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1.
From GCH and Pm(κ)-hypermeasurable (1 < m< gw), we construct a model satisfying 2 n = a( n) and 2 ω = ω+m for a monotone a:ω→ω satisfying a( n)> n. 相似文献
2.
It was proved by Dow and Simon that there are 2 ω1 (as many as possible) pairwise nonhomeomorphic compact, T2, scattered spaces of height ω 1 and width ω. In this paper, we prove that if is an ordinal withω 1 < ω 2 and θ = κ ξ: ξ < is a sequence of cardinals such that either κ ξ = ω or κ ξ = ω 1 for every ξ < , then there are 2 ω1 pairwise nonhomeomorphic compact, T2, scattered spaces whose cardinal sequence is θ. 相似文献
3.
We study the concept of strong equality of domination parameters. Let P1 and P2 be properties of vertex subsets of a graph, and assume that every subset of V( G) with property P2 also has property P1. Let ψ 1( G) and ψ 2( G), respectively, denote the minimum cardinalities of sets with properties P1 and P2, respectively. Then ψ 1( G)ψ 2( G). If ψ 1( G)=ψ 2( G) and every ψ 1( G)-set is also a ψ 2( G)-set, then we say ψ 1( G) strongly equals ψ 2( G), written ψ 1( G)≡ψ 2( G). We provide a constructive characterization of the trees T such that γ( T)≡ i( T), where γ( T) and i( T) are the domination and independent domination numbers, respectively. A constructive characterization of the trees T for which γ( T)=γ t( T), where γ t( T) denotes the total domination number of T, is also presented. 相似文献
4.
Let P be a poset, and let γ be a linear order type with |γ| ≥ 3. The γ-deviation of P, denoted by γ-dev P, is defined inductively as follows: (1) γ-dev P=0, if P contains no chain of order type γ; (2) γ-dev P = , if γ-dev P and each chain C of type γ in P contains elements a and b such that a< b and [ a, b] as an interval of P has γ-deviation <. There may be no ordinal such that γ-dev P = ; i.e., γ-dev P does not exist. A chain is γ-dense if each of its intervals contains a chain of order type γ. If P contains a γ-dense chain, then γ-dev P fails to exist. If either (1) P is linearly ordered or (2) a chain of order type γ does not contain a dense interval, then the converse holds. For an ordinal ξ, a special set S(ξ) is used to study ω ξ-deviation. The depth of P, denoted by δ( P) is the least ordinal β that does not embed in P*. Then the following statements are equivalent: (1) ω ξ-dev P does not exist; (2) S(ξ) embeds in P; and (3) P has a subset Q of cardinality ξ such that δ( Q*) = ω ξ + 1. Also ω ξ-dev P = <ω ξ + 1 if and only if |δ( P*)| ξ; if these equivalent conditions hold, then ω βξ < δ( P*) ≤ ω + 1ξ for all β < . Applications are made to the study of chains of submodules of a module over an associative ring. 相似文献
5.
In this note, we prove that if C is a duadic binary abelian code with splitting μ=μ −1 and the minimum odd weight of C satisfies d2− d+1≠ n, then d( d−1) n+11. We show by an example that this bound is sharp. A series of open problems on this subject are proposed. 相似文献
7.
Propositions about the nonexistence of complex zeros of the functions Hμ( z)= Jμ( z)+ zJ′μ( z), J′μ( z), J″μ( z), where J′μ( z) and J″μ( z) are the first two derivatives of the Bessel functions Jμ( z), for μ in general complex are proved. Bounds for the purely imaginary zeros of the above functions assuming their existence are given. Thus for the range of values for which these bounds are violated there are no purely imaginary zeros of the above functions. Finally, some known results from previous work are generalized in the present paper. 相似文献
8.
In Ramm, Phys. Lett. 99A, (1983), 258-260, it is proved that a compactly supported inhomogeneity in the velocity profile is uniquely determined by the values of the acoustic pressure collected for all positions of the source and receiver on the surface of the earth ( on the whole plane P) at low frequencies. Here it is proved that the data collected on ω 1 x ω 2 suffice for the uniqueness theorem to hold, where ω 1 and ω 2 are arbitrary open sets on the plane P. This result holds also for the data collected on ω 1 × ω 2 at a fixed frequency. 相似文献
9.
It is shown that there is no satisfactory first-order characterization of those subsets of ω 2 that have closed unbounded subsets in ω 1,ω 2 and GCH preserving outer models. These “anticharacterization” results generalize to subsets of successors of uncountable regular cardinals. Similar results are proved for trees of height and cardinality κ + and for partitions of [κ +] 2, when κ is an infinite cardinal. 相似文献
10.
For a connected graph G with n vertices, let {λ 1,λ 2,…,λ r} be the set of distinct positive eigenvalues of the Laplacian matrix of G. The Hoffman number μ( G) of G is defined by μ( G)=λ 1λ 2…λ r/ n. In this paper, we study some properties and applications of the Hoffman number. 相似文献
11.
Let G be a plane graph, and let χ k( G) be the minimum number of colors to color the vertices of G so that every two of them which lie in the boundary of the same face of the size at most k, receive different colors. In 1966, Ore and Plummer proved that χ k( G)2 k for any k3. It is also known that χ 3( G)4 (Appel and Haken, 1976) and χ 4( G)6 (Borodin, 1984). The result in the present paper is: χ 5( G)9, χ 6( G)11, χ 7( G)12, and χ k( G)2 k − 3 if k8. 相似文献
12.
A bisequence of complex numbers {μ n} −∞∞ determines a strong moment functional
satisfying L[ xn] = μ n. If
is positive-definite on a bounded interval ( a, b) R{0}, then
has an integral representation
, n=0, ±1, ±2,…, and quadrature rules { wni, xni} exist such that μ k = ∑ i=innsnikwni. This paper is concerned with establishing certain extremal properties of the weights wni and using these properties to obtain maximal mass results satisfied by distributions ψ( x) representing
when only a finite bisequence of moments {μ k} k=−nn−1 is given. 相似文献
13.
We have considered the problem of the weak convergence, as tends to zero, of the multiple integral processes in the space
, where fL2([0, T] n) is a given function, and {η ( t)} >0 is a family of stochastic processes with absolutely continuous paths that converges weakly to the Brownian motion. In view of the known results when n2 and f( t1,…, tn)=1 {t1<t2<<tn}, we cannot expect that these multiple integrals converge to the multiple Itô–Wiener integral of f, because the quadratic variations of the η are null. We have obtained the existence of the limit for any {η }, when f is given by a multimeasure, and under some conditions on {η } when f is a continuous function and when f( t1,…, tn)= f1( t1) fn( tn)1 {t1<t2<<tn}, with fiL2([0, T]) for any i=1,…, n. In all these cases the limit process is the multiple Stratonovich integral of the function f. 相似文献
14.
Let A be a positive definite, symmetric matrix. We wish to determine the largest eigenvalue, λ 1. We consider the power method, i.e. that of choosing a vector v0 and setting vk = Akv0; then the Rayleigh quotients Rk = ( Avk, vk)/( vk, vk) usually converge to λ 1 as k → ∞ (here ( u, v) denotes their inner product). In this paper we give two methods for determining how close Rk is to λ 1. They are both based on a bound on λ 1 − Rk involving the difference of two consecutive Rayleigh quotients and a quantity ω k. While we do not know how to directly calculate ω k, we can given an algorithm for giving a good upper bound on it, at least with high probability. This leads to an upper bound for λ 1 − Rk which is proportional to (λ 2/λ 1) 2k, which holds with a prescribed probability (the prescribed probability being an arbitrary δ > 0, with the upper bound depending on δ). 相似文献
15.
We show the existence of a solution to the Navier-Stokes equation taking the vorticity ω as the unknown: ω t + Aω + Bω = μ, ω(0) = ω 0. Here, ω 0 and μ are bounded Radon measures. This study is motivated by a numerical approximation which will be given in a forthcoming work [1]. 相似文献
16.
If a˜cardinal κ 1, regular in the ground model M, is collapsed in the extension N to a˜cardinal κ 0 and its new cofinality, ρ, is less than κ 0, then, under some additional assumptions, each cardinal λ>κ 1 less than cc( P(κ 1)/[κ 1] <κ1) is collapsed to κ 0 as well. If in addition N= M[ f], where f : ρ→κ 1 is an unbounded mapping, then N is a˜|λ|=κ 0-minimal extension. This and similar results are applied to generalized forcing notions of Bukovský and Namba. 相似文献
17.
We continue [21] and study partition numbers of partial orderings which are related to (ω)/ fin. In particular, we investigate Pf, be the suborder of ((ω)/ fin) ω containing only filtered elements, the Mathias partial order M, and (ω), (ω) ω the lattice of (infinite) partitions of ω, respectively. We show that Solomon's inequality holds for M and that it consistently fails for Pf. We show that the partition number of (ω) is C. We also show that consistently the distributivity number of (ω) ω is smaller than the distributivity number of (ω)/ fin. We also investigate partitions of a Polish space into closed sets. We show that such a partition either is countable or has size at least D, where D is the dominating number. We also show that the existence of a dominating family of size 1 does not imply that a Polish space can be partitioned into 1 many closed sets. 相似文献
18.
The slow growing hierarchy is commonly defined as follows: G0( x) = 0, Gx−1( x) := Gx( x) + 1 and Gλ( x) := Gλ[x]( x) where λ< 0 is a limit and ·[·]: 0∩ Lim × ω → 0 is a given assignment of fundamental sequences for the limits below 0. The first obvious question which is encountered when one looks at this definition is: How does this hierarchy depend on the choice of the underlying system of fundamental sequences? Of course, it is well known and easy to prove that for the standard assignment of fundamental sequence the hierarchy ( Gx) x<0 is slow growing, i.e. each Gx is majorized by a Kalmar elementary recursive function. It is shown in this paper that the slow growing hierarchy (Gx)x<0 — when it is defined with respect to the norm-based assignment of fundamental sequences which is defined in the article by Cichon (1992, pp. 173–193) — is actually fast growing, i.e. each PA-provably recursive function is eventually dominated by Gx for some <0. The exact classification of this hierarchy, i.e. the problem whether it is slow or fast growing, has been unsolved since 1992. The somewhat unexpected result of this paper shows that the slow growing hierarchy is extremely sensitive with respect to the choice of the underlying system of fundamental sequences. The paper is essentially self-contained. Only little knowledge about ordinals less than 0 — like the existence of Cantor normal forms, etc. and the beginnings of subrecursive hierarchy theory as presented, for example, in the 1984 textbook of Rose — is assumed. 相似文献
19.
Let R[ f] be the remainder of some approximation method, having estimates of the form f; R[ f] f; ρ i ; f(i) for i = 0,…, r. In many cases, ρ 0 and ρ r are known, but not the intermediate error constants ρ 1,…,ρ r−1. For periodic functions, Ligun (1973) has obtained an estimate for these intermediate error constants by ρ 0 and ρ r. In this paper, we show that this holds in the nonperiodic case, too. For instance, the estimates obtained can be applied to the error of polynomial or spline approximation and interpolation, or to numerical integration and differentiation. 相似文献
20.
Consider two transient Markov processes ( Xvt) tεR·, ( Xμt) tεR· with the same transition semigroup and initial distributions v and μ. The probability spaces supporting the processes each are also assumed to support an exponentially distributed random variable independent of the process. We show that there exist (randomized) stopping times S for (Xvt), T for (Xμt) with common final distribution, L(XvS|S < ∞) = L(XμT|T < ∞), and the property that for t < S, resp. t < T, the processes move in disjoint portions of the state space. For such a coupling (S, T) it is shown where
denotes the bounded harmonic functions of the Markov transition semigroup. Extensions, consequences and applications of this result are discussed. 相似文献
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