Wyniki wyszukiwania - BazTech

1

Modelling a solution of a homogeneous parabolic equation with random initial condition from Lp(Ω)

Kuchinka Katalin, Slyvka-Tylyshchak Ganna

Przegląd Elektrotechniczny

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2023

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R. 99, nr 5

77--82

EN

In this paper, a model of solutions to the heat equation with initial conditions from the Orlicz space Lp(Ω) of random variables is built. The constructed model approximates the solution of a homogeneous parabolic equation with given reliability and accuracy in some Orlicz space.

PL

W pracy zbudowano model rozwiązan równania ciepła z warunkami początkowymi z przestrzeni Orlicza Lp(Ω) zmiennych losowych. Skonstruowany model przybliza rozwiązanie jednorodnego równania parabolicznego z zadaną niezawodnoscią i dokładnoscią w pewnej przestrzeni Orlicza.

2

On perturbed quadratic integral equations and initial value problem with nonlocal conditions in Orlicz spaces

Metwali Mohamed M. A.

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

86--94

EN

The existence of a.e. monotonic solutions for functional quadratic Hammerstein integral equations with the perturbation term is discussed in Orlicz spaces. We utilize the strategy of measure of noncompactness related to the Darbo fixed point principle. As an application, we discuss the presence of solution of the initial value problem with nonlocal conditions.

3

Ryszard Grząślewicz (1953–2005)

Hudzik H., Mielczarek G., Płuciennik R.

Wiadomości Matematyczne

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2014

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T. 50, Nr 1

85--99

PL

Z wielkim wzruszeniem przyjęliśmy zaszczyt napisania wspomnienia o niezwykle zdolnym matematyku i naszym wielkim przyjacielu, profesorze Ryszardzie Grząślewiczu. Postaramy się przybliżyć sylwetkę człowieka, który niemal całe swoje dorosłe życie związał z Politechniką Wrocławską.

4

Effective energy integral functionals for thin films in the Orlicz-Sobolev space setting

Laskowski W., Nguyen H. T.

Demonstratio Mathematica

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2013

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Vol. 46, nr 3

585--604

EN

We consider an elastic thin film as a bounded open subset ω of R2. First, the effective energy functional for the thin film ω is obtained, by Γ-convergence and 3D-2D dimension reduction techniques applied to the sequence of re-scaled total energy integral functionals of the elastic cylinders (…) as the thickness ε goes to 0. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function for the elastic cylinders has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type and to satisfy the conditions (…) and (…) (that is equivalent to the reflexivity of Orlicz and Orlicz–Sobolev spaces generated by M). These results extend results of H. Le Dret and A. Raoult for the case M(t) = (…) for some (…).

5

On (∆2) condition in density-type topologies

Filipczak M., Terepeta M.

Demonstratio Mathematica

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2011

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Vol. 44, nr 2

423--432

EN

We discuss properties of density-type topologies Tψ connected with condition (∆2) similar to the condition considered in the theory of Orlicz spaces. Density-type topologies Tψ introduced in [5] may not be invariant under multiplication by a number. This property is strictly connected with the condition, which we call (∆2), by analogy with well known condition introduced in Orlicz spaces. Like in the theory of Orlicz spaces, (∆2) condition causes that the considered topologies are more convenient for examination and have simpler properties. Moreover, the power functions are also of great importance as a handy instrument. Recall some basic facts. Let (Ω, Σ, μ) be a measure space and A be a family of all functions φ: [0, ∞) → [0, ∞) which are continuous, nondecreasing, such that φ(0) = 0, φ(x) > 0 for x > 0 and limx→∞ φ(x) = ∞.

6

On a new sequence space related to the Orlicz sequence space

Khan V. A.

Journal of Mathematics and Applications

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2008

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Vol. 30

61-69

EN

The space m(Φ) was introduced by sargent[14]and further studied by Malkowsky and Mursaleen [8] and Mursaleen [9]. In this paper we extend this space to m(M, Φ, p) and study some of its properties, inclusions relations and its relation with the Orlicz sequence space l(sub M).

7

Sequences of bounded φ-variation and weighted unconditional convergence of series

Musielak J.

Demonstratio Mathematica

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2005

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Vol. 38, nr 1

153--162

EN

There are investigated spaces v0,φ of sequences of bounded φ-variation. Spaces v0, φ are applied to the problem of weighted unconditional convergence of series. It is shown that (vo,φ,lφ* ), where lφ* means the Orlicz sequence space generated by the N-function φ*, is a pair of weighted unconditional convergence. There are also considered nonlinear convolution - type operators in v0,φ .

8

Contractive projections onto isometric copies of L1(ν) in strictly monotone Banach lattices

Wójtowicz M.

Bulletin of the Polish Academy of Sciences. Mathematics

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2003

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Vol. 51, no 1

1-12

EN

Let Y be a Banach lattice and X a strictly monotone sublattice of Y. Every isometric copy of an L1-space in X is 1-complemented in Y (Theorem l). This is an extension of the classical result of Pełczyński for Y = X = L1(my), and of Dor for Y = X being q-concave. We also study the consequences of the existence of isometric copies of l1 in strictly monotone E[phi](my)-spaces, where E[phi](my) denotes the ideal of an Orlicz space L[phi](my) of the elements with absolutely continuous norm.

9

Orthogonal uniform convexity in Köthe spaces and Orlicz spaces

Kolwicz P.

Bulletin of the Polish Academy of Sciences. Mathematics

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2002

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Vol. 50, no 4

395-411

EN

We study a geometric property in Köthe spaces which is called orthogonal uniform convexity (UC┴). It was introduced in [19]. We prove that the class of Köthe spaces with property (UC┴) is a proper subset of the class of uniformly monotone and P-convex Köthe spaces. Next we consider connections between (UC┴) and property (β) of Rolewicz. We shown that the implication (UC┴) → (β) is true in any Köthe sequence space. Moreover, we find criteria for Orlicz function (sequence) spaces to be orthogonally uniformly convex. As a corollary we get that there holds (UC) → (UC┴) → (β) in any Köthe sequence space and the converse of any of these implications is not true. Furthermore, the implications (UC) → (β) → (UC┴) hold in any Köthe function space and the second one cannot be reversed.

10

An inequality of Bohr and Favard for Orlicz spaces

Bang H.

Bulletin of the Polish Academy of Sciences. Mathematics

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2001

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Vol. 49, no 4

381-387

EN

In this paper, we prove an inequality of Bohr and Favard for any Orlicz norm (with the same constants as in the Bohr-Favard inequality).

11

The separable quotient problem for symmetric function spaces

Śliwa W.

Bulletin of the Polish Academy of Sciences. Mathematics

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2000

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Vol. 48, no 1

13-27

EN

We study the separable quotient problem for some classes of symmetric function spaces on a measure space (Omega,Sigma,mi). In particular we prove that an infinite dimensional Orlicz space L[sup fi](Omega,Sigma,mi) has an infinite dimensional separable quotient if and only if the dual of L[sup fi](Omega,Sigma,mi) is total or there exists a measurable subset A of[Omega] such that the space L[sup fi] (Alpha,Sigma[sub Alpha],mi[sub Alpha)) is infinite dimensional and separable.

12

Approximation in Orlicz-Slobodeckii space by functions in C[infinity] (Omega)

Liskowski M.

Fasciculi Mathematici

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1999

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Nr 29

43-59

EN

We wish to prove that [...] is dense in Orlicz-Slobodeckii space Bk.M (n) for some n c RN offinite measure.

13

Weak-sequential compactness on non-locally convex Orlicz spaces

Nowak M.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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Vol. 46, no 3

225-231

EN

Let [L^fi] be an Orlicz space defined by a finite valued Orlicz function [fi] (not necesarilly convex) over a [sigma]-finite atomless measure space. Let (L^fi[...] be the order continous dual of [L^fi]. It is proved that a subset Z of [L^fi] is conditionally sequentially sigma([L^fi],(L^fi])[...)-compact (i.e., every sequence in Z contains a sigma([L^[fi],(L^fi])[...])-Cauchy subsequence) if and only if Z is norm bounded in some Orlicz space [L^psi] where psi increases more rapidly than [...] (the convex minorant of fi).