Abstract In this paper, the ill-posedness of derivative interpolation is discussed, and a regularized derivative interpolation for non-bandlimited signals is presented. The convergence of the regularized derivative interpolation is studied. The numerical results are given and compared with derivative interpolation using the Tikhonov regularization method. The regularized derivative interpolation in this paper is more accurate in computation.

Abstract Solving for currents of an electrical circuit with resistances and batteries has always been the ultimate test of proper understanding of Kirchoff’s rules. Yet, it is hardly ever emphasized that a systematic solution of more complex cases requires good understanding of the relevant part of Graph theory. Even though this is usually not covered by Physics’ curriculum, it may still be of interest to some teachers and their mathematically inclined students, who may want to learn details of the rigorous approach. The purpose of this article is to provide a concise derivation of a linear set of equations leading to a unique solution of the problem at hand. We also present a simple computer program which builds such a solution for circuits of any textbook size.

Abstract This paper does not claim to prove the Goldbach conjecture, but it does pro vide a new way of proof (LiKe sequence); And in detailed introduces the proof process of this method: by indirect transformation, Goldbach conjec ture is transformed to prove that, for any odd prime sequence (357 ,,, , )  Pn ,there must have no LiKe sequence when the terms must be less than 3× Pn . This method only studies prime numbers and corresponding composite numbers, replaced the relationship between even numbers and indeterminate prime numbers. In order to illustrate the importance of the idea of trans forming the addition problem into the multiplication problem, we take the twin prime conjecture as an example and know there must exist twin primes in the interval 2 3 , Pn Pn     . This idea is very important for the study of Gold bach conjecture and twin prime conjecture. It’s worth further study.

Abstract To stay competitive, the mobile telecommunication companies spend mil lions of Ghana cedi each year on building long-term relationships with their customers. Marketing managers are constantly challenged with the problem of where to channel the limited resources in order to retain existing custom ers. This study approaches the customer retention problem in the mobile phone sector from a behavioural perspective, applying the Behavioural Pers pective Model as the main analytical framework and further exploits some other factors that influence customer retention. The model includes a set of pre-behaviour and post-behaviour factors to study consumer choice, and ex plains its relevant drivers in a viable and comprehensive way, grounded in radical behaviourism. Data for the analysis were collected from tertiary stu dents from Accra and Takoradi. Data collected were analysed using the mul tinomial regression technique. Analysis of the data revealed that the Beha viour setting factor is the only significant element in Behaviour Perspective Model. Further exploitation of behaviour situation revealed that the number of networks a customer uses, previous experience of a customer and cus tomer’s intention are significant factors in determining customer retention in Ghana’s mobile telecommunication industry.

Abstract Coastal wastewater-discharged effluents contain a mixture of pollutants with decay rates that vary with water depth. Analytical models using a two-dimen sional advection-diffusion equation are presented to study the effects of a cross-stream sudden depth change and decay on mixing and dispersing steady discharge of effluents through a sea outfall. The solutions are illustrated graph ically by plotting contours of concentration, resembling snapshots of dis charged effluent plumes in the far-field. Different shapes of effluent plumes are observed due to the variability of length of the step seabed, and the con centration at the step seabed is formulated to measure how much has dis charged effluents dispersed into or out of the shallow coastal waters.

Abstract The paper aims to investigate different types of weighted ideal statistical con vergence and strongly weighted ideal convergence of double sequences of fuzzy numbers. Relations connecting ideal statistical convergence and strongly ideal convergence have been investigated in the environment of the newly de fined classes of double sequences of fuzzy numbers. At the same time, we have examined relevant inclusion relations concerning weighted (λ µ, ) -ideal statistical convergence and strongly weighted (λ µ, ) -ideal convergence of double sequences of fuzzy numbers. Also, some properties of these new se quence spaces are investigated.

Abstract This paper studies the generalized synchronization of a class of drive-response neural networks with time-varying delay. When the topological structures of the drive-response neural networks are known, by designing an appropriate nonlinear adaptive controller, the generalized synchronization of these two networks is obtained based on Lyapunov stability theory and LaSalle’s inva riance principle.

Abstract An epidemic model which describes Huanglongbing transmission is pro posed with the goal of investigating the effect of quarantine measures on the spread of diseases. First of all, the analytical formula for the basic reproduc tion number 0 is obtained by the means of next generation matrix, and the existence of disease-free equilibrium and endemic equilibrium is discussed. Then, the local stability and the global stability of equilibria are investigated by using Routh-Hurwitz criterion and Lyapunov function, respectively. Nu merical simulations indicate that comprehensive quarantine measures can ef fectively control the spread of Huanglongbing. It provides a reliable tactic ba sis for preventing the epidemic outbreak.

Abstract In this work, a highly efficient algorithm is developed for solving the parabolic partial differential equation (PDE) with the nonlocal condition. For this purpose, we employ orthogonal Chelyshkov polynomials as the basis. The convergence analysis of the proposed scheme is derived. Numerical experiments are carried out to explain the efficiency and precision of the proposed scheme. Furthermore, the reliability of the scheme is verified by comparisons with assured existing methods.

Abstract Some games may have a Nash equilibrium if the parameters (e.g. probabilities for success) take certain values but no equilibrium for other values. So there is a transition from Nash equilibrium to no Nash equilibrium in parameter space. However, in real games in business and economics, the input parameters are not given. They are typically observed in several similar occasions of the past. Therefore they have a distribution and the average is used. Even if the averages are in an area of Nash equilibrium, some values may be outside making the entire result meaningless. As the averages are sometimes just guessed, the distribution cannot be known. The main focus of this article is to show this effect in an example, and to explain the surprising result by topological explanations. We give an example of two players having three strategies each (e.g. player and keeper in penalty shooting) where we demonstrate the effect explicitly. As the transition of Nash equilibrium to no equilibrium is sharp, there may be a special form of chaos which we suggest to call topological chaos.

Abstract This paper considers practical, high-order methods for the iterative location of the roots of nonlinear equations, one at a time. Special attention is being paid to algorithms also applicable to multiple roots of initially known and unknown multiplicity. Efficient methods are presented in this note for the evaluation of the multiplicity index of the root being sought. Also reviewed here are super-linear and super-cubic methods that converge contrarily or alternatingly, enabling us, not only to approach the root briskly and confidently but also to actually bound and bracket it as we progress.

Abstract Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscribed by an arbitrary triangle of tangents, the vertices of which are lying on the circumference of the disk. They offered two non-elementary methods of proof, one using Poncelet’s Theorem, the other employing Blaschke products. In this paper, it is the intention to present an elementary proof by means of analytic geometry.

Abstract High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, various flexible distributions have been proposed. It is well known that mixture distributions produce flexible models with good statistical and probabilistic properties. In this work, a finite mixture of two special cases of Generalized Inverse Gaussian distribution has been constructed. Using this finite mixture as a mixing distribution to the Normal Variance Mean Mixture we get a Normal Weighted Inverse Gaussian (NWIG) distribution. The second objective, therefore, is to construct and obtain properties of the NWIG distribution. The maximum likelihood parameter estimates of the proposed model are estimated via EM algorithm and three data sets are used for application. The result shows that the proposed model is flexible and fits the data well.

Abstract We realize the function projective synchronization (FPS) between two discrete-time hyperchaotic systems, that is, the drive state vectors and the response state vectors can evolve in a proportional scaling function matrix. In this paper, a systematic scheme is explored to investigate the function projective synchronization of two identical discrete-time hyperchaotic systems using the back stepping method. Additionally, FPS of two different hyperchaotic systems is also realized. Numeric simulations are given to verify the effectiveness of our scheme.

Abstract In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of pre smoothed estimation of relative-risk function and the properties of the estimator by using methods of numerical modeling are discussed. In the model under consideration, the estimates were compared using numerical methods to determine which of the estimates is actually better.

Abstract Since the onset of the COVID-19 epidemic, the world has been impressed by two things: The number of people infected and the number of deaths. Here, we propose a mathematical model of the spread of this disease, analyze this model mathematically and determine one or more dominant factors in the propagation of the COVID-19 epidemic. We consider the S-E-I-R epidemic model in the form of ordinary differential equations, in a population structured in susceptibles S, exposed E as caregivers, travelers and assistants at public events, infected I and recovered R classes. Here we decompose the recovered class into two classes: The deaths class D and the class of those who are truly healed H. After the model construction, we have calculated the basic reproduction number R0 , which is a function of certain number of parameters like the size of the exposed class E. In our paper, the mathematical analysis, which consists in searching the equilibrium points and studying their stability, is done. The work identifies some parameters on which one can act to control the spread of the disease. The numerical simulations are done and they illustrate our theoretical analysis.

Abstract In this paper, we introduce AK' iteration scheme to approximate fixed point for Suzuki generalized non expansive mapping satisfying ( , ) B δ µ condition in the framework of Banach spaces. Also, an example is given to confirm the efficiency of AK' iteration scheme. Our results are generalizations in the existing literature of fixed points in Banach spaces.

Abstract The present aim is to update, upon arrival of new learning data, the parameters of a score constructed with an ensemble method involving linear discriminant analysis and logistic regression in an online setting, without the need to store all of the previously obtained data. Poisson bootstrap and stochastic approximation processes were used with online standardized data to avoid numerical explosions, the convergence of which has been established theoretically. This empirical convergence of online ensemble scores to a reference “batch” score was studied on five different datasets from which data streams were simulated, comparing six different processes to construct the online scores. For each score, 50 replications using a total of 10N observations (N being the size of the dataset) were performed to assess the convergence and the stability of the method, computing the mean and standard deviation of a convergence criterion. A complementary study using 100N observations was also performed. All tested processes on all datasets converged after N iterations, except for one process on one dataset. The best processes were averaged processes using online standardized data and a piecewise constant step-size.