This article will be devoted to generalisations of Fermat’s equation x + y = z. Very soon after the Wiles and Taylor proof of Fermat’s Last Theorem, it was wondered what would happen if the exponents in the three term equation would be chosen differently. Or if coefficients other than 1 would be chosen. We discuss the reduction of the resolution of such equations to the determination of rationa...

we prove the generalized hyers--ulam stability  of n--th order linear differential equation of the form $y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x)$, with condition that there exists a non--zero solution of corresponding homogeneous equation. our main results extend and improve the corresponding results obtained by many authors.

this paper studies the generalized version of thezakharov-kuznetsov benjamin-bona-mahoney equation. the functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. there are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. the results of this pape...

The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighboring but their relative velocity is arbitrary the corresponding geodesic deviation equation is the generalized Jacobi equation....

Ensuring safety on roadways and controlling conflicting merging streams of traffic at signalized intersections has become a major concern for transportation engineers road users globally locally. Many factors contribute to accident occurrence segments with driver behavior being the contributor.  Other include those related vehicle road. The primary aim this study is understand impact diffe...

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:begin{equation} sum_{ j = 1}^{n}fBig(-2 x_{j} + sum_{ i = 1, ineq j}^{n} x_{i}Big) =(n-6) fBig(sum_{ i = 1}^{n} x_{i}Big) + 9 sum_{ i = 1}^{n}f(x_{i}).end{equation}

We propose to analyze panel count data using a spline-based semiparametric projected generalized estimating equation (GEE) method with the proportional mean model E(N(t)|Z) = Λ(0)(t) e(β(0)(T)Z). The natural logarithm of the baseline mean function, logΛ(0)(t), is approximated by a monotone cubic B-spline function. The estimates of regression parameters and spline coefficients are obtained by pr...

We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and modify the generalized estimating equation to facilitate estimation and inference. We use local smoothing kernel to estimate the unspecified coefficient function...

The generalized estimating equation (GEE) approach of Zeger and Liang facilitates analysis of data collected in longitudinal, nested, or repeated measures designs. GEEs use the generalized linear model to estimate more efficient and unbiased regression parameters relative to ordinary least squares regression in part because they permit specification of a working correlation matrix that accounts...