共查询到20条相似文献,搜索用时 31 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.
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
3.
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
4.
We use a distortion to define the dual complex of a cubical subdivision of ℝ
n
as an n-dimensional subcomplex of the nerve of the set of n-cubes. Motivated by the topological analysis of high-dimensional digital image data, we consider such subdivisions defined
by generalizations of quad- and oct-trees to n dimensions. Assuming the subdivision is balanced, we show that mapping each vertex to the center of the corresponding n-cube gives a geometric realization of the dual complex in ℝ
n
. 相似文献
5.
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
6.
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
7.
Michael A. Burr 《Central European Journal of Mathematics》2012,10(2):530-542
For a complex irreducible projective variety, the volume function and the higher asymptotic cohomological functions have proven
to be useful in understanding the positivity of divisors as well as other geometric properties of the variety. In this paper,
we study the vanishing properties of these functions on hypersurfaces of ℙ
n
× ℙ
n
. In particular, we show that very general hypersurfaces of bidegree (k, k) obey a very strong vanishing property, which we define as asymptotic purity: at most one asymptotic cohomological function is nonzero for each divisor. This provides evidence for the truth of a conjecture
of Bogomolov and also suggests some general conditions for asymptotic purity. 相似文献
8.
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
9.
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
10.
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
11.
The simple incidence structure , formed by the points and the unordered pairs of distinct parallel lines of a finite affine plane of order n > 4, is a 2 – (n
2,2n,2n–1) design with intersection numbers 0,4,n. In this paper, we show that the converse is true, when n ≥ 5 is an odd integer.
Supported by M.I.U.R., Università di Palermo. 相似文献
12.
Il’dar Khamitovich Musin Polina V. Yakovleva 《Central European Journal of Mathematics》2012,10(2):665-692
For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ? n . Due to the conditions on M each function of this space admits a holomorphic extension in ? n . In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic functions satisfying some weighted L 2-bounds in a domain of holomorphy in ? n are obtained with the aid of L. Hörmander’s method of L 2-bounds for the \(\bar \partial\) operator. Also, some new facts on the Fourier-Laplace transform of tempered distributions complementing some well-known results of V.S. Vladimirov are employed. 相似文献
13.
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
14.
We study coherent systems of type (n, d, n + 1) on a Petri curve X of genus g ≥ 2. We describe the geometry of the moduli space of such coherent systems for large values of the parameter α. We determine the top critical value of α and show that the corresponding “flip” has positive codimension. We investigate also the non-emptiness of the moduli space
for smaller values of α, proving in many cases that the condition for non-emptiness is the same as for large α. We give some detailed results for g ≤ 5 and applications to higher rank Brill–Noether theory and the stability of kernels of evaluation maps, thus proving Butler’s
conjecture in some cases in which it was not previously known.
The authors are members of the research group VBAC (Vector Bundles on Algebraic Curves). The first two authors were supported
by EPSRC grant GR/T22988/01 for a visit to the University of Liverpool. The second author acknowledges the support of CONACYT
grant 48263-F. The third author thanks CIMAT, Guanajuato, México and California State University Channel Islands, where a
part of this paper was completed, and acknowledges support from the Academia Mexicana de Ciencias, under its exchange agreement
with the Royal Society of London. 相似文献
15.
A. Yu. Veretennikov 《Journal of Mathematical Sciences》2011,179(1):48-79
Smoothness with respect to a parameter is established under mild assumptions on the regularity of coefficients for Sobolev
solutions of the Poisson equations in the whole ℝ
d
in the “ergodic case.” An assertion of this kind serves as one of the key tools in diffusion approximation and some other
limit theorems. Bibliography: 12 titles. 相似文献
16.
Poincaré-type estimates for a logarithmically concave measure μ on a convex set Ω are obtained. For this purpose, Ω is endowed with a Riemannian metric g in which the Riemannian manifold with measure (Ω, g, μ) has nonnegative Bakry–Emery tensor and, as a corollary, satisfies the Brascamp–Lieb inequality. Several natural classes of metrics (such as Hessian and conformal metrics) are considered; each of these metrics gives new weighted Poincare, Hardy, or log-Sobolev type inequalities and other results. 相似文献
17.
E. E. Marenich 《Journal of Mathematical Sciences》2009,163(6):732-738
It is proved that every (n × n) Boolean matrix can be expressed as a product of primes and elementary matrices in the semigroup of Boolean matrices. 相似文献
18.
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
19.
Given E ? ? d , d ≥ 2, define to be the set of directions determined by E. We prove that if the Hausdorff dimension of E is greater than d ? 1, then σ(D(E)) > 0, where σ denotes the surface measure on S d?1. In the process, we prove some tight upper and lower bounds for the maximal function associated with the Radon-Nikodym derivative of the natural measure on D. This result is sharp, since the conclusion fails to hold if E is a (d ? 1)-dimensional hyper-plane. This result can be viewed as a continuous analog of a recent result of Pach, Pinchasi, and Sharir ([22, 23]) on directions determined by finite subsets of ? d . We also discuss the case when the Hausdorff dimension of E is precisely d ? 1, where some interesting counter-examples have been obtained by Simon and Solomyak ([25]) in the planar case. In response to the conjecture stated in this paper, T. Orponen and T. Sahlsten ([20]) have recently proved that if the Hausdorff dimension of E equals d ? 1 and E is rectifiable and is not contained in a hyper-pane, the Lebesgue measure of the set of directions is still positive. Finally, we show that our continuous results can be used to recover and, in some cases, improve the exponents for the corresponding results in the discrete setting for large classes of finite point sets. In particular, we prove that a finite point set P ? ? d , d ≥ 3, satisfying a certain discrete energy condition (Definition 3.1) determines ? #P distinct directions.
相似文献
$D(E) \equiv \left\{ {{{x - y} \over {\left| {x - y} \right|}}:x,y \in E} \right\} \subset {S^{d - 1}}$
20.
This paper is concerned with the bound of the cost of approximate controllability and null controllability of heat equations, i.e., the minimal Lp norm and L∞ norm of a control needed to control the system approximately or a control needed to steer the state of the system to zero. The methods we use combine observability inequalities, energy estimates for heat equations and the dual theory. 相似文献