Wyniki wyszukiwania - Biblioteka Nauki

1

On the integral quasicontinuity

100%

Grande Z. , Strońska E.

Journal of Applied Analysis

|

2006

|

tom Vol. 12, nr 2

233-248

EN

A function f : R w indeksie górnym m → R satisfies the condition [wzór] (resp. [wzór]) at a point x ∈ R w indeksie górnym m if for each real ε > 0 and for each set U ∋ x belongong to Euclidean topology in R w indeksie górnym (resp. to the strong density topolgy [to the ordinary density topology]) there is an open set 0 such that 0 ∩ U ≠ Ø and [wzór]. These notions are some analogies are some analogies of the quasicontinuity or the approximate quasicontinuity. In this article we compare these notions with the classical notion of the quasicontinuity.

2

On the Law of Large Numbers for Nonmeasurable Identically Distributed Random Variables

100%

Pruss A. R.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2013

|

tom Vol. 61, no 2

161--168

EN

Let Ω be a countable infinite product Ω₁N of copies of the same probability space Ω1, and let {Ξn} be the sequence of the coordinate projection functions from Ω to~Ω₁. Let Ψ be a possibly nonmeasurable function from Ω₁ to R, and let X_n(ω)=Ψ(Ξn(ω)). Then we can think of {X_n} as a sequence of independent but possibly nonmeasurable random variables on Ω. Let S_n=X₁+⋯+X_n. By the ordinary Strong Law of Large Numbers, we almost surely have E∗[X1]≤lim infSn/n≤lim supSn/n≤E∗[X₁], where E∗ and E∗ are the lower and upper expectations. We ask if anything more precise can be said about the limit points of Sn/n in the nontrivial case where E∗[X₁]1], and obtain several negative answers. For instance, the set of points of Ω where S_n/n converges is maximally nonmeasurable: it has inner measure zero and outer measure one.

3

Second-order viability result in Banach spaces

100%

Aitalioubrahim M. , Sajid S.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

|

2010

|

tom 30

|

nr 1

5-21

EN

We show the existence result of viable solutions to the second-order differential inclusion ẍ(t) ∈ F(t,x(t),ẋ(t)), x(0) = x₀, ẋ(0) = y₀, x(t) ∈ K on [0,T], where K is a closed subset of a separable Banach space E and F(·,·,·) is a closed multifunction, integrably bounded, measurable with respect to the first argument and Lipschitz continuous with respect to the third argument.

4

Strong Fubini properties of ideals

88%

Recław I. , Zakrzewski P.

Fundamenta Mathematicae

|

1999

|

tom 159

|

nr 2

135-152

EN

Let I and J be σ-ideals on Polish spaces X and Y, respectively. We say that the pair ⟨I,J⟩ has the Strong Fubini Property (SFP) if for every set D ⊆ X× Y with measurable sections, if all its sections $D_x = {y: ⟨x,y⟩ ∈ D}$ are in J, then the sections $D^y = {x: ⟨x,y⟩ ∈ D}$ are in I for every y outside a set from J (``measurable" means being a member of the σ-algebra of Borel sets modulo sets from the respective σ-ideal). We study the question of which pairs of σ-ideals have the Strong Fubini Property. Since CH excludes this phenomenon completely, sufficient conditions for SFP are always independent of ZFC. We show, in particular, that: • if there exists a Lusin set of cardinality the continuum and every set of reals of cardinality the continuum contains a one-to-one Borel image of a non-meager set, then ⟨MGR(X), J⟩ has SFP for every J generated by a hereditary $п^1_1$ (in the Effros Borel structure) family of closed subsets of Y (MGR(X) is the σ-ideal of all meager subsets of X), • if there exists a Sierpiński set of cardinality the continuum and every set of reals of cardinality the continuum contains a one-to-one Borel image of a set of positive outer Lebesgue measure, then $⟨NULL_μ, J⟩$ has SFP if either $J= NULL_ν$ or J is generated by any of the following families of closed subsets of Y ($NULL_μ$ is the σ-ideal of all subsets of X having outer measure zero with respect to a Borel σ-finite continuous measure μ on X): (i) all compact sets, (ii) all closed sets in $NULL_ν$ for a Borel σ-finite continuous measure ν on Y, (iii) all closed subsets of a $п^1_1$ set A ⊆ Y.

5

Co nieco o kryteriach reprezentyki

88%

Włodek J. J.

LAB Laboratoria, Aparatura, Badania

|

2008

|

tom R. 13, nr 4

38-39

PL

Reprezentyka jest samodzielną dyscypliną naukową, która zajmuje się wieloaspektowym badaniem relacji między tworami istniejącymi w otaczającym nas środowisku naturalnym, a ich reprezentantami w postaci mian bądź list opisowych. Korzysta ona ze zweryfikowanych metod badawczych stosowanych w różnych dziedzinach nauki. Bada, jak w reprezentancie danego tworu jest wyeksponowana nie tylko istota swoistości, ale także jego możliwości funkcjonalne.

6

Towards New Probabilistic Assumptions in Business Intelligence

75%

Schumann A. , Szelc A.

Studia Humana

|

2014

|

tom 3

|

nr 4

11-21

EN

One of the main assumptions of mathematical tools in science is represented by the idea of measurability and additivity of reality. For discovering the physical universe additive measures such as mass, force, energy, temperature, etc. are used. Economics and conventional business intelligence try to continue this empiricist tradition and in statistical and econometric tools they appeal only to the measurable aspects of reality. However, a lot of important variables of economic systems cannot be observable and additive in principle. These variables can be called symbolic values or symbolic meanings and studied within symbolic interactionism, the theory developed since George Herbert Mead and Herbert Blumer. In statistical and econometric tools of business intelligence we accept only phenomena with causal connections measured by additive measures. In the paper we show that in the social world we deal with symbolic interactions which can be studied by non-additive labels (symbolic meanings or symbolic values). For accepting the variety of such phenomena we should avoid additivity of basic labels and construct a new probabilistic method in business intelligence based on non-Archimedean probabilities.

7

Matematyczna notacja błędu wyniku pomiaru

63%

Włodek J. J.

LAB Laboratoria, Aparatura, Badania

|

2008

|

tom R. 13, nr 5

31-34

8

An innovative methodology for supporting the CLLD

63%

Aldorfai G. , Czabadai L. , Topa Z.

Polish Journal of Management Studies

|

2016

|

tom Vol. 13, No. 1

7--17

EN

Based on the LEADER initiative, the European Union created a new tool for the planning period 2014-2020: the Community Lead Local Development (CLLD). Both the LEADER and the CLLD programmes put great emphasis on studying the basic situation, but there is no universal methodology provided for it, which makes it almost impossible to compare regions with each other. Therefore, this study aims to provide a way to compare regional characteristics and indicators in the current planning period of the EU, which allows us to monitor the development path of the regions, and also the performance of regional development programmes. This study investigates a smaller region, as a test of our chosen method for later and larger investigations. Through the applied methodology important elements belonging to the CLLD, such as the indicators for life quality, organisational efficiency, sectoral performance and infrastructure, were examined. The output of the research is intended to provide a suitable tool for decision makers to compare different regional levels more efficiently.

PL

W oparciu o inicjatywy programu LEADER, Unia Europejska stworzyła nowe narzędzie do okresu planowania 2014-2020: Rozwój Lokalny Kierowany przez Społeczność (CLLD). Zarówno program LEADER, jak i program CLLD kładzie duży nacisk na badanie podstawowej sytuacji, nie ma jednak uniwersalnej metodologii do tego przewidzianej, co sprawia, że prawie niemożliwe jest porównanie ze sobą regionów. Dlatego też niniejsze badanie ma na celu dostarczenie sposobu na porównanie regionalnych cech i wskaźników w bieżącym okresie planowania UE, co pozwala nam monitorować ścieżkę rozwoju regionów, a także realizację programów rozwoju regionalnego. Niniejsze studium bada mniejszy region, jako sprawdzian wybranej przez nas metody dla późniejszych i większych badań. Za pośrednictwem zastosowanej metodologii zbadane zostały ważne elementy należące do CLLD, takie jak wskaźniki jakości życia, efektywność organizacji, wydajność sektorowa i infrastruktura. Wynik badań ma na celu zapewnienie odpowiedniego narzędzia dla decydentów, dla bardziej efektywnego porównania różnych poziomów regionalnych.

9

The Demyanov metric and measurable multifunctions

63%

Leśniewski A.

Journal of Mathematics and Applications

|

2010

|

tom Vol. 33

61-65

EN

We present in this paper measurability multifunctions in the family of all convex, bounded sets which need not be closed. The Demyanov metric is discussed.