On vanishing sums of m \,m\,th roots of unity in finite fields

In an earlier work, the authors have determined all possible weights $n$ for which there exists a vanishing sum $\zeta_1+\cdots +\zeta_n=0$ of $m$th roots of unity $\zeta_i$ in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic $p$. For given $m$ and $p$, results are obtained on integers $n_0$ such that all integers $n\geq n_0$ are in the ``weight set'' $W_p(m)$. The main result $(1.3)$ in this paper guarantees, under suitable conditions, the existence of solutions of $x_1^d+\cdots+x_n^d=0$ with all coordinates not equal to zero over a finite field

Neural processes of proactive and reactive controls modulated by motor-skill experiences

This study investigated the experience of open and closed motor skills on modulating proactive and reactive control processes in task switching. Fifty-four participants who were open-skilled

Topology design and performance analysis of an integrated communication network

A research study on the topology design and performance analysis for the Space Station Information System (SSIS) network is conducted. It is begun with a survey of existing research efforts in network topology design. Then a new approach for topology design is presented. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. The algorithm for generating subsets is described in detail, and various aspects of the overall design procedure are discussed. Two more efficient versions of this algorithm (applicable in specific situations) are also given. Next, two important aspects of network performance analysis: network reliability and message delays are discussed. A new model is introduced to study the reliability of a network with dependent failures. For message delays, a collection of formulas from existing research results is given to compute or estimate the delays of messages in a communication network without making the independence assumption. The design algorithm coded in PASCAL is included as an appendix

H∞ fuzzy filtering of nonlinear systems with intermittent measurements

This paper is concerned with the problem of H∞ fuzzy filtering of nonlinear systems with intermittent measurements. The nonlinear plant is represented by a Takagi-Sugeno (T-S) fuzzy model. The measurements transmission from the plant to the filter is assumed to be imperfect, and a stochastic variable satisfying the Bernoulli random binary distribution is utilized to model the phenomenon of the missing measurements. Attention is focused on the design of an H∞ filter such that the filter error system is stochastically stable and preserves a guaranteed H∞ performance. A basis-dependent Lyapunov function approach is developed to design the H∞ filter. By introducing some slack matrix variables, the coupling between the Lyapunov matrix and the system matrices is eliminated, which greatly facilitates the filter-design procedure. The developed theoretical results are in the form of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to show the effectiveness of the proposed approach. © 2009 IEEE.published_or_final_versio

Stability analysis of discrete-time recurrent neural networks with stochastic delay

This paper is concerned with the stability analysis of discrete-time recurrent neural networks (RNNs) with time delays as random variables drawn from some probability distribution. By introducing the variation probability of the time delay, a common delayed discrete-time RNN system is transformed into one with stochastic parameters. Improved conditions for the mean square stability of these systems are obtained by employing new Lyapunov functions and novel techniques are used to achieve delay dependence. The merit of the proposed conditions lies in its reduced conservatism, which is made possible by considering not only the range of the time delays, but also the variation probability distribution. A numerical example is provided to show the advantages of the proposed conditions. © 2009 IEEE.published_or_final_versio

Unification of bulk and interface electroresistive switching in oxide systems

We demonstrate that the physical mechanism behind electroresistive switching in oxide Schottky systems is electroformation, as in insulating oxides. Negative resistance shown by the hysteretic current-voltage curves proves that impact ionization is at the origin of the switching. Analyses of the capacitance-voltage and conductance-voltage curves through a simple model show that an atomic rearrangement is involved in the process. Switching in these systems is a bulk effect, not strictly confined at the interface but at the charge space region.Comment: 4 pages, 3 figures, accepted in PR