An upper bound for the absolute constant in the nonuniform version of the Berry-Esseen inequalities for nonidentically distributed summands

2012 ◽  
Vol 86 (1) ◽  
pp. 524-526 ◽  
Author(s):  
M. E. Grigor’eva ◽  
S. V. Popov
Keyword(s):  
Upper Bound ◽  
Absolute Constant ◽  
The Absolute

scholarly journals On the coefficients of transformation polynomials for the modular function

1974 ◽  
Vol 10 (2) ◽  
pp. 197-218 ◽  
Author(s):  
Kurt Mahler
Keyword(s):  
Upper Bound ◽  
Absolute Constant ◽  
Modular Function ◽  
Acta Arith ◽  
Level 1 ◽  
The Absolute ◽  
Image Position

In a previous paper (Acta Arith. 21 (1972), 89–97), I had proved that the sum of the absolute values of the coefficients of the mth transformation polynomial Fm (u, v) of the Weber modular function j(ω) of level 1 is not greater than 2(36n+57)2n when m = 2n is a power of 2. The aim of the present paper is to give an analogous bound for the case of general m. This upper bound is much less good and of the form where c > 0 is an absolute constant which can be determined effectively. It seems probable that also in the general case an upper bound of the form eO(m10gm) should hold, but I have not so far succeeded in proving such a result.

Suboptimality of a Decentralized Feedback Control Law

1999 ◽  
Vol 121 (2) ◽  
pp. 305-308
Author(s):  
El Kebi´r Boukas ◽  
A. Swierniak ◽  
H. Yang
Keyword(s):  
Feedback Control ◽  
Linear System ◽  
Upper Bound ◽  
Optimization Problem ◽  
Control Law ◽  
Relative Cost ◽  
Numerical Example ◽  
Uncertain Linear System ◽  
The Absolute ◽  
The Cost

In this note, a new estimating method for the upper bound of the cost of the uncertain linear system used by Trinh and Aldeen (1993) is proposed. We have also estimated the absolute cost loss and relative cost loss of this kind of optimization problem. To show the usefulness of our results a numerical example has been developed.

scholarly journals Thue Inequalities With Few Coefficients

2020 ◽  
Author(s):  
Paloma Bengoechea
Keyword(s):  
Upper Bound ◽  
Binary Form ◽  
Number Of Solutions ◽  
Absolute Value ◽  
Integer Coefficients ◽  
The Absolute

Abstract Let $F(x, y)$ be a binary form with integer coefficients, degree $n\geq 3$, and irreducible over the rationals. Suppose that only $s + 1$ of the $n + 1$ coefficients of $F$ are nonzero. We show that the Thue inequality $|F(x,y)|\leq m$ has $\ll s m^{2/n}$ solutions provided that the absolute value of the discriminant $D(F)$ of $F$ is large enough. We also give a new upper bound for the number of solutions of $|F(x,y)|\leq m$, with no restriction on the discriminant of $F$ that depends mainly on $s$ and $m$, and slightly on $n$. Our bound becomes independent of $m$ when $m<|D(F)|^{2/(5(n-1))}$, and also independent of $n$ if $|D(F)|$ is large enough.

Some properties of left 2α-Engel subgroups

2020 ◽  
pp. 2150068
Author(s):  
Ali Mohammad Z. Mehrjerdi ◽  
Mohammad Reza R. Moghaddam ◽  
Mohammad Amin Rostamyari
Keyword(s):  
Upper Bound ◽  
Factor Group ◽  
Central Factor ◽  
Famous Result ◽  
Commutator Formula ◽  
Autocommutator Subgroup ◽  
Derived Subgroup ◽  
The Absolute

In 1904, Schur proved his famous result which says that if the central factor group of a given group is finite, then so is its derived subgroup. In 1994, Hegarty showed that if the absolute central factor group, [Formula: see text], is finite, then so is its autocommutator subgroup, [Formula: see text]. In the present paper, for a given automorphism [Formula: see text] of the group [Formula: see text], we introduce the concept of left [Formula: see text]-Engel, [Formula: see text], and [Formula: see text]-Engel commutator, [Formula: see text]. Then under some condition, we prove that the finiteness of [Formula: see text] implies that [Formula: see text] is also finite. We also construct an upper bound for the order of [Formula: see text] in terms of the order of [Formula: see text].

scholarly journals A Subexponential Upper Bound for van der Waerden Numbers $W(3,k)$

10.37236/9704 ◽  
2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Tomasz Schoen
Keyword(s):  
Arithmetic Progression ◽  
Upper Bound ◽  
Absolute Constant ◽  
Upper Estimate

We show an improved upper estimate for van der Waerden number $W(3,k):$ there is an absolute constant $c>0$ such that if $\{1,\dots,N\}=X\cup Y$ is a partition such that $X$ does not contain any arithmetic progression of length $3$ and $Y$ does not contain any arithmetic progression of length $k$ then $$N\le \exp(O(k^{1-c}))\,.$$

scholarly journals Mean-square upper bound of Hecke $L$-functions on the critical line.

2003 ◽  
Vol Volume 26 ◽  
Author(s):  
A Sankaranarayanan
Keyword(s):  
Cusp Form ◽  
Upper Bound ◽  
Critical Line ◽  
Congruence Subgroup ◽  
Mean Square ◽  
Absolute Value ◽  
International Audience ◽  
The Mean ◽  
The Absolute

International audience We prove the upper bound for the mean-square of the absolute value of the Hecke $L$-functions (attached to a holomorphic cusp form) defined for the congruence subgroup $\Gamma_0 (N)$ on the critical line uniformly with respect to its conductor $N$.

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