Splittings

We investigate some notions of splitting families and estimate sizes of the corresponding cardinal coefficients. In particular we solve a problem of P. Simon. Received July 12, 1995     

Heegaard分解的重新分块

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＭｂｅａｃｏｍｐａｃｔ 3 ｍａｎｉｆｏｌｄ .ＩｆｔｈｅｒｅｉｓａｐｒｏｐｅｒｌｙｅｍｂｅｄｄｅｄｃｌｏｓｅｄｓｕｒｆａｃｅＳｉｎＭｗｈｉｃｈｓｅｐａｒａｔｅｓＭｉｎｔｏｔｗｏｃｏｍｐｒｅｓｓｉｏｎｂｏｄｉｅｓＨ1ａｎｄＨ2 ,ｔｈｅｎＭｃａｎｂｅｗｒｉｔｔｅｎａｓＭ =Ｈ1∪ＳＨ2 .ＴｈｉｓｓｔｒｕｃｔｕｒｅｏｎＭｉｓｃａｌｌｅｄａＨｅｅｇａａｒｄｓｐｌｉｔｔｉｎｇｏｆＭａｎｄＳｉｓａｓｐｌｉｔｔｉｎｇｓｕｒｆａｃｅ .Ｈ1∪ＳＨ2 ｉｓｓａｉｄｔｏｂｅｒｅｄｕｃｉｂｌｅ…     

Cohomology Splittings of Stiefel Manifolds

The complex Stiefel manifolds admit a stable decomposition asThom spaces of certain bundles over Grassmannians. The purposeof the paper is to identify the splitting in any complex orientedcohomology theory.     

关于Z－矩阵的弱正则分裂

本文主要考虑一类Ｚ－矩阵弱正则分裂的迭代矩阵的谱半径和特征值１的指数问题，推广了Ｒｏｓｅ在１９８４年得到的一个定理．     

On graph compatible Splittings of M-matrices

Let A ϵ Rⁿⁿ. Then A = M − N is called a regular splitting of A if M^-1 ⩾ 0 and N ⩾ 0, and A = M − N is called a graph compatible splitting of A if ⊼[Ggr](A)⊼ ⊇ [Ggr](M), where [Ggr](A) is the graph of A and ⊼[Ggr](A)⊼ its reflexive transitive closure. We answer in the negative a question raised by H. Schneider whether a regular splitting A = M − N of an M-matrix is graph compatible if all diagonal elements of A (or M) are positive.     

Thin Position of Heegaard Splittings

§１．ＢａｃｋｇｒｏｕｎｄａｎｄＭａｉｎＲｅｓｕｌｔｓＳｉｎｃｅｔｈｅｃｏｎｃｅｐｔｏｆｔｈｉｎｐｏｓｉｔｉｏｎｆｏｒｋｎｏｔｓｉｎｔｈｅ３－ｓｐｈｅｒｅｗａｓｄｅｖｅｌｏｐｅｄｂｙＧａｂａｉ［１］，ｍａｎｙｉｔｓａｐｐｌｉｃａｔｉｏｎｓｔｏｄｅａｌ...     

Two Splittings of a Square Matrix

In this note it is shown that any square matrix AC ^n×n can be represented as the sum A= , where is complex symmetric and rank . The corresponding persymmetric result can be used in finding the terms of a small rank perturbed Toeplitz matrix via an O(n ²) computation. This allows one to perform fast matrix–vector products in case n is large.     

On Separation Index of Heegaard Splittings

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｏｎｃｅｐｔｏｆｒｅｄｕｃｉｂｌｅＨｅｅｇａａｒｄｓｐｌｉｔｉｎｇｓｗａｓｆｉｒｓｔｄｅｖｅｌｏｐｅｄｂｙＨａｋｅｎ［１］．Ｉｔｓｒｅｌａ－ｔｉｏｎｔｏｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇ３－ｍａｎｉｆｏｌｄｓｃｏｎ...     

Error Bounds for Exponential Operator Splittings

Error bounds for the Strang splitting in the presence of unbounded operators are derived in a general setting and are applied to evolutionary Schrödinger equations and their pseudo-spectral space discretization.     

有界线性算子非负分裂的比较

本文研究有界线性算子非负分裂的比较,建立了若干比较定理,给出了保证两个迭代算子的谱半径间严格不等式成立的一些充分条件．这些结论蕴涵并推广了Ｍａｒｅｋ 和Ｓｚｙｌｄ［２］以及作者［４］的相应结果     

The pants sum of high distance Heegaard splittings简

Let Mi be a compact orientable 3-manifold, and Fi be an incompressible surface on δMi, i -= 1,2. Let f ： F1 →F2 be a homeomorphism, and M = M1 UI M2. In this paper, under certain assumptions for the attaching surface Fi, we show that if both M1 and M2 have Heegaavd splittings with distance at least 2（g（M1）＋ g（M2））＋ 1, then g（M） = g（M1）＋g（M2）.     

On S-Weak Regular Splittings of a Singular M-Matrix

ＯｎＳ－ＷｅａｋＲｅｇｕｌａｒＳｐｌｉｔｔｉｎｇｓｏｆａＳｉｎｇｕｌａｒＭ－ＭａｔｒｉｘＬｉＷｅｎ（黎稳）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＳｏｎｔｈｅＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ,Ｇｕａｎｇｚｈｏｕ,５１０６３１）Ａｂ...     

Splittings in the variety of residuated lattices

It is shown that the only algebra that splits the lattice of subvarieties of the variety of residuated lattices is the two element boolean algebra. Received October 4, 1999; accepted in final form August 11, 2000.     

Splittings of generalized Baumslag–Solitar groups

We study the structure of generalized Baumslag–Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity (fully reduced decompositions) and give a simplified proof of the existence of deformations. We also prove a finiteness theorem and solve the isomorphism problem for generalized Baumslag–Solitar groups with no non-trivial integral moduli.