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221.
Given a Hermitian manifold(M~n, g), the Gauduchon connections are the one parameter family of Hermitian connections joining the Chern connection and the Bismut connection. We will call▽~s=(1-s/2)▽~c+s/2▽~b the s-Gauduchon connection of M, where ▽~c and ▽~b are respectively the Chern and Bismut connections. It is natural to ask when a compact Hermitian manifold could admit a flat s-Gauduchon connection. This is related to a question asked by Yau. The cases with s = 0(a flat Chern connection) or s = 2(a flat Bismut connection) are classified respectively by Boothby in the1950 s or by the authors in a recent joint work with Q. Wang. In this article, we observe that if either s ≥ 4 + 2×3~(1/2) ≈ 7.46 or s ≤ 4-2×3~(1/2) ≈ 0.54 and s ≠ 0, then g is K?hler. We also show that, when n = 2,g is always K?hler unless s = 2. Therefore non-K?hler compact Gauduchon flat surfaces are exactly isosceles Hopf surfaces. 相似文献
222.
We introduce two new linear differential operators which are invariant with respect to the unitary group SU(n). They constitute analogues of the twistor and the Rarita-Schwinger operator in the orthogonal case. The natural setting for doing this is Hermitian Clifford Analysis. Such operators are constructed by twisting the two versions of the Hermitian Dirac operator 6z_ and 6z_ and then projecting on irreducible modules for the unitary group. We then study some properties of their spaces of nullsolutions and we find a formulation of the Hermitian Rarita-Schwinger operators in terms of Hermitian monogenic polynomials. 相似文献
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224.
Ai-Li Yang 《Applied mathematics and computation》2010,216(6):1715-1722
Based on the HSS (Hermitian and skew-Hermitian splitting) and preconditioned HSS methods, we will present a generalized preconditioned HSS method for the large sparse non-Hermitian positive definite linear system. Our method is essentially a two-parameter iteration which can extend the possibility to optimize the iterative process. The iterative sequence produced by our generalized preconditioned HSS method can be proven to be convergent to the unique solution of the linear system. An exact parameter region of convergence for the method is strictly proved. A minimum value for the upper bound of the iterative spectrum is derived, which is relevant to the eigensystem of the products formed by inverse preconditioner and splitting. An efficient preconditioner based on incremental unknowns is presented for the actual implementation of the new method. The optimality and efficiency are effectively testified by some comparisons with numerical results. 相似文献
225.
The extremal ranks of matrix expression of A − BXC with respect to XH = X have been discussed by applying the quotient singular value decomposition Q-SVD and some rank equalities of matrices in this paper. 相似文献
226.
The minimum number of rows in covering arrays (equivalently, surjective codes) and radius-covering arrays (equivalently, surjective codes with a radius) has been determined precisely only in special cases. In this paper, explicit constructions for numerous best known covering arrays (upper bounds) are found by a combination of combinatorial and computational methods. For radius-covering arrays, explicit constructions from covering codes are developed. Lower bounds are improved upon using connections to orthogonal arrays, partition matrices, and covering codes, and in specific cases by computation. Consequently for some parameter sets the minimum size of a covering array is determined precisely. For some of these, a complete classification of all inequivalent covering arrays is determined, again using computational techniques. Existence tables for up to 10 columns, up to 8 symbols, and all possible strengths are presented to report the best current lower and upper bounds, and classifications of inequivalent arrays. 相似文献
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In this paper, we study the algebraic geometry of any two-point code on the Hermitian curve and reveal the purely geometric nature of their dual minimum distance. We describe the minimum-weight codewords of many of their dual codes through an explicit geometric characterization of their supports. In particular, we show that they appear as sets of collinear points in many cases. 相似文献
230.
In this article we study relations between groups and quantum error correcting codes. Groups of central type are used to construct quantum error correcting codes. Both stabilizer and Clifford codes can be derived from a construction involving this kind of groups. A more general construction of Clifford codes will be given and their correcting properties will be examined using group theoretical techniques. 相似文献