Solving equations of the form H(x)=0 is one most faced problem in mathematics and other science fields such as chemistry or physics. This kind cannot be solved without use iterative methods. The Steffensen-type methods, defined using divided differences are derivative free, usually considered to solve these problems when H a non-differentiable operator due its accuracy efficiency. However, gene...

Nature ofphysical problem A lot of problems in physics, chemistry, applied mathematics as well as in engineering and in other fields, are quite often reduced tominimizing a function of several variables. MERLIN is a system designed to minimize a multidimensional function. Method of solution Six algorithms are implemented. Three of them make use of the function’s gradient and hence are suitable ...

Scale Relativity Theory (SRT) affirms that the laws of physics apply in all reference systems, whatever its state of motion and its scale. In consequence, SRT imply [1-3] the followings: i. Particle movement on continuous and non-differentiable curve (or almost nowhere differentiable), that is explicitly scale dependent and its length tends to infinity, when the scale interval tends to zero. ii...

Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the "critical order" 2-s and not so for orders between 2-s and 1, where s, 1<s<2 is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local ...

We review a nonparametric version of Amari’s information geometry in which the set of positive probability densities on a given sample space is endowed with an atlas of charts to form a differentiable manifold modeled on Orlicz Banach spaces. This nonparametric setting is used to discuss the setting of typical problems in machine learning and statistical physics, such as black-box optimization,...

We prove a necessary optimality condition for isoperimetric problems under nabla-differentiable curves. As a consequence, the recent results of [M.R. Caputo, A unified view of ostensibly disparate isoperimetric variational problems, Appl. Math. Lett. (2008), doi:10.1016/j.aml.2008.04.004], that put together seemingly dissimilar optimal control problems in economics and physics, are extended to ...

A simple and deep standard mathematical theorem asserts the existence, for any oneparameter differentiable group, of an additive parameter, such as the angle for rotations and the rapidity parameter for Lorentz transformations. The importance of this theorem for the applications of group theory in physics is stressed, and an elementary proof is given. The theorem then is applied to the construc...

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...