Complex dynamic regimes connected with the noise-induced mixed-mode oscillations in the thermochemical model of flow reactor are studied. It is revealed that the underlying reason of such excitability is in the high stochastic sensitivity of the equilibrium. The problem of stabilization of the excitable equilibrium regimes is investigated. We develop the control approach using feedback regulators which reduce the stochastic sensitivity and keep the randomly forced system near the stable equilibrium. We consider also a case when the information about system state is incomplete. Our new mathematical technique is applied to the stabilization of operating modes in the flow chemical reactors forced by random disturbances.
We compared by chlorophyll (Chl) fluorescence imaging the effects of two strains of the same virus (Italian and Spanish strains of the Pepper mild mottle virus - PMMoV-I and-S, respectively) in the host plant Nicotiana benthamiana. The infection was visualized either using conventional Chl fluorescence parameters or by an advanced statistical approach, yielding a combinatorial set of images that enhances the contrast between control and PMMoV-infected plants in the early infection steps. Among the conventional Chl fluorescence parameters, the non-photochemical quenching parameter NPQ was found to be an effective PMMoV infection reporter in asymptomatic leaves of N. benthamiana, detecting an intermediate infection phase. The combinatorial imaging revealed the infection earlier than any of the standard Chl fluorescence parameters, detecting the PMMoV-S infection as soon as 4 d post-inoculation (dpi), and PMMoV-I infection at 6 dpi; the delay correlates with the lower virulence of the last viral strain. and M. Pineda ... [et al.].
In this paper, we investigate the convergence behavior of the asymmetric Deffuant-Weisbuch (DW) models during the opinion evolution. Based on the convergence of the asymmetric DW model that generalizes the conventional DW model, we first propose a new concept, the separation time, to study the transient behavior during the DW model's opinion evolution. Then we provide an upper bound of the expected separation time with the help of stochastic analysis. Finally, we show relations of the separation time with model parameters by simulations.
We provide new sufficient convergence conditions for the convergence of the secant-type methods to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, and Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than earlier ones and under our convergence hypotheses we can cover cases where earlier conditions are violated. Numerical examples are also provided.
We consider the second order initial value problem in a Hilbert space, which is a singular perturbation of a first order initial value problem. The difference of the solution and its singular limit is estimated in terms of the small parameter $\varepsilon .$ The coefficients are commuting self-adjoint operators and the estimates hold also for the semilinear problem.
This paper deals with convergence model of interest rates, which explains the evolution of interest rate in connection with the adoption of Euro currency. Its dynamics is described by two stochastic differential equations - the domestic and the European short rate. Bond prices are then solutions to partial differential equations. For the special case with constant volatilities closed form solutions for bond prices are known. Substituting its constant volatilities by instantaneous volatilities we obtain an approximation of the solution for a more general model. We compute the order of accuracy for this approximation, propose an algorithm for calibration of the model and we test it on the simulated and real market data.
An approximated gradient method for training Elman networks is considered. For the finite sample set, the error function is proved to be monotone in the training process, and the approximated gradient of the error function tends to zero if the weights sequence is bounded. Furthermore, after adding a moderate condition, the weights sequence itself is also proved to be convergent. A numerical example is given to support the theoretical findings.
Existence of fixed points of multivalued mappings that satisfy a certain contractive condition was proved by N. Mizoguchi and W. Takahashi. An alternative proof of this theorem was given by Peter Z. Daffer and H. Kaneko. In the present paper, we give a simple proof of that theorem. Also, we define Mann and Ishikawa iterates for a multivalued map $T$ with a fixed point $p$ and prove that these iterates converge to a fixed point $q$ of $T$ under certain conditions. This fixed point $q$ may be different from $p$. To illustrate this phenomenon, an example is given.
We extend Rump’s verified method (S.Oishi, K.Tanabe, T.Ogita, S.M.Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices with full column (row) rank. We establish the convergence of our numerical verified method for computing the Moore-Penrose inverse. We also discuss the rank-deficient case and test some ill-conditioned examples. We provide our Matlab codes for computing the Moore-Penrose inverse., Yunkun Chen, Xinghua Shi, Yimin Wei., and Obsahuje seznam literatury