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.     

Stereoselective synthesis of alpha-C-glucosyl serine and alanine via a cross-metathesis/cyclization strategy

C-Glycosyl amino acids represent stable mimics of monomeric units within natural O-linked glycoproteins. Olefin cross-metathesis has been used to provide alkene precursors for a mercury(II)-mediated cyclization, yielding alpha-C-glucosyl serine and alanine.     

Three-dimensional elastic wave scattering by a layer containing vertical periodic fractures

Elastic wave scattering off a layer containing a single set of vertical periodic fractures is examined using a numerical technique based on the work of Hennion et al. [J. Acoust. Soc. Am. 87, 1861-1870 (1990)]. This technique combines the finite element method and plane wave method to simulate three-dimensional scattering off a two-dimensional fractured layer structure. Each fracture is modeled explicitly, so that the model can simulate both discrete arrivals of scattered waves from individual fractures and multiply scattered waves between the fractures. Using this technique, we examine changes in scattering characteristics of plane elastic waves as a function of wave frequency, angle of incidence, and fracture properties such as fracture stiffness, height, and regular and irregular spacing.     

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.     

A theorem of Cohen on parapolar spaces

We give an elementary proof of a critical lemma of Arjeh Cohen used in his fundamental paper giving an axiomatic characterization of Grassmann spaces of finite singular rank.     

SR XRF and micro-PIXE studies on ancient metallurgy of thirteen Dacian gold bracelets

A thorough microscopic investigation by SR XRF and micro-PIXE brings insight into the probable techniques used in the manufacture of thirteen Dacian gold bracelets, one of the most spectacular archaeological finds ever on the territory of Romania.