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Differential Transform Algorithm for Functional Differential Equations with Time-Dependent Delays
(Hindawi, 2020-02-28)An algorithm using the differential transformation which is convenient for finding numerical solutions to initial value problems for functional differential equations is proposed in this paper. We focus on retarded equations ... -
The role of Campylobacter spp. in chronic enteropathy in dogs
(2019-10-31)The aim of the study is to identify Campylobacter species in a group of patients with chronic gastrointestinal problems and to investigate the relationship between the presence of Campylobacter spp. in stool samples and ... -
Lower and upper estimates of solutions to systems of delay dynamic equations on time scales
(Springer, 2013-11-27)In this paper we study a system of delay dynamic equations on the time scale $\T$ of the form $$y^{\Delta}(t)=f(t,y_{\tau}(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$, $y_\tau(t)=(y_1(\tau_ ... -
Series of Semihypergroups of Time-Varying Articial Neurons and Related Hyperstructures
(MDPI, 2019-07-17)Detailed analysis of the function of multilayer perceptron (MLP) and its neurons together with the use of time-varying neurons allowed the authors to find an analogy with the use of structures of linear differential ... -
Elements of Hyperstructure Theory in UWSN Design and Data Aggregation
(MDPI, 2019-05-29)In our paper we discuss how elements of algebraic hyperstructure theory can be used in the context of underwater wireless sensor networks (UWSN). We present a mathematical model which makes use of the fact that when deploying ... -
Modeling of applied problems by stochastic systems and their analysis using the moment equations
(Springer Nature, 2013-10-09)The paper deals with systems of linear differential equations with coefficients depending on the Markov process. Equations for particular density and the moment equations for given systems are derived and used in the ... -
Explicit general solution of planar linear discrete systems with constant coefficients and weak delays
(Springer Nature, 2013-03-06)In this paper, planar linear discrete systems with constant coefficients and two delays $$ x(k+1)=Ax(k)+Bx(k-m)+Cx(k-n) $$ are considered where $k\in\bZ_0^{\infty}:=\{0,1,\dots,\infty\}$, $x\colon \bZ_0^{\infty}\to\mathbb{R}^2$, ... -
Boundedness character of a fourth-order system of difference equations
(Springer Nature, 2015-12-01)Sufficient conditions for boundedness character of solutions of a fourth-order system of difference equations is given. -
Two-dimensional product-type system of difference equations solvable in closed form
(Springer Nature, 2016-10-03)A solvable two-dimensional product-type system of difference equations of interest is presented. Closed form formulas for its general solution are given. -
Existence of solutions converging to zero for nonlinear delayed differential systems
(Springer, 2015-11-17)We present a result about an interesting asymptotic property of real two-dimensional delayed differential systems satisfying certain sufficient conditions. We employ two previous results, which were obtained using a ... -
On a delay population model with quadratic nonlinearity
(Springer Nature, 2012-12-28)In this paper, a nonlinear delay differential equation with quadratic nonlinearity is investigated. It is proved that the positive equilibrium is globally asymptotically stable without any further limitations on parameters ... -
An efficient new perturbative Laplace method for space-time fractional telegraph equations
(Springer Nature, 2012-11-27)In this paper, we propose a new technique for solving space-time fractional telegraph equations. This method isbased on perturbation theory and the Laplace transformation. -
Discrete matrix delayed exponential for two delays and its property
(Springer Nature, 2013-06-13)In recent papers, a discrete matrix delayed exponential for a single delay was defined and its main property connected with the solution of linear discrete systems with a single delay was proved. In the present paper, a ... -
Bounded solutions of delay dynamic equations on time scales
(Springer Nature, 2012-10-24)In this paper we discuss the asymptotic behavior of solutions of a delay dynamic equation $$y^{\Delta}(t)=f(t,y(\tau(t)))$$ where $f\colon\mathbb{T}\times\mathbb{R}\rightarrow\mathbb{R}$, \tau\colon\T\rightarrow \T$ is a ... -
Stabilization of Lure-type Nonlinear Control Systems by Lyapunov-Krasovskii Functionals
(Springer Nature, 2012-10-24)The paper deals with the stabilization problem of Lure-type nonlinear indirect control systems with time-delay argument. The sufficient conditions for absolute stability of the control system are established in the form ... -
Solving certain classes of Lane-Emden type equations using differential transformation method
(Springer Nature, 2012-10-05)In this paper, differential transformation method (DTM) is applied to solve singular initial problems represented by certain classes of Lane-Emden type equations. Some new differential tranformation formulas for certain ... -
Newton-Kantorovich convergence theorem of a new modified Halleys method family in a Banach space
(Springer, 2013-11-12)A Newton-Kantorovich convergence theorem of a new modified Halleys method family is established in a Banach space to solve nonlinear operator equations -
Stabilization of company’s income modeled by a system of discrete stochastic equations
(Springer Nature, 2014-11-15)The paper deals with a system of difference equations where the coefficients depend on Markov chains. The functional equations for a particular density and the moment equations for the system are derived and used in the ... -
On a product-type system of difference equations of second order solvable in closed form
(BioMed Central, 2015-10-12)Sufficient conditions for solving a system of difference equations of second order in closed form are given. Moreover, sufficient conditions for existence of periodic solutions and asymptotic stability of solutions are ... -
Exponential stability of perturbed linear discrete systems
(Springer, 2016-01-29)The paper considers the problem of exponential stability and convergence rate to solutions of perturbed linear discrete homogeneous systems. New criteria on exponential stability are derived by using the second method of ...
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