Characterization of the tori via density of the solution set of linear equations

2001 ◽  
pp. 107-116
Author(s):  
Dikran Dikranjan ◽  
Michael Tkachenko
Keyword(s):  
Linear Equations ◽  
Solution Set

On a Congruence Related to Character Sums

1985 ◽  
Vol 28 (4) ◽  
pp. 431-439 ◽  
Author(s):  
J. H. H. Chalk
Keyword(s):  
Prime Power ◽  
Dirichlet Character ◽  
Character Sums ◽  
Arithmetic Progressions ◽  
Solution Set ◽  
Character Sum ◽  
Equal Degree

AbstractIf χ is a Dirichlet character to a prime-power modulus pα, then the problem of estimating an incomplete character sum of the form ∑1≤x≤h χ (x) by the method of D. A. Burgess leads to a consideration of congruences of the typef(x)g'(x) - f'(x)g(x) ≡ 0(pα),where fg(x) ≢ 0(p) and f, g are monic polynomials of equal degree with coefficients in Ζ. Here, a characterization of the solution-set for cubics is given in terms of explicit arithmetic progressions.

scholarly journals AE Regularity of Interval Matrices

2018 ◽  
Vol 33 ◽  
pp. 137-146
Author(s):  
Milan Hladík
Keyword(s):  
Computational Complexity ◽  
Coefficient Matrix ◽  
Solution Set ◽  
System Of Equations ◽  
Existential Quantifier ◽  
Open Problems ◽  
Linear System Of Equations ◽  
Classes Of Matrices ◽  
Interval Coefficients

Consider a linear system of equations with interval coefficients, and each interval coefficient is associated with either a universal or an existential quantifier. The AE solution set and AE solvability of the system is defined by ∀∃- quantification. The paper deals with the problem of what properties must the coefficient matrix have in order that there is guaranteed an existence of an AE solution. Based on this motivation, a concept of AE regularity is introduced, which implies that the AE solution set is nonempty and the system is AE solvable for every right-hand side. A characterization of AE regularity is discussed, and also various classes of matrices that are implicitly AE regular are investigated. Some of these classes are polynomially decidable, and therefore give an efficient way for checking AE regularity. Eventually, there are also stated open problems related to computational complexity and characterization of AE regularity.

A characterization of Prüfer $v$-multiplication domains in terms of linear equations

2020 ◽  
Vol 12 (3) ◽  
pp. 435-445
Author(s):  
Lei Qiao ◽  
Qianyu Shu ◽  
Fanggui Wang
Keyword(s):  
Linear Equations

scholarly journals A Generalized Nonuniform Contraction and Lyapunov Function

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Fang-fang Liao ◽  
Yongxin Jiang ◽  
Zhiting Xie
Keyword(s):  
Lyapunov Function ◽  
Lyapunov Functions ◽  
Linear Equations ◽  
Complete Characterization ◽  
Nonlinear Perturbations ◽  
Linear Perturbations ◽  
The Stability

For nonautonomous linear equationsx′=A(t)x, we give a complete characterization of general nonuniform contractions in terms of Lyapunov functions. We consider the general case of nonuniform contractions, which corresponds to the existence of what we call nonuniform(D,μ)-contractions. As an application, we establish the robustness of the nonuniform contraction under sufficiently small linear perturbations. Moreover, we show that the stability of a nonuniform contraction persists under sufficiently small nonlinear perturbations.

scholarly journals Thermophysical Characterization of Two DyethylMethylAmmonium Ionic Liquids

Proceedings ◽  
2018 ◽  
Vol 9 (1) ◽  
pp. 29
Author(s):  
◽  
◽  
◽  
◽  
◽  
...  
Keyword(s):  
Thermal Expansion ◽  
Water Content ◽  
Speed Of Sound ◽  
Linear Equations ◽  
Vacuum Pump ◽  
Direct Measurements ◽  
Influence Of Water ◽  
Opposite Behavior ◽  
Thermophysical Characterization

Density (ρ), speed of sound (U), and the derived magnitudes of two diethylmethylammoniumionic liquids (ILs) against temperature have been studied in this work. The chosen ILs were diethylmethylammonium trifluoromethanesulfonate [C2C2C1N][OTf] and diethylmethylammonium methanesulfonate [C2C2C1N][MeSO3]. In order to analyze the influence of water content, saturated and dried samples of these ILs were studied. The ILs were dried using a vacuum pump, and the saturation level (28% and 6% in weight for [C2C2C1N][MeSO3] and [C2C2C1N][OTf], respectively) was achieved by keeping the ILs in an open bottle at ambient temperature. Direct measurements of density and speed of sound were taken with an Anton Paar DSA 5000. Linear equations were used to express the correlation of both properties with temperature, and the thermal expansion coefficient, αp, and the adiabatic bulk modulus constant, KS, have been also obtained. Additionally, results were compared with previous literature data in order to have a deeper understanding of the liquid properties and detect possible anomalous behaviors. The effect of water content is different on both properties. Thus, the density of the samples slightly increases when water is removed, whereas the opposite behavior was found with regard to the speed of sound, which decreased when the water content was completely removed.

scholarly journals The Solution Set Characterization and Error Bound for the Extended Mixed Linear Complementarity Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Hongchun Sun ◽  
Yiju Wang
Keyword(s):  
Error Bound ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Solution Set ◽  
Global Error Bound ◽  
Mixed Linear Complementarity Problem

For the extended mixed linear complementarity problem (EML CP), we first present the characterization of the solution set for the EMLCP. Based on this, its global error bound is also established under milder conditions. The results obtained in this paper can be taken as an extension for the classical linear complementarity problems.

Incorporating crown ratio into prediction equations for Douglas-fir stem volume

1987 ◽  
Vol 17 (1) ◽  
pp. 17-22 ◽  
Author(s):  
David W. Hann ◽  
David K. Walters ◽  
John A. Scrivani
Keyword(s):  
Statistical Significance ◽  
Linear Equations ◽  
Douglas Fir ◽  
Stem Volume ◽  
Validation Data ◽  
Data Set ◽  
Component Approach ◽  
Modeling Data ◽  
Volume Equations

Crown ratio was incorporated into four Douglas-fir (Pseudotsugamenziesii (Mirb.) Franco) total-stem cubic volume equations as a nonlinear multiplier. Two of the equations are traditional linear equations, one is nonlinear, and one is a new component approach that divides stem volume into that above and that below breast height. These equations, with and without crown ratio terms, were fitted to a modeling data set, and the statistical significance of the crown ratio terms was examined. All equations were then applied to a validation data set for comparison of their predictive abilities. The crown ratio term proved to be highly significant in the component approach, and component equations that included crown ratio had the smallest bias and the greatest prediction precision of all equations examined. That form was therefore selected as the most accurate characterization of Douglas-fir stem volume.

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