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1.
M. M. Zarichnyi 《Mathematical Notes》1996,60(6):638-641
LetC be one of the absolute Borel classesM
α
,A
α
, with 1≤α<ω
1 or one of the absolute projective classesP
k
,k≥1. A map of ann-dimensional spaceX ∈ C onto the Hilbert cube which is ann-soft map in Shchepin's sense and universal in the class of maps of spaces of dimension smaller that or equal ton from the classC into separable metrizable spaces is constructed.
Translated fromMatematicheskie Zametki, Vol. 60, No. 6, pp. 845–850, December, 1996. 相似文献
2.
We introduce new classes of sets called Λ
g
-closed sets and Λ
g
-open sets in topological spaces. We also investigate several properties of such sets. It turns out that Λ
g
-closed sets and Λ
g
-open sets are weaker forms of closed sets and open sets, respectively and stronger forms of g-closed sets and g-open sets, respectively.
Dedicated to Professor Maximilian Ganster on the occasion of his 50th birthday 相似文献
3.
Interval Valued Intuitionistic (S, T)-fuzzy Hv-submodules 总被引:1,自引:0,他引:1
Jian Ming ZHAN W.A. DUDEK 《数学学报(英文版)》2006,22(4):963-970
On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and an s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic (S, T)-fuzzy Hv-submodules and interval valued intuitionistic (S, T)-fuzzy submodules are discussed. 相似文献
4.
Alejandro Balbás José Garrido Silvia Mayoral 《Methodology and Computing in Applied Probability》2009,11(3):385-399
The current literature does not reach a consensus on which risk measures should be used in practice. Our objective is to give
at least a partial solution to this problem. We study properties that a risk measure must satisfy to avoid inadequate portfolio
selections. The properties that we propose for risk measures can help avoid the problems observed with popular measures, like
Value at Risk (VaR
α
) or Conditional VaR
α
(CVaR
α
). This leads to the definition of two new families: complete and adapted risk measures. Our focus is on risk measures generated by distortion functions. Two new properties are put forward for these:
completeness, ensuring that the distortion risk measure uses all the information of the loss distribution, and adaptability,
forcing the measure to use this information adequately.
This research was partially funded by
1,3
Welzia Management, SGIIC SA, RD Sistemas SA, Comunidad Autónoma de Madrid Grant s-0505/tic/000230, and MEyC Grant BEC2000-1388-C04-03 and by
2
the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 36860-06. 相似文献
5.
Jian Ming ZHAN Bijan DAVVAZ K. P. SHUM 《数学学报(英文版)》2007,23(8):1345-1356
We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in (Fuzzy Sets Syst., 117: 477- 484, 2001) and Bhakat and Das in (Fuzzy Sets Syst., 80: 359-368, 1996). The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued (α,β)-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued (α,β)-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy 相似文献
6.
Ferenc Móricz 《Acta Mathematica Hungarica》2008,120(4):355-366
We introduce the higher order Lipschitz classes Λ
r
(α) and λ
r
(α) of periodic functions by means of the rth order difference operator, where r = 1, 2, ..., and 0 < α ≦ r. We study the smoothness property of a function f with absolutely convergent Fourier series and give best possible sufficient conditions in terms of its Fourier coefficients
in order that f belongs to one of the above classes.
This research was supported by the Hungarian National Foundation for Scientific Research under Grant T 046 192. 相似文献
7.
In this paper we characterize the boundedness and compactness of weighted composition operators of H∞ into α-Bloch spaces on the unit ball in C^n. 相似文献
8.
We introduce the notions of δ-I- open sets and semi δ-I-continuous functions in ideal topological spaces and investigate some of their properties. Additionally, we obtain decompositions
of semi-I-continuous functions and α-I-continuous functions by using δ-I-open sets.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
By two relations belonging to and quasi-coincidence (q) between fuzzy points and fuzzy sets, we define the concept of (α, β)-fuzzy subalgebras where α, β are any two of with . We state and prove some theorems in (α, β)-fuzzy B-algebras. 相似文献
10.
Characterizations and Extensions of Lipschitz-α Operators 总被引:1,自引:0,他引:1
Huai Xin CAO Jian Hua ZHANG Zong Ben XU 《数学学报(英文版)》2006,22(3):671-678
In this work, we prove that a map F from a compact metric space K into a Banach space X over F is a Lipschitz-α operator if and only if for each σ in X^* the map σoF is a Lipschitz-α function on K. In the case that K = [a, b], we show that a map f from [a, b] into X is a Lipschitz-1 operator if and only if it is absolutely continuous and the map σ→ (σ o f)' is a bounded linear operator from X^* into L^∞([a, b]). When K is a compact subset of a finite interval (a, b) and 0 〈 α ≤ 1, we show that every Lipschitz-α operator f from K into X can be extended as a Lipschitz-α operator F from [a, b] into X with Lα(f) ≤ Lα(F) ≤ 3^1-α Lα(f). A similar extension theorem for a little Lipschitz-α operator is also obtained. 相似文献
11.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL
p[−π,π], algebraic polynomial approximation inL
p[−1,1], algebraic polynomial approximation inL
p(S), and entire function of exponential type approximation inL
p(R), and characterizeK-functionals for certain pairs of function spaces including (L
p[−π,π],B
s
a(L
p[−π,π])), (L
p(R),s
a(Lp(R))),
, and
, where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.
This project is supported by the National Science Foundation of China. 相似文献
12.
It is proved that ifX is a connected locally continuumwise connected coanalytic nowhere topologically complete space, then the hyperspace 2
X
of all nonempty compact subsets ofX is strongly universal in the class of all coanalytic spaces. Moreover, 2
X
is homeomorphic to Π2 ifX is a Baire space, and toQ∖Π1 ifX contains a dense absoluteG
δ-setG ⊂X such that the intersectionG ∩U is connected for any open connectedU ⊂X. (Here Π1, Π1⊂X are the standard subsets of the Hilbert cubeQ absorbing for the classes of analytic and coanalytic spaces, respectively.) Similar results are obtained for higher projective
classes.
Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 35–51, July, 1997.
Translated by O. V. Sipacheva 相似文献
13.
Let X denote a specific space of the class of X
α,p
Banach sequence spaces which were constructed by Hagler and the first named author as classes of hereditarily ℓp Banach spaces. We show that for p > 1 the Banach space X contains asymptotically isometric copies of ℓp. It is known that any member of the class is a dual space. We show that the predual of X contains isometric copies of ℓp where 1/p + 1/q = 1. For p = 1 it is known that the predual of the Banach space X contains asymptotically isometric copies of c
0. Here we give a direct proof of the known result that X contains asymptotically isometric copies of ℓ1. 相似文献
14.
The simplest way to perform a fuzzy risk assessment is to calculate the fuzzy expected value and convert fuzzy risk into non-fuzzy
risk, i.e., a crisp value. In doing so, there is a transition from the fuzzy set to the crisp set. Therefore, the first step
is to define an α level value, and then select the elements x with a subordinate degree A(x)≥α. The higher the value of α, the lower the degree of uncertainty—the probability is closer to its true value. The lower the value of α, the higher the degree of uncertainty—this results in a lower probability serviceability. The possibility level α is dependant on technical conditions and knowledge. A fuzzy expected value of the possibility-probability distribution is
a set with
and
as its boundaries. The fuzzy expected values
and
of a possibility-probability distribution represent the fuzzy risk values being calculated. Therefore, we can obtain a conservative
risk value, a venture risk value and a maximum probability risk value. Under such an α level, three risk values can be calculated. As α adopts all values throughout the set [0,1], it is possible to obtain a series of risk values. Therefore, the fuzzy risk may
be a multi-valued risk or set-valued risk. Calculation of the fuzzy expected value of flood risk in the Jinhua River basin
has been performed based on the interior-outer set model. Selection of an α value depends on the confidence in different groups of people, while selection of a conservative risk value or venture risk
value depends on the risk preference of these people. 相似文献
15.
Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion 总被引:1,自引:0,他引:1
Let E be a real Banach space with property (α) and let W
Γ be an E-valued Brownian motion with distribution Γ. We show that a function is stochastically integrable with respect to W
Γ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence
of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution
equations driven by an E-valued Brownian motion.
The first named author gratefully acknowledges the support by a ‘VIDI subsidie’ in the ‘Vernieuwingsimpuls’ programme of The
Netherlands Organization for Scientific Research (NWO) and the Research Training Network HPRN-CT-2002–00281. The second named
author was supported by grants from the Volkswagenstiftung (I/78593) and the Deutsche Forschungsgemeinschaft (We 2847/1–1). 相似文献
16.
Xiao Hong Fu 《数学学报(英文版)》2008,24(9):1475-1482
This paper considers the isometric extension problem concerning the mapping from the unit sphere S
1(E) of the normed space E into the unit sphere S
1(l
∞(Γ)). We find a condition under which an isometry from S
1(E) into S
1(l
∞(Γ)) can be linearly and isometrically extended to the whole space. Since l
∞(Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are
solved. More precisely, if E and F are two normed spaces, and if V
0: S
1(E) → S
1(F) is a surjective isometry, where c
00(Γ) ⊆ F ⊆ l
∞(Γ), then V
0 can be extended to be an isometric operator defined on the whole space.
This work is supported by Natural Science Foundation of Guangdong Province, China (Grant No. 7300614) 相似文献
17.
A. G. Smirnov 《Theoretical and Mathematical Physics》2007,151(2):591-603
We study the localization properties of generalized functions defined on a broad class of spaces of entire analytic test functions.
This class, which includes all Gelfand-Shilov spaces S
α
β
(R
k
) with β < 1, provides a convenient language for describing quantum fields with a highly singular infrared behavior. We show
that the carrier cone notion, which replaces the support notion, can be correctly defined for the considered analytic functionals.
In particular, we prove that each functional has a uniquely determined minimal carrier cone.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 2, pp. 179–194, May, 2007. 相似文献
18.
In the present paper, we define the difference sequence space r
q
(p, Δ), which is defined as follows:
where r
q
(p) is the Riesz sequence space given by Altay and Basşar. We give some topological properties and compute the α-, β- duals of this space.
相似文献
19.
V. A. Smirnov 《Mathematical Notes》1999,66(6):754-759
The notion ofA
∞-topological group is introduced. It is proved that, if a space
is obtained by deformation retraction of a topological groupG, then it has the structure of anA
∞-topological group, and theA
∞-homotopy equivalence
holds.
Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 913–919, December, 1999. 相似文献
20.
δ- and θ-modifications of generalized topologies 总被引:1,自引:1,他引:0
Á. Császár 《Acta Mathematica Hungarica》2008,120(3):275-279
It is shown that the theory of δ-and θ-modifications of topological spaces (see [3]) can be generalized for the case when the topology is replaced by a generalized
topology in the sense of [1].
Research supported by Hungarian Foundation for Scientific Research, grant No. T 49786. 相似文献