Some Industrial Applications of Linear Programming

Three examples of the applications of linear programming are given, drawn from the manufacture of plywood, the distribution of grain, and industrial fermentation. In each of these widely different industries there is a problem which can be treated quite precisely by a linear programming model. The quantities evaluated are in the first case, the plywood product mix with the maximum return; in the second case, the routings and transit credits for shipping grain with the minimum freight costs; and in the third case, the production schedule for the fermentation process which yields the minimum labour cost. In most cases, the results obtained could be extended to evaluate other factors, and in all cases the formulation of the problem in linear programming form led to a greater understanding of the industry concerned.     

The photoelectron spectrum and molecular geometry of bicyclo[2.1.1]hexane

The He(I) photoelectron spectrum of bicyclo[2.1.1]hexane shows excellent correlation with a theoretical spectrum based on the eigenvalues obtained in an ab initio calculation at the theoretical molecular geometry. By contrast, a calculation performed at the experimental geometry exhibits an effect of enhanced ring strain in showing a first ionization energy which is considerably lower than the experimental value. This observation offers experimental support for the recent claim that the published structure for bicyclo [2.1.1]hexane based on electron-diffraction measurements is incorrect. It also accounts for inconsistencies observed in the calculated values of some spin—spin coupling constants for substituted bicyclo[2.1.1]hexanes.     

Further correlations between fragment ion intensity and critical energy. Unimolecular covalent bond fragmentation

A correlation of fragment ion intensity with critical energy found in the collisional activation spectra of [C₄Ph]⁺˙ ions produced by electron impact can also be found in the unimolecular mass-analysed ion kinetic energy spectra of these ions. The P(E) functions of the unimolecular and collisionally activated ions should differ not only in width but also in structure and therefore, the hypothesis that P(E) functions do not have an important effect on these correlations is tested successfully.     

Concise preparation of amino-5,6,7,8-tetrahydroquinolines and amino-5,6,7,8-tetrahydroisoquinolines via catalytic hydrogenation of acetamidoquinolines and acetamidoisoquinolines

A method to prepare amino-substituted 5,6,7,8-tetrahydroquinolines and 5,6,7,8-tetrahydroisoquinolines via catalytic hydrogenation of the corresponding acetamido-substituted quinolines and isoquinolines followed by acetamide hydrolysis is described. The yields of the products are good when the acetamido substituent is present on the pyridine ring and moderate with the acetamido substituent on the benzene ring. This method has also been applied to the regioselective reduction of quinoline substrates bearing other substituents (R = OMe, CO(2)Me, Ph).     

Enzymatic resolution of bicyclic 1-heteroarylamines using Candida antarctica lipase B

Candida antarctica lipase B has been used to kinetically resolve a structurally diverse series of bicyclic 1-heteroaryl primary amines by enantioselective acetylation. High yields of either enantiomer could be obtained with excellent enantioselectivity (90-99% ee), while the undesired enantiomer could, in some cases, be recycled by thermal racemization. The absolute stereochemistry of the products was confirmed by an X-ray crystal structure.     

Semiempirical local spin: Theory and implementation of the ZILSH method for predicting Heisenberg exchange constants of polynuclear transition metal complexes

The local spin formalism ( 3 ) for computing expectation values 〈S_A · S_B〉 that appear in the Heisenberg spin model has been extended to semiempirical single determinant wave functions. An alternative derivation of expectation values in restricted and unrestricted cases is given that takes advantage of the zero differential overlap (ZDO) approximation. A formal connection between single determinant wave functions (which are not in general spin eigenfunctions) and the Heisenberg spin model was established by demonstrating that energies of single determinants that are eigenfunctions of the local spin operators with eigenvalues corresponding to high‐spin radical centers are given by the same Heisenberg coupling constants {J_AB} that describe the true spin states of the system. Unrestricted single determinant wave functions for transition metal complexes are good approximations of local spin eigenfunctions when the metal d orbitals are local in character and all unpaired electrons on each metal have the same spin (although spins on different metals might be reversed). Good approximations of the coupling constants can then be extracted from local spin expectation values 〈S_A · S_B〉 energies of the single determinant wave functions. Once the coupling constants are obtained, diagonalization of the Heisenberg spin Hamiltonian provides predictions of the energies and compositions of the spin states. A computational method is presented for obtaining coupling constants and spin‐state energies in this way for polynuclear transition metal complexes using the intermediate neglect of differential overlap Hamiltonian parameterized for optical spectroscopy (INDO/S) in the ZINDO program. This method is referred to as ZILSH, derived from ZINDO, Davidson's local spin formalism, and the Heisenberg spin model. Coupling constants and spin ground states obtained for 10 iron complexes containing from 2 to 6 metals are found to agree well with experimental results in most cases. In the case of the complex [Fe₆O₃(OAc)₉(OEt)₂(bpy)₂]⁺, a priori predictions of the coupling constants yield a ground‐state spin of zero, in agreement with variable‐temperature magnetization data, and corroborate spin alignments proposed earlier on the basis of structural considerations. This demonstrates the potential of the ZILSH method to aid in understanding magnetic interactions in polynuclear transition metal complexes. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

At-column heating and a resistively heated, liquid-cooled thermal modulator for a low-resource bench-top GC x GC

A transportable GC x GC instrument is under development for on-site applications that would benefit from the enhanced resolution and powers of detection, which can be achieved by this method. In the present study, a low-resource GC x GC instrument using an electrically heated and liquid-cooled single-stage thermal modulator that requires no cryogenic materials is evaluated. The instrument also uses at-column heating, thus eliminating the need for a convection oven to house the two columns. The stainless-steel modulator tube is coated with PDMS, which can be heated to 350 degrees C for sample injection into the second-dimension column. The modulator is cooled to -30 degrees C by a 100 mL/min flow of PEG by means of a commercial liquid chiller and a small recirculating pump. Resistive heating of the modulator tube is provided by a programmable power supply, which uses a voltage program that results in increasing modulator temperature during an analysis. This, together with more rapid cooling by the use of a liquid cooling medium, results in reduced solute breakthrough following each heating cycle as the modulator cools to a temperature where quantitative trapping resumes. As a result, modulated peak widths at half-height of less than 40 ms are observed. Design and performance details are presented along with chromatograms of gasoline and an essential oil sample.