scholarly journals Smoothness of topological equivalence on the half line for nonautonomous systems

2019 ◽  
Vol 150 (5) ◽  
pp. 2484-2502
Author(s):  
Álvaro Castañeda ◽  
Gonzalo Robledo ◽  
Pablo Monzón
Keyword(s):  
Sufficient Conditions ◽  
Half Line ◽  
Topological Equivalence ◽  
Asymptotically Stable ◽  
Nonautonomous Systems ◽  
Perturbed System ◽  
Continuity Properties ◽  
Differentiability Properties ◽  
Positive Half ◽  
Stable Linear

AbstractWe study the differentiability properties of the topological equivalence between a uniformly asymptotically stable linear nonautonomous system and a perturbed system with suitable nonlinearities. For this purpose, we construct a homeomorphism inspired in the Palmer's one restricted to the positive half line, studying additional continuity properties and providing sufficient conditions ensuring its Cr–smoothness.

scholarly journals Frames associated with shift invariant spaces on positive half line

2021 ◽  
Vol 13 (1) ◽  
pp. 23-44
Author(s):  
Owais Ahmad ◽  
Mobin Ahmad ◽  
Neyaz Ahmad
Keyword(s):  
Sufficient Conditions ◽  
Gabor Frames ◽  
Half Line ◽  
Necessary Condition ◽  
Wavelet Frames ◽  
Invariant Space ◽  
Unified Approach ◽  
Shift Invariant Spaces ◽  
Invariant Spaces ◽  
Positive Half

Abstract In this paper, we introduce the notion of Walsh shift-invariant space and present a unified approach to the study of shift-invariant systems to be frames in L2(ℝ+). We obtain a necessary condition and three sufficient conditions under which the Walsh shift-invariant systems constitute frames for L2(ℝ+). Furthermore, we discuss applications of our main results to obtain some known conclusions about the Gabor frames and wavelet frames on positive half line.

Compensator conditions for stochastic ordering of point processes

1991 ◽  
Vol 28 (04) ◽  
pp. 751-761 ◽  
Author(s):  
A. Kwieciński ◽  
R. Szekli
Keyword(s):  
Probability Space ◽  
Point Processes ◽  
Sufficient Conditions ◽  
Stochastic Ordering ◽  
Half Line ◽  
Simple Point ◽  
Martingale Approach ◽  
Random Elements ◽  
Markov Point Processes ◽  
Positive Half

Sufficient conditions are given under which two simple point processes on the positive half-line can be stochastically compared as random elements of D(0,∞) or R∞ + Using a martingale approach to point processes, the conditions are proposed via a compensator function family. Appropriate versions of the processes being compared are constructed on the same probability space. The results are illustrated by replacement policies and semi-Markov point processes.

Compensator conditions for stochastic ordering of point processes

1991 ◽  
Vol 28 (4) ◽  
pp. 751-761 ◽  
Author(s):  
A. Kwieciński ◽  
R. Szekli
Keyword(s):  
Probability Space ◽  
Point Processes ◽  
Sufficient Conditions ◽  
Stochastic Ordering ◽  
Half Line ◽  
Simple Point ◽  
Martingale Approach ◽  
Random Elements ◽  
Markov Point Processes ◽  
Positive Half

Sufficient conditions are given under which two simple point processes on the positive half-line can be stochastically compared as random elements of D(0,∞) or R∞+ Using a martingale approach to point processes, the conditions are proposed via a compensator function family. Appropriate versions of the processes being compared are constructed on the same probability space. The results are illustrated by replacement policies and semi-Markov point processes.

scholarly journals Complete Controllability Conditions for Linear Singularly Perturbed Time-Invariant Systems with Multiple Delays via Chang-Type Transformation

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 71 ◽  
Author(s):  
Olga Tsekhan
Keyword(s):  
Sufficient Conditions ◽  
Singularly Perturbed ◽  
Degenerate System ◽  
Multiple Delays ◽  
Complete Controllability ◽  
Singularly Perturbed System ◽  
System With Delay ◽  
Perturbed System ◽  
Time Invariant ◽  
Controllability Conditions

The problem of complete controllability of a linear time-invariant singularly-perturbed system with multiple commensurate non-small delays in the slow state variables is considered. An approach to the time-scale separation of the original singularly-perturbed system by means of Chang-type non-degenerate transformation, generalized for the system with delay, is used. Sufficient conditions for complete controllability of the singularly-perturbed system with delay are obtained. The conditions do not depend on a singularity parameter and are valid for all its sufficiently small values. The conditions have a parametric rank form and are expressed in terms of the controllability conditions of two systems of a lower dimension than the original one: the degenerate system and the boundary layer system.

WAVELET PACKETS ASSOCIATED WITH NONUNIFORM MULTIRESOLUTION ANALYSIS ON POSITIVE HALF LINE

2013 ◽  
Vol 06 (01) ◽  
pp. 1350007 ◽  
Author(s):  
Vikram Sharma ◽  
P. Manchanda
Keyword(s):  
Multiresolution Analysis ◽  
Wavelet Packets ◽  
Half Line ◽  
State University ◽  
Spectral Pairs ◽  
Funct Anal ◽  
Positive Half

Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal.158 (1998) 209–241] introduced the Nonuniform multiresolution analysis (NUMRA) whose translation set is not a group. Farkov [Orthogonal p-wavelets on ℝ+, in Proc. Int. Conf. Wavelets and Splines (St. Petersburg State University, St. Petersburg, 2005), pp. 4–26] studied multiresolution analysis (MRA) on positive half line and constructed associated wavelets. Meenakshi et al. [Wavelets associated with Nonuniform multiresolution analysis on positive half line, Int. J. Wavelets, Multiresolut. Inf. Process.10(2) (2011) 1250018, 27pp.] studied NUMRA on positive half line and proved the analogue of Cohen's condition for the NUMRA on positive half line. We construct the associated wavelet packets for such an MRA and study its properties.

scholarly journals Permanence and Almost Periodic Solution for an Enterprise Cluster Model Based on Ecology Theory with Feedback Controls on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Yuanhong Zhi ◽  
Zunling Ding ◽  
Yongkun Li
Keyword(s):  
Periodic Solution ◽  
Time Scales ◽  
Cluster Model ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Competition And Cooperation ◽  
Enterprise Cluster

We present a model with feedback controls based on ecology theory, which effectively describes the competition and cooperation of enterprise cluster in real economic environments. Applying the comparison theorem of dynamic equations on time scales and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the existence of uniformly asymptotically stable almost periodic solution of the system are obtained.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

scholarly journals THIRD-ORDER GENERALIZED DISCONTINUOUS IMPULSIVE PROBLEMS ON THE HALF-LINE

2021 ◽  
Vol 26 (4) ◽  
pp. 548-565
Author(s):  
Feliz Minhós ◽  
Rui Carapinha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Flow Problem ◽  
Sufficient Conditions ◽  
Half Line ◽  
Third Order ◽  
Impulsive Problems ◽  
Layer Flow

In this paper, we improve the existing results in the literature by presenting weaker sufficient conditions for the solvability of a third-order impulsive problem on the half-line, having generalized impulse effects. More precisely, our nonlinearities do not need to be positive nor sublinear and the monotone assumptions are local ones. Our method makes use of some truncation and perturbed techniques and on the equiconvergence at infinity and the impulsive points. The last section contains an application to a boundary layer flow problem over a stretching sheet with and without heat transfer.

scholarly journals On number of moduli for gradient surface height function flows

2018 ◽  
Vol 20 (4) ◽  
pp. 419-428
Author(s):  
V. E. Kruglov
Keyword(s):  
Finite Number ◽  
Sufficient Conditions ◽  
Height Function ◽  
Orientable Surface ◽  
Topological Conjugacy ◽  
Topological Equivalence ◽  
Gradient Flows ◽  
A Chain ◽  
Gradient Surface ◽  
Equivalence Invariant

In 1978 J. Palis invented continuum topologically non-conjugate systems in a neighbourhood of a system with a heteroclinic contact; in other words, he invented so-called moduli. W. de Melo and С. van Strien in 1987 described a diffeomorphism class with a finite number of moduli. They discovered that a chain of saddles taking part in the heteroclinic contact of such diffeomorphism includes not more than three saddles. Surprisingly, such effect does not happen in flows. Here we consider gradient flows of the height function for an orientable surface of genus g>0. Such flows have a chain of 2g saddles. We found that the number of moduli for such flows is 2g−1 which is the straight consequence of the sufficient topological conjugacy conditions for such systems given in our paper. A complete topological equivalence invariant for such systems is four-colour graph carrying the information about its cells relative position. Equipping the graph's edges with the analytical parameters --- moduli, connected with the saddle connections, gives the sufficient conditions of the flows topological conjugacy.

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