共查询到20条相似文献,搜索用时 15 毫秒
1.
To a given immersion ${i:M^n\to \mathbb S^{n+1}}$ with constant scalar curvature R, we associate the supremum of the squared norm of the second fundamental form sup |A|2. We prove the existence of a constant C n (R) depending on R and n so that R ≥ 1 and sup |A|2 = C n (R) imply that the hypersurface is a H(r)-torus ${\mathbb S^1(\sqrt{1-r^2})\times\mathbb S^{n-1} (r)}$ . For R > (n ? 2)/n we use rotation hypersurfaces to show that for each value C > C n (R) there is a complete hypersurface in ${\mathbb S^{n+1}}$ with constant scalar curvature R and sup |A|2 = C, answering questions raised by Q. M. Cheng. 相似文献
2.
We characterize active redundancy through compensator transform and use the reverse rule of order 2 (RR2) property between compensator processes to investigate the problem of where to allocate a spare in a k-out-of-n:F system of dependent components through active redundancy. 相似文献
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Let S and {iaR} be two associative rings, let S C R be a semidualizing (S,R)-bimodule. We introduce and investigate properties of the totally reflexive module with respect to S C R and we give a characterization of the class of the totally C R -reflexive modules over any ring R. Moreover, we show that the totally C R -reflexive module with finite projective dimension is exactly the finitely generated projective right R-module. We then study the relations between the class of totally reflexive modules and the Bass class with respect to a semidualizing bimodule. The paper contains several results which are new in the commutative Noetherian setting. 相似文献
5.
Lenny Fukshansky 《Journal of Combinatorial Theory, Series A》2011,118(2):690-701
We find sharp absolute constants C1 and C2 with the following property: every well-rounded lattice of rank 3 in a Euclidean space has a minimal basis so that the solid angle spanned by these basis vectors lies in the interval [C1,C2]. In fact, we show that these absolute bounds hold for a larger class of lattices than just well-rounded, and the upper bound holds for all. We state a technical condition on the lattice that may prevent it from satisfying the absolute lower bound on the solid angle, in which case we derive a lower bound in terms of the ratios of successive minima of the lattice. We use this result to show that among all spherical triangles on the unit sphere in RN with vertices on the minimal vectors of a lattice, the smallest possible area is achieved by a configuration of minimal vectors of the (normalized) face centered cubic lattice in R3. Such spherical configurations come up in connection with the kissing number problem. 相似文献
6.
O. V. Kulikova 《Mathematical Notes》2013,93(5-6):837-849
Let N 1 (N 2) be the normal closure of a finite symmetrized set R 1 (R 2, respectively) in a finitely generated free group F = F(A). As is known, if R i satisfies condition C(6), then the conjugacy problem is decidable in F/N i . In the paper, it is proved that, if one adds to condition C(6) on the set R 1 ∪ R 2 the atoricity condition for the presentation 〈A | R 1, R 2〉, then the conjugacy problem is decidable in the group F/N 1 ∩ N 2 as well. In particular, for the decidability of the conjugacy problem in F/N 1 ∩ N 2, it is sufficient to assume that the set R 1 ∪ R 2 satisfies condition C(7). 相似文献
7.
Segal-Bargmann space F2(Cn) and monogenic Fock space M2(Rn+1) are introduced first. Then, with the help of exponential functions in Clifford analysis, two integral operators are defined to connect F2(Cn) and M2(Rn+1) together. The corresponding integral properties are studied in detail. 相似文献
8.
Consider an operator T:C2(R)→C(R) and isotropic maps A1,A2:C1(R)→C(R) such that the functional equation
9.
Alexander Barvinok 《Advances in Mathematics》2010,224(1):316-757
We consider the set Σ(R,C) of all m×n matrices having 0-1 entries and prescribed row sums R=(r1,…,rm) and column sums C=(c1,…,cn). We prove an asymptotic estimate for the cardinality |Σ(R,C)| via the solution to a convex optimization problem. We show that if Σ(R,C) is sufficiently large, then a random matrix D∈Σ(R,C) sampled from the uniform probability measure in Σ(R,C) with high probability is close to a particular matrix Z=Z(R,C) that maximizes the sum of entropies of entries among all matrices with row sums R, column sums C and entries between 0 and 1. Similar results are obtained for 0-1 matrices with prescribed row and column sums and assigned zeros in some positions. 相似文献
10.
It is proved that a ring R is right perfect if and only if it is Σ-cotorsion as a right module over itself. Several other conditions are shown to be equivalent. For example, that every pure submodule of a free right R-module is strongly pure-essential in a direct summand, or that the countable direct sum of the cotorsion envelope of RR is cotorsion.If CR is a flat Σ-cotorsion module, then CR admits a decomposition into a direct sum of indecomposable modules with a local endomorphism ring. The Jacobson radical J(S) of the endomorphism ring S=EndRC is characterized as the maximum ideal that acts locally T-nilpotently on CR. If R is semilocal and C=C(R), then the radical consists of those endomorphisms whose image is contained in CJ. 相似文献
11.
In the paper we prove the double centralizer theorem for semiprime algebras. To be precise, let R be a closed semiprime algebra over its extended centroid F, and let A be a closed semiprime subalgebra of R, which is a finitely generated module over F. Then C R (A) is also a closed semiprime algebra and C R (C R (A))?=?A. In addition, if C R (A) satisfies a polynomial identity, then so does the whole ring R. Here, for a subset T of R, we write C R (T):?=?{x?∈?R|xt?=?tx???t?∈?T}, the centralizer of T in R. 相似文献
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Wies?aw Kubi? 《Topology and its Applications》2006,153(18):3383-3396
We study compact spaces which are obtained from metric compacta by iterating the operation of inverse limit of continuous sequences of retractions. This class, denoted by R, has been introduced in [M. Burke, W. Kubi?, S. Todor?evi?, Kadec norms on spaces of continuous functions, http://arxiv.org/abs/math.FA/0312013]. Allowing continuous images in the definition of class R, one obtains a strictly larger class, which we denote by RC. We show that every space in class RC is either Corson compact or else contains a copy of the ordinal segment ω1+1. This improves a result of Kalenda from [O. Kalenda, Embedding of the ordinal segment [0,ω1] into continuous images of Valdivia compacta, Comment. Math. Univ. Carolin. 40 (4) (1999) 777-783], where the same was proved for the class of continuous images of Valdivia compacta. We prove that spaces in class R do not contain cutting P-points (see the definition below), which provides a tool for finding spaces in RC?R. Finally, we study linearly ordered spaces in class RC. We prove that scattered linearly ordered compacta belong to RC and we characterize those ones which belong to R. We show that there are only 5 types (up to order isomorphism) of connected linearly ordered spaces in class R and all of them are Valdivia compact. Finally, we find a universal pre-image for the class of all linearly ordered Valdivia compacta. 相似文献
13.
D.P. Patil 《Journal of Pure and Applied Algebra》2006,205(2):266-278
In this article we characterize noetherian local one-dimensional analytically irreducible and residually rational domains (R,mR) which are non-Gorenstein, the non-negative integer is equal to τR-1 and ?(R/(C+xR))=2, where τR is the Cohen-Macaulay type of R, C is the conductor of R in the integral closure of R in its quotient field Q(R) and xR is a minimal reduction of m by giving some conditions on the numerical semi-group v(R) of R. 相似文献
14.
In this paper we show that the Ramsey number R(Cn,Wm)=2n-1 for even m and n?5m/2-1. 相似文献
15.
Let m be a fixed integer, m = {0,1,?,m ? 1}; let C be a family of nonvoid subsets of m, and let R be a hereditary subfamily of C. Given finite sets Am,…,Am?1 such that ∩ i?BAi = Ø for all B ? m, B ? C, the vector of |∩i?RAi| (Rj?R) is called a C-supported R-intersection pattern. The characterization of the YRC of such patterns is a difficult combinatorial problem even for m=5 and simple families R and C. We study the algebraic structure of the convex cone YRC and its dual, and an integer linear-programming aspect of the problem; in particular we introduce the notion of content and pseudocontent. A relaxation leads to quadratic and higher forms over certain subsets of reals. As an application we study the natural link between highly symmetric patterns and two-symbol balanced arrays. 相似文献
16.
Majid Rahro Zargar 《Archiv der Mathematik》2013,100(1):25-34
Let ${(R,\mathfrak{m})}$ be a local ring, and let C be a semidualizing R-module. In this paper, we are concerned with the C-injective and G C -injective dimensions of certain local cohomology modules of R. Firstly, the injective dimension of C and the above quantities are compared. Secondly, as an application of the above comparisons, a characterization of a dualizing module of R is given. Finally, it is shown that if R is Cohen-Macaulay of dimension d such that ${\rm H}_{\mathfrak{m}}^{d}(C)$ is C-injective, then R is Gorenstein. This is an answer to a question which was recently raised. 相似文献
17.
Robert W. Irving 《Discrete Mathematics》1974,9(3):251-264
The generalised Ramsey number R(G1, G2,..., Gk) is defined as the smallest integer n such that, if the edges of Kn, the complete graph on n vertices, are coloured using k colours C1, C2,..., Ck, then for some i(1≤i≤k) there is a subgraph Gi of Kn with all of its edges colour Ci. When G1=G2=...,Gk=G, we use the more compact notation Rk(G).The generalised Ramsey numbers Rk(G) are investigated for all graphs G having at most four vertices (and no isolates). This extends the work of Chvátal and Harary, who made this investigation in the case k=2. 相似文献
18.
For a compact manifold M ofdim M=n≥4, we study two conformal invariants of a conformal class C on M. These are the Yamabe constant YC(M) and the Ln/2-norm WC(M) of the Weyl curvature. We prove that for any manifold M there exists a conformal class C such that the Yamabe constant YC(M) is arbitrarily close to the Yamabe invariant Y(M), and, at the same time, the constant WC(M) is arbitrarily large. We study the image of the mapYW:C→(YC(M), WC(M))∈R 2 near the line {(Y(M), w)|w∈R}. We also apply our results to certain classes of 4-manifolds, in particular, minimal compact Kähler surfaces of Kodaira dimension 0, 1 or 2. 相似文献
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20.
Gilles Pisier 《Israel Journal of Mathematics》2014,203(1):223-273
We introduce and study a generalization of the notion of exact operator space that we call subexponential. Using Random Matrices we show that the factorization results of Grothendieck type that are known in the exact case all extend to the subexponential case, but we exhibit (a continuum of distinct) examples of non-exact subexponential operator spaces, as well as a C*-algebra that is subexponential with constant 1 but not exact. We also show that OH, R + C and max(?2) (or any other maximal operator space) are not subexponential. 相似文献