共查询到20条相似文献,搜索用时 20 毫秒
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é. I. Kovalevskaya 《Mathematical Notes》1978,23(2):99-101
Let the surface R3 be defined by the equation z = f(x, y), where f(x, y) is a function 3 times continuously differentiable in R2. It is proved that if the total (Gaussian) curvature of the surface is nonzero almost everywhere on in the sense of Lebesgue measure in R2), then is extremal, i.e., for almost all (x,y) R2 the inequality max (||qx||, ||qy, qf (x, y)) > q–1/s–. holds for all integral q qo (f), where x is the distance from the real number x to the nearest integer and > 0 is arbitrarily small.Translated from Matematicheskie Zametki, Vol. 23, No. 2, pp. 177–181, February, 1978.In conclusion, the author thanks V. G. Sprindzhuk for suggesting the problem. 相似文献
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In this work, we initiate the study of the geometry of the variable exponent sequence space when . In 1931 Orlicz introduced the variable exponent sequence spaces while studying lacunary Fourier series. Since then, much progress has been made in the understanding of these spaces and of their continuous counterpart. In particular, it is well known that is uniformly convex if and only if the exponent is bounded away from 1 and infinity. The geometry of when either or remains largely ill‐understood. We state and prove a modular version of the geometric property of when , known as uniform convexity in every direction. We present specific applications to fixed point theory. In particular we obtain an analogue to the classical Kirk's fixed point theorem in when . 相似文献
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D. V. Prokhorov 《Mathematical Notes》1971,10(3):597-600
We determined the maximum radius
(r) of the disk r, possessing the property that every functionf (z), starlike of order, is starlike in ¦z¦r. The problem is reduced to that of finding the minimum of a certain functional for which extremal function is determined.Translated from Matematicheskie Zametki, Vol. 10, No. 3, pp. 287–293, September, 1971. 相似文献
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LetG be a graph,VP(G) its vertex packing polytope and letA(G) be obtained by reflectingVP(G) in all Cartersian coordinates. Denoting byA*(G) the set obtained similarly from the fractional vertex packing polytope, we prove that the segment connecting any two non-antipodal
vertices ofA(G) is contained in the surface ofA(G) and thatG is perfect if and only ifA*(G) has a similar property. 相似文献
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O. N. Kosukhin 《Moscow University Mathematics Bulletin》2008,63(5):205-207
The following new geometric criterion is proved: a real Banach space (X, ‖ · ‖) is a Hilbert space if and only if for any three points A,B,C of this space not belonging to a line there are three altitudes in the triangle ABC intersecting at one point. 相似文献
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Let B(R^n) be the set of all n x n real matrices, Sr the set of all matrices with rank r, 0 ≤ r ≤ n, and Sr^# the number of arcwise connected components of Sr. It is well-known that Sn =GL(R^n) is a Lie group and also a smooth hypersurface in B(R^n) with the dimension n × n. 相似文献
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In this paper, we will show that any geometric Lorenz flow in a definite class satisfies the parameter-shifted shadowing property.
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Rudolf Drieschner 《Numerical Algorithms》1993,5(10):509-522
An algorithm is presented and proved correct, for the efficient approximation of finite point sets in 2 and 3 by geometric elements such as circles, spheres and cylinders. It is shown that the approximation criterion used, viz. minimising the maximum orthogonal deviation, is best modelled mathematically through the concept of aparallel body. This notion, besides being a valuable tool for form assessment in metrology, contributes to approximation theory by introducing a new kind of approximation, here called geometric or orthogonal. This approach is closely related to but different from Chebyshev approximation.The work described is part of a Commission of the European Communities project (Contract 3327/1/0/158/89/9-BCR-UK(30)). 相似文献
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T. S. S. R. K. Rao 《Proceedings Mathematical Sciences》1997,107(1):35-42
In this paper we study a geometric property for Banach spaces called condition (*), introduced by de Reynaet al in [3], A Banach space has this property if for any weakly null sequencex
n of unit vectors inX, ifx
*
n
is any sequence of unit vectors inX
* that attain their norm at xn’s, then
. We show that a Banach space satisfies condition (*) for all equivalent norms iff the space has the Schur property. We also
study two related geometric conditions, one of which is useful in calculating the essential norm of an operator. 相似文献
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舒世昌 《纯粹数学与应用数学》2008,24(2)
研究了欧氏空间En p中具常数量曲率n(n-1)r的n(n>2)维完备连通子流形,得到了En p截面曲率非负且法联络平坦的完备连通子流形的一个分类定理. 相似文献
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Jeaman Ahn 《Journal of Pure and Applied Algebra》2007,209(2):337-360
In this paper, we will give some geometric results using generic initial ideals for the degree reverse lex order. The main goal of the paper is to improve on results of Bigatti, Geramita and Migliore concerning geometric consequences of maximal growth of the Hilbert function of the Artinian reduction of a set of points. When the points have the Uniform Position Property, the consequences are even more striking. Here we weaken the growth condition, assuming only that the values of the Hilbert function of the Artinian reduction are equal in two consecutive degrees, and that the first of these degrees is greater than the second reduction number of the points. We continue to get nice geometric consequences even from this weaker assumption. However, we have surprising examples to show that imposing the Uniform Position Property on the points does not give the striking consequences that one might expect. This leads to a better understanding of the Hilbert function, and the ideal itself, of a set of points with the Uniform Position Property, which is an important open question. In the last section we describe the role played by the Weak Lefschetz Property (WLP) in this theory, and we show that the general hyperplane section of a smooth curve may not have the WLP. 相似文献