Boundary behaviour of holomorphic functions on the cardioid domain with some applications

The objective of this research paper is to show how the Bennan'sconjecture become a useful tool to construct a holomorphic function on the cardioid domain, and on the boundary of unit disk. Moreover , we have addressed some applications on the existence of cusp on the boundary of arising from integrability of conformalmaps through one of the polar function in the general solution of Laplace equation.

Visualization of Schrodinger Equations Polar Wave Functions for Non-Central Coulombic Rosen Morse Potential in ExcitationState nr = 2 and l = 1

Research has been conducted which shows the quantization visualization of hydrogen atom orbitals angular space in Rosen Morse potential system interference when the electrons are excited in the state of nr= 2 and l = 1 through the polar function analysis of the Schrödinger Potential of Non-Central Coloumbic Rosen Morse. The polar Schrödinger equation is solved using the Romanovski polynomial method to obtain the polar wave function. To show the accuracy of the analysis, the polar wave function spectrum i s visualized with Matlab-based computer programming.

POLAR PARTICLE SWARM OPTIMIZATION ALGORITHM FOR SOLVING OPTIMAL REACTIVE POWER PROBLEM

This paper presents Polar Particle Swarm optimization (PPSO) algorithm for solving optimal reactive power problem. The standard Particle Swarm Optimization (PSO) algorithm is an innovative evolutionary algorithm in which each particle studies its own previous best solution and the group’s previous best to optimize problems. In the proposed PPSO algorithm that enhances the behaviour of PSO and avoids the local minima problem by using a polar function to search for more points in the search space in order to evaluate the efficiency of proposed algorithm, it has been tested on IEEE 30 bus system and compared to other algorithms. Simulation results demonstrate good performance of the Polar Particle Swarm optimization (PPSO) algorithm in solving an optimal reactive power problem.

Polar Particle Swarm Algorithm for Solving Cloud Data Migration Optimization Problem

Particle Swarm Optimization (PSO) has proved to be a common meta-heuristic algorithm for determining the minimum value among a set of values but it is known to suffer from the local minima problem. In this paper, we propose a novel optimization algorithm called POLARPSO that enhances the behavior of PSO and avoids the local minima problem by using a polar function to search for more points in the search space. The algorithm has been tested on 23 well-known benchmark factions and the results are verified by comparing them with state of the art algorithms: Grey Wolf Optimizer (GWO), Sine Cosine Algorithm (SCA), Multi-Verse Optimizer (MVO) as well as PSO. The paper also considers a solution to the cloud data migration problem where data migrates from highly loaded nodes to less loaded nodes in a process aims at achieving a kind of load balancing. The results prove that the proposed algorithm is applicable to solve this challenging problem in cloud environment and is able to find the best node to migrate to quickly and effectively. Our empirical results show that the proposed algorithm has enhanced the PSO behavior in reaching the best solution and outperformed the other algorithms over the tested benchmarked functions.

Graphing Polar Curves

Graphing the polar function on a rectangular plane simplifies graphing, increases student understanding, and reinforces connections.

Influence of Rubber Crumb Addition to Portland Cement Concrete

In this paper, two kinds of rubber surface modifying methods were studied. One was bis[3-(triethoxysilyl) propyl] tetrasulfide (Si-69) silicon alkane coupling agent and the other was crylic acid coupling agent. The mechanical properties of cement concrete with modified rubber crumb and with non-modified rubber crumb were tested respectively. The results show that as the rubber crumb addition rises, the toughness of concrete with non-modified rubber crumb increases while the compressive strength decreases, and both thoughness and compressive strength of cement concrete with modified rubber crumb increase. The chloride impermeability of the rubber concrete are much better than that of the Portland cement concrete. After surface modification the chloride impermeability can be improved more. The thermoanalysis proves that the surface of modified rubber crumb is grafted by polar function groups, so the surface changes from hydrophobic to hydrophilic. The scanning electron microscopy (SEM) analysis confirms that the interface between rubber crumb and cement matrix is improved.

Functorial polar functions

W∞ denotes the category of archimedean ℓ-groups with designated weak unit and complete ℓ-homomorphisms that preserve the weak unit. CmpT2,∞ denotes the category of compact Hausdorff spaces with continuous skeletal maps. This work introduces the concept of a functorial polar function on W∞ and its dual a functorial covering function on CmpT2,∞.We demonstrate that functorial polar functions give rise to reflective hull classes in W ∞ and that functorial covering functions give rise to coreflective covering classes in CmpT 2,∞. We generate a variety of reflective and coreflecitve subcategories and prove that for any regular uncountable cardinal α, the class of α-projectable ℓ-groups is reflective in W ∞, and the class of α-disconnected compact Hausdorff spaces is coreflective in CmpT 2,∞. Lastly, the notion of a functorial polar function (resp. functorial covering function) is generalized to sublattices of polars (resp. sublattices of regular closed sets).