共查询到20条相似文献,搜索用时 23 毫秒
1.
Three geometric inequalities for a simplex 总被引:3,自引:0,他引:3
Yang Shiguo 《Geometriae Dedicata》1995,57(1):105-110
In this paper, we obtain three new geometric inequalities for ann-dimensional simplex in then-dimensional Euclidean spaceE
n
. As special cases we find two known inequalities from L. Fejes Tóth and M. S. Klamkin, respectively. 相似文献
2.
R. J. Gregorac 《Geometriae Dedicata》1996,60(1):65-88
Ptolemy's equality for four points on a circle is related to a Feuerbach-type area relation. This suggested an extension of Ptolemy's inequality to a Feuerbach type volume relation between simplexes formed from n+2 points in R
n
(n2). Extensions of the Möbius-Neuberg and Pompeiu Theorems in R
2 are given for R
n
. Ptolemy's inequality is also extended to convex n-gons in R
2 yielding an extension of Fuhrmann's hexagon theorem to 2n-gons in R
2 (n3). 相似文献
3.
A convex hull construction in Minkowski space defines a canonical cell decomposition for a cusped hyperbolicn-manifold. An algorithm to compute the canonical cell decomposition uses the concept of the tilt of ann-simplex relative to each of its (n–1)-dimensional faces. An essential tool for computing tilts is the tilt theorem. The tilt theorem was previously known only in dimensionsn3, and the proof was needlessly complicated. Here we offer a new, simplified proof which applies in all dimensions. We also offer a second geometric interpretation of the tilt. 相似文献
4.
5.
Adam Stephanides 《Geometriae Dedicata》1994,53(3):263-270
Given a regular incidence (quasi-)polytopeP of type {a
1,a
2, ...,a
n–1} and a function on its directed edges satisfying certain conditions, we construct for everym 2 a regular incidence (quasi-)polytope of type {ma
1,a
2, ...,a
n–1} with the same vertex figure asP. 相似文献
6.
In this paper, we obtained three geometric inequalities for theu-dimensional polar sines and the dihedral angles of ann-dimensional simples. Besides, we obtained an inequality for the dihedral angles of ann-dimensional simplex in then-dimensional hyperbolic spaceH
n.Project Supported by National Natural Foundation P. R. China 相似文献
7.
Summary Inn-dimensions the problem of Apollonius is to determine the (n–1)-spheres tangent ton+1 given (n–1)-spheres. In case no two of the given (n–1)-spheres intersect and no three have the property that one separates the other two, the expected number of solutions is 2
n+1. Whenn=2 this special problem does indeed always have 8 solutions, but for higher dimensions it turns out that the number of solutions becomes dependent on the relative size and location of the given (n–1)-spheres. We describe in detail the dependence of the number of solutions in the case of the 3-dimensional problem of Apollonius on the 6 inversively invariant parameters that describe configurations of 4 given spheres. We find that the number of solutions, if finite, can be any integer from 0 to 16 and, if infinite, can be a one-, two- or three-fold infinity where the stated multiplicity refers to the number of one-parameter families of solutions that are present. 相似文献
8.
We obtain expressions for the vacuum expectations of the energy–momentum tensor of the scalar field with an arbitrary coupling to the curvature in an N-dimensional homogeneous isotropic space for the vacuum determined by diagonalization of the Hamiltonian. We generalize the n-wave procedure to N-dimensional homogeneous isotropic space–time. Using the dimensional regularization, we investigate the geometric structure of the terms subtracted from the vacuum energy–momentum tensor in accordance with the n-wave procedure. We show that the geometric structures of the first three subtractions in the n-wave procedure and in the effective action method coincide. We show that all the subtractions in the n-wave procedure in a four- and five-dimensional homogeneous isotropic space correspond to a renormalization of the coupling constants of the bare gravitational Lagrangian. 相似文献
9.
B. A. Ivanov 《Mathematical Notes》1976,20(3):763-766
Let K be a convex body in Rn andO be a point inside K. We examine the Grassmann manifold of k-planes passing throughO. We take as exceptional the planes intersecting K along a body having at least one (k – 1)-dimensional face such that it does not have points inside the hyperfaces of body K. We prove that in the Grassmann manifold G
k
n
the set of such exceptional planes is of measure zero.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 365–371, September, 1976.The author thanks V. A. Zalgaller for aid and advice on the work. 相似文献
10.
In this paper, we characterize a class of graphs which can be embedded on a boolean cube. Some of the graphs in this class are identified with the well known graphs such asmulti-dimensional mesh of trees, tree of meshes, etc. We suggest (i) an embedding of anr-dimensional mesh of trees ofn
r
(r+1)–rn
r–1
nodes on a boolean cube of (2n)
r
nodes, and (ii) an embedding of a tree of meshes with 2n
2 logn+n
2 nodes on a boolean cube withn
2 exp2 (log (2 logn+1)]) nodes. 相似文献
11.
12.
Sun Mingbao 《Journal of Geometry》2004,81(1-2):114-125
In this paper, we establish some geometric inequalities for two n-dimensional simplexes in the n-dimensional Euclidean space En.This work is supported by the Hunan Provincial Science Foundation, P. R. China. S. Mingbao is a doctorate candidate of Nanjing University of Science and Technology. 相似文献
13.
Summary Abstract regular polytopes are complexes which generalize the classical regular polytopes. This paper discusses the topology of abstract regular polytopes whose vertex-figures are spherical and whose facets are topologically distinct from balls. The case of toroidal facets is particularly interesting and was studied earlier by Coxeter, Shephard and Grünbaum. Ann-dimensional manifold is associated with many abstract (n + 1)-polytopes. This is decomposed inton-dimensional manifolds-with-boundary (such as solid tori). For some polytopes with few faces the topological type or certain topological invariants of these manifolds are determined. For 4-polytopes with toroidal facets the manifolds include the 3-sphereS
3, connected sums of handlesS
1
× S
2
, euclidean and spherical space forms, and other examples with non-trivial fundamental group. 相似文献
14.
Krzysztof Witczyński 《Journal of Geometry》2004,81(1-2):192-198
H. Bailey and D. DeTemple [1] considered some properties of squares inscribed in triangles. In this article we generalise their results to the n-dimensional space. 相似文献
15.
We study the functionb(n, d), the maximal number of atoms defined byn d-dimensional boxes, i.e. parallelopipeds in thed-dimensional Euclidean space with sides parallel to the coordinate axes.
We characterize extremal interval families definingb(n, 1)=2n-1 atoms and we show thatb(n, 2)=2n
2-6n+7.
We prove that for everyd,
exists and
.
Moreover, we obtainb*(3)=8/9. 相似文献
16.
In this paper we give a complete expansion formula for Bernstein polynomials defined on ans-dimensional simplex. This expansion for a smooth functionf represents the Bernstein polynomialB
n
(f) as a combination of derivatives off plus an error term of orderO(n–s
).Communicated by Wolfgang Dahmen. 相似文献
17.
We consider the Turan n-dimensional extremum problem of finding the value of An(hB
n
) which is equal to the maximum zero Fourier coefficient
of periodic functions f supported in the Euclidean ball hB
n
of radius h, having nonnegative Fourier coefficients, and satisfying the condition f(0)= 1. This problem originates from applications to number theory. The case of A1([–h,h]) was studied by S. B. Stechkin. For An(hB
n
we obtain an asymptotic series as h 0 whose leading term is found by solving an n-dimensional extremum problem for entire functions of exponential type. 相似文献
18.
We define the n-dimensional logarithmic capacity for convex bodies in Rn, with n2; then, for this quantity, we prove a Brunn–Minkowski type inequality, and we characterize the corresponding equality case.
Mathematics Subject Classifications (2000) 31C15, 31A35, 52A20, 39B62. 相似文献
19.
Masataka Tomari 《Mathematische Nachrichten》1993,164(1):37-48
The Milnor number μ and the geometric genus pg of normal 2-dimensional double points are studied by using Zariski's canonical resolution. By using formulas due to E. HORIKAWA and H. LAUFER, we represent μ ? 8pg in terms of the number of blowing-ups along ?1 and the number l of ?even”? components in the resolution process. A key point of our arguments is the fact that if l is small then the resolution process is restricted very much. For rational double points and double points with pa = 1, each classes are characterized by numerical invariants appearing in this resolution process. For the case pa = 1, we can make our inequality sharper and can prove 12 · pg ? 3 ≤ μ. This is an another proof of Xu-Yau's inequality for the singularity with pa = 1 in our situation. 相似文献
20.
An inequality for a simplex and its applications 总被引:4,自引:0,他引:4
Yang Shiguo 《Geometriae Dedicata》1995,55(2):195-198
In this paper, we improve some inequalities for ann-dimensional simplex in Euclidean spaceE
n
and give some applications. 相似文献