scholarly journals On the lower bondary for time complexity of a decidability problem of a theory of integers with a successor function and the least fixed point operator

2016 ◽  
pp. 97-109
Author(s):  
Alexander Zolotov ◽  
Keyword(s):  
Fixed Point ◽  
Time Complexity ◽  
Successor Function ◽  
Decidability Problem ◽  
Point Operator

scholarly journals An Inflationary Fixed Point Operator in XQuery

2008 ◽  
Author(s):  
Loredana Afanasiev ◽  
Torsten Grust ◽  
Maarten Marx ◽  
Jan Rittinger ◽  
Jens Teubner
Keyword(s):  
Fixed Point ◽  
Point Operator

THE ANCHORED VORONOI DIAGRAM: STATIC, DYNAMIC VERSIONS AND APPLICATIONS

2006 ◽  
Vol 16 (04) ◽  
pp. 315-332
Author(s):  
J. M. DÍAZ-BÁÑEZ ◽  
F. GÓMEZ ◽  
I. VENTURA
Keyword(s):  
Fixed Point ◽  
Voronoi Diagram ◽  
Line Segment ◽  
Time Complexity ◽  
Optimization Problems ◽  
Dynamic Version

For a given set S of n points in the plane and a fixed point o, we introduce the Voronoi diagram of S anchored at o. It will be defined as an abstract Voronoi diagram that uses as bisectors the following curves. For each pair of points p, q in S, the bisecting curve between p and q is the locus of points x in the plane such that the line segment [Formula: see text] is equidistant to both p and q. We show that those bisectors have nice properties and, therefore, this new structure can be computed in O(n log n) time and O(n) space both for nearest-site and furthest-site versions. Also, we prove that the dynamic version of this diagram can be built in O(n2λ6s+2(n) log n) time complexity, where s is a constant depending on the function that describes the motion of the points. Finally, we show how to use these structures for solving several locational optimization problems.

scholarly journals Existence Results of a Nonlocal Fractional Symmetric Hahn Integrodifference Boundary Value Problem

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2174
Author(s):  
Rujira Ouncharoen ◽  
Nichaphat Patanarapeelert ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Existence Results ◽  
Difference Operators ◽  
Point Problem ◽  
Point Operator

The existence of solutions of nonlocal fractional symmetric Hahn integrodifference boundary value problem is studied. We propose a problem of five fractional symmetric Hahn difference operators and three fractional symmetric Hahn integrals of different orders. We first convert our nonlinear problem into a fixed point problem by considering a linear variant of the problem. When the fixed point operator is available, Banach and Schauder’s fixed point theorems are used to prove the existence results of our problem. Some properties of (q,ω)-integral are also presented in this paper as a tool for our calculations. Finally, an example is also constructed to illustrate the main results.

scholarly journals Equational Axioms for Probabilistic Bisimilarity (Preliminary Report)

2002 ◽  
Vol 9 (6) ◽  
Author(s):  
Luca Aceto ◽  
Zoltán Ésik ◽  
Anna Ingólfsdóttir
Keyword(s):  
Fixed Point ◽  
Preliminary Report ◽  
Monotonic Functions ◽  
Finite State ◽  
Point Operator ◽  
Bisimulation Equivalence ◽  
State Agents

This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finite-state agents previously studied by Stark and Smolka ((2000) <em>Proof, Language, and Interaction: Essays in Honour of Robin Milner</em>, pp. 571-595). The axiomatization is obtained by extending the general axioms of iteration theories (or iteration algebras), which characterize the equational properties of the fixed point operator on (omega-)continuous or monotonic functions, with three axiom schemas that express laws that are specific to probabilistic bisimilarity. Hence probabilistic bisimilarity (over finite-state agents) has an equational axiomatization relative to iteration algebras.

scholarly journals Finiteness Conditions for Strictness Analysis

1993 ◽  
Vol 22 (447) ◽  
Author(s):  
Flemming Nielson ◽  
Hanne Riis Nielson
Keyword(s):  
Fixed Point ◽  
Upper Bounds ◽  
Functional Languages ◽  
Finiteness Conditions ◽  
Point Operator ◽  
Strictness Analysis

We give upper bounds on the number of times the fixed point operator needs to be unfolded for strictness analysis of functional languages with lists. This extends previous work both in the syntax-directed nature of the approach and in the ability to deal with Wadler's method for analysing lists. Limitations of the method are indicated.

scholarly journals Stability Results for an Age-Structured SIS Epidemic Model with Vector Population

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
He-Long Liu ◽  
Jing-Yuan Yu ◽  
Guang-Tian Zhu
Keyword(s):  
Fixed Point ◽  
Epidemic Model ◽  
Fixed Point Problem ◽  
Host Population ◽  
Point Problem ◽  
Sis Epidemic Model ◽  
Vector Population ◽  
Point Operator ◽  
Age Structured ◽  
Sis Epidemic

We formulate an age-structured SIS epidemic model with periodic parameters, which includes host population and vector population. The host population is described by two partial differential equations, and the vector population is described by a single ordinary differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on locally integrable periodic functions. We obtain that if the spectral radius of the Fréchet derivative of the fixed point operator at zero is greater than one, there exists a unique endemic periodic solution, and we investigate the global attractiveness of disease-free steady state of the normalized system.

Optimal Feedback Design for Uncertain Systems: A Time-Domain Fixed-Point Approach in L∞

1993 ◽  
Vol 115 (3) ◽  
pp. 319-324
Author(s):  
R. Barnard ◽  
S. Beydoun
Keyword(s):  
Fixed Point ◽  
Time Domain ◽  
Uncertain Systems ◽  
Design Procedure ◽  
Tracking Errors ◽  
Operator Equations ◽  
Fixed Point Approach ◽  
Point Operator ◽  
Explicit Bounds ◽  
Dynamics Stability

This paper considers an alternative to quantitative feedback theory (QFT), an alternative deriving solely from a time-domain setting in Banach space L∞ and providing both a precise, amplitude-oriented design formulation and a general, computer-oriented design procedure. System dynamics, stability, and tracking are characterized as fixed-point operator equations and conditions under which tracking errors satisfy explicit bounds. The design formulation and procedure are illustrated by two design examples.

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