scholarly journals A Distributed Approach to the Evasion Problem

Algorithms ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 149
Author(s):  
Denis Khryashchev ◽  
Jie Chu ◽  
Mikael Vejdemo-Johansson ◽  
Ping Ji
Keyword(s):  
Distributed Algorithm ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Movement Pattern ◽  
Sheaf Theory ◽  
Distributed Approach ◽  
Sufficient And Necessary Conditions ◽  
Evasion Problem ◽  
Over Time ◽  
Path Detection

The Evasion Problem is the question of whether—given a collection of sensors and a particular movement pattern over time—it is possible to stay undetected within the domain over the same stretch of time. It has been studied using topological techniques since 2006—with sufficient conditions for non-existence of an Evasion Path provided by de Silva and Ghrist; sufficient and necessary conditions with extended sensor capabilities provided by Adams and Carlsson; and sufficient and necessary conditions using sheaf theory by Krishnan and Ghrist. In this paper, we propose three algorithms for the Evasion Problem: one distributed algorithm extension of Adams’ approach for evasion path detection, and two different approaches to evasion path enumeration.

Dynamics of an autonomous Gilpin–Ayala competition model with random perturbation

2021 ◽  
pp. 2050043
Author(s):  
Jing Fu ◽  
Qixing Han ◽  
Daqing Jiang ◽  
Yanyan Yang
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Necessary Conditions ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Interacting Species ◽  
Sufficient And Necessary Conditions ◽  
Global Positive Solution

This paper discusses the dynamics of a Gilpin–Ayala competition model of two interacting species perturbed by white noise. We obtain the existence of a unique global positive solution of the system and the solution is bounded in [Formula: see text]th moment. Then, we establish sufficient and necessary conditions for persistence and the existence of an ergodic stationary distribution of the model. We also establish sufficient conditions for extinction of the model. Moreover, numerical simulations are carried out for further support of present research.

scholarly journals Injectivity of linear combinations in $\mathcal{B}(\mathcal{H})$

2021 ◽  
Vol 37 ◽  
pp. 359-369
Author(s):  
Marko Kostadinov
Keyword(s):  
Linear Combination ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Combinations ◽  
Special Cases ◽  
Sufficient And Necessary Conditions ◽  
Alpha Beta ◽  
Necessary And Sufficient

The aim of this paper is to provide sufficient and necessary conditions under which the linear combination $\alpha A + \beta B$, for given operators $A,B \in {\cal B}({\cal H})$ and $\alpha, \beta \in \mathbb{C}\setminus \lbrace 0 \rbrace$, is injective. Using these results, necessary and sufficient conditions for left (right) invertibility are given. Some special cases will be studied as well.

scholarly journals Second-Order Impulsive Delay Differential Systems: Necessary and Sufficient Conditions for Oscillatory or Asymptotic Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 722
Author(s):  
Shyam Sundar Santra ◽  
Khaled Mohamed Khedher ◽  
Osama Moaaz ◽  
Ali Muhib ◽  
Shao-Wen Yao
Keyword(s):  
Asymptotic Behavior ◽  
Differential System ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Sufficient And Necessary Conditions ◽  
Impulsive Delay ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient

In this work, we aimed to obtain sufficient and necessary conditions for the oscillatory or asymptotic behavior of an impulsive differential system. It is easy to notice that most works that study the oscillation are concerned only with sufficient conditions and without impulses, so our results extend and complement previous results in the literature. Further, we provide two examples to illustrate the main results.

scholarly journals Necessary and sufficient conditions on weighted multilinear fractional integral inequality

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhou Yongliang ◽  
Deng Yangkendi ◽  
Wu Di ◽  
Yan Dunyan
Keyword(s):  
Integral Inequality ◽  
Sobolev Inequality ◽  
Fractional Integral ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Integral Inequalities ◽  
Multilinear Fractional Integral ◽  
Sufficient And Necessary Conditions ◽  
Necessary And Sufficient

<p style='text-indent:20px;'>We consider certain kinds of weighted multi-linear fractional integral inequalities which can be regarded as extensions of the Hardy-Littlewood-Sobolev inequality. For a particular case, we characterize the sufficient and necessary conditions which ensure that the corresponding inequality holds. For the general case, we give some sufficient conditions and necessary conditions, respectively.</p>

scholarly journals Economic Dynamics under Heterogeneous Adaptive Learning: General Criteria and Sufficient Conditions for Stability

2019 ◽  
Vol 19 (4) ◽  
pp. 87-103
Author(s):  
A. S. Bogomolova ◽  
D. V. Kolyuzhnov
Keyword(s):  
Adaptive Learning ◽  
Necessary Conditions ◽  
Learning Algorithm ◽  
Sufficient Conditions ◽  
Dsge Models ◽  
Shock Process ◽  
Sufficient And Necessary Conditions ◽  
Process Behavior ◽  
The Stability ◽  
Sign Conditions

The article extends the results of Honkapohja and Mitra (2006) and Kolyuzhnov (2011) and provides criteria and sufficient conditions for stability in a structurally heterogeneous economy under heterogeneous adaptive learning of agents. The criteria for stability under heterogeneous mixed RLS/SG learning for four classes of models – without lags and with lags of the endogenous variable and with t or t – 1 – dating of expectations – and sufficient conditions for stability for the cases of the diagonal structure of the shock process behavior or the heterogeneous RLS learning are presented in terms of the corresponding Jacobian matrices. In addition, the study presents a very useful criterion for the stability for all types of models under mixed RLS/SG learning with equal degrees of inertia for each type of learning algorithm in terms of stability of a suitably defined average economy with two agents. The derived criteria and sufficient conditions for stability are based on the results of the theory of stochastic approximation and are presented in terms of mixture of structural and learning heterogeneity, which are essential to get sufficient and necessary conditions for stability irrespective of heterogeneity in learning presented in terms of E-stability of suitably defined aggregate economies, the “same sign” conditions and the E-stability of a suitably defined average economy and its subeconomies. The fundamental nature of the approach adopted in the paper makes it possible to apply the results to a vast majority of the existing and prospective linear and linearized economic models (including estimated DSGE models) with adaptive learning of agents.

On two-weight estimates for the maximal operator in local Morrey spaces

2014 ◽  
Vol 25 (11) ◽  
pp. 1450099 ◽  
Author(s):  
Natasha Samko
Keyword(s):  
Maximal Operator ◽  
General Type ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Logarithmic Factor ◽  
Sufficient And Necessary Conditions ◽  
Local Morrey Spaces

For two weighted local Morrey spaces [Formula: see text] and [Formula: see text] we obtain general type sufficient conditions and necessary conditions imposed on the functions φ and ψ and the weights u and v for the boundedness of the maximal operator from [Formula: see text] to [Formula: see text], with some "logarithmic gap" between the sufficient and necessary conditions. Both the conditions formally coincide if we omit a certain logarithmic factor in these conditions.

scholarly journals On projection constant problems and the existence of metric projections in normed spaces

2001 ◽  
Vol 6 (7) ◽  
pp. 401-411 ◽  
Author(s):  
Entisarat El-Shobaky ◽  
Sahar Mohammed Ali ◽  
Wataru Takahashi
Keyword(s):  
Banach Spaces ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Metric Projection ◽  
Infinite Matrix ◽  
Normed Spaces ◽  
Reflexive Banach Spaces ◽  
Linear Spaces ◽  
Sufficient And Necessary Conditions ◽  
Projection Constant

We give the sufficient conditions for the existence of a metric projection onto convex closed subsets of normed linear spaces which are reduced conditions than that in the case of reflexive Banach spaces and we find a general formula for the projections onto the maximal proper subspaces of the classical Banach spacesl p,1≤p<∞andc 0. We also give the sufficient and necessary conditions for an infinite matrix to represent a projection operator froml p,1≤p<∞orc 0onto anyone of their maximal proper subspaces.

scholarly journals First-order impulsive differential systems: sufficient and necessary conditions for oscillatory or asymptotic behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Dumitru Baleanu ◽  
Khaled Mohamed Khedher ◽  
Osama Moaaz
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
First Order ◽  
Impulsive Differential Systems ◽  
Sufficient And Necessary Conditions

AbstractIn this paper, we study the oscillatory and asymptotic behavior of a class of first-order neutral delay impulsive differential systems and establish some new sufficient conditions for oscillation and sufficient and necessary conditions for the asymptotic behavior of the same impulsive differential system. To prove the necessary part of the theorem for asymptotic behavior, we use the Banach fixed point theorem and the Knaster–Tarski fixed point theorem. In the conclusion section, we mention the future scope of this study. Finally, two examples are provided to show the defectiveness and feasibility of the main results.

scholarly journals Oscillation criteria for second order nonlinear delay inequalities

1976 ◽  
Vol 14 (3) ◽  
pp. 331-341 ◽  
Author(s):  
S. Nababan ◽  
E.S. Noussair
Keyword(s):  
Differential Inequality ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Sufficient And Necessary Conditions ◽  
Delay Differential ◽  
Nonlinear Delay ◽  
Delay Differential Inequality

Oscillation criteria are obtained, for the nonlinear delay differential inequality u(u″+f(t, u(t), u(g(t)))) ≤ 0. The main theorems give sufficient conditions (and in some cases sufficient and. necessary conditions) for all solutions u(t) to have arbitrary large zeros. Generalizations to more general cases are discussed.

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