The synthesis and reactivity of the heptanuclear dianion [Os7(CO)20]2− including the synthesis and structural characterizations of the compounds [Os7(CO)20(AuPEt)3 2] and [Os8(CO)20(η6-C6H6]

Reduction of the heptaosmium cluster [Os₇(CO)₂₁] With [Et₄N][NH₄) gives the cluster dianion [Os₇(CO)₂₀]^2–,1, in high yield. The reaction of the dianion with [AuPR ₃Cl] (R=Et or Ph) in the presence of TlPF₆ forms [Os₇((CO)₂₀(AuPR ₃)₂] [R=Et (2a);R = Ph(2b)] in 80% yield, while the corresponding reaction with (Os(C₆H₆)(CH₃CN)₃]²⁺ gives [Os₈(CO)₂₀ ( ⁶-C₆H₆)] (3) in reasonable yield (ca. 30%). The dianion,1, and the clusters2 and3 have been fully characterized by bout spectroscopic and crystallographic methods. The crystal structure of the [Ph₄P]⁺ salt of1 shows that the metals in the anion adopt a capped octahedral geometry, with all twenty carbonyl ligands in terminal sites. The metal core geometry in2a is best described as a tricapped octahedron, and is based on the structure of the dianion1 with two adjacent octahedral faces capped by the Au atoms of the two AuPEt₃ groups. In a similar fashion, the geometry of3 is related to that of1 with the addition of an Os(C₆H₆) unit capped to a triangular face, to give a bicapped octahedral framework.     

Atmospheric pressure laser desorption/chemical ionization mass spectrometry: a new ionization method based on existing themes

We have designed and constructed an atmospheric pressure laser desorption/chemical ionization (AP-LD/CI) source that utilizes a laser pulse to desorb intact neutral molecules, followed by chemical ionization via reagent ions produced by a corona discharge. This source employs a heated capillary atmospheric pressure inlet coupled to a quadrupole ion trap mass spectrometer and allows sampling under normal ambient air conditions. Preliminary results demonstrate that this technique provides approximately 150-fold increase in analyte ions compared to the ion population generated by atmospheric pressure infrared matrix-assisted laser desorption/ionization (AP-IR-MALDI).     

Lewis-Base Adducts of Group 11 Metal(I) Compounds. LXXVI Structural Studies in the Copper(I) Halide : Norbornadiene System

The structural characterizations of some copper(I) halide (CuX) adducts with norbornadiene (nbd) are recorded. CuCl : nbd (1:1)₄ (a redetermination), (2:1)_2(|), are systems both based around Cu₄Cl₄ cubane-type cluster arrays. CuBr : nbd (7:3)_(|)( 0.5 MeOH), a complex polymer with 3-symmetry, is believed to be the complex previously described as an adduct of 2:1 stoichiometry. Attempts to obtain an iodide counterpart have resulted in the definition of an ephemeral adduct CuI : MeCN (3:2)_(|). 0.5 C₇H₈ in which, remarkably, the nbd is uncoordinated; the complex is a polymer, related to the [AgX(quinoline)]_(|) (X = Cl, Br) saddle polymer.     

The number oft-wise balanced designs

We prove that the number oft-wise balanced designs of ordern is asymptotically , provided that blocks of sizet are permitted. In the process, we prove that the number oft-profiles (multisets of block sizes) is bounded below by and above by for constants c₂>c₁>0.     

Interface interactions in modulated phases,and upsilon points

Certain features in Frenkel-Kontorova and other models of phases with a one-dimensional modulation can be analyzed by assuming parallel interfaces separating sets of lattice planes belonging to two different phases, and treating the free energy to create interfaces, as well as the interaction of two, three, or more interfaces, as phenomenological parameters. A strategy employed by Fisher and Szpilka for interacting defects can be extended to the case of interfaces, allowing a systematic study of the phase diagram by ignoring all interface interactions, and then successively taking into account pair, triple, and higher-order terms. The possible phase diagrams which can occur near the point where =0 include: various sorts of endpoints analogous to critical endpoints, an accumulation point of first-order transitions and triple points, and a self-similar structure which we call an upsilon point, which turns out to be an accumulation point of an infinite number of segments of first-order transition lines, each of which terminates in two upsilon points.     

Ramsey partitions of integers and pair divisions

Ifk ₁ andk ₂ are positive integers, the partitionP = (₁,₂,..., _n ) ofk ₁+k ₂ is said to be a Ramsey partition for the pairk ₁,k ₂ if for any sublistL ofP, either there is a sublist ofL which sums tok ₁ or a sublist ofP –L which sums tok ₂. Properties of Ramsey partitions are discussed. In particular it is shown that there is a unique Ramsey partition fork ₁,k ₂ having the smallest numbern of terms, and in this casen is one more than the sum of the quotients in the Euclidean algorithm fork ₁ andk ₂.An application of Ramsey partitions to the following fair division problem is also discussed: Suppose two persons are to divide a cake fairly in the ratiok ₁k ₂. This can be done trivially usingk ₁+k ₂-1 cuts. However, every Ramsey partition ofk ₁+k ₂ also yields a fair division algorithm. This method yields fewer cuts except whenk ₁=1 andk ₂=1, 2 or 4.     

Geometrization of the physics with teleparallelism. I. The classical interactions

A connection viewed from the perspective of integration has the Bianchi identities as constraints. It is shown that the removal of these constraints admits a natural solution on manifolds endowed with a metric and teleparallelism. In the process, the equations of structure and the Bianchi identities take standard forms of field equations and conservation laws.The Levi-Civita (part of the) connection ends up as the potential for the gravity sector, where the source is geometric and tensorial and contains an explicit gravitational contribution.Nonlinear field equations for the torsion result. In a low-energy approximation (linearity andlow energy-momentumtransfer), the postulate that only charge and velocities contribute to the source transforms these equations into the Maxwell system. Moreover, the affine geodesics become the equations of motion of special relativity with Lorentz force in the same approximation [J. G. Vargas,Found. Phys. 21, 379 (1991)]. The field equations for the torsion must then be viewed as applying to an electromagnetic/strong interaction.A classical unified theory thus arises where the underlying geometry confers their contrasting characters to Maxwell-Lorentz electrodynamics and to an Einstein's-like theory of gravity. The highly compact field equations must, however, be developed in phase-spacetime, since the connection is velocity-dependent, i.e., Finsler-like.Further opportunities for similarities with present-day physics are discussed: (a) teleparallelism allows for the formulation of the torsion sector of the theory as a flat space theory with concomitant point-dependent transformations; (b) spinors should replace Lorentz frames in their role as the subjects to which the connection refers; (c) the Dirac equation consistent with the frame bundle for a velocity-dependent metric with Lorentz signature generates a weak-like interaction in the torsion sector.Work done at the Department of Mathematics and Physics of the Interamerican University of Puerto Rico, San German, Puerto Rico 00683.     

Orthogonal separations of nicotine and nicotine-related alkaloids by various capillary electrophoretic modes

The migration behaviour of nicotine and related tobacco alkaloids was investigated using three different capillary electrophoretic (CE) modes. Novel separations were achieved both using microemulsion electrokinetic chromatography (MEEKC) and nonaqueous CE (NACE). Improved resolution compared to previous studies was obtained using free-solution CE (FSCE). Each technique resulted in different, orthogonal separation selectivity. The suitability of each method for application to the analysis of nicotine lozenges is discussed. The FSCE method was applied to the analysis of nicotine lozenges due to its compatibility with an established lozenge extraction solvent. The method used gave good injection precision and linearity. Good agreement of CE and high-performance liquid chromatography (HPLC) results was obtained. The CE method is therefore considered suitable for the quantitative determination of nicotine in nicotine lozenges.