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1.
Let X be a Banach space, S(X) - x ε X : #x02016; = 1 be the unit sphere of X.The parameter, modulus of W*-convexity, W*(ε) = inf <(xy)/2, fx> : x, y S(X), xy ≥ ε, fx Δx , where 0 ≤ ε ≤ 2 and Δx S(X*) be the set of norm 1 supporting functionals of S(X) at x, is investigated_ The relationship among uniform nonsquareness, uniform normal structure and the parameter W*(ε) are studied, and a known result is improved. The main result is that for a Banach space X, if there is ε, where 0 < ε < 1/2, such that W*(1 + ε) > ε/2 where W*(1 + ε) = lim→ε W* (1 + ), then X has normal structure.  相似文献   

2.
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 ωξ-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) ωξ-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*) = ωξ + 1. Also ωξ-dev P = <ωξ + 1 if and only if |δ(P*)|ξ; if these equivalent conditions hold, then ωβξ < 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   

3.
Consider the following Itô stochastic differential equation dX(t) = ƒ(θ0, X(t)) dt + dW(t), where (W(t), t 0), is a standard Wiener process in RN. On the basis of discrete data 0 = t0 < t1 < …<tn = T; X(t1),...,X(tn) we would like to estimate the parameter θ0. We shall define the least squares estimator and show that under some regularity conditions, is strongly consistent.  相似文献   

4.
In a recent paper, D.J. Kleitman and M.E. Saks gave a proof of Huang's conjecture on alphabetic binary trees.

Given a set E = {ei}, I = 0, 1, 2, …, m and assigned positive weights to its elements and supposing the elements are indexed such that w(e0) ≤ w(e1) ≤ … ≤w (em), where w(ei) is the weight of ei, we call the following sequence E* a ‘saw-tooth’ sequence

E*=(e0,em,e1,…,ej,emj,…).

Huang's conjecture is: E* is the most expensive sequence for alphabetic binary trees. This paper shows that this property is true for the L-restricted alphabetic binary trees, where L is the maximum length of the leaves and log2(m + 1) ≤Lm.  相似文献   


5.
Only photons are needed to explain the masses of the π0, η, Λ, Σ0, Ξ0, Ω, Λc+, Σc0, Ξc0 and Ωc0 mesons and baryons with the sum of the energies contained in the frequencies of standing electromagnetic waves in a cubic black body. Only neutrinos are needed to explain the mass of the π± mesons with the sum of the energies of standing oscillations of muon and electron neutrinos in a cubic lattice plus the energies contained in the rest masses of the neutrinos. Neutrinos and photons are needed to explain the masses of the K± mesons. Surprisingly the mass of the μ± mesons can also be explained without an additional assumption by the oscillation energies and rest masses of a neutrino lattice. From the difference of the masses of the π± mesons and μ± mesons we find that the rest mass of the muon neutrino is 47.5 meV/c2. From the difference of the masses of the neutron and proton we find that the rest mass of the electron neutrino is 0.55 meV/c2. The potential of the weak force between the lattice points can be determined from Born’s lattice theory. From the weak force between the lattice points follows automatically the existence of a strong force between the sides of two lattices. The strong nuclear force is the sum of the unsaturated weak forces at the sides of each lattice and is therefore about 106 times stronger than the weak force.  相似文献   

6.
Let the family OL(3) contain all graphs which can be colored on-line with 3 colors. Gyárfás and Lehel suggested the problem of determining the on-line chromatic number χ*(OL(3)) of OL(3). They showed that 4 χ*(OL(3)) 16. We present an algorithm that colors every on-line-3-chromatic graph with 4 colors. Thus χ*(OL(3)) = 4.  相似文献   

7.
The fundamental solutions for the fractional diffusion-wave equation   总被引:6,自引:0,他引:6  
The time fractional diffusion-wave equation is obtained from the classical diffusion or wave equation by replacing the first- or second-order time derivative by a fractional derivative of order 2β with 0 < β ≤ 1/2 or 1/2 < β ≤ 1, respectively. Using the method of the Laplace transform, it is shown that the fundamental solutions of the basic Cauchy and Signalling problems can be expressed in terms of an auxiliary function M(z;β), where z = |x|/tβ is the similarity variable. Such function is proved to be an entire function of Wright type.  相似文献   

8.
Suppose {k, −∞ < k < ∞} is an independent, not necessarily identically distributed sequence of random variables, and {cj}j=0, {dj}j=0 are sequences of real numbers such that Σjc2j < ∞, Σjd2j < ∞. Then, under appropriate moment conditions on {k, −∞ < k < ∞}, yk Σj=0cjk-j, zk Σj=0djk-j exist almost surely and in 4 and the question of Gaussian approximation to S[t]Σ[t]k=1 (yk zkE{yk zk}) becomes of interest. Prior to this work several related central limit theorems and a weak invariance principle were proven under stationary assumptions. In this note, we demonstrate that an almost sure invariance principle for S[t], with error bound sharp enough to imply a weak invariance principle, a functional law of the iterated logarithm, and even upper and lower class results, also exists. Moreover, we remove virtually all constraints on k for “time” k ≤ 0, weaken the stationarity assumptions on {k, −∞ < k < ∞}, and improve the summability conditions on {cj}j=0, {dj}j=0 as compared to the existing weak invariance principle. Applications relevant to this work include normal approximation and almost sure fluctuation results in sample covariances (let dj = cj-m for jm and otherwise 0), quadratic forms, Whittle's and Hosoya's estimates, adaptive filtering and stochastic approximation.  相似文献   

9.
Let q be a nonnegative real number, and λ and σ be positive constants. This article studies the following impulsive problem: for n = 1, 2, 3,…,
. The number λ* is called the critical value if the problem has a unique global solution u for λ < λ*, and the solution blows up in a finite time for λ > λ*. For σ < 1, existence of a unique λ* is established, and a criterion for the solution to decay to zero is studied. For σ > 1, existence of a unique λ* and three criteria for the blow-up of the solution in a finite time are given respectively. It is also shown that there exists a unique T* such that u exists globally for T> T*, and u blows up in a finite time for T < T*.  相似文献   

10.
Shooting methods are used to obtain solutions of the three-point boundary value problem for the second-order dynamic equation, yΔΔ = f (x, y, yΔ), y(x1) = y1, y(x3) − y(x2) = y2, where f : (a, b)T × 2 → is continuous, x1 < x2 < x3 in (a, b)T, y1, y2 ε , and T is a time scale. It is assumed such solutions are unique when they exist.  相似文献   

11.
It is shown that there is no satisfactory first-order characterization of those subsets of ω2 that have closed unbounded subsets in ω12 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   

12.
It is known that the volume function for hyperbolic manifolds of dimension 3 is finite-to-one. We show that the number of nonhomeomorphic hyperbolic 4-manifolds with the same volume can be made arbitrarily large. This is done by constructing a sequence of finite-sided finite-volume polyhedra with side-pairings that yield manifolds. In fact, we show that arbitrarily many nonhomeomorphic hyperbolic 4-manifolds may share a fundamental polyhedron. As a by-product of our examples, we also show in a constructive way that the set of volumes of hyperbolic 4-manifolds contains the set of even integral multiples of 4π2/3. This is “half” the set of possible values for volumes, which is the integral multiples of 4π2/3 due to the Gauss-Bonnet formula Vol(M) = 4π2/3 · χ(M).  相似文献   

13.
It is shown that the maximum value over p vertex graphs of the product of the independent domination numbers of a graph and its complement is at most min {(p + 3)2/8, (p + 8)2/10.8}.  相似文献   

14.
A new proof is given of the theorem that no submatrix of the p×p matrix S=(ζ(i-1)(j-1)) is singular, where ζis a primitive pth root of unity and p is a prime. Some related results are also discussed.  相似文献   

15.
Let denote a field, and let V denote a vector space over with finite positive dimension. We consider a pair of linear transformations A:VV and A*:VV satisfying both conditions below:

1. [(i)] There exists a basis for V with respect to which the matrix representing A is diagonal and the matrix representing A* is irreducible tridiagonal.

2. [(ii)] There exists a basis for V with respect to which the matrix representing A* is diagonal and the matrix representing A is irreducible tridiagonal.

We call such a pair a Leonard pair on V. Refining this notion a bit, we introduce the concept of a Leonard system. We give a complete classification of Leonard systems. Integral to our proof is the following result. We show that for any Leonard pair A,A* on V, there exists a sequence of scalars β,γ,γ*,,* taken from such that both

where [r,s] means rssr. The sequence is uniquely determined by the Leonard pair if the dimension of V is at least 4. We conclude by showing how Leonard systems correspond to q-Racah and related polynomials from the Askey scheme.  相似文献   


16.
A holey Schröder design of type h1n1h2n2hknk (HSD(h1n1h2n2hknk)) is equivalent to a frame idempotent Schröder quasigroup (FISQ(h1n1h2n2hknk)) of order n with ni missing subquasigroups (holes) of order hi, (1 i k), which are disjoint and spanning, that is, Σ1 i k nihi = n. In this paper, it is shown that an HSD(hn) exists if and only if h2n(n − 1) 0 (mod 4) with expceptions (h, n) ε {{(1,5),(1,9),(2,4)}} and the possible exception of (h, n) = (6,4).  相似文献   

17.
Let A be a positive definite, symmetric matrix. We wish to determine the largest eigenvalue, λ1. 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 λ1 as k → ∞ (here (u, v) denotes their inner product). In this paper we give two methods for determining how close Rk is to λ1. They are both based on a bound on λ1Rk involving the difference of two consecutive Rayleigh quotients and a quantity ωk. While we do not know how to directly calculate ωk, 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 λ1Rk which is proportional to (λ21)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   

18.
Let[2+k2n(x1,x3)]u(x1,x2,x3)=−δ(x1,y1δ(x2,y2)δ(x3,y3) in R3+. Assume that u(x1,x2,x3=0,y1,y2=0,y3=0,k) is measured at the plane P {x:x3=0} for all positions of the source on the line y = (y1,y2 = 0,y3 = 0), -∞ < y1 < ∞, and receiver on the plane(x1,x2,x3 − <x1,x2 < ∞, and for low-frequencies 0 < k <k0, k0 > 0 is an arbitrary small wave number. Assume thatn(x1,x3) is an arbitrary bounded piecewise-continuous function. The basic result is: the above low-frequency surface data determinen(x1,x3)uniquely.  相似文献   

19.
For a 1-dependent stationary sequence {Xn} we first show that if u satisfies p1=p1(u)=P(X1>u)0.025 and n>3 is such that 88np131, then
P{max(X1,…,Xn)u}=ν·μn+O{p13(88n(1+124np13)+561)}, n>3,
where
ν=1−p2+2p3−3p4+p12+6p22−6p1p2,μ=(1+p1p2+p3p4+2p12+3p22−5p1p2)−1
with
pk=pk(u)=P{min(X1,…,Xk)>u}, k1
and
|O(x)||x|.
From this result we deduce, for a stationary T-dependent process with a.s. continuous path {Ys}, a similar, in terms of P{max0skTYs<u}, k=1,2 formula for P{max0stYsu}, t>3T and apply this formula to the process Ys=W(s+1)−W(s), s0, where {W(s)} is the Wiener process. We then obtain numerical estimations of the above probabilities.  相似文献   

20.
The paper obtains a functional limit theorem for the empirical process of a stationary moving average process Xt with i.i.d. innovations belonging to the domain of attraction of a symmetric -stable law, 1<<2, with weights bj decaying as j−β, 1<β<2/. We show that the empirical process (normalized by N1/β) weakly converges, as the sample size N increases, to the process cx+L++cxL, where L+,L are independent totally skewed β-stable random variables, and cx+,cx are some deterministic functions. We also show that, for any bounded function H, the weak limit of suitably normalized partial sums of H(Xs) is an β-stable Lévy process with independent increments. This limiting behavior is quite different from the behavior of the corresponding empirical processes in the parameter regions 1/<β<1 and 2/<β studied in Koul and Surgailis (Stochastic Process. Appl. 91 (2001) 309) and Hsing (Ann. Probab. 27 (1999) 1579), respectively.  相似文献   

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