scholarly journals On Nonsingularity of RSFPLR Circulant Matrices

2019 ◽  
pp. 1-7
Author(s):  
Xiyou Cui ◽  
Nan Jiang
Keyword(s):  
Circulant Matrices ◽  
Absolute Value ◽  
The Matrix ◽  
The Absolute

In this paper, we discuss the non-singularity of a row skew rst-plus-last right (RSFPLR) circulant matrices with the rst row (a1; a2; : : : ; an),which is determined by entries of the first row. First,the suffient condition for the matrix to be nonsingular is that,there exists an element ai0 belonging to the first row,whose absolute value is greater than the sum of the corresponding power of 2 and the absolute values of the remaining (n − 1) elements, that is, $$|a_{i_0}|>\sum_{{i=1},{i\neq i_0}}^{n}2^{i-i_0}|a_i|.$$ Moreover, we derive other suffcient conditions for judging the non-singularity of the matrix.

A Preconditioned AOR Iterative Method for the Absolute Value Equations

2017 ◽  
Vol 14 (02) ◽  
pp. 1750016 ◽  
Author(s):  
Cui-Xia Li
Keyword(s):  
Iterative Method ◽  
Comparison Theorems ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Comparison Results ◽  
Preconditioning Technique ◽  
The Matrix ◽  
The Absolute ◽  
Theoretical Results ◽  
Better Than

In this paper, coupled with preconditioning technique, a preconditioned accelerated over relaxation (PAOR) iterative method for solving the absolute value equations (AVEs) is presented. Some comparison theorems are given when the matrix of the linear term is an irreducible [Formula: see text]-matrix. Comparison results show that the convergence rate of the PAOR iterative method is better than that of the accelerated over relaxation (AOR) iterative method whenever both are convergent. Numerical experiments are provided in order to confirm the theoretical results studied in this paper.

scholarly journals Photoelastic Properties of Trigonal Crystals

Crystals ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 1095
Author(s):  
Bohdan Mytsyk ◽  
Nataliya Demyanyshyn ◽  
Anatoliy Andrushchak ◽  
Oleh Buryy
Keyword(s):  
Elastic Stiffness ◽  
Interferometric Method ◽  
Absolute Value ◽  
Interferometric Technique ◽  
Stiffness Coefficients ◽  
Half Wave ◽  
Compliance Coefficient ◽  
The Matrix ◽  
The Absolute ◽  
The Right

All possible experimental geometries of the piezo-optic effect in crystals of trigonal symmetry are studied in detail through the interferometric technique, and the corresponding expressions for the calculation of piezo-optic coefficients (POCs) πim and some sums of πim based on experimental data obtained from the samples of direct and X/45°-cuts are given. The reliability of the values of POCs is proven by the convergence of πim obtained from different experimental geometries as well as by the convergence of some sums of POCs. Because both the signs and the absolute values of POCs π14 and π41 are defined by the choice of the right crystal-physics coordinate system, we here use the system whereby the condition S14 > 0 is fulfilled (S14 is an elastic compliance coefficient). The absolute value and the sign of S14 are determined by piezo-optic interferometric method from two experimental geometries. The errors of POCs are calculated as mean square values of the errors of the half-wave stresses and the elastic term. All components of the matrix of elasto-optic coefficients pin are calculated based on POCs and elastic stiffness coefficients. The technique is tested on LiTaO3 crystal. The obtained results are compared with the corresponding data for trigonal LiNbO3 and Ca3TaGa3Si2O14 crystals.

scholarly journals New Duality Operator for Complex Circulant Matrices and a Conjecture of Ryser

10.37236/5237 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Luis H. Gallardo
Keyword(s):  
Hadamard Matrices ◽  
Circulant Matrices ◽  
Complex Matrix ◽  
Absolute Value ◽  
The Absolute

We associate to any given circulant complex matrix $C$ another one $E(C)$ such that $E(E(C)) = C^{*}$ the transpose conjugate of $C.$ All circulant Hadamard matrices of order $4$ satisfy a condition $C_4$ on their eigenvalues, namely, the absolute value of the sum of all eigenvalues is bounded above by $2.$ We prove by a "descent" that uses our operator $E$ that the only circulant Hadamard matrices of order $n \geq 4$, that satisfy a condition $C_n$ that generalizes the condition $C_4$ and that consist of a list of $n/4$ inequalities for the absolute value of some sums of eigenvalues of $H$ are the known ones.

scholarly journals Incentive Function of Audit Opinion for the Increase of Regional Operational Expenditure and Own-Source Revenues Through Sensitivity Analysis in Indonesia

2020 ◽  
Vol 11 (1) ◽  
pp. 20
Author(s):  
Muhammad Ikbal Abdullah ◽  
Andi Chairil Furqan ◽  
Nina Yusnita Yamin ◽  
Fahri Eka Oktora
Keyword(s):  
Sensitivity Analysis ◽  
Significant Influence ◽  
Provincial Government ◽  
Sensitivity Testing ◽  
Audit Opinion ◽  
Absolute Value ◽  
Operating Expenditure ◽  
The Absolute ◽  
Operational Expenditure

This study aims to analyze the sensitivity testing using measurements of realization of regional own-source revenues and operating expenditure and to analyze the extent of the effect of sample differences between Java and non-Java provinces by using samples outside of Java. By using sensitivity analysis, the results found the influence of audit opinion on the performance of the provincial government mediated by the realization of regional operating expenditure. More specifically, when using the measurement of the absolute value of the realization of regional operating expenditure it was found that there was a direct positive and significant influence of audit opinion on the performance of the Provincial Government. However, no significant effect of audit opinion was found on the realization value of regional operating expenditure and the effect of the realization value of regional operating expenditure on the performance of the Provincial Government. This result implies that an increase in audit opinion will be more likely to be used as an incentive for the Provincial Government to increase the realization of regional operating expenditure.

Die Bedeutung der Homogenisationsart und -intensität für die Größe und Konstanz der Sauerstoffaufnahme von Meerschweinchen-Leberhomogenat / The Influence of Mode and Intensity of Homogenization on the Absolute Value and Stability of Oxygen Consumption of Guinea Pig Liver Homogenates

1977 ◽  
Vol 32 (11-12) ◽  
pp. 908-912 ◽  
Author(s):  
H. J. Schmidt ◽  
U. Schaum ◽  
J. P. Pichotka
Keyword(s):  
Oxygen Uptake ◽  
Guinea Pig ◽  
Measuring Time ◽  
Pig Liver ◽  
Absolute Value ◽  
Modified Method ◽  
Simultaneous Measurements ◽  
Liver Homogenates ◽  
The Absolute ◽  
Guinea Pig Liver

Abstract The influence of five different methods of homogenisation (1. The method according to Potter and Elvehjem, 2. A modification of this method called Potter S, 3. The method of Dounce, 4. Homogenisation by hypersonic waves and 5. Coarce-grained homogenisation with the “Mikro-fleischwolf”) on the absolute value and stability of oxygen uptake of guinea pig liver homogenates has been investigated in simultaneous measurements. All homogenates showed a characteristic fall of oxygen uptake during measuring time (3 hours). The modified method according to Potter and Elvehjem called Potter S showed reproducible results without any influence by homogenisation intensity.

Thue equations that simultaneously fail the Hasse principle

2021 ◽  
pp. 1-10
Author(s):  
PALOMA BENGOECHEA
Keyword(s):  
Positive Integer ◽  
Hasse Principle ◽  
Fixed Degree ◽  
Binary Forms ◽  
Absolute Value ◽  
Positive Proportion ◽  
The Absolute

Abstract We refine a previous construction by Akhtari and Bhargava so that, for every positive integer m, we obtain a positive proportion of Thue equations F(x, y) = h that fail the integral Hasse principle simultaneously for every positive integer h less than m. The binary forms F have fixed degree ≥ 3 and are ordered by the absolute value of the maximum of the coefficients.

Comparison of the acceleration due to gravity at the National Physical Laboratory, Teddington, the Bureau International des Poids et Mesures, Sèvres, the Physikalisch-Technische Bundesanstalt, Brunswick, and the Geodetic Institute, Potsdam

1952 ◽  
Vol 213 (1114) ◽  
pp. 408-424 ◽  
Keyword(s):  
National Physical Laboratory ◽  
Absolute Value ◽  
Geodetic Institute ◽  
Physical Laboratory ◽  
The Absolute

The values of gravity at these stations have been compared by means of pendulum observations with Invar invariable pendulums. The observed differences of gravity from the National Physical Laboratory are: B. I. P. M. -256·73 ± 0·49 mgal P. T. B. + 68·68 ± 0·49 mgal Bad Harzburg - 15·68 ± 0·49 mgal The accuracy of the measurements is not so great as has been achieved once or twice previously with the same apparatus, mainly because the changes in the lengths of the pendulums were greater than usual. These differences have been combined with German pendulum observations and with gravimeter comparisons with the following results: Value of gravity at N. P. L. on the Potsdam system: 981196·29 ± 0·3 mgal. Differences between sites of absolute determinations of gravity: N. P. L. - B. I. P. M. +256·45 ± 0·3 mgal N. P. L. - P. T. B. - 68·98 ± 0·3 mgal P. T. B. - Potsdam - 8·95 ± 0·4 mgal ( g at Potsdam = 981274 mgal.) The effects of these results on gravity surveys based on Cambridge and on the absolute value of gravity are indicated.

GPS Meteorology: Direct Estimation of the Absolute Value of Precipitable Water

1996 ◽  
Vol 35 (6) ◽  
pp. 830-838 ◽  
Author(s):  
Jingping Duan ◽  
Michael Bevis ◽  
Peng Fang ◽  
Yehuda Bock ◽  
Steven Chiswell ◽  
...  
Keyword(s):  
Precipitable Water ◽  
Absolute Value ◽  
Direct Estimation ◽  
Gps Meteorology ◽  
The Absolute
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