PARAMETERS OF DARBOUX TRANSFORMATION FOR REDUCED AKNS, KAUP-NEWELL AND PCF SYSTEMS

51.IntroductionDarbouxtransformationisapowerfulmethodtogetexplicitsollltionsofnonlinearPDEs.In1 1dimensions,itgivesauniversalalgorithmtogetaseriesofsolutionsbysolvinglinearODEsonlyonce.TheconstructionsofDarbouxtransformationshavebeenwidelyinvestigated(see,e.g.[1,3,5,7,8,9,10,11,13]).In1 1dimensions,aDarbouxtransformationisusuallygivenbyaDarbouxmatrixwhichisapolynomialofthespectralparameter.ThemostfundamentalDarbouxmatrixisaDarbouxmatrixofdegreeone,whichislinearinthespectralparameter.Letg…     

WEIGHTED HILBERT TRANSFORM AND BαMETRIC

ItiswelLknownthatthesimplestsingularintegraliswheretheintegralisunderstoodasCauchyprincipalvalue-TheaboveintegraloperatorHisregardedasHilberttransformation.Itisafundamentalissueinharmonicanalysistodiscusstheboundednessofthiskindofintegraloperatorinvariousfunctionspaces.In1915,itwasLusinwhofirstprovedthatiffEL2,thenHfeL2.In1927,M.meszgeneralizedLusin'sresultandobtainedthefollowingfamou8theorem.Theorem1IffEL.,withpsatisfies1相似文献   

RQI DYNAMICS FOR NON-NORMAL MATRICES WITHREAL EIGENVALUES

1.IntroductionAswellknown,RQI(RayleighQuotientiteration)isapracticalalgorithmforeigen-valueproblemsofsymmetricmatrices.In1974,B.N.ParlettprovedthatthesequencegeneratedbyRQIalwaysconvergestoaneigenvectorforalmostallofinitialvectorsifthematrixinquestionisanormalone.NamelythesetofvectorsinR",forwhichRQIdiverges,hajszeromeasure.Nevertheless,healsopointedouttheconvergelitspeedbeingcubicone[1].In1989,S.BarttsonandJ.SmillieconsideredRQIforsymmetricmatrixagain.Theydiscoveredthatthedynamicsof…     

ON INTERACTION OF SHOCK AND SOUND WAVE (Ⅰ)

1.IntroductionRecentlythestudyofdiscontinuoussolutionforthesystemofconservationlawsinhigherdimensionalspacehasbeenconsiderablydeveloped.In[1,W12]thelocalekistenceof8olutionforsuclisystemwithdiscontinuityinvolvingsingleshock,rarefactionwaveorsoundwav(gradientwave)hasbeenestablished.In[2Jand[14]theproblemsoninteractionoftwoshocksorinteractionofweaksingularitiesarealsoconsidered.Itisnaturaltoaskwhatabouttheresultwhenashockisinteractedbyawavewitliweakersillgularities,particularly,forthenbynsystem…     

PERSISTENCE OF POPULATIONS FOR A PREDATOR-PREY SYSTEM IN A POLLUTED ENVIRONMENT

1IntroductionTheinfluenceoftoxicantsonthepersistenceandextinctionofpopulationsinapollutedenvironmentisveryimportant.In1983,T.C.Hallametal.firstproposedadeterministicmodeltostudythetoxiceffectsonpopulationgrowth[fi.In1986,T.G.HallamandZ.Maproposedtheconceptofpersistenceinthemeanofpopulations[2],anewmethodtodeterminethethresholdsbetweenpersistenceandextinctionofpopulationsofnonautonomousmodelshasbeenprovidedintheirpaper.Thethresholdsbetweenpersistenceandextinctionforsomemodelshavebeenobtaine…     

GEOMETRIC CONSTRUCTION OF ASSOCIATION SCHEMES FROM NON-DEGENERATE QUADRICS

1. IntroductionThe geometry of quadrics in finite-dimensional projective spaces has been studiedby E.J.F. Primrose[1], D.K. Ray-ChaudhUxi[','] and I.M. Chakravarti[4]. In 1993, 1.M.Chakravartils] derived some association schemes from nondegenerate and degenerate Hermitian varieties. In [6], we constructed association schemes from the set of isotropic points inpseudthsymplectic spaces. In this paper) we will construct three-class association schemesfrom nolldegenerate quadrics.Let Fi be …     

Fibre of Toric Map and Solving Affine Polynomial System

In[1],B.Sturmfelsdiscussedthecomputationaltheoryoftoricvariety.In[2],I.M.GelfanddiscussedsystematicallythetheoryofsolvingLaurentpolynomialsystemintorus(C*)n,C*=C\{0}.Butinmostapplyingcases,moreimportantthingisdoinginaffinespaceCn.Results,wehavebefore...     

The Pointwise Characterizations of Fuzzy Ideals and Fuzzy Prime Ideals

TheconceptofthefuzzysubgroupsintroducedinRosenfeld[l],wasappliedtogeneralizesomeofthebasicconceptsofalgebra.In[2,3,4]LuWangjindefinedfuzzysubringsandfuzzyideals,introducedtheoperationsonfuzzyidea1s.In[5]theautherdiscussedaboutthenatureoffuzzysubringsbythenestedsubring.Butthepointwisedefinitionsoffuzzysubgroupsandfuzzysubringsarerare.Inthispaper,theautherprogramsanddiscussesthefuzzysubrings,fuzzyidealsandfuzzyprimeidealsbyfuzzyPoints..5l.PreliminariesLetusrecallsomeconceptsoccurrjnginthe[2,3…     

L—fuzzy群（Ⅱ）

This paper is a continuation of [1].In paper[1],the concept of LF group was introduced.In this paper,the concept of OP homomorphism will be introduced and its properties will be discussed.     

具有极大乘积的型理想阵列空间的结构和循环模性质

设I1，…，In是有限域上双周期理想，称它们具有极大乘积，如果本文决定了具有极大乘积的型理想I1，…；In的结构，并证明了乘积空间G(I1*…*In）是循环模.     

Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization

We present a numerical study of the long time behavior of approximation solution to the Extended Fisher–Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system. Furthermore, we obtain the long-time stability and convergence of the difference scheme and the upper semicontinuity $d(\mathcal{A}_{h,τ} ,\mathcal{A}) → 0$. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.     

Vanishing of the third simplicial cohomology group of

We show that . We first use the Connes-Tzygan exact sequence to prove that this is equivalent to the vanishing of the third cyclic cohomology group , where is the non-unital Banach algebra , and then prove that .

     

关于余挠三元组的余星子范畴和余倾斜子范畴

设$\mathcal{A}$ 是一个Abel范畴,且 $(\mathcal{X}, \mathcal{Z},\mathcal{Y})$ 是一个完全遗传余挠三元组.介绍 $\mathcal{A}$ 的 $n$-$\mathcal{Y}$-余倾斜子范畴的定义,并给出 $n$-$\mathcal{Y}$-余倾斜子范畴的一个刻画,类似于 $n$-余倾斜模的 Bazzoni 刻画.作为应用,证明了在一个几乎 Gorenstein 环 $R$ 上, 如果 $\mathcal{GP}$ 是 $n$-$\mathcal{GI}$-余倾斜的, 那么 $R$ 是一个 $n$-Gorenstein 环, 其中 $\mathcal{GP}$ 表示 Gorenstein 投射 $R$-模组成的子范畴且 $\mathcal{GI}$ 表示 Gorenstein 内射 $R$-模组成的子范畴. 进而, 研究 任意环$R$上的$n$-余星子范畴, 以及关于余挠三元组 $(\mathcal{P}, R$-Mod, $\mathcal{I})$ 的 $n$-$\mathcal{I}$-子范畴与 $n$-余星子范畴之间的关系, 其中 $\mathcal{P}$ 表示投射左 $R$-模组成的子范畴且 $\mathcal{I}$ 表示内射左 $R$-模组成的子范畴.     

与截面相关的Morrey空间与奇异积分

In this paper, we define the Morrey spaces M_F~(p,q) (Rn) and the Campanato spaces E_F~(p,q) (R~n) associated with a family F of sections and a doubling measure μ, where F is closely related to the Monge-Amp`ere equation. Furthermore, we obtain the boundedness of the Hardy-Littlewood maximal function associated to F, Monge-Amp`ere singular integral operators and fractional integrals on M_F~(p,q)(R~n). We also prove that the Morrey spaces M_F~(p,q) (R~n)and the Campanato spaces E_F~(p,q) (R~n) are equivalent with 1 ≤ q ≤ p ∞.     

On Proximal Relations in Transformation Semigroups Arising from Generalized Shifts

For a finite discrete topological space $X$ with at least two elements, a nonempty set $\Gamma$, and a map $\varphi:\Gamma \to \Gamma$, $\sigma_{\varphi}:X^{\Gamma} \to X^{\Gamma}$with $\sigma_{\varphi}((x_{\alpha})_{\alpha \in \Gamma})=(x_{\varphi(\alpha)})_{\alpha \in \Gamma}$ (for $(x_{\alpha})_{\alpha \in \Gamma} \in X^{\Gamma}$) is a generalized shift. In this text for $\mathcal{S} = \{\sigma_{\varphi}:\varphi \in \Gamma^{\Gamma}\}$ and $\mathcal{H}=\{\sigma_{\varphi}:\Gamma \xrightarrow{\varphi} \Gamma$ is bijective$\}$ we study proximal relations of transformation semigroups $(\mathcal{S}, X^{\Gamma})$ and $(\mathcal{H}, X^{\Gamma})$. Regarding proximal relation we prove: $$P(\mathcal{S}, X^{\Gamma}) = \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \exists \beta \in \Gamma (x_{\beta} = y_{\beta})\}$$and $P(\mathcal{H}, X^{\Gamma} ) \subseteq \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \{\beta \in \Gamma : x_{\beta} = y_{\beta}\}$ is infinite$\}$ $\cup\{($ $x,x) : x \in \mathcal{X}\}$. Moreover, for infinite $\Gamma$, both transformation semigroups $(\mathcal{S}, X^{\Gamma})$ and $(\mathcal{H}, X^{\Gamma})$ are regionally proximal, i.e., $Q(\mathcal{S}, X^{\Gamma}) = Q(\mathcal{H}, X^{\Gamma} ) = X^{\Gamma} \times X^{\Gamma}$, also for sydetically proximal relation we have $L(\mathcal{H}, X^{\Gamma}) = \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \{\gamma ∈ \Gamma :$ $x_{\gamma} \neq y_{\gamma}\}$ is finite$\}$.     

On the boundedness of the non-centered Gaussian Hardy-Littlewood maximal function

The purpose of this paper is to prove the boundedness, for 1$">, of the non-centered Hardy-Littlewood maximal operator associated with the Gaussian measure .

     

Schur–Weyl Theory for C*‐algebras

To each irreducible infinite dimensional representation $(\pi ,\mathcal {H})$ of a C*‐algebra $\mathcal {A}$, we associate a collection of irreducible norm‐continuous unitary representations $\pi _{\lambda }^\mathcal {A}$ of its unitary group ${\rm U}(\mathcal {A})$, whose equivalence classes are parameterized by highest weights in the same way as the irreducible bounded unitary representations of the group ${\rm U}_\infty (\mathcal {H}) = {\rm U}(\mathcal {H}) \cap (\mathbf {1} + K(\mathcal {H}))$ are. These are precisely the representations arising in the decomposition of the tensor products $\mathcal {H}^{\otimes n} \otimes (\mathcal {H}^*)^{\otimes m}$ under ${\rm U}(\mathcal {A})$. We show that these representations can be realized by sections of holomorphic line bundles over homogeneous Kähler manifolds on which ${\rm U}(\mathcal {A})$ acts transitively and that the corresponding norm‐closed momentum sets $I_{\pi _\lambda ^\mathcal {A}}^{\bf n} \subseteq {\mathfrak u}(\mathcal {A})^{\prime }$ distinguish inequivalent representations of this type.     

Boundedness of the Cesàro Operator in Hardy Spaces

The Ces\aro operator $\mathcal{C}_{\alpha}$ is defined by \begin{equation*} (\mathcal{C}_{\alpha}f)(x) = \int_{0}^{1}t^{-1}f\left( t^{-1}x \right)\alpha (1-t)^{\alpha -1}\,dt~, \end{equation*} where $f$ denotes a function on $\mathbb{R}$. We prove that $\mathcal{C}_{\alpha}$, $\alpha >0$, is a bounded operator in the Hardy space $H^{p}$ for every $0 < p \leqq 1$.     

A Connection Between the Logarithmic Capacity and the Sequence of the Analytical Function

Let E be a bounded closed set, d(E) be the logarithmic capacity of E. If A is any bounded set, then $[d(A) = \mathop {\sup }\limits_{E \in A} d(E)\]$ For each $Z_0 \in E$, and $\delta >0$, let $[\Delta = \Delta _{{Z_0}}^\delta = CE \cap (|Z - {Z_0}| < \delta )\]$ where CE is complement of E, then \Delta is an open set. By [{\bar \Delta ^0}\] we denote the interior of the closure A of A. Clearly,$\Delta \subset [{\bar \Delta ^0}\]$ and $d(\Delta) \leq d([{\bar \Delta ^0}\])$, and there exists an open set D such that d(D) 0, the equation $d(\Delta)=d([{\bar \Delta ^0}\])$ holds.     

On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors

A class of structured multi-linear system defined by strong $\mathcal{M}_z$-tensors is considered. We prove that the multi-linear system with strong $\mathcal{M}_z$-tensors always has a nonnegative solution under certain condition by the fixed point theory. We also prove that the zero solution is the only solution of the homogeneous multi-linear system for some structured tensors, such as strong $\mathcal{M}$-tensors, $\mathcal{H}^+$-tensors, strictly diagonally dominant tensors with positive diagonal elements. Numerical examples are presented to illustrate our theoretical results.