Global Existence of Smooth Solutions for Partially Dissipative Hyperbolic Systems with a Convex Entropy

We consider the Cauchy problem for a general one-dimensional n×n hyperbolic symmetrizable system of balance laws. It is well known that, in many physical examples, for instance for the isentropic Euler system with damping, the dissipation due to the source term may prevent the shock formation, at least for smooth and small initial data. Our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions, and possibly to investigate their asymptotic behavior. For systems which are entropy dissipative, a quite natural generalization of the Kawashima condition for hyperbolic-parabolic systems can be given. In this paper, we first propose a general framework for this kind of problem, by using the so-called entropy variables. Then we go on to prove some general statements about the global existence of smooth solutions, under different sets of conditions. In particular, the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension. Our main tools will be some refined energy estimates and the use of a suitable version of the Kawashima condition.     

GENERALIZATION OF STEINER FORMULAFOR THE HOMOTHETIC MOTIONS ONTHE PLANAR KINEMATICS

The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.     

Trimethylsilylcyanid als Umpolungsreagens,VI. Anionische 1,4- O→C-Silylgruppen-Umlagerung

Trimethylsilyl Cyanide — A Reagent for Umpolung, VI. Anionic 1,4-O→C-Silyl Group Rearrangement The adducts 6 from substituted acroleins 5a – f and trimethylsilyl cyanide form the anions 6 _A on deprotonation at −78°C, which are silylated by trimethylsilyl chloride to 7 or (and) 8 in positions 3 or (and) 1. On warming up to room temperature, 6a _A and 6b _A undergo smoothly 1,4-O→C-silyl group rearrangements to form 13a _A and 13b _A which can be trapped by silylation. 6c – d _A decompose on warming up. Triethylsilyl instead of trimethylsilyl groups decelerate the rearrangement appreciably. Structure and configuration of the different products are determined.     

A facile access to α-phenylselenenyl carbonyl compounds by electrochemical oxidation

A novel α-phenylselenenylation of carbonyl compounds has been performed by electrolysis of a solution of ketones, diphenyl diselenide, tetraethylammonium bromide, and magnesium bromide in polar solvents (MeOH, AcOH, MeCN). The electrolysis enables us to prepare the desired seleno-carbonyl compounds without employing strong bases and the activated selenenyl reagents PhSeX.     

Action du N-bromosuccinimide sur les dioxolannes en série bicyclo [2.2.1 ]heptanique. Limitation des transpositions de wagner-meerwein

Vicinal benzoyloxy-trans-bicyclo [2.2.1] heptanic bromhydrins, otherwise difficult to obtain are formed from N-bromosuccinimide and norbornanes bearing a 2-aryl-1,3 dioxolane skeleton. The greater stability of the intermediate dioxolenium ion reduces the tendency towards both Wagner-Meerwein rearrangement and neighbouring group participation by chlorine, processes usually observed when a less stable intermediate is involved. Nevertheless, methoxycarbonyl neighbouring group participation and Wagner Meerwein rearrangment occur in methoxycarbonylbicyclo [2.2.1]heptane and in a bornanic compound respectively.     

Reduction des oxydes de phosphines par le systeme Cp2TiCl2-Mg

Phosphine oxides with at least one aryl-P bond are reduced into the corresponding phosphines by stoechiometric amounts of Mg-Cp₂TiCl₂ in boiling THF.     

Unexpected formation of rearrangement and fragmentation products during the thermal activation of pyrazolino diazepines

Ionic and radical mechanistic steps are postulated in order to explain the formation of the rearrangement-, the isomerization- and the fragmentation-products isolated during the thermal treatment of pyrazolo-diazepines.     

淬火处理对原位TiCp／Fe复合材料组织及耐磨性的影响

研究了淬火处理对原位ＴｉＣｐ／Ｆｅ复合材料组织和耐磨性的影响。结果表明,复合材料经淬火处理后,其基体组织转变为马氏体,且进一步析出了一定量的细小ＴｉＣ颗粒,这种组织变化使复合材料的冲击韧性下降,但其硬度和耐磨性均显著提高,且其耐磨性是高铬白口铸铁的１．３倍,用扫描电镜和能谱观察分析发现,在淬火复合材料的磨损表面上,ＴｉＣ颗粒未剥落,因而能继续起抑制磨料磨损的作用。     

Multilevel graph partitioning: an evolutionary approach

The graph partitioning problem is defined as that of dividing the vertices of an undirected graph into a set of balanced parts through the removal of a set of edges, whose size is to be minimized. A number of researchers have investigated multilevel schemes, which coarsen the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partitioning of the original graph. In this paper, a genetic algorithm for the coarsening phase of a multilevel scheme for graph partitioning is presented. The proposed approach has been demonstrated to improve the solution quality at the expense of running time.     

Locating Active Sensors on Traffic Networks

Sensors are used to monitor traffic in networks. For example, in transportation networks, they may be used to measure traffic volumes on given arcs and paths of the network. This paper refers to an active sensor when it reads identifications of vehicles, including their routes in the network, that the vehicles actively provide when they use the network. On the other hand, the conventional inductance loop detectors are passive sensors that mostly count vehicles at points in a network to obtain traffic volumes (e.g., vehicles per hour) on a lane or road of the network.This paper introduces a new set of network location problems that determine where to locate active sensors in order to monitor or manage particular classes of identified traffic streams. In particular, it focuses on the development of two generic locational decision models for active sensors, which seek to answer these questions: (1) “How many and where should such sensors be located to obtain sufficient information on flow volumes on specified paths?”, and (2) “Given that the traffic management planners have already located count detectors on some network arcs, how many and where should active sensors be located to get the maximum information on flow volumes on specified paths?”The problem is formulated and analyzed for three different scenarios depending on whether there are already count detectors on arcs and if so, whether all the arcs or a fraction of them have them. Location of an active sensor results in a set of linear equations in path flow variables, whose solution provide the path flows. The general problem, which is related to the set-covering problem, is shown to be NP-Hard, but special cases are devised, where an arc may carry only two routes, that are shown to be polynomially solvable. New graph theoretic models and theorems are obtained for the latter cases, including the introduction of the generalized edge-covering by nodes problem on the path intersection graph for these special cases. An exact algorithm for the special cases and an approximate one for the general case are presented.