Crack behavior in a welded polyolefin pipe

A three-dimensional model of a pressured polymer pipe with a weld is created in order to estimate the stress intensity factor for a crack located inside the weld. A comparison with values obtained for an edge-cracked tension specimen, usually employed for an experimental determination of weld properties, is performed. The difference between the stress intensity factor in a homogeneous pipe and the results taking into account the changes in material properties inside the weld is presented. A conservative and easily applicable relationship for calculating the stress intensity factor in a pipe weld is proposed.     

Heat transfer enhancement for boundary layer flow over a wedge by the use of electric fields

The effect of an electric field is investigated for heat transfer properties in a laminar, incompressible, non-isothermal boundary layer gas flow over a wedge. The governing boundary layer equations are reduced to an ordinary differential equation system using similarity transformations. The reduced equations are solved numerically for different values of electric and flow field parameters characterizing the ratio of electric force to fluid inertia force, Joule heating and ion kinetic work. For specific electric field function forms, leading to similarity solutions, velocity boundary layers are observed to become thinner and heat transfer properties are shown to be enhanced near the wall. The level of enhancement is controlled by the electric body force with additional effects of Joule heating and ion kinetic work on the bulk flow. The effects of low and high Prandtl numbers are also demonstrated. Heat transfer enhancement is observed to increase with increasing Prandtl number.     

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     

On constructing total orders and solving vector optimization problems with total orders

In this paper, we introduce a construction method of total ordering cone on \mathbbRⁿ{\mathbb{R}^n} . It is shown that any total ordering cone on \mathbbRⁿ{\mathbb{R}^n} is isomorphic to the cone \mathbbRⁿ_lex{\mathbb{R}^n_{lex}} . Existence of a total ordering cone that contain given cone with a compact base is shown. By using this cone, a solving method of vector and set valued optimization problems is presented.     

A cyclic scheduling problem with an undetermined number of parallel identical processors

This paper presents two integer linear programming (ILP) models for cyclic scheduling of tasks with unit/general processing time. Our work is motivated by digital signal processing (DSP) applications on FPGAs (Field-Programmable Gate Arrays)—hardware architectures hosting several sets of identical arithmetic units. These hardware units can be formalized as dedicated sets of parallel identical processors. We propose a method to find an optimal periodic schedule of DSP algorithms on such architectures where the number of available arithmetic units must be determined by the scheduling algorithm with respect to the capacity of the FPGA circuit. The emphasis is put on the efficiency of the ILP models. We show the advantages of our models in comparison with common ILP models on benchmarks and randomly generated instances.     

Tetramers Cu4(μ4-O)(η-X)6(L4): Analysis of structural data

This review summarizes structural parameters for forty five Cu₄(μ₄-O)(η-X)₆(L₄) tetramers. There are four types of structurally equal core units, CuCl₃ON, CuCl₃OO, CuCl₃OCl and CuBr₃ON. There are also tetramers which contain structurally unequal core units: CuCl₃ON (x2) and CuCl₂BrON (x2); CuCl₃ON (x1), CuCl₂BrON (x2) and CuCl₃OCl (x1). There is a tendency for an elongated Cu?Cu separation as well as Cu–L bond distances with increase of the covalent radius of the coordinating atom(s). Tetrahedral distortion around oxygen atom (OCu₄) increases in the order: 1.67° (CuCl₃OCl) < 2.10° (CuCl₃ON) < 2.11° (CuCl₃OO′) < 2.27° (CuBr₃ON). The mean Cu–Cl–Cu bridge angle of 80.5° is about 4.0° more open than that of a Cu–Br–Cu (76.5°). The cluster Cu₁₆O₄Br₇Cl₁₇(4-Mepy)₁₆ (4-Mepy = 4-methylpyridine) contains four crystallographically independent tetramers: Cu₄OBrCl₅(4-Mepy)₄ (1), Cu₄OBrCl₅(4-Mepy)₄ (2) Cu₄OBr₂Cl₄(4-Mepy)₄ (3) and Cu₄OBr₃Cl₃(4-Mepy)₄ (4), which is a unique example of stereoisomerism. There are other examples which exist in two isomeric forms. Another contains two or even four crystallographically independent tetramers within the same crystal, differing mostly by degree of distortion and is an examples of distortion isomerism. Pairs of Cu₄OCl₆(n-Meim)₄ (n-Meim = n-methylimidazole) (n = 1 or 2) are examples of ligand isomerism.     

Copper‐Catalyzed Bis(methoxycarbonyl)carbene Reactions of α,β‐Unsaturated Carboxamides

The [Cu(acac)₂]‐catalyzed reactions of α,β‐unsaturated carboxamides with dimethyl diazomalonate yielded dihydrofuran derivatives by a 1,5‐electrocyclic reaction at C(β), and butadiene derivatives by carbene addition reaction at C(α) (Schemes 4 and 5; Table). Phenyl substituents at the N‐atom of the amides seem to be effective on the reaction pathways (Table).