the most commonly used utility functional forms are reviewed and their properties compared. then, using data collected from west azarbaijan province, utility functions are estimated and absolute risk aversion coefficients measured. exponential and expopower utility functions classified all farmers as risk averse, but quadratic and cubic utility functions classified 75% and 65% of farmers as...

‎In 1897‎, ‎Hensel introduced a normed space which does‎ ‎not have the Archimedean property‎. ‎During the last three decades‎ ‎theory of non--Archimedean spaces has gained the interest of‎ ‎physicists for their research in particular in problems coming‎ ‎from quantum physics‎, ‎p--adic strings and superstrings‎. ‎In this paper‎, ‎we prove‎ ‎the generalized Hyers--Ulam--Rassias stability for a‎ ...

The reversible Hopf bifurcation with 1:1 resonance holds the key to the presence of spatially localized steady states in many partial differential equations on the real line. Two different techniques for computing the normal form for this bifurcation are described and applied to the Swift-Hohenberg equation with cubic/quintic and quadratic/cubic nonlinearities.

Soliton damping in weakly dissipative media has been studied for several decades, usually using the asymptotic theory of the slowly-varying solitary wave solution of the Korteweg-de Vries (KdV) equation. Damping then occurs according to the energy balance equation, and a shelf is generated behind the soliton. Various examples of this process have been given by Ott & Sudan (1970) Pelinovsky (197...

In this paper, we investigate the Hyers-Ulam stability of the orthogonally  cubic equation and  Pexiderized cubic equation [f(kx+y)+f(kx-y)=g(x+y)+g(x-y)+frac{2}{k}g(kx)-2g(x),]in multi-normed spaces by the direct method and the fixed point method. Moreover, we prove the Hyers-Ulam stability of the  $2$-variables cubic  equation [ f(2x+y,2z+t)+f(2x-y,2z-t) =2...

In this paper, we obtain the general solution of a generalized cubic functional equation, the Hyers-Ulam-Rassias stability, and the stability by using the alternative fixed point for a generalized cubic functional equation

As is well known, equations of degree up to 4 can be solved in radicals . The solutions can be obtained, apart from the usual arithmetic operations, by the extraction of roots. In the case of the quadratic equation, this has a very concrete meaning. Even if the coefficients are arbitrary complex numbers, the solutions can always be calculated by the extraction of roots from nonnegative real num...