Wyniki wyszukiwania - Biblioteka Nauki

1

Elementy rachunku frakcjalnego całko-pochodne dowolnego rzędu (I)

100%

Turski A. J. , Atamaniuk B. , Turska E.

Prace Instytutu Podstawowych Problemów Techniki PAN

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2004

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tom nr 2

1-37

PL

Przedstawiono elementy teorii i zastosowań pochodnych rzędu niecałkowitego i całek niecałkowitej krotności. Mamy do czynienia z operacją liniową, która w szczególności jest równoważna operacji różnicznowania i całkowania. Dla funkcji wielu zmiennych takie operacje nazywane są pseudoróżniczkowymi. Praca została podzielona na dwie części. W części pierwszej (I) omówiono myśl prowadzącą do unifikacji pojęcia pochodnej rzędu całkowitego- n i całki n-krotnej. W klasycznej analizie pojęcia te są prezentowane oddzielnie. Przedstawiony zostanie przykład oparty na dwumianie Newtona całkowitego dodatniego stopnia i przejście do ujemnego i dodatniego, ale niecałkowitego stopnia. Przedstawiona zostanie pochodna rzędu całkowitego- n dostatecznie gładkiej funkcji f(x) przy pomocy granicy ilorazu różnicowego zawierającego n + 1 wyrazów. Następnie uogólnione zostanie to wyrażenie, stosując funkcje gamma, na ujemny ca lkowity stopień- -n prowadząc do nielokalnego pojęcia n-krotnie iterowanej całki i wreszcie otrzymamy wzór Grünwalda-Letnikowa definiujący całko-pochodną dowolnego rzędu. W dalszym ciągu przedstawione zostaną proste przykłady całko-pochodnych funkcji potęgowych, wykładniczych i trygonometrycznych. Wprowadzona zostanie ogólna definicja całki i pochodnej rzędu niecałkowitego odniesionych do przedziału. Zwrócona zostanie uwaga na równoważność i warunki równoważności definicji Grünwalda-Letnikowa i Riemanna-Lioville`a. Praca zostanie zakończona przykładami, odpowiedziai na pytania zadane w tekście, zadaniami, tablicą całko-pochodnych i obszernym wykazem literatury.

2

Social Networks with Competing Products

80%

Apt K. R. , Markakis E.

Fundamenta Informaticae

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2014

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tom Vol. 129, nr 3

225--250

EN

We introduce a new threshold model of social networks, in which the nodes influenced by their neighbours can adopt one out of several alternatives. We characterize social networks for which adoption of a product by the whole network is possible (respectively necessary) and the ones for which a unique outcome is guaranteed. These characterizations directly yield polynomial time algorithms that allow us to determine whether a given social network satisfies one of the above properties. We also study algorithmic questions for networks without unique outcomes. We show that the problem of determining whether a final network exists in which all nodes adopted some product is NP-complete. In turn, we also resolve the complexity of the problems of determining whether a given node adopts some (respectively, a given) product in some (respectively, all) network(s). Further, we show that the problem of computing the minimum possible spread of a product is NPhard to approximate with an approximation ratio better than W(n), in contrast to the maximum spread, which is efficiently computable. Finally, we clarify that some of the above problems can be solved in polynomial time when there are only two products.

3

An analysis of digital selective calling system with regard to generating false distress signals within Global Maritime Distress and Safety System

80%

Czajkowski J.

Polish Maritime Research

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2001

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tom 08

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nr 3

4

Deciding Whether or Not a Synchronous Relation is Regular Prefix

70%

Choffrut C.

Fundamenta Informaticae

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2014

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tom Vol. 132, nr 4

439--459

EN

Eilenberg and al. introduced and studied in the late sixties the family of n-ary relations over the free monoid recognized by finite n-tape automata where the where the n reading heads tapes move simultaneously from left to right. We call these relations synchronous. In the eighties Angluin and Hoover and then L¨auchli and Savioz introduced a proper subfamily which the first authors called regular prefix. Our main result shows that given a synchronous relation it is decidable whether or not it is regular prefix. Incidentallywe also show that the family of regular prefix relations is uniformizable in the sense that all such relations contain a partial function with the same domain whose graph is a regular prefix relation.

5

Aksjomat wyboru w pracach Wacława Sierpińskiego

70%

Lewandowska K.

Zagadnienia Filozoficzne w Nauce

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2013

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nr 52

9-33

PL

This paper presents Wacław Sierpiński – the first advocate of the axiom of choice. We focus on the philosophical and mathematical topics related to the axiom of choice which were considered by Sierpiński. We analyze some of his papers to show how his results effected the debate over Zermelo’s axiom. Sierpiński’s impact on this discussion is of particular importance since he was the first who tried to explore consequences of the axiom of choice thoroughly and asserted its undoubted significance to mathematics as a whole.

6

An investigation on the effective mass of the robot: dependence on the end-effector position

70%

Sharkawy A.-N.

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tom Vol. 69, iss. 3

293--313

EN

In this paper, the mathematical analysis of the robot effective mass is presented. The calculation of this effective mass and its ellipsoid are included. The relationship between the robot effective mass and the external force (collision) affecting the robot end-effector is investigated. The effective mass is analyzed using different robot configurations and different end-effector positions. This analysis is conducted using 2-DOF and 3-DOF planar robots and executed using MATLAB. The results from this analysis prove that the robot effective mass depends on the its configurations and end-effector position. Effective mass can thus be considered as one of the criteria in optimizing robot kinematics and configuration.

7

Studying Word Equations by a Method of Weighted Frequencies

70%

Saarela A.

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2018

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tom Vol. 162, nr 2/3

223--235

EN

We briefly survey some results and open problems on word equations, especially on those equations where the right-hand side is a power of a variable. We discuss a method that was recently used to prove one of the results, and we prove improved versions of some lemmas that are related to the method and can be used as tools when studying word equations. We use the method and the tools to give new, simple proofs for several old results.

8

Periodic Partial Words and Random Bipartite Graphs

70%

Idiatulina L. A. , Shur A. M.

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tom Vol. 132, nr 1

15--31

EN

The interaction property (or the Fine-Wilf property) for periodic partial words is studied. Partial words with two periods are represented by bipartite graphs and the interaction property is related to the edge connectedness property of these graphs. Threshold functions for the edge connectedness of random bipartite graphs and multigraphs are found. As a corollary, the interaction property is described in probabilistic terms.

9

Matematicheskoe modelirovanie dvukhehlektrodnogo pervichnogo preobrazovatelja

70%

Gons'or O.

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2016

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tom 18

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nr 5

10

On the Relationship Between Monadic and Weak Monadic Second Order Logic on Arbitrary Trees, with Applications to the mu-Calculus

70%

Janin D. , Lenzi G.

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2004

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tom Vol. 61, nr 3,4

247--265

EN

In 1970, in Weakly definable relations and special automata, Math. Log. and Found. of Set Theory, pp 1-23, Rabin shows that a language is recognizable by a tree automaton with Büchi like infinitary condition if and only if it is definable as the projection of a weakly definable language. In this paper, we refine this result characterizing such languages as those definable in the monadic Σ2 level of the quantifier alternation depth hierarchy of monadic second order logic (MSO). This new result also contributes to a better understanding of the relationship between the quantifier alternation depth of hierarchy of MSO and the fixpoint alternation depth hierarchy of the mu-calculus: it shows that the bisimulation invariant fragment of the monadic Σ2 level equals the νμ-level of the mu-calculus hierarchy.

11

Abstract Interpretation against Races

70%

Barbuti R. , Cataudella S. , Tesei L.

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2004

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tom Vol. 60, nr 1-4

67--79

EN

In this paper we investigate the use of abstract interpretation techniques for statically preventing race conditions. To this purpose we enrich the concurrent object calculus concV by annotating terms with the set of ``locks'' owned at any time. We use an abstract form of the object calculus to check the absence of race conditions. We show that abstract interpretation is more flexible than type analyses, and it allows to certify as ``race free'' a larger class of programs.

12

co-Semi-analytic Functors

70%

Zawadowski M.

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2019

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tom Vol. 164, nr 4

359--373

EN

We give an abstract characterization of the category of co-semi-analytic functors and describe an action of semi-analytic functors on co-semi-analytic functors.

13

Badanie energii rozpraszanej mieszanek mineralno-asfaltowych

60%

Radziszewski P.

Zeszyty Naukowe Politechniki Białostockiej. Budownictwo

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2000

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tom Z.20

205-216

PL

W artykule przedstawiono wyniki badań nad energią rozpraszaną mieszanek mineralno-asfaltowych z lepiszczami modyfikowanymi. Energię rozpraszaną określono na podstawie badań pod obciążeniem cyklicznym. Wyznaczono równanie trwałości zmęczeniowej na podstawie kryterium energetycznego. Przeprowadzono badania laboratoryjne nad mieszankami mineralno-asfaltowymi, określając sumaryczną energię rozpraszaną, energię rozpraszaną na jeden cykl obciążenia, współczynnik energetyczny oraz trwałość zmęczeniową. Wyniki badań opracowane na podstawie analizy korelacji, składowych głównych i analizy regresji potwierdziły adekwatność wyznaczonego równania energetycznego.

EN

In the paper are presented dissipated energy research results of asphalt concrete with modified bitumen dissipated energy. Dissipated energy was determined on the fatigue test basis. Fatigue equation on the energy criterion basis was defined. Asphalt concrete test was carried out to determine: cumulative dissipated energy to failure, dissipated energy per load cycle, energy ratio factor and fatigue life. Research results worked out on correlation, principal components and regression analyses bases proved the adequacy of the dissipated energy model.

14

About definition of a periodic function

60%

Rygał G. , Bryll G.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

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tom Vol. 12

375-380

EN

In this paper we consider various definitions of a periodic function and establish connections between them, in particular, we prove equivalence of some of them. In papers and textbooks one can find different definitions of a periodic function. This raises the question which of them are equivalent.

15

Mathematical Analysis for a New Tennis Ball Launcher

60%

Wójcicki K. , Puciłowski K. , Kulesza Z. S.

Acta Mechanica et Automatica

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2011

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tom Vol. 5, no. 4

110-119

EN

The paper presents the mathematical analysis for the design of a new tennis ball launcher in order to assess the possibilities for its technical implementation. First, traditional launchers are described. Next, several new requirements improving training possibilities of such machines are suggested. The motion equation of the flying tennis ball is formulated and numerically solved. This makes it possible to analyze the trajectories of the ball for different initial conditions: elevation and heading angles, as well as the rollers angle. Then, the mathematical analysis of the launcher with two counter rotating rollers is presented. Stiffness (Young's) modulus and friction coefficients for the typical tennis ball have been determined ex-perimentally. Based on these, initial conditions for the throw have been found: rotating speeds of the rollers and powers of the driving motors.

16

Płaski wymiennik ciepła jako kolektor słoneczny - analiza możliwości wykorzystania i próba opisu matematycznego

60%

Zimny J. , Wolczko A.

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tom R. 42, nr 1-2

29-33

PL

W ciągu ostatnich lat wykorzystanie energii słonecznej na świecie wzrasta w szybkim tempie, w rezultacie wysiłków badawczych i wdrożeniowych zbadano szereg możliwości energetycznego wykorzystania padającego promieniowania słonecznego. Celem niniejszego referatu jest przedstawienie możliwości wykorzystania płaskiego wymiennika ciepła jako kolektora słonecznego. Autorzy prezentują urządzenie opierające się na zupełnie innym rozwiązaniu technicznym i zastosowaniu innej technologii, proponują kolektor absorpcyjny w miejsce dotychczas produkowanych refleksyjnych.

EN

Over the years exploit of solar energy grow quickly because a lot of scientists make researches and experiments about full use of potential solar radiation. The aim of this article is proposal for an improvement - practical application of heat exchanger as solar energy collector. Authors present new technological solution and new process engineering. They create mathematical model of solar collector which is a base for subsequent scientific researches.

17

Władysław Kretkowski (1840 –1910)

60%

Ciesielska D.

Kwartalnik Historii Nauki i Techniki

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2014

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tom 59

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nr 4

17–53

EN

Władysław Kretkowski was a mathematician and an engineer. He graduated École Imperiale des Ponts et Chauseés in Paris and also Sorbonne. He obtained PhD from the Jagiellonian University in Kraków, he was a private docent at the Polytechnic and University in Lvov. The first chapter of the paper contains a short biography of Kretkowski, including information about his education and interests. The participation of Kretkowski in the January Uprising is described here as well. In the main Chapter, i.e. Chapter 2, mathematical achievements of Kretkowski in the theory of determinants and their applications in mathematical analysis and geometry is presented. The history of his academic career is also presented in this chapter. The last chapters are devoted to the mathematical contests announced by Kretkowski (especially the most famous one on the problem which is nowadays known as the Third Hilbert Problem from 1900) and to the Dr Władysław Kretkowski Fundation

18

Model zdegenerowany w opisie procesu przebicia elementów maszynowych poddanych obciążeniom udarowym

60%

Jamroziak K. , Kulisiewicz M. , Piesiak S. , Wajda M.

Problemy Maszyn Roboczych

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2003

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tom Z. 22

25-36

PL

Zjawiska przebicia elementów maszynowych poddanych obciążeniom udarowym zależą nie tylko od własności materiałów, ale także od warunków ich zamocowania. Ponadto quasi statyczne badania eksperymentalne materiałów wykazują istotny wpływ nie tylko wartości siły, ale także prędkości przebijania na efekt zniszczenia. Prowadzi to do konieczności stosowania w opisie procesu przebicia modeli bardziej złożonych niż model Hooke'a. Autorzy niniejszej pracy proponują stosowanie do opisu zjawiska przebicia modelu zdegenerowanego, którego podstawowym elementem jest model standardowy w odpowiedniej konfiguracji z elementem plastycznym umożliwiającym plastyczną deformację po przekroczeniu granicznej siły "h". W oparciu o ten model wykonano analizę matematyczną oraz symulację komputerową procesu przebijania, której rezultaty przedstawiono w niniejszej pracy.

EN

Phenomena of puncture of serfs' machine elements do not depend on properties of materials only, but also on conditions of fastening. Speed of piercing but not the value of strength solely have the essential influence on effect of destruction according to the quasistatic experimental tests. This enables the application of models more complicated then the Hooke's one in description of a puncture process. The authors of the present paper propose the application of degenerate model in description of a puncture phenomenon. The standard model together with suitable configuration of plastic element enabling plastic deformation for exceeded limit force h constitute the basic of the degenerate model. Mathematical analysis as well as numerical simulations of a piercing process were performed accordingly to the proposed model.

19

Derivation of the formula for the filtration coefficient by application of Poiseuille's law in membrane transport

60%

Jarzynska M. , Pietruszka M.

Acta Societatis Botanicorum Poloniae

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2009

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tom 78

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nr 2

93-96

EN

On the basis of Kedem-Katchalsky equations a mathematical analysis of volume flow (Jv) of a binary solution through a membrane (M) is presented. Two cases of transport generators have been considered: hydrostatic (Δp) as well as osmotic (Δπ) pressure difference. Based on the Poiseuille's law we derive the formula for the membrane filtration coefficient (Lp) which takes into account the membrane properties, kinetic viscosity and density of a solution flowing across the membrane. With use of this formula we have made model calculations of the filtration coefficient Lp and volume flow Jv for a polymer membrane in the case when the solutions on both sides of the membrane are mixed.

20

Logic-based Verification of the Distributed Dining Philosophers Protocol

60%

Delzanno G.

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2018

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tom Vol. 161, nr 1/2

113--133

EN

We present a logic-based framework for the specification and validation of distributed protocols. Our specification language is a logic-based presentation of update rules for arbitrary graphs. Update rules are specified via conditional rewriting rules defined over a relational language. We focus our attention on unary and binary relations as a way to specify predicates over nodes and edges of a graph. For the considered language, we define assertions that can be applied to specify correctness properties for arbitrary configurations. We apply the language to model the distributed version of the Dining Philosopher Protocol. The protocol is defined for asynchronous processes distributed over a graph with arbitrary topology. We propose then validation methods based on source to source transformations and deductive reasoning. We apply the resulting method to provide a succint correctness proof of the considered case-study.