We consider a class of “box-like” statistically self-affine functions, and compute the almost-sure box-counting dimension their graphs. Furthermore, we differentiability our prove that, depending on an explicitly computable functional model, they are almost surely either differentiable everywhere or non-differentiable everywhere.

In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in a complementary approach, using the fractal concept and the corresponding non-differentiable theoret...

In this paper we consider how to use the convolution method to construct approximations, which consist of fuzzy numbers sequences with good properties, for a general fuzzy number. It shows that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers which have finite nondifferentiable points. In the previous work, this convolution method only can be ...

Relativistic particle physics is described by relativistic quantum field theory; the theories explaining the fundamental interactions are gauge theories. QFT as it is formulated in terms of Lagrangians and functional integration has to be regularized. The only known regularization scheme that retains the gauge symmetry is replacement of the space-time continuum by a space-time lattice. For conv...

Abstract. In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. Two sets of test problems are introduced, in the first one both the objective function and constraints are differentiable functions and in the second one they are non-differentiable. Each series of tests contains 3 problems...

Economic dispatch problem has grown along with the development of electric power business, for example in a competitive electric power business that offers electrical energy in the form of the step function, non-differentiable function. This is not a continuous function so there is no guarantee that those methods can execute the optimization problem well, especially the Lagrange and Direct meth...

We consider the problem of Bayesian inference in the family of probabilistic models implicitly defined by stochastic generative models of data. In scientific fields ranging from population biology to cosmology, low-level mechanistic components are composed to create complex generative models. These models lead to intractable likelihoods and are typically non-differentiable, which poses challeng...