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 ...

Plasma supports collective modes and particle–wave interactions that lead to complex behaviour in, for example, inertial fusion energy applications. While plasma can sometimes be modelled as a charged fluid, kinetic description is often crucial studying nonlinear effects in the higher-dimensional momentum–position phase space describes full complexity of dynamics. We create differentiable solve...

Image hashing embeds the image to binary codes which can boost efficiency of approximately nearest neighbors search. F-measure is a widely-used metric for evaluating performance methods. However, it non-differentiable and hence has not been used as an object function hashing. Heuristic algorithms, e.g. evolutionary computation particle swarm optimization (PSO), are good at optimizing objectives...

The existence of infinitely many solutions for an anisotropic discrete non-linear problem with variable exponent according to p(k)–Laplacian operator with Dirichlet boundary value condition, under appropriate behaviors of the non-linear term, is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Ricceri. We point out a theorem as a spe...