The paper discusses the asymptotic properties of solutions of the scalar functional differential equation \[ y^{\prime }(x)=ay(\tau (x))+by(x),\qquad x\in [x_0,\infty ) \] of the advanced type. We show that, given a specific asymptotic behaviour, there is a (unique) solution $y(x)$ which behaves in this way.
We study the asymptotic behavior of the solutions of a differential equation with unbounded delay. The results presented are based on the first Lyapunov method, which is often used to construct solutions of ordinary differential equations in the form of power series. This technique cannot be applied to delayed equations and hence we express the solution as an asymptotic expansion. The existence of a solution is proved by the retract method.
Asymptotic properties of solutions of the difference equation of the form ∆ mxn = anϕ(xτ1(n) , . . . , xτk(n) ) + bn are studied. Conditions under which every (every bounded) solution of the equation ∆myn = bn is asymptotically equivalent to some solution of the above equation are obtained.
This paper establishes existence of nonoscillatory solutions with specific asymptotic behaviors of second order quasiiinear functional differential equations of neutral type. Then sufficient, sufficient and necessary conditions are proved under which every solution of the equation is either oscillatory or tends to zero as t → ∞.
Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by dX(t) = A(ξ(t))X(t) dt + H(ξ(t))X(t) dw(t), where ξ(t) is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition.
As an important artificial neural network, associative memory model can be employed to mimic human thinking and machine intelligence. In this paper, first, a multi-valued many-to-many Gaussian associative memory model (M3GAM) is proposed by introducing the Gaussian unidirectional associative memory model (GUAM) and Gaussian bidirectional associative memory model (GBAM) into Hattori {et al}'s multi-module associative memory model ((MMA)2). Second, the M3GAM's asymptotical stability is proved theoretically in both synchronous and asynchronous update modes, which ensures that the stored patterns become the M3GAM's stable points. Third, by substituting the general similarity metric for the negative squared Euclidean distance in M3GAM, the generalized multi-valued many-to-many Gaussian associative memory model (GM3GAM) is presented, which makes the M3GAM become its special case. Finally, we investigate the M3GAM's application in association-based image retrieval, and the computer simulation results verify the M3GAM's robust performance.
Linear relations, containing measurement errors in input and output data, are taken into account in this paper. Parameters of these so-called \emph{errors-in-variables} (EIV) models can be estimated by minimizing the \emph{total least squares} (TLS) of the input-output disturbances. Such an estimate is highly non-linear. Moreover in some realistic situations, the errors cannot be considered as independent by nature. \emph{Weakly dependent} (α- and φ-mixing) disturbances, which are not necessarily stationary nor identically distributed, are considered in the EIV model. Asymptotic normality of the TLS estimate is proved under some reasonable stochastic assumptions on the errors. Derived asymptotic properties provide necessary basis for the validity of block-bootstrap procedures.
The variance of the number of lattice points inside the dilated bounded set $rD$ with random position in $\Bbb R^d$ has asymptotics $\sim r^{d-1}$ if the rotational average of the squared modulus of the Fourier transform of the set is $O(\rho ^{-d-1})$. The asymptotics follow from Wiener's Tauberian theorem.
This paper studies the leader-following consensus problem of second-order multi-agent systems with directed topologies. By employing the asynchronous sampled-data protocols, sufficient conditions for leader-following consensus with both constant velocity leader and variable velocity leader are derived. {Leader-following quasi-consensus can be achieved in multi-agent systems when all the agents sample the information asynchronously.} Numerical simulations are provided to verify the theoretical results.
The atherogenic impact and functional capacity of LCAT was studied and discussed over a half century. This review aims to clarify the key points that may affect the final decision on whether LCAT is an anti-atherogenic or atherogenic factor. There are three main processes involving the efflux of free cholesterol from peripheral cells, LCAT action in intravascular pool where cholesterol esterification rate is under the control of HDL, LDL and VLDL subpopulations, and finally the destination of newly produced cholesteryl esters either to the catabolism in liver or to a futile cycle with apoB lipoproteins. The functionality of LCAT substantially depends on its mass together with the composition of the phospholipid bilayer as well as the saturation and the length of fatty acyls and other effectors about which we know yet nothing. Over the years, LCAT puzzle has been significantly supplemented but yet not so satisfactory as to enable how to manipulate LCAT in order to prevent cardiometabolic events. It reminds the butterfly effect when only a moderate change in the process of transformation free cholesterol to cholesteryl esters may cause a crucial turn in the intended target. On the other hand, two biomarkers - FERHDL (fractional esterification rate in HDL) and AIP [log(TG/HDL-C)] can offer a benefit to identify the risk of cardiovascular disease (CVD). They both reflect the rate of cholesterol esterification by LCAT and the composition of lipoprotein subpopulations that controls this rate. In clinical practice, AIP can be calculated from the routine lipid profile with help of AIP calculator www.biomed.cas.cz/fgu/aip/calculator.php., M. Dobiášová., and Obsahuje bibliografii