The Distribution Search:An O(n) Expected Time Search

Provided an algorithm for the distribution search and proves the time complexity of the algorithm. This algorithm uses a mathematical formula to search n elements in the sequence of n elements in O(n)expected time,and experimental reesult proves that distribution search is superior to binary search.

A Note on the Expectation Value of Time

In this note, the expectation value of time based on quantum mechanics formalism is derived. It is found that the expectation value of time does not depend on space.

Statistical analysis of generalized exponential distribution under progressive censoring with binomial removals

The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.

A statistical inference for generalized Rayleigh model under Type-Ⅱ progressive censoring with binomial removals

This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.

Convergence Analysis of Cuckoo Search by Creating Markov Chain

Cuckoo search(CS) has been used successfully for solving global optimization problems.From a theoretical point of view,the convergence of the CS is an important issue.In this paper,convergence analysis of CS was studied.The transition probability characteristics of the population to construct a Markov chain were analyzed.The homogeneity of the Markov chain was derived based on stochastic process theory.Then it was proved to be an absorbing state Markov chain.Consequently,the global convergence of CS was deduced based on conditions of convergence sequence and total probability formula,and the expected convergence time was given.Finally,a series of experiments were conducted.Experimental results were analyzed and it is observed that CS seems to perform better than PSO.

Degradation of Polymer &Elastomer Exposed to Chlorinated Water—A Review

In water industry, the chlorine is mostly used as a disinfectant agent. The chlorine present in potable water as a disinfectant has been reported to reduce the lifetime of contact polymeric material. This occurs in polymer pipes and it is now very common in plumbing and other parts of the drinking water distribution system. For more than 50 years, Polymer & Elastomeric materials have been used ubiquitously in drinking water distribution systems. Polymer & Elastomeric materials have successfully been used in a variety of applications ranging from rubber gaskets, to valves, to hydrants, to fittings. Polymer & Elastomers that degrade more quickly than expected create service problems, make it difficult for utilities to cost efficient plan preventive maintenance programs, and negatively affect customer relations. This review paper gives an insight idea to a reader about the selection of proper polymer & elastomer and predicting its performance in chlorinated water. Also the mechanism of degradation of Polymer & elastomer in chlorine environment and some model of life expectancy of in-service of Polymer & elastomer in various conditions and parameter in chlorinated water were discussed.

On a Flexible Loan Repayment Method Depending on Borrower's Asset with an Early Termination Clause

Aiming at the problem that the asset’s fluctuation influences the borrower’s repayment ability,a loan with a new and flexible repayment method is designed,which depends on the asset value of the borrower.The repayment method can reduce the loan default probability,but it causes the uncertainty of the pay off time.Because the repayment term is related to the regular repayment amount in this method,a boundary for the regular repayment amount is set up in order to avoid too long repayment term.This will balance the benefit of borrowers and lenders and improve the applicability of this method.By establishing a mathematical model of the residual value of the loan,this model can be transformed into an initial-boundary problem of a partial differential equation.The analytic solution and the expected time to pay off the loan are obtained.Finally,numerical analysis are shown.

Balancing Frequencies and Fault Detection in the In-Parameter-Order Algorithm

The In-Parameter-Order （IPO） algorithm is a widely used strategy for the construction of software test suites for combinatorial testing （CT） whose goal is to reveal faults triggered by interactions among parameters. Variants of IPO have been shown to produce test suites within reasonable amounts of time that are often not much larger than the smallest test suites known. When an entire test suite is executed, all faults that arise from t-way interactions for some fixed t are surely found. However, when tests are executed one at a time, it is desirable to detect a fault as early as possible so that it can be repaired. The basic IPO strategies of horizontal and vertical growth address test suite size, but not the early detection of faults. In this paper, the growth strategies in IPO are modified to attempt to evenly distribute the values of each parameter across the tests. Together with a reordering strategy that we add, this modification to IPO improves the rate of fault detection dramatically （improved by 31% on average）. Moreover, our modifications always reduce generation time （2 times faster on average） and in some eases also reduce test suite size.