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  1. 29 International Journal of Applied Mathematics and Computer Science

  2. 4 Annales Polonici Mathematici

  3. 3 Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

  4. 3 Applicationes Mathematicae

  5. 2 Commentationes Mathematicae

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Autorzy help

  1. 4 Foryś U.

  2. 3 Clempner J.

  3. 2 Busłowicz M.

  4. 2 Kaczorek T.

  5. 2 Schiermeyer I.

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  1. 2 2019

  2. 1 2018

  3. 1 2017

  4. 2 2016

  5. 1 2015

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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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On the stability for pancyclicity

100%
Schiermeyer I.
Discussiones Mathematicae Graph Theory
|
2001
|
tom 21
|
nr 2
223-228
EN
A property P defined on all graphs of order n is said to be k-stable if for any graph of order n that does not satisfy P, the fact that uv is not an edge of G and that G + uv satisfies P implies $d_G(u) + d_G(v) < k$. Every property is (2n-3)-stable and every k-stable property is (k+1)-stable. We denote by s(P) the smallest integer k such that P is k-stable and call it the stability of P. This number usually depends on n and is at most 2n-3. A graph of order n is said to be pancyclic if it contains cycles of all lengths from 3 to n. We show that the stability s(P) for the graph property "G is pancyclic" satisfies max(⎡6n/5]⎤-5, n+t) ≤ s(P) ≤ max(⎡4n/3]⎤-2,n+t), where t = 2⎡(n+1)/2]⎤-(n+1).
2
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The stability study of a plane engine

100%
Kołodziej R., Nowicki T.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 1
35-44
EN
We study the dynamical properties of a plane engine vibrations modelled by a system of ODE.
3
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On the superstability of generalized d’Alembert harmonic functions

100%
EL-Fassi I.-i.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2016
|
tom 15
EN
The aim of this paper is to study the superstability problem of the d’Alembert type functional equation f(x+y+z)+f(x+y+σ(z))+f(x+σ(y)+z)+f(σ(x)+y+z)=4f(x)f(y)f(z) $$f(x + y + z) + f(x + y + \sigma (z)) + f(x + \sigma (y) + z) + f(\sigma (x) + y + z) = 4f(x)f(y)f(z)$$ for all x, y, z ∈ G, where G is an abelian group and σ : G → G is an endomorphism such that σ(σ(x)) = x for an unknown function f from G into ℂ or into a commutative semisimple Banach algebra.
4
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Explicit Difference Schemes for Nonlinear Differential Functional Parabolic Equations with Mixed Derivatives - Convergence Analysis

80%
Poliński A.
Commentationes Mathematicae
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2005
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tom 45
|
nr 2
EN
We study the initial-value problem for parabolic equations with mixed partial derivatives and constant coefficients, and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.
5
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Stability of forward-backward finite difference schemes for certain problems in biology

80%
Zwierkowski P.
Commentationes Mathematicae
|
2005
|
tom 45
|
nr 2
EN
We present a discretization method for a generalized von Foerster-type equation in many spatial variables. Stability of finite difference schemes on regular meshes is studied. If characteristic curves are decreasing, there are forward difference quotients applied. Otherwise, the derivatives are replaced by backward difference quotients.
6
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Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control

80%
Qi R., Brdys M.
International Journal of Applied Mathematics and Computer Science
|
2009
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tom 19
|
nr 4
619-630
EN
In this paper, a unified nonlinear modeling and control scheme is presented. A self-structuring Takagi-Sugeno (T-S) fuzzy model is used to approximate the unknown nonlinear plant based on I/O data collected on-line. Both the structure and the parameters of the T-S fuzzy model are updated by an on-line clustering method and a recursive least squares estimation (RLSE) algorithm. The rules of the fuzzy model can be added, replaced or deleted on-line to allow a more flexible and compact model structure. The overall controller consists of an indirect adaptive controller and a supervisory controller. The former is the dominant controller, which maintains the closed-loop stability when the fuzzy system is a good approximation of the nonlinear plant. The latter is an auxiliary controller, which is activated when the tracking error reaches the boundary of a predefined constraint set. It is proven that global stability of the closed-loop system is guaranteed in the sense that all the closed-loop signals are bounded and simulation examples demonstrate the effectiveness of the proposed control scheme.
7
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An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination

80%
Ding D., Ma Q., Ding X.
International Journal of Applied Mathematics and Computer Science
|
2014
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tom 24
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nr 3
635-646
EN
In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that difference equations have the same dynamics as the original differential system, such as the positivity of the solutions and the stability of the equilibria, without being restricted by the time step. Our proof of global stability utilizes the method of Lyapunov functions. Numerical simulation illustrates the effectiveness of our results.
8
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Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

80%
Busłowicz M., Ruszewski A.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 2
401-408
EN
Asymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.
9
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A modified van der Pol equation with delay in a description of the heart action

80%
Zduniak B., Bodnar M., Foryś U.
International Journal of Applied Mathematics and Computer Science
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2014
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tom 24
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nr 4
853-863
EN
In this paper, a modified van der Pol equation is considered as a description of the heart action. This model has a number of interesting properties allowing reconstruction of phenomena observed in physiological experiments as well as in Holter electrocardiographic recordings. Our aim is to study periodic solutions of the modified van der Pol equation and take into consideration the influence of feedback and delay which occur in the normal heart action mode as well as in pathological modes. Usage of certain values for feedback and delay parameters allows simulating the heart action when an accessory conducting pathway is present (Wolff-Parkinson-White syndrome).
10
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Stable invariant subspaces for operators on Hilbert space

80%
Conway J., Hadwin D.
Annales Polonici Mathematici
|
1997
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tom 66
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nr 1
49-61
EN
If T is a bounded operator on a separable complex Hilbert space ℋ, an invariant subspace ℳ for T is stable provided that whenever ${T_n}$ is a sequence of operators such that $‖T_n - T‖ → 0$, there is a sequence of subspaces ${ℳ_n}$, with $ℳ_n$ in $Lat T_n$ for all n, such that $P_{ℳ_n} → P_{ℳ}$ in the strong operator topology. If the projections converge in norm, ℳ is called a norm stable invariant subspace. This paper characterizes the stable invariant subspaces of the unilateral shift of finite multiplicity and normal operators. It also shows that in these cases the stable invariant subspaces are the strong closure of the norm stable invariant subspaces.
11
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Effective computation of the first Lyapunov quantities for a planar differential equation

80%
Gasull A., Prohens R.
Applicationes Mathematicae
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1996-1997
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tom 24
|
nr 3
243-250
EN
We take advantage of the complex structure to compute in a short way and without using any computer algebra system the Lyapunov quantities $V_3$ and $V_5$ for a general smooth planar system.
12
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Some families of pseudo-processes

80%
Kłapyta J.
Annales Polonici Mathematici
|
1994-1995
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tom 60
|
nr 1
33-45
EN
We introduce several types of notions of dis persive, completely unstable, Poisson unstable and Lagrange uns table pseudo-processes. We try to answer the question of how many (in the sense of Baire category) pseudo-processes with each of these properties can be defined on the space $ℝ^m$. The connections are discussed between several types of pseudo-processes and their limit sets, prolongations and prolongational limit sets. We also present examples of applications of the above results to pseudo-processes generated by differential equations.
13
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Delay-dependent asymptotic stabilitzation for uncertain time-delay systems with saturating actuators

80%
Liu P.-L.
International Journal of Applied Mathematics and Computer Science
|
2005
|
tom 15
|
nr 1
45-51
EN
This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.
14
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Sufficient conditions for the strong consistency of least squares estimator with α-stable errors

80%
Mexia J., da Silva J.
Discussiones Mathematicae Probability and Statistics
|
2007
|
tom 27
|
nr 1-2
27-45
EN
Let $Y_{i} = x_{i}^{T}β + e_{i}$, 1 ≤ i ≤ n, n ≥ 1 be a linear regression model and suppose that the random errors e₁, e₂, ... are independent and α-stable. In this paper, we obtain sufficient conditions for the strong consistency of the least squares estimator β̃ of β under additional assumptions on the non-random sequence x₁, x₂,... of real vectors.
15
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Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays

80%
Xu C., Liao M., He X.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 1
97-107
EN
In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also included.
16
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Local analysis of hybrid systems on polyhedral sets with state-dependent switching

80%
Leth J., Wisniewski R.
International Journal of Applied Mathematics and Computer Science
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2014
|
tom 24
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nr 2
341-355
EN
This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.
17
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18th International Conference on Functional Equations and Inequalities, Będlewo, Poland, July 9-15, 2019

80%
Meeting R. o.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2019
|
tom 18
167-192
EN
Report from the conference.
18
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Unbounded stability of two-term recurrence sequences modulo $2^k$

80%
Carlip W., Jacobson E.
Acta Arithmetica
|
1996
|
tom 74
|
nr 4
329-346
19
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On the dynamics of a vaccination model with multiple transmission ways

80%
Liao S., Yang W.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 4
761-772
EN
In this paper, we present a vaccination model with multiple transmission ways and derive the control reproduction number. The stability analysis of both the disease-free and endemic equilibria is carried out, and bifurcation theory is applied to explore a variety of dynamics of this model. In addition, we present numerical simulations to verify the model predictions. Mathematical results suggest that vaccination is helpful for disease control by decreasing the control reproduction number below unity.
20
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On delay-dependent stability for neutral delay-differential systems

80%
Han Q.-L.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
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nr 4
965-976
EN
This paper deals with the stability problem for a class of linear neutral delay-differential systems. The time delay is assumed constant and known. Delay-dependent criteria are derived. The criteria are given in the form of linear matrix inequalities which are easy to use when checking the stability of the systems considered. Numerical examples indicate significant improvements over some existing results.
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