态射的和与积的Moore-Penrose逆

态射的Moore-Penrose逆是矩阵的Moore-Penrose逆在有对合*的范畴中的推广。本文给出加法范畴及Abel范畴中态射的和与积的Moore-Penrose逆存在的充分条件和一些性质。     

ON ORTHOGONAL (0,f)-FACTORIZATIONS

1991MRSubjectClassification05C701IntroductionAllgraphsconsi(lere(1arefilliteulldirectedsimplegraphs.LetgandfI)einteger-v;tllle(1fllnctionsdefinedonV(G)suchthat05g(x)5f(x)foreverya:EV(G).A(g,f)--tActorofGisaspanningsubgraphFofGsuchthatg(x)5da(x)5f(x)foreveryxEV(G).IfGitselfisa(g,f)-factor,thenGiscalls(1a(g,f)--graph.A(g,f)--factorizationF={FI,F2,'.F,,,}ofGisapartitionofGilltoedge-disjoint(g,f)--factorsFI5F2,'5Fm.LetHbeasubgrapllofGwith?nedges,thenFiscalledorthogonaltoHifeach…     

Solving AKNS equations via Jacobi inversion problem

1.IntroductionRecelltlymuchworkhasbeencarriedoutinthestudyoftheseparationofvariablesofacompletelyintegrableHalniltoniansystemll--6].Forclassicalilltegrablesystemssubjecttoinversescatteringtransformationthestandardconstructionoftheaction-anglevariablesusingthepolesoftheBaker-Anheizerfullctionisequivalenttotheseparationofvariablesl31.Theabategapsolutionsofthesolitonequationsareconstructedduetotheseparationofvariablesofthestationarysolitonequationsll].Forsomekindoffinite-dimensionalintegrableHt…     

Efficient Rabin-type Digital Signature Scheme

Rabin's cryptosystem was proved to be as hard as factorization. However, Rabin's digital signature schemes is probabilistic. This paper shows two efficient Rabin type digital signature schemes, a basic scheme and an improved scheme. Both schemes run much faster than Rabin's scheme. They are deterministic and the size of a signature is much smaller than that of a signature in Rabin's scheme. Furthermore, it is proved that, by applying the technique of Bellare and Rogaway, the proposed scheme is secure against chosen plaintext attack. More precisely, breaking the proposed digital signature scheme by chosen plaintext attack is as hard as factoring N.     

图的色因子分解

设 ｎ１ ≥ ｎ ２ ≥ … ≥ ｎｋ ≥ ２ 是整数． 若图 Ｇ 能边分解成 Ｇ１  Ｇ２  …  Ｇｋ , 这里 χ（ Ｇｉ） ＝ ｎ ｉ, ｉ＝１,２,…,ｋ ,则称 Ｇ 有（ｎ１ , ｎ２ , …, ｎｋ ）色因子 分解． 本文改进 了 Ｈａｋｉｍ ｉ和 Ｓｃｈｍ ｅｉｃｈ ｅｌ 关于图的色因 子分解的结果,作为推 论,推广了 Ｍ ａｔｕｌａ 和 Ｈａｒａｒｙ 等人的结果     

Some results about GMRES in the singular case

In this paper, we study the Generalized Minimal Residual (GMRES) method for solving singular linear systems, particularly when the necessary and sufficient condition to obtain a Krylov solution is not satisfied. Thanks to some new results which may be applied in exact arithmetic or in finite precision, we analyze the convergence of GMRES and restarted GMRES. These formulas can also be used in the case when the systems are nonsingular. In particular, it allows us to understand what is often referred to as stagnation of the residual norm of GMRES. This revised version was published online in June 2006 with corrections to the Cover Date.     

Uniform factorization for compact sets of operators

We prove a factorization result for relatively compact subsets of compact operators using the Bartle and Graves Selection Theorem, a characterization of relatively compact subsets of tensor products due to Grothendieck, and results of Figiel and Johnson on factorization of compact operators. A further proof, essentially based on the Banach-Dieudonné Theorem, is included. Our methods enable us to give an easier proof of a result of W.H. Graves and W.M. Ruess.

     

Circular shallow spherical shells with central circular hole under simultaneous actions of arbitrary unsteady temperature field and arbitrary dynamic normal load

In this paper, under assumption that tempeature is linearly distributed along the thickness of the shell, we deal with problems as indicated in the title and obtain general solutions of them which are expressed in analytic form.In the first part, we investigate free vibration of circular shallow spherical shells with circular holes at the center under usual arbitrary boundary conditions. As an example, we calculate fundamental natural frequency of a circular shallow spherical shell whose edge is fixed (m=0). Results we get are expressed in analytic form and check well with E. Reissner’s [1]. Method for calculating frequency equation is recently suggested by Chien Wei-zang and is to be introduced in appendix 3.In the second part, we investigate forced vibration of shells as indicated in the title under arbitrary harmonic temperature field and arbitrary harmonic dynamic normal load.In the third part, we investigate forced vibration of the above mentioned shells with initial conditions under arbitrary unsteady temperature field and arbitrary normal load.In appendix 1 and 2, we discuss how to express displacement boundary conditions with stress function and boundary conditions in the case m=1.     

与路2—正交的（g,f）—因子分解

设ｇ和ｆ分别是定义在图Ｇ的机点集合Ｖ（Ｇ）上的整数值函数且对每个ｘ∈Ｖ（Ｇ）有４≤ｇ（ｘ）≤ｆ（ｘ）。证明了若Ｇ是一个（ｍｇ＋ｍ－１,ｍｆ－ｍ＋１）－图,则对Ｇ中任意给定的长为２ｍ的路Ｐ,Ｇ有一个（ｇ,ｆ＿－因子分解２－正交于Ｐ。     

关于数论函数若干不等式的一个注记

改进与数论函数σ（ｎ）（整数ｎ的所有正因数的和）及Ｅｕｌｅｒ函数φ（ｎ）有关的几个不等式,并对不等式σ（ｎ）＾φ（ｎ）〈ｎ＾ｎ〈φ（ｎ）＾σ（ｎ）（ｎ∈Ｚ且ｎ≥７）给出了一个较为简便的证明。