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41.
We study Einstein warped product spaces. As a result, we prove the following: if is an Einstein warped product space with nonpositive scalar curvature and compact base, then is simply a Riemannian product space.
42.
YunYanYANG 《数学学报(英文版)》2003,19(1):63-68
In this paper,we derive an elementary identity for smooth solutions of the following equation:△u(x) K(x)e^2u(x)=0 in R^2 and use it to get some global properties of the solutions. 相似文献
43.
Pavel Rehak 《Czechoslovak Mathematical Journal》2001,51(2):303-321
We study oscillatory properties of the second order half-linear difference equation
. It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation
. We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given. 相似文献
44.
Let G be a -compact, locally compact group and I be a closed2-sided ideal with finite codimension in L1(G). It is shownthat there are a closed left ideal L having a right boundedapproximate identity and a closed right ideal R having a leftbounded approximate identity such that I = L + R. The proofuses ideas from the theory of boundaries of random walks ongroups. 2000 Mathematics Subject Classification: primary 43A20;secondary 42A85, 43A07, 46H10, 46H40, 60B11. 相似文献
45.
Cecí lia Ferreira Armando Machado 《Proceedings of the American Mathematical Society》2000,128(7):2181-2186
Let denote the set of all -roots of the identity in a Lie group . We show that is always an embedded submanifold of , having the conjugacy classes of its elements as open submanifolds. These conjugacy classes are examples of -symmetric spaces and we show, more generally, that every -symmetric space of a Lie group is a covering manifold of an embedded submanifold of . We compute also the Hessian of the inclusions of and into , relative to the natural connection on the domain and to the symmetric connection on .
46.
Ramanujan's partition congruences can be proved by first showing that the coefficients in the expansions of (q; q)
r
satisfy certain divisibility properties when r = 4, 6 and 10. We show that much more is true. For these and other values of r, the coefficients in the expansions of (q; q)
r
satisfy arithmetic relations, and these arithmetic relations imply the divisibility properties referred to above. We also obtain arithmetic relations for the coefficients in the expansions of (q; q)
r
(q
t; q
t)
s
, for t = 2, 3, 4 and various values of r and s. Our proofs are explicit and elementary, and make use of the Macdonald identities of ranks 1 and 2 (which include the Jacobi triple product, quintuple product and Winquist's identities). The paper concludes with a list of conjectures. 相似文献
47.
A. Pellicier 《Applied Acoustics》2007,68(10):1192-1212
In this paper, various methods for calculating partition transparency are investigated. These methods are all based on the wave approach, yet they differ in the way of considering the incident field, partition leaf dimensions and the absorbing material, or absorbent, incorporated between the partition leaves. The method verification has been done through comparison with the experimental data available in the literature. Results are very convincing and the wave approach proves to be highly accurate. The basic wave approach is well suited for modeling of infinite single or double-leaf partitions, although the diffuse incident field requires spatial windowing to achieve agreement with experimental data. When porous material is incorporated inside double-leaf partitions, the model needs to be enhanced, based on the Biot theory, to ensure coincidence with experimental data. In the case of partitions, which cannot be considered infinite, spatial windowing is applied to the transparency to correct for the dimensional effect, especially in the low-frequency range. The final model turns out to be highly accurate, as long as spatial windowing is limited to the first coincidence frequency. The wave approach therefore proves to be a suitable method and calculation times are moreover acceptable. 相似文献
48.
Yunhee Euh JeongHyeong Park Kouei Sekigawa 《Differential Geometry and its Applications》2013,31(4):463-471
We give an integral formula for the first Pontrjagin number of a compact almost Hermitian surface and derive curvature identities from the integral formula based on the fundamental fact that the first Pontrjagin number in the deRham cohomology group is a topological invariant. Further, we provide some applications of the identities. 相似文献
49.
何勇 《高校应用数学学报(A辑)》1997,(4):467-474
设有整数集S={r1,r2;p1,p2,…,pn},这里ri≥0,pj>0(i=1,2;j=1,2,…,n),寻找一个S的最优分划P=(S*1,S*2)使得:(1)ri属于不同子集,(2)S*1与S*2中元素总和较大者尽可能地小.这是一个NP-完备问题,本文给出一个线性时间近似算法,它的近似界为87. 相似文献
50.
周焕芹 《纯粹数学与应用数学》2008,24(1):41-44
对任意正整数n,著名的Smarandache函数S(n)定义为最小的正整数m使得n|m!.即S(n)=min{m∶m ∈N,n|m!).本文的主要目的是利用初等方法研究一类包含S(n)的Dirichlet级数与Riemann zeta-函数之间的关系,并得到了一个有趣的恒等式. 相似文献