scholarly journals Proof of Goldbach Conjecture

2014 ◽  
Vol 7 ◽  
pp. 1-8
Author(s):  
Ren Yong Xue ◽  
Ren Yi
Keyword(s):  
Integral Equation ◽  
Coordinate System ◽  
Integration Method ◽  
Prime Numbers ◽  
Definite Integral ◽  
Rectangular Coordinate System ◽  
Coordinate Axis ◽  
The Creation ◽  
Infinite Sets

This paper through the creation of "double rectangular coordinate system", within the I quadrants, each coordinate axis coordinates all constitute the infinite sets. Coordinates with infinite sets one toone correspondence between the elements within and equal relationship. With any of the sum of two odd prime Numbers (a + b) to form a square area, length for a quarter of a square area A1 "square" diagonal integration method, a quarter of a square area A1 equation is derived with the definite integral equation; A1 area value of the argument as infinite generalized integral value, and deduce the equations, the Goldbach conjecture.

Features of Integration and Metaintegration in American Region

2019 ◽  
pp. 58-64
Keyword(s):  
Integration Method ◽  
South American ◽  
Legal Systems ◽  
Policy Integration ◽  
American Continent ◽  
Member States ◽  
The Creation ◽  
South American Continent ◽  
Andean Community ◽  
American Region

The analysis of integration of the legal systems of states in the American region is held. In the Southern subregion, a combination of integration and disintegration in cooperation of states led to the creation of two integration entities – MERCOSUR and the Andean Community (AC), in the Northern subregion – NAFTA. The author concludes that the convergence on the American continent, especially using the integration method, helped to implement a special scenario in the southern part of this continent – the meta-integration scenario, with the creation of the Union of South American Nations, uniting the Andean Community and MERCOSUR – something resembling a European one, but at the same time different from it. UNASUR is an effective mechanism for bringing together and integrating the states of the South American continent. Within this Union with notable leadership of Brazil and Argentina the first steps in the direction of the foreign policy integration of the member states are traced. In terms of economic integration, the Union uses the achievements of the AC and MERCOSUR, unifying the legal regulators in the economic sphere and bringing rapprochement to the legal systems of the member states.

The Numerical Methods of Peridynamics Theory Used in Failure Analysis of Materials

2014 ◽  
Vol 1030-1032 ◽  
pp. 223-227
Author(s):  
Lin Fan ◽  
Song Rong Qian ◽  
Teng Fei Ma
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Numerical Integration ◽  
Integration Method ◽  
Equation Of Motion ◽  
Numerical Integration Method ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Method Of Molecular Dynamics ◽  
Classic Theory

In order to analysis the force situation of the material which is discontinuity,we can used the new theory called peridynamics to slove it.Peridynamics theory is a new method of molecular dynamics that develops very quickly.Peridynamics theory used the volume integral equation to constructed the model,used the volume integral equation to calculated the PD force in the horizon.So It doesn’t need to assumed the material’s continuity which must assumed that use partial differential equation to formulates the equation of motion. Destruction and the expend of crack which have been included in the peridynamics’ equation of motion.Do not need other additional conditions.In this paper,we introduce the peridynamics theory modeling method and introduce the relations between peridynamics and classic theory of mechanics.We also introduce the numerical integration method of peridynamics.Finally implementation the numerical integration in prototype microelastic brittle material.Through these work to show the advantage of peridynamics to analysis the force situation of the material.

scholarly journals Mathematical Modelling of  RLC Circuit  Through Mixed Quadrature Rule

2018 ◽  
Author(s):  
Saumya jena ◽  
Damayanti Nayak
Keyword(s):  
Integral Equation ◽  
Mathematical Modelling ◽  
Electromotive Force ◽  
Quadrature Rule ◽  
Absolute Error ◽  
Definite Integral ◽  
Numerical Result ◽  
Rlc Circuit ◽  
Instantaneous Current

In this study, a mixed rule of degree of precision nine has been developed and implemented in the field of electrical sciences to obtain the instantaneous current in the RLC- circuit for particular value .The linearity has been performed with the Volterra’s integral equation of second kind with particular kernel . Then the definite integral has been evaluated through the mixed quadrature to obtain the numerical result which is very effective. A polynomial has been used to evaluate Volterra’s integral equation in the place of unknown functions. The accuracy of the proposed method has been tested taking different electromotive force in the circuit and absolute error has been estimated.

scholarly journals Revised finite sound ray integration method based on Kirchhoff's integral equation.

1989 ◽  
Vol 10 (2) ◽  
pp. 93-100 ◽  
Author(s):  
Hiroshi Asayama ◽  
Sho Kimura ◽  
Katsuaki Sekiguchi
Keyword(s):  
Integral Equation ◽  
Integration Method

Axisymmetric Isothermal Forging

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element ◽  
Coordinate System ◽  
Three Dimensions ◽  
Cold Forging ◽  
Axially Symmetric ◽  
Rectangular Coordinate System ◽  
Complex Deformation ◽  
Fem Method ◽  
Natural Coordinate System ◽  
Main Dimension

According to Spies, the majority of forgings can be classified into three main groups. The first group consists of compact shapes that have approximately the same dimensions in all three directions. The second group consists of disk shapes that have two of the three dimensions (length and width) approximately equal and larger than the height. The third group consists of the long shapes that have one main dimension significantly larger than the two others. All axially symmetric forgings belong to the second group, which includes approximately 30% of all commonly used forgings. A basic axisymmetric forging process is compression of cylinders. It is a relatively simple operation and thus it is often used as a property test and as a preforming operation in hot and cold forging. The apparent simplicity, however, turns into a complex deformation when friction is present at the die–workpiece interface. With the finite-element method, this complex deformation mode can be examined in detail. In this chapter, compression of cylinders and related forming operations are discussed. Since friction at the tool–workpiece interface is an important factor in the analysis of metal-forming processes, this aspect is also given particular consideration. Further, applications of the FEM method for complex-shaped dies are shown in the examples of forging and cabbaging. Finite-element discretization with a quadrilateral element is similar to that given in Chap. 8. The cylindrical coordinate system (r, ϑ, z) is used instead of the rectangular coordinate system. The element is a ring element with a quadrilateral cross-section, as shown in Fig. 9.1. The ξ and η of the natural coordinate system vary from −1 to 1 within each element.

A SIMPLIFIED TEXTURAL CLASSIFICATION DIAGRAM

1958 ◽  
Vol 38 (1) ◽  
pp. 54-55 ◽  
Author(s):  
J. A. Toogood
Keyword(s):  
Coordinate System ◽  
Rectangular Coordinate System

A textural diagram based on per cent clay and per cent sand is proposed. With a standard rectangular coordinate system it is easier to use than currently suggested triangles.

scholarly journals On the Volume in Homogeneous Spaces

1959 ◽  
Vol 15 ◽  
pp. 201-217 ◽  
Author(s):  
Minoru Kurita
Keyword(s):  
Euclidean Space ◽  
Coordinate System ◽  
Homogeneous Spaces ◽  
Closed Curve ◽  
Rectangular Coordinate System ◽  
Parametric Motion

Guldin-Pappus’s theorem about the volume of a solid of rotation in the euclidean space has been generalized in two ways. G. Koenigs [1] and J. Hadamard [2] proved that the volume generated by a 1-parametric motion of a surface D bounded by a closed curve c is equal to where are quantities attached to D with respect to a rectangular coordinate system, while are quantities determined by our motion.

scholarly journals A Recursive Formula for the Evaluation of Earth Return Impedance on Buried Cables

2015 ◽  
Vol 35 (3) ◽  
pp. 34-43
Author(s):  
Reynaldo Iracheta
Keyword(s):  
Infinite Series ◽  
Bessel Functions ◽  
Integration Method ◽  
Recursive Formula ◽  
Definite Integral ◽  
Mathematical Software ◽  
Font Size ◽  
Buried Cables ◽  
The Time Domain ◽  
Numerical Laplace Transform

<p class="Abstractandkeywordscontent"><span style="font-size: small;"><span style="font-family: Century Gothic;">This paper presents an alternative solution based on infinite series for the accurate and efficient evaluation of cable earth return impedances. This method uses Wedepohl and Wilcox’s transformation to decompose Pollaczek’s integral in a set of Bessel functions and a definite integral. The main feature of Bessel functions is that they are easy to compute in modern mathematical software tools such as Matlab. The main contributions of this paper are the approximation of the definite integral by an infinite series, since it does not have analytical solution; and its numerical solution by means of a recursive formula. The accuracy and efficiency of this recursive formula is compared against the numerical integration method for a broad range of frequencies and cable  configurations. Finally, the proposed method is used as a subroutine for cable parameter calculation in the inverse Numerical Laplace Transform (NLT) to obtain accurate transient responses in the time domain.</span></span></p>

Calculation of Meshing Efficiency of Helical Gear Based on Double Integral Method

2016 ◽  
Vol 693 ◽  
pp. 458-462
Author(s):  
D.G. Chang ◽  
F. Shu ◽  
X.B. Chen ◽  
Y.J. Zou
Keyword(s):  
Experimental Data ◽  
Coordinate System ◽  
Theoretical Basis ◽  
Integral Method ◽  
Helical Gear ◽  
Design Parameters ◽  
Double Integral ◽  
Rectangular Coordinate System ◽  
Helical Gears ◽  
Theoretical Results

The meshing efficiency of helical gear transmission is calculated by using the method of double integral. The external involute helical gear meshing is taken and the model of helical gears is simplified by the idea of differential. The instantaneous efficiency equation of a meshing point is derived, and further more the rectangular coordinate system of meshing zone of helical gears is established. The average meshing efficiency of helical gears is achieved by using double integral method. Then, the influence of design parameters is studied and the efficiency formula is verified by comparing the theoretical results with relevant experimental data, which can provide a theoretical basis for decide the design parameters.

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