Line graphs of multigraphs and Hamilton‐connectedness of claw‐free graphs

We introduce a closure concept that turns a claw‐free graph into the line graph of a multigraph while preserving its (non‐)Hamilton‐connectedness. As an application, we show that every 7‐connected claw‐free graph is Hamilton‐connected, and we show that the well‐known conjecture by Matthews and Sumner (every 4‐connected claw‐free graph is hamiltonian) is equivalent with the statement that every 4‐connected claw‐free graph is Hamilton‐connected. Finally, we show a natural way to avoid the non‐uniqueness of a preimage of a line graph of a multigraph, and we prove that the closure operation is, in a sense, best possible. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:152‐173, 2011     

Stock portfolio selection using aspiration level-oriented procedure: real case on the RM-SYSTEM Czech stock exchange

Central European Journal of Operations Research - Many approaches have been designed to solve a stock portfolio selection problem. The aim of this paper is to provide a complex supporting tool for...     

Norms of embeddings of logarithmic Bessel potential spaces

Let be a subset of with finite volume, let and let be a Young function with for large . We show that the norm on the Orlicz space is equivalent to

We also obtain estimates of the norms of the embeddings of certain logarithmic Bessel potential spaces in which are sharp in their dependences on provided that is large enough.

     

Improved boolean formulas for the Ramsey graphs

In the theory of the random graphs, there are properties of graphs such that almost all graphs satisfy the property, but there is no effective way to find examples of such graphs. By the well-known results of Razborov, for some of these properties, e.g., some Ramsey property, there are Boolean formulas in ACC representing the graphs satisfying the property and having exponential number of vertices with respect to the number of variables of the formula. Razborov's proof is based on a probabilistic distribution on formulas of n variables of size approximately nd² log d, where d is a polynomial in n, and depth 3 in the basis { ∧, ⊕} with the following property: The restriction of the formula randomly chosen from the distribution to any subset A of the Boolean cube {0, 1}ⁿ of size at most d has almost uniform distribution on the functions A → {0, 1}. We show a modified probabilistic distribution on Boolean formulas which is defined on formulas of size at most nd log² d and has the same property of the restrictions to sets of size at most d as the original one. This allows us to obtain formulas the complexity of which is a polynomial of a smaller degree in n than in Razborov's paper while the represented graphs satisfy the same properties.     

Determination of hydrochloric acid in organic solutions by gas chromatography

Summary A method is described for the determination of small quantities of hydrochloric acid in two chlorinated organic solvents (CHCl₃ and CCl₄). An excess of gaseous ethylene oxide is added to a liquid sample; the 2-chloroethanol formed is then analyzed by gas chromatography. The procedure is simpler and more sensitive in comparison with other conventional methods. It can be modified for other organic solvents.D.G.R.C.S.T. grant.     

Photostabilizing activity of sterically hindered piperidines—II: Radical trapping ability

The abilities of both 2,2,6,6-tetramethylpiperidine (I) and its nitroxyl (II) to trap radicals involved in hydrocarbon photo-oxidations have been studied in cumene and 1,3,5-trimethylcyclohexane at 27° using AIBN, hydroperoxide and dialkylperoxide as initiators: the light was either the band 300–400 nm or 366 nm. Under conditions of photolysis of ROOH (degenerate branching), I is oxidized to II. II is capable of trapping R' radicals, the rate constant being ～50 times lower than that for RO^.₂ formation. RO^.₂ radicals react with neither I nor II. Under the condition of degenerate branching, II is capable of intercepting the radical fragments from decomposing hydroperoxide. The rate constant of this process is ～500 times higher than that for hydrogen abstraction by these fragments. A reaction mechanism is suggested: hydrogen bonded associates formed between an N-containing stabilizer and ROOH play a dominant role. The principal intermediates in this mechanism are represented by >NO^., >NOH and >NOR species.     

On the complexity of paths avoiding forbidden pairs

Given a graph G=(V,E), two fixed vertices s,t∈V and a set F of pairs of vertices (called forbidden pairs), the problem of a path avoiding forbidden pairs is to find a path from s to t that contains at most one vertex from each pair in F. The problem is known to be NP-complete in general and a few restricted versions of the problem are known to be in P. We study the complexity of the problem for directed acyclic graphs with respect to the structure of the forbidden pairs.We write x?y if and only if there exists a path from x to y and we assume, without loss of generality, that for every forbidden pair (x,y)∈F we have x?y. The forbidden pairs have a halving structure if no two pairs (u,v),(x,y)∈F satisfy v?x or v=x and they have a hierarchical structure if no two pairs (u,v),(x,y)∈F satisfy u?x?v?y. We show that the PAFP problem is NP-hard even if the forbidden pairs have the halving structure and we provide a surprisingly simple and efficient algorithm for the PAFP problem with the hierarchical structure.     

Splitting schemes for hyperbolic heat conduction equation

Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of heat fluxes. In this case, the mathematical model is based on a hyperbolic equation of second order or a system of equations for the temperature and heat fluxes. In this paper we construct for the hyperbolic heat conduction equation the additive schemes of splitting with respect to directions. Unconditional stability of locally one-dimensional splitting schemes is established. New splitting schemes are proposed and studied for a system of equations written in terms of the temperature and heat fluxes.     

Local projection stabilization for advection–diffusion–reaction problems: One-level vs. two-level approach

Local projection stabilization (LPS) of finite element methods is a new technique for the numerical solution of transport-dominated problems. The main aim of this paper is a critical discussion and comparison of the one- and two-level approaches to LPS for the linear advection–diffusion–reaction problem. Moreover, the paper contains several other novel contributions to the theory of LPS. In particular, we derive an error estimate showing not only the usual error dependence on the mesh width but also on the polynomial degree of the finite element space. Based on this error estimate, we propose a definition of the stabilization parameter depending on the data of the solved problem. Unlike other papers on LPS methods, we observe that the consistency error may deteriorate the convergence order. Finally, we explain the relation between the LPS method and residual-based stabilization techniques for simplicial finite elements.