In this paper, borrowing the intuition in Rao et al. (2004), we introduce a cumulative version of the inaccuracy measure (CIM). Also we obtain interesting and applicable properties of CIM for different cases based on the residual, past and interval lifetime random variables. Relying on various applications of stochastic classes in reliability and information theory fields, we stu...

Using a probabilistic approach we establish new residual properties of the modular group PSL2(Z), and of more general free products. We prove that the modular group is residually in any infinite collection of finite simple groups not containing a Suzuki group Sz(q) or a 4dimensional symplectic group PSp4(q) with q a power of 2 or 3. This result is best possible, since the groups excluded are no...

Let M(Σ,P) be the mapping class group of a punctured oriented surface (Σ,P) (where P may be empty), and let Tp(Σ,P) be the kernel of the action of M(Σ,P) on H1(Σ \ P ,Fp). We prove that Tp(Σ,P) is residually p. In particular, this shows that M(Σ,P) is virtually residually p. For a group G we denote by Ip(G) the kernel of the natural action of Out(G) on H1(G,Fp). In order to achieve our theorem,...

We study the residual properties of geometric 3–manifold groups. In particular, we study conditions under which geometric 3–manifold groups are virtually residually p for a prime p, and conditions under which they are residually torsion–free nilpotent. We show that for every prime p, every geometric 3–manifold group is virtually residually p. We show that geometric 3– manifold groups are virtua...

Contour lines totally fix the structure of leftcontinuous t-norms. For each t-norm, these contour lines are determined by the corresponding residual implicator. Most properties involving residual implicators can now easily be translated into properties involving contour lines. As the portation law expresses associativity, we dispose of a powerful tool for constructing left-continuous t-norms. I...

the parallel systems are special important types of coherent structures and have many applications in various areas.in this paper we consider a two-exchangeable-component parallel system for the generalized farlie-gumbel-morgenstern (generalized fgm) distribution. we study the reliability properties of the residual lifetime of the system under the condition that both components of the system ar...

Direct metal SLS processes use a high power laser beam to selectively fuse fully metallic powder to directly produce functional metal components or tooling. As a thermal dynamic process, it inevitably causes thermal stresses, stress-induced deformations and cracking. Understanding these is very important in controlling residual stresses and stress-induced deformations. In this research, the res...