Interaction of Mn(acac)3 with Asymmetrical Schiff Base Ligands containing an Amido Group

Interaction of asymmetrical Schiff base ligands H₃Lⁿ [where H₃Lⁿ are substituted 3–aza–4–(2–hydroxyphenyl)–N– (2–hydroxyphenyl)but–3–enamide] with Mn(acac)₃ (acac = acetylacetonate) has been investigated. Two different type of manganese(III) complexes have been obtained depending on the nature of the substituents on the ligand. We have found that ligands containing donor substituents drives to the formation of two different kinds of complexes from the same reaction: Mn(Lⁿ)(H₂O)_x ( 1a–5a ) and [Mn(HLⁿ)(acac)](H₂O)_y ( 1b–5b ) (where Lⁿ and HLⁿ signify the ligand in its trianionic and dianionic form, respectively). However, when the substituents are electron withdrawing or poor donor only compounds of the type [Mn(HLⁿ)(acac)](H₂O)_y ( 6–10 ) are obtained. All these compounds have been characterized by elemental analyses, IR and ¹H NMR spectroscopy, FAB mass spectrometry, magnetic measurements and molar conductivities. The electrochemical behaviour of these complexes has also been studied.     

Classical simulations of magnetic structures for chromium clusters: Size effects

Classical (Heisenberg) simulations show that the total magnetization of the lowest-energy states of clusters made of antiferromagnetically coupled chromium atoms is planar, rather than collinear, depending on the arrangement of the atoms. Although the model Hamiltonian is not restrictive, many cluster configurations of various numbers of atoms do not use all three directions for the spins. This result confirms the conclusion drawn from the local-spin DFT calculation by Kohl and Bertsch that clusters of N≤13 have non-collinear magnetic moments. The present simulations show non-collinear spin ordering also for bigger clusters, designed to be as spherical as possible following the bcc arrangement, when atoms interact both with the nearest and next-nearest neighbours. Depending on the signs of the coupling constants frustration appears. The advantage of the discrete model, despite the simplicity, is that very large clusters and magnetization at finite temperatures can be studied. This model predicts that clusters with specific numbers of atoms interacting only with the nearest neighbours have collinear spins as in the bulk. We also apply the model to simulate the destruction of the anti-ferromagnetic ordering by thermal fluctuations. This model shows no unique magnetization of mixed Fe _0.33 Cr _0.67, which is consistent with experimental observations.     

Ground state rotational spectrum of nitrogen trifluoride: The K = 3 splittings of NF3 and NF3

The ground state rotational spectrum of the ¹⁴NF₃ and ¹⁵NF₃ isotopic species of nitrogen fluoride has been observed in the ∼450-810 GHz frequency range. This investigation allowed us to improve the rotational parameters for both isotopologues. In particular, for the first time the K = 3 line splitting parameter and the sextic centrifugal distortion constants have been determined for ¹⁵NF₃.     

Synthesis of optical standard frequencies in the S, C and L telecommunication bands by use of four-wave mixing in semiconductor optical amplifiers

The generation of standard reference frequencies close to the ITU channels is essential for the calibration and maintenance of DWDM systems. This work describes a method to synthesize frequency references in the range from 187.1 to 205.1 THz (1462-1602 nm). The method is based on the generation of four equispaced frequencies (by the process of four-wave mixing in a semiconductor amplifier) of which two are locked to absorption lines of the acetylene ¹²C₂H₂ (1511-1542 nm).     

Aza-Michael reactions with vinyl sulfones and Amberlyst-15 as catalyst

Vinyl p-aminophenylsulfone and methyl vinyl sulfone were shown to react, as Michael acceptors, with a broad range of secondary and primary amines using Amberlyst as catalyst. The reactions occurred, generally, with high yields and in a short time.     

Resonance in open coaxial cylindrical resonators

A study of the electrodynamical properties of open coaxial cylindrical resonators using a partially conical inner rod is made along with experimental verification. On the basis of a geometrical criterion for the occurrence of high-Q resonances, it turns out to be possible to discriminate certain classes of TE modes by keeping to a minimum value their diffrationQ factors. In particular, for an especially designed cavity only TE_0.2 and TE_1.3 modes appear to have strong resonance in the 6 · 14GH _z range as a result of the action of the coaxial insert.     

Rubber network in elastomer nanocomposites

The influence of inorganic nanoparticles on crosslinking mechanism of elastomers has been evaluated by applying the tube model on equilibrium statistical mechanics. The results have shown that a highly ordered structure with a huge amount of entanglements, wherein the polymer is nanoscopically confined, is formed by the addition of nanoparticles. These physical links exhibit freedom of movement under stretching, but in a lower volume because of confinement. That is, network molecular parameters such as lateral tube dimensions or average molecular mass of the chains decreased in presence of nanoparticles.     

Polynomial time approximation schemes for dense instances of minimum constraint satisfaction

It is known that large fragments of the class of dense Minimum Constraint Satisfaction (MIN‐CSP) problems do not have polynomial time approximation schemes (PTASs) contrary to their Maximum Constraint Satisfaction analogs. In this paper we prove, somewhat surprisingly, that the minimum satisfaction of dense instances of kSAT ‐formulas, and linear equations mod 2, Ek‐LIN2, do have PTASs for any k. The MIN‐Ek‐LIN2 problems are equivalent to the k‐ary versions of the Nearest Codeword problem, the problem which is known to be exceedingly hard to approximate on general instances. The method of solution of the above problems depends on the development of a new density sampling technique for k‐uniform hypergraphs which could be of independent interest. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 73–91, 2003     

Testing for cointegration using induced-order statistics

In this paper we explore the usefulness of induced-order statistics in the characterization of integrated series and of cointegration relationships. We propose a non-parametric test statistic for testing the null hypothesis of two independent random walks against wide cointegrating alternatives including monotonic nonlinearities and certain types of level shifts in the cointegration relationship. We call our testing device the induced-order Kolmogorov–Smirnov cointegration test (KS), since it is constructed from the induced-order statistics of the series, and we derive its limiting distribution. This non-parametric statistic endows the test with a number of desirable properties: invariance to monotonic transformations of the series, and robustness for the presence of important parameter shifts. By Monte Carlo simulations we analyze the small sample properties of this test. Our simulation results show the robustness of the induced order cointegration test against departures from linear and constant parameter models. This paper is an extension of the work of Aparicio and Granger (1995) and Aparicio and Escribano (1998).     

A Multivalued Approach to the Planar Isosceles Three Body Problem

The isosceles three body problem consists of three point masses located on the vertices of an isosceles triangle on the plane. The two masses on the asymmetric edge are equal. This problem has been extensively studied but not as a perturbation of the Kepler problem. In this case we arrive at a differential inclusion as a natural formulation when we regularize the problem. We also derive an extension of the vectorfield that allows us to consider orbits across singular sets.