Resolution of ternary mixtures of nitrofurantoin, furazolidone and furaltadone by application of Partial Least Squares analysis to the differential pulse polarographic signals

The abilities of the Partial Least Squares (PLS) methods in the resolution of ternary mixtures of organic compounds (furaltadone, furazolidone and nitrofurantoin) by using their differential pulse polarographic (DPP) signals are reported. The applicability of these methods to resolve very overlapped peaks whose E(p) also changes with concentration is demonstrated. The analysis of both synthetic and real samples has been made with satisfactory results. The relative error of prediction (REP) is 8.7% for FD, 7.7% for FZ and 6.7% for NF by application of the PLS-2 method.     

Colorimetric method for determination of chlorine with 3,3',5,5'-tetramethylbenzidine

A new method is developed for the calorimetric determination in water of chlorine (free and combined) with 3,3′,5,5′-tetramethylbenzidine. The procedure proposed achieves a detection limit of 2 ng/ml and its sensitivity is greater than that of the methods used at present.     

Quantum groups in the higgs phase

In the Higgs phase we may be left with a residual finite symmetry groupH of the condensate. The topological interactions between the magnetic and electric excitations in these so-called discreteH gauge theories are completely described by the Hopf algebra or quantum groupD(H). In 2+1 dimensional space time we may add a Chern-Simons term to such a model. This deforms the underlying Hopf algebraD(H) into the quasi-Hopf algebraD (H) by means of a 3-cocycle onH. Consequently, the finite number of physically inequivalent discreteH gauge theories obtained in this way are labelled by the elements of the cohomology groupH ³(H,U(1)). We briefly review the above results in these notes. Special attention is given to the Coulomb screening mechanism operational in the Higgs phase. This mechanism screens the Coulomb interactions, but not the Aharonov-Bohm interactions.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 509–523, March, 1994     

Near-perfect matrices

A 0, 1 matrixA isnear-perfect if the integer hull of the polyhedron {x0: Ax } can be obtained by adding one extra (rank) constraint. We show that in general, such matrices arise as the cliquenode incidence matrices of graphs. We give a colouring-like characterization of the corresponding class of near-perfect graphs which shows that one need only check integrality of a certain linear program for each 0, 1, 2-valued objective function. This in contrast with perfect matrices where it is sufficient to check 0, 1-valued objective functions. We also make the following conjecture: a graph is near-perfect if and only if sequentially lifting any rank inequality associated with a minimally imperfect graph results in the rank inequality for the whole graph. We show that the conjecture is implied by the Strong Perfect Graph Conjecture. (It is also shown to hold for graphs with no stable set of size eleven.) Our results are used to strengthen (and give a new proof of) a theorem of Padberg. This results in a new characterization of minimally imperfect graphs: a graph is minimally imperfect if and only if both the graph and its complement are near-perfect.The research has partially been done when the author visited Mathematic Centrum, CWI, Amsterdam, The Netherlands.     

On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds

We consider a new algorithm, an interior-reflective Newton approach, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generatesstrictly feasible iterates by using a new affine scaling transformation and following piecewise linear paths (reflection paths). The interior-reflective approach does not require identification of an activity set. In this paper we establish that the interior-reflective Newton approach is globally and quadratically convergent. Moreover, we develop a specific example of interior-reflective Newton methods which can be used for large-scale and sparse problems.Research partially supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under grant DE-FG02-86ER25013.A000, and in part by NSF, AFOSR, and ONR through grant DMS-8920550, and by the Advanced Computing Research Institute, a unit of the Cornell Theory Center which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State and members of its Corporate Research Institute.Corresponding author.     

Helicity amplitudes for matter-coupled gravity

The great simplicity attained by the Weyl-van der Waerden spinor technique in the evaluation of helicity invariant amplitudes is shown to apply in the cumbersome calculations within the framework of linearized gravitation. Once the graviton couplings to spin-0, 1/2, 1, and 3/2 particles are given, we exhibit the reach of this method by evaluating, as an example, the helicity amplitudes for the process electron + positron photon + graviton in a very straightforward way.     

An exponential upper bound for the survival probability in a dynamic random trap model

We consider a symmetric translation-invariant random walk on thed-dimensional lattice ? ^d . The walker moves in an environment of moving traps. When the walker hits a trap, he is killed. The configuration of traps in the course of time is a reversible Markov process satisfying a level-2 large-deviation principle. Under some restrictions on the entropy function, we prove an exponential upper bound for the survival probability, i.e., $$\mathop {lim sup}\limits_{t \to \infty } \frac{1}{t}\log \mathbb{P}(T \geqslant t)< 0$$ whereT is the survival time of the walker. As an example, our results apply to a random walk in an environment of traps that perform a simple symmetric exclusion process.     

Phase de-locking in cubic 3k-antiferromagnets

It is shown that the temperature dependence ofSR spectra of some simple cubic (NaCl, CsCl, AuCu₃ structures) compounds involving rare earths and actinides differs for a 1k when compared to a a 3k spin structure. This allows their distinction. In the 3 k structure magnetic pseudo excitations resulting from phase de-locking diffuse slowly (1–5MHz).This work was supported by the German Federal Minister for Research and Technology (Bundesminister für Forschung und Technologie [BMFT]) under Contract Nr. 03KA2-TUM-4.