A mixed dominating set S of a graph G = (V; E) is a subset of vertices and edges like S  V [ E such that each element v 2 (V [ E) n S is adjacent or incident to at least one element in S. The mixed domination number m(G) of a graph G is the minimum cardinality among all mixed dominating sets in G. The problem of finding m(G) is known to be NP-complete. In this paper, we present an explicit polynomial-time algorithm using the parse tree to construct a mixed dominating set of size m(G) where G is a Generalized Series-Parallel graph.

In this paper, we discuss the usual stochastic, likelihood ratio, dispersive and convex transform order between two Parallel systems with independent heterogeneous extended Generalized exponential components. We also establish the usual stochastic order between Series systems from two independent heterogeneous extended Generalized exponential samples. Finally, we find lower and upper bounds for the Renyi entropy and cumulative residual entropy of Series and Parallel systems.

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This paper presents a novel topology of single-phase multilevel inverter for low and high power applications. It consists of polarity (Level) generation circuit and H Bridge. The proposed topology can produce higher output voltage levels by connecting DC voltage sources in Series and Parallel. The proposed topology utilizes minimum number of power electronic devices which helps in reduction of the cost, size, and weight. The proposed topology consumes low power therefore improves the efficiency of the converter. Switching pulses are generated using Phase disposition (PD) pulse width modulation technique. Finally the effectiveness of the proposed topology is verified using MATLAB/SIMULINK software tool. 7level asymmetrical multilevel inverter prototype hardware is prepared to support the proposed topology to verify the effectiveness and its validity.

In this work, we study various stochastic orderings of the smallest and largest order statistics arising from independent heterogeneous Generalized modified Weibull (GMW) random variables. We also conduct stochastic comparison on the extreme order statistics from GMW samples with Archimedean copulas. The results established in this paper strengthen and generalize those known in the Balakrishnan et al. (2018).

Fuzzy set based methods have been proved to be effective in handling many types of uncertainties in different fields, including reliability engineering. This paper presents a new approach on fuzzy reliability, based on the use of beta type distribution as membership function. Considering experts' ideas and by asking operators linguistic variables, a rule base is designed to determine the level of reliability of each component. Hence, we can determine the level of reliability of components with expending low costs. Also in this work a simple approach is presented for reducing the number of rules. The outputs of the presented model are fuzzy sets representing the reliability levels of components. In order to determine the level of reliability as linguistic variables, a new method is presented. Also the validity of the model is investigated by two methods. After determining the level of reliability of each component, the reliability of the composed system can be determined by using t-norm and s-norm functions. The system can be Parallel, Series, Parallel- Series or Series-Parallel. The presented model has been applied in a glass manufacturing company.