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  • Author: Indranil Ghosh x
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Abstract

In the area of stress-strength models, there has been a large amount of work regarding the estimation of the reliability R=Pr(X<Y). The algebraic form for R=Pr(X<Y) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, forms of R are considered when (X,Y) follow bivariate distributions with dependence between X and Y. In particular, explicit expressions for R are derived when the joint distribution are dependent bivariate beta and bivariate Kumaraswamy. The calculations involve the use of special functions.

Abstract

In this paper a new probability density function with bounded domain is presented. This distribution arises from the Marshall–Olkin extended exponential distribution proposed by Marshall and Olkin (1997). It depends on two parameters and can be considered as an alternative to the classical beta and Kumaraswamy distributions. It presents the advantage of not including any additional parameter(s) or special function in its formulation. The new transformed model, called the unit-Marshall–Olkin extended exponential (UMOEE) distribution which exhibits decreasing, increasing and then bathtub shaped density while the hazard rate has increasing and bathtub shaped. Various properties of the distribution (including quantiles, ordinary moments, incomplete moments, conditional moments, moment generating function, conditional moment generating function, hazard rate function, mean residual lifetime, Rényi and δ-entropies, stress-strength reliability, order statistics and distributions of sums, difference, products and ratios) are derived. The method of maximum likelihood is used to estimate the model parameters. A simulation study is carried out to examine the bias, mean squared error and 95  asymptotic confidence intervals of the maximum likelihood estimators of the parameters. Finally, the potentiality of the model is studied using two real data sets. Further, a bivariate extension based on copula concept of the proposed model are developed and some properties of the distribution are derived. The paper is motivated by two applications to real data sets and we hope that this model will be able to attract wider applicability in survival and reliability.

Abstract

In this paper, we observe simple yet subtle interconnections among design theory, coding theory and cryptography. Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is nontrivial to find MDS matrices which could be used in lightweight cryptography. In the SAC 2004 paper [], Junod and Vaudenay considered bi-regular matrices which are useful objects to build MDS matrices. Bi-regular matrices are those matrices all of whose entries are nonzero and all of whose 2×2 submatrices are nonsingular. Therefore MDS matrices are bi-regular matrices, but the converse is not true. They proposed the constructions of efficient MDS matrices by studying the two major aspects of a d×d bi-regular matrix M, namely v1(M), i.e. the number of occurrences of 1 in M, and c1(M), i.e. the number of distinct elements in M other than 1. They calculated the maximum number of ones that can occur in a d×d bi-regular matrices, i.e. v1d,d for d up to 8, but with their approach, finding v1d,d for d9 seems difficult.

In this paper, we explore the connection between the maximum number of ones in bi-regular matrices and the incidence matrices of Balanced Incomplete Block Design (BIBD). In this paper, tools are developed to compute v1d,d for arbitrary d. Using these results, we construct a restrictive version of d×d bi-regular matrices, introducing by calling almost-bi-regular matrices, having v1d,d ones for d21. Since, the number of ones in any d×d MDS matrix cannot exceed the maximum number of ones in a d×d bi-regular matrix, our results provide an upper bound on the number of ones in any d×d MDS matrix.

We observe an interesting connection between Latin squares and bi-regular matrices and study the conditions under which a Latin square becomes a bi-regular matrix and finally construct MDS matrices from Latin squares. Also a lower bound of c1(M) is computed for d×d bi-regular matrices M such that v1(M)=v1d,d, where d=q2+q+1 and q is any prime power. Finally, d×d efficient MDS matrices are constructed for d up to 8 from bi-regular matrices having maximum number of ones and minimum number of other distinct elements for lightweight applications.

An n-hexane extract of fresh, mature leaves of Argemone mexicana (Papaveraceae), containing thin-layer epicuticular waxes, has been analysed for the first time by TLC, IR and GLC using standard hydrocarbons. Seventeen long-chain alkanes (n-C18 to n-C34) were identified and quantified. Nonacosane (n-C29) was established as the n-alkane with the highest amount, whilst octadecane (n-C18) was the least abundant component of the extracted wax fraction. The carbon preference index (CPI) calculated for the hydrocarbon sample with the chain lengths between C18 and C34 was 1.2469, showing an odd to even carbon number predominance.

Abstract

Background: Prevention of surgical site infection and wound dehiscence are imperative and also challenging in clinical practice. This study examines the healing response of laparotomy wounds following application of silver nanoparticles.

Materials and Methods: Dermal fibroblasts were exposed to incremential doses of silver nanoparticles and its effect on collagen synthesis and cytotoxicity was assessed. Laparotomy surgery was performed on rabbits and the operation site was treated topically either with silver nanoparticle once, or once daily for 14 days or with vehicle. Healing response and local tissue reaction was evaluated clinically by histopathology and scanning electron microscopy (SEM); microbial load on the operation site was assessed. Clinical tests and histopathology were performed to assess systemic toxicity.

Results: Silver nanoparticles increased collagen expression from dermal fibroblasts and longer time exposure increased caspase 3 expression and produced cyotoxic effect with an IC50 of 0.16 mg/mL. Daily treatment of operation sites resulted in increased collagen deposition and improved wound healing, microbial load was reduced. Although a sub dermal edema was evident in histopathology, SEM showed normal architecture of cells with infiltration of lymphocytes. There was no systemic toxicity.

Conclusions: Silver nanoparticles exhibit a positive influence on wound healing but its effect on local tissue remains a concern.

Abstract

We introduce a new family of univariate continuous distributions called the Marshall–Olkin transmuted-G family which extends the transmuted-G family pioneered by Shaw and Buckley (2007). Special models for the new family are provided. Some of its mathematical properties including quantile measure, explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of two applications to real data sets.