scholarly journals Avoiding long Berge cycles II, exact bounds for all $n$

2021 ◽  
Vol 12 (2) ◽  
pp. 247-268
Author(s):  
Zoltán Füredi ◽  
Alexandr Kostochka ◽  
Ruth Luo
Keyword(s):  
Exact Bounds

Exact bounds for the minimum norm of extension operators for Sobolev spaces

1997 ◽  
Vol 61 (1) ◽  
pp. 1-43 ◽  
Author(s):  
V I Burenkov ◽  
A L Gorbunov
Keyword(s):  
Sobolev Spaces ◽  
Minimum Norm ◽  
Exact Bounds

On a method for proving exact bounds on derivational complexity in thue systems

2012 ◽  
Vol 92 (1-2) ◽  
pp. 3-15
Author(s):  
S. I. Adian
Keyword(s):  
Exact Bounds

scholarly journals Global Bounds for the Generalized Jensen Functional with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2105
Author(s):  
Slavko Simić ◽  
Bandar Bin-Mohsin
Keyword(s):  
Power Mean ◽  
Jensen Functional ◽  
Exact Bounds ◽  
Harmonic Means ◽  
Stolarsky Means ◽  
Generalized Arithmetic

In this article we give sharp global bounds for the generalized Jensen functional Jn(g,h;p,x). In particular, exact bounds are determined for the generalized power mean in terms from the class of Stolarsky means. As a consequence, we obtain the best possible global converses of quotients and differences of the generalized arithmetic, geometric and harmonic means.

scholarly journals Reliable Approximated Number System with Exact Bounds and Three-Valued Logic

2018 ◽  
Vol 33 (6) ◽  
pp. 447-455
Author(s):  
Reeseo Cha ◽  
Wonhong Nam ◽  
Jin-Young Choi
Keyword(s):  
Number System ◽  
Exact Bounds

scholarly journals Exact bounds for tail probabilities of martingales with bounded differences

2009 ◽  
Vol 50 ◽  
Author(s):  
Dainius Dzindzalieta
Keyword(s):  
Random Walks ◽  
General Principle ◽  
Isoperimetric Problem ◽  
Maximal Inequality ◽  
Tail Probabilities ◽  
Bounds For Tail Probabilities ◽  
Maximal Inequalities ◽  
Exact Bounds ◽  
Natural Classes

We consider random walks, say Wn = {0, M1, . . ., Mn} of length n starting at 0 and based on a martingale sequence Mk = X1 + ··· + Xk with differences Xm. Assuming |Xk| \leq 1 we solve the isoperimetric problem Bn(x) = supP\{Wn visits an interval [x,∞)\},  (1) where sup is taken over all possible Wn. We describe random walks which maximize the probability in (1). We also extend the results to super-martingales.For martingales our results can be interpreted as a maximalinequalitiesP\{max 1\leq k\leq n Mk   \geq x\} \leq Bn(x).The maximal inequality is optimal since the equality is achieved by martingales related to the maximizing random walks. To prove the result we introduce a general principle – maximal inequalities for (natural classes of) martingales are equivalent to (seemingly weaker) inequalities for tail probabilities, in our caseBn(x) = supP{Mn  \geq  x}.Our methods are similar in spirit to a method used in [1], where a solution of an isoperimetric problem (1), for integer x is provided and to the method used in [4], where the isoperimetric problem of type (1) for conditionally symmetric bounded martingales was solved for all x ∈ R.

Asymptotic analysis and local lattice central limit theorems

1979 ◽  
Vol 16 (03) ◽  
pp. 541-553 ◽  
Author(s):  
P.A.P. Moran
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Stirling Numbers ◽  
Central Limit Theorems ◽  
Discrete Distributions ◽  
Asymptotic Formulae ◽  
Local Lattice ◽  
Exact Bounds ◽  
Direct Numerical Integration ◽  
Positive Coefficients

Methods of evaluating the coefficients of high powers of functions defined by power series with positive coefficients are considered. Such methods, which were originally used by Laplace, can, for example, be used to obtain asymptotic formulae for Stirling numbers. They are equivalent to using local lattice central limit theorems. An alternative method using direct numerical integration on a contour integral giving the required coefficient is described. Exact bounds for the accuracy of this method can often be obtained by considerations of the unimodality of discrete distributions. The results are illustrated using convolutions of the rectangular and logarithmic distributions.

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