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1.
Minihypers were introduced by Hamada to investigate linear codes meeting the Griesmer bound. Hamada (Bull Osaka Women’s Univ 24:1–47, 1985; Discrete Math 116:229–268, 1993) characterized the non-weighted minihypers having parameters , with k−1 > λ1 > λ2 > ... > λ h ≥ 0, as the union of a λ1-dimensional space, λ2-dimensional space, ..., λ h -dimensional space, which all are pairwise disjoint. We present in this article a weighted version of this result. We prove that a weighted -minihyper , with k−1 > λ1 > λ2 > ... > λ h ≥ 0, is a sum of a λ1-dimensional space, λ2-dimensional space, ..., and λ h -dimensional space. This research was supported by the Project Combined algorithmic and theoretical study of combinatorial structures between the Fund for Scientific Research Flanders-Belgium (FWO-Flanders) and the Bulgarian Academy of Sciences. This research is also part of the FWO-Flanders project nr. G.0317.06 Linear codes and cryptography.  相似文献   

2.
In this paper we prove Harnack inequality for nonnegative functions which are harmonic with respect to random walks in ℝ d . We give several examples when the scale invariant Harnack inequality does not hold. For any α ∈ (0,2) we also prove the Harnack inequality for nonnegative harmonic functions with respect to a symmetric Lévy process in ℝ d with a Lévy density given by $c|x|^{-d-\alpha}1_{\{|x|\leq 1\}}+j(|x|)1_{\{|x|>1\}}$c|x|^{-d-\alpha}1_{\{|x|\leq 1\}}+j(|x|)1_{\{|x|>1\}}, where 0 ≤ j(r) ≤ cr  − d − α , ∀ r > 1, for some constant c. Finally, we establish the Harnack inequality for nonnegative harmonic functions with respect to a subordinate Brownian motion with subordinator with Laplace exponent ϕ(λ) = λ α/2ℓ(λ), λ > 0, where ℓ is a slowly varying function at infinity and α ∈ (0,2).  相似文献   

3.
Summary. Hyperbolic branching Brownian motion is a branching diffusion process in which individual particles follow independent Brownian paths in the hyperbolic plane ? 2 , and undergo binary fission(s) at rate λ > 0. It is shown that there is a phase transition in λ: For λ≦ 1/8 the number of particles in any compact region of ? 2 is eventually 0, w.p.1, but for λ > 1/8 the number of particles in any open set grows to w.p.1. In the subcritical case (λ≦ 1/8) the set Λ of all limit points in ∂? 2 (the boundary circle at ) of particle trails is a Cantor set, while in the supercritical case (λ > 1/8) the set Λ has full Lebesgue measure. For λ≦ 1/8 it is shown that w.p.1 the Hausdorff dimension of Λ is δ = (1−√1−8 λ)/2. Received: 2 November 1995 / In revised form: 22 October 1996  相似文献   

4.
An asymptotic minimax problem of signal detection for signals froml q -ellipsoids with an lp-ball removed (p>2 or q<p<2) in a Gaussian white noise is considered. Asymptotically sharp distinguishability conditions and some estimates of the minimax probability of errors of signal detection for ellipsoids with axes an≈n−λ λ>0, are obtained. The proofs use results and techniques developed by Yu. I. Ingster. Bibliography:6 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 228, 1996, pp. 312–332  相似文献   

5.
We consider the nonlinear eigenvalue problem −Δuf(u) in Ω u=0 on ∂Ω, where Ω is a ball or an annulus in RN (N ≥ 2) and λ > 0 is a parameter. It is known that if λ >> 1, then the corresponding positive solution uλ develops boundary layers under some conditions on f. We establish the asymptotic formulas for the slope of the boundary layers of uλ with the exact second term and the ‘optimal’ estimate of the third term.  相似文献   

6.
The real-valued Lambert W-functions considered here are w 0(y) and w  − 1(y), solutions of we w  = y, − 1/e < y < 0, with values respectively in ( − 1,0) and ( − ∞ , − 1). A study is made of the numerical evaluation to high precision of these functions and of the integrals ò1 [-w0(-xe-x)]a x-bx\int_1^\infty [-w_0(-xe^{-x})]^\alpha x^{-\beta}\d x, α > 0, β ∈ ℝ, and ò01 [-w-1(-x e-x)]a x-bx\int_0^1 [-w_{-1}(-x e^{-x})]^\alpha x^{-\beta}\d x, α > − 1, β < 1. For the latter we use known integral representations and their evaluation by nonstandard Gaussian quadrature, if α ≠ β, and explicit formulae involving the trigamma function, if α = β.  相似文献   

7.
Abstract. It is proved that the semilinear elliptic problem with zero boundary value  相似文献   

8.
Summary. We introduce a new inductive approach to the lace expansion, and apply it to prove Gaussian behaviour for the weakly self-avoiding walk on ℤ d where loops of length m are penalised by a factor e −β/m p (0<β≪1) when: (1) d>4, p≥0; (2) d≤4, . In particular, we derive results first obtained by Brydges and Spencer (and revisited by other authors) for the case d>4, p=0. In addition, we prove a local central limit theorem, with the exception of the case d>4, p=0. Received: 29 October 1997 / In revised form: 15 January 1998  相似文献   

9.
We obtain the best approximation in L 1(ℝ), by entire functions of exponential type, for a class of even functions that includes e λ|x|, where λ>0, log |x| and |x| α , where −1<α<1. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.  相似文献   

10.
Bounds on the number of row sums in ann×n, non-singular (0,1)-matrixA sarisfyingA tA=diag (k 11,…,k nn),k jj>0,λ1=…=λee+1=…=λn are obtained which extend previous results for such matrices.  相似文献   

11.
 We define the index of composition λ(n) of an integer n ⩾ 2 as λ(n) = log n/log γ(n), where γ(n) stands for the product of the primes dividing n, and first establish that λ and 1/λ both have asymptotic mean value 1. We then establish that, given any ɛ > 0 and any integer k ⩾ 2, there exist infinitely many positive integers n such that . Considering the distribution function F(z,x) := #{n < x : λ(n) > z}, we prove that, given 1 < z < 2 and ɛ > 0, then, if x is sufficiently large,
this last inequality also holding if z ⩾ 2. We then use these inequalities to obtain probabilistic results and we state a conjecture. Finally, using (*), we show that the probability that the abc conjecture does not hold is 0.  相似文献   

12.
We consider the equation on a smooth bounded domain of with zero Dirichlet boundary conditions where p ≥ 2, λ > 0 and f satisfies typical assumptions in the subject of extremal solutions. We prove that, for such general nonlinearities f, the extremal solution u * belongs to L  ∞ (Ω) if N < p + p/(p − 1) and if N < p(1 + p/(p − 1)). This work was partially supported by MCyT BMF 2002-04613-CO3-02.  相似文献   

13.
Let (M n ,g) be a compact Riemannian manifold with Ric ≥−(n−1). It is well known that the bottom of spectrum λ 0 of its universal covering satisfies λ 0≤(n−1)2/4. We prove that equality holds iff M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy. The author was partially supported by NSF Grant 0505645.  相似文献   

14.
We explore connections between Krein's spectral shift function ζ(λ,H 0, H) associated with the pair of self-adjoint operators (H 0, H),H=H 0+V, in a Hilbert spaceH and the recently introduced concept of a spectral shift operator Ξ(J+K *(H 0−λ−i0)−1 K) associated with the operator-valued Herglotz functionJ+K *(H 0−z)−1 K, Im(z)>0 inH, whereV=KJK * andJ=sgn(V). Our principal results include a new representation for ζ(λ,H 0,H) in terms of an averaged index for the Fredholm pair of self-adjoint spectral projections (E J+A(λ)+tB(λ)(−∞, 0)),E J((−∞, 0))), ℝ, whereA(λ)=Re(K *(H 0−λ−i0−1 K),B(λ)=Im(K *(H 0−λ-i0)−1 K) a.e. Moreover, introducing the new concept of a trindex for a pair of operators (A, P) inH, whereA is bounded andP is an orthogonal projection, we prove that ζ(λ,H 0, H) coincides with the trindex associated with the pair (Ξ(J+K *(H 0−λ−i0)K), Ξ(J)). In addition, we discuss a variant of the Birman-Krein formula relating the trindex of a pair of Ξ operators and the Fredholm determinant of the abstract scattering matrix. We also provide a generalization of the classical Birman—Schwinger principle, replacing the traditional eigenvalue counting functions by appropriate spectral shift functions.  相似文献   

15.
Summary Suppose that 1/2 ≦ λ < 1. Balog and Harman proved that for any real θ there exist infinitely many primes p satisfying pλ-θ < p-(1-λ)/2+ ε (with an asymptotic result). In the present paper we establish that for almost all θ in the interval 0 ≦ θ < 1 there exist infinitely many primes p such that {pλ-θ} < p-min{(2-λ)/6,(14-9λ)/32}+ε. Thus we obtain a better result for almost all θ than for a single θ if λ>1/2.  相似文献   

16.
 We define the index of composition λ(n) of an integer n ⩾ 2 as λ(n) = log n/log γ(n), where γ(n) stands for the product of the primes dividing n, and first establish that λ and 1/λ both have asymptotic mean value 1. We then establish that, given any ɛ > 0 and any integer k ⩾ 2, there exist infinitely many positive integers n such that . Considering the distribution function F(z,x) := #{n < x : λ(n) > z}, we prove that, given 1 < z < 2 and ɛ > 0, then, if x is sufficiently large,
this last inequality also holding if z ⩾ 2. We then use these inequalities to obtain probabilistic results and we state a conjecture. Finally, using (*), we show that the probability that the abc conjecture does not hold is 0. Research supported in part by a grant from NSERC. Re?u le 17 décembre 2001; en forme révisée le 23 mars 2002 Publié en ligne le 11 octobre 2002  相似文献   

17.
In this paper, the use of N-AGE and Newton-N-AGE iterative methods on a variable mesh for the solution of one dimensional parabolic initial boundary value problems is considered. Using three spatial grid points, a two level implicit formula based on Numerov type discretization is discussed. The local truncation error of the method is of O(k2hl-1 +khl +hl3)O({k^2h_l^{-1} +kh_l +h_l^3}), where h l  > 0 and k > 0 are the step lengths in space and time directions, respectively. We use a special technique to handle singular parabolic equations. The advantage of using these algorithms is highlighted computationally.  相似文献   

18.
With some applications in view, the following problem is solved in some special case which is not too special. LetF(s) =Σ n =1an λ n −s be a generalized Dirichlet series with 1 =λ 1 <λ 2 < …,λ nDn, andλ n+1 -λ nD − 1 λ n+1 − a where α>0 andD(≥ 1) are constants. Then subject to analytic continuation and some growth conditions, a lower bound is obtained for . These results will be applied in other papers to appear later.  相似文献   

19.
We consider the two-parameter nonlinear eigenvalue problem?−Δu = μu − λ(u + u p + f(u)), u > 0 in Ω, u = 0 on ∂Ω,?where p>1 is a constant and μ,λ>0 are parameters. We establish the asymptotic formulas for the variational eigencurves λ=λ(μ,α) as μ→∞, where α>0 is a normalizing parameter. We emphasize that the critical case from a viewpoint of the two-term asymptotics of the eigencurve is p=3. Moreover, it is shown that p=5/3 is also a critical exponent from a view point of the three-term asymptotics when Ω is a ball or an annulus. This sort of criticality for two-parameter problems seems to be new. Received: February 9, 2002; in final form: April 3, 2002?Published online: April 14, 2003  相似文献   

20.
A concentrated (ξ, m) almost monotone measure inR n is a Radon measure Φ satisfying the two following conditions: (1) Θ m (Φ,x)≥1 for every x ∈spt (Φ) and (2) for everyxR n the ratioexp [ξ(r)]r−mΦ(B(x,r)) is increasing as a function of r>0. Here ξ is an increasing function such thatlim r→0-ξ(r)=0. We prove that there is a relatively open dense setReg (Φ) ∋spt (Φ) such that at each x∈Reg(Φ) the support of Φ has the following regularity property: given ε>0 and λ>0 there is an m dimensional spaceWR n and a λ-Lipschitz function f from x+W into x+W so that (100-ε)% ofspt(Φ) ∩B (x, r) coincides with the graph of f, at some scale r>0 depending on x, ε, and λ.  相似文献   

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