The main goal of the present paper is to construct some families of the Carlitz's q-Bernoulli polyno-mials and numbers. We  rstly introduce the Modi ed Carlitz's q-Bernoulli polynomials and numbers with weight (p. We then de ne the Modi ed degenerate Carlitz's q-Bernoulli polynomials and num-bers with weight ( ;  ) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the Modi ed Carlitz's q-Bernoulli polynomials with weight ( ;  ), the Modi ed degenerate Carlitz's q-Bernoulli polynomials with weight ( ;  ), the Stirling numbers of the  rst kind and second kind.

The original version of Grey Wolf Optimization (GWO) algorithm has a few disadvantages such as low solving accuracy, unsatisfactory ability of local searching, and slow convergence rate. In order to compensate these disadvantages of grey wolf optimizer, a new version of grey wolf optimizer algorithm was proposed by Modifying the encircling behavior and position update equations of GWO algorithm. The accuracy and convergence performances of the Modi ed variant were tested on several well-known classical, sine datasets, and cantilever beam design functions. For veri cation, the results were compared with some of the most powerful, well-known algorithms, i. e., particle swarm optimization, grey wolf optimizer, and mean grey wolf optimization. The experimental solutions demonstrated that the Modi ed variant was able to provide very comparable solutions in terms of improved minimum value of objective function, maximum value of objective function, mean, standard deviation, and convergence rate.

The power version of the Modi, ed Lindley distribution is introduced in this paper, o, ering a new two-parameter lifetime distri-bution. As a main interest, it provides a motivated alternative to the Weibull and power Lindley distributions. We discuss its main charac-teristics and properties, including shapes of the probability density and hazard rate functions, incomplete moments, crude moments, variance, skewness, kurtosis and order statistics. Then, a statistical study of the model is developed. The parameters are estimated by the maximum likelihood method. A simulation study examines the numerical com-portment of the bias and mean square error of the maximum likelihood estimates of the parameters. Application of the new model to three data sets is presented, showing that the model has a better , t behavior in comparison to some other well-known lifetime models, including the Weibull and power Lindley models.

In this paper, a new topology of quasi-Y-source impedance networks is presented. This converter utilizes the factor of change of winding and shoot through state in order to improve the gain of network. The proposed impedance network employs low turns ratio compared to quasi-Y-source and Y-source networks to achieve high voltage gain. The continuous input current of the proposed converter is an advantage, particularly for the applications related to the renewable energy sources such as Fuel Cell (FC) and photovoltaic (PV) systems. Furthermore, there are dc-current-blocking capacitors in the proposed network, which help to avoid the saturation of the coupled inductor. Operation principles of the converter are discussed and the steady-state relations as well as voltage gain and voltage stress across the dc-blocking capacitors are derived. The proposed converter is compared with the conventional quasi-Y-source network to show the advantages of the converter. Several simulations are performed and the results are shown to indicate the performance of the proposed network. In this paper, an experimental prototype of a converter is presented. To prove the validity and consistency of the proposed network, several tests are carried out. This plan can have a negative gain, similar to the quasi-Ysource network.

The nonlinear dynamic response, Limit Cycle Oscillations (LCOs), of High-Aspect-Ratio (HAR) wings using novel indicial aerodynamics in subsonic ow was investigated. Using the nonlinear beam theory, the structural model was derived with in-plane and out-of-plane bending and torsional motions, all nonlinearities up to cubic order arising from large deformation, mass distribution, and cross-sectional mass imbalance. Based on new approximations of the indicial functions, a comprehensive unsteady aerodynamic model was used. Coupling such indicial aerodynamics to nonlinear structural equations can result in a uni ed nonlinear aeroelastic formulation in both incompressible and subsonic compressible ows. The e ects of ight conditions, wing tip initial disturbances, Sti ness Ratio (SR) between bending modes, and nonlinearity due to inertia and cross-sectional mass imbalance on the characteristics of LCO are discussed. The results showed that compressibility could a ect the LCO boundary up to 12 percent, which implied that appropriate Mach-dependent aerodynamics was required to achieve a more reasonable and realistic description of dynamic behavior of the system. It was observed that the presence of LCO before the linear utter speed depended on the initial disturbances as well as wing characteristics.

As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with  nite jumps) are most suitable and reliable. Therefore, Modi ed numerical method based on Taylor series expansion and Haar wavelets is presented for solving coupled system of nonlinear partial di erential equations. E ciency and accuracy of the proposed method is depicted by comparing with classical methods.

A viscoelastic microcantilever beam is analytically analyzed based on the Modi ed strain gradient theory. Kelvin-Voigt scheme is used to model beam viscoelasticity. By applying Euler-Bernoulli inextensibility of the centerline condition based on Hamilton's principle, the nonlinear equation of motion and the related boundary conditions are derived from shortening e ect theory and discretized by Galerkin method. Inner damping, nonlinear curvature e ect, and nonlinear inertia terms are also taken into account. In the present study, the generalized derived formulation allows modeling any nonlinear combination such as nonlinear terms that arise due to inertia, damping, and sti ness, as well as modeling the size e ect using Modi ed coupled stress or Modi ed strain gradient theories. First-mode nonlinear frequency and time response of the viscoelastic microcantilever beam are analytically evaluated using multiple time scale method and then, validated through numerical  ndings. The obtained results indicate that nonlinear terms have an appreciable e ect on natural frequency and time response of a viscoelastic microcantilever. Moreover, further investigations suggest that due to the size e ects, natural frequency would drastically increase, especially when the thickness of the beam and the length scale parameter are comparable. The  ndings elaborate the signi cance of size e ects in analyzing the mechanical behavior of small-scale structures.

In this paper we introduce new Modi ed implicit and explicit algorithms and prove strong convergence of the two algorithms to a common  xed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real re exive Banach space with a uniformly G^ateaux di erentiable norm. Our result is applicable in Lp(`p) spaces, 1 < p < 1 and consequently in sobolev spaces.

In this article, we propose some Modi cations to the maximum likelihood estimation for estimating the parameters of the Pareto distribution and evaluate the performance of these Modi ed estimators in comparison with the existing maximum likelihood estimators. Total Relative Deviation (TRD), Total Mean Square Error (TMSE), and Stein Loss Function (SLF) were used as performance indicators of goodness of  t analysis. The Modi ed and traditional estimators were compared for di erent sample sizes and di erent parameter combinations using a Monte Carlo simulation in R-language. We concluded that the Modi ed maximum likelihood estimator based on expectation of empirical Cumulative Distribution Function (CDF) of  rst-order statistic performed much better than the traditional ML estimator and other Modi ed estimators based on median and coe cient of variation. The superiority of the mentioned estimator was independent of sample size and choice of true parameter values. The simulation results were further corroborated by employing the proposed estimation strategies for two real-life datasets.