Removable ears of 1-extendable graphs

<正> Carvalho,Lucchesi and Murty proved that any 1-extendable graph G different from K_2and C_(2n)has at least Δ(G)edge-disjoint removable ears,and any brick G distinct from K_4 and■hasat least Δ(G)-2 removable edges,where Δ(G)denotes the maximum degree of G.In this paper,weimprove the lower bounds for numbers of removable ears and removable edges of 1-extendable graphs.It is proved that any 1-extendable graph G different from K_2 and C_(2n)has at least χ′(G)edge-disjointremovable ears,and any brick G distinct from K_4 and■has at least χ′(G)-2 removable edges,whereχ′(G)denotes the edge-chromatic number of G.     

A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence

1.INTRODUCTION Considerthefollowingdelaydifferentialequations(DDEs)y′(x)=f(x,y(x),y(x-τ(x))),a≤x≤b y(x)=φ(x),xmin≤x≤a(1)wherey,f,φaren vectorfunctions,φ(x)isinitial valuefunction,τ(x)≥0isdelayfunction.Definition1DDEs(1)issingularatthepoint xαifthelagsatisfiesτ(xα)=0.Ifthereisnosuch pointxα∈[a,b],thentheDDEs(1)isnon singular.InthenumericalsolutionofDDEs(1)byacon tinuousexplicitRunge Kuttamethod,wesuppose thatwehaveanapproximationyntoy(x)atxnand wishtocomputeanapproxima…     

A Note on the Tu-Deng Conjecture

Abstract Let k be a positive integer.For any positive integer x=∑∞i=0x i2i,where x i=0,1,we define the weight w(x)of x by w(x):=∑∞i=0x i.For any integer t with 0t2k-1,let S t:={(a,b)∈Z2|a+b≡t(mod 2k-1),w(a)+w(b)k,0≤a,b≤2k-2}.This paper gives explicit formulas for cardinality of S t in the cases of w(t)≤3 and an upper bound for cardinality of S t when w(t)=4.From this one then concludes that a conjecture proposed by Tu and Deng in 2011 is true if w(t)≤4.     

ASYMPTOTIC EXPANSION AND ASYMPTOTIC BEHAVIOR OF THE SOLUTION FOR THE TIME-DEPENDENT NEUTRON TRANSPORT PROBLEM IN A SLAB WITH GENERALIZED BOUNDARY CONDITIONS

In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary nonhomogeneous medium possibly with cavity,withthe anisotropic scattering and fission,and with continuous energy varying from null to any finiteconstant or from one positive constant to another positive constant.We prove that the correspon-ding neutron transport operator A has finite Spectrum points in any strip {λ|β_1≤R(?)λ≤β_2}whereβ_2>β1>-λ~*(λ~* is the essential infimum of v∑(x,v)),and obtain the asymptotic expansion ofthe time-dependent solution which exists and is unique.Furthermore,we give the existence ofthe dominant eigenvalue and indicate the asymptotic behavior of the neutron density as t→+∞.     

Lax-Friedrichs Difference Approximations to Isentropic Equations of Gas Dynamics

We are concerned with I.V.P for the isentropic equations of gas dynamics(?) (1)(ρ,u)|_(t=0)=(ρ_0(x),u_0(x)), (2)where ρ=(ρ~r)/r,2相似文献   

A PRIOR ESTIMATE AND EXISTENCE OF POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATION WITH THE THIRD BOUNDARY VALUE PROBLEM

1 IntroductionLet n be a bounded open domain with boundary aa, n c R", N 3 2. We consider a priorestimate and ekistence of positive solution of the fOllowing equationsWhere operatorL conforms to the Sum Ru1es, that is: for a repeated i or j, it mean to sum them up from 1 toN, ai;(x), ai(x), a(x) are bounded measurable in a. FOr operator L, we alWays assume: thereealst positive constants po and U1) such thatf(u) is a nonlinear function which grows in the form of Up with p 2 1, n is the out…     

STATISTICAL INFERENCE FOR CONTAMINATION DISTRIBUTION

1 IntroductionThe generaJ model of contamination distribution can be described as follOwing. Let 0 相似文献   

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

This paper considers the Rosenau equation with a moving control?t u + ?_t?_x~4 u + ?_xu + u?x u = a(x + ct)h(x, t), c = 0, x ∈ T = R/(2πZ), t 0.The authors prove that the Rosenau equation with a moving control is locally exact controllable in Hs(T) with s ≥ 0 and globally exponential stable in H~s(T) with s ≥ 2. The two results nontrivially extend the work of(Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.     

LOWER BOUNDS OF RAMSEY NUMBERS

The lower bounds for any R(l_1,…,l_q;r)are investigated.Let K_n~r be the completer-uniform hypergraph on n points.Define R(l_1,…,l_q;r)as the minimal natural number n sothat if the edges of K_n~r are q-colored,there is a set S of l_i(i∈{1,…,q})vertices such that alledges on S are of the i-th color.For the special case of q=r=2,the lower bounds were got byP.Erd(?)s and J.Spencer.In this paper,we shall give the lower bounds for any R(l_1,…,l_q;r).     

STRONG CONSISTENCY OF THE PERIODIC SMOOTHING SPLINES

Consider the regression model Y_i=u(x_i)+ε_i,i=1,2,…,n,where u(x)∈W_(2,per)~2[0,1],x_i=(i-1)/n,{ε_i}(?)are i.i.d,random variables.We use the periodic smoothing spline u_(λp)(x)toestimate u(x).Under certain conditions,strong consistency results of u_(λp)(x)are obtained,i.e.,forall 0相似文献   

ON A NONLINEAR DEGENERATE PARABOLIC EQUATION

1.IntroductionInthispaperwedealwiththeexistenceofweaksolutionsofnonlineardegenerateparabolicinitial-boundaryvalueproblemonthespaceX=LP(0,T,V)whereQ~ax(0,T),V=Wb'~(~,n)whichisaweightedSobolevspace(seeSection2).Thedegenerationisdeterminedbyavectorfunctionv(x)(yi(x),yi(x),''9VN(x))withpositivecomponentsyi(x)inasatisfyingcertainintegrabilityassumptions.Nondegenerateparabolicequationsindivergentformhavebeenconsideredbyseveralauthorse.g.F.E.Browderll],R.Landes[2].Parabolicfunctionaldifferen…     

Global Convergence of the Conjugate Descent Method Under a kind of Inexact Line Search Conditions

1　 IntroductionWe consider the unconstrained optimizatoin problem( P) :minf( x) ,x∈ Rnwhere f:Rn→R is continuously differentiable and its gradient f( x) is denoted by g( x) .The conjugate gradient method is useful for calculating local unconstrained optimizationproblem of differentiable functions of many variables,it has the following form:xk 1 =xk λkdk ( 1 .1 )dk=-gk,k =1-gk βkdk- 1 ,k 2 ( 1 .2 )whereλk is a step-size obtained by a line search,andβk is a parameter,which can beobtaine…     

A ROBUST SQP METHOD BASED ON A SMOOTHING APPROXIMATE PENALTY FUNCTION FOR INEQUALITY CONSTRAINED OPTIMIZATION

1 IntroductionConsider the following inequality constrained optiInization problem:Inin f(x)xeRn(1)s.t. g(x) 5 0where f: R1'-R, g: R"-Rm are cofltinuousIy differentiable functions.SQP method for soIving problem(1) is to gellerate a sequence {xk} converging…     

SOME INITIAL-OBLIQUE DERIVATIVE BOUNDARY VALUE PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS WITH UNBOUNDED COEFFICIENTS

1 IntroductionThis paper is concerned with the a priori estimates and the ekistence of solutions of theinitiaLoblique derivative boundary value problem for quasilinear non-divergence parabolic equa-tions as follows:where O is a bounded domain in R"(N > 2) with smooth boundary 0a e C' ', QT =[o,T) x a be the parabolic domain in H" ,, ST = [o,T) x aa is the lateral boundary, andarQT is the parabolic boundary of QT' The repeated indices means summatiOns from 1 to N.In [11, the first bounda…     

SKIES AND MONADS

In ~*R_+,we define(↑↓)~-equivalence similar to that given by Puritzfor ~*N,and callthe(↑↓)~-equivalence classes skies.For x∈~*R_+,let μ(x)be the monad of x defined by Watten-Wattenberg,and let(?)(x)=sup{|y-z|/y,z∈μ(x)}∈~*R.Then it is proved that x↑↓y iff(?)(x)=(?)(y).Furthermore,sup{y/y↑↓x}=(?)(x)~(-1),and (?)(x)~2=(?)(x).     

ON THE BOUNDARY STABILIZATION OF WAVE EQUATION WITH VARIABLE COEFFICIENT

1.IntroductionLetfibeaboundedopendomaininR"(n22)withsmoothboundaryr,u~u(s)betheoutwordnormalofrats.GivenavectorxoER",denotem(x)gx--xo(x6R"),Rgsup{lm(x)fjxCfi}.SetLndsupposer nrAI~0.Weconsiderthefollowingwaveequationonfiwithboundaryfeedback:whereK=(m'u)k,L…     

ASYMPTOTIC STABILITY OF SOLUTION TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR SCALAR VISCOUS CONSERVATION LAWS CORRESPONDING TO RAREFACTION WAVES

1.IntroductionWeconsidertheinitial-boundaryvalueproblem(IBVP)forscalarviscousconservationlaw(ut f(u).=uxx,xE(0, co)=R ,t>0,o,(n \--9,ifI~9,f~M(IBVP){u(0't)=u~(t)-1~i---t:7),[u(x,0)=u000={=:0)f:LO .,wheref"(u)>0foralluunderconsideration,andu--u (1.1),andu~(t)~u~EL'(R ),U'(t)EL'(R ).(1.2)Undercondition(1.l)or(l.l)',thecorrespondingRiemannproblem{;;ot:<:>;i,>=x{,:3'f:,:(13)yieldstherarefaCtionwavesolution(u~)x5f'(u~)t,r"(X,t)=17j,)~1(…     

A NOTE ON THE SPECTRUM OF NEUTRON TRANSPORT OPERATOR IN A SLAB WITH GENERALIZED BOUNDARY CONDITIONS

The spectrum of neutron transport operator A in an arbitrary non-homogeneous slab geometry is discussed in consideration of anisotropic scatteringand fission.Under the assumptions that the boundary reflection coefficient func-tion α(v,μ),γ(v,μ)and the scattering-fission kernel k(x,v,v′,μ,μ′)are boundedmeasurable,and the total collision frequency v∑(x,v)is square integrable,it isshown that A has at most finite spectrum points in any strip{λ=β+i(?)|β_1(?)β(?)β_2},where β_2>β_1>-λ~*,with λ~* the essential infimum of v∑(x,v).Fi-nally,the asymptotic expansion of the solution for the time-dependent equation(dN)/(dt)=AN,N(0)=N_0 is given as a corollary.     

AN ALGORITHM FOR CONTINUOUS TYPE OPTIMAL SPHERICAL FACILITY LOCATION PROBLEM

1.IntroductionLetabeasmoothcurvedsurfaceonthe3-dimellsiollalsphereS={x6R3;IIxll=1},where11.ifisthe2-norm.Itsareacanbefound.LetW(u)beapositivecontinuousfunctioninQ.Letcos--'(.)denotethegeodesicdistanceorgreatcircledistance.Wewanttofindapoilltx*ESsuchthatf(X*)=alejj.W(U)COS~'(U"X)du.Thisiscalledthecontinuoustypeoptimalsphericalfacilitylocationproblem(P).ThecontinuouslysphericalfacilitylocationproblemisageneralizationoftheplanarEuclideancontinuousfacilitylocationproblem,andanedensionofth…     

ON ISOTOPY CLASSIFICATION OF EMBEDDINGS OF n-MANIFOLDS IN 2n-MANIFOLDS

Let M be a compact n-manifold without boundary, U a 2n-manifold andf: M→U a map. Under the condition that f_*: π_1(M)→π(U) is surjective and thatker f_* contains no elements represented by orentation-reversing loops, we calculate the set[M U]_f=π_1(U~M, E, f) where E is the space of embeddings of M into U which arehomotopic to f.