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 Quantitative Equidistribution for Certain Quadruples in Quasi-Random Groups: Erratum

2015 ◽  
Vol 25 (3) ◽  
pp. 484-485 ◽  
Author(s):  
TIM AUSTIN
Keyword(s):  
First Line ◽  
Absolute Value ◽  
Formula Group ◽  
The Absolute ◽  
Image Position ◽  
The Right ◽  
Random Groups ◽  
Complex Valued

In my recent paper [1] there is a mistake in the proof of Corollary 3. The first line of the displayed equation in that proof asserts that \[\int_G|\langle u,\pi^g v\rangle_V|^2\,\rm{d} g = \int_G\langle u\otimes u,(\pi^g\otimes \pi^g)(v\otimes v)\rangle_{V\otimes V}\, \rm{d} g.\] However, since the paper uses complex-valued representations, the integrand on the right here may not retain the absolute value of that on the left. Without this equality, the proof of Corollary 3 can no longer be reduced to an application of Lemma 2. However, it can be proved directly from Schur Orthogonality along very similar lines to the proof of Lemma 2.

scholarly journals HERMITE–HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHEN A POWER OF THE ABSOLUTE VALUE OF THE FIRST DERIVATIVE IS P-CONVEX

2011 ◽  
Vol 86 (1) ◽  
pp. 126-134 ◽  
Author(s):  
A. BARANI ◽  
S. BARANI
Keyword(s):  
Type Inequality ◽  
Absolute Value ◽  
Trapezoidal Formula ◽  
First Derivative ◽  
Right Hand ◽  
Special Means ◽  
The Absolute ◽  
The Right

AbstractIn this paper we extend some estimates of the right-hand side of a Hermite–Hadamard type inequality for functions whose derivatives’ absolute values are P-convex. Applications to the trapezoidal formula and special means are introduced.

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 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.

scholarly journals Deformation Time Series and Driving-Force Analysis of Glaciers in the Eastern Tienshan Mountains Using the SBAS InSAR Method

2020 ◽  
Vol 17 (8) ◽  
pp. 2836
Author(s):  
Weibing Du ◽  
Weiqian Ji ◽  
Linjuan Xu ◽  
Shuangting Wang
Keyword(s):  
Time Series ◽  
Synthetic Aperture Radar ◽  
Melting Rate ◽  
Synthetic Aperture ◽  
Glacier Mass Balance ◽  
Interferometric Method ◽  
Study Region ◽  
Absolute Value ◽  
The Absolute ◽  
Aperture Radar

Glacier melting is one of the important causes of glacier morphology change and can provide basic parameters for calculating glacier volume change and glacier mass balance, which, in turn, is important for evaluating water resources. However, it is difficult to obtain large-scale time series of glacier changes due to the cloudy and foggy conditions which are typical of mountain areas. Gravity-measuring satellites and laser altimetry satellites can monitor changes in glacier volume over a wide area, while synthetic-aperture radar satellites can monitoring glacier morphology with a high spatial and temporal resolution. In this article, an interferometric method using a short temporal baseline and a short spatial baseline, called the Small Baseline Subsets (SBAS) Interferometric Synthetic-Aperture Radar (InSAR) method, was used to study the average rate of glacier deformation on Karlik Mountain, in the Eastern Tienshan Mountains, China, by using 19 Sentinel-1A images from November 2017 to December 2018. Thus, a time series analysis of glacier deformation was conducted. It was found that the average glacier deformation in the study region was −11.77 ± 9.73 mm/year, with the observation sites generally moving away from the satellite along the Line of Sight (LOS). Taking the ridge line as the dividing line, it was found that the melting rate of southern slopes was higher than that of northern slopes. According to the perpendicular of the mountain direction, the mountain was divided into an area in the northwest with large glaciers (Area I) and an area in the southeast with small glaciers (Area II). It was found that the melting rate in the southeast area was larger than that in the northwest area. Additionally, through the analysis of temperature and precipitation data, it was found that precipitation played a leading role in glacier deformation in the study region. Through the statistical analysis of the deformation, it was concluded that the absolute value of deformation is large at elevations below 4200 m while the absolute value of the deformation is very small at elevations above 4500 m; the direction of deformation is always away from the satellite along the LOS and the absolute value of glacier deformation decreases with increasing elevation.

scholarly journals Фотоупругие свойства кристаллов сульфата калия

2019 ◽  
Vol 61 (11) ◽  
pp. 2154
Author(s):  
В.И. Стадник ◽  
Р.Б. Матвиив ◽  
П.А. Щепанский ◽  
М.Я. Рудиш ◽  
З.А. Когут
Keyword(s):  
Ultraviolet Radiation ◽  
Short Wavelength ◽  
Elastic Stiffness ◽  
Potassium Sulfate ◽  
Dispersion Dependence ◽  
Transparency Region ◽  
Stiffness Coefficients ◽  
Strontium Borate ◽  
The Matrix ◽  
Order Of Magnitude

The spectral dependences of the absolute piezo-optic coefficients of potassium sulfate crystals are studied and their insignificant dispersion dependence is established. The matrix of elasto-optic coefficients рin of these crystals is filled using the values of elastic stiffness coefficients and absolute piezo-optic coefficients. The coefficient of the acousto-optic efficiency М2 is estimated and it is shown that, considering the highest values, it is more than an order of magnitude higher than that of quartz and strontium borate crystals. Taking into account the short-wavelength boundary of the transparency region of potassium sulfate crystals (~ 170 nm), it is proposed to use them for acousto-optic modulation of ultraviolet radiation.

scholarly journals Refinements of Hermite-Hadamard Inequalities for Functions When a Power of the Absolute Value of the Second Derivative IsP-Convex

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
A. Barani ◽  
S. Barani ◽  
S. S. Dragomir
Keyword(s):  
Second Derivative ◽  
Absolute Value ◽  
Right Hand ◽  
Special Means ◽  
Second Derivatives ◽  
The Absolute ◽  
The Right

We extend some estimates of the right-hand side of Hermite-Hadamard-type inequalities for functions whose second derivatives absolute values areP-convex. Applications to some special means are considered.

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.

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