scholarly journals A combined methodology for the approximate estimation of the roots of the general sextic polynomial equation

2021 ◽  
Author(s):  
Giorgos P. Kouropoulos
Keyword(s):  
Mathematical Model ◽  
Regression Analysis ◽  
Polynomial Equation ◽  
Approximate Solutions ◽  
The Other ◽  
Polynomial Equations ◽  
Polynomial Coefficients ◽  
Approximate Estimation ◽  
Predetermined Interval

Abstract In this article we present the methodology, according to which it is possible to derive approximate solutions for the roots of the general sextic polynomial equation as well as some other forms of sextic polynomial equations that normally cannot be solved by radicals; the approximate roots can be expressed in terms of polynomial coefficients. This methodology is a combination of two methods. The first part of the procedure pertains to the reduction of a general sextic equation H(x) to a depressed equation G(y), followed by the determination of solutions by radicals of G(y) which does not include a quintic term, provided that the fixed term of the equation depends on its other coefficients. The second method is a continuation of the first and pertains to the numerical correlation of the roots and the fixed term of a given sextic polynomial P(x) with the radicals and the fixed term of the sextic polynomial Q(x), where the two polynomials P(x) and Q(x) have the same coefficients except for the fixed term which might be different. From the application of the methodology presented above, the following formulation is derived; For any given general sextic polynomial equation P with coefficients within the interval [a, b], a defined polynomial equation Q corresponds which has equal coefficients to P except for its fixed term which might be different and dependent on the other coefficients so that Q has radical solutions. If we assume a pair of equations P, Q with coefficients within a predetermined interval [a, b], the numerical correlation through regression analysis of the radicals of Q, the roots of P and the fixed terms of P, Q, leads to the derivation of a mathematical model for the approximate estimation of the roots of sextic equations whose coefficients belong to the interval [a, b].

scholarly journals A combined methodology for the approximate estimation of the roots of the general sextic polynomial equation

2021 ◽  
Author(s):  
Giorgos P. Kouropoulos
Keyword(s):  
Mathematical Model ◽  
Regression Analysis ◽  
Polynomial Equation ◽  
Approximate Solutions ◽  
The Other ◽  
Polynomial Equations ◽  
Polynomial Coefficients ◽  
Approximate Estimation ◽  
Predetermined Interval

Abstract In this article we present the methodology, according to which it is possible to derive approximate solutions for the roots of the general sextic polynomial equation as well as some other forms of sextic polynomial equations that normally cannot be solved by radicals; the approximate roots can be expressed in terms of polynomial coefficients. This methodology is a combination of two methods. The first part of the procedure pertains to the reduction of a general sextic equation H(x) to a depressed equation G(y), followed by the determination of solutions by radicals of G(y) which does not include a quintic term, provided that the fixed term of the equation depends on its other coefficients. The second method is a continuation of the first and pertains to the numerical correlation of the roots and the fixed term of a given sextic polynomial P(x) with the radicals and the fixed term of the sextic polynomial Q(x), where the two polynomials P(x) and Q(x) have the same coefficients except for the fixed term which might be different. From the application of the methodology presented above, the following formulation is derived; For any given general sextic polynomial equation P with coefficients within the interval [a, b], a defined polynomial equation Q corresponds which has equal coefficients to P except for its fixed term which might be different and dependent on the other coefficients so that Q has radical solutions. If we assume a pair of equations P, Q with coefficients within a predetermined interval [a, b], the numerical correlation through regression analysis of the radicals of Q, the roots of P and the fixed terms of P, Q, leads to the derivation of a mathematical model for the approximate estimation of the roots of sextic equations whose coefficients belong to the interval [a, b].

scholarly journals Accurate Computation of Periodic Regions' Centers in the General M-Set with Integer Index Number

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Wang Xingyuan ◽  
He Yijie ◽  
Sun Yuanyuan
Keyword(s):  
Polynomial Equation ◽  
Negative Integer ◽  
The Other ◽  
Index Number ◽  
Polynomial Equations ◽  
Decimal Point ◽  
Numerical Accuracy ◽  
Index Numbers ◽  
Accurate Computation ◽  
The Relationship

This paper presents two methods for accurately computing the periodic regions' centers. One method fits for the general M-sets with integer index number, the other fits for the general M-sets with negative integer index number. Both methods improve the precision of computation by transforming the polynomial equations which determine the periodic regions' centers. We primarily discuss the general M-sets with negative integer index, and analyze the relationship between the number of periodic regions' centers on the principal symmetric axis and in the principal symmetric interior. We can get the centers' coordinates with at least 48 significant digits after the decimal point in both real and imaginary parts by applying the Newton's method to the transformed polynomial equation which determine the periodic regions' centers. In this paper, we list some centers' coordinates of general M-sets'k-periodic regions(k=3,4,5,6)for the index numbersα=−25,−24,…,−1, all of which have highly numerical accuracy.

scholarly journals Determination of the level of separate rail failure using the indicator of their reliability

2018 ◽  
Vol 230 ◽  
pp. 01016
Author(s):  
Anatolii Shtompel ◽  
Oleksii Skoryk ◽  
Vadym Novikov ◽  
Yuliia Kravchenko ◽  
Yevhen Korostelov
Keyword(s):  
Mathematical Model ◽  
Regression Analysis ◽  
Railway Track ◽  
Track Structure ◽  
Safety Level ◽  
Track Maintenance ◽  
Maintenance System ◽  
Operation Conditions ◽  
Reported Data

During the operation, the upper railway track structure constantly tends to age, which includes the increasing number of failures. This process is controlled by the track maintenance system, which provides for the current maintenance of the track in a certain railway section. As part of the current maintenance of the track, in particular, works are performed to eliminate defective elements of the upper railway track structure, which appeared during functioning of the track structure. The dependence of the operational cargo turnover on the amount of transported cargoes has been analyzed. It is directly related to the issues of organization of maintenance of the railway track structure taking into account the current track operation conditions. Regression analysis of the reported data allowed establishing a mathematical model of the dependence of the value of operational cargo turnover on the value of the transported cargo. The service life of rails (rail bars) in the track section has been established to be related to the indicator separate rail failure during the period of operation of the upper railway track structure by defects. The safety level of rails (rail bars) can be determined based on the value of this indicator.

Thermal Solutions for a Plate With an Arbitrary Temperature Transient on One Surface and Convection on the Other: Direct and Inverse Formulations

2019 ◽  
Author(s):  
Albert E. Segall ◽  
Craig C. Schoof ◽  
Daniel E. Yastishock
Keyword(s):  
Thermal Stresses ◽  
The Other ◽  
Engineering Practice ◽  
Time Interval ◽  
Internal Heating ◽  
Surface Loading ◽  
Polynomial Coefficients ◽  
Loaded Surface ◽  
Walled Cylinder

Abstract Thick plates that are thermally loaded on one surface with convection on the other are often encountered in engineering practice. Given this wide utility and the limitations of most existing solutions to an adiabatic boundary condition, generalized direct thermal solutions were first derived for an arbitrary surface loading as modeled by a polynomial and its coefficients on the loaded surface with convection on the other. Once formulated, the temperature solutions were then used with elasticity relationships to determine the resulting thermal stresses. Additionally, the Inverse thermal problem was solved using a least-squares determination of the aforementioned polynomial coefficients based on the direct-solution and temperatures measured at the surface with convection. Previously published relationships for a thick-walled cylinder with internal heating/cooling and external convection are also included for comparison. Given the versatility of the polynomial solutions advocated, the method appears well suited for complicated thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties do not vary with temperature.

scholarly journals PENGARUH KONFLIK TERHADAP KINERJA PEGAWAI DI SEKRETARIAT DPRD KABUPATEN SIAK

2020 ◽  
Vol 11 (1) ◽  
pp. 77-91
Author(s):  
Eka Putra
Keyword(s):  
Regression Analysis ◽  
Data Analysis ◽  
Linear Regression ◽  
Linear Regression Analysis ◽  
The Other ◽  
Coefficient Of Determination ◽  
Linear Regression Equation ◽  
Simple Linear Regression ◽  
Work Unit

This research was conducted at the DPRD Secretariat Of The Siak Regency. The purpose of this study was to determined the effect of conflict on the performance of employees in the DPRD Secretariat of Siak Regency. The population in this study were 44 people from the DPRD Secretariat Of The Siak Regency. While the number of samples set in this study are all of the population of 44 people. Data analysis using simple linear regression analysis with SPSS 16.00 for Windows. Based on a simple linear regression equation Y = 18,397 + 0,656X. Conflict variables (X) with t count (4,336) > t table (2,018) and probability (0,00) <0,05. Then Ho is rejected and Ha is accepted, meaning that the conflict variable has a positive and significant effect on the performance of the DPRD Secretariat Of The Siak Regency. R-square value can be obtained (coefficient of determination) of 0.309 or 30.9%. This shows that conflict contributes to the performance of the Siak Regency DPRD Secretariat employees by 30.9%, while the remaining 60.1% is influenced by other variables outside the variables in this study. The recommendation given that better to be able to create a conducive atmosphere related to the delegation of tasks from a work unit to another work unit in order to facilitate the performance of employees with measurable to avoid accumulating a job in a work unit. In the other side, employees must know and  understand about their task and job desk in order to improve their performance.

Thermal Solutions for a Plate With an Arbitrary Temperature Transient on One Surface and Convection on the Other: Direct and Inverse Formulations

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Albert E. Segall ◽  
Craig C. Schoof ◽  
Daniel E. Yastishock
Keyword(s):  
Thermal Stresses ◽  
The Other ◽  
Engineering Practice ◽  
Time Interval ◽  
Internal Heating ◽  
Surface Loading ◽  
Polynomial Coefficients ◽  
Loaded Surface ◽  
Walled Cylinder

Abstract Thick plates that are thermally loaded on one surface with convection on the other are often encountered in engineering practice. Given this wide utility and the limitations of most existing solutions to an adiabatic boundary condition, generalized direct thermal solutions were first derived for an arbitrary surface loading as modeled by a polynomial and its coefficients on the loaded surface with convection on the other. Once formulated, the temperature solutions were then used with elasticity relationships to determine the resulting thermal stresses. Additionally, the inverse thermal problem was solved using a least-squares type determination of the aforementioned polynomial coefficients based on the direct-solution and temperatures measured at the surface with convection. Previously published relationships for a thick-walled cylinder with internal heating/cooling and external convection are also included for comparison. Given the versatility of the polynomial solutions advocated, the method appears well suited for complicated thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties do not vary with temperature.

A Mathematical Model for Roll Damping Prediction

2015 ◽  
Author(s):  
Henry Piehl ◽  
Ould el Moctar
Keyword(s):  
Mathematical Model ◽  
Regression Analysis ◽  
Shape Parameter ◽  
Roll Motion ◽  
Damping Properties ◽  
Roll Damping ◽  
Ship Hulls ◽  
Damping Coefficients ◽  
Analytic Expression

A ship in seaway is always prone to roll motion. For the safety of personnel, ship and cargo it is essential to optimize the roll damping properties of the hull shape in order to prevent exceeding roll angles. Therefore, a tool for the prediction of roll damping is an important requirement during the design phase of ship hulls. The objective of this study is to use regression analysis and numerical simulation of roll motion to develop an analytic expression for the determination of roll damping. The development procedure starts with a variation of several hull shape parameter that influence the roll damping. For each of the parameter variants, a numerical roll simulation is conducted and the according roll damping coefficients are determined by time series analysis. Finally, regression analysis is applied to the computed results in order to derive a mathematical model that allows to determine the roll damping coefficient depending on the hull shape parameter.

Determination of the lattice translation across {110} APBs in GaAs

1988 ◽  
Vol 46 ◽  
pp. 600-601
Author(s):  
D.R. Rasmussen ◽  
N.-H. Cho ◽  
C.B. Carter
Keyword(s):  
Grain Boundaries ◽  
Lower Energy ◽  
Antiphase Boundary ◽  
The Other ◽  
Boundary Structure ◽  
Interface Plane ◽  
Inversion Symmetry ◽  
High Angle ◽  
Equilibrium Distance

Domains in GaAs can exist which are related to one another by the inversion symmetry, i.e., the sites of gallium and arsenic in one domain are interchanged in the other domain. The boundary between these two different domains is known as an antiphase boundary [1], In the terminology used to describe grain boundaries, the grains on either side of this boundary can be regarded as being Σ=1-related. For the {110} interface plane, in particular, there are equal numbers of GaGa and As-As anti-site bonds across the interface. The equilibrium distance between two atoms of the same kind crossing the boundary is expected to be different from the length of normal GaAs bonds in the bulk. Therefore, the relative position of each grain on either side of an APB may be translated such that the boundary can have a lower energy situation. This translation does not affect the perfect Σ=1 coincidence site relationship. Such a lattice translation is expected for all high-angle grain boundaries as a way of relaxation of the boundary structure.

Determination of the Burgers vector of a dislocation in a Fe-Mn alloy by weak-beam image in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 330-331
Author(s):  
Y. Ishida ◽  
H. Ishida ◽  
K. Kohra ◽  
H. Ichinose
Keyword(s):  
High Order ◽  
Simulation Technique ◽  
The Other ◽  
Image Simulation ◽  
Diffraction Vector ◽  
Burgers Vector ◽  
Weak Beam ◽  
Beam Image ◽  
Edge Component

IntroductionA simple and accurate technique to determine the Burgers vector of a dislocation has become feasible with the advent of HVEM. The conventional image vanishing technique(1) using Bragg conditions with the diffraction vector perpendicular to the Burgers vector suffers from various drawbacks; The dislocation image appears even when the g.b = 0 criterion is satisfied, if the edge component of the dislocation is large. On the other hand, the image disappears for certain high order diffractions even when g.b ≠ 0. Furthermore, the determination of the magnitude of the Burgers vector is not easy with the criterion. Recent image simulation technique is free from the ambiguities but require too many parameters for the computation. The weak-beam “fringe counting” technique investigated in the present study is immune from the problems. Even the magnitude of the Burgers vector is determined from the number of the terminating thickness fringes at the exit of the dislocation in wedge shaped foil surfaces.

Plasma Levels of Protein S, Protein C, and Factor X: Effects of Sex, Hormonal State and Age

1995 ◽  
Vol 74 (05) ◽  
pp. 1271-1275 ◽  
Author(s):  
C M A Henkens ◽  
V J J Bom ◽  
W van der Schaaf ◽  
P M Pelsma ◽  
C Th Smit Sibinga ◽  
...  
Keyword(s):  
Regression Analysis ◽  
Postmenopausal Women ◽  
Protein C ◽  
Blood Donors ◽  
Premenopausal Women ◽  
Protein S ◽  
The Other ◽  
Factor X ◽  
Normal Ranges

SummaryWe measured total and free protein S (PS), protein C (PC) and factor X (FX) in 393 healthy blood donors to assess differences in relation to sex, hormonal state and age. All measured proteins were lower in women as compared to men, as were levels in premenopausal women as compared to postmenopausal women. Multiple regression analysis showed that both age and subgroup (men, pre- and postmenopausal women) were of significance for the levels of total and free PS and PC, the subgroup effect being caused by the differences between the premenopausal women and the other groups. This indicates a role of sex-hormones, most likely estrogens, in the regulation of levels of pro- and anticoagulant factors under physiologic conditions. These differences should be taken into account in daily clinical practice and may necessitate different normal ranges for men, pre- and postmenopausal women.

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