正线性方程组的半正解

通过引入正线性方程组Ax=b的可去变量,得到了没有可去变量的正线性方程组有无穷多个半正解情形的充分必要条件以及有惟一半正解情形的充分必要条件.     

拆边法求最短路径

本文利用局部比较法 ,在图中定义子图、无效路径、以及可去边 .利用推导的有关定理 ,拆去可去边 ,利用最短路径相同的等价性 ,达到化简图 ,从而求出最短路径     

Acridin-9-ylmethoxycarbonyl （Amoc）： A New Photochemically Removable Protecting Group for Alcohols

Synthesis and photochemistry of acridin-9-ylmethoxycarbonyl(Amoc)as a new photochemically removableprotecting group for alcohols were described.Three carbonates of alcohols 1—3 were synthesized throughcondensation of 9-hydroxymethylacridine and chloroformates of alcohols,including benzyl alcohol,phenethylalcohol and one galactose derivative.The photolysis of protected alcohols can efficiently release the correspondingalcohol in the efficiencies(Q_(u1)ε)of 100—200(quantum yield Q_(u1)=0.011—0.023,and molar absorptivity ε=9.1×10~3—9.8×10~3 mol~(-1)·L·cm~(-1))under 360 nm light.     

Removable sets for continuous solutions of quasilinear elliptic equations

We show that sets of Hausdorff measure zero are removable for -Hölder continuous solutions to quasilinear elliptic equations similar to the -Laplacian. The result is optimal. We also treat larger sets in terms of a growth condition. In particular, our results apply to quasiregular mappings.

     

Explicit Expressions for the Ruin Probabilities of Erlang Risk Processes with Pareto Individual Claim Distributions

In this paper we first consider a risk process in which claim inter-arrival times and the time untilthe first claim have an Erlang (2) distribution.An explicit solution is derived for the probability of ultimateruin,given an initial reserve of u when the claim size follows a Pareto distribution.Follow Ramsay,Laplacetransforms and exponential integrals are used to derive the solution,which involves a single integral of realvalued functions along the positive real line,and the integrand is not of an oscillating kind.Then we showthat the ultimate ruin probability can be expressed as the sum of expected values of functions of two differentGamma random variables.Finally,the results are extended to the Erlang(n) case.Numerical examples aregiven to illustrate the main results.     

Removable singularities of plurisubharmonic functions of restricted growth

LetG be a domain in ⁿ ,n2, letA be a connected complex (n–1)-dimensional submanifold ofG, and let be a plurisubharmonic function inGA. We obtain conditions on the growth of that guarantee the local boundedness of at a point a A G and the existence of a plurisubharmonic extension of toG.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 64–72, July, 1998.The author wishes to express her gratitude to Professor E. M. Chirka for numerous useful discussions and for his assistance in writing the present text.     

On removable cycles through every edge

Mader and Jackson independently proved that every 2‐connected simple graph G with minimum degree at least four has a removable cycle, that is, a cycle C such that G/E(C) is 2‐connected. This paper considers the problem of determining when every edge of a 2‐connected graph G, simple or not, can be guaranteed to lie in some removable cycle. The main result establishes that if every deletion of two edges from G remains 2‐connected, then, not only is every edge in a removable cycle but, for every two edges, there are edge‐disjoint removable cycles such that each contains one of the distinguished edges. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 155–164, 2003