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1

Realia i efektywność nauczania matematyki na kierunkach ekonomicznych

Arkit Aleksandra

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

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2021

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Nr 72

11--14

PL

Celem artykułu jest zaprezentowanie wyników weryfikacji efektów kształcenia w latach 2015-2021 w kontekście dyskusji na temat kierunków rozwoju dydaktyki matematyki na poziomie akademickim. Przedstawione wyniki dotyczą rozumienia przez studentów wybranych pojęć analizy matematycznej i ich użycia w analizie zjawisk ekonomiczno-społecznych. Przedstawione zostaną zastosowane metody i sformułowane wnioski związane z aktualnymi warunkami organizacyjno-dydaktycznymi oraz problemami wnikającymi z nauczania matematyki w szkołach średnich.

EN

The aim of the article is to present the results of the verification of the learning outcomes in 2015-2021 in the context of the discussion on the directions of development of mathematics didactics at the academic level. The presented results concern students' understanding of selected concepts of mathematical analysis and their use in the analysis of economic and social phenomena. The methods used and conclusions related to the current organizational and didactic conditions as well as problems related to teaching mathematics in secondary schools will be presented.

2

Mathematical analysis of dual-frequency load current of two-inverter power supply for induction heating systems

Herasymenko Pavlo

Przegląd Elektrotechniczny

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2021

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R. 97, nr 3

69--74

EN

The aim of this research work is to obtain analytical expressions that allow analyzing the dual-frequency current of the induction coil, as well as, the currents of the inverters for the “two inverter power supplies” converter topology. To take into account frequency-dependent parameters of an induction heater load, their implementation is shown through series-parallel connections of frequency-independent resistances and inductances. A simulation study is performed to verify the obtained analytical expressions of the currents.

PL

Celem artykułu było otrzymanie analitycznego opisu umożliwiającego analizę prądu podwójnej częstotliwości stosowanego w nagrzewaniu indukcyjnym. Analizowano prąd w cewce oraz współpracującego z nią przekształtnika. Przeprowadzono też symulację potwierdzającą model analityczny.

3

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

Sharkawy Abdel-Nasser

Engineering Transactions

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2021

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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.

4

Mathematical analysis of the influence of the flux-cored wire chemical composition on the electrical parameters and quality in the underwater wet cutting

Parshin S., Levchenko A., Wang P., Maystro A.

Advances in Materials Science

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2021

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Vol. 21, nr 1(67)

77--89

EN

The paper presents research in the field of underwater wet cutting with the use of flux-cored wires in order to improve the quality and performance. The research has resulted into the development of gas and slag systems for flux-cored wires and determination of , optimal parameters for cutting stability and quality. The underwater wet cutting mechanism is a cyclical process with the formation of periodic keyholes in metal, and it consists of operating and idle cycles. Efficiency of the cutting process can be determined by analyzing cycle times, welding current, voltage, power and a number of short circuits. To assess the stability and efficiency of the underwater wet cutting process, the authors have developed the method for analyzing oscillograms to calculate the probability density of current, voltage and power. To determine the quality of cutting, the authors have provided a criterion based on the ratio of the voltage probability density in the idle and operating cycles.

5

co-Semi-analytic Functors

Zawadowski Marek

Fundamenta Informaticae

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2019

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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.

6

Studying Word Equations by a Method of Weighted Frequencies

Saarela A.

Fundamenta Informaticae

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2018

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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.

7

Logic-based Verification of the Distributed Dining Philosophers Protocol

Delzanno G.

Fundamenta Informaticae

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2018

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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.

8

Defeasible Reasoning in SROEL : from Rational Entailment to Rational Closure

Giordano L., Dupré D. T.

Fundamenta Informaticae

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2018

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Vol. 161, nr 1/2

135--161

EN

In this work we study a rational extension SROEL(⊓, x)R T of the low complexity description logic SROEL(⊓, x), which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and Magidor’s ranked models and allows for the definition of defeasible inclusions. We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is in general ∏2P -hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance checking under rational entailment and exploit it, with stratified negation, for computing the rational closure of simple KBs in polynomial time.

9

Multidimensional MCA correspondence model supporting intelligent transport management

Topolski M.

Archives of Transport System Telematics

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2018

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Vol. 11, iss. 4

52--56

EN

The article presents a multiple model using the multiple correspondence analysis MCA in the task of intelligent transport management. It is an exploratory technique of quality data analysis which facilitates graphic presentation of variables in low dimensional space. The model using multiple correspondence analysis looms relatively easily interpretable results. The article will present a data reduction technique. MCA is the method of co-occurrence of categories of variables which are measurable on a nominal scale. Graphic development of variables and determination of the relations among them will also be presented. Thus making it possible to obtain a map of points using the multiple correspondence analysis and identification of occurring concentrations of categories of variables which support use of telematic tools in intelligent transport management.

10

The constructive solution and calculation of elements of the unified module of the mobile bridge overcrossing

Kadyrov A., Balabekova K., Ganyukov A., Akhmediyev S.

Transport Problems

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2017

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T. 12, z. 3

59--69

EN

In the article the construction of a modular mobile overcrossing is offered. Calculation of its constructive elements is performed and the optimum length of one module is determined. The purpose is the development of the technique and calculation for the new construction of a mobile bridge overcrossing intended for reduction of traffic jams. Methods: The methods uses are mathematical analysis, method of finite elements, method of finite differences, and analytical method of relocation. Dependencies for determination of the optimum length of the module of bridge overcrossing are identified. The calculation of the constructive-orthotropic plate for the carriageway of the bridge overcrossing using numerical methods of finite differences and finite elements is performed; the reliability of results is confirmed with coincidence of deflection values. The solution matrix of the method of finite differences developed in this work allows calculation of arbitrary plates with a wide variety of geometrical sizes, and also for different values of flexural stiffness properties of the plate and reinforcing elements. The calculation of the spatial frame of the bridge overcrossing is performed by the precise analytical method of relocation taking into account the bend and torsion of its elements.

11

Zarys dziejów recepcji i rozwoju analizy matematycznej w Polsce

Duda R.

Kwartalnik Historii Nauki i Techniki

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2016

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R. 61, nr 4

7--61

EN

Mathematics in Poland had good names in medieval times and in the first two centuries of modern times, e.g. Vitello, Copernicus, Broscius, Kochanski. Since mid-XVII c., however, there begun a decline of the Polish-Lithuanian state and its culture which led to the loss of sovereignty and to partitions 1795–1918. On the other hand, it was a time of Newton and Leibniz who invented calculus and of their followers, the time of its fast development in XVIII and XIX centuries and the emergence of its many new branches, the totality of which is called mathematical analysis. That development was followed in Poland with a large delay and for a long time it resembled a pursuit after a fast running train. In spite of a long run, the pursuit eventually proved successful. The article traces its history since the translation of Bézout’s extensive manual by Jakubowski (1781), soon followed by other translations from French, accompanied by the emerging Polish terminology related to higher mathematics. In consequence, the level of authority of Polish mathematicians concerning the area of higher mathematics was gradually increasing. The first Polish manual of mathematical analysis appeared in 1822 (Buchowski), then there were other ones, and the number of research papers in the area, predominantly concerning differential equations, grew as well. Near the end of the XIXth century some of those papers gained a high status and became widely known, e.g. some by Sochocki (analytic functions), Zaremba (differential equations), Żorawski (Lie groups). The number of Polish mathematicians and books in Polish grew, and in the last decade of XIX c. there appeared Polish mathematical journals. In 1918 there was a wave of a common enthusiasm upon regaining independence. Polish mathematicians have used the opportunity and soon there appeared mathematical schools in Warsaw and in Lvov, centered upon “the theory of sets and its applications”. However, the choice of such a main area of interest meant a conscious neglect of mathematical analysis. Nevertheless, an interest in the latter, although for the time being in the shadow of flourishing schools, has not been altogether abandoned. And when, after War World II, the center of gravity of common mathematics has moved away from the main subjects of the Polish school, it was precisely mathematical analysis which allowed Polish mathematicians to keep abreast. Nowadays Polish mathematics has many areas of interest, including domains of modern mathematical analysis, and in most of them its high level is confirmed by an international cooperation.

12

Ocena wpływu interferencji w postaci sygnału szerokopasmowego na dokładność wyznaczania pozycji obiektów BSP

Komorek A., Bieńczak R., Kowalik R.

Autobusy : technika, eksploatacja, systemy transportowe

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2016

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R. 17, nr 6

915--920

PL

W artykule omówiono analizę matematyczną wpływu sygnału szerokopasmowego na poprawne funkcjonowanie odbiornika nawigacji satelitarnej GNSS znajdującego się na wyposażeniu bezzałogowego statku powietrznego BSP. Zaprezentowane w artykule modele matematyczne poddano badaniom symulacyjnym, a uzyskane na tym etapie wyniki zaprezentowano w postaci charakterystyk szumowych (BER). Jakkolwiek przedstawione w referacie wyniki odnoszą się do konkretnego odbiornika GNSS, stąd mogą się one różnić w zależności o rodzajów radiowych urządzeń nawigacyjnych.

EN

The article discusses the mathematical analysis of the impact of broadband signal on the proper functioning of the GNSS receiver located supplied unmanned aircraft BSP. Presented in this paper mathematical models were tested simulation, and from this step results presented in the form of noise characteristics (BER). Although the results presented in this paper relate to specific GNSS receiver, so they can vary depending on the type of radio navigation equipment.

13

Badania teoretyczne i konstrukcja łożyskowania gazowego wrzeciona szlifierskiego

Oryński F., Kawczyński S.

Mechanik

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2015

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R. 88, nr 8-9CD1

244--249

PL

W artykule zaprezentowano nową konstrukcję łożyska gazostatycznego. Łożysko powstało na podstawie analizy istniejących konstrukcji, jednak ma prostszą budowę. W drugiej części artykułu zaprezentowano metodę obliczeń i wyniki analizy matematycznej łożyska.

EN

The article presents a new gasostatic bearing design. Bearing was established on the basis of existing structures, but has a simpler design. In the second part of the article the calculation method and the results of mathematical analysis have been presented.

14

Wyznaczanie granicznych błędów pomiaru parametrów sygnału sinusoidalnego spowodowanych kwantyzacją

Kontorski K.

Pomiary Automatyka Kontrola

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2014

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R. 60, nr 11

975--977

PL

Często w celu wyznaczenia amplitudy i fazy pewnej harmonicznej sygnału próbkowanego przetwornikiem A/C korzysta się z DFT. Dokładność pomiaru wyznacza się numerycznie stosując metodę Monte-Carlo przy założeniu, że próbki nie są skorelowane między sobą. Założenie to jest błędne, gdy próbkuje się sygnał sinusoidalny. W artykule zostanie wyznaczony zbioru sygnałów sinusoidalnych, na podstawie którego można wyznaczyć amplitudę i fazę sygnału mono-harmonicznego próbkowanego. Przeprowadzono badania dokładności transformaty DFT.

EN

Signals probed with finite resolution ADC's are affected by quantization errors. If we assume that value of each probe is uncorrelated with the value of each other probe then we may assess the accuracy of the first harmonic determined by DFT using Monte-Carlo method [1]. But if we probe a sinusoidal signal it is an incorrect assumption. In the paper we analyze the set of the sinusoidal signals that are inevitably connected with acquired single harmonic signal probes. In the Figure 1 we can see that the set of probes may be generated by a few different signals. We prove that set of signals that give the same set of the probes represents a non-fragmented surface on the amplitude and phase angle plane (Fig. 2). Secondly we determine the set of signals for the specified set of probes D3 acquired by the simulated ADC. We construct function F represented by equation (9) which consists of the function which block diagram is presented in the Fig. 3. This function F is discrete so statistical methods must be used to determine the set of signals (A, φ) which give the maximal value [2]. Final shape of the set is given on the Fig. 5. Some experiment was conducted to check the accuracy of the DFT algorithm. The Figure 6 represent values of amplitudes acquired by DFT (triangles), amplitudes from the computed sets (dots) against number of acquired probes of the 1 V sinusoidal signal. The error bars corresponds to the extreme amplitudes (Fig. 6) in the set. The results differ, because DFT computes parameters of the first harmonic of the probes which only approximately represents the input signal. This method with modifications may be applied to the multi-harmonic signals. Keywords: signal sampling, ADC, periodic signal, amplitude and phase angle, mathematical analysis, DFT.

15

Zastosowanie rachunku różniczkowo-całkowego niecałkowitych rzędów w nauce i technice : artykuł przeglądowy

Nowocień A., Luft M., Pietruszczak D.

Logistyka

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2014

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nr 3

4748--4754

PL

Inspiracją do napisania artykułu było zainteresowanie autorów szybkim rozwojem w ostatnich latach zastosowania rachunku róŜniczkowo-całkowego niecałkowitych rzędów w róŜnych dziedzinach nauki i techniki. Artykuł przedstawia historię rozwoju i obecny stanu wiedzy nt. stosowania tego rachunku. Podano definicję Riemanna-Liouville'a pochodnych rzędu ułamkowej, definicję Caputo pochodnej ułamkowej oraz definicję Grunwalda-Letnikova pochodnej rzędów niecałkowitych. Wskazano na zalety i wady rachunku niecałkowitego rzędu.

EN

An inspiration for this paper was its author’s interest in the latest rapid development of the use of fractional calculus in different areas of science. The paper outlines the history of the development and the present state of research concerning the use of fractional calculus in different sciences. Important definitions are given: the Riemann-Liouville definition of fractional order derivatives, the Caputo’s definition of the fractional derivative and the Grünwald-Letnikov definition of the derivative in fractional calculus as well as the notation of the operator, continuous fractional transmittance. The advantages and disadvantages of fractional calculus in modelling dynamic elements were also indicated. Dynamic development of recent research into the use of fractional calculus for the dynamic system analysis encouraged the authors of this paper to attempt the use of it for the analysis and modelling in dynamic measurements.

16

Social Networks with Competing Products

Apt K.R., Markakis E.

Fundamenta Informaticae

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2014

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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.

17

Periodic Partial Words and Random Bipartite Graphs

Idiatulina L. A., Shur A. M.

Fundamenta Informaticae

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2014

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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.

18

Deciding Whether or Not a Synchronous Relation is Regular Prefix

Choffrut C.

Fundamenta Informaticae

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2014

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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.

19

Rough Net Structures : Example of Information System

Czaja L.

Fundamenta Informaticae

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2013

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Vol. 127, nr 1-4

81--97

EN

Information system of net structures based on their calculus (a distributive lattice) is introduced and, in this context, basic notions of rough set theory are re-formulated and exemplified.

20

A Contact Problem with Normal Compliance, Finite Penetration and Unilateral Constraint

Barboteu M., Sofonea M.

Machine Dynamics Research

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2011

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Vol. 35, No. 1

60-69

EN

We consider a quasistatic problem which describes the contact between a viscoplastic body and an obstacle, the so-called foundation. The contact is frictionless and is modelled with a version of the normal compliance condition in which the penetration is restricted with unilateral constraint. The mathematical analysis of the problem, including, existence, uniqueness and convergence results, was provided by Barboteu et al. (2011). Here we present numerical simulations in the study of an academic two-dimensional contact example.