Meromorphic solutions to certain differential-difference equations

The aim of this paper is to investigate the growth and constructions of meromorphic solutions of the nonlinear differential-difference equation$$f^n(z)+h(z)\Delta_cf^{(k)}(z)=A_0(z)+A_1(z)e^{\alpha_1z^q}+\cdots+A_m(z)e^{\alpha_mz^q},$$where $n, m, q\in \mathbb{N}^+$, $\alpha_1,\cdots,\alpha_m$ are distinct nonzero complex numbers, $h(z)$ is a nonzero entire function and $A_j(z)~(0\leq j\leq m)$ are meromorphic functions. In particular, for $A_0(z)\equiv 0$, we give the exact form of meromorphic solutions of the above equation under certain conditions. In addition, our results are shown to be sharp

Some identities involving degenerate Cauchy numbers and polynomials of the fourth kind

In this paper, we study the constant equations associated with the degenerate Cauchy polynomials of the fourth kind using the generating function and Riordan array. By using the generating function method and the Riordan array method, we establish some new constants between the degenerate Cauchy polynomials of the fourth kind and two types of Stirling numbers, Lab numbers, two types of generalized Bell numbers, Daehee numbers, Bernoulli numbers and polynomials

New Types of Pythagorean Fuzzy Modules and Applications in Medical Diagnosis

In this article, we discuss several distinct categories of pythagorean fuzzy modules, study pythagorean fuzzy relations, and provide applications in the field of medical diagnosis. The concept of pythagorean fuzzy prime modules, along with its characteristics, is presented. In addition,an investigation is conducted into a pythagorean fuzzy multiplication module. Moreover, pythagorean fuzzy relations and pythagorean fuzzy homomorphisms are introduced. By making use of pythagorean fuzzy sets and pythagorean fuzzy relations., we propose a novel approach to the medical diagnosis process. This approach is achieved by pointing the smallest distance between the symptoms of the patients and the symptoms related to diseases

Numerical Methods for Convex Quadratic Programming with Nonnegative Constraints

This paper deals with some problems in numerical simulation for convex quadratic programming with nonnegative constraints. For systems of ordinary differential equations which derived from the above mentioned problem, we construct a kind of new numerical method: the modified implicit Euler method. Under some restrictions for step-size, we obtained the numerical solution which satisfied with the termination condition. Compared with the classical Matlab command ODE23, the new method has ideal computation cost

SPC using size Biased Maxwell Distribution

This paper elucidates the control limits for size biased Maxwell distribution for different sample size(s) with fixed scale parameter. The performance of the control chart observed through the average run length (ARL). The propose control limits, size biased Maxwell (SBMW), compare with existing Maxwell Distribution with same parameter setting and found majority of times better in performance as compare to existing control chart

Mathematical Modelling of Cholera Incorporating The Dynamics of The Induced Achlorhydria Condition And Treatment

Cholera is an infectious disease caused by the bacterium Vibrio cholerae rampant in countries with inadequate access to clean water and proper sanitation. In this work a mathematical model for cholera incorporating the dynamics of the induced achlorhydria condition and treatment is analysed. Michaelis-menten equation in microbiology is used to show variation in pH level of the hydrochloric acid in the digestive system. Vibrio cholerae are acid labile and thrive well in alkaline medium.Once the gastric pH is raised by factors like antacid drugs or surgery the stomach medium become suitable for Vibrio cholerae to thrive and multiply very fast than healthy people. This lead to cholera transmission as the infected individuals with induced achlorhydria condition shed more folds of Vibrio cholerae to the environment. If individuals with achlorhydria condition are treated, the effect of cholera outbreak is reduced. The existence and stability of the equilibrium points is established. Analysis of the model show that the disease free equilibrium is both locally and globally asymptotically stable when the basic reproduction number is less than unity, while the endemic equilibrium is locally asymptotically stable when the reproduction number is greaterthan unity. Numerical simulations is done using MATLAB software to show the effect of the induced achlorhydria condition on the spread of cholera and individuals with this condition suffer severe infection during cholera outbreak

Feelings About the Importance of Physical Exercise and its Effects on Mental Health

Regular physical exercise is associated with numerous health benefits. Individuals that cultivate physically active lifestyles tend to live longer, have lower rates of disease, and have a higher overall quality of life. Regular exercise is also positively associated with mental health. Data for this study were collected from 285 participants. The findings show that a clear majority of participants believe that exercising improves their overall mood (76.5%) and makes them feel better. Around 3 out of 4 respondents stated that exercise lowers stress, while 7 out of 10 stated that it reduces anxiety. Most of the respondents also reported that physical exercise reduces feelings of depression (60.5%). Seven out of 10 participants prefer to exercise alone. Most of the participants wish they had more time to exercise (80.5%), and most also think that they should make time to exercise more often (83.2%). Women were significantly more likely than men to state that they wish they had more time, and should make more time, to exercise. The most preferred and enjoyed forms of exercise reported were going to gym (lifting weights and cardio) and walking/running. This study shows that people generally feel that physical exercise is important for overall mental health.        &nbsp

Two Classes of Optimal Fourth-Order Iterative Methods Free from Second Derivative for Solving Nonlinear Equations

This work proposes new fourth-order iterative methods to solve non-linear equations   . The iterative methods proposed here are presented by modifications of a third-order iterative method to be two classes of optimal fourth order. Convergence analysis was done for the iterative methods proposed in this paper. Multiple numerical examples were taken to explain the accuracy and efficiency of the proposed iterative methods

Stability and Oscillation of θ-methods for Differential Equation with Piecewise Constant Arguments

This paper studies the numerical properties of θ-methods for the alternately advanced and retarded differential equation u′(t) = au(t)+bu(2[(t+1)/2]). Using two classes of θ-methods, namely the linear θ-method and the one-leg θ-method, the stability regions of numerical methods are determined, and the conditions of oscillation for the θ-methods are derived. Moreover, we give the conditions under which the numerical stability regions contain the analytical stability regions. It is shown that the θ-methods preserve the oscillation of the analytic solution. In addition, the relationships between stability and oscillation are presented. Several numerical examples are given

Traveling wave solutions and numerical solutions for a mBBM equation

In this paper, some exact meromorphic solutions and generalized trigonometric solutions of the space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation are established by a new transformation and reliable methods. Moreover, some numerical solutions are obtained by using the optimal decomposition method (ODM), and their accuracy is shown in tables and images