A high-order nonlinear Schrödinger equation with the weak non-local nonlinearity and its optical solitons

Abstract The present paper explores a high-order nonlinear Schrodinger equation in a non-Kerr law media with the weak non-local nonlinearity describing solitons' propagation through nonlinear optical fibers. To this end, the real and imaginary parts of the model are firstly extracted using a wave variable transformation. The modified Kudryashov method and symbolic computations are then adopted to successfully retrieve optical solitons of the model. The results presented in the current study demonstrate the great performance of the modified Kudryashov method in handling high-order nonlinear Schrodinger equations

An improved Runge-Kutta method for solving fuzzy differential equations under generalized differentiability

In this paper, a new Runge-Kutta method be presented which has the fifth order local truncation error with lower function evaluation in comparison with classical one's. Also we use the generalized derivative instead of Seikkala's derivative to illustrate the efficiency of this derivative. The method's applicability is illustrated by solving a linear first order fuzzy differential equation

Nearest interval-valued approximation of interval-valued fuzzy numbers

In this paper, we proposed a new interval-valued approximation of interval-valued fuzzy numbers, which is the best one with respect to a certain measure of distance between interval-valued fuzzy numbers. Also, a set of criteria for interval-valued approximation operators is suggested

On a numerical solution for fuzzy fractional differential equation using an operational matrix method

In the current manuscript we suggest an approach to obtain the solutions of the fuzzy fractional differential equations (FFDEs). We found the operational matrix within the modified Laguerre functions. In this way the investigated equations are turned into a set of algebraic equations. We provide examples to illustrate both accuracy and simplicity of the suggested approach

Evaluating the performance of rural areas in improving entrepreneurship infrastructure for the development of rural entrepreneurship in Khalilabad city

Entrepreneurship in order to generate income and employment is one of the most important tools for rural development and the present study has been prepared with the same purpose and as the evaluation of rural performance in improving entrepreneurship infrastructure for rural entrepreneurship development in Khalilabad city. The present research is applied in terms of purpose and in terms of descriptive-analytical method, which used library and field methods to collect information and a researcher-made questionnaire for field data. The sample population was randomly studied using Cochran's formula including 370 people in 23 villages of the city. The results obtained in the villages of the city show that the performance of rural villagers in Khalilabad city in order to develop rural entrepreneurship has been weak. The villages of the city, except for the development of public infrastructure (water, electricity, etc.) in other areas of entrepreneurial infrastructure have not performed well and have not been able to achieve the desired goals

A Gradient Weighted Moving Finite-Element Method with Polynomial Approximation of Any Degree

A gradient weighted moving finite element method (GWMFE) based on piecewise polynomial of any degree is developed to solve time-dependent problems in two space dimensions. Numerical experiments are employed to test the accuracy and effciency of the proposed method with nonlinear Burger equation

Evaluating the performance of modern rural management (Dehyari) in improving social contexts and attracting financial resources for the development of rural entrepreneurship in Khalilabad

Entrepreneurship is one of the most important tools for planning and achieving the development of rural communities. Today, due to the problems in these communities, attention and emphasis on rural entrepreneurship is very important; Because entrepreneurship can play an effective role in improving the economic and living conditions of villages by creating new employment and income opportunities, and the present study aims to evaluate the performance of modern rural management (rural) in improving social contexts and attracting financial resources. It has been prepared for the development of rural entrepreneurship in Khalilabad city. The present research is applied in terms of purpose and in terms of descriptive-analytical method, which used library and field methods to collect information and a researcher-made questionnaire for field data. The sample population was randomly studied using Cochran's formula including 370 people in 23 villages of the city. The results obtained in the villages of the city show that the performance of rural villagers in Khalilabad city in order to develop rural entrepreneurship has been weak. Villages have not improved the social context and attracted financial resources for the development of rural entrepreneurship and have not been able to achieve the desired goals

Cryptanalysis and Improvement of a Flexible and Lightweight Group Authentication Scheme

Shamir’s secret sharing scheme is one of the substantial threshold primitives, based on which many security protocols are constructed such as group authentication schemes. Notwithstanding the unconditional security of Shamir\u27s secret sharing scheme, protocols that are designed based on this scheme do not necessarily inherit this property. In this work, we evaluate the security of a lightweight group authentication scheme, introduced for IoT networks in IEEE IoT Journal in 2020, and prove its weakness against the linear subspace attack, which is a recently-proposed cryptanalytical method for secret sharing-based schemes. Then, we propose an efficient and attack-resistant group authentication protocol for IoT networks