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1.
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
2.
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
3.
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
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.
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
6.
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
7.
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
8.
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
9.
Let M
m
be a m-dimensional submanifold in the n-dimensional unit sphere S
n
without umbilic point. Two basic invariants of M
m
under the M?bius transformation group of S
n
are a 1-form Φ called M?bius form and a symmetric (0,2) tensor A called Blaschke tensor. In this paper, we prove the following rigidity theorem: Let M
m
be a m-dimensional (m≥3) submanifold with vanishing M?bius form and with constant M?bius scalar curvature R in S
n
, denote the trace-free Blaschke tensor by . If , then either ||?||≡0 and M
m
is M?bius equivalent to a minimal submanifold with constant scalar curvature in S
n
; or and M
m
is M?bius equivalent to in for some c≥0 and .
Received: 15 May 2002 / Revised version: 3 February 2003
Published online: 19 May 2003
RID="*"
ID="*" Partially supported by grants of CSC, NSFC and Outstanding Youth Foundation of Henan, China.
RID="†"
ID="†" Partially supported by the Alexander Humboldt von Stiftung and Zhongdian grant of NSFC.
Mathematics Subject Classification (2000): Primary 53A30; Secondary 53B25 相似文献
10.
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
11.
Ron Shaw 《Designs, Codes and Cryptography》2007,45(2):229-246
For a given hypersurface ψ in PG(n, 2), with equation Q(x) = 0, where Q is a polynomial of (reduced) degree d > 1, a definition is given of the ψ-associate X
# of a flat X in PG(n, 2). The definition involves the fully polarized form of the polynomial Q; in the cubic case d = 3 it reads: X
# = {z ∈ PG(n, 2) | T(x, y, z) = 0 for all x, y ∈ X}, where T(x, y, z) denotes the alternating trilinear form obtained by completely polarizing Q. Some general results, valid for any degree d and projective dimension n, are first expounded. Thereafter several choices of ψ are visited, but for each choice just a few aspects are highlighted. Despite the partial nature of the survey quite a variety
of behaviours of the ψ-associate are uncovered. Many of the choices of ψ which are considered are of cubic hypersurfaces in PG(5, 2). If ψ is the Segre variety it is shown that the 48 planes external to fall into eight pairs of ordered triplets {(P
1, R
1, S
1), (P
2, R
2, S
2)} such that and . Further those lines L of PG(5, 2) which are singular, satisfying that is L
# = PG(5.2), are in this case shown to form a complete spread of 21 lines. Another result of note arises in the case where
ψ is the underlying 35-set of a non-maximal partial spread Σ5 of five planes in PG(5, 2), where it is shown that one plane is singled out by the property that every line is singular.
相似文献
12.
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
13.
In this paper, we study the high-dimensional fractional Hausdorff operators and establish their boundedness on the real Hardy spaces H p (? n ) for 0 < p < 1. 相似文献
14.
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
$J\left( u\right) =\int\limits_{\Omega } \left\vert \partial u\right\vert^{p}\,dx$
15.
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
16.
The minimum number of total independent partition sets of V ∪ E of graph G(V,E) is called the total chromatic number of G denoted by χ
t
(G). If the difference of the numbers of any two total independent partition sets of V ∪ E is no more than one, then the minimum number of total independent partition sets of V ∪ E is called the equitable total chromatic number of G, denoted by χ
et
(G). In this paper, we obtain the equitable total chromatic number of the join graph of fan and wheel with the same order.
Supported by the National Natural Science Foundation of China (No. 10771091). 相似文献
17.
In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H(B^n) satisfying ||f||0 = 1 and det f'(0) = α ∈ (0, 1], where||f||0 = sup{(1 - |z|^2 )n+1/2n det(f'(z))[1/n : z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f(0). When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara. 相似文献
18.
We show, conditional on a uniform version of the prime k-tuples conjecture, that there are x/(log x)1+o(1) numbers not exceeding x common to the ranges of φ and σ. Here φ is Euler’s totient function and σ is the sum-of-divisors function. 相似文献
19.
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
20.
We assign to each pair of positive integers n and k ⩾ 2 a digraph G(n, k) whose set of vertices is H = {0, 1, ..., n − 1} and for which there is a directed edge from a ∈ H to b ∈ H if a
k
≡ b (mod n). We investigate the structure of G(n, k). In particular, upper bounds are given for the longest cycle in G(n, k). We find subdigraphs of G(n, k), called fundamental constituents of G(n, k), for which all trees attached to cycle vertices are isomorphic. 相似文献