scholarly journals On an explicit lower bound for the star discrepancy in three dimensions

2018 ◽  
Vol 143 ◽  
pp. 158-168
Author(s):  
Florian Puchhammer
Keyword(s):  
Lower Bound ◽  
Three Dimensions ◽  
Explicit Lower Bound ◽  
Star Discrepancy

On the infimum of the spectrum of a relativistic Schrödinger operator

2017 ◽  
Vol 29 (3) ◽  
Author(s):  
Mohammed El Aïdi
Keyword(s):  
Lower Bound ◽  
Euclidean Space ◽  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Relativistic Schrödinger Operator ◽  
Explicit Lower Bound

AbstractIn this paper, we look for an explicit lower bound of the smallest value of the spectrum for a relativistic Schrödinger operator in a domain of the Euclidean space.

scholarly journals On Proinov’s Lower Bound for the Diaphony

2020 ◽  
Vol 15 (2) ◽  
pp. 39-72
Author(s):  
Nathan Kirk
Keyword(s):  
Lower Bound ◽  
Uniform Distribution ◽  
Lower Bounds ◽  
Unit Cube ◽  
Integral Approximation ◽  
Quantitative Theory ◽  
Dimensional Unit ◽  
Explicit Lower Bound ◽  
Irregularities Of Distribution ◽  
Infinite Sequences

AbstractIn 1986, Proinov published an explicit lower bound for the diaphony of finite and infinite sequences of points contained in the d−dimensional unit cube [Proinov, P. D.:On irregularities of distribution, C. R. Acad. Bulgare Sci. 39 (1986), no. 9, 31–34]. However, his widely cited paper does not contain the proof of this result but simply states that this will appear elsewhere. To the best of our knowledge, this proof was so far only available in a monograph of Proinov written in Bulgarian [Proinov, P. D.: Quantitative Theory of Uniform Distribution and Integral Approximation, University of Plovdiv, Bulgaria (2000)]. The first contribution of our paper is to give a self contained version of Proinov’s proof in English. Along the way, we improve the explicit asymptotic constants implementing recent, and corrected results of [Hinrichs, A.—Markhasin, L.: On lower bounds for the ℒ2-discrepancy, J. Complexity 27 (2011), 127–132.] and [Hinrichs, A.—Larcher, G.: An improved lower bound for the ℒ2-discrepancy, J. Complexity 34 (2016), 68–77]. (The corrections are due to a note in [Hinrichs, A.—Larcher, G. An improved lower bound for the ℒ2-discrepancy, J. Complexity 34 (2016), 68–77].) Finally, as a main result, we use the method of Proinov to derive an explicit lower bound for the dyadic diaphony of finite and infinite sequences in a similar fashion.

scholarly journals Lower Bound for the Class Number of ℚn2+4

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Hasan Sankari ◽  
Ahmad Issa
Keyword(s):  
Lower Bound ◽  
Class Number ◽  
Quadratic Field ◽  
Real Quadratic Field ◽  
Prime Divisors ◽  
Explicit Lower Bound ◽  
Real Quadratic

In this paper, we give an explicit lower bound for the class number of real quadratic field ℚd, where d=n2+4 is a square-free integer, using  ωn which is the number of odd prime divisors of n.

scholarly journals On the sum of the non-negative Lyapunov exponents for some cocycles related to the Anderson model

2015 ◽  
Vol 37 (2) ◽  
pp. 369-388
Author(s):  
ILIA BINDER ◽  
MICHAEL GOLDSTEIN ◽  
MIRCEA VODA
Keyword(s):  
Lyapunov Exponent ◽  
Lower Bound ◽  
Lyapunov Exponents ◽  
Anderson Model ◽  
Explicit Lower Bound

We provide an explicit lower bound for the the sum of the non-negative Lyapunov exponents for some cocycles related to the Anderson model. In particular, for the Anderson model on a strip of width $W$, the lower bound is proportional to $W^{-\unicode[STIX]{x1D716}}$, for any $\unicode[STIX]{x1D716}>0$. This bound is consistent with the fact that the lowest non-negative Lyapunov exponent is conjectured to have a lower bound proportional to $W^{-1}$.

Sign in / Sign up

Export Citation Format

Share Document