Coefficient Analysis and Regression for Calculating Perimeter of Ellipse

Coefficient for computing ellipse perimeter is analyzed deeply in this article, relevant characteristics and numeric results are achieved too. A polynomial function to compute ellipse perimeter is obtained by regression, which may be applied widely, and has higher accuracy verified by C programming via computer.

Application of Advance Constrained Simplex Method for MIMO Systems in Quantum Communication Networks

This paper first describes advanced constrained simplex method (advanced complex method), then it shows that this complex procedure has any problems when it’s taken for finding the maximum of a general nonlinear function of several variables within a constrained region is described in wireless communication systems, especially for multiple-input multiple-out (MIMO Configuration). Next advanced constrained simplex method is described how to resolve the problem of the multiple-input multiple-out, and shown how to be efficient compared with the complex method and the simplex method by some simulations. And this wireless network design can be used to MIMO systems in Quantum Communication networks. The feature of technology by which the system told by this paper can get optimum solution by a little search number of times compared with a conventional system in the MIMO environment with more than one optimal value, and is at the place. This system was applied to the Quantum network environment by this paper. This can achieve more compact than the conventional Quantum network environment.

Simulation and Analysis of Fluid-Solid Coupling of Wave Impact Sandcastle Based on COMSOL

It is a complex problem to study the interaction between sand castle and flowing water, which needs to consider the complexity of seawater flow and the stress of sand castle structure. The authors use the fluid-solid coupling model to establish the connection between the fluid field and the structural mechanical field, and use the finite element analysis to complete the simulation modeling of the transient process of wave impact and sandcastle foundation deformation. This paper analyzes the stress and the first principal strain of the sand castle foundation in the direction of flow velocity when the sand castle foundation is hit by waves, as a method to judge the strength of the sand castle.The best shape: the boundary value of sand castle collapse caused by strain have been determined, so as to obtain the maximum stress that a sand castle foundation can bear before collapse, which makes it possible to use the fatigue strength calculation theory of sand castle solid to carry out the quantitative calculation of sand castle durability. At the same time, the impact of waves is abstracted as wave motion equation. Finally, the finite element analysis technology is adopted to calculate the main strain of sandcastles of different shapes under the impact of the same wave, and through the comparison of the main strain, the authors get the sandcastle shape with the strongest anti-wave impact ability, which is the eccentric circular platform body.Affected by rain: the authors considered the effect of rainwater infiltration on the sandcastle's stress, and simplified the process of rain as a continuous and uniform infiltration of rain into the sandcastle's surface. The rain changes the gravity of the sand on the castle's surface. Simulation analysis is adopted to calculate the surface stress of sand castle with different degree of water seepage and different geometry. By comparison, it has been found that the smooth cone is more able to withstand the infiltration of rain without collapse.

Preliminary Discussion on Several Problems Related to the Divisor Function

This paper is divided into three parts to discuss the divisor function. It mainly combines the high power sum of the divisor function to study the solution number of the polynomial with integer coefficients "g(x)=0(modq)", and to improve some of the conclusions in the second chapter of Additive Theory of Prime Numbers and prove the improved conclusions.

Piecewise Curve Fitting Based on Least Square Method in 3D Space

Least squares curve fitting is widely used in various neighborhoods, such as industry, agriculture, and economy. The method of piecewise curve fitting is used to deal with some experimental studies with large amounts of data. It can not only be used for plane space points, but also for three-dimensional space points. Firstly, this article introduces the principles of curve fitting and least squares. Secondly, it clarifies the steps based on least square fitting and gives examples of improvements made based on the principle of least square fitting functions by some scientists. Finally, the piecewise curve fitting in the three-dimensional space is obtained using the least squares piecewise curve fitting. It lays a certain theoretical foundation for drawing the laws between data in three-dimensional space.

Supplement to the Theory of Relativity

The problem about "who is right in relativity and Newtonian mechanics" is analyzed and discussed, and the theoretical results described in this study are only used as reference. This study reveals that there is no contradiction between relativity and Newtonian mechanics, and the essence of the relativity lies in the mass energy equation.

Generalized Fractional Calculus Operators Associated with K-function

The aim of this paper is to study some properties of K-function introduced by Sharma. Here we establish two theorems which give the image of this K-function under the generalized fractional integral operators involving Fox’s H-function as kernel. Corresponding assertions in term of Euler, Whittaker and K-transforms are also presented. On account of general nature of H-function and K-function a number of results involving special functions can be obtained merely by giving particular values for the parameters.

FREE SEMIGROUP PRESENTATIONS

Let and be two free semigroups. We define external direct product of two free semigroups as an ordered pair of words such that and .We investigate the presentations of external direct product of free semigroups, state and prove under some conditions that the external direct product of two finitely generated free semigroups is finitely generated, also the external direct product of two finitely presented free semigroups is finitely presented.

On Some Properties of Metals Under Complex Loading

Drucker’s Associated Law of yielding and gradient plasticity cannot always adequately reflect the processes of stress-strain state in deformable continua. Aim of this issue explains these effects via theory of complex loading processes by Ilyushin.

Statistical mechanics of hard spheres: the scaled particle theory of the hard sphere fluid revisited

The aim of this paper is to exhaust the possibilities offered by the scaled particle theory as far as possible and to confirm the reliability of the virial coefficients found in the literature, especially the estimated ones: B i for i > 11. In a previous article (J.Math.Phys.36,201,1995) a theoretical equation of state for the hard sphere fluid was derived making use of the ideas of the so called scaled particle theory which has been developed by Reiss et al.(J.Chem.Phys.31,369,1959). It contains two parameters which could be calculated. The equation of state agrees with the simulation data up to high densities, where the fluid is metastable. The derivation was besed on a generalized series expansion. The virial coefficients B 2 , B 3 and B 4 are exactly reproduced and B 5 , B 6 and B 7 to within small deviations, but the higher ones up to B 18 are systematically and significantly smaller than the values found in the literature. The scaled particle theory yields a number of equations of which only four were used. In this paper we make use of seven equations to calculate the compressibility factors of the fluid. They agree with the simulation data slightly better than those yielded by the old equation. Moreover, the differences between the calculated virial coefficients B i and those found in the literature up to B 18 are very small (less than 4 percent).