Volume 23 – Issue 2

In this paper, we will define some new class of generalized closed sets called weakly binary generalized 𝛼-closed sets, weakly binary 𝛼 generalized closed sets, binary generalized *^𝛼-closed sets and weakly binary generalized *^𝛼-closed sets in binary topological spaces and study some of their characterizations and properties.

In this study, the singular boundary method (SBM) is employed for the simulation of nonlinear Klein-Gordon equation with initial and Dirichlet-type boundary conditions. The 𝜃-weighted and Houbolt finite difference method is used to discretize the time derivatives. Then the original equations are split into a system of partial differential equations. A splitting scheme is applied to split the solution of the inhomogeneous governing equation into homogeneous solution and particular solution. To solve this system, the method of particular solution in combination with the singular boundary method is used for particular solution and homogeneous solution, respectively. Finally, several numerical examples are provided and compared with the exact analytical solutions to show the accuracy and efficiency of method in comparison with other existing methods.

In this paper, we generalize the concept of single conformable Sehu transformation (CSHT) to double conformable transformation (CDFSHT). Moreover, we are able to prove some theorems and properties related to this work. We apply the double conformable Sehu transform to solve the initial and boundary problems of linear and (non)homogenous conformable fractional partial differential equations (PDEs). The validity and the applicability of the proposed technique are shown by three numerical examples. Mathematica software is used for Euclidean division of polynomials and drawing graphs.

Properties of a large class of (𝑀, 𝑘)-*-quasi-parahyponormal operators are established in the present article. It is shown that these operators have finite ascent and the single valued extension property. The matrix representation and the multicyclicity on a separable complex Hilbert space are proved too.

This paper deals with a general class of nonlinear fractional differential equations with p-Laplacian operator that involves some φ-sequential Caputo derivatives. New criteria on the existence and uniqueness of solutions are established. The stability analysis in the sense of Ulam Hyers is discussed. An illustrative example is presented.

In this article, we introduce adaptive estimators for parameters of the (GPD) Generalized Pareto Distribution under censored data via the KIB-estimator. The KIBestimator is based on the Maximum Likelihood Estimates (MLE) by the exceedances over the threshold t under random censoring which was developed by [1]. Hence, it was proved that the KIB-estimator is Maximum Likelihood (ML) estimator with the uncensored case. We use the standardized MLE based on the exceedances on the uncensored situation which converge to a centered bivariate normal distribution. Whose found by [2] to standardized our adaptive KIB estimator of the GPD parameters under random censorship. As an application, we establish the asymptotic normality of an estimator of the excess-of- loss reinsurance premium for heavy-tailed distribution, through the adapted KIB estimator of GPD under censored data.

In this paper, we firstly introduce definition of weak interpolative HardyRogers type contractions and we give an example for a class of this mappings. We also prove a fixed point theorem under some appropriate conditions on complete 𝑏 −metric spaces. Finally, we discuss an application to homotopy theory of our main result.

In this paper we have introduced two stronger functions namely Strongly Soft Jc open(closed) maps and Strongly Soft Jc homeomorphism. Further we have studied some of their properties in detail.

Principal component analysis is commonly used as a pre-step before employing a classifier to avoid the negative effect of the dimensionality and multicollinearity. The performance of a classifier is severely affected by the deviations from the linearity of the data structure and noisy samples. In this paper, we propose a new classification system that overcomes the drawback of these crucial problems, simultaneously. Our proposal is relying on the kernel principal component analysis with a proper parameter selection approach with data complexity measures. According to the empirical results, F1, T2 and T3 in AUC, T3 in GMEAN and T2 and T3 in MCC performed better than classical and other complexity measures. Comparison of classifiers showed that Radial SVM performs better in AUC, and KNN performs better in GMEAN and MCC using KPCA with complexity measures. As a result, our proposed system produces better results in various classification algorithms with respect to classical approach.

Our work is study the geometry of oscillator groups; they are the only non commutative simply connected solvable Lie groups which have a biinvariant Lorentzian metric. The oscillator group has been generalized to one dimension equals 2n ≥ 4 , and several aspects of its geometry have been intensively studied, both in differential geometry and in mathematical physics. In this paper, we find geodesic curves on the oscillator group (G_λ, g_a ) of dimension four

In this work we have applied a very important the hyperbolic tangent (tanh) method in the analytical study of nonlinear coupled KdV systems of partial differential equations. Compared to existing sophisticated approaches, this proposed method gives more general exact traveling wave solutions without much extra effort. Two applications from the literature of non linear PDE systems have been solved by the method.

In the current investigation, we have developed the efficient predictive estimator for finite population mean using auxiliary variable in case of post stratification. Up to the first order of approximation, the expressions for bias and mean square error (MSE) are derived for the proposed estimator. This also reveals the constant’s ideal value, which reduces the MSE of the developed estimator. The developed estimator performs better than the existing estimators.Numerical study is also carried out by using the real data sets.

There are many common combination methods for solving fractional differential equations. In this work, we propose a new technique called Adomian decomposition transform method (ADTM) in order to provide a new approximate series solution of fractional order Bratu-type differential equations. The fractional order derivative is described in the Caputo sense. The ADTM is a combination of two powerful methods, the Jafari transform method and Adomian decomposition method. For accelerating the convergence of ADTM when used for these equations, we replace the nonlinear terms by their Taylor expansion. To demonstrate the efficiency and validity of the proposed method, four numerical examples are presented and we compare our obtained results with the analytical results. Finally, the numerical results obtained are represented graphically using MATLAB software.

Stratified sample size which determined in Stratified Random Sampling (SRS) with the help of different allocation techniques. The multivariate stratified sampling with linear or nonlinear time function can be optimized using generalized model of time function. After formulation as generalized model with time function (linear or nonlinear), in which the information given that there is only one varying time (time of transportation) and different time involved are constants or insignificant. The formulated generalized model was solved using different techniques but in present paper we use Lagrange multiplier technique to get the optimal solution (i.e. by minimizing the variance) with the involved time constraints. The generalized model with time of transportation is derived under optimum allocation and other involved time is fixed, when the sample size and its variances for a given time is unknown, then different allocation techniques are required for proportionality constant and a given time.

We propose an effective general approach for accurately calculating the electron-electron, nuclear-electron and nuclear-nuclear Coulomb electrostatic interaction energies. Since these interaction energies are fundamental terms in the ab initio, density function and semi-empirical theories, their general examination will make an important contribution to the accurate calculation of the physical and chemical properties of atoms and molecules. It is well known that electron-electron, nuclear-electron and nuclear-nuclear Coulomb electrostatic interaction energies can be reduced to basic two-center Coulomb integrals. The analytical calculation of electrostatic interaction energies with respect to basic two-center Coulomb integrals over Slater type orbitals (STOs) in molecular coordinate systems allows for the routine evaluation of molecular structures and their related properties. In this study, we introduce a new full analytical algorithm for calculating the basic two-center Coulomb integrals over STOs using Guseinov’s auxiliary functions, especially the interactions between electrons. The auxiliary functions are calculated by using the exact recurrence relations developed by Guseinov. Our new approach is successfully tested on data from previously published studies, and can be recommended for the evaluation of related problems in atomic and molecular physics.

Romania, through RATEN ICN, is involved in the construction of the ALFRED demonstrator (Advanced Lead Fast Reactor European Demonstrator), in which the core of the reactor uses cooling in the liquid lead environment. This constitutes one of the arguments for the development of studies on innovative materials of generation IV, having the stated objective of the problem of the contact between the liquid lead and the structural materials specific to this type of reactor. The purpose of this paper is to highlight the changes in the thermomechanical behaviour induced by the contact between the 316L austenitic steel and the liquid lead, as well as its modelling through the equation of the Ramberg-Osgoodtype mechanical stress-strain curve. The tensile tests in air and liquid lead were carried out at strain rates of the specimens in the range 10^-3 s^-1~ 10^-5 s^-1 and in a range of temperatures 350°C – 400°C. To highlight the changes induced by the contact with the liquid lead on the thermomechanical behaviour of the 316L steel, the artificial neural network method, called the “Multilayer Feedforward Neural Network”, was used in the processing of the experimental database. The obtained Ramberg-Osgood-type mechanical stress-strain curve is applied for both the air and the liquid lead environment at a temperature of 375°C and includes the following parameters as input: temperature, strain rate, yield stress, and maximum stress at necking. The two equations obtained for the air environment and the liquid lead environment at a temperature of 375°C were verified to the experimental data and a very good prediction agreement was obtained.

The interest that Internet of Things (IoT) enjoys is particular not only from a technical point of view, but also through the lens of the special contribution in terms of economic competitiveness or development of public services. As a result, at the European level, IoT development is a goal for both companies and individual users. In our study, we aimed to analyze from a statistical point of view what is the situation of equipping private homes with IoT devices, the factors that exert an influence on invididual behavior and the extent to which Member States differ from each other, as a premise for future public measures that will be adopted in this field.