<abstract xmlns="http://www.w3.org/1999/xhtml">Clustering as a fundamental unsupervised learning is considered an important method of data analysis, and <italic>K</italic>-means is demonstrably the most popular clustering algorithm. In this paper, we consider clustering on feature space to solve the low efficiency caused in the Big Data clustering by <italic>K</italic>-means. Different from the traditional methods, the algorithm guaranteed the consistency of the clustering accuracy before and after descending dimension, accelerated <italic>K</italic>-means when the clustering centeres and distance functions satisfy certain conditions, completely matched in the preprocessing step and clustering step, and improved the efficiency and accuracy. Experimental results have demonstrated the effectiveness of the proposed algorithm.</abstract>

Improvement of the Fast Clustering Algorithm Improved by <italic>K</italic>-Means in the Big Data

<abstract xmlns="http://www.w3.org/1999/xhtml">A model for predator-prey interactions with herd behaviour is proposed. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). The model is analysed using standard stability and bifurcations techniques. We prove that the system undergoes a Hopf bifurcation as we vary the parameter that represents the efficiency of predators (dependent on the predation rate, for instance), giving rise to sustained oscillations in the system. The proposed model appears to possess more realistic features than the previous approaches while being also relatively easier to analyse and understand.</abstract>

Instituto de Ciências Naturais Humanas e Sociais

Faculdade de Ciências Exatas e Tecnológicas

Dipartimento di Matematica “Giuseppe Peano”

A Mathematical Model to describe the herd behaviour considering group defense

<abstract xmlns="http://www.w3.org/1999/xhtml">In recent years, China’s environmental pollution is serious, manufacturing industry has become one of the main targets of government environmental regulation. This paper uses the SBM model to calculate efficiency value of 29 manufacturing industries from 2008 to 2017. The results show that the overall performance of environmental regulation in manufacturing industry is high (the average efficiency value is 0.7806), but it shows a declining trend. The efficiency of environmental regulation also varies widely. The government should consider focusing on the 11 industries with low SBM value in the next step to improve the performance of environmental regulation.</abstract>

Empirical Analysis on Environmental Regulation Performance Measurement in Manufacturing Industry: A Case Study of Chongqing, China

<abstract xmlns="http://www.w3.org/1999/xhtml">In order to handle the non-linear system and the complex disturbance in marine engines, a finite-time convergence active disturbance rejection control (ADRC) technique is developed for the control of engine speed. First, a model for the relationship between engine speed and fuel injection is established on the basis of the mean value engine model. Then, to deal with the load disturbances and model parameter perturbation of the diesel engine, this paper designs an ADRC approach to achieve finite-time stability. Finally, simulation experiments show that the proposed method has better control effect and stronger disturbance rejection ability in comparison with the standard linear ADRC.</abstract>

Finite-time active disturbance rejection control for marine diesel engine

<abstract xmlns="http://www.w3.org/1999/xhtml">Swap trailer transport organisation problem originates from the traditional vehicle routing problem (VRP). Most of the studies on the problems assume that the travelling times of vehicles are fixed values. In this paper, the uncertainties of driving times are considered and a chance constrained programming problem is proposed. An improved simulated annealing algorithm is used to solve the problem proposed. The model and algorithm described in this paper are studied through a case study, and the influence of uncertainty on the results is analysed. The conclusion of this study provides theoretical support for the practice of trailer pickup transport.</abstract>

Research Institute of Highway Ministry of Transport

Transport Planning and Research Institute, Ministry of Transport

Solution to Chance Constrained Programming Problem in Swap Trailer Transport Organisation based on Improved Simulated Annealing Algorithm

<abstract xmlns="http://www.w3.org/1999/xhtml">According to the analysis from the number of tourists who went to Lanzhou during 2009–2019, the ARIMA model of the number of tourists to Lanzhou was established. The results show that the AR(3) model is used to predict the number of tourists who traveled to Lanzhou during 2009–2019. The average relative error between the predicted value and the actual value is 1.03%, which can be used to predict and analyze the number of tourists in Lanzhou in the future.</abstract>

Tourists Forecast Lanzhou Based on the Baolan High-Speed Railway by the Arima Model

<abstract xmlns="http://www.w3.org/1999/xhtml">The trade effect, in this article, mainly refers to the trade impacts of member countries and non-member states. This article first summarises the empirical analysis methods of trade effects of regional economic integration and then combines the methods widely used in the current research, proposes research methods suitable for Trans-Pacific Partnership (TPP) trade effect analysis, establishes models and conducts empirical analysis and then analyses empirical evidence, by which to predict the trend of post-TPP and its future influence.</abstract>

Analysis of Trade Effect in Post-Tpp Era: Based on Gravity Model and Gtap Model

<abstract xmlns="http://www.w3.org/1999/xhtml">A new approach to achieve fault diagnosis and prognosis of bearing based on hidden Markov model (HMM) with multi-features is proposed. Firstly, the time domain, frequency domain, and wavelet packet decomposition are utilized to extract the condition features of bearing vibration signals, and the PCA method is merged into multi-features to reduce their dimensionality. Then the low-dimensional features are processed to obtain the scalar probabilities of each bearing condition, which are multiplied to generate the observed values of HMM. The results reveal that the established approach can well diagnose fault conditions and achieve the remaining life estimation of bearing.</abstract>

Fault Diagnosis and Prognosis of Bearing Based on Hidden Markov Model with Multi-Features

<abstract xmlns="http://www.w3.org/1999/xhtml">In the present frame work, we studied the semi generalized recurrent, semi generalized <italic>ϕ</italic>-recurrent, extended generalized <italic>ϕ</italic>-recurrent and concircularly locally <italic>ϕ</italic>-symmetric on generalized Sasakian space forms.</abstract>

Some Results on Generalized Sasakian Space Forms

<abstract xmlns="http://www.w3.org/1999/xhtml">In this article, the study of qualitative properties of a special type of non-autonomous nonlinear second order ordinary differential equations containing Rayleigh damping and generalized Duffing functions is considered. General conditions for the stability and periodicity of solutions are deduced via fixed point theorems and the Lyapunov function method. A gyro dynamic application represented by the motion of axi-symmetric gyro mounted on a sinusoidal vibrating base is analyzed by the interpretation of its dynamical motion in terms of Euler’s angles via the deduced theoretical results. Moreover, the existence of homoclinic bifurcation and the transition to chaotic behaviour of the gyro motion in terms of main gyro parameters are proved. Numerical verifications of theoretical results are also considered.</abstract>

On the existence of periodic solution and the transition to chaos of Rayleigh-Duffing equation with application of gyro dynamic

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we have extended the Fractional Differential Transform method for the numerical solution of the system of fractional partial differential-algebraic equations. The system of partial differential-algebraic equations of fractional order is solved by the Fractional Differential Transform method. The results exhibit that the proposed method is very effective.</abstract>

Analytical and approximate solutions of Fractional Partial Differential-Algebraic Equations

<abstract xmlns="http://www.w3.org/1999/xhtml">Based on the data of China’s Marine engineering equipment industry, in this Paper, the key influencing factors are identified by using Grounded theory and GRNN-DEMATEL method. The study results show the key influencing factors include enterprise’s operational, technical capabilities, enterprise’s social recognition, enterprise’s willingness to cooperate, trust between enterprises, communication and collaboration, opportunism and external environment. Second, enterprise’s operational and technical capabilities are the most important and critical factors, external environment is an irresistible factor. This study enriches and develops the study of supply chain management, and provides theoretical guidance and reference for improving the industry competitiveness.</abstract>

Department of Economics and Management School

Weifang University of Science and Technology

Factors Influencing the Cooperative Relationship between Enterprises in the Supply Chain of China’s Marine Engineering Equipment Manufacturing Industry-An study based on GRNN-DEMATEL method

<abstract xmlns="http://www.w3.org/1999/xhtml">Infectious diseases have caused the death of many people throughout the world for centuries. For this purpose, many researchers have investigated these diseases for establishing new treatment and protective measures. The most important of these is HIV disease. In this study, an HIV infection model of <italic>CD</italic>4+<italic>T</italic> cells is handled comprehensively with the newly defined Atangana-Baleanu (AB) fractional derivative. The existence and uniqueness of the solutions for fractionalized HIV disease model with the new derivative by considering the Arzela-Ascoli theorem.</abstract>

System Analysis of HIV Infection Model with <italic>CD</italic>4+<italic>T</italic> under Non-Singular Kernel Derivative

<abstract xmlns="http://www.w3.org/1999/xhtml">In this study, motivated by the frequent use of Fox-Wright function in the theory of special functions, we first introduced new generalizations of gamma and beta functions with the help of Fox-Wright function. Then by using these functions, we defined generalized Gauss hypergeometric function and generalized confluent hypergeometric function. For all the generalized functions we have defined, we obtained their integral representations, summation formulas, transformation formulas, derivative formulas and difference formulas. Also, we calculated the Mellin transformations of these functions.</abstract>

A study on certain properties of generalized special functions defined by Fox-Wright function

<abstract xmlns="http://www.w3.org/1999/xhtml">The exact solution is calculated for fractional telegraph partial differential equation depend on initial boundary value problem. Stability estimates are obtained for this equation. Crank-Nicholson difference schemes are constructed for this problem. The stability of difference schemes for this problem is presented. This technique has been applied to deal with fractional telegraph differential equation defined by Caputo fractional derivative for fractional orders <italic>α</italic> = 1.1, 1.5, 1.9. Numerical results confirm the accuracy and effectiveness of the technique.</abstract>

Faculty of Arts and Sciences, Department of Mathematics

Art and Science Faculty, Department Of Mathematics

On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integer-order derivatives. Finally, we obtain the analytical solutions of some ℳ-series fractional differential equations.</abstract>

A generalization of truncated M-fractional derivative and applications to fractional differential equations

<abstract xmlns="http://www.w3.org/1999/xhtml">We obtain asymptotic result for the solutions of neutral differential equations. Our technique depends on characteristic equations.</abstract>

An Asymptotic Result for neutral differential equations

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we obtain the existence of a global attractor for the higher-order evolution type equation. Moreover, we discuss the asymptotic behavior of global solution.</abstract>

Global Attractors for the Higher-Order Evolution Equation

<abstract xmlns="http://www.w3.org/1999/xhtml">The paper presents an first type boundary value problem for a Schrödinger equation. The aim of paper is to give the existence and uniqueness theorems of the boundary value problem using Galerkin’s method. Also, a priori estimate for its solution is given.</abstract>

The Solvability of First Type Boundary Value Problem for a Schrödinger Equation

<abstract xmlns="http://www.w3.org/1999/xhtml">Many investigations related to the analytical solutions of the nonlinear sub-diffusion equation exist. In this paper, we investigate the conditions under which the analytical and the approximate solutions of the nonlinear sub-diffusion equation and the nonlinear sub-advection dispersion equation exist. In other words, the problems of existence and uniqueness of the solutions the fractional diffusion equations have been addressed. We use the Banach fixed Theorem. After proving the existence and uniqueness, we propose the analytical and the approximate solutions of the nonlinear sub-diffusion, and the nonlinear sub-advection dispersion equations. We analyze the impact of the sub-diffusion coefficient, the advection coefficient and the dispersion coefficient in the diffusion processes. The homotopy perturbation Laplace transform method has been used in this paper. Some numerical examples are provided to illustrate the main results of the article.</abstract>

Département de Mathématiques de la Décision

Université Cheikh Anta Diop de Dakar, Faculté des Sciences Economiques et Gestion

Nonlinear sub-diffusion and nonlinear sub-diffusion dispersion equations and their proposed solutions

<abstract xmlns="http://www.w3.org/1999/xhtml">Pseudo null curves were studied by some geometers in both Euclidean and Minkowski spaces, but some special characters of the curve are not considered. In this paper, we study weak <italic>AW</italic> (<italic>k</italic>) – <italic>type</italic> and <italic>AW</italic> (<italic>k</italic>) – <italic>type</italic> pseudo null curve in Minkowski 3-space 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00021_ieq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mi>E</mi><mn>1</mn><mn>3</mn></msubsup></mrow></math><tex-math>[E_1^3 </tex-math></alternatives></inline-formula>
. We define helix and slant helix according to Bishop frame in 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00021_ieq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mi>E</mi><mn>1</mn><mn>3</mn></msubsup></mrow></math><tex-math>[E_1^3 </tex-math></alternatives></inline-formula>
. Furthermore, the necessary and sufficient conditions for the slant helix and helix in Minkowski 3-space are obtained.</abstract>

Special Curves According to Bishop Frame in Minkowski 3-Space

<abstract xmlns="http://www.w3.org/1999/xhtml">In our study, we give the associated evolution equations for curvature and torsion as a system of partial differential equations. In addition, we study second binormal motions of inextensible curves in 4-dimensional Galilean space.</abstract>

Department of Mathematics, Faculty of Arts and Sciences

Department of Mathematics, Faculty of Science

Second Binormal Motions of Inextensible Curves in 4-dimensional Galilean Space

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we introduce a new generalization of the Pochhammer symbol by means of the generalization of extended gamma function <xref ref-type="disp-formula" rid="j_amns.2020.1.00023_eq_004_w2aab3b7e1462b1b6b1ab1ab3c51Aa">(4)</xref>. Using the generalization of Pochhammer symbol, we give a generalization of the extended hypergeo-metric functions one or several variables. Also, we obtain various integral representations, derivative formulas and certain properties of these functions.</abstract>

A New Generalization of Pochhammer Symbol and Its Applications

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, the hybrid method (differential transform and finite difference methods) and the RDTM (reduced differential transform method) are implemented to solve Rosenau-Hyman equation. These methods give the desired accurate results in only a few terms and the approach procedure is rather simple and effective. An experiment is given to demonstrate the efficiency and reliability of these presented methods. The obtained numerical results are compared with each other and with exact solution. It seems that the results of the hybrid method and the RDTM show good performance as the other methods. The most important part of this study is that these methods are suitable to solve both some linear and nonlinear problems, and reduce the size of computation work.</abstract>

The Comparison Study of Hybrid Method with RDTM for Solving Rosenau-Hyman Equation

<abstract xmlns="http://www.w3.org/1999/xhtml">In the recent years, there has been a lot of interest in studying the global behavior of, the socalled, max-type difference equations; see, for example, [<xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_001_w2aab3b7e1584b1b6b1ab2ab1Aa">1</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_002_w2aab3b7e1584b1b6b1ab2ab2Aa">2</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_003_w2aab3b7e1584b1b6b1ab2ab3Aa">3</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_004_w2aab3b7e1584b1b6b1ab2ab4Aa">4</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_005_w2aab3b7e1584b1b6b1ab2ab5Aa">5</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_006_w2aab3b7e1584b1b6b1ab2ab6Aa">6</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_007_w2aab3b7e1584b1b6b1ab2ab7Aa">7</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_008_w2aab3b7e1584b1b6b1ab2ab8Aa">8</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_009_w2aab3b7e1584b1b6b1ab2ab9Aa">9</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_010_w2aab3b7e1584b1b6b1ab2ac10Aa">10</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_011_w2aab3b7e1584b1b6b1ab2ac11Aa">11</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_012_w2aab3b7e1584b1b6b1ab2ac12Aa">12</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_013_w2aab3b7e1584b1b6b1ab2ac13Aa">13</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_014_w2aab3b7e1584b1b6b1ab2ac14Aa">14</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_015_w2aab3b7e1584b1b6b1ab2ac15Aa">15</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_016_w2aab3b7e1584b1b6b1ab2ac16Aa">16</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_017_w2aab3b7e1584b1b6b1ab2ac17Aa">17</xref>]. The study of max type difference equations has also attracted some attention recently. We study the behaviour of the solutions of the following system of difference equation with the max operator: paper deals with the behaviour of the solutions of the max type system of difference equations,
<disp-formula id="j_amns.2020.1.00025_eq_001_w2aab3b7e1584b1b6b1aab1c16b1c35Aa"><label>(1)</label><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00025_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi mathvariant="italic">max</mi><mrow><mo>{</mo><mrow><mfrac><mi>A</mi><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>,</mo><mfrac><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow></mfrac></mrow><mo>}</mo></mrow><mo>;</mo></mrow></mtd><mtd><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi mathvariant="italic">max</mi><mrow><mo>{</mo><mrow><mfrac><mi>A</mi><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>,</mo><mfrac><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow></mfrac></mrow><mo>}</mo><mo>,</mo></mrow></mrow></mtd></mtr></mtable></mrow></math><tex-math>\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} &amp; {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\},}}</tex-math></alternatives></disp-formula>
where the parametr <italic>A</italic> and initial conditions <italic>x</italic>−1,<italic>x</italic>0, <italic>y</italic>−1,<italic>y</italic>0 are positive reel numbers.</abstract>

Solution of the Maximum of Difference Equation 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00025_ieq_001.png"/><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mtable><mtr><mtd><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi mathvariant="italic">max</mi><mrow><mo>{</mo><mrow><mfrac><mi>A</mi><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>,</mo><mfrac><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow></mfrac></mrow><mo>}</mo></mrow><mo>;</mo></mrow></mtd><mtd><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi mathvariant="italic">max</mi><mrow><mo>{</mo><mrow><mfrac><mi>A</mi><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>,</mo><mfrac><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow></mfrac></mrow><mo>}</mo></mrow></mrow></mtd></mtr></mtable></mrow></math><tex-math>\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} &amp; {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\}}}</tex-math></alternatives></inline-formula>

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper different curvature tensors on Lorentzian Kenmotsu manifod are studied. We investigate constant <italic>ϕ</italic>–holomorphic sectional curvature and <italic>ℒ</italic>-sectional curvature of Lorentzian Kenmotsu manifolds, obtaining conditions for them to be constant of Lorentzian Kenmotsu manifolds in such condition. We calculate the Ricci tensor and scalar curvature for all the cases. Moreover we investigate some properties of semi invariant submanifolds of a Lorentzian Kenmotsu space form. We show that if a semi-invariant submanifold of a Lorentzian Kenmotsu space form M is totally geodesic, then M is an <italic>η−</italic>Einstein manifold. We consider sectional curvature of semi invariant product of a Lorentzian Kenmotsu manifolds.</abstract>

Some Properties Curvture of Lorentzian Kenmotsu Manifolds

<abstract xmlns="http://www.w3.org/1999/xhtml">In this study, a robust hybrid method is used as an alternative method, which is a different method from other methods for the approximate of the telegraph equation. The hybrid method is a mixture of the finite difference and differential transformation methods. Three numerical examples are solved to prove the accuracy and efficiency of the hybrid method. The reached results from these samples are shown in tables and graphs.</abstract>

The Numerical Study of a Hybrid Method for Solving Telegraph Equation

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we define a new class of analytic functions with negative coefficients involving the q-differential operator. Our main purpose is to determine coefficient inequalities and distortion theorems for functions belonging to this class. Connections with previous results are pointed out.</abstract>

Properties of a New Subclass of Analytic Functions With Negative Coefficients Defined by Using the Q-Derivative

<abstract xmlns="http://www.w3.org/1999/xhtml">In this article, some new travelling wave solutions of the (3+1) dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation are obtained using the modified exponential function method. When the solution functions obtained are examined, it is seen that functions with periodic functions are obtained. Two and three dimensional graphs of the travelling wave solutions of the BLMP equation are drawn by selecting the appropriate parameters</abstract>

Department of Mathematics and Science Education, Faculty of Education

A New Approach to (3+1) Dimensional Boiti–Leon–Manna–Pempinelli Equation

<abstract xmlns="http://www.w3.org/1999/xhtml">In this study, we present a model which represents the interaction of financial companies in their network. Since the long time series have a global memory effect, we present our model in the terms of fractional integro-differential equations. This model characterize the behavior of the complex network where vertices are the financial companies operating in <italic>XU</italic>100 and edges are formed by distance based on Pearson correlation coefficient. This behavior can be seen as the financial interactions of the agents. Hence, we first cluster the complex network in the terms of high modularity of the edges. Then, we give a system of fractional integro-differential equation model with two parameters. First parameter defines the strength of the connection of agents to their cluster. Hence, to estimate this parameter we use vibrational potential of each agent in their cluster. The second parameter in our model defines how much agents in a cluster affect each other. Therefore, we use the disparity measure of PMFGs of each cluster to estimate second parameter. To solve model numerically we use an efficient algorithmic decomposition method and concluded that those solutions are consistent with real world data. The model and the solutions we present with fractional derivative show that the real data of Borsa Istanbul Stock Exchange Market always seek for an equilibrium state.</abstract>

Fractional Interaction of Financial Agents in a Stock Market Network

<abstract xmlns="http://www.w3.org/1999/xhtml">In this study, a new method to obtain approximate probability density function (pdf) of random variable of solution of stochastic differential equations (SDEs) by using generalized entropy optimization methods (GEOM) is developed. By starting given statistical data and Euler–Maruyama (EM) method approximating SDE are constructed several trajectories of SDEs. The constructed trajectories allow to obtain random variable according to the fixed time. An application of the newly developed method includes SDE model fitting on weekly closing prices of Honda Motor Company stock data between 02 July 2018 and 25 March 2019.</abstract>

An Application of New Method to Obtain Probability Density Function of Solution of Stochastic Differential Equations

<abstract xmlns="http://www.w3.org/1999/xhtml">The theory of time scales calculus have long been a subject to many researchers from different disciplines. Beside the unification and the extension aspects of the theory, it emerge as a powerful tool for mimetic discretization process. In this study, we present a framework to find normal vector fields of discrete point sets in ℝ3 by using symmetric differential on time scales. A surface parameterized by the tensor product of two time scales can be analogously expressed as the vertex set of non-regular rectangular grids. If the time scales are dense, then the discrete grid structure vanishes. If the time scales are isolated, then the further geometric analysis can be executed by using symmetric dynamic differential. Moreover, we present an algorithmic procedure to determine the symmetric dynamic differential structure on the neighborhood of points in surfaces. Our results indicate that the method we present has good approximation to unit normal vector fields of parameterized surfaces rather than the Delaunay triangulation for some points.</abstract>

Discrete Normal Vector Field Approximation via Time Scale Calculus

<abstract xmlns="http://www.w3.org/1999/xhtml">In this work we investigate the completeness, minimality and basis properties of the eigenfunctions of one class discontinuous Sturm-Liouville equation with a spectral parameter in boundary conditions.</abstract>

On Basis Property of Root Functions For a Class Second Order Differential Operator

<abstract xmlns="http://www.w3.org/1999/xhtml">Here, our aim is to demonstrate some formulae of generalization of the extended hypergeometric function by applying fractional derivative operators. Furthermore, by applying certain integral transforms on the resulting formulas and develop a new futher generalized form of the fractional kinetic equation involving the generalized Gauss hypergeometric function. Also, we obtain generating functions for generalization of extended hypergeometric function..</abstract>

Fractional Calculus of the Extended Hypergeometric Function

<abstract xmlns="http://www.w3.org/1999/xhtml">This paper investigates the optimal placement of piezoelectric actuators for the active vibration attenuation of beams. The governing equation of the beam is achieved by coupled first order shear deformation theory with two node element. The velocity feedback controller is designed and used to calculate the feedback gain and then apply to the beam. In order to search for the optimal placement of the piezoelectric actuators, a new optimization criterion is considered based on the use of genetic algorithm to reduce the displacement output of the beam. The proposed optimization technique has been tested for two boundary conditions configurations; clamped -free and clamped-clamped beam. Numerical examples have been provided to analyze the effectiveness of the proposed technic.</abstract>

Mechanics of structures and solids laboratory

Department of mechanics, Faculty of technology

DjillaliLiabès University of SidiBel-Abbès

Optimal position of piezoelectric actuators for active vibration reduction of beams

<abstract xmlns="http://www.w3.org/1999/xhtml">A work on a mathematical modeling is very popular in applied sciences. Nowadays many mathematical models have been considered and new methods have been used for approaching of these models. In this paper we are considering mathematical modeling of nuclear family model with fractional order Caputo derivative. Also the existence and uniqueness results and numerical scheme are given with Adams-Bashforth scheme via fractional order Caputo derivative.</abstract>

Department of Mathematics, Faculty of Sciences

A new approach for nuclear family model with fractional order Caputo derivative

<abstract xmlns="http://www.w3.org/1999/xhtml">In this study we investigated the singularly perturbed boundary value problems for semilinear reaction-difussion equations. We have introduced a basic and computational approach scheme based on Numerov’s type on uniform mesh. We indicated that the method is uniformly convergence, according to the discrete maximum norm, independently of the parameter of <italic>ɛ</italic>. The proposed method was supported by numerical example.</abstract>

Dep. of Mathematics and Science Education

A Numerical Scheme For Semilinear Singularly Perturbed Reaction-Diffusion Problems

<abstract xmlns="http://www.w3.org/1999/xhtml">Null cartan curves have been studied by some geometers in both Euclidean and Minkowski spaces, but some special characters of the curves are not considered. In this paper, we study weak <italic>AW</italic> (<italic>k</italic>) – <italic>type</italic> and <italic>AW</italic> (<italic>k</italic>) – <italic>type</italic> null cartan curve in Minkowski 3-space 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00039_ieq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mi>E</mi><mn>1</mn><mn>3</mn></msubsup></mrow></math><tex-math>E_1^3</tex-math></alternatives></inline-formula>
. We define helix according to Bishop frame in 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00039_ieq_002.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mi>E</mi><mn>1</mn><mn>3</mn></msubsup></mrow></math><tex-math>E_1^3</tex-math></alternatives></inline-formula>
. Furthermore, the necessary and sufficient conditions for the helices in Minkowski 3-space are obtained.</abstract>

A study on null cartan curve in Minkowski 3-space

<abstract xmlns="http://www.w3.org/1999/xhtml">The purpose of this paper is to present a uniform finite difference method for numerical solution of a initial value problem for semilinear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.</abstract>

A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, the new exact solutions of nonlinear conformable fractional partial differential equations(CFPDEs) are achieved by using auxiliary equation method for the nonlinear space-time fractional Klein-Gordon equation and the (2+1)-dimensional time-fractional Zoomeron equation. The technique is easily applicable which can be applied successfully to get the solutions for different types of nonlinear CFPDEs. The conformable fractional derivative(CFD) definitions are used to cope with the fractional derivatives.</abstract>

Exact Travelling Wave Solutions for Space-Time Fractional Klein-Gordon Equation and (2+1)-Dimensional Time-Fractional Zoomeron Equation via Auxiliary Equation Method

<abstract xmlns="http://www.w3.org/1999/xhtml">The main purpose of this article is to obtain the new solutions of fractional bad and good modified Boussinesq equations with the aid of auxiliary equation method, which can be considered as a model of shallow water waves. By using the conformable wave transform and chain rule, nonlinear fractional partial differential equations are converted into nonlinear ordinary differential equations. This is an important impact because both Caputo definition and Riemann–Liouville definition do not satisfy the chain rule. By using conformable fractional derivatives, reliable solutions can be achieved for conformable fractional partial differential equations.</abstract>

Department of Computer Engineering, Faculty of Engineering

Department of Mathematics, Faculty of Science and Art

New Analytical Solutions of Conformable Time Fractional Bad and Good Modified Boussinesq Equations

<abstract xmlns="http://www.w3.org/1999/xhtml">This paper proposes obtaining the new wave solutions of time fractional sixth order nonlinear Equation (KdV6) using sub-equation method where the fractional derivatives are considered in conformable sense. Conformable derivative is an understandable and applicable type of fractional derivative that satisfies almost all the basic properties of Newtonian classical derivative such as Leibniz rule, chain rule and etc. Also conformable derivative has some superiority over other popular fractional derivatives such as Caputo and Riemann-Liouville. In this paper all the computations are carried out by computer software called Mathematica.</abstract>

New Travelling Wave Solutions for KdV6 Equation Using Sub Equation Method

<abstract xmlns="http://www.w3.org/1999/xhtml">The purpose of this study is extended the TOPSIS method based on interval-valued fuzzy set in decision analysis. After the introduction of TOPSIS method by Hwang and Yoon in 1981, this method has been extensively used in decision-making, rankings also in optimal choice. Due to this fact that uncertainty in decision-making and linguistic variables has been caused to develop some new approaches based on fuzzy-logic theory. Indeed, it is difficult to achieve the numerical measures of the relative importance of attributes and the effects of alternatives on the attributes in some cases. In this paper to reduce the estimation error due to any uncertainty, a method has been developed based on interval-valued fuzzy set. In the suggested TOPSIS method, we use Shannon entropy for weighting the criteria and apply the Euclid distance to calculate the separation measures of each alternative from the positive and negative ideal solutions to determine the relative closeness coefficients. According to the values of the closeness coefficients, the alternatives can be ranked and the most desirable one(s) can be selected in the decision-making process.</abstract>

naiyer.mohammadi.lanbaran13@ogr.atauni.edu.tr

Evaluation of Investment Opportunities With Interval-Valued Fuzzy Topsis Method

<abstract xmlns="http://www.w3.org/1999/xhtml">Compactification is the process or result of making a topological space into a compact space. An embedding of a topological space <italic>X</italic> as a dense subset of a compact space is called a compactification of <italic>X</italic>. There are a lot of compactification methods but we study with Fan- Gottesman compactification. A topological space <italic>X</italic> is said to be scattered if every nonempty subset <italic>S</italic> of <italic>X</italic> contains at least one point which is isolated in <italic>S</italic>. Compact scattered spaces are important for analysis and topology. In this paper, we investigate the relation between the Fan-Gottesman compactification of <italic>T</italic>3 space and scattered spaces. We show under which conditions the Fan-Gottesman compactification <italic>X</italic>* is a scattered.</abstract>

Fan-Gottesman Compactification and Scattered Spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">Cryptology is defined as the science of making communication incomprehensible to third parties who have no right to read and understand the data or messages. Cryptology consists of two parts, namely, cryptography and cryptanalysis. Cryptography analyzes methods of encrypting messages, and cryptanalysis analyzes methods of decrypting encrypted messages. Encryption is the process of translating plaintext data into something that appears to be random and meaningless. Decryption is the process of converting this random text into plaintext. Cloud computing is the legal transfer of computing services over the Internet. Cloud services let individuals and businesses to use software and hardware resources at remote locations. Widespread use of cloud computing raises the question of whether it is possible to delegate the processing of data without giving access to it. However, homomorphic encryption allows performing computations on encrypted data without decryption. In homomorphic encryption, only the encrypted version of the data is given to the untrusted computer to process. The computer will perform the computation on this encrypted data, without knowing anything on its real value. Finally, it will send back the result, and whoever has the proper deciphering key can decrypt the cryptogram correctly. The decrypted result will be equal to the intended computed value. In this paper, homomorphic encryption and their types are reviewed. Also, a simulation of somewhat homomorphic encryption is examined.</abstract>

Simulation of a Homomorphic Encryption System

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, solution of the following difference equation is examined
<disp-formula id="j_amns.2020.1.00047_ueq_001_w2aab3b7e2838b1b6b1aab1c16b1b1Aa"><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00047_ueq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>13</mn></mrow></msub></mrow><mrow><mn>1</mn><mo>+</mo><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>3</mn></mrow></msub><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>5</mn></mrow></msub><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>7</mn></mrow></msub><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>9</mn></mrow></msub><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>11</mn></mrow></msub></mrow></mfrac><mo>,</mo></mrow></math><tex-math>{x_{n + 1}} = {{{x_{n - 13}}} \over {1 + {x_{n - 1}}{x_{n - 3}}{x_{n - 5}}{x_{n - 7}}{x_{n - 9}}{x_{n - 11}}}},</tex-math></alternatives></disp-formula>
where the initial conditions are positive real numbers.</abstract>

Solution of the Rational Difference Equation 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00047_ieq_001.png"/><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>13</mn></mrow></msub></mrow><mrow><mn>1</mn><mo>+</mo><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>3</mn></mrow></msub><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>5</mn></mrow></msub><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>7</mn></mrow></msub><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>9</mn></mrow></msub><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>11</mn></mrow></msub></mrow></mfrac></mrow></math><tex-math>{x_{n + 1}} = {{{x_{n - 13}}} \over {1 + {x_{n - 1}}{x_{n - 3}}{x_{n - 5}}{x_{n - 7}}{x_{n - 9}}{x_{n - 11}}}}</tex-math></alternatives></inline-formula>

<abstract xmlns="http://www.w3.org/1999/xhtml">Different types of number theories such as elementary number theory, algebraic number theory and computational number theory; algebra; cryptology; security and also other scientific fields like artificial intelligence use applications of quadratic fields. Quadratic fields can be separated into two parts such as imaginary quadratic fields and real quadratic fields. To work or determine the structure of real quadratic fields is more difficult than the imaginary one.The Dirichlet class number formula is defined as a special case of a more general class number formula satisfying any types of number field. It includes regulator, <italic>ℒ</italic>-function, Dedekind zeta function and discriminant for the field. The Dirichlet’s class number <italic>h</italic>(<italic>d</italic>) formula in real quadratic fields claims that we have 
<disp-formula id="j_amns.2019.2.00033_ueq_001_w2aab3b7b1b1b6b1aab1c16b2b7Aa"><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2019.2.00033_ueq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>h</mi><mrow><mo>(</mo><mi>d</mi><mo>)</mo></mrow><mo>.</mo><mi mathvariant="italic">log</mi><msub><mo>ε</mo><mi>d</mi></msub><mo>=</mo><msqrt><mrow><mo>Δ</mo><mo>.</mo></mrow></msqrt><mo>ℒ</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><mo> </mo><msub><mo>χ</mo><mi>d</mi></msub></mrow><mo>)</mo></mrow></mrow></math><tex-math>h\left(d \right).log {\varepsilon _d} = \sqrt {\Delta} {\scr L} \left({1,\;{\chi _d}}\right)</tex-math></alternatives></disp-formula>
for positive <italic>d</italic> > 0 and the fundamental unit <italic>ɛ</italic><italic>d</italic> of 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2019.2.00033_ieq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>ℚ</mo><mrow><mo>(</mo><mrow><msqrt><mi>d</mi></msqrt></mrow><mo>)</mo></mrow></mrow></math><tex-math>{\rm{\mathbb Q}}\left({\sqrt d} \right)</tex-math></alternatives></inline-formula>
. It is seen that discriminant, <italic>ℒ</italic>-function and fundamental unit <italic>ɛ</italic><italic>d</italic> are significant and necessary tools for determining the structure of real quadratic fields.The focus of this paper is to determine structure of some special real quadratic fields for <italic>d ></italic> 0 and <italic>d</italic> ≡ 2,3 (<italic>mod</italic>4). In this paper, we provide a handy technique so as to calculate particular continued fraction expansion of integral basis element <italic>w</italic><italic>d</italic>, fundamental unit <italic>ɛ</italic><italic>d</italic>, and so on for such real quadratic number fields. In this paper, we get fascinating results in the development of real quadratic fields.</abstract>

A Handy Technique for Fundamental Unit in Specific Type of Real Quadratic Fields

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we adopt the model of [<xref ref-type="bibr" rid="j_amns.2019.2.00035_ref_012_w2aab3b7c39b1b6b1ab2b1c12Aa">12</xref>] by including fuzzy initial values to study the interaction of a monoclonal brain tumor and the macrophages for a condition of extinction of GB(Glioblastoma) by using Allee threshold. Numerical simulations will give detailed information on the behavior of the model at the end of the paper. We perform all the computations in this study with the help of the Maple software.</abstract>

An Allee Threshold Model for a Glioblastoma(GB)-Immune System(IS) Interaction with Fuzzy Initial Values

<abstract xmlns="http://www.w3.org/1999/xhtml">The parafree Lie algebras are an extraordinary class of Lie algebras which shares many properties with a free Lie algebra. In this work, we turn our attention to soluble product of parafree Lie algebras. We show that soluble product of parafree Lie algebras is parafree. Furthermore, we investigate some residual properties of that product.</abstract>

Soluble Product of Parafree Lie Algebras and Its Residual Properties

<abstract xmlns="http://www.w3.org/1999/xhtml">In this study we define the notion of (<italic>k,m</italic>)-type slant helices in Minkowski 4-space and express some characterizations for partially and pseudo null curves in 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00048_ieq_002.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mo>𝔼</mo><mn>1</mn><mn>4</mn></msubsup></mrow></math><tex-math>{\rm{\mathbb E}}_1^4</tex-math></alternatives></inline-formula>
.</abstract>

(<italic>k,m</italic>)-type slant helices for partially null and pseudo null curves in Minkowski space 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00048_ieq_001.png"/><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mo>𝔼</mo><mn>1</mn><mn>4</mn></msubsup></mrow></math><tex-math>{\rm{\mathbb E}}_1^4</tex-math></alternatives></inline-formula>

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Applied Mathematics and Nonlinear Sciences

 Applied Mathematics and Nonlinear Sciences has been classified in the 3rd place with the result of 2.7 JCI metrics in Mathematics, Applied Category Ranking released by Clarivate Analytics in the Journal Citation Report 2021!   Applied Mathematics and Nonlinear Sciences (AMNS) provides a forum for the rapid publication of original research in this field. The journal’s scope encompasses all nonlinear dynamic phenomena associated with mechanical, structural, civil, aeronautical, oceanography, electrical, and control systems.   We particularly welcome papers in the fields of celestial mechanics, mathematical physics, high-energy astrophysics, astrophysical studies of the interstellar medium, planetary and space science.   Review articles and original contributions are based on analytical, computational, and experimental methods.   Applied Mathematics and Nonlinear Sciences (AMNS) is dedicated to the publication of the highest quality short papers, regular papers, and expository papers. AMNS considers only original and timely contributions containing new results in various fields of Applied Mathematics and Nonlinear Sciences. Manuscripts may discuss fundamental or applied issues, and should offer clear evidence of novelty and significance. Papers devoted, for the most part, to pure mathematical and computational issues, with limited direct connection to current trends of nonlinear sciences research, are generally not suitable for publication in AMNS. Similarly, small, technical advances, or papers concerned only with mathematical applications or issues of basic science may not be considered favourably.   AMNS publishes in a continuous volume open model - Issue 1 is opened in January and closed at the at the end of December.     AMNS accepts papers through single peer blind external review by professional colleagues in the relevant fields. Unless clearly below the standard required by the journal, submitted articles will be sent to referees. They will generally be reviewed by at least two experts with the aim of reaching a decision as soon as possible. Where possible, the final decision is made on the basis that the referees are in accordance with one another. When there is a strong disagreement between referees, advice is sought from a member of the journals Editorial Board.   AMNS provides a forum for the rapid publication of original research in the field. The journal’s scope encompasses all nonlinear dynamic phenomena associated with mechanical, structural, civil, aeronautical, oceanography, electrical, and control systems. Review articles and original contributions are based on analytical, computational, and experimental methods.   The journal examines such topics as perturbation and computational methods, symbolic manipulation, dynamic stability, local and global methods, bifurcations, chaos, and deterministic and random vibrations. The journal also investigates Lie groups, multibody dynamics, robotics, fluid-solid interactions, system modelling and identification, friction and damping models, signal analysis, and measurement techniques.   The scope of this journal covers but is not limited to:    Numerical analysis   Numerical algebra   Numerical methods for ODE, PDE, FDE　   Computational geometry　   Computational fluid dynamics　   Computational optimisation　   Computational probability　   Statistical computation and simulation　   Computational intelligence　   Computational complexity　   Theoretical computer science　   Computational physics　   Computational biology　   Dynamical systems   Mathematical analysis   Topology and its applications   Nonlinear methods and its applications   Related applications in physics, engineering, chemistry, economics and the social sciences    Archiving   Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.　   Plagiarism Policy   The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.　 

Applied Mathematics and Nonlinear Sciences

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