The intersection problem for K_4-e designs

A G-design of order n is a pair (P,B) where P is the vertex set of the complete graph K-n and B is an edge-disjoint decomposition of K-n into copies of the simple graph G. Following design terminology, we call these copies ''blocks''. Here K-4 - e denotes the complete graph K-4 with one edge removed. It is well-known that a K-4 - e design of order n exists if and only if n = 0 or 1 (mod 5), n greater than or equal to 6. The intersection problem here asks for which k is it possible to find two K-4 - e designs (P,B-1) and (P,B-2) of order n, with \B-1 boolean AND B-2\ = k, that is, with precisely k common blocks. Here we completely solve this intersection problem for K-4 - e designs.

d-cube decompositions of K-n/K-m

Necessary conditions on n, m and d are given for the existence of an edge-disjoint decomposition of K-n\K-m into copies of the graph of a d-dimensional cube. Sufficiency is shown when d = 3 and, in some cases, when d = 2(t). We settle the problem of embedding 3-cube decompositions of K-m into 3-cube decompositions of K-n; where n greater than or equal to m.

On the extent of genetic variation for transpiration efficiency in sorghum

A glasshouse study examined 49 diverse sorghum lines for variation in transpiration efficiency. Three of the 49 lines grown were Sorghum spp, native to Australia; one was the major weed Johnson grass (Sorghum halepense), and the remaining 45 lines were cultivars of Sorghum bicolor. All plants were grown under non-limiting water and nutrient conditions using a semi-automatic pot watering system designed to facilitate accurate measurement of water use. Plants were harvested 56-58 days after sowing and dry weights of plant parts were determined. Transpiration efficiency differed significantly among cultivars. The 3 Australian native sorghums had much lower transpiration efficiency than the other 46 cultivars, which ranged from 7.7 to 6.0 g/kg. For the 46 diverse cultivars, the ratio of range in transpiration efficiency to its l.s.d. was 2.0, which was similar to that found among more adapted cultivars in a previous study. This is a significant finding as it suggests that there is likely to be little pay-off from pursuing screening of unadapted material for increased variation in transpiration efficiency. It is necessary, however, also to examine absolute levels of transpiration efficiency to determine whether increased levels have been found. The cultivar with greatest transpiration efficiency in this study (IS9710) had a value 9% greater (P < 0.05) than the accepted standard for adapted sorghum cultivars. The potential impact of such an increase in transpiration efficiency warrants continued effort to capture it. Transpiration efficiency has been related theoretically and experimentally to the degree of carbon isotope discrimination in leaf tissue in sorghum, which thus offers a relatively simple selection index. In this study, the variation in transpiration efficiency was not related simply to carbon isotope discrimination. Significant associations of transpiration efficiency with ash content and indices of photosynthetic capacity were found. However, the associations were not strong. These results suggest that a simple screening technique could not be based on any of the measures or indices analysed in this study. A better understanding of the physiological basis of the observed genetic differences in transpiration efficiency may assist in developing reliable selection indices. It was concluded that the potential value of the improvement in transpiration efficiency over the accepted standard and the degree of genetic variation found warrant further study on this subject. It was suggested that screening for genetic variation under water-limiting conditions may provide useful insights and should be pursued.

Percutaneous absorption of sunscreen agents from liquid paraffin: Self-association of octyl salicylate and effects on skin flux

This study provides an investigation of the availability of octyl salicylate (OS), a common sunscreen agent, from liquid paraffin and the effect of OS on skin permeability. A model membrane system to isolate the vehicle effect from membrane permeability has been developed. Partitioning of OS between liquid paraffin and aqueous receptor phases was conducted. Partition coefficients increased with increase in OS concentration. A range of OS concentrations in liquid paraffin was diffused across human epidermis and synthetic membranes into 4% bovine serum albumin in phosphate-buffered saline and 50% ethanol. Absorption profiles of OS obtained from silicone and low-density polyethylene (LDPE) membranes were similar to each other but higher than for the high-density polyethylene [HDPE (3 times)] membrane and human epidermis (15 times). The steady state fluxes and apparent permeability coefficients (K-p') obtained from the diffusion studies showed the same trends with all membranes, except for the HDPE membrane which showed greater increase in flux and K-p' at concentrations above 30%. IR spectra showed that several bands of OS were shifted with concentrations, and the molecular models further suggested that the main contribution to the self-association is from non-1,4 van der Waals interactions.

2m-cycle systems of K2m+1/C-m

For all m greater than or equal to 3 the edges of complete graph on 2m + 1 vertices can he partitioned into m 2m-cycles and an m-cycle.

Emotions at multiple levels: An integration

Weiss and Isen have provided many supportive comments about the multi-level perspective, but also found limitations. Isen noted the importance of integrating affect, cognition, and motivation. Weiss commented similarly that the model lacked an integrating “thread.” He suggested that, to be truly multilevel, each level should constrain processes at other levels, and also provide guidance for the development of new concepts. Weiss also noted that the focus on biological processes was a strength of the model. I respond by suggesting that these very biological processes may constitute the “missing” thread. To illustrate this, I discuss some of the recent research on emotions in organizational settings, and argue that biology both constrains and guides theory at each level of the model. Based on this proposition, I revisit each of the five levels in the model, to demonstrate how this integration can be accomplished in this fashion. Finally, I address two additional points: aggregation bias, and the possibility of extending the model to include higher levels of industry and region.

The mu-way intersection problem for m-cycle systems

An m-cycle system of order upsilon is a partition of the edge-set of a complete graph of order upsilon into m-cycles. The mu -way intersection problem for m-cycle systems involves taking mu systems, based on the same vertex set, and determining the possible number of cycles which can be common to all mu systems. General results for arbitrary m are obtained, and detailed intersection values for (mu, m) = (3, 4), (4, 5),(4, 6), (4, 7), (8, 8), (8, 9). (For the case (mu, m)= (2, m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (Cc,m)=(3,3), see Milici and Quattrochi (Ars Combin. A 24 (1987) 175. (C) 2001 Elsevier Science B.V. All rights reserved.

The metamorphosis of lambda-fold 4-wheel systems into lambda-fold 4-cycle systems

A 4-wheel is a simple graph on 5 vertices with 8 edges, formed by taking a 4-cycle and joining a fifth vertex (the centre of the 4-wheel) to each of the other four vertices. A lambda -fold 4-wheel system of order n is an edge-disjoint decomposition of the complete multigraph lambdaK(n) into 4-wheels. Here, with five isolated possible exceptions when lambda = 2, we give necessary and sufficient conditions for a lambda -fold 4-wheel system of order n to be transformed into a lambda -fold Ccyde system of order n by removing the centre vertex from each 4-wheel, and its four adjacent edges (retaining the 4-cycle wheel rim), and reassembling these edges adjacent to wheel centres into 4-cycles.

Star decompositions of cubes

Let Sk denote the complete bipartite graph K-1k and let e,, denote the ii-cube. We prove that the obvious necessary conditions for the existence of an S-k-decomposition of Q(n) are sufficient.

On the intersection problem for 1-factorizations and near 1-factorizations of K-v

The number of 1-factors (near 1-factors) that mu 1-factorizations (near 1-factorizations) of the complete graph K-v, v even (v odd), can have in common, is studied. The problem is completely settled for mu = 2 and mu = 3.

Probing the effect of vehicles on topical delivery: Understanding the basic relationship between solvent and solute penetration using silicone membranes

Purpose. In the present study we examined the relationship between solvent uptake into a model membrane (silicone) with the physical properties of the solvents (e.g., solubility parameter, melting point, molecular weight) and its potential predictability. We then assessed the subsequent topical penetration and retention kinetics of hydrocortisone from various solvents to define whether modifications to either solute diffusivity or partitioning were dominant in increasing permeability through solvent-modified membranes. Methods. Membrane sorption of solvents was determined from weight differences following immersion in individual solvents, corrected for differences in density. Permeability and retention kinetics of H-3-hydrocortisone, applied as saturated solutions in the various solvents, were determined over 48 h in horizontal Franz-type glass diffusion cells. Results. Solvent sorption into the membrane could be related to differences in solubility parameters, MW and hydrogen bonding (r(2) = 0.76). The actual and predicted volume of solvent sorbed into the membrane was also found to be linearly related to Log hydrocortisone flux, with changes in both diffusivity and partitioning of hydrocortisone observed for the different solvent vehicles. Conclusions. A simple structure-based predictive model can be applied to the sorption of solvents into silicone membranes. Changes in solute diffusivity and partitioning appeared to contribute to the increased hydrocortisone flux observed with the various solvent vehicles. The application of this predictive model to the more complex skin membrane remains to be determined.

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations. (C) 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:504-520, 2001.

Individual and societal bases of national identity - A comparative multi-level analysis

In a previous study (Jones and Smith, 1999) we established that much the same core pattern of national identity characterizes many developed countries. Using the national identity module from the 1995 International Social Survey Programme, we identified two dimensions of national identity: an ascriptive dimension resembling the concept of ethnic identity described in the historical and theoretical literature, and a voluntarist dimension closer to the notion of civic identity. Some writers view these dimensions in terms of a historical sequence but we find that both constructs coexist in the minds of individual respondents in the nations we examine (we exclude Bulgaria and the Philippines from the present but not the earlier analysis). The dataset used for the multilevel analyses reported here consists of 28 589 respondents in the remaining 21 countries included in the national identity database for the 1995 round of surveys. The macrosociological literature on national identity does not offer well-defined predictions about what precise patterns of national identification we might expect to find among the masses of the developed countries. There are, however, recurring themes from which one can construct plausible hypotheses about how countries might differ according to their level of development, broadly conceived. Thus, we hypothesize that forces such as post-industrialism and globalization tend to favour the more open voluntaristic form of national identity over the more restrictive ascribed form. We develop different multi-level models in order to evaluate specific hypotheses pertaining to such issues, by simultaneously relating individual and societal characteristics to the relative strength of individual commitment to these different types of national identity.

Hepatocyte [H-3]-palmitate uptake: effect of albumin surface charge modification

The role of plasma proteins on the cellular uptake of lipophilic substrates has perplexed investigators for many years. We tested the hypothesis that an ionic interaction between the protein-ligand complex and hepatocyte surface may be responsible for supplying more ligand to the cell for uptake. The surface-charged groups on albumin were modified to yield proteins having a range of isoelectric points (ALB, ALBs, ALBm, ALBe had values of 4.8-5.0, 4.5-4.7, 3.0-3.5, 8.4-8.6, respectively). [H-3]-Palmitate uptake studies were performed with adult rat hepatocyte suspensions using similar unbound ligand fractions in the presence of the different binding proteins. Mass spectrometry, isoelectric focusing (pI), and heptane : water partitioning were used to determine protein molecular weight, pI, and protein-palmitate equilibrium binding constant, respectively. Hepatocyte [H-3]-palmitate clearance in the presence of ALBs and ALBm were significantly lower (p < 0.05) than ALB, whereas [H-3]-palmitate clearance in the presence of ALBe was significantly higher (p < 0.05) than ALB. The data were consistent with the notion that ionic interactions between extracellular protein-ligand complexes and the hepatocyte surface facilitate the uptake of long-chain fatty acids.