Related papers: The inverse problem for fractal curves solved with…
Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer…
Complex-dynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution of arbitrary interaction problem (physics/0305119,…
The most usual procedure for deriving curvature corrections to effective actions for topological defects is subjected to a critical reappraisal. A logically unjustified step (leading to overdetermination) is identified and rectified, taking…
A progress report on two recent theoretical approaches proposed to understand the physics of irreversible fractal aggregates showing up a structural transition from a rather dense to a more multibranched growth is presented. In the first…
Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…
This paper contains a comparative study of two families of simple curves drawn in the plane. On the one hand, we have the fractal curves on the unit interval, with self-similar structure, which have associated a Hausdorff dimension. On the…
In this paper we cover a few topics on how to treat inverse problems. There are two different flows of ideas. One approach is based on Morse Lemma. The other is based on analyticity which proves that the number of solutions to the inverse…
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with…
In this paper, we study the topology associated to the fractal manifold model. It turns out that this topology is actually a family of topologies that gives to the fractal manifold a structure of variable topological space. Additionally, we…
The image fractal analysis is actively used in all science branches. In particular in materials science the fractal analysis is applied to study microstructure of deformed metals because its structure can be interpreted as the fractal…
A fractal mobile-immobile (MIM in short) solute transport model in porous media is set forth, and an inverse problem of determining the fractional orders by the additional measurements at one interior point is investigated by Laplace…
This contribution presents a concept to dynamic fracture with continuum-kinematics-based peridynamics. Continuum-kinematics-based peridynamics is a geometrically exact formulation of peridynamics, which adds surface- or volumetric-based…
Decomposition of tomographic reconstructions has many different practical application. We propose two new reconstruction methods that combines the task of tomographic reconstruction with object decomposition. We demonstrate these…
The main aim of this paper is to investigate the nature of invariancy of rectifying curve under conformal transformation and obtain a sufficient condition for which such a curve remains conformally invariant. It is shown that the normal…
Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their…
This work presents a detailed analytical and geometrical investigation of the (2+1)-dimensional Boiti-Leon-Pempinelli system, a nonlinear dispersive model arising in the context of fluid and plasma dynamics. By employing a projective…
In this paper, we study the fractal dimension of the graph of a fractal transformation and also determine the quantization dimension of a probability measure supported on the graph of the fractal transformation. Moreover, we estimate the…
We describe a new method for constructing a spectrahedral representation of the hyperbolicity region of a hyperbolic curve in the real projective plane. As a consequence, we show that if the curve is smooth and defined over the rational…
To the reduct problems of decision system, the paper proposes the notion of dynamic core according to the dynamic reduct model. It describes various formal definitions of dynamic core, and discusses some properties about dynamic core. All…
The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating…