Modular lattices over cyclotomic fields

This paper is concerned with modular lattices over cyclotomic fields. In particular, the notion of Arakelov modular ideal lattice is introduced. All the cyclotomic fields over which there exists an Arakelov modular lattice of given level are characterised.     

New developments in the application of Pontryagin's Principle for the hydrothermal optimization

^** Email: bayon{at}uniovi.es In this paper we have developed a much simpler theory than previousones that resolves the problem of the optimization of hydrothermalsystems. The problem involves non-holonomic inequality constraints.In particular, we have established a necessary condition forthe stationary functions of the functional. We shall use Pontryagin'sMinimum Principle as the basis for proving this theorem, settingout our problem in terms of optimal control in continuous time,with the Lagrange-type functional. This theorem allows us toelaborate the optimization algorithm that leads to the determinationof the optimal solution of the hydrothermal system. We generalizethe problem, taking into account a cost associated with thewater, to then set out and solve the corresponding Bolza's problem.Finally, we present an example employing the algorithm developedfor this purpose with the ‘Mathematica’ package.     

Absolute intensities and pressure broadening coefficients measured at different temperatures for the 201II ← 000 band of 12C16O2 at 4978cm-1

Absolute line intensities and self-broadening coefficients have been measured at 197° and 294°K for the 201_II ← 000 band of ¹²C¹⁶O₂ at about 4978cm^-1. The vibration-rotation factor (F_VR), the purely vibrational transition moment (∣R(O)∣), and the integrated band intensity (S_band) are deduced from the measurements. The results are: F_VR(m)=1+(0.24±0.08)x10^-4m+(0.55+0.21)x10^-4m², ∣R(O)∣= (4.340±0.008x10^-3 debye, S_band=96372±190cm^-1km^-1atm^-1_STP. The results for self-broadening coefficients, as well as for individual vibration-rotation lines, are presented in the text.     

Single facility location on a network under mill and delivered pricing

^** E-mail: pelegrin{at}um.es Firms normally use either a mill price or a delivered pricepolicy, depending on market conditions (type of good, transportationway, customers location, costs, etc). In this paper, the problemof selecting the best location for an entering firm in competitionwith some pre-existing firms, under each price policy, is studiedon a network for the first time. With mill pricing, an equilibriumin price rarely exists and it is assumed that all competingfirms set a common mill price for all customers. With deliveredpricing, there exists a Nash equilibrium in price and it isassumed that the equilibrium price in each area is offered tothe customers in that area. In both cases, we consider thatcustomers buy from the cheapest facility and the same rulesare used for tie breaking in the lowest cost. While the profitmaximization problem for the entering firm always has optimalsolutions under mill pricing, this problem might not have anoptimal solution under delivered pricing. We show some discretizationresults and give procedures to find the full set of optimal,or -optimal, solutions to the problem under the two price policies.A comparison of results with the two price policies is givenby using an illustrative example.     

Quantum chemical study on the coordination environment of the catalytic zinc ion in matrix metalloproteinases

X-ray analyses of matrix metalloproteinases (MMPs) have shown that the catalytic zinc ion (Zn1) can bind to one to three water molecules in addition to three conserved histidine residues. To estimate the relative stability of the possible Zn1 coordination structures in the active site of the MMPs, we carry out computational analyses on the coordination environment of the Zn1 ion in the gelatinase A enzyme (or matrix metalloproteinase 2; MMP-2). Four-, five-, and six-coordinated complexes representative of the Zn1 site are fully characterized by means of quantum mechanical (QM) methodologies. On one hand, B3LYP/LACVP* minimizations of various cluster models of the MMP-2 active site show that the trigonal bipyramidal geometry is energetically favored in the gas phase and that continuum solvent effects stabilize preferentially the tetrahedral complexes. On the other hand, B3LYP/OPLS-AA hybrid QM/molecular mechanical calculations in the solvated catalytic domain of the MMP-2 enzyme complemented with electrostatic Poisson-Boltzmann calculations show that the mature enzyme presents most likely a Zn1 ion coordinated by three histidine residues and two water molecules, while the active site glutamic acid is negatively charged. In consonance with X-ray diffraction data, other possible Zn1 configurations, a six-coordinated structure with Zn1-water as well as four- and five-coordinated complexes with a Zn1-bound hydroxide, are predicted to be very close in energy.     

Microwave-assisted regioselective cycloaddition reactions between 9-substituted anthracenes and levoglucosenone

The cycloaddition reactions of 9-substituted anthracenes and levoglucosenone were investigated under microwave irradiation and conventional heating conditions. Considering time, yields, and regioselectivity, microwave technology has proven to be an ideal tool to achieve this chemical transformation. [reaction: see text].     

Defect clustering in double doped fluorite crystals with Lu and Gd

Abstract

Solid solutions Ca¹ x-^yLu^xGd^y F_2+x+y for 10^?4 ≤ x ≤ 2 × 10^?2 and y=0.0001 have been studied by electron paramagnetic resonance (EPR) and ionic thermal currents (ITC). It has been found that the ITC spectrum from 77 to 420 K is very weak and the main peak is attributed to the relaxation of both Lu³⁺-F^? _x and Gd³⁺F^? _i nn dipoles. No polarizable clusters are present in the temperature range explored here. The EPR spectra show the presence of Gd³⁺ tetragonal and cubic centers due to the local and non local compensation, respectively. The continuous decrease in the molar fraction of Gd³⁺ tetragonal centers together with the low concentration of Lu nn dipoles is an evidence of the existence at these low and intermediate concentrations of large clusters such as the cubo-octahedral hexamer which has been proposed for CaF₂ crystals very highly doped with small trivalent cations.     

Classical spin dynamics of anisotropic Heisenberg dimmers

In the present work we study the deterministic spin dynamics of two interacting anisotropic magnetic particles in the presence of an external magnetic field using the Landau-Lifshitz equation. The interaction between particles is through the exchange energy. We study both conservative and dissipative cases. In the first one, we characterize the dynamical behavior of the system by monitoring the Lyapunov exponents and bifurcation diagrams. In particular, we explore the dependence of the largest Lyapunov exponent respect to the magnitude of applied magnetic field and exchange constant. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated topology of intricately intermingled chaotic and regular regions. In the dissipative case, we calculate the final saturation states as a function of the magnitude of the applied magnetic field, exchange constant as well as the anisotropy constants.     

Inverse problem for zeros of certain koebe-related functions

If w₁,…,w _N is a finite sequence of nonzero points in the unit disk, then there are distinct points λ₁,…, λ_N on the unit circle and positive numbers Μ₁,…,Μ _N such that is the zero sequence of the function 1 — . The points λ₁,…, λ_N and numbers Μ₁,…,Μ_N are unique (except for reorderings).     

Three 4,7‐diaryl‐2‐ethylsulfanylpyrazolo[1,5‐a][1,3,5]triazines

The molecular dimensions of 2‐ethylsulfanyl‐7‐(4‐methylphenyl)‐4‐phenylpyrazolo[1,5‐a][1,3,5]triazine, C₂₀H₁₈N₄S, (I), 7‐(4‐chlorophenyl)‐2‐ethylsulfanyl‐4‐phenylpyrazolo[1,5‐a][1,3,5]triazine, C₁₉H₁₅ClN₄S, (II), and 4,7‐bis(4‐chlorophenyl)‐2‐(ethylsulfanyl)pyrazolo[1,5‐a][1,3,5]triazine, C₁₉H₁₄Cl₂N₄S, (III), show evidence for some aromatic delocalization in the pyrazole rings. The conformations adopted by the ethylsulfanyl substituents are different in all three compounds. There are no hydrogen bonds in any of the crystal structures, but pairs of molecules in (II) and (III) are linked into centrosymmetric dimers by π‐stacking interactions.