Schweizer and Smítal introduced the distributional chaos for continuous maps of the interval in B. Schweizer, J. Smítal, Measures of chaos and a spectral decomposition of dynamical systems on the interval. Trans. Amer. Math. Soc. 344 (1994), 737–854. In this paper, we discuss the distributional chaos DC1–DC3 for flows on compact metric spaces. We prove that both the distributional chaos DC1 and DC2 of a flow are equivalent to the time-1 maps and so some properties of DC1 and DC2 for discrete systems also hold for flows. However, we prove that DC2 and DC3 are not invariants of equivalent flows although DC2 is a topological conjugacy invariant in discrete case.
We give characterizations of the distributional derivatives $D^{1,1}$, $D^{1,0}$, $D^{0,1}$ of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.
We apply the larger sieve to bound the number of $2\times 2$ matrices not having large order when reduced modulo the primes in an interval. Our motivation is the relation with linear recursive congruential generators. Basically our results establish that the probability of finding a matrix with large order modulo many primes drops drastically when a certain threshold involving the number of primes and the order is exceeded. We also study, for a given prime and a matrix, the existence of nearby non-similar matrices having large order. In this direction we find matrices of large order when the trace is restricted to take values in a short interval.
We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.
We present a formal scheme which whenever satisfied by relations of a given relational lattice L containing only reflexive and transitive relations ensures distributivity of L.
In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given.
This paper deals with implications defined from disjunctive uninorms U by the expression I(x,y)=U(N(x),y) where N is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a t-norm or a t-conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works when the implications are derived from t-conorms.
-axis subsystems are firstly transformed into two linear subsystems by using feedback linearization technique, then, integral terminal sliding mode controller and finite-time controller are designed respectively. The proof of finite time stability are given for the PMSM closed-loop system. Compared with the corresponding asymptotical stability control method, the proposed controller can make the system output track the desired speed reference signal in finite time and obtain a better dynamic response and anti-disturbance performance. Meanwhile, considering the large chattering phenomenon caused by high switching gains, a composite integral terminal sliding mode control method based on disturbance observer is proposed to reduce chattering phenomenon. Through disturbance estimation based feed-forward compensation, the composite integral terminal sliding mode controller may take a smaller value for the switching gain without sacrificing disturbance rejection performance. Experimental results are provided to show the superiority of proposed control method.
This paper presents a composite controller that combines nonlinear disturbance observer and second order sliding mode controller for attitude tracking of flexible spacecraft. First, a new nonsingular sliding surface is introduced. Then, a second order sliding mode attitude controller is designed to achieve high-precision tracking performance. An extended state observer is also developed to estimate the total disturbance torque consisting of environmental disturbances, system uncertainties and flexible vibrations. The estimated result is used as feed-forward compensation. Although unknown bounded disturbances, inertia uncertainties and the coupling effect of flexible modes are taken into account, the resulting control method offers robustness and finite time convergence of attitude maneuver errors. Finite-time stability for the closed-loop system is rigorously proved using the Lyapunov stability theory. Simulation results are presented to demonstrate the effectiveness and robustness of the proposed control scheme.
Nearly all epileptic seizures in patients are characterized by deranged consciousness. We started to study changes in motivated behavior (drinking in thirsty rats) as a possible analogue of compromised consciousness during and after epileptic seizures. Epileptic afterdischarges (ADs) were elicited by stimulation of the dorsal hippocampus and/or thalamus. Rats with implanted electrodes (deprived of water for 24 hours) were trained to lick water from a narrow tube. After pretraining ADs were elicited eight times in each animal and access to water was allowed during different phases of the AD. Stimulation did not affect licking if no AD was induced. If stimulation was successful, licking was stopped in nearly 70 % of stimulations and modified (biting the tube) in 30 %. Hippocampal ADs (characterized by serrated waves in the EEG and by an arrest of behavior with subsequent automatisms) completely blocked licking, signs of recovery appeared during the interval between the AD and recurrent AD and it progressed during recurrent ADs. Thalamic ADs abolished licking in 82% of cases and immediately after ADs normal licking reappeared in 49 % of these observations. Our results suggest that changes in motivated behavior might serve as an analogue of compromised human consciousness., P. Mareš, L. Chocholová., and Obsahuje bibliografii