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1
Content available On some properties of the superposition operator on topological manifolds
100%
Dronka J.
Opuscula Mathematica
|
2010
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tom Vol. 30, no. 1
69-77
EN
In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation is obtained.
2
Content available remote The Basic Existence Theorem of Riemann-Stieltjes Integral
100%
Nakasho K. , Narita K. , Shidama Y.
Formalized Mathematics
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2016
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tom 24
|
nr 4
253-259
EN
In this article, the basic existence theorem of Riemann-Stieltjes integral is formalized. This theorem states that if f is a continuous function and ρ is a function of bounded variation in a closed interval of real line, f is Riemann-Stieltjes integrable with respect to ρ. In the first section, basic properties of real finite sequences are formalized as preliminaries. In the second section, we formalized the existence theorem of the Riemann-Stieltjes integral. These formalizations are based on [15], [12], [10], and [11].
3
Content available Level sets of continuous functions increasing with respect to each variable
100%
Sajbura K.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2005
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tom 25
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nr 1
19-26
EN
We are going to prove that level sets of continuous functions increasing with respect to each variable are arcwise connected (Theorem 3) and characterize those of them which are arcs (Theorem 2). In [3], we will apply the second result to the classical linear functional equation φ∘f = gφ + h (cf., for instance, [1] and [2]) in a case not studied yet, where f is given as a pair of means, that is so-called mean-type mapping.
4
Content available remote More on weak δs-continuity in topological spaces
88%
Jafari S. , Noiri T.
Fasciculi Mathematici
|
2016
|
tom Nr 56
99--109
EN
The notion of weakly δs-continuous functions is introduced by Ekici in [6]. In this paper, we further investigate some more properties of weakly δs-continuous functions. This type of continuity is a generalization of super continuity [16].
5
Content available A handful of theorems about point increase
75%
Janaszak T.
Didactics of Mathematics
|
2013
|
nr 10(14)
33-44
EN
In classic calculus increasing functions are considered. The idea of increasing is connected with an interval. In this article the idea of increasing function is connected with a point and some neighbourhood of the point. It is defined as an increasing point of the function. This is proved by the theorem: if each point of an interval is a point of increasing a function then the function is increasing at an interval.
6
Content available remote Uniform continuity and normality of metric spaces in ZF
75%
Keremedis K.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2017
|
tom Vol. 65, no. 2
113--124
EN
Let X = (X, d) and Y = (Y, ρ) be two metric spaces. (a) We show in ZF that: (i) If X is separable and f: X → Y is a continuous function then f is uniformly continuous iff for any A, B ⊆ X with d(A, B) = 0, ρ (f(A), f(B)) = 0. But it is relatively consistent with ZF that there exist metric spaces X, Y and a continuous, nonuniformly continuous function f : X → Y such that for any A, B ⊆ X with d(A, B) = 0, ρ (f(A), f(B)) = 0. (ii) If S is a dense subset of X, Y is Cantor complete and f : S → Y a uniformly continuous function, then there is a unique uniformly continuous function F : X → Y extending f. But it is relatively consistent with ZF that there exist a metric space X, a complete metric space Y, a dense subset S of X and a uniformly continuous function f : S → Y that does not extend to a uniformly continuous function on X. (iii) X is complete iff for any Cauchy sequences (xn)n∈N and (yn)n∈N in X, if [wzór] then d({xn : n ∈ N},{yn : n ∈ N}) > 0. (b) We show in ZF+CAC that if f : X → Y is a continuous function, then f is uniformly continuous iff for any A, B ⊆ X with d(A, B) = 0, ρ (f(A), f(B)) = 0.
7
Content available remote Knot Point Method in Extrapolation of Boundary Measurement Results
75%
Pisarek J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2006
|
tom Vol. 11
67--78
EN
The new measurement technique that relies on distinguishing the ranges in object's space in which the searched quantities are approximated by multiparameter continuous functions has been introduced. The parameters of these functions are calculated by minimizing the functional describing the distance between different functions determined at the same points and distance between numerical solution and experimental results and assumed’a priori’ theoretical guidelines. Functions’ spaces might be determined in any way and might be changed during the computation. This method is especially usefull in extrapolation of the boundary measurement results on the object interior and in joining the local and whole object (global) solutions.
8
Content available Some properties of openly ϱ-continuous functions
75%
Nowakowska K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2016
|
tom Vol. 21
73--84
EN
In the paper we present definition and some properties of openly ϱ-upper continuous functions. Connections with ϱ-upper continuous and porouscontinuous functions are studied.
9
Content available On local Whitney convergence
63%
Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2012
|
tom Vol. 17
57-68
EN
In this paper we will give definitions of local Whitney convergence in F(X,Y ) and in C(X,Y ), where X is a topological space, (Y,d) is a metric space and F(X,Y ) is the space of all functions from X to Y and C(X,Y ) is the space of all continuous functions from X to Y . We will study some properties of this notion and connections with other kinds of convergence.
10
Content available remote Exponent in one of the variables
63%
Mityushev V.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
tom Vol. 12
77-79
EN
A periodicity functional equation of one complex variable which characterizes the exponential function is discussed. This functional equation can be generalized to equation for functions depending on two complex variables. It is conjectured that the second functional equation also characterizes the exponent. Applications to representations of complex continuous elementary functions are discussed.
11
Modelowanie maszyn szyjących
63%
Zajączkowski J.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
|
2001
|
tom z. 17
231-236
PL
W pracy opisano algorytm tworzenia modeli matematycznych maszyn szyjących. Uwzględniono silnik indukcyjny, przekładnię pasową oraz mechanizmy dźwigniowe i krzywkowe. Równania dynamiczne ruchu wyprowadzono korzystając z zasady prac wirtualnych i zasady d’ Alamberta. Związki kinematyczne znaleziono wykorzystując metodę Brenta. Ich postać dyskretną zastąpiono funkcjami ciągłymi korzystają z wielomianów. Przybliżenia atraktorów znaleziono całkując układ równań numerycznie przez odpowiednio długi czas.
EN
An algorithm of creating mathematical model of a sewing machine is described in this paper. The electric motor, the belt drive, the linkage and cam mechanisms are taken into account. The equations of the motion are derived by the use of the principle of virtual work together with d ’ Alambert principle. The kinematics relationships were found by the utilization of Brent method. Their discrete form was replaced by a continuous one using polynomials. The approximations of attractors were found by integrating the set of differential eąuations for sufficiently long time.
12
Content available Operators with memory in Schramm spaces
63%
Wróbel M.
Journal of Applied Mathematics and Computational Mechanics
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2023
|
tom Vol. 22, nr 3
69--80
EN
We show that every operator with memory acting between Banach spaces CΦBV(I) of continuous functions of bounded variation in the sense of Schramm defined on a compact interval I of a real axis, is a Nemytskij composition operator with the continuous generating function. Moreover, some consequences for uniformly bounded operators with memory will be given. As a by-product, we obtain that a Banach space CΦBV(I) has the uniform Matkowski property.
13
Content available remote On gβ-regular and gβ-normal spaces
63%
Tahiliani S.
Demonstratio Mathematica
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2007
|
tom Vol. 40, nr 3
739-743
EN
The aim of this paper is to introduce and study two new classes of spaces, called gβ-regular and gβ-normal spaces. The concept of gβ-regularity and gβ-normality are separation properties obtained by utilizing gβ-closed sets. Recall that a subset A of a space (X, r ) is called gβ-closed if β Cl(A) is a subset of U where A is a subset of U and U is open in X.
14
Content available Schramm spaces and composition operators
51%
Wróbel M.
Journal of Applied Mathematics and Computational Mechanics
|
2023
|
tom Vol. 22, nr 2
87--98
EN
We give some properties of Schramm functions; among others, we prove that the family of all continuous piecewise linear functions defined on a real interval I is contained in the space ΦBV (I) of functions of bounded variation in the sense of Schramm. Moreover, we show that the generating function of the corresponding Nemytskij composition operator acting between Banach spaces CΦBV (I) of continuous functions of bounded Schramm variation has to be continuous and additionally we show that a space CΦBV (I) has the Matkowski property.
15
Content available remote Functions characterized by images of sets
51%
Ciesielski K. , Dikrajan D. , Watson S.
Colloquium Mathematicum
|
1998
|
tom 77
|
nr 2
211-232
EN
For non-empty topological spaces X and Y and arbitrary families $\cal A$ ⊆ $\cal P(X)$ and $\cal B ⊆ \cal P(Y)$ we put $\cal C_{\cal A,\cal B}$={f ∈ $Y^X$ : (∀ A ∈ $\cal A$)(f[A] ∈ $\cal B)$}. We examine which classes of functions $\cal F$ ⊆ $Y^X$ can be represented as $\cal C_{\cal A,\cal B}$. We are mainly interested in the case when $\cal F=\cal C(X,Y)$ is the class of all continuous functions from X into Y. We prove that for a non-discrete Tikhonov space X the class $\cal F=\cal C$(X,ℝ) is not equal to $\cal C_{\cal A,\cal B}$ for any $\cal A$ ⊆ $\cal P(X)$ and $\cal B$ ⊆ $\cal P$(ℝ). Thus, $\cal C$(X,ℝ) cannot be characterized by images of sets. We also show that none of the following classes of real functions can be represented as $\cal C_{\cal A,\cal B}$: upper (lower) semicontinuous functions, derivatives, approximately continuous functions, Baire class 1 functions, Borel functions, and measurable functions.
16
Zastosowanie funkcji ciągłych (continuous pedotransfer function) do wyznaczania parametrów równania Van Genuchtena
51%
Peczkowski G.
Zeszyty Problemowe Postępów Nauk Rolniczych
|
2010
|
tom 548
|
nr 2
PL
Istotnymi zagadnieniami związanymi bezpośrednio z modelowaniem i tym samym rozwiązywaniem równań różniczkowych związanych z przepływem wody w glebie jest zastosowanie analitycznych zależności opisujących krzywe retencyjności wodnej gleb. Zależności te mogą w znaczny sposób ułatwić, czy nawet skrócić czas wykonania bezpośrednich oznaczeń laboratoryjnych. W pracy poddano szczegółowej analizie wyznaczenie parametrów do wzoru van Genuchtena opisującego związek wilgotności i ciśnienienia, z zastosowaniem funkcji ciągłych Stena. Wykorzystano także oprogramowania RETC (US Salinity Laboratory, USDA, ARS) algorytm iteracyjny Marquardta - optymalizacji nieliniowej. Stwierdzono, że zależność van Genuchtena z wyznaczonymi parametrami przy pomocy funkcji ciągłych Wöstena jak i programu opartego na algorytmie Marquardta znajduje zastosowanie dla gleb poddanych analizie. Obliczone miary statystyczne w omawianych przypadkach wykazują dobrą zgodność dla pomierzonych i obliczonych wartości wilgotności w przypadku glin pylastych i glin ciężkich.
EN
Important problems directly connected with modeling and thus solving the differential equations connected with soil water flow is the application of analytical correlation describing the curves of water retential characterization of soils. These correlations may to a great degree facilitate or even to shorten the time of performing direct laboratory determinations. A detailed analysis of determining parameters to the van Genuchten’s equation describing the connection between the humidity and pressure using the Stena continuous functions is described in this paper. The RETC programmings (US Salinity Laboratory, USDA, ARS) were also applied using the Marquardt’s algorithm of the non-linear optimization. It was noted that the van Genuchten correlation with the parameters determined with the help of Wösten continuous functions and the programme basad on the Marquardt’s algorithm could be applied to the analyzed soils. The calculated statistical measurements in the discussed cases show a good compatibility for the measured and calculated values of humidity in the case of the silty and heavy loams.
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