Uncomplemented subspaces of Lorentz spaces

In the paper we construct a system of bounded functions which generates an uncomplemented subspace in the Lorentz space Λ(α) for all α∈(0,1). Lower bounds of the norms of the projector onto such subspaces are obtained. Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 57–65, July, 2000.     

Cycle embedding in star graphs with more conditional faulty edges

The star graph is one of the most attractive interconnection networks. The cycle embedding problem is widely discussed in many networks, and edge fault tolerance is an important issue for networks since edge failures may occur when a network is put into use. In this paper, we investigate the cycle embedding problem in star graphs with conditional faulty edges. We show that there exist fault-free cycles of all even lengths from 6 to n! in any n-dimensional star graph S_n (n ? 4) with ?3n − 10 faulty edges in which each node is incident with at least two fault-free edges. Our result not only improves the previously best known result where the number of tolerable faulty edges is up to 2n − 7, but also extends the result that there exists a fault-free Hamiltonian cycle under the same condition.     

Exact analytic solutions to the problem on plane buckling modes of rectangular orthotropic plates with free edges under biaxial loading

A two-dimensional linearized problem on plane buckling modes (BMs) of a rectangular plate with free edges, made of an elastic orthotropic material, underbiaxial tension-compression is considered. With the use of double trigonometric basis functions, displacement functions exactly satisfying all static boundary condition on plate edges are constructed. It is shown that the exact analytic solutions found describe only the pure shear BMs, and if the normal stress in one direction is assumed equal to zero, an analog of the solution given by the kinematic Timoshenko model can be obtained. Upon performing the limit passage to the zero harmonic in the displacement functions of one of the directions, the solution to the problem of biaxial compression can be obtained by equating the Poisson ratio to zero; in the case of uniaxial compression, this solution exactly agrees with that following from the classical Bernoulli-Euler model. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 149–170, March–April, 2007.     

应用小波边缘检测技术分析荧光寿命显微像

研究了小波图象边缘检测技术在荧光寿命显微像分析中的应用，利用小波分析的多尺度特性进行了荧光寿命显微像的边缘提取，结果表明，这种方法非常有效。     

Superorbital expansion tube tests of a caret waverider

A computational and experimental study was conducted to assess the potential of testing waverider configurations in a high-performance, short-duration expansion tube facility. The tests were performed in the newly commissioned X3 superorbital expansion tube and provide the first experimental data of a waverider tested at a stagnation enthalpy and equivalent flight speed exceeding 40 MJ/kg and 9 km/s, respectively. Two simple caret configurations were chosen as benchmark test cases to test the use of the facility, instrumentation and numerical models to investigate these flows. The general performance of the sharp and blunt leading edge waveriders at angles of attack ranging from 0° to 5° were analyzed and compared to CFD and theoretical predictions. For the conditions tested, the presence of a strong viscous interaction caused the shock wave to be detached from the leading edge of the models resulting in a significant loss in performance. An analytical model was developed to account for the strong coupling between the shock wave and boundary layer. Results were shown to be in very good agreement with CFD estimates for both configurations at all angles of attack considered. Finite-rate chemistry CFD simulations indicated that real gas effects other than the residual levels of nonequilibrium freestream dissociation present in the expansion tube flow were negligible for the conditions tested. The study also revealed that a past flow visualization technique gave a false indication of the leading edge shock location. An improved experimental visualization technique was successfully tested with results from these tests correlating well with computational estimates. This study successfully demonstrated the use of the facility to study waverider performance at speeds representative of orbital flight.      

Disjoint Paths in Decomposable Digraphs

The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].     

On an empty triangle with the maximum area in planar point sets

Let P be a finite set of points in general position in the plane. We evaluate the ratio between the maximum area of an empty triangle of P and the area of the convex hull of P.     

(Un)stable matchings with blocking costs

We introduce and study weighted bipartite matching problems under strict preferences where blocking edges can be paid for, thus imposing costs rather than constraints as in classical models. We focus on the setting in which the weight of an edge represents the benefit from including it in the matching and/or the cost if it is a blocking edge. We show that this setting encompasses interesting special cases that remain polynomially-solvable, although it becomes APX-hard even in a quite restricted case.     

On the Properties of Convex Multilayered Cyclofusene

Cyclofusene is a corona-condensed benzenoid whose graph-theoretic representation consists of hexacycles each having exactly two non-adjacent shared edges. Multilayered cyclofusene is a fused hexacylic system which can be partitioned into successive layers of cyclofusene. In such systems, an edge shared by two consecutive hexacycles in the same layer is termed radial. We present upper bounds for the number of radial π-bonds in a convex k-layered cyclofusene.     

度和与图中具有给定阶数的点不交的路

设G是一个n阶图，n=∑^ki=1ni，其中,ni≥2(i=1,2,…，k）是整数。我们利用度和给出图G中存在n1,n2，…，nk阶点不交路的充分条件。