共查询到20条相似文献,搜索用时 46 毫秒
1.
. . 《Ukrainian Mathematical Journal》1997,49(8):1011-1015
Одержано точцу оцінку похибки оптимального відновлення інтеграла на множині монотонних на [a, b] функційf(t) з опуклою мажорантою модуля неперервності при умові |f(b)−f(a)|=L>0.
An exact estimate is obtained for error of the optimal recovery of integral on a set of functionsf(t), which are monotone in [a, b] and possess a convex majorant of the module of continuity under the condition |f(b)−f(a)|=L>0.相似文献
2.
Let D, D′ ⊂ ℂn be bounded domains with smooth real analytic boundaries and ƒ: D → D′ be a proper holomorphic map. Our main result implies
that if the graph of ƒ extends as an analytic set to a neighborhood of a poìnt (a, a′) ∈ ∂D × 3D′ with a′ ∈ clƒ(a), then ƒ extends holomorphically to a neighborhood of a. 相似文献
3.
P. M. Edwards 《Semigroup Forum》1989,39(1):257-262
For a congruence σ on a semigroupS a congruence μ(σ) onS, containing σ, is defined such that the semigroupS/σ is fundamental if and only if σ=μ(σ). The congruence μ(σ) is shown to possess maximality properties and for idempotent-surjective
semigroups, μ(σ) is the maximum congruence with respect to the partition of the idempotents determined by σ. Thus μ is the
maximum idempotent-separating congruence on any idempotent-surjective semigroup. It is shown that μ(μ(σ))=μ(σ).
If ρ is another congruence onS, possibly with the same partition of the idempotents as σ, then it is of interest to know when ρ⊆σ (or ρ⊆μ(σ)) implies μ(ρ)⊆μ(σ)
or even μ(ρ)=μ(σ). These implications are not true in general but if σ⊆ρ⊆μ(σ) then μ(ρ)⊆μ(σ). IfS is an idempotent-surjective semigroup and ρ and σ have the same partition of the idempotents then μ(ρ)=μ(σ). 相似文献
4.
Stephen Dias Barreto 《Proceedings Mathematical Sciences》2000,110(4):347-356
We study a quantum spin glass as a quantum spin system with random interactions and establish the existence of a family of
evolution groups {τt(ω)}ω∈/Ω of the spin system. The notion of ergodicity of a measure preserving group of automorphisms of the probability space Ω, is
used to prove the almost sure independence of the Arveson spectrum Sp(τ(ω)) of τt(ε). As a consequence, for any family of (τ(ω),β) — KMS states {ρ(ω)}, the spectrum of the generator of the group of unitaries
which implement τ(ω) in the GNS representation is also almost surely independent of ω. 相似文献
5.
Provability interpretations of modal logic 总被引:5,自引:0,他引:5
Robert M. Solovay 《Israel Journal of Mathematics》1976,25(3-4):287-304
We consider interpretations of modal logic in Peano arithmetic (P) determined by an assignment of a sentencev
* ofP to each propositional variablev. We put (⊥)*=“0 = 1”, (χ → ψ)* = “χ* → ψ*” and let (□ψ)* be a formalization of “ψ)* is a theorem ofP”. We say that a modal formula, χ, isvalid if ψ* is a theorem ofP in each such interpretation. We provide an axiomitization of the class of valid formulae and prove that this class is recursive. 相似文献
6.
Let G be an extension of ℚ by a direct sum of r copies of ℚ. (1) If G is abelian, then G is a direct sum of r + 1 copies of ℚ and AutG ≅ GL(r + 1, Q); (2) If G is non-abelian, then G is a direct product of an extraspecial ℚ-group E and m copies of ℚ, where E/ζE is a linear space over Q with dimension 2n and m + 2n = r. Furthermore, let AutG′G be the normal subgroup of AutG consisting of all elements of AutG which act trivially on the derived subgroup G′ of G, and AutG/ζG,ζGG be the normal subgroup of AutG consisting of all central automorphisms of G which also act trivially on the center ζG of G. Then (i) The extension 1 → AutG′G → AutG → AutG′ → 1 is split; (ii) AutG′G/AutG/ζG,ζGG ≅ Sp(2n,Q) × (GL(m, Q) ⋉ ℚ(m)); (iii) AutG/ζG,ζGG/InnG ≅ ℚ(2nm). 相似文献
7.
Wolfgang M. Schmidt 《Monatshefte für Mathematik》2003,138(1):61-71
Subsets 𝒜, 𝒮 of an additive group G are complementary if 𝒜 + 𝒮 = G. When 𝒜 is of finite cardinality ∣𝒜∣, and G is ℤ or ℝ, we give sufficient conditions for the existence of a complementary set 𝒮 with “density” not much larger than
1/∣𝒜∣.
Supported in part by NSF DMS-0074531.
Received February 14, 2002; in revised form July 18, 2002
RID="a"
ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday 相似文献
8.
Janusz Matkowski 《Central European Journal of Mathematics》2003,1(4):435-440
In [4], assuming among others subadditivity and submultiplicavity of a function ψ: [0, ∞)→[0, ∞), the authors proved a Hyers-Ulam
type stability theorem for “ψ-additive” mappings of a normed space into a normed space. In this note we show that the assumed
conditions of the function ψ imply that ψ=0 and, consequently, every “ψ-additive” mapping must be additive 相似文献
9.
V. V. Meleshko A. A. Bondarenko A. N. Trofimchuk R. Z. Abasov 《Journal of Mathematical Sciences》2010,167(2):197-216
In this paper, the normal modes of an elastic rectangular waveguide are analyzed. We retrace the key aspects of the almost
150-year history of this problem. Using the superposition method, we have obtained an analytical solution of the problem for
four types of symmetry of the wave field. In addition, we have established important differences of the dispersion characteristics
of normal modes in a rectangle from the Rayleigh–Lamb modes for an infinite plate and the Pochhammer–Chree modes for a cylinder.
We give also an estimate of a series of approximate theories for a rectangular waveguide.
The numerical interpretation of the results of analysis is however necessary, and it is a degree of perfection which it would be very important to give to every application of analysis to the natural sciences. So long as it is not obtained, the solutions may be said to remain incomplete and useless, and the truth which it is proposed to discover is no less hidden in the formulas of analysis than it was in the physical problem itself.
J. Fourier [28, Sec. 13]相似文献
10.
It is shown that a large class of events in a product probability space are highly sensitive to noise, in the sense that with
high probability, the configuration with an arbitrary small percent of random errors gives almost no prediction whether the
event occurs. On the other hand, weighted majority functions are shown to be noise-stable. Several necessary and sufficient
conditions for noise sensitivity and stability are given.
Consider, for example, bond percolation on ann+1 byn grid. A configuration is a function that assigns to every edge the value 0 or 1. Let ω be a random configuration, selected
according to the uniform measure. A crossing is a path that joins the left and right sides of the rectangle, and consists
entirely of edges ℓ with ω(ℓ)=1. By duality, the probability for having a crossing is 1/2. Fix an ɛ ∈ (0, 1). For each edge
ℓ, let ω′(ℓ)=ω(ℓ) with probability 1 − ɛ, and ω′(ℓ)=1 − ω(ℓ) with probability ɛ, independently of the other edges. Letp(τ) be the probability for having a crossing in ω, conditioned on ω′ = τ. Then for alln sufficiently large,P{τ : |p(τ) − 1/2| > ɛ}<ɛ. 相似文献
11.
Let G : Ω→Ω' be a closed unital map between commutative, unital quantales. G induces a functor G^- from the category of Ω-categories to that of Ω'-categories. This paper is concerned with some basic properties of G^-. The main results are: (1) when Ω, Ω' are integral, G : Ω→Ω' and F : Ω'→Ω are closed unital maps, F is a left adjoint of G^- if and only if F is a left adjoint of G; (2) G^- is an equivalence of categories if and only if G is an isomorphism in the category of commutative unital quantales and closed unital maps; and (3) a sufficient condition is obtained for G^- to preserve completeness in the sense that GA is a complete Ω'-category whenever A is a complete Ω-category. 相似文献
12.
Yu. V. Nagrebetskaya 《Algebra and Logic》2000,39(4):276-291
We deal with the decidability problem for first-order theories of a complete linear group GL(n,ℤ) of all integral matrices
of order n ≥ 3. and of a respective complete linear monoid ML(n,ℤ). It is proved that theories ∀? ∧ GL(3,ℤ). ∃∀∧ GL(3,ℤ).
∀? ∧ ML(3,ℤ), and ∃? ∧ ML(3,ℤ) are critical. and that ∃∀ ∧ νGL(n,ℤ) and ∃∀ ∧ML(n,ℤ) are decidable for any n ≥ 3.
Translated fromAlgebra i Logika, Vol. 39, No. 4, pp. 480–504, July–August, 2000. 相似文献
13.
In this paper we consider decompositions of semigroups induced by identities. Here we give some new characterizations of a
semilattice of Archimedean semigroups and, using this, we describe all identities which induce decompositions into a semilattice
of Archimedean semigroups. Also, we give a solution for one problem ofШеврин andСуханов [27].
Supported by Grant 0401A of RFNS through Math. Inst. SANU 相似文献
14.
. . 《Ukrainian Mathematical Journal》1997,49(8):1137-1142
Для скалярного лінійлого звичайпого диференціалыюго рівняння другого порядку, коефіцієнт при другій похідній якого, набуваючи
нульового значешя, може змішовати знак, одержано достатни умови існування періодичного розв'язку для довільюї неоднорідности.
We consider a scalar linear ordinary differential equation of second order, whose coefficient of the second derivative may change the sign when vanishing. For this equation, we obtain sufficient conditions for the existence of a periodic solution in the case of arbitrary periodic nonhomogeneity.相似文献
15.
T. Landolfi 《Ukrainian Mathematical Journal》1999,51(3):410-412
We prove that every group factorizable into a product of finitely many pairwise permutable central-by-finite minimax subgroups
is a soluble-by-finite group.
This work was done while the author was visiting the Ukrainian Academy of Sciences in Kiev. He is grateful to the Institute of Mathematics for its warm hospitality. 相似文献
Про групи, факторизовані скінченним числом шдгруп
Розвивається спектральна теорія та теорія розсіяння для одпого класу самоспряжених матричних диференціальних операторів змішаного порядку.
This work was done while the author was visiting the Ukrainian Academy of Sciences in Kiev. He is grateful to the Institute of Mathematics for its warm hospitality. 相似文献
16.
A natural way to prove that a particular linear extension of an ordered set is ‘optimal’ with respect to the ‘jump number’
is to transform this linear extension ‘canonically’ into one that is ‘optimal’. We treat a ‘greedy chain interchange’ transformation
which has applications to ordered sets for which each ‘greedy’ linear extension is ‘optimal’. 相似文献
17.
We consider the random variable ζ = ξ1ρ+ξ2ρ2+…, where ξ1, ξ2, … are independent identically distibuted random variables taking the values 0 and 1 with probabilities P(ξi = 0) = p0, P(ξi = 1) = p1, 0 < p0 < 1. Let β = 1/ρ be the golden number.
The Fibonacci expansion for a random point ρζ from [0, 1] is of the form η1ρ + η2ρ2 + … where the random variables ηk are {0, 1}-valued and ηkηk+1 = 0. The infinite random word η = η1η2 … ηn … takes values in the Fibonacci compactum and determines the so-called Erdős measure μ(A) = P(η ∈ A) on it. The invariant
Erdős measure is the shift-invariant measure with respect to which the Erdős measure is absolutely continuous.
We show that the Erdős measures are sofic. Recall that a sofic system is a symbolic system that is a continuous factor of
a topological Markov chain. A sofic measure is a one-block (or symbol-to-symbol) factor of the measure corresponding to a
homogeneous Markov chain. For the Erdős measures, the corresponding regular Markov chain has 5 states. This gives ergodic
properties of the invariant Erdős measure.
We give a new ergodic theory proof of the singularity of the distribution of the random variable ζ. Our method is also applicable
when ξ1, ξ2, … is a stationary Markov chain with values 0, 1. In particular, we prove that the distribution of ζ is singular and that
the Erdős measures appear as the result of gluing together states in a regular Markov chain with 7 states. Bibliography: 3
titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 28–47. 相似文献
18.
D. K. Faddeev 《Journal of Mathematical Sciences》1990,52(3):3198-3198
Let σ be a Dedekind ring, let σ be a maximal order in a quadratic extension K of the field k of quotients of the ring σ, let
Λ be a subring of the ring σ, containing σ and such that ΛK=K. It is proved that σ/Λ is a cyclic Λ-module. From here there
follows, in particular, that each finitely generated torsion-free Λ-module is a direct sum of modules which are isomorphic
to the ideals of ring Λ.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 160, pp. 262, 1987. 相似文献
19.
Wojciech Jaworski 《Journal d'Analyse Mathématique》1996,68(1):183-208
Given a probability measure μ on a locally compact second countable groupG the space of bounded μ-harmonic functions can be identified withL
∞(η, α) where (η, α) is a BorelG-space with a σ-finite quasiinvariant measure α. Our goal is to show that when μ is an arbitrary spread out probability measure
on a connected solvable Lie groupG then the μ-boundary (η, α) is a contractive homogeneous space ofG. Our approach is based on a study of a class of strongly approximately transitive (SAT) actions ofG. A BorelG-space η with a σ-finite quasiinvariant measure α is called SAT if it admits a probability measurev≪α, such that for every Borel set A with α(A)≠0 and every ε>0 there existsg∈G with ν(gA)>1−ε. Every μ-boundary is a standard SATG-space. We show that for a connected solvable Lie group every standard SATG-space is transitive, characterize subgroupsH⊆G such that the homogeneous spaceG/H is SAT, and establish that the following conditions are equivalent forG/H: (a)G/H is SAT; (b)G/H is contractive; (c)G/H is an equivariant image of a μ-boundary. 相似文献
20.
Let T be a tree and let Ω ( f ) be the set of non-wandering points of a continuous map f: T→ T. We prove that for a continuous
map f: T→ T of a tree T: ( i) if x∈ Ω( f) has an infinite orbit, then x∈ Ω( fn) for each n∈ ℕ; (ii) if the topological entropy of f is zero, then Ω( f) = Ω( fn) for each n∈ ℕ. Furthermore, for each k∈ ℕ we characterize those natural numbers n with the property that Ω(fk) = Ω(fkn) for each continuous map f of T. 相似文献