共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper theI andII regularn-simplices are introduced. We prove that the sufficient and necessary conditions for existence of anI regularn-simplex in ℝ
n
are that ifn is even thenn = 4m(m + 1), and ifn is odd thenn = 4m + 1 with thatn + 1 can be expressed as a sum of two integral squares orn = 4m - 1, and that the sufficient and necessary condition for existence of aII regularn-simplex in ℝ
n
isn = 2m
2 - 1 orn = 4m(m + 1)(m ∈ ℕ). The connection between regularn-simplex in ℝ
n
and combinational design is given. 相似文献
2.
M. A. Ovcharenko 《Siberian Mathematical Journal》2018,59(5):931-937
We study isotropic homogeneous tori in ?n and ?Pn. We find necessary and sufficient conditions for their Hamiltonian minimality. 相似文献
3.
In this paper, we consider the problem of distortion theorems for mappings which map the unit ball biholomorphically onto
convex domains in ℂ
n
. In particular, we discuss two distortion conjectures for such mappings. 相似文献
4.
Gabriel Ruiz-Hernández 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2011,81(1):55-67
An immersed surface M in N
n
×ℝ is a helix if its tangent planes make constant angle with ∂
t
. We prove that a minimal helix surface M, of arbitrary codimension is flat. If the codimension is one, it is totally geodesic. If the sectional curvature of N is positive, a minimal helix surfaces in N
n
×ℝ is not necessarily totally geodesic. When the sectional curvature of N is nonpositive, then M is totally geodesic. In particular, minimal helix surfaces in Euclidean n-space are planes. We also investigate the case when M has parallel mean curvature vector: A complete helix surface with parallel mean curvature vector in Euclidean n-space is a plane or a cylinder of revolution. Finally, we use Eikonal f functions to construct locally any helix surface. In particular every minimal one can be constructed taking f with zero Hessian. 相似文献
5.
Diarmuid Crowley 《Geometriae Dedicata》2010,148(1):15-33
We calculate \({\mathcal{S}^{{\it Diff}}(S^p \times S^q)}\), the smooth structure set of S p × S q , for p, q ≥ 2 and p + q ≥ 5. As a consequence we show that in general \({\mathcal{S}^{Diff}(S^{4j-1}\times S^{4k})}\) cannot admit a group structure such that the smooth surgery exact sequence is a long exact sequence of groups. We also show that the image of the forgetful map \({\mathcal{S}^{Diff}(S^{4j}\times S^{4k}) \rightarrow \mathcal{S}^{Top}(S^{4j}\times S^{4k})}\) is not in general a subgroup of the topological structure set. 相似文献
6.
We give necessary conditions for certain real analytic tube generic submanifolds in n to be locally algebraizable. As an application, we exhibit families of real analytic non locally algebraizable tube generic submanifolds in n. During the proof, we show that the local CR automorphism group of a minimal, finitely nondegenerate real algebraic generic submanifold is a real algebraic local Lie group. We may state one of the main results as follows. Let M be a real analytic hypersurface tube in n passing through the origin, having a defining equation of the form v= (y), where (z,w)=(x+iy,u+iv)n–1×. Assume that M is Levi nondegenerate at the origin and that the real Lie algebra of local infinitesimal CR automorphisms of M is of minimal possible dimension n, i.e. generated by the real parts of the holomorphic vector fields z1,...,z n–1,w. Then M is locally algebraizable only if every second derivative 2yky l; is an algebraic function of the collection of first derivatives y1,,ym.Mathematics Subject Classification (2000): 32V40, 32V25, 32H02, 32H40, 32V10 相似文献
7.
Guy David 《Journal of Geometric Analysis》2010,20(4):837-954
We give a new proof and a partial generalization of Jean Taylor’s result (Ann. Math. (2) 103(3), 489–539, 1976) that says that Almgren almost-minimal sets of dimension 2 in ℝ3 are locally C
1+α
-equivalent to minimal cones. The proof is rather elementary, but uses a local separation result proved in Ann. Fac. Sci.
Toulouse 18(1), 65–246, 2009 and an extension of Reifenberg’s parameterization theorem (David et al. in Geom. Funct. Anal. 18, 1168–1235, 2008). The key idea is still that if X is the cone over an arc of small Lipschitz graph in the unit sphere, but X is not contained in a disk, we can use the graph of a harmonic function to deform X and substantially diminish its area. The local separation result is used to reduce to unions of cones over arcs of Lipschitz
graphs. A good part of the proof extends to minimal sets of dimension 2 in ℝ
n
, but in this setting our final regularity result on E may depend on the list of minimal cones obtained as blow-up limits of E at a point. 相似文献
8.
Tiziano Granucci 《Annali dell'Universita di Ferrara》2010,56(2):283-293
Using Tilli’s technique [Cal Var 25(3):395–401, 2006], we shall give a new proof of the regularity of the local minima of the functionalwith Ω a domain of class C 0, 1 in \({\mathbb{R}^{n}}\) and 2 ≤ p < n.
相似文献
$J\left( u\right) =\int\limits_{\Omega } \left\vert \partial u\right\vert^{p}\,dx$
9.
Let M n (n ? 3) be a complete Riemannian manifold with sec M ? 1, and let \(M_i^{n_i }\) (i = 1, 2) be two complete totally geodesic submanifolds in M. We prove that if n1 + n2 = n ? 2 and if the distance |M1M2| ? π/2, then M i is isometric to \(\mathbb{S}^{n_i } /\mathbb{Z}_h\), \(\mathbb{C}P^{n_i /2}\), or \(\mathbb{C}P^{n_i /2} /\mathbb{Z}_2 \) with the canonical metric when n i > 0; and thus, M is isometric to S n /? h , ?Pn/2, or ?Pn/2/?2 except possibly when n = 3 and \(M_1 (or M_2 )\mathop \cong \limits^{iso} \mathbb{S}^1 /\mathbb{Z}_h \) with h ? 2 or n = 4 and \(M_1 (or M_2 )\mathop \cong \limits^{iso} \mathbb{R}P^2 \). 相似文献
10.
S. V. Konyagin A. A. Kuleshov 《Proceedings of the Steklov Institute of Mathematics》2016,293(1):186-193
Necessary conditions are established for the continuity of finite sums of ridge functions defined on convex subsets E of the space Rn. It is shown that under some constraints imposed on the summed functions ?i, in the case when E is open, the continuity of the sum implies the continuity of all ?i. In the case when E is a convex body with nonsmooth boundary, a logarithmic estimate is obtained for the growth of the functions ?i in the neighborhoods of the boundary points of their domains of definition. In addition, an example is constructed that demonstrates the accuracy of the estimate obtained. 相似文献
11.
Tao Feng 《Designs, Codes and Cryptography》2009,51(2):175-194
Let D be a (v, k, λ)-difference set in an abelian group G, and (v, 31) = 1. If n = 5p
r
with p a prime not dividing v and r a positive integer, then p is a multiplier of D. In the case 31|v, we get restrictions on the parameters of such difference sets D for which p may not be a multiplier.
相似文献
12.
G. A. Karapetyan A. A. Darbinyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2007,42(5):278-291
The paper investigates the index of some linear, differential, semielliptic operators with variable coefficients of a special form in ? n . In particular, additional conditions on the symbol are found that render the index finite. The operators are considered in the weighted Sobolev spaces. 相似文献
13.
The notion of derivatives for smooth representations of GL(n, ? p ) was defined in [BZ77]. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations in [Sah89] and called the “adduced” representation. In this paper we define derivatives of all orders for smooth admissible Fréchet representations of moderate growth. The real case is more problematic than the p-adic case; for example, arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation.In the companion paper [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations.We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS13a]. 相似文献
14.
Topological free involutions on S
1 × S
n
are classified up to conjugation. We prove that this is the same as classifying quotient manifolds up to homeomorphism. There
are exactly four possible homotopy types of such quotients, and surgery theory is used to classify all manifolds within each
homotopy type. 相似文献
15.
Peng-fei Yang 《应用数学学报(英文版)》2011,27(4):639-646
In this paper, we define a class of domains in R
n
. Using the synchronous coupling of reflecting Brownian motion, we obtain the monotonicity property of the solution of the
heat equation with the Neumann boundary conditions. We then show that the hot spots conjecture holds for this class of domains. 相似文献
16.
In this paper the unique solvability of regular hypoelliptic equations in multianisotropic weighted functional spaces is proved by means of special integral representation of functions through a regular operator. The existence of the solutions is proved by constructing approximate solutions using multianisotropic integral operators. 相似文献
17.
V. V. Pernay 《Mathematical Notes》2016,99(3-4):534-544
Estimates of quantities characterizing the complexity of the family of convex subsets of the d-dimensional cube [1, n]d as n→∞ are given. The geometric properties of spaces with norm generated by the generalized majorant of partial sums are studied. 相似文献
18.
There is a natural duality between orbits of a real form G of a complex semisimple group G
on a homogeneous rational manifold Z=G
/P and those of the complexification K
of any of its maximal compact subgroups K: (,) is a dual pair if is a K-orbit. The cycle space C() is defined to be the connected component containing the identity of the interior of {g:g() is non-empty and compact}. Using methods which were recently developed for the case of open G-orbits, geometric properties of cycles are proved, and it is shown that C() is contained in a domain defined by incidence geometry. In the non-Hermitian case this is a key ingredient for proving that C() is a certain explicitly computable universal domain.Research of the first author partially supported by Schwerpunkt Global methods in complex geometry and SFB-237 of the Deutsche Forschungsgemeinschaft.The second author was supported by a stipend of the Deutsche Akademische Austauschdienst. 相似文献
19.
We present a new (1+ε)-spanner for sets of n points in ℝ
d
. Our spanner has size O(n/ε
d−1) and maximum degree O(log
d
n). The main advantage of our spanner is that it can be maintained efficiently as the points move: Assuming that the trajectories
of the points can be described by bounded-degree polynomials, the number of topological changes to the spanner is O(n
2/ε
d−1), and using a supporting data structure of size O(nlog
d
n), we can handle events in time O(log
d+1
n). Moreover, the spanner can be updated in time O(log n) if the flight plan of a point changes. This is the first kinetic spanner for points in ℝ
d
whose performance does not depend on the spread of the point set. 相似文献
20.
A. Kh. Khachatryan Kh. A. Khachatryan 《P-Adic Numbers, Ultrametric Analysis, and Applications》2018,10(2):90-99
In the present work the existence of continuous and bounded solutions for a class of nonlinear pseudo-differential equations on ? n is proved. The monotonicity, asymptotic behavior and other properties for obtained solutions are also presented. Mentioned class of equations arises in p-adic string theory. 相似文献