scholarly journals Perron units which are not Mahler measures

1986 ◽  
Vol 6 (4) ◽  
pp. 485-488 ◽  
Author(s):  
David W. Boyd
Keyword(s):  
Unit Circle ◽  
Ergodic Theory ◽  
Minimal Polynomial ◽  
Algebraic Integer ◽  
Mahler Measure ◽  
Absolute Value ◽  
Perron Number ◽  
The Absolute

AbstractThe Mahler measure M(α) of an algebraic integer α is the product of the absolute value of the conjugates of α which lie outside the unit circle. The quantity log M(α) occurs in ergodic theory as the entropy of an endomorphism of the torus. Adler and Marcus showed that if β = M(α) then β is a Perron number which is a unit if α is a unit. They asked whether the Perron number β whose minimal polynomial is tm −t −1 is the measure of any algebraic integer. We show here that the answer is negative for all m > 3.

scholarly journals On real algebraic numbers in which the derivative of their minimal polynomial is small

2021 ◽  
Vol 57 (2) ◽  
pp. 135-147
Author(s):  
D. V. Koleda
Keyword(s):  
Algebraic Number ◽  
Minimal Polynomial ◽  
Algebraic Numbers ◽  
Absolute Value ◽  
Positive Degree ◽  
Integer Polynomials ◽  
The Absolute

Algebraic numbers are the roots of integer polynomials. Each algebraic number α is characterized by its minimal polynomial Pα that is a polynomial of minimal positive degree with integer coprime coefficients, α being its root. The degree of α is the degree of this polynomial, and the height of α is the maximum of the absolute values of the coefficients of this polynomial. In this paper we consider the distribution of algebraic numbers α whose degree is fixed and height bounded by a growing parameter Q, and the minimal polynomial Pα is such that the absolute value of its derivative P'α (α) is bounded by a given parameter X. We show that if this bounding parameter X is from a certain range, then as Q → +∞ these algebraic numbers are distributed uniformly in the segment [-1+√2/3.1-√2/3]

Reciprocal Algebraic Integers Whose Mahler Measures are Non-Reciprocal

1987 ◽  
Vol 30 (1) ◽  
pp. 3-8 ◽  
Author(s):  
David W. Boyd
Keyword(s):  
Unit Circle ◽  
Algebraic Integer ◽  
Mahler Measure ◽  
Algebraic Integers

AbstractThe Mahler measure M (α) of an algebraic integer α is the product of the moduli of the conjugates of α which lie outside the unit circle. A number α is reciprocal if α- 1 is a conjugate of α. We give two constructions of reciprocal a for which M (α) is non-reciprocal producing examples of any degree n of the form 2h with h odd and h ≥ 3, or else of the form with s ≥ 2. We give explicit examples of degrees 10, 14 and 20.

A Note on Integer Symmetric Matrices and Mahler's Measure

2008 ◽  
Vol 51 (1) ◽  
pp. 57-59 ◽  
Author(s):  
Edward Dobrowolski
Keyword(s):  
Lower Bound ◽  
Minimal Polynomial ◽  
Symmetric Matrix ◽  
Symmetric Matrices ◽  
Absolute Value ◽  
The Absolute

AbstractWe find a lower bound on the absolute value of the discriminant of the minimal polynomial of an integral symmetric matrix and apply this result to find a lower bound on Mahler's measure of related polynomials and to disprove a conjecture of D. Estes and R. Guralnick.

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.

Sign in / Sign up

Export Citation Format

Share Document