uniform linear triangle-free hypergraphs
PublicationThe independence number a(H) of a hypergraph H is the maximum cardinality of a set of vertices of H that does not contain an edge of H. Generalizing Shearer’s classical lower bound on the independence number of triangle-free graphs Shearer (1991), and considerably improving recent results of Li and Zang (2006) and Chishti et al. (2014), we show a new lower bound for a(H) for an r-uniform linear triangle-free hypergraph H with r>=2.
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Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs
PublicationGiven a graph G= (V, E), the subdivision of an edge e=uv∈E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G is the minimum number of subdivisions...
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Rothe’s method for physiologically structured models with diffusion
PublicationWe consider structured population models with diffusion and dynamic boundary conditions. The respective approximation, called Rothe’s method, produces positive and exponentially bounded solutions. Its solutions converge to the exact solution of the original PDE.
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Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator
PublicationA new approach is used to investigate the analytical solutions of the mathematical fractional Casson fluid model that is described by the Constant Proportional Caputo fractional operator having non-local and singular kernel near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, and the governing equations were then transformed in non-dimensional form. For the sake of generalized...
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Graphs with equal domination and certified domination numbers
PublicationA setDof vertices of a graphG= (VG,EG) is a dominating set ofGif every vertexinVG−Dis adjacent to at least one vertex inD. The domination number (upper dominationnumber, respectively) ofG, denoted byγ(G) (Γ(G), respectively), is the cardinality ofa smallest (largest minimal, respectively) dominating set ofG. A subsetD⊆VGis calleda certified dominating set ofGifDis a dominating set ofGand every vertex inDhas eitherzero...
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Differential equations with a singular matrix and convergence of approximate solutions
PublicationZastosowano metodę kwazilinearyzacji dla równań różniczkowych z macierzą osobliwą aby pokazać, że odpowiednie ciągi rozwiązań przybliżonych są kwadratowo zbieżne do rozwiązania naszego problemu.Metodę tę zastosowano do układów takich równań różniczkowych.
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Lower bound on the distance k-domination number of a tree
PublicationW artykule przedstawiono dolne ograniczenie na liczbę k-dominowania w drzewach oraz scharakteryzowano wszystkie grafy ekstremalne.
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Performance and Emission Modelling and Simulation of Marine Diesel Engines using Publicly Available Engine Data
PublicationTo analyse the behaviour of marine diesel engines in unsteady states for different purposes, for example to determine the fuel consumption or emissions level, to adjust the control strategy, to manage the maintenance, etc., a goal-based mathematical model that can be easily implemented for simulation is necessary. Such a model usually requires a wide range of operating data, measured on a test stand. This is a time-consuming process...
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Sześćdziesięciolecie Wydziału Mechanicznego
PublicationPrzedstawiono skrótowo 60. letnią historię Wydziału Mechanicznego Politechniki Gdańskiej. Omówiono zmiany w strukturze organizacyjnej wydziału w latach 1945-2005 oraz główne w obszarach edukacji i nauki.
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Twenty five years of the School of Hydraulics
PublicationPodsumowano dorobek naukowy 25 lat Ogólnopolskiej Szkoły Hydrauliki. Przedstawiono historię szkoły, tematykę naukową, wycieczki studialne i inne formy aktywności. Przypomniano również rozwój karier naukowych uczestników Szkół.
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Analysis and improvement attempt of prof. Alan Fowler’s negotiation game
PublicationThe main goal of the following article is to design an improved version of the negotiation game created by prof. Alan Fowler (Fowler, 1997). I have tried to achieve this by constructing four separate versions of the game which represent different approaches while preserving rules, chosen basic technical assumptions and the simplicity of the base game. Each version of the game is supposed to i.a. make it less obvious, create new...
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Preeclampsia Risk Prediction Using Machine Learning Methods Trained on Synthetic Data
PublicationThis paper describes a research study that investigates the use of machine learning algorithms on synthetic data to classify the risk of developing preeclampsia by pregnant women. Synthetic datasets were generated based on parameter distributions from three real patient studies. Four models were compared: XGBoost, Support Vector Machine (SVM), Random Forest, and Explainable Boosting Machines (EBM). The study found that the XGBoost...
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Green analytical chemistry : theory and practice
PublicationThis tutorial review summarises the current state of green analytical chemistry with special emphasis on environmentally friendly sample preparation techniques. Green analytical chemistry is a part of the sustainable development concept; its history and origins are described. Miniaturisation of analytical devices and shortening the time elapsing between performing analysis and obtaining reliable analytical results are important...
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Human factors in nuclear power engineering in Polish conditions
PublicationThe paper “Human factors in nuclear power engineering in polish conditions” focuses on analysis of dynamics of preparing polish society to build first nuclear power plant in XXI century in Poland. Authors compare experience from constructing nuclear power plant Sizewell B (Great Britain) and Sizewell C, which is in preparation phase with polish nuclear power program. Paper includes aspects e.g. of creating nuclear safety culture...
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Human Factors in Nuclear Power Engineering in Polish Conditions
PublicationThe paper “Human factors in nuclear power engineering in polish conditions” focuses on analysis of dynamics of preparing polish society to build fi rst nuclear power plant in XXI century in Poland. Authors compare experience from constructing nuclear power plant Sizewell B (Great Britain) and Sizewell C, which is in preparation phase with polish nuclear power program. Paper includes aspects e.g. of creating nuclear safety culture and...
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A multi-agent method for periodicity detection in distributed events
PublicationMulti-agent systems working in constantly changing environments may be challenged by instantaneous unavailability of their autonomous agents caused e.g. by limited computing resources. A new method of self-organization of distributed service components is proposed, suitable for multi-agent systems. This method relies on particular agents carrying out separate analyzes of their individual processing loads or other specific events....
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Experimental dynamic study on a timber-frame house using shaking table
PublicationThe aim of this paper is to show the results of the shaking table experimental study concerning the behaviour of the model of the timber-frame house under earthquake excitation and impact loading. In order to determine the basic dynamic properties of the undamaged structure, the free vibration and the sweep-sine tests were first conducted. Then, the model was excited using the time history record of the El Centro earthquake of...
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THE CASE OF MANAGEMENT CONCEPTS IN CIVIL AVIATION BUSINESS.
PublicationThe article presents the changes in management concepts used in civil aviation business in last 25 years. There is a need to make prognosis and support decision-making processes with different models but each model is adapted to current management concept. This article will present the changes and possible future trends in management concepts with the description of strengths and weaknesses of each of them. These might be used...
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Kształtowanie tożsamości na przykładzie małych miast województwa pomorskiego
PublicationSmall towns form an important element of the landscape, economy, both social and cultural life of our regions. Moreover, the way they develop determine regional indicators of the quality of life. These centers take today attempt to redefine its role and place in the spatial structures of the region, looking for new impulses and development opportunities to improve the living conditions of the local public. They have deeply divergent...
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LCT, PIV and IR Imaging Detection in Selected Technical and Biomedical Applications
PublicationThermochromic liquid crystals (TLC), Particle Image Velocimetry (PIV) and Infrared Imaging Themography (IR) have been successfully used in non-intrusive technical, industrial and biomedical studies and applications. These four tools (based on the desktop computers) have come together during the past two decades to produce a powerful advanced experimental technique as a judgment of quality of information that cannot be obtained...
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HYDRODYNAMIC THRUST BEARINGS WITH POLYMER LINING
PublicationPolymeric linings of sliding surfaces of the hydrodynamic bearings have been used successfully for over 50 years. Despite of their long history of operation and research, they have not become wide spread in industrial applications. This fact may be surprising, considering th e conclusions that have been published concerning bearing operation and design. This paper summarizes the current...
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DIRECTIONS OF THE SCIENTIFIC RESEARCH CONDUCTED IN THE DEPARTMENT OF MARINE AND POWER PLANTS OF THE FACULTY OF OCEAN ENGINEERING AND SHIP TECHNOLOGY OF THE GDANSK UNIVERSITY OF TECHNOLOGY
PublicationIn this article the short historical outline of the Department of Marine and Land Power Plants of the Faculty of Ocean Engineering and Ship Technology of the Gdansk University of Technology was introduced. Its activity beginnings, in the post-war history of the University, reach 1952. The leading scientific issues, which have been developed for years in three principal directions: design, manufacture and operation of machines and...
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Liquid Crystals, PIV and IR-Photography in Selected Technical and Biomedical Applications
PublicationThermochromic liquid crystals (TLC), Particle Image Velocimetry (PIV), Infrared Imaging Themography (IR) and True-Colour Digital Image Processing (TDIP) have been successfully used in non-intrusive technical, industrial and biomedical studies and applications. These four tools (based on the desktop computers) have come together during the past two decades to produce a powerful advanced...
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Oliwa. Ogrody**2002 nr 12(44) s. 72-76, 7 fot. 1 rys.
PublicationArtykuł przedstawia historię Parku w Oliwie od jego początków w końcu XIIwieku do współczesności oraz omawia zasługi opata Jacka Rybińskiego, KarolaHohenzollerna i Gustawa Schondorfa dla wyglądu parku.
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Pojęcie czasu a termodynamika.
PublicationPrzedstawiono skrótowo najkrótszą historie czasu, po czym omówiono znaczenie tego pojęcia w mechanice klasycznej i współczesnej. Zaprezentowano pojęcie czasu w kosmologii. Powiązano pojecie czasu, z dorobkiem termodynamiki.
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Contra Bellum: Bell's Theorem as a Confusion of Languages
PublicationBell's theorem is a conflict of mathematical predictions formulated within an infinite hierarchy of mathematical models. Inequalities formulated at level k ∈ Z are violated by probabilities at level k+1. We are inclined to think that k=0 corresponds to the classical world, while k=1 — to the quantum one. However, as the k=0 inequalities are violated by k=1 probabilities, the same relation holds between k=1 inequalities violated...
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Unifying Aspects of Generalized Calculus
PublicationNon-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory. The formalism, being very general, is as simple as the calculus we know from undergraduate courses of mathematics. Its theoretical potential is huge, and yet it remains unknown or unappreciated.
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Frame sawing machines for accurate wood re-sawing
PublicationPrzedstawiono zwięzłą historię pilarek ramowych. Zaprezentowano ekologiczne i ekonomiczne zalety pilarek ramowych nowej generacji. Opisano podstawowe cechy układów kinematycznych nowoczesnych pilarek ramowych oraz podano ich podstawowe dane techniczne.
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Wystąpienie z okazji otrzymania tytułu doktora honoris causa Politechniki Łódzkiej
PublicationZdefiniowano określenie geotechnika i jej nauki wyjściowe, historia rozwoju geotechniki, przedstawienie własnych badań naukowych i nowoczesnej tematyki badawczej w geotechnice. Podano autorską działalność wydawniczą w Polsce i zagranicą.
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Edward Kajdański. Z Harbinu do Gdańska - śladami wybitnego absolwenta.
PublicationPrzedstawiono niezwykłe życie i twórczość absolwenta Wydziału Mechanicznego z roku 1960, dyplomaty, pisarza i dziennikarza, wybitnego znawcy historii, kultury i medycyny Dalekiego Wschodu, wpisane w losy harbińskiej Polonii.
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Konserwacja zamku w Malborku jako przykład kształtowania się doktryny konserwatorskiej
PublicationTekst przedstawia historię działań konserwatorskich prowadzonych na zamku w Malborku od końca XVIII w do czasów współczesnych jako przykład ilustrujący kształtowanie się teorii i praktyki konserwatorskiej w Europie.
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RADIATION OF HIGH INTENSITY SOUND BY CIRCULAR DISC BY MEANS OF THE NUMERICAL METHOD
PublicationThe main goal of this paper is to find sound pressure distribution radiated by the circular piezoelectric disc that vibrates with the finite amplitude. There has been presented the pressure distribution close to the radiating surface. Also it is shown the sound pressure distribution in the 3D form. The mathematic modeling was carried out on the base of the nonlinear acoustic equation with the proper boundary condition. The axial...
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Problematyka konserwatorska Zielonej Bramy w Gdańsku.
PublicationDzieje Zielonej Bramy są historią jej konserwacji. W dziejach tych wyróżniają się czytelne okresy, z których każdy powinien być oceniany przez pryzmat zachowanych wartości oryginału Waloryzacja, rozumiana jako poszukiwanie wartości oryginału, staje się drogowskazem dla współczesnych rozważań, dotyczących właściwej strategii działań konserwatorskich. Pierwszy okres, związany z powstaniem monumentalnej budowli renesansowej, trwający...