Commutative Moufang loops and alternative algebras

We describe bases of free commutative Moufang loop with seven generators and calculate the order of this loop. (c) 2011 Published by Elsevier Inc.

The smallest simple Moufang loop

We study the simple Moufang loop GLL(F(2)) and give a complete description of its lattice of subloops. (C) 2008 Elsevier Inc. All rights reserved.

THE STRUCTURE OF FREE AUTOMORPHIC MOUFANG LOOPS

We describe the structure of a free loop of rank n in the variety of automorphic Moufang loops as a subdirect product of a free group and a free commutative Moufang loop, both of rank n. In particular, the variety of automorphic Moufang loops is the join of the variety of groups and the variety of commutative Moufang loops.

Sylow`s theorem for Moufang loops

For finite Moufang loops, we prove an analog of the first Sylow theorem giving a criterion for the existence of a p-Sylow subloop. We also find the maximal order of p-subloops in the Moufang loops that do not possess p-Sylow subloops. (c) 2009 Elsevier Inc. All rights reserved.

POLYNOMIAL AND GROUP IDENTITIES IN ALTERNATIVE LOOP ALGEBRAS

We investigate polynomial identities on an alternative loop algebra and group identities on its (Moufang) unit loop. An alternative loop ring always satisfies a polynomial identity, whereas whether or not a unit loop satisfies a group identity depends on factors such as characteristic and centrality of certain kinds of idempotents.

COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p(3)

A loop is said to be automorphic if its inner mappings are automorphisms. For a prime p, denote by A(p) the class of all 2-generated commutative automorphic loops Q possessing a central subloop Z congruent to Z(p) such that Q/Z congruent to Z(p) x Z(p). Upon describing the free 2-generated nilpotent class two commutative automorphic loop and the free 2-generated nilpotent class two commutative automorphic p-loop F-p in the variety of loops whose elements have order dividing p(2) and whose associators have order dividing p, we show that every loop of A(p) is a quotient of F-p by a central subloop of order p(3). The automorphism group of F-p induces an action of GL(2)(p) on the three-dimensional subspaces of Z(F-p) congruent to (Z(p))(4). The orbits of this action are in one-to-one correspondence with the isomorphism classes of loops from A(p). We describe the orbits, and hence we classify the loops of A(p) up to isomorphism. It is known that every commutative automorphic p-loop is nilpotent when p is odd, and that there is a unique commutative automorphic loop of order 8 with trivial center. Knowing A(p) up to isomorphism, we easily obtain a classification of commutative automorphic loops of order p(3). There are precisely seven commutative automorphic loops of order p(3) for every prime p, including the three abelian groups of order p(3).

CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).

Design and characterization of bridged loop-gap resonators for use in electron paramagnetic resonance measurements

This paper revisits the design of L and S band bridged loop-gap resonators (BLGRs) for electron paramagnetic resonance applications. A novel configuration is described and extensively characterized for resonance frequency and quality factor as a function of the geometrical parameters of the device. The obtained experimental results indicate higher values of the quality factor (Q) than previously reported in the literature, and the experimental analysis data should provide useful guidelines for BLGR design.

One-loop energy-momentum tensor in QED with electriclike background

We have obtained nonperturbative one-loop expressions for the mean-energy-momentum tensor and current density of Dirac's field on a constant electriclike back-round. One of the goals of this calculation is to give a consistent description of backreaction in such a theory. Two cases of initial states are considered: the vacuum state and the thermal equilibrium state. First, we perform calculations for the vacuum initial state. In the obtained expressions, we separate the contributions due to particle creation and vacuum polarization. The latter contribution,, are related to the Heisenberg-Euler Lagrangian. Then, we Study the case of the thermal initial state. Here, we separate the contributions due to particle creation, vacuum polarization, and the contributions due to the work of the external field on the particles at the initial state. All these contributions are studied in detail, in different regimes of weak and strong fields and low and high temperatures. The obtained results allow us to establish restrictions on the electric field and its duration under which QED with a strong constant electric field is consistent. Under such restrictions, one can neglect the backreaction of particles created by the electric field. Some of the obtained results generalize the calculations of Heisenberg-Euler for energy density to the case of arbitrary strong electric fields.

Flat tori, lattices and bounds for commutative group codes

We show that commutative group spherical codes in R(n), as introduced by D. Slepian, are directly related to flat tori and quotients of lattices. As consequence of this view, we derive new results on the geometry of these codes and an upper bound for their cardinality in terms of minimum distance and the maximum center density of lattices and general spherical packings in the half dimension of the code. This bound is tight in the sense it can be arbitrarily approached in any dimension. Examples of this approach and a comparison of this bound with Union and Rankin bounds for general spherical codes is also presented.

Theoretical and Experimental Study of Polarization Dependent Loss in a Optical Recirculating Loop

An experimental study of the Polarization Dependent Loss (PDL) is performed in an Optical Recirculating Loop (RCL). The RCL enables to simulate the transmission through various optical links using just one optical fiber spool, one in line amplifier, some optical filters and devices in a low cost manner. The total amount of PDL in a Recirculating loop, due to its statistical nature, is different of the simple sum of each element of the recirculating loop because of the alignment variation of the PDL elements with time, depending on the environmental conditions such as fiber stress and temperature. In this paper theoretical studies are also performed using formalism of Jones and Mueller matrices in order to represent the different optical elements in the recirculating loop. The PDL must be correctly characterized in order to evaluate properly the impact on the performance of next generation DWDM systems. Theoretical and experimental results comparison shows that a depolarization of 7% occurs in the experimental setup, probably by the optical amplifier due to the depolarized nature of the amplified spontaneous emission.

An approach of optimal sensitivity applied in the tertiary loop of the automatic generation control

This paper proposes an approach of optimal sensitivity applied in the tertiary loop of the automatic generation control. The approach is based on the theorem of non-linear perturbation. From an optimal operation point obtained by an optimal power flow a new optimal operation point is directly determined after a perturbation, i.e., without the necessity of an iterative process. This new optimal operation point satisfies the constraints of the problem for small perturbation in the loads. The participation factors and the voltage set point of the automatic voltage regulators (AVR) of the generators are determined by the technique of optimal sensitivity, considering the effects of the active power losses minimization and the network constraints. The participation factors and voltage set point of the generators are supplied directly to a computational program of dynamic simulation of the automatic generation control, named by power sensitivity mode. Test results are presented to show the good performance of this approach. (C) 2008 Elsevier B.V. All rights reserved.

Implementation of a Control Loop Experiment in a Network-Based Control System With LonWorks Technology and IP Networks

Considering the increasing popularity of network-based control systems and the huge adoption of IP networks (such as the Internet), this paper studies the influence of network quality of service (QoS) parameters over quality of control parameters. An example of a control loop is implemented using two LonWorks networks (CEA-709.1) interconnected by an emulated IP network, in which important QoS parameters such as delay and delay jitter can be completely controlled. Mathematical definitions are provided according to the literature, and the results of the network-based control loop experiment are presented and discussed.

Kinetics and Modeling of Fatty Alcohol Ethoxylation in an Industrial Spray Loop Reactor

The kinetics of the ethoxylation of fatty alcohols catalyzed by potassium hydroxide was studied to obtain the rate constants for modeling of the industrial process. Experimental data obtained in a lab-scale semibatch autoclave reactor were used to evaluate kinetic and equilibrium parameters. The kinetic model was employed to model the performance of an industrial-scale spray tower reactor for fatty alcohol ethoxylation. The reactor model considers that mass transfer and reaction occur independently in two distinct zones of the reactor. Good agreement between the model predictions and real data was found. These findings confirm the reliability of the kinetic and reactor model for simulating fatty alcohol ethoxylation processes under industrial conditions.

Valve friction and nonlinear process model closed-loop identification

Among several process variability sources, valve friction and inadequate controller tuning are supposed to be two of the most prevalent. Friction quantification methods can be applied to the development of model-based compensators or to diagnose valves that need repair, whereas accurate process models can be used in controller retuning. This paper extends existing methods that jointly estimate the friction and process parameters, so that a nonlinear structure is adopted to represent the process model. The developed estimation algorithm is tested with three different data sources: a simulated first order plus dead time process, a hybrid setup (composed of a real valve and a simulated pH neutralization process) and from three industrial datasets corresponding to real control loops. The results demonstrate that the friction is accurately quantified, as well as ""good"" process models are estimated in several situations. Furthermore, when a nonlinear process model is considered, the proposed extension presents significant advantages: (i) greater accuracy for friction quantification and (ii) reasonable estimates of the nonlinear steady-state characteristics of the process. (C) 2010 Elsevier Ltd. All rights reserved.