PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Powiadomienia systemowe
  • Sesja wygasła!
  • Sesja wygasła!
  • Sesja wygasła!
  • Sesja wygasła!
  • Sesja wygasła!

Znaleziono wyników: 13

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  calculus
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available Dodatnia pochodna Grünwalda-Letnikova jako pochodna funkcji drogi
Cioć R.
Autobusy : technika, eksploatacja, systemy transportowe
|
2017
|
R. 18, nr 12
786--791, CD
PL
W artykule przeanalizowano pochodną Grünwalda-Letnikova ƒ(ƞ)(t) w odniesieniu do klasycznego zagadnienia prędkości, jako pierwszej pochodnej funkcji drogi w czasie ƒ(1)(t). Autor argumentuje, że dodatnia pochodna Grünwalda-Letnikova nie spełnia twierdzenia Lagrange’a, co wiąże się z problemami jednoznacznej fizycznej jej interpretacji.
EN
The paper analyses Grünwald-Letnikov ƒ(ƞ)(t) derivative in space of first order derivative ƒ(1)(t) and also analyses the classical interpretation of derivative of path function as velocity. The author argues that the Grünwald-Letnikov positive derivative does not fulfil the Lagrange Theorem (Mean-Value Theorem for Derivatives) and this problem causes not clear physical interpretation of the Grünwald-Letnikov positive derivative.
2
Content available remote Recenzja książki pt. „Markowe wykłady z matematyki” autorstwa Marka Zakrzewskiego
Winiarska T.
Mathematica Applicanda
|
2014
|
Vol. 42, No. 2
273--276
PL
“Markowe wykłady z matematyki”, trzystu sześćdziesięcio pięcio (365) stronicowa książka autorstwa Marka Zakrzewskiego [1] została podzielona na pięć rozdziałów (w nawiasie podane są tytuły podrozdziałów): I. Analiza z lotu ptaka: granica, pochodna i całka (Prolog; Granica ciągu; Granica i ciągłość. Eksponenta i logarytm naturalny; Pochodna: pierwsze podejście; Całka: pierwsze podejście) II. Pochodne i aproksymacje (Obliczanie pochodnych; Funkcje trygonometryczne i kołowe; Kilka twierdzeń o istnieniu; Monotoniczność, ekstrema i wypukłość; Aproksymacje wielomianowe; Przybliżone rozwiązywanie równań) III. Całka: pole, długość i objętość (Całka oznaczona; Techniki całkowania; Całkowanie funkcji wybranych klas; Pola, długości i objętości; Metody przybliżone; Całki niewłaściwe; Objętość kuli i funkcja gamma; Wzór Stirlinga i wzór Wallisa) IV. Szeregi (Szeregi i iloczyny; Kryteria zbieżności szeregów; Szeregi potęgowe; Operacje na szeregach i wzór Leibniza; Liczby zespolone i funkcje przestępne; Szeregi Fouriera) V. Krótkie spojrzenie na równania różniczkowe (Równania o zmiennych rozdzielonych; Równanie rozpadu i modele wzrostu populacji; Liniowość i układy drgające; Równania różniczkowe i szeregi; Transformata Laplace‘a)
XX
The reviewed book is divided into five chapters (in brackets are the titles of subsections): I. The analysis of aerial: limit, derivative and integral (Prologue; the limit of sequence, the limit and the continuity; the exponent and the natural logarithm; a derivative and an antiderivative (primitive integral): the first approach) II. Derivatives and approximations (Calculation of derivatives, trigonometric functions and their inverse; the existence theorems, monotonicity, extremes and convexity; polynomial approximations; approximate solutions of equations) III. Integral: field area, length, and volume (Definite integral, techniques of integration, Integration of functions of selected classes, field area, length and volume; approximate methods; improper integrals, volume of a sphere and the gamma function; Stirling’s formula and the formula Wallis) IV. Series (Series and intersections; criteria for convergence of series, power series; operations ranks and pattern Leibniz Complex numbers and functions leap; Fourier series) V A look at the differential equations (equations with separated variables, equation degradation and population growth models, linearity and vibrating systems, differential equations and series, Laplace transform)
3
Zastosowanie rachunku różniczkowo-całkowego niecałkowitych rzędów w nauce i technice : artykuł przeglądowy
Nowocień A., Luft M., Pietruszczak D.
Logistyka
|
2014
|
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.
4
Content available remote On the π-calculus and Co-intuitionistic Logic : Notes on Logic for Concurrency and λP Systems
Bellin G., Menti A.
Fundamenta Informaticae
|
2014
|
Vol. 130, nr 1
21--65
EN
We reconsider work by Bellin and Scott in the 1990s on R. Milner and S. Abramsky’s encoding of linear logic in the π-calculus and give an account of efforts to establish a tight connection between the structure of proofs and of the cut elimination process in multiplicative linear logic, on one hand, and the input-output behaviour of the processes that represent them, on the other, resulting in a proof-theoretic account of (a variant of) Chu’s construction. But Milner’s encoding of the linear lambda calculus suggests consideration of multiplicative co-intuitionistic linear logic: we provide a term assignment for it, a calculus of coroutines which presents features of concurrent and distributed computing. Finally, as a test case of its adequacy as a logic for distributed computation, we represent our term assignment as a λP system. We argue that translations of typed functional languages in concurrent and distributed systems (such as π-calculi or λP systems) are best typed with co-intuitionistic logic, where some features of computations match the logical properties in a natural way.
5
Content available remote On the Computational Interpretation of CKn for Contextual Information Processing
Mendler M., Scheele S.
Fundamenta Informaticae
|
2014
|
Vol. 130, nr 1
125--162
EN
We aim to establish the multi-modal logic CKn as a baseline for a constructive correspondence theory of constructive modal logics. Just like many classical multi-modal logics may be studied as theories of the basic system K obtained by model-theoretic specialisation, we envisage constructive modal logics to be derived as proof-theoretic enrichments of CKn. The system CKn would then act as a core system for constructive contextual reasoning with controlled information flow. In this paper, as a first step towards this goal, we study CKn as a type theory and introduce its computational λ-calculus, λCKn. Extending previous work on CKn, we present a cut-free contextual sequent system in the spirit of Masini’s two-dimensional generalisation of natural deduction and Brünnler’s nested sequents and give a computational interpretation for CKn following the Curry- Howard Correspondence. The associated modal type theory λCKn permits an interpretation for both the modalities □ and ⋄ of CKn as type operators with simple and independent constructors and destructors, which has been missing in the literature. It is shown that the calculus satisfies subject reduction, strong normalisation and confluence. Since normal forms can be characterised by way of a Gentzen-style typing system with sub-formula property, CKn is suitable for proof search in CKn. At the same time, λCKn enjoys natural deduction style typing which is important for programming applications. In contrast to most existing modal type theories, which are obtained as theories of the constructive modal logic S4, CKn is not bound to a particular contextual interpretation. Thus, λCKn constitutes the core of a functional language which provides static type checking of information processing to support safe contextual navigation in relational structures like those treated by description logics. We review some existing work on modal type theories and discuss their relation to λCKn.
6
Content available Application of geogebra for teaching mathematics
Majerek D
Advances in Science and Technology. Research Journal
|
2014
|
Vol. 8, nr 24
51--54
EN
This paper shows how GeoGebra can be helpful in teaching mathematics. GeoGebra is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. It can be used for active and problem oriented teaching and fosters mathematical experiments and discoveries both in classroom and at home. In this work we show the sketch of using the above-mentioned software to build, solve and illustrate mathematical problems.
7
Content available remote Rough Net Structures : Example of Information System
Czaja L.
Fundamenta Informaticae
|
2013
|
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.
8
Content available Derivative of a function at a point and integral by professor Igor Kluvánek
Gunčaga J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
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.
9
Content available remote Equations f(x) = f-1(x) as a generator of mathematics teaching problems
Gunčaga J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
215-220
EN
Within the secondary school mathematics, the notion of an inverse function and its relationships to the original function does not attract much attention. In this article we deal with equations of the type f(x) = f-1(x) as a source of problems the solution of which leads to a better understanding of the notion of an inverse function. We make use of the PC programs Derive and WinPlot.
10
Content available remote Abstract Interpretation against Races
Barbuti R., Cataudella S., Tesei L.
Fundamenta Informaticae
|
2004
|
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.
11
Fractional derivative analysis of Helmholtz and paraxial-wave equations
Turski A. J., Atamaniuk B., Turska E.
Journal of Technical Physics
|
2003
|
Vol. 44, no 2
193-206
EN
Fundamental rules and definitions of Fractional Calculus are outlined. Factorizing 1-D and 2-D Helmholtz equations, four semi-differential eigenfunctions are determined. The functions exhibit incident and reHected plane waves as well as diffracted incident and reflected waves on the half-plane edge. They allow to construct the Sommerfeld half-plane diffraction solutions. Parabolic-Wave Equation (PWE, Leontovich-Fock) for paraxial propagation is factorized and differential fractional solutions of Fresnel-integral type are determined. We arrived at two solutions, which are the mothers of known and new solutions.
12
Content available remote A Method of Axiomatic Rejection of Formulas in Propositional Logics
Borowik P., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1999
|
Vol. 7
5--8
13
Content available remote Calculus Infinitesimalis
Rys P., Zdráhal T.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2000/2001
|
Vol. 8
161--168
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.