In this article, we propose a generalized class of exponential factor type estimators for estimation of the finite population distribution function (PDF) using an auxiliary variable in the form of the mean and rank of the auxiliary variable exist. The expressions of the bias and mean square error of the estimators are computed up to the first order approximation. The proposed estimators provide minimum mean square error as compared to all other considered estimators. Three real data sets are used to check the performance of the proposed estimators. Moreover, simulation studies are also carried out to observe the performances of the proposed estimators. The proposed estimators confirmed their superiority numerically as well as theoretically by producing efficient results as compared to all other competing estimators.

This study concentrates on adaptive event-triggered control of complex dynamical networks with unpredictable coupling delays and stochastic deception attacks. The adaptive event-triggered mechanism is used to avoid the wasting of limited bandwidth. The probability of data communicated by the network is established by statistical properties and Bernoulli stochastic variables with an uncertain occurrence probability. Stability analysis based on Lyapunov–Krasovskii functional (LKF) and the stability of the closed-loop system is guaranteed. Using the LMI technique, we obtain triggered parameters. To demonstrate the feasibility and usefulness of the suggested methodology, two examples are shown.

Owing to the various physical aspects of nanofluids as thermally enhanced working fluids and the significance of swirling flows in rheological devices as well as in the spin coating and lubrication applications, the current comprehensive examination aimed to explore the important features of spinning flows of chemically reactive Newtonian nanofluids over a uniformly revolving disk in the existence of a radially applied magnetic field along with an exponentially decaying space-dependent heat source, in the case where the disk surface is heated convectively and unaffected by the vertical nanoparticles’ mass flux. Based on feasible boundary layer approximations and Buongiorno’s nanofluid formulation, the leading coupled differential equations are stated properly in the sense of Arrhenius’s and Von Kármán’s approaches. By employing an advanced generalized differential quadrature algorithm, the obtained boundary layer equations are handled numerically with a higher order of accuracy to generate adequate graphical and tabular illustrations for the different values of the influencing flow parameters. As findings, the graphical results confirm that the nanofluid motion decelerates meaningfully thanks to the resistive magnetic influence. A significant thermal amelioration can be achieved by strengthening the magnetic impact, the generation of heat, the thermal convective process, and the thermophoresis mechanism. Moreover, it is found that the thermo-migration of nanoparticles can be reinforced more via the intensification in the convective process, the thermo-migration of nanoparticles, and the activation energy.

<abstract><p>In cluster synchronization (CS), the constituents (i.e., multiple agents) are grouped into a number of clusters in accordance with a function of nodes pertaining to a network structure. By designing an appropriate algorithm, the cluster can be manipulated to attain synchronization with respect to a certain value or an isolated node. Moreover, the synchronization values among various clusters vary. The main aim of this study is to investigate the asymptotic and CS problem of coupled delayed complex-valued neural network (CCVNN) models along with leakage delay in finite-time (FT). In this paper, we describe several sufficient conditions for asymptotic synchronization by utilizing the Lyapunov theory for differential systems and the Filippov regularization framework for the realization of finite-time synchronization of CCVNNs with leakage delay. We also propose sufficient conditions for CS of the system under scrutiny. A synchronization algorithm is developed to indicate the usefulness of the theoretical results in case studies.</p></abstract>