scholarly journals Determining Knots with Quadratic Polynomial Precision

2007 ◽  
pp. 130-137
Author(s):  
Zhang Caiming ◽  
Ji Xiuhua ◽  
Liu Hui
Keyword(s):  
Quadratic Polynomial

The Solvability of Polynomial Pell’s Equation

2020 ◽  
Vol 25 (2) ◽  
pp. 125-132
Author(s):  
Bal Bahadur Tamang ◽  
Ajay Singh
Keyword(s):  
Trivial Solution ◽  
Continued Fraction ◽  
Laurent Series ◽  
Quadratic Polynomial ◽  
Continued Fraction Expansion ◽  
Pell’S Equation ◽  
Integer Polynomials

This article attempts to describe the continued fraction expansion of ÖD viewed as a Laurent series x-1. As the behavior of the continued fraction expansion of ÖD is related to the solvability of the polynomial Pell’s equation p2-Dq2=1  where D=f2+2g  is monic quadratic polynomial with deg g<deg f  and the solutions p, q  must be integer polynomials. It gives a non-trivial solution if and only if the continued fraction expansion of ÖD  is periodic.

scholarly journals On three-variable expanders over finite valuation rings

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Le Quang Ham ◽  
Nguyen Van The ◽  
Phuc D. Tran ◽  
Le Anh Vinh
Keyword(s):  
Valuation Ring ◽  
Product Type ◽  
Quadratic Polynomial ◽  
Valuation Rings

AbstractLet {\mathcal{R}} be a finite valuation ring of order {q^{r}}. In this paper, we prove that for any quadratic polynomial {f(x,y,z)\in\mathcal{R}[x,y,z]} that is of the form {axy+R(x)+S(y)+T(z)} for some one-variable polynomials {R,S,T}, we have|f(A,B,C)|\gg\min\biggl{\{}q^{r},\frac{|A||B||C|}{q^{2r-1}}\bigg{\}}for any {A,B,C\subset\mathcal{R}}. We also study the sum-product type problems over finite valuation ring {\mathcal{R}}. More precisely, we show that for any {A\subset\mathcal{R}} with {|A|\gg q^{r-\frac{1}{3}}} then {\max\{|AA|,|A^{d}+A^{d}|\}}, {\max\{|A+A|,|A^{2}+A^{2}|\}}, {\max\{|A-A|,|AA+AA|\}\gg|A|^{\frac{2}{3}}q^{\frac{r}{3}}}, and {|f(A)+A|\gg|A|^{\frac{2}{3}}q^{\frac{r}{3}}} for any one variable quadratic polynomial f.

A Characterization of a Quadratic Polynomial: 10848

2002 ◽  
Vol 109 (1) ◽  
pp. 80
Author(s):  
Kenneth Stolarsky ◽  
NSA Problems Group ◽  
O. P. Lossers
Keyword(s):  
Quadratic Polynomial

scholarly journals The optimal mating distance resulting from heterosis and genetic incompatibility

2018 ◽  
Vol 4 (11) ◽  
pp. eaau5518 ◽  
Author(s):  
Xinzhu Wei ◽  
Jianzhi Zhang
Keyword(s):  
Animal Model ◽  
Genetic Distance ◽  
Polynomial Function ◽  
Genetic Distances ◽  
Quadratic Polynomial ◽  
Model Organisms ◽  
Genetic Incompatibility ◽  
Large Numbers ◽  
Practical Implications

Theory predicts that the fitness of an individual is maximized when the genetic distance between its parents (i.e., mating distance) is neither too small nor too large. However, decades of research have generally failed to validate this prediction or identify the optimal mating distance (OMD). Respectively analyzing large numbers of crosses of fungal, plant, and animal model organisms, we indeed find the hybrid phenotypic value a humped quadratic polynomial function of the mating distance for the vast majority of fitness-related traits examined, with different traits of the same species exhibiting similar OMDs. OMDs are generally slightly greater than the nucleotide diversities of the species concerned but smaller than the observed maximal intraspecific genetic distances. Hence, the benefit of heterosis is at least partially offset by the harm of genetic incompatibility even within species. These results have multiple theoretical and practical implications for speciation, conservation, and agriculture.

scholarly journals CONVERGENCE OF COMONOTONE HISTOPOLATING SPLINES

2015 ◽  
Vol 20 (1) ◽  
pp. 124-138 ◽  
Author(s):  
Helle Hallik ◽  
Peeter Oja
Keyword(s):  
Convergence Rate ◽  
Finite Number ◽  
Numerical Results ◽  
Quadratic Polynomial

The convergence rate of histopolation on an interval with combined splines of class C1 having linear/linear rational or quadratic polynomial pieces is studied. The function to histopolate may have finite number of derivative zeros and established convergence rate depends mainly on the behaviour of the derivative near its zeros. Given numerical results are completely consistent with theoretical ones.

scholarly journals The degree of regularity of a quadratic polynomial

2013 ◽  
Vol 217 (2) ◽  
pp. 207-217 ◽  
Author(s):  
Timothy J. Hodges ◽  
Jacob Schlather
Keyword(s):  
Quadratic Polynomial

scholarly journals Inversion of higher order isotropic tensors with minor symmetries and solution of higher order heterogeneity problems

2010 ◽  
Vol 467 (2126) ◽  
pp. 314-332 ◽  
Author(s):  
Vincent Monchiet ◽  
Guy Bonnet
Keyword(s):  
Closed Form ◽  
Strain Field ◽  
Spherical Inclusion ◽  
Higher Order ◽  
Quadratic Polynomial ◽  
Elastic Matrix ◽  
Closed Form Expression ◽  
Form Expression ◽  
Order Tensor ◽  
Strain Fields

In this paper, the derivation of irreducible bases for a class of isotropic 2 n th-order tensors having particular ‘minor symmetries’ is presented. The methodology used for obtaining these bases consists of extending the concept of deviatoric and spherical parts, commonly used for second-order tensors, to the case of an n th-order tensor. It is shown that these bases are useful for effecting the classical tensorial operations and especially the inversion of a 2 n th-order tensor. Finally, the formalism introduced in this study is applied for obtaining the closed-form expression of the strain field within a spherical inclusion embedded in an infinite elastic matrix and subjected to linear or quadratic polynomial remote strain fields.

scholarly journals Evaluation of Physical and Mechanical Properties of Cotton Warps Under a Cyclic Load of Stretch-Abrasion

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Min Guo ◽  
Jianli Liu ◽  
Bo Zhu ◽  
Weidong Gao
Keyword(s):  
Mechanical Properties ◽  
Fatigue Behavior ◽  
Physical And Mechanical Properties ◽  
Strong Relationship ◽  
Quadratic Polynomial ◽  
Fatigue Cycle ◽  
Continuous Increase ◽  
Load Simulator ◽  
Relationship Of ◽  
Strength Retention

AbstractThe fatigue behavior of cotton warps was studied by a newly weaving load simulator (WLS) developed in our laboratory. Reborn hairiness, strength retention, and elongation retention of sized warps were adopted to evaluate the physical and mechanical properties of sized warps under stretch-abrasion cyclic loading. The influences of different fatigue cycles on the above three indicators were also discussed. The results indicated that the fatigue behavior of the cotton warps accompanied by abrasion yields a three-parameter Weibull distribution. All the fitting plots show acceptable linearity. Moreover, there is a strong relationship of quadratic polynomial between the tensile properties and the fatigue cycle of the sized warps according to the scatter fitting (R2 > 91.08%). Similarly, there is also a good relationship of quadratic polynomial between the reborn hairiness index and the fatigue cycle of the sized warps (R2 > 94.51%). Finally, regardless of the strength retention, elongation retention, and reborn hairiness, the physical and mechanical properties of the cotton warps still change with the continuous increase of the fatigue cycle after 40% of the fatigue cycle, but it is not significant. The research was helpful to estimate the capacity of the warps to sustain failure.

Sign in / Sign up

Export Citation Format

Share Document