共查询到20条相似文献,搜索用时 31 毫秒
1.
周云华 《数学物理学报(B辑英文版)》2011,31(1):102-108
Let T : X → X be a uniformly continuous homeomorphism on a non-compact metric space (X, d). Denote by X* = X ∪ {x*} the one point compactification of X and T * : X* → X* the homeomorphism on X* satisfying T *|X = T and T *x* = x*. We show that their topological entropies satisfy hd(T, X) ≥ h(T *, X*) if X is locally compact. We also give a note on Katok’s measure theoretic entropy on a compact metric space. 相似文献
2.
The nonlinear Klein-Gordon equation ?μ?μΦ + M2Φ + λ1Φ1?m + λ2Φ1?2m = 0 has the exact formal solution Φ = [u2m ?λ1um/(m ? 2)M2+λ12/(m?2)2M4?λ2/4(m ? 1)M2]1/mu?1, m ≠ 0, 1, 2, where u and v?1 are solutions of the linear Klein-Gordon equation. This equation is a simple generalization of the ordinary second order differential equation satisfied by the homogeneous function y = [aum + b(uv)m/2 + cvm]k/m, where u and v are linearly independent solutions of y″ + r(x) y′ + q(x) y = 0. 相似文献
3.
《Finite Fields and Their Applications》2000,6(1):1-22
We show that for an odd prime p the exponent of an abelian group of order pa+b containing a relative (pa, pb, pa, pa−b)-difference set cannot exceed p⌊a/2⌋+1. Furthermore, we give a new local ring construction of relative (q2u, q, q2u, q2u−1)-difference sets for prime powers q. Finally, we discuss an important open case concerning the existence of abelian relative (pa, p, pa, pa−1)-difference sets. 相似文献
4.
X. П. Рустамов 《Analysis Mathematica》1987,13(2):93-119
Пустьf — характерист ика, аΦ — соответству ющий символ n-мерного сингу лярного интегрального опера тора, которые являютс я однородными функция ми нулевой степени вR n,n≧2, с нулевыми средни ми значениями на един ичной сфереS n?1 пространств аR n . В статье установлива ются связи между хара ктеристикойf и символом? в термин ах наилучших равномерн ых приближений полин омами по сферическим гармони кам и сферических равномерных модулей непрерывности, котор ые позволяют установить связь так же в терминах пространст вW r H w (S n?1). Доказывается, ч то установленные резул ьтаты в терминах пространствW r H w (S n?1) неу лучшаемые. 相似文献
5.
In this paper we consider extreme points and support points for compact subclasses of normalized biholomorphic mappings of the Euclidean unit ball Bn in Cn. We consider the class S0(Bn) of biholomorphic mappings on Bn which have parametric representation, i.e., they are the initial elements f (·, 0) of a Loewner chain f (z, t) = etz + ··· such that {e-tf (·, t)}t 0 is a normal family on Bn. We show that if f (·, 0) is an extreme point (respectively a support point) of S0(Bn), then e-tf (·, t) is an extreme point of S0(Bn) for t 0 (respectively a support point of S0(Bn) for t ∈[0, t0] and some t0 > 0). This is a generalization to the n-dimensional case of work due to Pell. Also, we prove analogous results for mappings which belong to S0(Bn) and which are bounded in the norm by a fixed constant. We relate the study of this class to reachable sets in control theory generalizing work of Roth. Finally we consider extreme points and support points for biholomorphic mappings of Bn generated by using extension operators that preserve Loewner chains. 相似文献
6.
Cedric A.B Smith 《Journal of Combinatorial Theory, Series B》1974,16(1):64-76
A matroid M over a set E of elements is semiseparated by a partition {S1, S2} of E iff rank E = rank S1 + rank S2 + 1. Such a semiseparation defines in each Si a pair of matroids or patroid Pi = (Mi, mi); the two patroids P1, P2 weld to form M. The operations of removing and contracting a non-degenerate element of a matroid produce a patroid. The properties of patroids, their bases, and circuits are discussed. 相似文献
7.
Daniel Meyer 《Acta Mathematica》2013,210(1):95-171
We consider Thurston maps, i.e., branched covering maps f:S 2 → S 2 that are post-critically finite. In addition, we assume that f is expanding in a suitable sense. It is shown that each sufficiently high iterate F = f n of f is semi-conjugate to z d :S 1 → S 1, where d = deg F. More precisely, for such an F we construct a Peano curve γ:S 1 → S 2 (onto), such that F°γ(z) = γ(z d ) (for all z∈S 1). 相似文献
8.
It is well known that the commutator Tb of the Calderón-Zygmund singular integral operator is bounded on Lp(Rn) for 1 < p < +∞ if and only if b ∈ BMO [1]. On the other hand, the commutator Tb is bounded from H1(Rn) into L1(Rn) only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσ be the operators that its symbol is S01,δ with 0 ≤ δ < 1, if b ∈ LMO∞, then, the commutator [b, Tσ] is bounded from H1(Rn) into L1(Rn) and from L1(Rn) into BMO(Rn); If [b, Tσ] is bounded from H1(Rn) into L1(Rn) or L1(Rn) into BMO(Rn), then, b ∈ LMOloc. 相似文献
9.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(4):453-458
We consider the second order Stochastic Differential Equation dPtβ = Vtβ dt with P0β = p0, dVtβ = βVtβdt − βω2Ptβ + βdWt with V0β = v0, where W stands for a standard Wiener process and where ω is a real constant. It is well-known that Pβ converges, as β goes to infinity, to an Ornstein-Uhlenbeck process P. In this Note, we study the convergence of the crossings of Pβ at level u during the time interval [0, t] · (NtPβ (u)) to the local time of P(LtP (u)). 相似文献
10.
Volker Ziegler 《Journal of Number Theory》2006,120(2):303-325
We consider the relative Thue inequalities
|X4−t2X2Y2+s2Y4|?2|t|−2|s|−2, 相似文献
11.
《Communications in Nonlinear Science & Numerical Simulation》2005,10(4):441-450
A theorem is proved to show that the third order differential equation x‴+f(t,x,x′,x″)=0 has nontrivial solutions characterized by x′(0)=x′(τ)=0 when x,x′,x″ and f(t,x,x′,x″) are bounded. A second condition is introduced to prove the existence of periodic solution for this equation. It is shown that the equation has a τ-periodic solution if f(t,x,x′,x″) is an even function with respect to x′. The existence and periodicity conditions would be applied to third order systems such as viscoelastic mechanical vibration isolator system. The concepts of Green’s function and the Schauder’s fixed-point theorem have been used for proving the third-order-existence theorem. 相似文献
12.
In this paper, we investigate the nonnegative sectional curvature hypersurfaces in a real space form M n+1(c). We obtain some rigidity results of nonnegative sectional curvature hypersurfaces M n+1(c) with constant mean curvature or with constant scalar curvature. In particular, we give a certain characterization of the Riemannian product S k (a) × S n-k (√1 ? a 2), 1 ≤ k ≤ n ? 1, in S n+1(1) and the Riemannian product H k (tanh2 r ? 1) × S n-k (coth2 r ? 1), 1 ≤ k ≤ n ? 1, in H n+1(?1). 相似文献
13.
A normal subgroup N of a finite group G is called an n-decomposable subgroup if N is a union of n distinct conjugacy classes of G. Each finite nonabelian nonperfect group is proved to be isomorphic to Q 12, or Z 2 × A 4, or G = ??a, b, c | a 11 = b 5 = c 2 = 1, b ?1 ab = a 4, c ?1 ac = a ?1, c ?1 bc = b ?1?? if every nontrivial normal subgroup is 2- or 4-decomposable. 相似文献
14.
An explicit expression is obtained for a pair of generalized inverses (B?,A?) such that B?A?=(AB)+MN, and a class of pairs (B?,A? of this property is shown. A necessary and sufficient condition for (AB)? to have the expression B?A? is also given. 相似文献
15.
Fred B. Weissler 《Journal of Functional Analysis》1979,32(1):102-121
Let e?zH, Re z ? 0, be the Hermite semigroup on R with Gauss measure μ. Necessary and sufficient conditions for e?zH to be a bounded map from Lp(μ) into Lq(μ), 1 ? p, q ? ∞, are found and in many cases it is proved that e?zH: Lp(μ) → Lq(μ) is in fact a contraction. Furthermore, these results and a formula relating the Hermite semigroup with the Gauss-Weierstrass semigroup ezΔ enable one to calculate the precise norm of ezΔ:Lp(dx) → Lq(dx) in a large number of cases. 相似文献
16.
Let G be a finite group. The prime graph of G is denoted by Γ(G). In this paper, as the main result, we show that if G is a finite group such that Γ(G) = Γ(2 D n (3α)), where n = 4m+ 1 and α is odd, then G has a unique non-Abelian composition factor isomorphic to 2 D n (3α). We also show that if G is a finite group satisfying |G| = |2 D n (3α)|, and Γ(G) = Γ(2 D n (3α)), then G ? 2 D n (3α). As a consequence of our result, we give a new proof for a conjecture of Shi and Bi for 2 D n (3α). Application of this result to the problem of recognition of finite simple groups by the set of element orders are also considered. Specifically, it is proved that 2 D n (3α) is quasirecognizable by the spectrum. 相似文献
17.
Marko Jakovac 《Discrete Mathematics》2009,309(6):1548-1556
Vertex-colorings, edge-colorings and total-colorings of the Sierpiński gasket graphs Sn, the Sierpiński graphs S(n,k), graphs S+(n,k), and graphs S++(n,k) are considered. In particular, χ″(Sn), χ′(S(n,k)), χ(S+(n,k)), χ(S++(n,k)), χ′(S+(n,k)), and χ′(S++(n,k)) are determined. 相似文献
18.
Let C and K be closed cones in Rn. Denote by φ (K∩C) the face of C generated by K ∩ C, by φ(K ∩ D)D the dual face of φ(K ∩ C) in C1, and by φ(-K1 ∩ C1) the face of C1 generated by -K1 ∩ C1. It is proved that φ(K ∩ C1) if and only if -C1 ∩ [span(K ∩ C)] ⊥ ? C1 + K1. In particular, the closedness of C1 + K1 is a sufficient condition. Our result contains a generalization of the Gordon-Stiemke theorem which appeared in a recent paper of Saunders and Schneider. 相似文献
19.
Necessary and sufficient conditions for uniqueness of analytic continuation are investigated for a system of m ? 1 first-order linear homogeneous partial differential equations in one unknown, with complex-valued ∞ coefficients, in some connected open subset of k, k ? 2. The type of system considered is one for which there exists a real k-dimensional, ∞, connected C-R submanifold Mk of n, for k, n ? 2, such that the system may be identified with the induced Cauchy-Riemann operators on Mk. The question of uniqueness of analytic continuation for a system of partial differential equations is thus transformed to the question of uniqueness of analytic continuation for C-R functions on the manifold Mk ? Cn. Under the assumption that the Levi algebra of Mk has constant dimension, it is shown that if the excess dimension of this algebra is maximal at every point, then Mk has the property of uniqueness of analytic continuation for its C-R functions. Conversely, under certain mild conditions, it is shown that if Mk has the property of uniqueness of analytic continuation for all ∞ C-R functions, and if the Levi algebra has constant dimension on all of Mk, then the excess dimension must be maximal at every point of Mk. 相似文献
20.
Two proofs are given, one combinatorial, the other by character theory, for the identity, ∏λa1! a2! … an! = ∏λ1a12a2 … nan, where λ ranges over all partitions λ = (1a12a2 … nan) of n. The two demonstrations yield a simple proof of the known formula, det2T(n) = [∏λ1a12a2 … nan]2, where T(n) is the matrix formed by the character table of Sn. Finally a sufficient condition is given so that the permanent of T(n) is zero. 相似文献