Wyniki wyszukiwania - BazTech

1

Nieoczywistości ciągłości

Gawron Piotr

MINUT Matematyka i Informatyka na Uczelniach Technicznych

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2023

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Nr 5

256-260

PL

Przytaczamy definicje ciągłości funkcji rzeczywistej i nieoczywiste przykłady jej zastosowania.

2

Wspomnienia. Krzysztof Gawędzki (1947 - 2022)

Lewenstein Maciej, Wehr Jan

Postępy Fizyki

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2022

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T. 73, z. 1

36--43

EN

One of the most prominent mathematical physicists and my friend, Krzysztof Gawędzki, passed away 21 January 2022.

3

Selection of gensets using multicriteria analysis

Barešić Dejan, Hederić Željko, Barukčić Marinko

Journal of Power Technologies

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2022

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Vol. 102, nr 2

56--67

EN

The paper presents a procedure for the optimal selection of diesel generators used to supply electrical units in military camps. Using a multi-criteria analysis based on the criteria presented in the paper, a new method is introduced that's not been used before for making decisions on optimal equipment. Daily load curves were created for the selection of diesel generators. These curves, together with the performance diagrams, served as the basis for calculating diesel consumption. The results allow an accurate assessment of the relative importance of the criteria used in the multi-criteria analysis. In addition to fuel consumption, other criteria such as maintenance costs, reliability, noise level, etc. were also examined. Their relative importance was assigned on the basis of technical documentation and existing maintenance records showing the frequency of breakdowns and maintenance costs. The AHP method was used to solve problems with multiple criteria. The results were processed using Expert Choice software. The analysis showed that an appropriate choice of diesel generator power can lead to lower fuel consumption. The results based on the established criteria show that the optimal choice is a 100 kW diesel generator.

4

Mathematical analysis of mass and heat transfer through arterial stenosis

Hussain Azad, Sarwar Luba, Akbar Sobia, Malik M. Y.

Journal of Power Technologies

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2022

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Vol. 102, nr 3

88--95

EN

The article investigates the steady state flow of an incompressible fluid which is treated as a Williamson fluid through a stenoised region in the shape of cosine constriction. Blood is taken as a Williamson fluid. Mathematical formulation leads us to nonlinear compatibility and energy equations, which are then deciphered by the shooting technique to obtain the numerical solution. Suitable resemblance transformations are used to change partial differential equations into an embellished form of ordinary differential equations. Further, the consequences of the different parameters involved are shown by graphs and a conclusion is presented. Velocity and temperature fields are canvassed graphically for the distinct values of emerging parameters and discussed in tabular form. Skin friction and the coefficient of heat transfer are also covered in the discussion. The resulting Nusselt number curve exhibits negative deflection for variational values of λ and height of the stenosis δ.

5

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.

6

Recenzja. Język, którym mówi Bóg

Heller Michał

Postępy Fizyki

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2021

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T. 72, z. 2

41--43

PL

Analiza matematyczna, czyli rachunek różniczkowy i całkowy (po angielsku po prostu calculus) jest naszym narzędziem na co dzień. Trudno byłoby znaleźć roboczy dzień w życiu fizyka teoretyka, w którym nie musiałby czegoś zróżniczkować albo scałkować. Wielu z nas przez lata wkładało innym do głowy zasady obliczania różniczek i całek. Czy można jeszcze z podręczników analizy wyczytać coś odświeżającego? Jeżeli mamy co do tego wątpliwości, to weźmy do ręki książkę Stevena Strogatza „Potęga nieskończoności.”

7

Uwagi o ewolucji pojęcia ciągłości

Gawron Piotr

MINUT Matematyka i Informatyka na Uczelniach Technicznych

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2021

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Nr 3

255-257

PL

Pojęcie funkcji ciągłej a ogólniej ciągłości leży u podstaw analizy matematycznej. W tym artykule przestawimy krótko kilka uwag natury historycznej o ewolucji definicji ciągłości funkcji. Czytelników bardziej zainteresowanych tym zagadnieniem zachęcamy do zapoznania się z załączoną literaturą a w szczególności pozycjami [2], [4], [7], [12] mimo, że nie we wszystkich pracach autorzy mają podobne poglądy.

8

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.

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

About a class of analytic functions defined by Noor-Sǎlǎgean integral operator

Engel O., Chung Y. L.

Journal of Mathematics and Applications

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2016

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Vol. 39

59--67

EN

In this paper we intoduce a new integral operator as the convolution of the Noor and Salagean integral operators. With this integral operator we define the class CNS(α), where α ϵ [0,1) and we study some properties of this class.

13

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.

14

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.

15

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.

16

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.

17

Mathematical Analysis for a New Tennis Ball Launcher

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

Acta Mechanica et Automatica

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2011

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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.

18

Derivative of a function at a point and integral by professor Igor Kluvánek

Gunčaga J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2009

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Vol. 14

37-50

EN

Professor Igor Kluvánek had developed a unique course of calculus (mathematical analysis) to teach students the differential and integral calculus. In the present paper, this concept is briefly outlined. The notion of derivative is introduced via continuity. The definition of integral given in this article applies an idea of Archimedes.

19

The brushless permanent magnet micromotor in the smallest drive system

Nesterin V., Nesterina A., Romanov R., Scherbakov A., Junin S.

Prace Instytutu Elektrotechniki

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2009

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Z. 240

231-240

EN

The article presents the results of the work of contactless fractional-horsepower motor (micromotor) with excitation from constant magnets, which can be used in MEMS (Micro-Electro-Mechanical Systems). These MEMS are used in Medicine, flaw detection, military equipment and in microrobots of different usage. Also article presents the results of mathematics Simulation of magnetic field in work zone of micromotor and the analysis of the basic datas and characteristics of experimental Sample with electronic device System control. The Sample of micromotor is made in the form of glass body with the usage of technology of making slim multi capillary glass tubes. The rotor of micromotor is made in the form cylinderic constant magnet from FeNdBr material. Basic datas: lengt – 6 mm; outside diameter - 2,5 mm; the number of phase - 3; rotation rates - 9600 rpm; stress (voltage, tension) - 0,5 V. Electronic unit (block) with microprocessor device realizes the work of micromotor in sensorless regime and allows to control the rotation speed in the rotation speed in the range 1:1000. The results of theoretical research agree with experimental datas, received in the process of experimental micromotor Sample.

PL

Artykuł przedstawia wyniki pracy dotyczącej bezstykowego silnika o mocy ułamkowej (mikrosilnika) ze wzbudzeniem od magnesów trwałych, który może być użyty w MEMS (Micro-Electro-Mechanical-Systems). MEMSy stosowane są w medycynie, detekcji wad, wyposażeniu wojskowym i różnych mikrorobotach. Praca przedstawia również wyniki matematycznej symulacji pola magnetycznego w strefie pracy mikrosilnika i analizę podstawowych danych i charakterystyk eksperymentalnego egzemplarza próbnego ze sterowaniem elektronicznym. Próbny egzemplarz jest wykonany w postaci korpusu ze szkła z użyciem technologii cienkich, multi - kapilarnych rurek szklanych. Wirnik mikrosilnika jest wykonany w postaci cylindrycznego magnesu trwałego wykonanego z FeNdBr. Podstawowe dane: długość – 6 mm, średnica zewnętrzna - 2,5 mm, liczba faz - 3, prędkość obrotowa - 9600 obr/min, napięcie - 0,5 V. Jednostka elektroniczna (blok) z mikroprocesorem realizuje pracę mikrosilnika w reżymie bezczujnikowym i pozwala sterować prędkość obrotową w zakresie 1:1000. Wyniki badań teoretycznych zgadzają się z danymi doświadczalnymi uzyskanymi w pracy eksperymentalnej mikrosilnika próbnego.

20

Ocena skuteczności normatywnych środków ochrony odgromowej urządzeń zasilanych z sieci NN

Sobolewski K.

Przegląd Elektrotechniczny

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2008

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R. 84, nr 10

68-71

PL

Poniższy referat przedstawia możliwość wykorzystania komputerowej analizy matematycznej do badania układów przepięciowych w sieciach niskiego napięcia. Autor przedstawia krótkie wprowadzenie w tematykę różnych układów zasilających i związanych z tym różnic w sposobie ochrony zasilanych urządzeń. Zaprezentowany został przykładowy model układu umożliwiającego przeprowadzenie analizy zagrożenia przepięciowego typowego zasilacza komputerowego.

EN

Presented below article contains information about possibility of using computer based mathematical analysis to investigate overvoltage protection systems mounted in low voltage installations. Author presented a short introduction into the subject of overvoltage protection in various types of low voltage power supply systems. Next, the practicable model used to analysis overvoltage hazard for typical computer feeder is presented.