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).

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.

Evidence of the Importance of the First Intracellular Loop of Prokineticin Receptor 2 in Receptor Function

Prokineticin receptors (PROKR) are G protein-coupled receptors (GPCR) that regulate diverse biological processes, including olfactory bulb neurogenesis and GnRH neuronal migration. Mutations in PROKR2 have been described in patients with varying degrees of GnRH deficiency and are located in diverse functional domains of the receptor. Our goal was to determine whether variants in the first intracellular loop (ICL1) of PROKR2 (R80C, R85C, and R85H) identified in patients with hypogonadotropic hypogonadism interfere with receptor function and to elucidate the mechanisms of these effects. Because of structural homology among GPCR, clarification of the role of ICL1 in PROKR2 activity may contribute to a better understanding of this domain across other GPCR. The effects of the ICL1 PROKR2 mutations on activation of signal transduction pathways, ligand binding, and receptor expression were evaluated. Our results indicated that the R85C and R85H PROKR2 mutations interfere only modestly with receptor function, whereas the R80C PROKR2 mutation leads to a marked reduction in receptor activity. Cotransfection of wild-type (WT) and R80C PROKR2 showed that the R80C mutant could exert a dominant negative effect on WT PROKR2 in vitro by interfering with WT receptor expression. In summary, we have shown the importance of Arg80 in ICL1 for PROKR2 expression and demonstrate that R80C PROKR2 exerts a dominant negative effect on WT PROKR2. (Molecular Endocrinology 26: 1417-1427, 2012)

PD controller synthesis from open-loop response measurements of rotating system

In this work, a method of computing PD stabilising gains for rotating systems is presented based on the D-decomposition technique, which requires the sole knowledge of frequency response functions. By applying this method to a rotating system with electromagnetic actuators, it is demonstrated that the stability boundary locus in the plane of feedback gains can be easily plotted, and the most suitable gains can be found to minimise the resonant peak of the system. Experimental results for a Laval rotor show the feasibility of not only controlling lateral shaft vibration and assuring stability, but also helps in predicting the final vibration level achieved by the closed-loop system. These results are obtained based solely on the input-output response information of the system as a whole.

Manipulation effects of prior exercise intensity feedback by the Borg scale during open-loop cycling

Objective To verify the effects of exercise intensity deception by the Borg scale on the ratings of perceived exertion (RPE), heart rate (HR) and performance responses during a constant power output open-loop exercise. Methods Eight healthy men underwent a maximal incremental test on a cycle ergometer to identify the peak power output (PPO) and heart rate deflection point (HRDP). Subsequently, they performed a constant power output trial to exhaustion set at the HRDP intensity, in deception (DEC) and informed (INF) conditions: DEC-subjects were told that they would be cycling at an intensity corresponding to two categories below the RPE quantified at the HRDP; INF-subjects were told that they would cycle at the exact intensity corresponding to the RPE quantified at the HRDP. Results The PPO and power output at the HRDP obtained in maximal incremental tests were 247.5 +/- 32.1 W and 208.1 +/- 27.1 W, respectively. No significant difference in the time to exhaustion was found between DEC (525 +/- 244 s) or INF (499 +/- 224 s) trials. The slope and the first and second measurements of the RPE and HR parameters showed no significant difference between trials. Conclusions Psychophysiological variables such as RPE and HR as well as performance were not affected when exercise intensity was deceptively manipulated via RPE scores. This may suggest that unaltered RPE during exercise is a regulator of performance in this open-loop exercise.

COMMUTATIVE ALGEBRAS IN DRINFELD CATEGORIES OF ABELIAN LIE ALGEBRAS

We describe (braided-) commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over these algebras and classify commutative algebras with a finite number of simple local modules.

Gauge and integrable theories in loop spaces

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1 + 1) dimensions, Chern-Simons theories in (2 + 1) dimensions, and non-abelian gauge theories in (2 + 1) and (3 + 1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3 + 1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations. (C) 2012 Elsevier B.V. All rights reserved.

Closed-loop stable model predictive control of integrating systems with dead time

Model predictive control (MPC) applications in the process industry usually deal with process systems that show time delays (dead times) between the system inputs and outputs. Also, in many industrial applications of MPC, integrating outputs resulting from liquid level control or recycle streams need to be considered as controlled outputs. Conventional MPC packages can be applied to time-delay systems but stability of the closed loop system will depend on the tuning parameters of the controller and cannot be guaranteed even in the nominal case. In this work, a state space model based on the analytical step response model is extended to the case of integrating time systems with time delays. This model is applied to the development of two versions of a nominally stable MPC, which is designed to the practical scenario in which one has targets for some of the inputs and/or outputs that may be unreachable and zone control (or interval tracking) for the remaining outputs. The controller is tested through simulation of a multivariable industrial reactor system. (C) 2012 Elsevier Ltd. All rights reserved.

All-loop finiteness of the two-dimensional noncommutative supersymmetric gauge theory

Within the superfield approach, we discuss the two-dimensional noncommutative super-QED. Its all-order finiteness is explicitly shown. Copyright (C) EPLA, 2012

Generalized non-commutative inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f (E) = E/pc (not equal 1) for massless particles. This distorted energy-momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007) 021 and JCAP11(2007) 013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the a family of curves f (E) = 1 + (lambda E)(alpha). We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of SL(2, C). We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

Running coupling and pomeron loop effects on inclusive and diffractive DIS cross sections

Within the framework of a (1 + 1)-dimensional model which mimics high-energy QCD, we study the behavior of the cross sections for inclusive and diffractive deep inelastic gamma*h scattering cross sections. We analyze the cases of both fixed and running coupling within the mean-field approximation, in which the evolution of the scattering amplitude is described by the Balitsky-Kovchegov equation, and also through the pomeron loop equations, which include in the evolution the gluon number fluctuations. In the diffractive case, similarly to the inclusive one, suppression of the diffusive scaling, as a consequence of the inclusion of the running of the coupling, is observed.

Conformation analysis of a surface loop that controls active site access in the GH11 xylanase A from Bacillus subtilis

Xylanases (EC 3.2.1.8 endo-1,4-glycosyl hydrolase) catalyze the hydrolysis of xylan, an abundant hemicellulose of plant cell walls. Access to the catalytic site of GH11 xylanases is regulated by movement of a short beta-hairpin, the so-called thumb region, which can adopt open or closed conformations. A crystallographic study has shown that the D11F/R122D mutant of the GH11 xylanase A from Bacillus subtilis (BsXA) displays a stable "open" conformation, and here we report a molecular dynamics simulation study comparing this mutant with the native enzyme over a range of temperatures. The mutant open conformation was stable at 300 and 328 K, however it showed a transition to the closed state at 338 K. Analysis of dihedral angles identified thumb region residues Y113 and T123 as key hinge points which determine the open-closed transition at 338 K. Although the D11F/R122D mutations result in a reduction in local inter-intramolecular hydrogen bonding, the global energies of the open and closed conformations in the native enzyme are equivalent, suggesting that the two conformations are equally accessible. These results indicate that the thumb region shows a broader degree of energetically permissible conformations which regulate the access to the active site region. The R122D mutation contributes to the stability of the open conformation, but is not essential for thumb dynamics, i.e., the wild type enzyme can also adapt to the open conformation.