scholarly journals BOOLEAN POLYNOMIAL EXPRESSION OF THE DISCRETE AVERAGE ON THE SPACE OF RHYTHMS

2021 ◽  
Vol 52 (2) ◽  
pp. 179-242
Author(s):  
Fumio Hazama
Keyword(s):  
Polynomial Expression

Development and evaluation of trans-Amadi groundwater parameters: The integration of finite element techniques

2019 ◽  
Author(s):  
Chem Int
Keyword(s):  
Finite Element ◽  
Polynomial Regression ◽  
Nitrate Concentration ◽  
Strong Relationship ◽  
Total Iron ◽  
Coefficient Of Determination ◽  
Port Harcourt ◽  
Polynomial Expression ◽  
The Relationship ◽  
Best Fit

Mathematical model was developed and evaluated to monitor and predict the groundwater characteristics of Trans-amadi region in Port Harcourt City. In this research three major components were considered such as chloride, total iron and nitrate concentration as well as the polynomial expression on the behavious on the concentration of each component was determined in terms of the equation of the best fit as well as the square root of the curve. The relationship between nitrate and distance traveled by Nitrate concentration by the model is given as Pc = 0.003x2 - 0.451x + 14.91with coefficient of determination, R² = 0.947, Chloride given as Pc = 0.000x2 - 0.071x + 2.343, R² = 0.951while that of Total Iron is given as Pc = 2E-05x2 - 0.003x + 0.110, R² = 0.930. All these show a strong relationship as established by Polynomial Regression Model. The finite element techniques are found useful in monitoring, predicting and simulating groundwater characteristics of Trans-amadi as well as the prediction on the variation on the parameters of groundwater with variation in time.

scholarly journals Lattice constants and thermal expansion of H2O and D2O Ice Ih between 10 and 265 K. Addendum

2012 ◽  
Vol 68 (1) ◽  
pp. 91-91 ◽  
Author(s):  
K. Röttger ◽  
A. Endriss ◽  
Jörg Ihringer ◽  
S. Doyle ◽  
W. F. Kuhs
Keyword(s):  
Thermal Expansion ◽  
Unit Cell ◽  
Acta Cryst ◽  
Lattice Constants ◽  
Temperature Range ◽  
Polynomial Fit ◽  
Polynomial Expression ◽  
Cell Data ◽  
Cell Volumes ◽  
Volume Cell

In a previous paper we reported the lattice constants and thermal expansion of normal and deuterated ice Ih [Röttger et al. (1994). Acta Cryst. B50, 644–648]. Synchrotron X-ray powder diffraction data were used to obtain the lattice constants and unit-cell volumes of H2O and D2O ice Ih in the temperature range 15–265 K. A polynomial expression was given for the unit-cell volumes. It turns out that the coefficients quoted have an insufficient number of digits to faithfully reproduce the volume cell data. Here we provide a table with more significant digits. Moreover, we also provide the coefficients of a polynomial fit to the previously published a and c lattice constants of normal and deuterated ice Ih for the same temperature range.

ELASTO-PLASTIC PROPERTIES OF Mo-MODIFIED Ti DEDUCED FROM INDENTATION TESTS AND FINITE ELEMENT ANALYSIS

2019 ◽  
Vol 26 (07) ◽  
pp. 1850225
Author(s):  
YONG MA ◽  
ZHAO YANG ◽  
SHENGWANG YU ◽  
BING ZHOU ◽  
HONGJUN HEI ◽  
...  
Keyword(s):  
Finite Element ◽  
Surface Treatment ◽  
Load Capacity ◽  
Indentation Test ◽  
Element Analysis ◽  
Plastic Properties ◽  
Polynomial Expression ◽  
Indentation Tests ◽  
Graded Material ◽  
Micro Indentation

The aim of this paper is to establish an approach to quantitatively determine the elasto-plastic parameters of the Mo-modified Ti obtained by the plasma surface alloying technique. A micro-indentation test is conducted on the surface under 10[Formula: see text]N. Considering size effects, nanoindentation tests are conducted on the cross-section with two loads of 6 and 8[Formula: see text]mN. Assuming nanoindentation testing sublayers are homogeneous, finite element reverse analysis is adopted to determine their plastic parameters. According to the gradient distributions of the elasto-plastic parameters with depth in the Mo-modified Ti, two types of mathematical expressions are proposed. Compared with the polynomial expression, the linear simplified expression does not need the graded material to be sectioned and has practical utility in the surface treatment industry. The validation of the linear simplified expression is verified by the micro-indentation test and corresponding finite element forward analysis. This approach can assist in improving the surface treatment process of the Mo-modified Ti and further enhancing its load capacity and wear resistance.

scholarly journals Almost Exact Computation of Eigenvalues in Approximate Differential Problems

2019 ◽  
Vol 24 (4) ◽  
pp. 96 ◽  
Author(s):  
José M. A. Matos ◽  
Maria João Rodrigues
Keyword(s):  
Eigenvalue Problems ◽  
High Accuracy ◽  
Second Step ◽  
Matlab Toolbox ◽  
Differential Problem ◽  
Algebraic Problem ◽  
Polynomial Expression ◽  
Computation Of Eigenvalues ◽  
Potential Use ◽  
Mathematics And Physics

Differential eigenvalue problems arise in many fields of Mathematics and Physics, often arriving, as auxiliary problems, when solving partial differential equations. In this work, we present a method for eigenvalues computation following the Tau method philosophy and using Tau Toolbox tools. This Matlab toolbox was recently presented and here we explore its potential use and suitability for this problem. The first step is to translate the eigenvalue differential problem into an algebraic approximated eigenvalues problem. In a second step, making use of symbolic computations, we arrive at the exact polynomial expression of the determinant of the algebraic problem matrix, allowing us to get high accuracy approximations of differential eigenvalues.

scholarly journals An Improved Analysis for the Harmonic Distortion of MOS Voltage-Controlled-Resistors

1997 ◽  
Vol 19 (4) ◽  
pp. 253-260
Author(s):  
Muhammad Taher Abuelma'atti
Keyword(s):  
Fourth Order ◽  
Harmonic Distortion ◽  
Voltage Characteristic ◽  
Current Voltage Characteristic ◽  
Mos Transistor ◽  
Current Voltage ◽  
Order Polynomial ◽  
Polynomial Expression ◽  
Analytical Expressions ◽  
Fourth Order Polynomial

In this paper, a fourth-order polynomial expression is obtained for the nonlinear current-voltage characteristic of a MOS transistor operating in the triode region. Using this expression, closed-form expressions are obtained for the second-, third- and fourth-harmonic distortion of a MOS voltage-controlled- resistors. The analytical expressions obtained in this paper can be used for a quantitative study of the effect of different parameters of the performance of MOS voltage-controlled-resistors.

scholarly journals Polynomial expressions of p-ary auction functions

2019 ◽  
Vol 13 (2) ◽  
pp. 69-80
Author(s):  
Shizuo Kaji ◽  
Toshiaki Maeno ◽  
Koji Nuida ◽  
Yasuhide Numata
Keyword(s):  
Homomorphic Encryption ◽  
Target Function ◽  
Fully Homomorphic Encryption ◽  
Degree Polynomial ◽  
Prime Field ◽  
Polynomial Expression ◽  
The Common ◽  
Finite Prime Field ◽  
Maximum Minimum ◽  
Unique Polynomial

Abstract One of the common ways to design secure multi-party computation is twofold: to realize secure fundamental operations and to decompose a target function to be securely computed into them. In the setting of fully homomorphic encryption, as well as some kinds of secret sharing, the fundamental operations are additions and multiplications in the base field such as the field {\mathbb{F}_{2}} with two elements. Then the second decomposition part, which we study in this paper, is (in theory) equivalent to expressing the target function as a polynomial. It is known that any function over the finite prime field {\mathbb{F}_{p}} has a unique polynomial expression of degree at most {p-1} with respect to each input variable; however, there has been little study done concerning such minimal-degree polynomial expressions for practical functions. This paper aims at triggering intensive studies on this subject, by focusing on polynomial expressions of some auction-related functions such as the maximum/minimum and the index of the maximum/minimum value among input values.

Orientation-Singularity and Orientation Capability Analyses of the Stewart-Gough Manipulator

2005 ◽  
Author(s):  
Y. Cao ◽  
Z. Huang ◽  
Q. J. Ge
Keyword(s):  
Central Angle ◽  
Capability Index ◽  
Polynomial Expression ◽  
Moving Platform ◽  
Singularity Locus

In this paper, the orientation-singularity and orientation capability analyses of the Stewart-Gough manipulator are presented. Based on a particular kind of orientation representation of the manipulator, a polynomial expression of degree thirteen is derived, which represents the orientation-singularity locus of the manipulator at a given position, and examples are given to illustrate the result. The description of the orientation capability of the manipulator and the orientation capability index are discussed. In addition, effects of the geometry parameters of the moving platform, including the central angle, the ratio of the moving platform to the base one and the position of the moving platform on the orientation capability of the manipulator are also presented in this paper.

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