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1.
T. Nakashima 《Archiv der Mathematik》2000,74(2):148-153
In this paper we study stable bundles with trivial first Chern class on a K3 surface. A necessary and sufficient condition for the existence of such bundles is proved and it is shown that Mukai's reflection functor gives a new compactification of the moduli space. A relation to the notion of T-duality in theoretical physics is also discussed. 相似文献
2.
Consider an analytic germ f:(Cm, 0)(C, 0) (m3) whose criticallocus is a 2-dimensional complete intersection with an isolatedsingularity (icis). We prove that the homotopy type of the Milnorfiber of f is a bouquet of spheres, provided that the extendedcodimension of the germ f is finite. This result generalizesthe cases when the dimension of the critical locus is zero [8],respectively one [12]. Notice that if the critical locus isnot an icis, then the Milnor fiber, in general, is not homotopicallyequivalent to a wedge of spheres. For example, the Milnor fiberof the germ f:(C4, 0)(C, 0), defined by f(x1, x2, x3, x4) =x1x2x3x4 has the homotopy type of S1xS1xS1. On the other hand,the finiteness of the extended codimension seems to be the rightgeneralization of the isolated singularity condition; see forexample [912, 17, 18]. In the last few years different types of bouquet theoremshave appeared. Some of them deal with germs f:(X, x)(C, 0) wheref defines an isolated singularity. In some cases, similarlyto the Milnor case [8], F has the homotopy type of a bouquetof (dim X1)-spheres, for example when X is an icis [2],or X is a complete intersection [5]. Moreover, in [13] Siersmaproved that F has a bouquet decomposition FF0Sn...Sn (whereF0 is the complex link of (X, x)), provided that both (X, x)and f have an isolated singularity. Actually, Siersma conjecturedand Tibr proved [16] a more general bouquet theorem for thecase when (X, x) is a stratified space and f defines an isolatedsingularity (in the sense of the stratified spaces). In thiscase FiFi, where the Fi are repeated suspensions of complexlinks of strata of X. (If (X, x) has the Milnor property,then the result has been proved by Lê; for details see[6].) In our situation, the space-germ (X, x) is smooth, but f hasbig singular locus. Surprisingly, for dim Sing f1(0)2,the Milnor fiber is again a bouquet (actually, a bouquet ofspheres, maybe of different dimensions). This result is in thespirit of Siersma's paper [12], where dim Sing f1(0)= 1. In that case, there is only a rather small topologicalobstruction for the Milnor fiber to be homotopically equivalentto a bouquet of spheres (as explained in Corollary 2.4). Inthe present paper, we attack the dim Sing f1(0) = 2 case.In our investigation some results of Zaharia are crucial [17,18]. 相似文献
3.
设p_1,p_2,p_3为不同的奇素数,c1是整数.给出了Pell方程组x~2-(c~2-1)y~2=y~2-2p_1p_2p_3z~2=1的所有非负整数解(x,y,z),从而推广了Keskin (2017)和Cipu(2018)等人的结果. 相似文献
4.
5.
In this article, we prove a decomposition theorem for I2-convergent double sequences and introduce the notions of I2-Cauchy and I*2)-Cauchy double sequence, and then study their certain properties. Finally, we introduce the notions of regularly (I2,I)-convergence and (I2,I)-Cauchy double sequence. 相似文献
6.
Pengfei Guan & Junfang Li 《数学研究》2021,54(1):56-80
New types of hypersurface flows have been introduced recently with goals
to establish isoperimetric type inequalities in geometry. These flows serve as efficient
paths to achieve the optimal solutions to the problems of calculus of variations in geometric setting. The main idea is to use variational structures to develop hypersurface
flows which are monotonic for the corresponding curvature integrals (including volume and surface area). These new geometric flows pose interesting but challenging
PDE problems. Resolution of these problems have significant geometric implications. 相似文献
7.
In this paper, we study cyclic codes over the rings Z
2 + uZ
2 and Z
2 + uZ
2 + u
2
Z
2 . We find a set of generators for these codes. The rank, the dual, and the Hamming distance of these codes are studied as
well. Examples of cyclic codes of various lengths are also studied.
相似文献
8.
The three numbers 1, 5, 10 have the property that the product of any two numbers decreased by 1 is a perfect square. In this paper it is proved that there is no other positive integer N which shares this property with 1, 5, and 10. 相似文献
9.
本文用生成元、关系式构造了任意域K上扭Chevalley单群2B2(K)的泛中心扩张.(域K=GF(23)除外)当域K为GF(25)的代数扩域时,证明了2B2(K)的Schur乘子是平凡的. 相似文献
10.
Horst von Lienen 《Journal of Number Theory》1978,10(1):10-15
Using known properties of continued fractions, we give a very simple and elementary proof of the theorem of Epstein and Rédei on the impossibility in a certain case of representing ?1 by the quadratic form x2 ? 2py2. Two of our theorems, which concern the representation of a2 and ?2a2, serve to extend our method to an unknown case in which ?1 is not representable. 相似文献
11.
12.
13.
This work contains an improvement of earlier results of Boggess and Dwilewicz regarding global approximation of CR functions
by entire functions in the case of hypersurface graphs. In this work, we show that if ω, an open subset of a real hypersurface in ℂ
n
, can be graphed over a convex subset in ℝ2n−1, then ω is CR-Runge in the sense that continuous CR functions on ω can be approximated by entire functions on ℂ
n
in the compact open topology of ω. Examples are presented to show that this approximation result does not hold for graphed CR submanifolds in higher codimension.
R. Dwilewicz is partially supported by the Polish Science Foundation (KBN) grant N201 019 32/805. 相似文献
14.
对非负整数序列π=(d1,d2……,dn),0≤di≤n-1,本分别给出了它蕴含导出子图为几乎处处完全图,完全图去掉一个Hamilton圈的边,完全k-部图可图(即蕴含aw^1,Aw^2和Ar,r2…,rk-可图)的判别准则。 相似文献
15.
The matrix least squares (LS) problem minx ||AXB^T--T||F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ||A1X1B1^T + A2X2B2^T - T||F can also be regarded as the constrained LS problem minx=diag(x1,x2) ||AXB^T -T||F with A = [A1, A2] and B = [B1, B2]. The authors transform T to T such that min x1,x2 ||A1X1B1^T+A2X2B2^T -T||F is equivalent to min x=diag(x1 ,x2) ||AXB^T - T||F whose solutions are included in the solution set of unconstrained problem minx ||AXB^T - T||F. So the general solutions of min x1,x2 ||A1X1B^T + A2X2B2^T -T||F are reconstructed by selecting the parameter matrix in that of minx ||AXB^T - T||F. 相似文献
16.
Let a, b, c be nonzero integers having no prime factors ≡ 3 (mod 4), not all of the same sign, abc squarefree, and for which Legendre's equation ax2 + by2 + cz2 = 0 is solvable in nonzero integers x, y, z. A property is proved yielding a congruence which must be satisfied by any solution x, y, z. 相似文献
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18.
应用共轭梯度方法,结合线性投影算子,给出迭代算法求解了线性矩阵方程组A_1XB_1=C_1,A_2XB_2=C_2在任意线性子空间上的约束解及其最佳逼近.当矩阵方程组A_1XB_1=C_1,A_2XB_2=C_2相容时,可以证明,所给迭代算法经过有限步迭代可得到矩阵方程组的约束解、极小范数解和最佳逼近.文中的数值例子证实了该算法的有效性. 相似文献
19.
Tavan T Trent 《Journal of Functional Analysis》1985,64(2):163-177
It is shown that P2(μ) ≠ L2(μ) if and only if there exists a probability measure ν with ν ⊥ μ and 6pz.dfnc;1,ν ? Cz.dfnc;pz.dfnc;2,μ for all polynomials p and a fixed constant C < ∞. The relationship between this method and theorems of Berger and of Carey and Pincus concerning rationally cyclic vectors for powers of nonnormal subnormal Operators is examined. 相似文献
20.
William M Kantor 《Journal of Combinatorial Theory, Series A》1982,32(2):299-302
Large numbers of translation planes are constructed which have order ?6 and admit a collineation group SL(2, ?2) generated by elations. 相似文献