In this paper, asymptotic stability of zero solution of a kind of delay singular system is investigated. Based on the delayed-decomposition approach, two new results are obtained on the asymptotic stability of the considered system by using of some well-known inequalities and Lyapunov- Krasovskiĭ functionals (LKFs). Finally, two examples with numerical simulation are given to illustrate effectiveness of the proposed method by MATLAB-Simulink.

Classification, boundedness, and existence of solutions of a second order nonlinear difference equation are investigated. First, it is proved that all solutions are eventually monotone. Then, the necessary and sufficient conditions for the boundedness of all solutions are established. Finally, the existence of different types of monotonic solutions are presented. The obtained results have extended and improved some existing ones.

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models. This paper considers mixture of Topp-Leone distributions under classical and Bayesian perspective based on complete sample. The new distribution which exhibits decreasing and upside down bathtub shaped density while the distribution has the ability to model lifetime data with decreasing, increasing and upside down bathtub shaped failure rates. We derive several properties of the new distribution such as moments, moment generating function, conditional moment, mean deviation, Bonferroni and Lorenz curves and the order statistics of the proposed distribution. Moreover, we estimate the parameters of the model by using frequentist and Bayesian approaches. For Bayesian analysis, five loss functions, namely the squared error loss function (SELF), weighted squared error loss function (WSELF), modified squared error loss function (MSELF), precautionary loss function (PLF), and K-loss function (KLF) and uniform as well as gamma priors are considered to obtain the Bayes estimators and posterior risk of the unknown parameters of the model. Furthermore, credible intervals (CIs) and highest posterior density (HPD) intervals are also obtained. Monte Carlo simulation study is done to access the behavior of these estimators. For the illustrative purposes, a real-life application of the proposed distribution to a tensile strength data set is provided

In this paper, we defined the notions of $(\in,\in)$ -fuzzy implicative deductive systems and $(\in,\in\vee q)$ -fuzzy implicative deductive systems of hoops and studied some traits and tried to define some definitions that are equivalent to them. Thus by using the notion of $(\in,\in)$ -fuzzy deductive system of hoop, we defined a new congruence relation on hoop and show that the algebraic structure that is made by it is a Brouwerian semilattice , Heyting algebra and Wajesberg hoop.

This paper considers an inverse eigenvalue problem for‎ bisymmetric nonnegative matrices‎. ‎We first discuss the specified‎ structure of the bisymmetric matrices‎. ‎Then for a given set of real‎ numbers of order maximum ‎‎five‎ with special conditions‎, ‎we construct‎ a nonnegative bisymmetric matrix such that the given set is its spectrum‎‎. ‎Finally, we solve the problem for ‎arbitrary ‎order $n$ in the special case of the spectrum‎.

We say that an isometric immersion hypersurface $ x:M^n\rightarrow\mathbb{E}^{n+1}$ is ofnull $L_k$-2-type if $x =x_1+x_2$, $ x_1, x_2:M^n\rightarrow\mathbb{E}^{n+1}$ are smooth maps and $L_k x_1 =0, ~ L_k x_2 =\lambda x_2$, $\lambda$ is non-zero real number, $L_k$ is the linearized operator ofthe $(k + 1)$th mean curvature of the hypersurface, i.e., $L_k( f ) =\text{tr} (P_k \circ \text{Hessian} f )$ for$f \in C^\infty(M)$, where $P_k$ is the $k$th Newton transformation, $L_k x = (L_k x_1, \ldots , L_k x_{n+1}), ~x = (x_1, \ldots, x_{n+1})$. In this article, we classify $\delta (2)$-idealEuclidean hypersurfaces of null $L_1$-2-type.

In this paper, we study the existence of nontrivial solutionsfor a fractional boundary value problem in Holder spaces by a technicalapproach based on Leray-Schauder nonlinear alternative. Moreover,using the concept of orthogonal set on Banach xed point theorem weobtain another existence result with weaker conditions. Also, recentresults are extended and improved. In addition, we give some examplesto illustrate the feasibility and eectiveness of our results.

In this paper, we propose inverse data envelopment analysis (DEA) models in the presence of ratio data. We present the inputs/output estimation process based on ratio based DEA (DEA-R) models. We first present a multiple objective linear programming (MOLP) model to determine the level of inputs based on the perturbed outputs, assuming that the relative efficiency of the under evaluation decision making unit (DMU) preserve. We also present the relationship between the Pareto solutions of the proposed MOLP model and the optimal level of inputs and outputs of the new DMU. We presented criterion models to determine the efficiency of the new DMU in the inputs/output estimation process based on inverse DEA-R models in the presence of ratio data. We showed that in the presence of ratio data the selection of criterion model can be important, in order to we provide a new criterion model in the inputs/output estimation process in the presence of ratio data, and so on the amount of calculations is reduced. We have shown that the results for the new criterion model are the same as the existing criterion model presented in the paper. In order to show the validity of the proposed approach in the inputs/output estimation process based on the inverse DEA-R models, we provide an application of our models in a real life for a set of data regarding to medical centers in Taiwan and finally we present the research results.

In this paper, we consider the problem of estimating stress-strength reliability R=P(X>Y) for Gompertz lifetime models having the same shape parameters but different scale parameters under a set of upper record values. We obtain the maximum likelihood estimator (MLE), the approximate Bayes estimator and the exact confidence intervals of stress-strength reliability when the shape parameter is known. Also, when the shape parameter is unknown, the MLE, the asymptotic confidence interval and some bootstrap confidence intervals of stress-strength reliability are studied. Furthermore, a Bayesian approach is proposed for estimating the parameters and then the corresponding credible interval are achieved using Gibbs sampling technique via OpenBUGS software. Monte Carlo simulations are performed to compare the performance of different proposed estimation methods.

Here, the approximations of common fixed points of a new iterativeprocess for asymptotically k-strict pseudocontractive typemappings in Hilbert spaces are studied. Finally, some examples are presentedto indicate the validity of our iterations.