Gluino zero-modes for non-trivial holonomy calorons

We couple fermion fields in the adjoint representation (gluinos) to the SU(2) gauge field of unit charge calorons defined on R^3 x S_1. We compute corresponding zero-modes of the Dirac equation. These are relevant in semiclassical studies of N=1 Super-symmetric Yang-Mills theory. Our formulas, show that, up to a term proportional to the vector potential, the modes can be constructed by different linear combinations of two contributions adding up to the total caloron field strength.Comment: 17 pages, 3 Postscript figures, late

A foundation for multi-level modelling

Multi-level modelling allows types and instances to be mixed in the same model, however there are several proposals for how meta- models can support this. This paper proposes a meta-circular basis for meta-modelling and shows how it supports two leading approaches to multi-level modelling

ON THE FRAGILITY OF HIGH-DIMENSIONAL CONTROLLERS

In this paper we study the fragility of controllers designed to optimize some performance indices. We trace the fragility problem to the dimension of the resulting controllers, and use results from high-dimensional geometry to analyze the problem both in the continuous and discrete domains

Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice four-torus

It is known that exactly self-dual gauge-field configurations with topological charge |Q|=1 cannot exist on the untwisted continuum 4-torus. We explore the manifestation of this remarkable fact on the lattice 4-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et. al. for SU(2). We identify three distinct signals for the instability of |Q|=1 configurations, and show that these manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for our |Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than local discretization effects. Monte-Carlo generated SU(3) gauge field configurations are cooled to the self-dual limit using an O(a^4)-improved gauge action chosen to have small but positive O(a^6) errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the O(a^4)-improved gauge-field action with an O(a^4)-improved action constructed from the square of an O(a^4)-improved lattice field-strength tensor, thus having different O(a^6) discretization errors. The number of action-density peaks, the instanton size and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of |Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.Comment: 12 pages, 9 figures, submitted to Phys. Rev.

Electrochemical reduction of carbamazepine in ethanol and water solutions using a glassy carbon electrode

The electrochemical reduction of carbamazepine in ethanol and water using a glassy carbon electrode has been studied. In all experimental conditions of scan rate and concentration of carbamazepine an irreversible cathodic wave was observed by cyclic voltammetry (CV). Electrochemical parameters and a plausible EqC mechanism have been reported from the electrochemical measurements and digital simulation. The values of thermodynamic E1/2 were correlated with solvent polarity parameters that it can be interesting for biological, pharmaceutical and forensic purposes. Limits of Detection (LOD) for DPV are 1.1 and 9.0 g/mL (4.65x10-6 and 3.81x10-5 M) in ethanol and water, respectively. The precision and recoveries obtained for tablets and plasma samples showed that the method could be successfully used for analysis

Doubly Periodic Instanton Zero Modes

Fermionic zero modes associated with doubly periodic SU(2) instantons of unit charge are considered. In cases where the action density exhibits two `instanton cores' the zero mode peaks on one of four line-segments joining the two constituents. Which of the four possibilities is realised depends on the fermionic boundary conditions; doubly periodic, doubly anti-periodic or mixed.Comment: 12 pages, 4 figure

Bounding the frequency response for digital transfer functions: results and applications

This paper introduces robust stability techniques for the computation of exact bounds for the frequency response of FIR and IIR digital filters in which the l∞ norm of the coefficients is bounded

H? robust memory controllers for networked control systems: uncertain sampling rates and time delays in polytopic domains

In this paper, the problem of controller design for networked control systems with time-varying sampling rates and time delays is investigated. By using a memory at the feedback loop, a digital robust controller that minimizes an upper bound to the Hinfin performance of the closed loop system is determined. The design conditions are obtained from the Finsler\u27s Lemma combined with the Lyapunov theory and expressed in terms of bilinear matrix inequalities. Extra variables introduced by the Finsler\u27s Lemma are explored in order to provide a better system behavior. The time-varying uncertainties are modelled using polytopic domains. The controller is obtained by the solution of an optimization problem formulated only in terms of the vertices of the polytope, avoiding grids in the parametric space. Numerical examples illustrate the efficiency of the proposed approach

Improved superposition schemes for approximate multi-caloron configurations

Two improved superposition schemes for the construction of approximate multi-caloron-anticaloron configurations, using exact single (anti)caloron gauge fields as underlying building blocks, are introduced in this paper. The first improvement deals with possible monopole-Dirac string interactions between different calorons with non-trivial holonomy. The second one, based on the ADHM formalism, improves the (anti-)selfduality in the case of small caloron separations. It conforms with Shuryak's well-known ratio-ansatz when applied to instantons. Both superposition techniques provide a higher degree of (anti-)selfduality than the widely used sum-ansatz, which simply adds the (anti)caloron vector potentials in an appropriate gauge. Furthermore, the improved configurations (when discretized onto a lattice) are characterized by a higher stability when they are exposed to lattice cooling techniques.Comment: New version accepted for publication in Nucl. Phys. B. Text partly shortened, changes in the introduction, new results added on the comparison with exact solution