The concept of return to scale is the ratio of proportional variations in outputs to proportional variations in inputs. A decision maker by determining the returns to scale of a unit can made a decision to limitation or extension of it. The radial models cannot determine the output changes after applying variations in the input vector. So far, the amount of input changes, output changes and efficiency

In this article, the mitigating Internet bottleneck including quadratic–cubic nonlinearity containing the \(\rho\)-derivative has been considered that describes the control of Internet traffic. This equation is analyzed utilizing two integration schemes, videlicet, the extended sinh-Gordon equation expansion technique and improved \(\tan (\Xi /2)\)-expansion technique. Various kinds of traveling wave

In this paper, the numerical solutions of the linear fractional Fredholm–Volterra integro-differential equations have been investigated. For this purpose, Laguerre polynomials have been used to develop an approximation method. Precisely, using the suitable collocation points, a system of linear algebraic equations arises which is resulted by the transformation of the integro-differential equation.

In this article, we work on the existence of solution of generalized fractional integral equations of two variables. To achieve our main objective, we establish a new fixed point theorem using measure of noncompactness and a new contraction operator which generalized the Darbo’s fixed point theorem (DFPT). Also we obtain the corresponding coupled fixed point theorem. Finally we apply this generalized

The present article deals with the solution of nonlinear fractional Klein–Fock–Gordon equation which involved the newly developed Caputo–Fabrizio fractional derivative with non-singular kernel. We adopt fractional homotopy perturbation transform method in order to find the approximate solution of fractional Klein–Fock–Gordon equation in the form of rapidly convergent series. Existence and uniqueness

Applications of misspecified models in the field of survival analysis particularly frailty models may result in poor generalization and biases. Since gamma and inverse Gaussian distributions are often used interchangeably as frailty distributions for heterogeneous survival data, clear distinction between them is necessary. Based on closed form expressions of unconditional hazards and survival functions

For every positive integer n and for a prime number p, we denote the wreath product of \(Z_p\) and \(Z_{p^n}\) by G(n, p). In this paper, we will consider three probabilistic concepts of finite groups. The first problem which we examine is the calculation of the kth-roots of elements in G(n, p) when \(k\ge 2\). The second problem which is investigated is the computation of the kth-commutative degree

This paper develops the approximate solution of the two-dimensional space-time fractional diffusion equation. Firstly, the time-fractional derivative is discretized with a scheme of order \({\mathcal {O}}({\delta \tau }^{2-\alpha }),~ 0<\alpha <1\) . Then, the Chebyshev spectral collocation of the third kind is implemented to approximate spatial variables and to obtain full discretization of the equation

In this paper, we will compute the chromatic number of \(D_9\) , \(D_{15}\), and we will present an algorithm to compute the chromatic number of any Latin square of \(D_n\) (for all n) order.

Key fobs are small security hardware devices that are used for controlling access to doors, cars and etc. There are many types of these devices, more secure types of them are rolling code. They often use a light weight cryptographic schemas to protect them against the replay attack. In this paper, by the mean of constructing a Hamiltonian graph, we propose a simple to implement and secure method which

It is assumed that the lifetime of a system is a random variable valued based on a probability model and reliability studies with a system as a function of time. In this study, by multi-layers and hierarchical coding, we initially recognize the common operations and then, considering the sources likely to cause a crash, the crash center will be detected followed by estimating the structure of reliability

In this paper, the discontinuous Legendre wavelet Galerkin method is proposed for the numerical solution of the Burgers–Fisher and generalized Burgers–Fisher equations. This method combines both the discontinuous Galerkin and the Legendre wavelet Galerkin methods. Various properties of Legendre wavelets have been used to find the variational form of the governing equation. This variational form transforms

In this paper, we have proposed a new generalized robust estimators of population mean under different ranked set sampling. Robust estimators are recently defined by Zaman and Bulut (Commun Stat Theory Methods 48(8):2039–2048, 2019a) and Ali et al. (Commun Stat Theory Methods, 2019. https://doi.org/10.1080/03610926.2019.1645857) under simple random sampling. We have generalized robust-type estimators

This paper presents a numerical solution of the temporal-fractional Black–Scholes equation governing European options (TFBSE-EO) in the finite domain so that the temporal derivative is the Caputo fractional derivative. For this goal, we firstly use linear interpolation with the \((2-\alpha)\)-order in time. Then, the Chebyshev collocation method based on the second kind is used for approximating the

In this paper, we apply Haar wavelet collocation method to solve the linear and nonlinear second-order singularly perturbed differential difference equations and singularly perturbed convection delayed dominated diffusion equations, arising in various modeling of chemical processes. First, we transform delay term by using Taylor expansion and then apply Haar wavelet method. To show the robustness,

Induced aggregation operators are more suitable for aggregating the individual preference relations into a collective fuzzy preference relation. Therefore, in this paper, we introduce the notion of some new types induced aggregation operators, namely induced interval-valued Pythagorean fuzzy ordered weighted geometric aggregation operator, induced interval-valued Pythagorean fuzzy hybrid geometric

Here, we shed light on the fractional linear and nonlinear Klein–Gorden partial differential equations via Fractional Shifted Legendre Tau Method. With this objective, the operational matrices of fractional-order shifted Legendre functions (FSLFs) are derived and combined with the Tau method to convert the fractional-order differential equations to a system of solvable algebraic equations. The validity

A fourth-order numerical method based on cubic B-spline functions has been proposed to solve a class of advection–diffusion equations. The proposed method has several advantageous features such as high accuracy and fast results with very small CPU time. We have applied the Crank–Nicolson method to solve the advection–diffusion equation. The stability analysis is performed, and the method is shown to

In this paper, the numerical solution of the modified regularized long wave equation is obtained using a quartic B-spline approach with the help of Butcher’s fifth-order Runge–Kutta (BFRK) scheme. Here, any kind of transformation or linearization technique is not implemented to tackle the nonlinearity of the equation. The BFRK scheme is applied to solve the systems of first-order ordinary differential

Data envelopment analysis (DEA) technique is commonly utilized for efficiency assessment in a variety of fields for both theoretical and applicational purposes. In classic cost efficiency measurement models, the input and output data and input prices should be known for each decision-making unit (DMU). However, in real-life markets the input prices are not precisely defined for DMUs. In this paper

In this paper, a meshless method with ridge basis functions for solving the time fractional two-flow domain model problem is proposed. The method uses the L1 approximation formula based on piecewise linear interpolation to discretize the Caputo time fractional derivative \( (0 < \alpha < 1) \), and by means of the ridge basis function to construct the approximation function, and uses the collocation

In this article, firstly the factors influencing the prices of cash market transactions on the basis of gold coin (Bahar Azadi coin) prices and futures contract trading on the Iran Mercantile Exchange are examined during a full year. Then, based on these factors, two new models for predicting the price of the futures contract of gold coin have been presented. These patterns are based on the general

In this paper, a high-order compact finite difference method (CFDM) with an operator-splitting technique for solving the 3D time-fractional diffusion equation is considered. The Caputo–Fabrizio time operator is evaluated by the \(L_1\) approximation, and the second-order space derivatives are approximated by the compact CFDM to obtain a discrete scheme. Alternating direction implicit method (ADI) is

This paper studies an investor’s optimal investment, optimal net debt ratio with collateral security and optimal consumption plan in an economy that faces both diffusion and jump risks. The underlying assets are tangible and intangible assets. There have been major challenges of quantifying intangible assets. In this paper, we assume that the price of our intangible asset follows a jump-diffusion process

Data envelopment analysis (DEA) is a model for measuring the efficiency of decision-making units (DMUs). The majority of DEA models suffer from drawbacks, in particular, changes in the weights of inputs and outputs. Consequently, the efficiency of DMUs is measured with different weights and so it is important to establish how to evaluate all DMUs using a common weight to optimize their efficiency at

The \((4+1)\)-dimensional Fokas (4DFK) equation is explicitly written out by means of the linearized operator of the 4DFK equation after introducing an additional auxiliary variable. Based on the bilinear form, bilinear Bäcklund transformations consisting of three bilinear equations are provided. A new class of lump solutions is given and analyzed using the extremum theory of multivariate function

In this paper, we consider a bivariate nonlinear Fredholm integral equation of the second kind. Then an approximate solution for some of these problems is investigated. To determine the aimed solution, the hybrid of 2D block-pulse functions with Chebyshev polynomials basis with the operational matrices is applied. In this work, we generalize the operational matrices stated by Behbahani (J Basic Appl

In this paper, complex reproducing kernel Hilbert spaces and their reproducing kernels are introduced. The reproducing kernel is constructed by combining Gaussian radical basis function kernel and spline kernel. In the spaces, using the related theory, a novel numerical method is developed to solve Schröinger equations. The present method is a meshless method and does not require connection between

This work introduces a direct method based on orthonormal Bernstein polynomials wavelet bases, to present a stable algorithm for numerical inversion of a system of generalized Abel integral equations. The application of all the currently existing numerical inversion methods was strictly limited to only one portion of the generalized Abel integral equations. The proposed method is quite accurate, and

In the present study, the problem of simulating a non-Newtonian and two-dimensional blood flow in a flexible stenosed artery is examined by an implicit finite difference method. The streaming blood in the human artery is represented as a micropolar fluid. The governing non-Linear partial differential equations are modeled in cylindrical coordinates system and following a suitable radial coordinate

An improved derivative-free trust-region method to solve systems of nonlinear equations in several variables is presented, combined with the Wolfe conditions to update the trust-region radius. We believe that producing step-sizes by the Wolfe conditions can control the trust-region radius. The new algorithm for which strong global convergence properties are proved is robust and efficient enough to

In this paper, a new and applied concept of topological spaces based upon relations is introduced. These topological spaces are called R-topological spaces and SR-topological spaces. Some of the properties of these spaces and their relationship with the initial topological space are verified. Moreover, some of their applications for example in fixed point theory, functional analysis, \(C^*\)-algebras

Multi-objective linear plus linear fractional programming problem is an emerging tool for solving problems in different environments such as production planning, financial and corporate planning and healthcare and hospital planning which has attracted many researchers in recent years. This paper presents a method to find a Pareto optimal solution for the multi-objective linear plus linear fractional

In this paper, we present the complex Rolle’s and Mean Value Theorems for \(\alpha\)-holomorphic functions and give some related results and applications of these theorems.

A method based on B-splines has been introduced for the solution of second-order nonlinear hyperbolic equation in 2-dimensions subject to appropriate initial and Dirichlet boundary conditions. We first convert the second-order equation into a system of first-order partial differential equations. Then, collocation of bi-cubic B-splines is used to discretize spatial variables and their derivatives to

Neutrosophy consists of neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalisation of classical sets, fuzzy set, intuitionistic fuzzy set, etc. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena where it is necessary

It is well known the connection between the growth of the Schwarzian with both the univalence [see Beardon and Gehring (Comment Math Helv 55: 50–64, 1980), Nehari (Bull Am Math Soc 55:545–551, 1949), Ovesea (Novi Sad J Math 26(1):69–76, 1996)] and the quasiconformal extension of the function [see Ahlfors and Weill (Proc Am Math Soc 13:975–978, 1962), Osgood (Old and new on the Schwarzian derivative

Here, we have studied the ideas of (s, t)-\(g_{\rho }\) and (s, t)-\(\lambda _{\rho }\)-closed sets \((s,t=1,2;\,\, s\not =t)\) and pairwise \(\lambda\)-closed sets in a generalized bitopological space \((X,{\rho_{1}}, {\rho_{2}})\). We have investigated the properties on some new separation axioms namely pairwise \(T_\frac{1}{4}\), pairwise \(T_\frac{3}{8}\), pairwise \(T_\frac{5}{8}\) and have established

In this work, we propose a numerical framework for solving a class of Lienard’s equation. This equation arises in the development of radio and vacuum tube technology. The spatial approximation is based on the Bernoulli collocation method in which the shifted Chebyshev collocation points are used as collocation nodes. The operational matrix of derivatives of Bernoulli is introduced. The matrix together

The ambition of this paper is to construct fixed point theorems fulfilling a generalized locally F-contractive multivalued mapping on a closed ball in complete b-metric-like space. Example and application are given to show the novelty of our results. Our results combine, extend and infer several comparable results in the existing literature.

Direct methods are applied to solve linear time-varying delay systems based on vector forms of block-pulse functions (BPFs) and triangular functions (TFs). Operational matrices of integration of BPFs and TFs are applied to transform linear time-varying delay systems to a linear set of algebraic equations. Further, some numerical examples are provided to indicate reliability and the accuracy of these

Nowadays, certain problems in automata theory, manufacturing systems, telecommunication networks, parallel processing systems and traffic control are intimately linked with linear systems over tropical semirings. Due to non-invertibility of matrices—except monomial matrices—over certain semirings, we cannot generally take advantage of having the inverse of the coefficient matrix of a system to solve

Detection of spam and non-spam emails is considered a great challenge for email service providers and users alike. Spam emails waste the Internet traffic and also contain malicious links that mostly direct users to phishing webpages. Another challenge of spams is their role in spreading malware on the network, further emphasizing the need for their detection. Despite the application of data mining

In this paper, we discuss and analyze methods for solving a system of linear equations over idempotent semifields. The first method is based on the pseudo-inverse of the system matrix. We then go over a specific version of Cramer’s rule which is also related to the pseudo-inverse of the system matrix. In these two methods, the constant vector plays an implicit role in solvability of the system. Another

In this article, the authors proposed Chebyshev pseudospectral method for numerical solutions of two-dimensional nonlinear Schrodinger equation with fractional-order derivative in both time and space. Fractional-order partial differential equations are considered as generalizations of classical integer-order partial differential equations. The proposed method is established in both time and space to

We show that the classical Marsden–Weinstein Reduction theorem for Hamiltonian systems with symmetries is still true for contact–symplectic pairs.

In this paper, we present a numerical method to solve fractional-order delay integro-differential equations. We use the operational matrices based on the fractional-order Euler polynomials to obtain numerical solution of the considered equations. By approximating the unknown function and its derivative in terms of the fractional-order Euler polynomials and substituting these approximations into the

In this paper, we introduce ternary quadratic Pompeiu functional equations in ternary Banach algebras. Moreover, we investigate the general solution and the generalized Hyers–Ulam stability of ternary quadratic Pompeiu functional equation and other type of this new equation$$\begin{aligned}&f(x+y+z+[xyz])+f(x+y+z-[xyz])+2f(x)+2f(y)+2f(z)\\&\quad =2f(x+y)+2f(y+z)+2f(x+z)+2[f(x)f(y)f(z)]. \end{aligned}$$

In this article, a fast numerical method based on orthogonal Chebyshev polynomials for pricing discrete double barrier option is illustrated. At first, a recursive formula for computing price of discrete double barrier option is obtained. Then, these recursive formulas are estimated by Chebyshev polynomials and expressed in operational matrix form that reduce CPU time of algorithm. Finally, the effectiveness

Identifying finite non-group semigroups for every positive integer is significant because of many applications of such semigroups are functional in various branches of sciences such as computer science, mathematics and finite machines. The finite non-commutative monoids as a type of such semigroups were identified in 2014, for every positive integer. We here attempt to identify the finite commutative

A fourth-order B-spline collocation method has been applied for numerical study of Burgers–Fisher equation, which illustrates many situations occurring in various fields of science and engineering including nonlinear optics, gas dynamics, chemical physics, heat conduction, and so on. The present method is successfully applied to solve the Burgers–Fisher equation taking into consideration various parametric

This article presents a parametric bootstrap approach to inference on the regression coefficients in panel data models. We aim to propose a method that is easily applicable for implement hypothesis testing and construct confidence interval of the regression coefficients vector of balanced and unbalanced panel data models. We show the results of our simulation study to compare of our parametric bootstrap

In this paper, at first for a given set of real numbers with only one positive number, and in continue for a given set of real numbers in special conditions, we construct a symmetric nonnegative matrix such that the given set is its spectrum.

Common set of weights (CSWs) method is one of the popular ranking methods in DEA which can rank efficient and inefficient units. Based on an identical criterion, the method selects the most favorable weight set for all units. An important issue is that in most common DEA models, the internal structure of the production units is ignored and the units are often considered as black boxes. In this paper

In this paper, we introduce a numerical method to obtain an accurate approximate solution of the integro-differential delay equations with state-dependent bounds. The method is based basically on the generalized Mott polynomial with the parameter-\(\beta\), Chebyshev–Lobatto collocation points and matrix structures. These matrices are gathered under a unique matrix equation and then solved algebraically

In this paper, a new bivariate discrete distribution is defined and studied in-detail, in the so-called the bivariate exponentiated discrete Weibull distribution. Several of its statistical properties including the joint cumulative distribution function, joint probability mass function, joint hazard rate function, joint moment generating function, mathematical expectation and reliability function for

This paper is concerned with obtaining approximate numerical solution of a classical integral equation of some special type arising in the problem of cruciform crack. This integral equation has been solved earlier by various methods in the literature. Here, approximation in terms of Daubechies scale function is employed. The numerical results for stress intensity factor obtained by this method for

In this paper, we develop a new hybrid conjugate gradient method that inherits the features of the Liu and Storey (LS), Hestenes and Stiefel (HS), Dai and Yuan (DY) and Conjugate Descent (CD) conjugate gradient methods. The new method generates a descent direction independently of any line search and possesses good convergence properties under the strong Wolfe line search conditions. Numerical results

This article deals with a fractional differential equation with a deviated argument defined on a nondense set. A fixed-point theorem and the concept of measure of noncompactness are used to prove the existence of a mild solution. Furthermore, by using the compactness of associated cosine family, we proved that system is approximately controllable and obtains an optimal control which minimizes the performance

In this paper, we derive a new jump-diffusion model for electricity spot price from the “Price-Cap” principle. Next, we show that the model has a non-classical mean-reverting linear drift. Moreover, using this model, we compute a new exact formula for the price of forward contract under an equivalent martingale measure and we compare it to Cartea et al. (Appl Math Finance 12(4):313–335, 2005) formula