共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we will discuss the average number of normals through a point in a convex body in a Minkowski plane where the unit disk is a polygon. 相似文献
2.
Jan Jakóbowski 《Geometriae Dedicata》1998,69(2):179-188
For any pseudo-ordered field F and some mappings f and g of F into itself we can construct a Minkowski plane such that one derived affine plane is a variation on W. A. Pierce's construction. Moreover, such a Minkowski plane induces nearaffine planes described by H. A. Wilbrink. 相似文献
3.
Convexity and the Average Curvature of Plane Curves 总被引:1,自引:0,他引:1
The average curvature of a rectifiable closed curve in R2 is its total absolute curvature divided by its length. If a rectifiable closed curve in R2 is contained in the interior of a convex set D then its average curvature is at least as large as the average curvature of the simple closed curve D which bounds the convex set. 相似文献
4.
We prove that a Minkowski plane with an automorphism group of type 51 is of order 5 and, if it is of type 4 or 7 it is of order 3 or 5.
Received 5 January 1999. 相似文献
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Bernd Su˙ssmann 《Annals of Global Analysis and Geometry》2006,29(4):323-332
In this paper the classical Banchoff–Pohl inequality, an isoperimetric inequality for nonsimple closed curves in the Euclidean plane, involving the square of the winding number, is generalized to symmetric Minkowski geometries. The proof uses the well-known curve shortening flow. 相似文献
8.
R. M. Garipov 《Algebra and Logic》2003,42(6):365-381
We are engaged in classifying up to isomorphism of discrete subgroups of an affine transformation group on a plane (a two-dimensional space) preserving the Minkowski metric. It is proved that, for subgroups that do not coincide with Euclidean ones, the orbit of almost every point is everywhere dense. 相似文献
9.
该文研究了一致cantor集的Minkowski容度,并且计算出了它的上Minkowski容度和下Minkowski容度. 由此推出它的Minkowski容度是不存在的. 相似文献
10.
In this paper, position vector of a time-like slant helix with respect to standard frame of Minkowski space E31 is studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine position vector of an arbitrary time-like slant helix. In terms of solution, we determine the parametric representation of the slant helices from the intrinsic equations. Thereafter, we apply this method to find the representation of a time-like Salkowski and time-like anti-Salkowski curves as examples of a slant helices, by means of intrinsic equations. Moreover, we present some new characterizations of slant helices and illustrate some examples of our main results. 相似文献
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利用Finsler法曲率A、Landsberg曲率Ly、法切曲率Fy、Berwald联络D以及第二基本形式Ⅱy,研究Minkowski空间中的子流形、子流形的旗曲率与李齐曲率. 相似文献
13.
We present an iterative algorithm for solving variational inequalities under the weakest monotonicity condition proposed so far. The method relies on a new cutting plane and on analytic centers. 相似文献
14.
R. M. Garipov 《Algebra and Logic》2008,47(1):18-31
On a crystallographic group, a condition of being topologically discrete is imposed which is weaker than is the conventional
requirement for an action on space to be discontinuous. Isomorphism classification is given for crystallographic groups in
three crystallographic classes in a 4-dimensional Minkowski space, which are defined by unimodular subgroups of the general
Lorentz group. In these classes are, respectively, 24, 36, and 68 crystallographic groups.
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Translated from Algebra i Logika, Vol. 47, No. 1, pp. 31–53, January–February, 2008. 相似文献
15.
Minkowski Geometric Algebra of Complex Sets 总被引:2,自引:0,他引:2
A geometric algebra of point sets in the complex plane is proposed, based on two fundamental operations: Minkowski sums and products. Although the (vector) Minkowski sum is widely known, the Minkowski product of two-dimensional sets (induced by the multiplication rule for complex numbers) has not previously attracted much attention. Many interesting applications, interpretations, and connections arise from the geometric algebra based on these operations. Minkowski products with lines and circles are intimately related to problems of wavefront reflection or refraction in geometrical optics. The Minkowski algebra is also the natural extension, to complex numbers, of interval-arithmetic methods for monitoring propagation of errors or uncertainties in real-number computations. The Minkowski sums and products offer basic 'shape operators' for applications such as computer-aided design and mathematical morphology, and may also prove useful in other contexts where complex variables play a fundamental role – Fourier analysis, conformal mapping, stability of control systems, etc. 相似文献
16.
Cauchy-Riemann equations in Minkowski plane 总被引:1,自引:0,他引:1
Peng Weiling 《Advances in Applied Clifford Algebras》2005,15(1):71-82
The properties of the symmetry and ordering of Minkowski plane are discussed by using hyperbolic imaginary unit and elliptic
imaginary unit of Clifford algebra, and the representations of Cauchy-Riemann equations are given in Minkowski plane. 相似文献
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Gloria Rinaldi 《Journal of Geometry》2001,70(1-2):160-163
We show that each known finite Minkowski plane of order even, contains embedded Miquelian inversive planes, (cf. Proposition 1).
Received 2 July 1999. 相似文献
19.
设Mn为Riemann流形,给定类空浸入:Mn→Rn,p,如果存在另一个类空浸入:Mn→Rn,p,使与在共形对应之下且对应点的地空间平行,则称类空子流形是可保高斯映射共形形变的.本文给出可保高斯映射共形形变的充要条件.对n=2,p=1的情形,如果上述形变是同向的,我们分类了曲面;如果是反向的,我们用主曲率满足的方程来描述. 相似文献
20.
As a generalization of Minkowski sums, products, powers, and roots of complex sets, we consider the Minkowski value of a given polynomial P over a complex set X. Given any polynomial P(z) with prescribed coefficients in the complex variable z, the Minkowski value P(X) is defined to be the set of all complex values generated by evaluating P, through a specific algorithm, in such a manner that each instance of z in this algorithm varies independently over X. The specification of a particular algorithm is necessary, since Minkowski sums and products do not obey the distributive law, and hence different algorithms yield different Minkowski value sets P(X). When P is of degree n and X is a circular disk in the complex plane we study, as canonical cases, the Minkowski monomial value
P
m
(X), for which the monomial terms are evaluated separately (incurring
n(n+1) independent values of z) and summed; the Minkowski factor value
P
f
(X), where P is represented as the product (z–r
1)(z–r
n
) of n linear factors – each incurring an independent choice zX – and r
1,...,r
n
are the roots of P(z); and the Minkowski Horner value
P
h
(X), where the evaluation is performed by nested multiplication and incurs n independent values zX. A new algorithm for the evaluation of P
h
(X), when 0X, is presented. 相似文献