A theorem on asymptotic expansion of Feynman amplitudes

For any Feynman amplitude, where any subset of invariants and/or squared masses is scaled by a real parameter going to zero or infinity, the existence of an expansion in powers of and ln is proved, and a method is given for determining such an expansion. This is shown quite generally in euclidean metric, whatever the external momenta (exceptional or not) and the internal masses (vanishing or not) may be, and for some simple cases in minkowskian metric, assuming only finiteness of the — eventually renormalized — amplitude before scaling. The method uses what is called Multiple Mellin representation, the validity of which is related to a generalized power-counting theorem.On leave of absence from University of Bahia (Brazil). Fellow of CAPES, Brazil     

Experiments in mixed-integer linear programming using pseudo-costs

This paper discusses heuristic branch and bound methods for solving mixed integer linear programming problems. The research presented on here is the follow on to that recorded in [3].After a resumé of the concept of pseudo-costs and estimations, new heuristic rules for generating a tree which make use of pseudo-costs and estimations are presented. Experiments have shown that models having a low percentage of integer variables behave in a radically different way from models with a high percentage of integer variables. The new heuristic rules seem to apply generally to the first type of model.Later, other heuristic rules are presented that are used with models having a high percentage of integer variables and with models having a special structure (models including special ordered sets.)The rules introduced here have been implemented in the IBM Mathematical Programming System Extended/370. They are used to solve large mixed integer linear programming models.Numerical results that permit comparisons to be made among the different rules are provided and discussed.     

Teaching Operational Research Technique

Good technique, i.e. competence in carrying out operational research, is as vital for the practitioner to acquire as competence in the traditional ‘techniques’. It is suggested that universities should teach students how to conduct simple projects prior to alerting them to more sophisticated methodological issues.As an aid to this task, the traditional five or six parts of an operational research project are broken down and extended into 39 steps, and regrouped into three phases. Also, five skills are identified as being conceptually essential to "good" operational research, which students can develop through tackling suitable case studies.     

Heterogeneous diastereoselective hydrogenation of pyridine and corresponding enamine covalently bound to pantolactone

The diastereoselective hydrogenation of 2-methyl nicotinic acid covalently bound to pantolactone was studied over supported metallic catalysts. With this chiral auxiliary, a two-steps reaction was observed with formation of tetrahydropyridine intermediate. The influence of different reaction parameters on the diastereoselectivity of the hydrogenation of pyridine and enamine substrates was studied.     

Coordination properties of a diarylaza crown ether appended with a luminescent [Ru(bipy)3]2+ unit

The [Ru(bipy)(2)(1)](PF(6))(2) (bipy refers to 2,2'-bipyridine) complex, comprising a ruthenium(II) tris(2,2'-bipyridine) luminophore covalently linked to a di[(o-triethyleneglycoxy)phenyl]amine crown ether 1, has been synthesized and fully characterized. The photophysical properties of this metal complex have been examined in solution at ambient temperature. Luminescence from the metal complex is enhanced significantly in the presence of various adventitious cations, including protons. In particular, Li(+) cations bind to the crown ether, as evidenced by (1)H NMR and luminescence spectroscopy. Cation binding serves to decrease the rate of reductive quenching of the triplet state of the metal complex, thereby increasing the extent of luminescence. The solution-phase conformation of [Ru(bipy)(2)(1)](PF(6))(2), with and without encapsulated Li(+), has been examined by 2-D NMR and by molecular dynamics simulations.     

Palladium salicylaldimine complexes containing boronate esters

Reactions of salicylaldehydes with boronate ester derivatives of aniline have been examined. Addition of these Schiff base ligands to palladium acetate or Na₂PdCl₄ afforded novel boron-containing trans-bis(N-arylsalicylaldiminato) palladium complexes.Condensation of salicylaldehyde (2-HOC₆H₄C(O)H) with H₂NC₆H₄Bpin (pin=1,2-O₂C₂Me₄) afforded the boron-containing Schiff bases, 2-HOC₆H₄C(H)=NC₆H₄Bpin (1–3a). Similar reactivity with 2-hydroxy-5-nitrobenzaldehyde and 2-hydroxy-1-naphthaldehyde gave the corresponding Schiff bases (1-3b) and (1-3c), respectively. Reaction of Schiff bases (2) and (3) with palladium acetate or Na₂PdCl₄ afforded complexes of the type PdL₂ (4,5), where L=deprotonated Schiff base. The molecular structure of the nitro-salicylaldehyde 4-Bpin palladium complex (5b) was characterized by an X-ray diffraction study. All new palladium compounds have been characterized fully and tested for their antifungal activity against Aspergillus niger and Aspergillus flavus.     

Rapid separation of phenylthiohydantoin amino acids: ambient pressure ion-mobility mass spectrometry (IMMS)

An electrospray ionization (ESI) ambient pressure ion-mobility spectrometer (APIMS) interfaced to an orthogonal reflector time-of-flight mass spectrometer (TOFMS) was evaluated for the first time as a detector for the identification of phenylthiohydantoin (PTH)-derivatized amino acids, the final products in the Edman sequencing process of peptides and proteins. The drift and flight times of the twenty common PTH amino acids were characterized by a well-defined 2-D mobility/mass spectral pattern. The combination of mobility/mass modes of analysis gave rise to a unique trend-line formation for the series of PTH amino acids. In addition, each PTH amino acid had a unique reduced mobility constant K(o), thus enabling the differentiation of all the amino acid derivatives including the PTH-leucine and PTH-isoleucine isomers. More importantly it was shown that it was possible to resolve a complete reference mixture of PTH amino acids in a single experimental run in less than 1 min. Detection limits for the PTH amino acids were found to range from 1.04 to 3.52 ng; indicating that the limits of detection were less than 17.0 pmol for all of the PTH amino acids.     

Synthesis,crystal structure and luminescent property of a novel H<Subscript>2</Subscript>O-bridged cobalt(II) polymer with one-dimensional chain structure

The coordination compound [Co(C₁₀H₇COO)₂(H₂O)₃]_2n · 4nH₂O was prepared by the reaction of 1-naphthoic acid and cobalt(II) acetate tetrahydrate in basic solution, and was fully characterized by X-ray diffraction, element analysis, FTIR, TG-DTA and luminescent spectra. In the crystal the six-coordinated Co(II) centers are linked into one-dimensional zigzag chains by water molecules, which are further assembled into a two-dimensional network through weak inter-chain C–H···π interactions. The solid complex exhibits favorable fluorescent properties similar to those of free ligand at room temperature, which can be assigned to the intraligand electronic transfer.     

The preparation of precisely defined lithium isotope mixtures

The need for accurate (< 0.06%) isotopic blends of ⁶Liand ⁷Li is explained and their preparation is discussed. It is shown that lithium must be determined at an accuracy level better than 0.035%. Four methods — acid-base titration with hydrochloric acid or benzoic acid, and weighing as sulphate or carbonate — were tested and improved for the precise and accurate analysis of lithium hydroxide solutions. The results of these four methods for a 0.1 M solution agreed within ± 0.02%. The preparation of pure isotopically enriched lithium hydroxide solutions, with specially purified cation- and anion-exchangers, is described. The prepared products contain as little as 100 μg of other alkali metals and 50 μg of alkaline-earth metals per gram of lithium, and are sufficiently free of anions to permit accurate chemical assay of lithium. No changes in the isotopic compositions of 99% ⁶Li or 99.99% ⁷Li were detected during the treatment.     

Conversion of 3-benzoyl-1-methyl-4-phenyl-γ-piperidol by arylamines and arylhydrazines. Synthesis of 3-arylamino-1-oxo-1-phenylpropanes and 1,3-diarylpyrazoles and their fragmentation under electron impact

It has been established that on heating, 3-benzoyl-4-hydroxy-1-methyl-4-phenylpiperidine is ring-opened in the presence of arylamines by a type of retroaldol reaction, with subsequent transamination of the intermediate Mannich base and the formation of 3-arylamino-1-oxo-1-phenylpropanes. When using arylhydrazines this γ-piperidol is recyclized with the formation of 1,3-diarylpyrazoles and their 4,5-dihydro derivatives. The mass spectral behavior of a series of 3-arylamino-substituted 1-phenylpropanones has been studied. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1486–1495, October, 2007.