An estimate of the remainder term in the Lyapunov theorem

1974 ◽  
Vol 14 (1) ◽  
pp. 33-37 ◽  
Author(s):  
A. Karoblis
Keyword(s):  
Remainder Term ◽  
Lyapunov Theorem

Asymptotics with remainder term for moments of the total cycle number of random A-permutation

2021 ◽  
Vol 31 (1) ◽  
pp. 51-60
Author(s):  
Arsen L. Yakymiv
Keyword(s):  
Remainder Term ◽  
Random Permutation ◽  
Natural Numbers ◽  
Cycle Number ◽  
Fixed Set ◽  
Cycle Lengths

Abstract Dedicated to the memory of Alexander Ivanovich Pavlov. We consider the set of n-permutations with cycle lengths belonging to some fixed set A of natural numbers (so-called A-permutations). Let random permutation τ n be uniformly distributed on this set. For some class of sets A we find the asymptotics with remainder term for moments of total cycle number of τ n .

scholarly journals On Appel-Type Quadrature Rules

2002 ◽  
Vol 9 (3) ◽  
pp. 405-412
Author(s):  
C. Belingeri ◽  
B. Germano
Keyword(s):  
Remainder Term ◽  
Quadrature Rule ◽  
Bernoulli Numbers ◽  
Quadrature Rules ◽  
Rule Based ◽  
Numerical Example ◽  
The Given ◽  
Derivatives Of

Abstract The Radon technique is applied in order to recover a quadrature rule based on Appel polynomials and the so called Appel numbers. The relevant formula generalizes both the Euler-MacLaurin quadrature rule and a similar rule using Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the endpoints of the considered interval. In the general case, the remainder term is expressed in terms of Appel numbers, and all derivatives appear. A numerical example is also included.

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

scholarly journals Adaptive 3D Distance-Based Formation Control of Multiagent Systems with Unknown Leader Velocity and Coplanar Initial Positions

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Xuejing Lan ◽  
Wenbiao Xu ◽  
Yun-Shan Wei
Keyword(s):  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Relative Position ◽  
Formation Control ◽  
Control Law ◽  
Asymptotically Stable ◽  
Coordinate Systems ◽  
Lyapunov Theorem ◽  
Globally Asymptotically Stable ◽  
3 Dimensional

This paper considers the distributed 3-dimensional (3D) distance-based formation control of multiagent systems, where the agents are connected based on an acyclic minimally structural persistent (AMSP) graph. A parameter is designed according to the desired formation shape and is used to solve the problem that there are two formation shapes satisfying the same distance requirements. The unknown moving velocity of the leader agent is estimated adaptively by the followers requiring only the relative position measurements with respect to their local coordinate systems. In addition, the proposed formation controller provides a new way for the agent to leave the initial coplanar location. The 3D formation control law is globally asymptotically stable and has been demonstrated based on the Lyapunov theorem. Finally, two numerical simulations are presented to support the theoretical analysis.

scholarly journals Spectral Distribution of Transport Operator Arising in Growing Cell Populations

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hongxing Wu ◽  
Shenghua Wang ◽  
Dengbin Yuan
Keyword(s):  
Remainder Term ◽  
Smooth Boundary ◽  
Linear Operators ◽  
Cell Populations ◽  
Resolvent Operators ◽  
Transport Operator ◽  
Growing Cell ◽  
Isolated Eigenvalues ◽  
Algebraic Multiplicities ◽  
Partly Smooth

Transport equation with partly smooth boundary conditions arising in growing cell populations is studied inLp  (1<p<+∞)space. It is to prove that the transport operatorAHgenerates aC0semigroup and the ninth-order remainder termR9(t)of the Dyson-Phillips expansion of the semigroup is compact, and the spectrum of transport operatorAHconsists of only finite isolated eigenvalues with finite algebraic multiplicities in a tripΓω. The main methods rely on theory of linear operators, comparison operators, and resolvent operators approach.

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