A (2 + )-Approximation Scheme for Minimum Domination on Circle Graphs

The main result of this paper is a (2 + )-approximation scheme for the minimum dominating set problem on circle graphs. We first present an O(n²) time 8-approximation algorithm for this problem and then extend it to an time (2 + )-approximation scheme for this problem. Here n and m are the number of vertices and the number of edges of the circle graph. We then present simple modifications to this algorithm that yield (3 + )-approximation schemes for the minimum connected and the minimum total dominating set problems on circle graphs. Keil (1993, Discrete Appl. Math.42, 51–63) shows that these problems are NP-complete for circle graphs and leaves open the problem of devising approximation algorithms for them. These are the first O(1)-approximation algorithms for domination problems on circle graphs.     

Periodic solutions of second order nonlinear difference equations with discrete -Laplacian

We use Brouwer degree to prove existence and multiplicity results for the periodic solutions of some nonlinear second order difference equations involving discrete -Laplacian. We obtain in particular upper and lower solutions theorems, Ambrosetti–Prodi type multiplicity results, sharp existence conditions for nonlinearities which are bounded from below or from above and necessary and sufficient conditions for the existence of positive periodic solutions when the nonlinearity is singular at 0.     

Existence and multiplicity results for some nonlinear problems with singular -Laplacian

Using Leray–Schauder degree theory we obtain various existence and multiplicity results for nonlinear boundary value problems

where l(u,u^′)=0 denotes the Dirichlet, periodic or Neumann boundary conditions on [0,T], is an increasing homeomorphism, (0)=0. The Dirichlet problem is always solvable. For Neumann or periodic boundary conditions, we obtain in particular existence conditions for nonlinearities which satisfy some sign conditions, upper and lower solutions theorems, Ambrosetti–Prodi type results. We prove Lazer–Solimini type results for singular nonlinearities and periodic boundary conditions.     

A (2+)-approximation algorithm for the generalized preemptive open shop problem with minsum objective

In this paper we consider a generalized version of the classical preemptive open shop problem with sum of weighted job completion times objective. The main result is a (2+)-approximation algorithm for this problem. In the last section we also discuss the possibility of improving our algorithm.     

Finite element analysis of an A– method for time-dependent Maxwell’s equations based on explicit-magnetic-field scheme

In this paper, error analysis of a finite element A– method for the time-dependent Maxwell’s equations is presented. An explicit-magnetic-field scheme is applied. Provided that the time-stepsize τ is sufficiently small, the proposed algorithm yields for finite time T an error of in the L²-norm for the electric field E and the magnetic field H, where h is the mesh size.     

Disjoint spine phenomena in certain contractible n-manifolds (n5)

If M is a compact PL manifold with boundary containing a subpolyhedron K in its interior, then K is said to be a PL spine of M provided M collapses to K (MK). Guilbault [Topology 34 (1) (1995) 99–108] has shown that certain nontrivial contractible manifolds possess disjoint spines. His results stem from a standing conjecture regarding disjoint spines in contractible 4-manifolds constructed by Mazur. More to the point, there is a dimensional requirement introduced by his techniques; Guilbault produces such manifolds in dimensions n9. We shall provide techniques which allow the construction of examples in dimensions n5 following the path laid out by Guilbault. The new techniques will provide a slight strengthening of some other Guilbault results as well.     

Weak stability of the Ishikawa iteration procedures for -hemicontractions and accretive operators

Let X be an arbitrary Banach space, K be a nonempty closed convex subset of X, and T : K → K be a Lipschitzian and hemicontractive mapping with the property lim inf_t→∞((t)/t) > 0. It is shown that the Ishikawa iteration procedures are weakly T-stable. As consequences, several related results deal with the weak stability of these procedures for the iteration proximation of solutions of nonlinear equations involving accretive operators. Our results improve and extend those corresponding results announced by Osilike.     

关于“T21／2LF拓扑空间和ST21／2LF拓扑空间的分离性”的一点注记

通过一个例子说明在[3]中定理2．2的证明中用到的一个结论是错误的，并给出该定理的一种正确证明。     

Isomorphism classes of elliptic and hyperelliptic curves over finite fields

We give the number and representatives of isomorphism classes of hyperelliptic curves of genus g defined over finite fields , g=1,2,3. These results have applications to hyperelliptic curve cryptography.     

正规弱空间的无限Tychonoff积

本文证明(1)如果X=∏σ∈∑Xσ是|Σ|-仿紧空间,则X是正规弱(-θ)-可加空间当且仅当 F∈[∑]＜ω,∏σ∈FXσ是正规弱(-θ)-可加空间.(2)设X=∏i∈ωXi是可数仿紧的,则下列三条等价X是正规弱(-θ)-可加的; F∈[ω]＜ω,∏i∈FXi是正规弱(-θ)-可加的; n∈ω,∏i≤nXi是正规弱(-θ)-可加的.     

-symmetry for (r,s)-hypergeometric series

Contiguous operators for a two-parameter analogue of hypergeometric series are constructed. These represent a two-parameter quantum enveloping algebra introduced by Takeuchi.     

The nature of quantum space-time and the Cantorian proposal

We point out that in the non-commutativity and breakdown of conventional space-time at micro scales lies the seed to the unification of gravitation and electromagnetism.     

String matching in quantum time

We show how to determine whether a given pattern p of length m occurs in a given text t of length n in time (where allows for logarithmic factors in m and n/m) with inverse polynomial failure probability. This algorithm combines quantum searching algorithms with a technique from parallel string matching, called Deterministic Sampling.     

环的左（N，U）－凝聚维数

设R和S是环，U是平坦右R-模，V是平坦右S-模．本中我们证明了(N，(U，V))-lc．dim(R S)=sup((N，U)-lc．dimR，(N，V)-lc．dimS)．     

Cn单位球上的向量值D函数

讨论了Cn单位球上的向量值Dpμ,q函数, 利用Banach空间几何学的方法,推广了标量值Dpμ,q函数的结果.