3-Homogeneous latin trades

Let T be a partial latin square and L be a latin square with T subset of L. We say that T is a latin trade if there exists a partial latin square T' with T' boolean AND T = theta such that (LT) U T' is a latin square. A k-homogeneous latin trade is one which intersects each row, each column and each entry either 0 or k times. In this paper, we construct 3-homogeneous latin trades from hexagonal packings of the plane with circles. We show that 3-homogeneous latin trades of size 3 m exist for each m >= 3. This paper discusses existence results for latin trades and provides a glueing construction which is subsequently used to construct all latin trades of finite order greater than three. Crown Copyright (c) 2005 Published by Elsevier B.V. All rights reserved.

Adsorption of argon on homogeneous graphitized thermal carbon black and heterogeneous carbon surface

In this paper we investigate the effects of surface mediation on the adsorption behavior of argon at different temperatures on homogeneous graphitized thermal carbon black and on heterogeneous nongraphitized carbon black surface. The grand canonical Monte Carlo (GCMC) simulation is used to study the adsorption, and its performance is tested against a number of experimental data on graphitized thermal carbon black (which is known to be highly homogeneous) that are available in the literature. The surface-mediation effect is shown to be essential in the correct description of the adsorption isotherm because without accounting for that effect the GCMC simulation results are always greater than the experimental data in the region where the monolayer is being completed. This is due to the overestimation of the fluid–fluid interaction between particles in the first layer close to the solid surface. It is the surface mediation that reduces this fluid–fluid interaction in the adsorbed layers, and therefore the GCMC simulation results accounting for this surface mediation that are presented in this paper result in a better description of the data. This surface mediation having been determined, the surface excess of argon on heterogeneous carbon surfaces having solid–fluid interaction energies different from the graphite can be readily obtained. Since the real heterogeneous carbon surface is not the same as the homogeneous graphite surface, it can be described by an area distribution in terms of the well depth of the solid–fluid energy. Assuming a patchwise topology of the surface with patches of uniform well depth of solid–fluid interaction, the adsorption on a real carbon surface can be determined as an integral of the local surface excess of each patch with respect to the differential area. When this is matched against the experimental data of a carbon surface, we can derive the area distribution versus energy and hence the geometrical surface area. This new approach will be illustrated with the adsorption of argon on a nongraphitized carbon at 87.3 and 77 K, and it is found that the GCMC surface area is different from the BET surface area by about 7%. Furthermore, the description of the isotherm in the region of BET validity of 0.06 to 0.2 is much better with our method than with the BET equation.

Minimal Homogeneous Latin Trades

A latin trade is a subset of a latin square which may be replaced with a disjoint mate to obtain a new latin square. A d-homogeneous latin trade is one which intersects each row, each column and each entry of the latin square either 0 or d times. In this paper we give a construction for minimal d-homogeneous latin trades of size dm, for every integer d >= 3, and m >= 1.75d(2) + 3. We also improve this bound for small values of d. Our proof relies on the construction of cyclic sequences whose adjacent sums are distinct. (c) 2006 Elsevier B.V. All rights reserved.

Modelling ocular monochromatic aberrations using schematic eyes with homogeneous optical media

Previous research has indicated that schematic eyes incorporating aspheric surfaces but lacking gradient index are unable to model ocular spherical aberration and peripheral astigmatism simultaneously. This limits their use as wide-angle schematic eyes. This thesis challenges this assumption by investigating the flexibility of schematic eyes comprising aspheric optical surfaces and homogeneous optical media. The full variation of ocular component dimensions found in human eyes was established from the literature. Schematic eye parameter variants were limited to these dimensions. The levels of spherical aberration and peripheral astigmatism modelled by these schematic eyes were compared to the range of measured levels. These were also established from the literature. To simplify comparison of modelled and measured data, single value parameters were introduced; the spherical aberration function (SAF), and peripheral astigmatism function (PAF). Some ocular components variations produced a wide range of aberrations without exceeding the limits of human ocular components. The effect of ocular component variations on coma was also investigated, but no comparison could be made as no empirical data exists. It was demonstrated that by combined manipulation of a number of parameters in the schematic eyes it was possible to model all levels of ocular spherical aberration and peripheral astigmatism. However, the unique parameters of a human eye could not be obtained in this way, as a number of models could be used to produce the same spherical aberration and peripheral astigmatism, while giving very different coma levels. It was concluded that these schematic eyes are flexible enough to model the monochromatic aberrations tested, the absence of gradient index being compensated for by altering the asphericity of one or more surfaces.

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

Precipitation of magnesium ammonium phosphate from homogeneous solution

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Fundamental Pd0/PdII redox steps in cross-coupling reactions:homogeneous, hybrid homogeneous-heterogeneous to heterogeneous mechanistic pathways for C-C couplings

C–C bond-forming, cross-coupling reactions of organohalides with nucleophilic compounds, catalysed by palladium, are amongst the most important chemical reactions available to the synthetic chemist. The intimate mechanisms of these reactions, involving Pd0/PdII redox steps, have been of great historical interest and continue to be so. The myriad of possible mechanisms is reviewed in this chapter. The interplay of mononuclear Pd species with higher order Pd species, e.g. nanoclusters/nanoparticles are considered as being equally important in cross-coupling reaction mechanisms. A focus is placed on trichotomic behaviour of cross-coupling catalytic manifolds, from homogeneous to hybrid homogeneous–heterogeneous to truly heterogeneous behaviour. For the latter, surface chemistry and metal atom leaching (and various experimental techniques) are broadly discussed. It is now clear that mechanism for general cross‐coupling reactions, that is as presented to undergraduate students studying Chemistry degrees across the world, is undoubtedly more complex than first thought. New opportunities for catalyst design have therefore emerged in the area of Pd nanoparticles and nanocatalysis, with some wonderful applications especially in chemical biology, providing a snapshot of what the future might hold.

Selective in vitro glycosylation of recombinant proteins:semi-synthesis of novel homogeneous glycoforms of human erythropoietin

Background: A natural glycoprotein usually exists as a spectrum of glycosylated forms, where each protein molecule may be associated with an array of oligosaccharide structures. The overall range of glycoforms can have a variety of different biophysical and biochemical properties, although details of structure–function relationships are poorly understood, because of the microheterogeneity of biological samples. Hence, there is clearly a need for synthetic methods that give access to natural and unnatural homogeneously glycosylated proteins. The synthesis of novel glycoproteins through the selective reaction of glycosyl iodoacetamides with the thiol groups of cysteine residues, placed by site-directed mutagenesis at desired glycosylation sites has been developed. This provides a general method for the synthesis of homogeneously glycosylated proteins that carry saccharide side chains at natural or unnatural glycosylation sites. Here, we have shown that the approach can be applied to the glycoprotein hormone erythropoietin, an important therapeutic glycoprotein with three sites of N-glycosylation that are essential for in vivo biological activity. Results: Wild-type recombinant erythropoietin and three mutants in which glycosylation site asparagine residues had been changed to cysteines (His10-WThEPO, His10-Asn24Cys, His10-Asn38Cys, His10-Asn83CyshEPO) were overexpressed and purified in yields of 13 mg l−1 from Escherichia coli. Chemical glycosylation with glycosyl-β-N-iodoacetamides could be monitored by electrospray MS. Both in the wild-type and in the mutant proteins, the potential side reaction of the other four cysteine residues (all involved in disulfide bonds) were not observed. Yield of glycosylation was generally about 50% and purification of glycosylated protein from non-glycosylated protein was readily carried out using lectin affinity chromatography. Dynamic light scattering analysis of the purified glycoproteins suggested that the glycoforms produced were monomeric and folded identically to the wild-type protein. Conclusions: Erythropoietin expressed in E. coli bearing specific Asn→Cys mutations at natural glycosylation sites can be glycosylated using β-N-glycosyl iodoacetamides even in the presence of two disulfide bonds. The findings provide the basis for further elaboration of the glycan structures and development of this general methodology for the synthesis of semi-synthetic glycoproteins. Results: Wild-type recombinant erythropoietin and three mutants in which glycosylation site asparagine residues had been changed to cysteines (His10-WThEPO, His10-Asn24Cys, His10-Asn38Cys, His10-Asn83CyshEPO) were overexpressed and purified in yields of 13 mg l−1 from Escherichia coli. Chemical glycosylation with glycosyl-β-N-iodoacetamides could be monitored by electrospray MS. Both in the wild-type and in the mutant proteins, the potential side reaction of the other four cysteine residues (all involved in disulfide bonds) were not observed. Yield of glycosylation was generally about 50% and purification of glycosylated protein from non-glycosylated protein was readily carried out using lectin affinity chromatography. Dynamic light scattering analysis of the purified glycoproteins suggested that the glycoforms produced were monomeric and folded identically to the wild-type protein. Conclusions: Erythropoietin expressed in E. coli bearing specific Asn→Cys mutations at natural glycosylation sites can be glycosylated using β-N-glycosyl iodoacetamides even in the presence of two disulfide bonds. The findings provide the basis for further elaboration of the glycan structures and development of this general methodology for the synthesis of semi-synthetic glycoproteins

FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials

In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results indicate that whereas F LQ runs on average faster (or quite faster) than LM Q, nonetheless the quality of the bounds computed by both is about the same; moreover, it was revealed that when VAS-CF is run on our benchmark polynomials using F LQ, LM Q and min(F LQ, LM Q) all three versions run equally well and, hence, it is inconclusive which one should be used in the VAS-CF method.

On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.