Search results for "Set theory"
showing 10 items of 751 documents
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …
The arithmetic decomposition of central Cantor sets
2018
Abstract Every central Cantor set of positive Lebesgue measure is the arithmetic sum of two central Cantor sets of Lebesgue measure zero. Under some mild condition this result can be strengthened by stating that the summands can be chosen to be C s regular if the initial set is of this class.
On the Calmness of a Class of Multifunctions
2002
The paper deals with the calmness of a class of multifunctions in finite dimensions. Its first part is devoted to various conditions for calmness, which are derived in terms of coderivatives and subdifferentials. The second part demonstrates the importance of calmness in several areas of nonsmooth analysis. In particular, we focus on nonsmooth calculus and solution stability in mathematical programming and in equilibrium problems. The derived conditions find a number of applications there.
Dynamical Models of Interrelation in a Class of Artificial Networks
2020
The system of ordinary differential equations that models a type of artificial networks is considered. The system consists of a sigmoidal function that depends on linear combinations of the arguments minus the linear part. The linear combinations of the arguments are described by the regulatory matrix W. For the three-dimensional cases, several types of matrices W are considered and the behavior of solutions of the system is analyzed. The attractive sets are constructed for most cases. The illustrative examples are provided. The list of references consists of 12 items.
Solutions of nonlinear PDEs in the sense of averages
2012
Abstract We characterize p-harmonic functions including p = 1 and p = ∞ by using mean value properties extending classical results of Privaloff from the linear case p = 2 to all pʼs. We describe a class of random tug-of-war games whose value functions approach p-harmonic functions as the step goes to zero for the full range 1 p ∞ .
Approximations in Statistics from a Decision-Theoretical Viewpoint
1987
The approximation of the probability density p(.) of a random vector x∊X by another (possibly more convenient) probability density q(.) which belongs to a certain class Q is analyzed as a decision problem where the action space is the class Qof available approximations, the relevant uncertain event is the actual value of the vector x and the utility function is a proper scoring rule. The logarithmic divergence is shown to play a rather special role within this approach. The argument lies entirely within a Bayesian framework.
On Horn spectra
1991
Abstract A Horn spectrum is a spectrum of a Horn sentence. We show that to solve Asser's problem, and consequently the EXPTIME = ? NEXPTIME question it suffices to consider the class of Horn spectra. We also pose the problem whether or not the generator of every Horn spectrum is a spectrum. We prove that from a negative solution of the generator problem, a negative answer for the EXPTIME = ? NEXPTIME question follows. Some other relations between the generator problem and Asser's problem are given. Finally, the relativized version of the generator problem is formulated and it is shown that it has an affirmative solution for some oracles, and a negative solution for some others.
Painlevé analysis and exact solutions for the coupled Burgers system
2006
We perform the Painleve test to a system of two coupled Burgers-type equations which fails to satisfy the Painleve test. In order to obtain a class of solutions, we use a slightly modified version of the test. These solutions are expressed in terms of the Airy functions. We also give the travelling wave solutions, expressed in terms of the trigonometric and hyperbolic functions.
On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations
2020
Abstract By using comparison principles, we analyze the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Due to less restrictive assumptions on the coefficients of the equation and on the deviating argument τ , our criteria improve a number of related results reported in the literature.
Relaxation for a Class of Control Systems with Unilateral Constraints
2019
We consider a nonlinear control system involving a maximal monotone map and with a priori feedback. We assume that the control constraint multifunction $U(t,x)$ is nonconvex valued and only lsc in the $x \in \mathbb{R}^{N}$ variable. Using the Q-regularization (in the sense of Cesari) of $U(t,\cdot )$, we introduce a relaxed system. We show that this relaxation process is admissible.