We prove that if t 7→ u(t) ∈ BV(R) is the entropy solution to a N × N strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields ut + f(u)x = 0, then up to a countable set of times {tn}n∈N the function u(t) is in SBV, i.e. its distributional derivative ux is a measure with no Cantorian part. The proof is based on the decomposition of ux(t) into waves belongin...

investigation of reliability characteristics under fuzzy environments is proposed in this paper. fuzzy weibull distribution and lifetimes of components are using it described. formulas of a fuzzy reliability function, fuzzy hazard function and their α-cut set are presented. furthermore, the fuzzy functions of series systems and parallel systems are discussed, respectively. finally, some numeric...

Investigation of reliability characteristics under fuzzy environments is proposed in this paper. Fuzzy Weibull distribution and lifetimes of components are using it described. Formulas of a fuzzy reliability function, fuzzy hazard function and their α-cut set are presented. Furthermore, the fuzzy functions of series systems and parallel systems are discussed, respectively. Finally, some num...

this paper presents a multi-objective formulation for optimal siting and sizing of distributed generation (dg) resources in distribution systems in order to minimize the cost of power losses and energy not supplied. the implemented technique is based on a genetic algorithm (ga) and weight method that employed to obtain the best compromise between these costs. simulation results on 33-bus distri...

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