A general synchronization method is proposed for a class of nonlinear chaotic systems involving uncertain parameters and nonlinear transmitted signals. Under some mild conditions, it shows that the class of nonlinear chaotic systems can be treated as linear time-varying systems driven by the additive white noise contaminated at the receiver, or the observed output. Synchronization can be achieved by using Kalman filtering technology. We present some sufficient conditions under which the states of the driven system are able to track the states of the drive system asymptotically, and good tracking performance can be obtained in the presence of the additive white noise involved in the observed output.
We generalize a Theorem of Koldunov [2] and prove that a disjointness proserving quasi-linear operator between Resz spaces has the Hammerstein property.
In this paper, a family of hybrid control algorithms is presented; where it is merged a free camera-calibration image-based control scheme and a direct force controller, both with the same priority level. The aim of this generalised hybrid controller is to regulate the robot-environment interaction into a two-dimensional task-space. The design of the proposed control structure takes into account most of the dynamic effects present in robot manipulators whose inputs are torque signals. As examples of this generalised structure of hybrid force/vision controllers, a linear proportional-derivative structure and a nonlinear proportional-derivative one (based on the hyperbolic tangent function) are presented. The corresponding stability analysis, using Lyapunov's direct method and invariance theory, is performed to proof the asymptotic stability of the equilibrium vector of the closed-loop system. Experimental tests of the control scheme are presented and a suitable performance is observed in all the cases. Unlike most of the previously presented hybrid schemes, the control structure proposed herein achieves soft contact forces without overshoots, fast convergence of force and position error signals, robustness of the controller in the face of some uncertainties (such as camera rotation), and safe operation of the robot actuators when saturating functions (non-linear case) are used in the mathematical structure. This is one of the first works to propose a generalized structure of hybrid force/vision control that includes a closed loop stability analysis for torque-driven robot manipulators.
Let $G$ be a locally compact group. We continue our work [A. Ghaffari: $\Gamma $-amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of $\Gamma $-amenability of a locally compact group $G$ defined with respect to a closed subgroup $\Gamma $ of $G\times G$. In this paper, among other things, we introduce and study a closed subspace $A_\Gamma ^p(G)$ of $L^\infty (\Gamma )$ and then characterize the $\Gamma $-amenability of $G$ using $A_\Gamma ^p(G)$. Various necessary and sufficient conditions are found for a locally compact group to possess a $\Gamma $-invariant mean.
There is a classical result known as Baer's Lemma that states that an $R$-module $E$ is injective if it is injective for $R$. This means that if a map from a submodule of $R$, that is, from a left ideal $L$ of $R$ to $E$ can always be extended to $R$, then a map to $E$ from a submodule $A$ of any $R$-module $B$ can be extended to $B$; in other words, $E$ is injective. In this paper, we generalize this result to the category $q_{\omega }$ consisting of the representations of an infinite line quiver. This generalization of Baer's Lemma is useful in proving that torsion free covers exist for $q_{\omega }$.
Let K be a field, A = K[X1, . . . , Xn] and M the set of monomials of A. It is well known that the set of monomial ideals of A is in a bijective correspondence with the set of all subsemiflows of the M-semiflow M. We generalize this to the case of term ideals of A = R[X1, . . . , Xn], where R is a commutative Noetherian ring. A term ideal of A is an ideal of A generated by a family of terms cXµ1 1 . . . Xµn n , where c ∈ R and µ1, . . . , µn are integers ≥ 0.
Let $R$ be a left and right Noetherian ring and $C$ a semidualizing $R$-bimodule. We introduce a transpose ${\rm Tr_{c}}M$ of an $R$-module $M$ with respect to $C$ which unifies the Auslander transpose and Huang's transpose, see Z. Y. Huang, On a generalization of the Auslander-Bridger transpose, Comm. Algebra 27 (1999), 5791–5812, in the two-sided Noetherian setting, and use ${\rm Tr_{c}}M$ to develop further the generalized Gorenstein dimension with respect to $C$. Especially, we generalize the Auslander-Bridger formula to the generalized Gorenstein dimension case. These results extend the corresponding ones on the Gorenstein dimension obtained by Auslander in M. Auslander, M. Bridger, Stable Module Theory, Mem. Amer. Math. Soc. vol. 94, Amer. Math. Soc., Providence, RI, 1969.
Let $R$ be a commutative Noetherian ring and ${\mathfrak a}$ an ideal of $R$. We introduce the concept of ${\mathfrak a}$-weakly Laskerian $R$-modules, and we show that if $M$ is an ${\mathfrak a}$-weakly Laskerian $R$-module and $s$ is a non-negative integer such that ${\rm Ext}^j_R(R/{\mathfrak a}, H^i_{{\mathfrak a}}(M))$ is ${\mathfrak a}$-weakly Laskerian for all $i<s$ and all $j$, then for any ${\mathfrak a}$-weakly Laskerian submodule $X$ of $H^s_{{\mathfrak a}}(M)$, the $R$-module ${\rm Hom}_R(R/{\mathfrak a},H^s_{{\mathfrak a}}(M)/X)$ is ${\mathfrak a}$-weakly Laskerian. In particular, the set of associated primes of $H^s_{\mathfrak a}(M)/X$ is finite. As a consequence, it follows that if $M$ is a finitely generated $R$-module and $N$ is an ${\mathfrak a}$-weakly Laskerian $R$-module such that $ H^i_{{\mathfrak a}}(N)$ is ${\mathfrak a}$-weakly Laskerian for all $i<s$, then the set of associated primes of $H^s_{\mathfrak a}(M, N)$ is finite. This generalizes the main result of S. Sohrabi Laleh, M. Y. Sadeghi, and M. Hanifi Mostaghim (2012).
Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.