Vanishing viscosity solutions for conservation laws with regulated flux

In this paper we introduce a concept of “regulated function” $v(t,x)$ of two variables, which reduces to the classical definition when v is independent of t. We then consider a scalar conservation law of the form $u_t+F{(v(t,x),u)}_x=0$, where F is smooth and v is a regulated function, possibly discontinuous w.r.t. both t and x. By adding a small viscosity, one obtains a well posed parabolic equation. As the viscous term goes to zero, the uniqueness of the vanishing viscosity limit is proved, relying on comparison estimates for solutions to the corresponding Hamilton–Jacobi equation.As an application, we obtain the existence and uniqueness of solutions for a class of $2\times 2$ triangular systems of conservation laws with hyperbolic degeneracy.     

Uniformities of Fréchet-Nikodym Type on Vitali Spaces

Vitali spaces are a simultaneous generalization of Riesz spaces, Boolean rings, MV-algebras. We study uniformities on Vitali spaces which make lattice operations, partial sum and subtraction uniformly continuous, proving that every such uniformity is generated by its 0-neighbourhood system. This result is not true in general for lattice uniformities on lattices. As consequence we obtain general decomposition theorems for exhaustive and locally exhaustive group-valued measures and decompositions of Lebesgue and Hewitt-Yosida type.     

螺旋波激发甲烷等离子体光谱诊断

利用螺旋波激发等离子体化学气相沉积(LPP-CVD)技术,以甲烷和氦气为反应气体产生等离子体.通过采集到甲烷的可见光到紫外发射光谱,对甲烷等离子体进行原位诊断,发现存在CH、Ha及Hβ等碎片粒子的光辐射,同时,分析了不同入射功率、气压下CH粒子以及Hβ、Hγ的相对强度变化情况.结果表明:CH粒子的相对强度随着射频功率是先增大而后减小,随工作气压的增大而逐渐减小;随气压及功率的增加,Hβ、Hγ相对强度变化的总体趋势都是先增加而后减小的.     

Longitudinal vibrations of pre-twisted bars with “asymmetric” boundary conditions

Summary In a previous paper concerning the determination of angular frequencies of a twisted straigth bar of constant section, only three simple constraint conditions at the ends had been considered (free end, constrained end). In the present paper the other seven possible (asymmetric) constraint conditions are considered and the corresponding frequency equations are found. A final numerical example with several increasing twisting degrees shows the different influence of this increase upon the frequencies having axial or torsional origin.

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Sommario In un precedente lavoro le equazioni di equilibrio dinamico di un'asta svergolata soggetta a vibrazioni libere lungo il proprio asse erano state risolte in forma chiusa per tre sole condizioni di vincolo al contorno particolarmente semplici (estremità torsionalmente ed assialmente libere o incastrate). Nel presente lavoro vengono determinate le formule finali relative alle altre sette condizioni di vincolo che si ottengono imponendo in almeno una delle estremità dell'asta la rotazione libera e lo spostamento assiale impedito o viceversa. Viene anche svolto un esempio di calcolo numerico determinando in uno dei casi considerati il modo di variare delle prime pulsazioni proprie al crescere dello svergolamento dell'asta.