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1.
We give a simple proof for the rotational symmetry of ancient solutions of Ricci flow on surfaces. As a consequence we obtain a simple proof of some results of Daskalopoulos, Hamilton and Sesum on the a priori estimates for the ancient solutions of Ricci flow on surfaces. We also give a simple proof for the solution to be a Rosenau solution under some mild conditions on the solutions of Ricci flow on surfaces.  相似文献   

2.
The image of the Poisson transform on a principal series representations on a boundary component of a Hermitian symmetric space is considered. We prove that the image is characterized by a covariant differential operator on a homogeneous line bundle on the symmetric space.  相似文献   

3.
We prove that a Baire measure (or a regular Borel measure) on a compact Hausdorff space is sequentially order continuous as a linear functional on the Banach space of all continuous functions if and only if it vanishes on meager Baire subsets, a result parallel to a much earlier theorem of Dixmier. We also give some results on the relation between sequentially order continuous measures on compact spaces and countably additive measures on Boolean algebras.

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4.
The purpose of this paper is to prove a result on the number of irreducible projective representations of a finite group with respect to a given factor set and a group of linear characters acting on them. It includes a determination of the number of classes of projectively equivalent representations as well as a result of M. Osima on the classes of linearly equivalent representations. Osima proved his result by defining and calculating on irreducible projective Brauer characters, whereas the method used here is based on Brauer's well-known result for the linear modular representations and an induction argument on suitable coverings.  相似文献   

5.
On a nonuniform gird, we consider twice continuously differentiable splines of third order and obtain calibration relations expressing the coordinate splines on the original grid as a linear combination of splines of the same type on a refined grid. We also obtain calibration relations representing the coordinate splines on an enlarged grid as a linear combination of splines of the same type on the original grid. We derive the reconstruction matrices on an interval and on a segment for the space of third order splines associated with infinite and finite nonuniform grids respectively. Bibliography: 10 titles.  相似文献   

6.
<正>1引言随着现代工业生产的飞速发展,航空、气象、环境监测等领域需要研究解决限制在曲面上的四维数据插值问题,即由有限个位置处的信息推测其它若干位置点的信息.例如,地球上某个地区的温度分布、降雨量分布、大气层的"温室效应"等;飞行器(飞机、火箭、导弹等)表面压力分布规律、肿瘤的生长规律等.这些在数学上都可归结为限制在曲面上的曲面插值与逼近问题.这个问题自Barnhill提出以后,人们针对限制在球面上  相似文献   

7.
This paper establishes bounds on the length of certain strictly monotone paths, relative to a given linear objective function, on a polymatroid or on the base of a polymatroid. Specialized bounds are given for a strict polymatroid and for a matroid polyhedron. Bounds on the diameter are included.  相似文献   

8.
Hilbert and Cohn-Vossen [2, p. 221] incorrectly suggested a flexible knitting needle, constrained to conform to a surface, as one model for a geodesic on a surface. This model actually gives a relaxed elastic line on the surface, and is not generally a geodesic unless the surface lies in a plane or on a sphere.In this paper we derive the intrinsic equations for a relaxed elastic line on an oriented surface. This formulation should give a more direct and more geometric approach to questions concerning relaxed elastic lines on a surface. We apply this formulation to give alternate proofs of some results of [3] found by the less direct method of Lagrange multipliers and to give additional results about relaxed elastic lines on various surfaces. For further considerations of a relaxed elastic line on a surface as a model of the DNA molecule, see [3].Partially supported by NIH grant GM 36284-01.  相似文献   

9.
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued system of imprimitivity has a dilation to a probability spectral system of imprimitivity acting on a Banach space. This completely generalizes a well-known result which states that every frame representation of a countable group on a Hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group. We also prove that isometric group representation induced framings on a Banach space can be dilated to unconditional bases with the same structure for a larger Banach space. This extends several known results on the dilations of frames induced by unitary group representations on Hilbert spaces.  相似文献   

10.
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