A Linear Hyperbolic System with Stiff Source Terms

We consider the behavior of solutions to the system ut ＋vx =0, vt ＋ux =（au-v）/τ as the relaxation parameter τ approaches 0. If the sub characteristic condition｜a｜ is satisfied, then u approaches a solution to the equilibrium equation ut ＋ aux = 0 and v approaches au. If this condition is violated then solutions have not Fourier transformation when τ→0.     

Integrability near the boundary of the Poisson integral of some singular measures

We consider the Poisson integral u = P＊μ on the half-space R＋^N＋1 （ N 〉 1 ） （or on the unit ball of the complex plane） of some singular measureμ. If μ is an s-measure （0 〈 s 〈 N）, then some sharp estimates of the integration of the harmonic function u near the boundary are given. In particular, we show that fpr p〉1,∫R^Nu^p（x,y）dx- y^-τ （y〉0,τ =（N-s）（p-1） ） （Given for p〉1, RN f 〉 0 and g 〉 0, ＂ f-g ＂ will mean that there exist constants C1 and C2, such that C1f ≤ g ≤ CEf ）.     

Chaos in the sense of Li-Yorke and the order of the inverse limit space

Let I= [0,1] and ω0 be the first limit ordinal number. Assume that f: I→I is continuous , piece-wise monotone and the set of periods of f is { 2': i∈ {0} ∪ N}. It is known that the order of (I, f) is ω0 or ω0 + 1. It is shown that the order of the inverse limit space (I, f) is ω0 (resp. ω0 + 1) if and only if f is not (resp. is) chaotic in the sense of Li-Yorke.     

A local asymptotic behavior for ruin probability in the renewal risk model

Let R（t）=u＋ct-∑ I=1^N（t） Xi,t≥0 be the renewal risk model, with Fx（x）being the distribution function of the claim amount X. Let ψ（u） be the ruin probability with initial surplus u. Under the condition of Fx（x） ∈ S^＊（γ）,y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ（u,u ＋ z] for every 0 （ z （ oo, On one hand, the asymptotic behavior of ψ（u） can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.     

Correlation between the standard formation enthalpy and the path index of pyridine-derivatives

A formulated as △fH _m ^◯ (PPDs,g)=a+Σb_iP_i + c_if_i is put forward for estimating standard formation enthalpies of pyridine-derivatives (PDDs), in which,P _i is path index andc _i f _i is an amended term of interaction between substituent and N atom on pyridine ring. The Calculations based on the model were carried out for some pyridine-derivatives. The values of standard formation enthalpy calculated are consistent with those in literature. Foundation item: Supported by the National Natural Science Foundation of China (29971024) Biography: LI Liang-chao (1958-), male, Associate professor, Research direction: calculating chemistry.     

Global and non-global solutions to some chemotaxis model

The paper is concerned with some chemotaxis model ∂u/∂t=D▿(u▿ln(u/w))+u(a−bu),∂w/∂t=f(u,w). To study the behavior of the solution, some function transformations are introduced, and the main tool is sup-sub-solution method. The result shows that, whether the solution blows up in finite time depends on the parameters and the initial data. As the chemical substance w has linear growth, f(u,w)=βu−δw, where β>0, δ>0 and a+δ>0, wherein the solution exists globally. However, as w possesses exponential growth, f(u,w)=(βu−δ)w, wherein both u and w share the same blowup point and time if the solution blows up in finite time. Biography: CHEN Hua(1956–), male, Professor, Ph. D., research direction: partial differential equation and its application.     

Existence of single-peaked solution of a semilinear elliptic problem

We discussed the Dirichlet problem of semilinear elliptic equationin (Pβ,α)D;-β△u=uε+εu,u>0,in Ω u=0, on(e),Ω where Ω(∪)RN(N≥4) is smooth and bounded domain,P=N+2/N-2,β,ε>0. We have proved that there exist positive ε0 and ε1 , such that when 0≤ε≤ε0,β>√ε1,(P0,1)has a single-peaked solution uβ, furthermore, |▽μβ|-0in the sense of measure as ε→0 and β→0.     

A Note on the Multifractal Decomposition of Directed Graph Self Similar Sets

We investigated the directed graph self similar sets under some weak overlapping condition. We get the multifractal decomposition formulas for these sets, i. e.,dim Ku^a DimKu^a =f(a), where fis the multifractal spectral function of the directed graph self similar measure. Especially, the results improve that of Edgar and Mauldin to the case which allows certain overlapping.     

Generalized Galerkin approximations for pseudoinverses and operator equations of the first kind

0 IntroductionLeqtuiliHnebaer afo rHimlbaenrtd sap baoceun.dLeedtlianaenardfufnbceti oan baolu onndeHd ,serse--spectively. Our goal is to seekv∈Hsuchthata(u,v) =f(u) , u∈ H (1)As a rule, we call the expression (1) a variational equationandva solutiontothis equation.By virtue of the Riesz repre-sentationtheorem,there exists a uniquely determined boundedlinear operatorA:H→Hsuchthata(u,v) =〈u,Av〉, u,v∈ H,where〈·,·〉is the inner product onH.If the sesquilinearformais also with posit…     

Nonlinear version of Holub’s theorem and its application

Holub proved that any bounded linear operator T or -T defined on Banach space L 1(μ) satisfies Daugavet equation1+‖T‖=Max{‖I+T‖, ‖I-T‖}.Holub's theorem is generalized to the nonlinear case: any nonlinear Lipschitz operator f defined on Banach space l 1 satisfies1+L(f)=Max{L(I+f), L(I-f)},where L(f) is the Lipschitz constant of f. The generalized Holub theorem has important applications in characterizing the invertibility of nonlinear operator.     

Non-linear elliptic equations on fractal domain

We consider the following non-linear elliptic equation △u＋ f（x,u）=0,x∈K on fractal domains with zero-Dirichlet boundary conditions, where K is self-similar fractal, △ is the Laplacian defined on K. f（x, t） is asymptotically linear as t→ ∞. We get the non-trivial and non-negative solution by using Mountain Pass lemma.     

Blowup rate of positive solution of a semilinear parabolic system

It is dealt with positive solutions to the systems: u-t-u- XX =v+p, v-t-v XX =u+q in Ω×(0, T) subject to either initial conditions or boundary_value conditions. The exact blowup rate estimates of solution are established under some monotonicity assumptions on the initial values.     

A Large Deviation Principle for the Risk Process with Varying Premium

Let u ∈ R ,for any ω 〉 0, the processes X^ε = {X^ε（t）; 0 ≤ t≤ 1} are governed by the following random evolution equations dX^ε（t）= b（X^ε（t）,v（t））dt-εdSt/ε, where S={St; 0≤t≤1} is a compound Poisson process, the process v={v（t）; 0≤t≤1} is independent of S and takes values in R^m. We derive the large deviation principle for{（X^ε,v（.））; ε〉0} when ε↓0 by approximation method and contraction principle, which will be meaningful for us to find out the path property for the risk process of this type.     

具p-Laplacian非线性奇异边值系统正解的存在性

研究了下面带有p-Laplacian算子的非线性奇异边值系统:(ф_p(u'_i))'+a_i(t)f_i(u₁,u₂)=0, 0＜t＜1,α_iф_p(u_i(0))-β_iф_p(u'_i(0))=0, γ_iф_p(u_i(1))+δ_iф_p(u'_i(1))=0,(i=1,2)正解的存在性。其中ф_p(s)为p-Laplacian 算子，即ф_p(s)=|s|^p-2s, p>1, (ф_p)^-1=ф_q,1/p+1/q=1, α_i＞0, β_i≥0, γ_i＞0, δ_i≥0, i=1,2.这里f_{i是下半连续函数(i=1,2). 通过使用锥上的不动点定理,在相当弱的条件下, 获得了这类奇异边值系统正解的存在性.}     

Influence of Characteristics on Bending Strength of Layered Steel Fiber Reinforced Concrete

The influence of two main characteristics of steel fiber, the aspect ratio （Df） and volume fraction （ρf）, on the bending strength of Layered Steel Fiber Reinforced Concrete （LSFRC） is investigated by using orthogonal test. Via the variance analysis on the experimental results and trend analysis on the two characteristics, Df is found significantly related to the bending strength of LSFRC. The influence ratio is 63.3%. The bending strength of LSFRC increases if Df increases, makes better when Df reaches 100. ρf has ordinary influence on the bending strength of LSFRC. The influence ratio is 29.2%. Other characteristics, such as the shape of steel fiber and the mix proportion, have less influence. The best ρf contributing to the bending strength of LSFRC is 1.5 %. If ρf is greater than 1.5%, it has negative influence on the bending strength of LSFRC. So, ρf makes a limited contribution to the bending strength of LSFRC.     

Additive characters and orthogonal systems of polynomials in several indeterminates over residue class rings

Letm, n andk be positive integers, m> 1 andk≤ n. Let ‰ _m =‰m‰ denote the residue class ring modulom. Let ‰ _m denote the group of additive characters of ‰ _m denote the identity of ‰ _m . A necessary and sufficient condition for the systemf ₁,...,f _k ∈ ‰ _m [x ₁, ...,x _m ] to be orthogonal is given: for all additive characters ψ₁, ..., ψ _k ∈ ‰ _m with ψ_i,≠x₀ forsomei, . As corollaries, the result of Shiue-Sun-Zhang and the result of Sun are obtained.     

Preparation by a rheological phase reaction method and thermal decomposition reaction mechanism of nickelous salicylate tetrahydrate

0　IntroductionInrecentyears,studiesonBinghamfluid ,suchasElec trorheologicalfluid ,areactivelypursued[1 6] .Rheologicaltechniqueshavebeenplayinganimportantroleinsyntheticchem istry .Therheologicalphasereactionmethodisthe processofpreparingcompoundsormaterialsfromasolid liquidrheologicalmixture.Thatis,thesolidreactantsarefullymixedinapropermolarratio ,andmadeupbyaproperamountofwaterorothersolventstoaBinghambodyinwhichthesolidparticlesandliquidsubstanceareuniformlydistributed ,sothattheprodu…     

B-Valued Dyadic Derivative

The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K （n∈N） is an approximate identity.     

Tree decomposition

A tree decomposition of graph G=(V, E) is referred to as a partition of edge set E into edge-disjoint trees. Given (not necessarily distinct) vertices u-1, u-2...u-k∈V with k≥2, a sufficient and necessary condition is given for a connected graph G=(V,E) to have a tree decomposition {T-1, T-2...T-k} such that V(T-i)=V{u-i}, i=1,2,... k.     

Julia sets of the random iteration systems and its subsystems

Suppose that P=(p\-1, p\-2, ..., p\-M)\% is a probability vector with p\-i>0 and Y={1, 2, ..., M}. Let (Y, 2\+Y, μ) be a probability space with μ(i)=p\-i, i=1, 2, ..., M, and (∑\-M, B, m)= Π \+∞\-0(Y, 2\+U, μ). It is shown that for any a \%(0≤a ≤1) \%, there exists a set U∈B such that m(U)=a and the Julia set associated with U is equal to the Julia set associated with ∑\-M\%. Moreover repelling fixed points with respect to U are dense in the Julia set associated with U.