Admissible Perturbation of Demicontractive Operators within Ant Algorithms for Medical Images Edge Detection

Nowadays, demicontractive operators in terms of admissible perturbation are used to solve difficult tasks. The current research uses several demicontractive operators in order to enhance the quality of the edge detection results when using ant-based algorithms. Two new operators are introduced, χ -operator and K H -operator, the latter one is a Krasnoselskij admissible perturbation of a demicontractive operator. In order to test the efficiency of the new operators, a comparison is made with a trigonometric operator. Ant Colony Optimization (ACO) is the solver chosen for the images edge detection problem. Demicontractive operators in terms of admissible perturbation are used during the construction phase of the matrix of ants artificial pheromone, namely the edge information of an image. The conclusions of statistical analysis on the results shows a positive influence of proposed operators for image edge detection of medical images.

Approximating fixed points of demicontractive mappings by iterative methods defined as admissible perturbations

The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces.

Approximating fixed points of demicontractive mappings by iterative methods defined as admissible perturbations

The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces.

Fibre Contraction Principle with respect to an Iterative Algorithm

We apply the fibre contraction principle in the case of a general iterative algorithm to approximate the fixed point of triangular operator using the admissible perturbation. A simple example and an application to a functional equation with parameter are given in order to illustrate the abstract results and to show the role of admissible perturbations.

Ruga mechanics of creasing: from instantaneous to setback creases

We present mechanics of surface creasing caused by lateral compression of a nonlinear neo-Hookean solid surface, with its elastic stiffness decaying exponentially with depth. Nonlinear bifurcation stability analysis reveals that neo-Hookean solid surfaces can develop instantaneous surface creasing under compressive strains greater than 0.272 but less than 0.456. It is found that instantaneous creasing is set off when the compressive strain is large enough, and the longest-admissible perturbation wavelength relative to the decay length of the elastic modulus is shorter than a critical value. A compressive strain smaller than 0.272 can only trigger bifurcation of a stable wrinkle that can prompt a setback crease upon further compression. The minimum compressive strain required to develop setback creasing is found to be 0.174. If the relative longest-admissible perturbation wavelength is long enough, then the wrinkle can fold before it creases, and the specimen can be compressed further beyond the Biot critical strain limit of 0.456. Various bifurcation branches on a plane of normalized longest-admissible wavelength versus compressive strain delineate different phases of corrugated surface configurations to form a ruga phase diagram. The phase diagram will be useful for understating surface crease, as well as for controlling ruga structures for various applications, such as designing stretchable electronics.

Approximating solutions of generalized pseudocontractive variational inequalities by admissible perturbation type iterative methods

In this paper we give the solvability class of generalized strongly nonlinear variational inequalities modified by the use of the new concept of admissible perturbation operator on nonempty closed convex sets in Hilbert spaces.

Static Stress Redesign of Plates by Large Admissible Perturbations

The LargE Admissible Perturbation (LEAP) methodology is developed further to solve static stress redesign problems for shell elements. The static stress general perturbation equation, which expresses the unknown stresses of the objective structure in terms of the baseline structure stresses, is derived first. This equation depends on the redesign variables for each element or group of elements; namely the plate thickness. LEAP enables the designer to redesign a structure to achieve specifications on modal properties, static displacements, forced response amplitudes, and static stresses. LEAP is implemented in code RESTRUCT which post-processes the FEA results of the baseline structure. Changes on the order of 100% in the above performance particulars and in redesign variables can be achieved without repetitive FEA’s. Several numerical applications on a simple plate and an offshore tower are used to verify the LEAP algorithm for stress redesign.