scholarly journals Reduction theorems for operators on the cones of monotone functions

2013 ◽  
Vol 405 (1) ◽  
pp. 156-172 ◽  
Author(s):  
Amiran Gogatishvili ◽  
Vladimir D. Stepanov
Keyword(s):  
Monotone Functions

Nowhere Monotone Functions

1976 ◽  
Vol 1 (1) ◽  
pp. 44
Author(s):  
Foran
Keyword(s):  
Monotone Functions

scholarly journals Tail Asymptotics for Monotone-Separable Networks

2007 ◽  
Vol 44 (02) ◽  
pp. 306-320
Author(s):  
Marc Lelarge
Keyword(s):  
Queueing Network ◽  
Network Models ◽  
Moment Generating Function ◽  
Stochastic Petri Nets ◽  
Arrival Process ◽  
Polling Systems ◽  
Tail Asymptotics ◽  
State Variables ◽  
Monotone Functions ◽  
Jackson Networks

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with independent and identically distributed driving sequences and the GI/GI/1/1 queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.

Moments of convex and monotone functions

1972 ◽  
Vol 76 (2) ◽  
pp. 135-137 ◽  
Author(s):  
Togo Nishiura ◽  
Franz Schnitzer
Keyword(s):  
Monotone Functions

A Class of Monotone Functions

1939 ◽  
Vol 61 (4) ◽  
pp. 941
Author(s):  
G. Baley Price
Keyword(s):  
Monotone Functions

Kolmogorov, Linear and Pseudo-Dimensional Widths of Classes of s-Monotone Functions in 𝕃p, 0 < p < 1

2008 ◽  
Vol 51 (2) ◽  
pp. 236-248
Author(s):  
Victor N. Konovalov ◽  
Kirill A. Kopotun
Keyword(s):  
Unit Ball ◽  
Finite Interval ◽  
Divided Differences ◽  
Monotone Functions ◽  
Image Position

AbstractLet Bp be the unit ball in 𝕃p, 0 < p < 1, and let , s ∈ ℕ, be the set of all s-monotone functions on a finite interval I, i.e., consists of all functions x : I ⟼ ℝ such that the divided differences [x; t0, … , ts] of order s are nonnegative for all choices of (s + 1) distinct points t0, … , ts ∈ I. For the classes Bp := ∩ Bp, we obtain exact orders of Kolmogorov, linear and pseudo-dimensional widths in the spaces , 0 < q < p < 1:

Sign in / Sign up

Export Citation Format

Share Document