Cost operator algorithms for the transportation problem

A primal transportation algorithm is devised via post-optimization on the costs of a modified problem. The procedure involves altering the costs corresponding to the basic cells of the initial (primal feasible) solution so that it is dual feasible as well. The altered costs are then successively restored to their true values with appropriate changes in the optimal solution by the application of cell or area cost operators discussed elsewhere. The cell cost operator algorithm converges to optimum within (2T – 1) steps for primal nondegenerate transportation problems and [(2T + 1) min (m, n)] – 1 steps for primal degenerate transportation problems, whereT is the sum of the (integer) warehouse availabilities (also the sum of the (integer) market requirements) andm andn denote the number of warehouses and markets respectively. For the area cost operator algorithm the corresponding bounds on the number of steps areT and (T + 1) min (m, n) respectively.This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie—Mellon University, under Contract N00014-67-A-0314-0007 NR 047-048 with the U.S. Office of Naval Research.     

Synthesis and Structure of the New Compound La2O(CN2)2 Possessing an Interchanged Anion Proportion Compared to the Parent La2O2(CN2). Synthese und Kristallstruktur der neuen Verbindung La2O(CN2)2 mit einem vertauschten Anionenverhältnis gegenüber der Bezugsverbindung La2O2(CN2)

La₂O(CN₂)₂ was synthesized from a 1:1:2 molar reaction mixture of LaCl₃, LaOCl, and Li₂(CN₂) at 650 °C. Well developed single crystals were grown from a LiCl‐KCl flux. The crystal structure was refined as monoclinic (space group C2/c, Z = 2, a = 13.530(2) Å, b = 6.250(1) Å, c = 6.1017(9) Å, β = 104.81(2)°) from single crystal X‐ray diffraction data. The La³⁺ and (CN₂)^2— ions in the crystal structure of La₂O(CN₂)₂ can be compared to Fe³⁺ and S₂^2— ions in the cubic pyrite structure, being arranged like in a distorted NaCl type structure with their centers of gravity. In addition, the O^2— ions in La₂O(CN₂)₂ are occupying 1/4 of the tetrahedral voids formed by the arrangement of metal ions.     

Main‐chain viologen polymers with organic counterions exhibiting thermotropic liquid‐crystalline and fluorescent properties*

A series of viologen polymers with bromide, tosylate, and triflimide as counterions were prepared by either the Menshutkin reaction or metathesis reaction in a common organic solvent. Their polyelectrolyte behavior in methanol was determined by solution viscosity measurements, and their chemical structures were determined by Fourier transform infrared and Fourier transform NMR spectroscopy. They were characterized for their thermotropic liquid‐crystalline properties with a number of experimental techniques. Each of the viologen polymers with organic counterions had a low melting transition or fusion temperature above which it formed either a high‐order smectic phase or a low‐order smectic phase. Each of them also exhibited a smectic‐to‐isotropic transition. The ranges of the liquid‐crystalline phase were 80–88 °C for viologen polymers with tosylate as a counterion and 120–146 °C for viologen polymers with triflimide as a counterion. They had excellent thermal stability. The ranges of thermal stability were 288–329 °C for viologen polymers with tosylate as a counterion and 343–350 °C for viologen polymers with triflimide as a counterion. The fluorescence property for all of the viologen polymers in either aqueous or methanol solution was also included in this study. For example, the viologen polymer containing the 4,4′‐bipyridinium and p‐xylyl units along the backbone of the polymer chain with triflimide as a counterion had an absorption spectrum (λ_max = 265 nm), an excitation spectrum (λ_ex values = 357, 443, and 454 with monitoring at 533 nm), and an emission spectrum (λ_em = 536 nm with excitation at 430 and 450 nm) in methanol. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 659–674, 2002; DOI 10.1002/pola.10134     

In situ measurement of conformational changes in proteins at liquid interfaces by circular dichroism spectroscopy

A new circular dichroism (CD) spectroscopy technique for studying conformational changes in proteins in situ at the air-water interface is described. By using this technique, conformations of four proteins, viz., beta-casein, bovine serum albumin (BSA), lysozyme, and fibrinogen in the adsorbed state at the air-water interface have been studied. beta-Casein, which is predominantly in a disordered state in solution, assumes a beta-sheet conformation at the air-water interface. On the other hand, lysozyme and fibrinogen, which are alpha+beta-type proteins in solution, become beta-type proteins by completely transforming their alpha-helix structure into beta-sheets. Bovine serum albumin, which is an alpha-type protein in solution, loses its alpha-helix and becomes a disordered protein at the air-water interface. The results indicated that during unfolding and film formation at the interface, structural changes in proteins, regardless of their initial native state, follow the course of increasing beta-sheet and disordered structure and decreasing alpha-helix content. Although this seems to be the general trend, the exceptional case of BSA suggests, however, that this is not universal.     

On-Line Monitoring of the Photolysis of Benzyl Acetate and 3,5-Dimethoxybenzyl Acetate by Membrane Introduction Mass Spectrometry

Membrane introduction mass spectrometry (MIMS) allows on-line monitoring of the products of photolysis (254 nm) of benzyl acetate in aqueous methanol and 3,5-dimethoxybenzyl acetate in water. The reaction mixture is continuously exposed to a silicone membrane through which analyte molecules permeate into a triple quadrupole mass spectrometer for qualitative and quantitative analysis. Ionization is achieved by either isobutane or ammonia chemical ionization, and ions characteristic of the reactant ester and its products are monitored simultaneously and continuously. Three products, benzyl methyl ether, ethylbenzene, and bibenzyl are observed in the benzyl acetate photolysis. Two products, 3,5-dimethoxybenzyl alcohol and 3,5-dimethoxyethylbenzene, are formed in the photolysis of 3,5-dimethoxybenzyl acetate. Quantitation is achieved through calibration using external standard solutions and, in the case of benzyl methyl ether, tandem mass spectrometry is used to verify product identification. During the photolysis of benzyl acetate, benzyl methyl ether and ethylbenzene are produced at onset with similar efficiencies. For the 3,5-dimethoxy ester photolysis, performed in aqueous solution, the efficiency of formation of the polar product 3,5-dimethoxybenzyl alcohol is about 300 times greater than that of the nonpolar product 3,5-dimethoxyethylbenzene. The results show that the relative reaction rates are dependent on the solvent and on the photon intensity and are consistent with earlier off-line experiments by Pincock et al. which showed that the photolysis proceeds through both ion and radical pair intermediates. To the best of our knowledge, the work reported here describes the first analysis of the photochemistry of an aralkyl ester in water and the first use of on-line mass spectrometry in a mechanistic study.     

Selective reduction of anomeric azides to amines with tetrathiomolybdate: synthesis of beta-D-glycosylamines

A number of beta-d-glycosyl azide derivatives undergo reduction on treatment with tetrathiomolybdate to produce the corresponding beta-d-glycosylamines exclusively without anomerization under very mild and neutral reaction conditions. Acetyl, allyl, benzoyl, and benzyl protective groups are left untouched under the reaction conditions. An exclusive selectivity in the reduction of anomeric azides is observed, while the C-2 and C-6 azides are left untouched.     

Laser Raman spectra of mixed crystals of [(NH4)1−x Kx]2 SO4

The Raman spectra of mixed crystals of [(NH₄)_1?x K _x ]₂ SO₄ in the region 50–3400 cm^?1 at 293 K and below 223 K have been reported. At room temperature 293 K, as the concentration of K⁺ ion increases in the crystal up to 50%, the frequencies of the totally symmetric vibrations of SO ₄ ^2? and NH ₄ ⁺ ions increase and thereafter the frequency of SO ₄ ^2? vibration decreases and attains the value in K₂SO₄. This change in frequency up to 50% of potassium concentration is due to the breaking of hydrogen bonds of the type N-H...O. The behaviour of Raman intensities of A _g (v ₁) mode of SO ₄ ^2? for various concentrations (x=0, 0·03, 0·11, 0·5, 0·85) suggest that the phase transition changes from first order type to one of second order. The phase transition in mixed crystals of [(NH₄)_1?x K _x ]₂ SO₄ can be a cooperative phenomenon arising from a coupling between (NH₄)⁺ ions through hydrogen bonds with the distorted SO ₄ ^2? ions in the low temperature phase.     

PHOTOCHEMISTRY OF FLAVINS—I. CONVENTIONAL AND LASER FLASH PHOTOLYSIS STUDY OF ALLOXAZINE

Abstract— The photobleaching of alloxazine in buffered aqueous solution has been studied by means of flash photolysis using conventional and laser excitation sources. Several transient species have been characterized. The alloxazine triplet state (Λ_max 420 nm and 550 nm, times; = 9 μs) was identified with the aid of low-temperature comparison experiments in ethanol. Transient absorption with Λ_max 440 nm, which appears after decay of the triplet state, and whose second-order decay is pH-dependent, is postulated to be due to the semiquinone radical (AH₂*) and a radical derived from alloxazine by addition of water and loss of a hydrogen atom (HAOH*), which are in equilibrium with their conjugate cation radicals. The results of experiments in the presence of oxygen indicate that these species are not primarily formed from the triplet state. The enhanced second-order decay of the flavin radicals in oxygen-containing solutions is interpreted in terms of their reaction with the peroxy radicals. The proposed mechanisms account for the production of hydroxylated alloxazines.     

Synthesis and photochromic properties of molecules containing [e]-annelated dihydropyrenes. Two and three way pi-switches based on the dimethyldihydropyrene-metacyclophanediene valence isomerization

The syntheses of several new simple negative, a simple positive, and multiple negative photochromes containing the dihydropyrene-cyclophanediene photochromic system are described. The photo-openings of the negative photochromes, the [e]-annelated benzo (7), naphtho (9), anthro (11), furano (19), and triphenyleno (15) derivatives of the parent 2,7-di-tert-butyl-trans-10b,10c-dimethyl-dihydropyrene (5), as well as its 4,5-dibromo derivative (13), are described to give the corresponding cyclophanedienes, as well as their photoclosures and thermal closures back to the dihydropyrenes. These are compared to the results obtained for the positive photochrome dibenzo[e,l]dihydropyrene (21) and to the bis(dihydropyreno)chrysene (44) and the (dihydropyrenobenzo)(benzo)metacyclophanediene (47) photochromes, which have more than one photochromic switch present and thus have more than a simple "on-off" state. Thermodynamic data are obtained for the thermal closing reactions. The anthrodihydropyrene (12) has the fastest thermal closing (tau(1/2) = 20 min), while the furanodihydropyrene (19') has the slowest (tau(1/2) = 63 h) at 46 degrees C. An electrochemical readout of the state of the switch is demonstrated for the benzodihydropyrene (7).     

STUDIES ON THE INTERACTION OF EPOXY POLYMERS WITH HOMOPOLYUREAS

INTRODUCTION Epoxy resins are reactive polymers which when cured with a variety of chemicals lead to a host of useful thermosets. Since the epoxide is a strained ring, it readily undergoes addition and homopolymerization. The homopolymerization is a process catalysed by acids, bases, Lewis acids, t-amines as well as by inorganic salts.