146号初等元胞自动机的演化语言的复杂性

Symbolic dynamics of cellular automata is introduced by coarse-graining the temporal evolution orbits. Evolution languages are defined. By using the theory of formal languages and automata, the complexity of evolution languages of the elementary cellular automaton of rule 146 is studied and it is proved that its width 1-evolution language is regular, but for every n ≥ 2 its width n-evolution language is not context-free but context-sensitive. Also, the same results hold for the equivalent （under conjugation） elementary cellular automaton of rule 182.     

THE CONFOCAL INVOLUTIVE SYSTEM AND THE INTEGRABILITY OF THE NONLINEARIZED LAX SYSTEMS FOR AKNS HIERARCHY

The completely integrable Hamiltonian systems generated by the general confocal involutive system are proposed. It is proved that the nonlinearized eigenvalue problem for AKNS hierarchy is such an integrable system and showed that the time evolution equations for n≤3 obtained by nonlinearizing the time parts of Lax systems for AKNS hierarchy are Liouville integrable under the constraint of the spatial part.     

The Degree of Unsolvability of Models

The purpose of this paper is to describe the complexity of models by theirdegrees of unsolvability,J.Richter defined the degree of a structure to be deg ()=sup{deg(),deg(R_i),i=1,…,n},Where is a model for afinite language L={R_i,i=1,…,n}and the universe of is a subset of ω. Shepointed out that, according to her definition, there can be models which areisomorphic but their degrees are different.Also,her discussions are restricted tofinite languages and models whose universes are subsets of ω.     

利用李代数构造非线性可积及双可积哈密顿耦合

With the help of a Lie algebra,two kinds of Lie algebras with the forms of blocks are introduced for generating nonlinear integrable and bi-integrable couplings.For illustrating the application of the Lie algebras,an integrable Hamiltonian system is obtained,from which some reduced evolution equations are presented.Finally,Hamiltonian structures of nonlinear integrable and bi-integrable couplings of the integrable Hamiltonian system are furnished by applying the variational identity.The approach presented in the paper can also provide nonlinear integrable and bi-integrable couplings of other integrable system.     

CONSTRUCTION OF SOLUTION FOR EVOLUTION EQUATION xttt＋iCx=f

The construction of solution for three-order evolution equation xttt=A^3x is skillfully obtained and the semigroup of equation operator is theoretically proved,then the solution for three-order evolution equation xttt＋iCx=f is constructed from the appropriate transformation, and the necessary and sufficient conditions of its unitary semigroup are presented.     

On the Transformations of the Potentials, Integrable Evolution Equations and Backhand Transformations

The generalization of the AKNS method, Calogero method and Konopelchenko method is given in three respects. First, the new fundamental relations associated with the matrix spectral problem and a new explicit expression related to the matrixes В and G which are contained in the transformations of the transition matrixes are obtained. Then the wide classes of the integrable evolution equations are conveniently derived without improperly assuming B=C. Finally, an important property of the operator LA is showed, the conditions connected with the temporal half of the Baeklund transformations and the new simple expressions of the integrals of motion are deduced.     

一个与Toda格相关的微分差分方程族及其反散射变换

By combined power evolution laws of the spectral parameter and the initial constants of integration,a new differential-difference hierarchy is presented from the Toda spectral problem.The hierarchy contains the classic Toda lattice equation,the nonisospectral Toda lattice equation and the mixed Toda lattice equation as reduced cases.The evolution of the scattering data in the inverse scattering transform is analyzed in detail and exact soliton solutions are computed through the corresponding inverse scattering transform.     

ON THE TRANSFORMATIONS OF THE POTENTIALS,INTEGRABLE EVOLUTION EQUATIONS AND B(A|¨)CKLUND TRANSFORMATIONS

The generalization of the AKNS method,Calogero method and Konopelchenkomethod is given in three respects,First,the new fundamental relations associated with thematrix spectral problem and a new explicit expression related to the matrixes B and Cwhich are contained in the transformations of the transition matrixes are obtained.Thenthe wide classes of the integrable evolution equations are conveniently derived withoutimproperly assuming B=C.Finally,an important property of the operator L_A is showed,the conditions connected with the temporal half of the B(a|¨)cklund transformations and thenew simple expressions of the integrals of motion are deduced.     

Branching structure of uniform recursive trees

The branching structure of uniform recursive trees is investigated in this paper. Using the method of sums for a sequence of independent random variables, the distribution law of ηn, the number of branches of the uniform recursive tree of size n are given first. It is shown that the strong law of large numbers, the central limit theorem and the law of iterated logarithm for ηn follow easily from this method. Next it is shown that ηn and ξn, the depth of vertex n, have the same distribution, and the distribution law of ζn,m, the number of branches of size m, is also given, whose asymptotic distribution is the Poisson distribution with parameter λ= 1/m. In addition, the joint distribution and the asymptotic joint distribution of the numbers of various branches are given. Finally, it is proved that the size of the biggest branch tends to infinity almost sure as n→∞.     

HIGH-ORDER WENO SIMULATIONS OF THREE-DIMENSIONAL RESHOCKED RICHTMYER-MESHKOV INSTABILITY TO LATE TIMES:DYNAMICS,DEPENDENCE ON INITIAL CONDITIONS,AND COMPARISONS TO EXPERIMENTAL DATA

The dynamics of the reshocked multi-mode Richtmyer-Meshkov instability is investigated using 513×257 2three-dimensional ninth-order weighted essentially nonoscillatory shock-capturing simulations.A two-mode initial perturbation with superposed random noise is used to model the Mach 1.5 air/SF6 Vetter-Sturtevant shock tube experiment. The mass fraction and enstrophy isosurfaces,and density cross-sections are utilized to show the detailed flow structure before,during,and after reshock.It is shown that the mixing layer growth agrees well with the experimentally measured growth rate before and after reshock.The post-reshock growth rate is also in good agreement with the prediction of the Mikaelian model.A parametric study of the sensitivity of the layer growth to the choice of amplitudes of the short and long wavelength initial interfacial perturbation is also presented.Finally,the amplification effects of reshock are quantified using the evolution of the turbulent kinetic energy and turbulent enstrophy spectra,as well as the evolution of the baroclinic enstrophy production,buoyancy production,and shear production terms in the enstrophy and turbulent kinetic transport equations.     

On Cycles Containing a Given Arc in Regular Multipartite Tournaments

In this paper we prove that if T is a regular n-partite tournament with n≥4, then each arc of T lies on a cycle whose vertices are from exactly κ partite sets for κ=4,5,…,n. Our result, in a sense, generalizes a theorem due to Alspach.     

Some Conditions for Matrices over an Incline To Be Invertible and General Linear Group on an Incline

Inclines are the additively idempotent semirings in which products are less than or equal to either factor. In this paper, some necessary and sufficient conditions for a matrix over L to be invertible are given, where L is an incline with 0 and 1. Also it is proved that L is an integral incline if and only if GLn（L） = PLn （L） for any n （n 〉 2）, in which GLn（L） is the group of all n × n invertible matrices over L and PLn（L） is the group of all n × n permutation matrices over L. These results should be regarded as the generalizations and developments of the previous results on the invertible matrices over a distributive lattice.     

On the number of views of polyhedral terrains

We show that the number of topologically different orthographic views of a polyhedral terrain withn edges isO(n ^5+ɛ ), and that the number of topologically different perspective views of such a terrain isO(n ^8+ɛ ), for any ɛ>0. Both bounds are almost tight in the worst case. The proofs are simple consequences of the recent almost-tight bounds of [11] on the complexity of lower envelopes in higher dimensions. Pankaj Agarwal has been supported by National Science Foundation Grant CCR-91-06514. Micha Sharir has been supported by National Science Foundation Grant CCR-91-22103, and by grants from the U.S.—Israeli Binational Science Foundation, the G.I.F.—the German Israeli Foundation for Scientific Research and Development- and the Fund for Basic Research administered by the Israeli Academy of Sciences.     

MASLOV-TYPE INDEX THEORY FOR SYMPLECTIC PATHS AND SPECTRAL FLOW （II）

1.IntroductionandMainResultsStartingfromthepioneeringworks[5,61ofH.AmannandE.Zehnderin1980,C.ConleyandE.Zehnderestablishedanindextheoryin1984intheircelebratedwork[if]fornondegeneratepathsinSp(Zn)startedfromtheidentitymatrixwithn22.Thisindextheorywasextendedtothenondegeneratecaseofn~1byE.Zehnderandthefirstauthorin[28]of1990.ThisindextheoryforthedegenerateHamiltoniansystemswasestablishedbythefirstauthorin[21]of1990andC.Viterboin[34]of1990viadifferentmethods,andthenextendedtoalldegenerates…     

On the value distribution of <Emphasis Type="Italic">ƒ</Emphasis> + <Emphasis Type="Italic">a</Emphasis>(<Emphasis Type="Italic">ƒ</Emphasis>′)<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

Let ƒ be a transcendental meromorphic function, a a nonzero finite complex number, and n ⩾ 2 a positive integer. Then ƒ + a(ƒ′) ⁿ assumes every complex value infinitely often. This answers a question of Ye for n = 2. A related normality criterion is also given. This work was supported by the National Natural Science Foundation of China (Grant No. 10771076), the Natural Science Foundation of Guangdong Province, China (Grant No. 07006700) and by the German-Israeli Foundation for Scientific Research and Development (Grant No. G-809-234.6/2003)     

Lip microbundles

In this paper, we mainly prove that everyn-dimensional Lip microbundle over a locally finite simplicial complex is micro-identical to a Lip-S ⁿ (R ⁿ)-bundle, and any two such are micro-identical, isomorphicS ⁿ (R ⁿ)-bundles.Project supported by the National Natural Science Foundation of China.     

Holomorphic 2-spheres in Grassmann manifolds

A generalized Frenet formula for holomorphic 2-spheresS ² in Grassmann manifoldsG(k,n) is introduced and a generalized Pliicker formula is achieved. By use of these formulae some pinching theorems for Gaussian curvature are obtained which generalize the corresponding results about holomorphic and minimalS ² inCP ^n-1. Einsteinian holomorphic subbundle of the trivial bundleS ² ×C ⁿ is investigated. Project supported partially by the National Natural Science Foundation of China, the Natural Science Foundation of Jiangxi Province and Doctoral Programmer Foundation of Institution High Education.     

On n-Contractive and n-Hypercontractive Operators, II

This paper studies the n-contractive and n-hypercontractive Hilbert space operators (n = 1, 2, . . .), classes weaker than, but related to, the class of subnormal operators. The k-hyponormal operators are the more thoroughly explored examples of classes weaker than subnormal; we show that k-hyponormality implies 2k-contractivity. Turning to weighted shifts, it is shown that if a weighted shift is extremal in the sense that the general nonnegativity test for n-contractivity is satisfied with equality to zero, then the shift is necessarily the unweighted unilateral shift. Also considered are the n-contractivity of back step extensions and perturbations of subnormal weighted shifts and some connections with the Berger measure of a subnormal shift. The second author was supported by the Korean Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-312-C00027). The third author was supported by the Korean Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF- 2007-359-C00005.     

A parallel algorithm for generating multiple ordering spanning trees in undirected weighted graphs

1.IntroductionLetG=(V,E,W)beaconnected,weightedandundirectedgraph,VeEE,w(e)(相似文献   

A Note on the Homology of Signed Posets

Let S be a signed poset in the sense of Reiner [4]. Fischer [2] defines the homology of S, in terms of a partial ordering P (S) associated to S, to be the homology of a certain subcomplex of the chain complex of P (S).In this paper we show that if P (S) is Cohen-Macaulay and S has rank n, then the homology of S vanishes for degrees outside the interval [n/2, n].Research partially supported by the National Science Foundation and the John Simon Guggenheim Foundation.