Beurling zeta functions, generalised primes, and fractal membranes

We study generalised prime systems P (1 < p(1) <= p(2) <= ..., with p(j) is an element of R tending to infinity) and the associated Beurling zeta function zeta p(s) = Pi(infinity)(j=1)(1 - p(j)(-s))(-1). Under appropriate assumptions, we establish various analytic properties of zeta p(s), including its analytic continuation, and we characterise the existence of a suitable generalised functional equation. In particular, we examine the relationship between a counterpart of the Prime Number Theorem (with error term) and the properties of the analytic continuation of zeta p(s). Further we study 'well-behaved' g-prime systems, namely, systems for which both the prime and integer counting function are asymptotically well-behaved. Finally, we show that there exists a natural correspondence between generalised prime systems and suitable orders on N-2. Some of the above results are relevant to the second author's theory of 'fractal membranes', whose spectral partition functions are given by Beurling-type zeta functions, as well as to joint work of that author and R. Nest on zeta functions attached to quasicrystals.

Correlations between microphysical properties of large-scale semi-transparent cirrus and the state of the atmosphere

By making use of TOVS Path-B satellite retrievals and ECMWF reanalyses, correlations between bulk microphysical properties of large-scale semi-transparent cirrus (visible optical thickness between 0.7 and 3.8) and thermodynamic and dynamic properties of the surrounding atmosphere have been studied on a global scale. These clouds constitute about half of all high clouds. The global averages (from 60°N to 60°S) of mean ice crystal diameter, De, and ice water path (IWP) of these clouds are 55 μm and 30 g m−2, respectively. IWP of these cirrus is slightly increasing with cloud-top temperature, whereas De of cold cirrus does not depend on this parameter. Correlations between De and IWp of large-scale cirrus seem to be different in the midlatitudes and in the tropics. However, we observe in general stronger correlations between De and IWP and atmospheric humidity and winds deduced from the ECMWF reanalyses: De and IWP increase both with increasing atmospheric water vapour. There is also a good distinction between different dynamical situations: In humid situations, IWP is on average about 10 gm−2 larger in regions with strong large-scale vertical updraft only that in regions with strong large-scale horizontal winds only, whereas the mean De of cold large-scale cirrus decreases by about 10 μm if both strong large-scale updraft and horizontal winds are present.

The effects of dwarfing genes on seedling root growth of wheat

Most modern wheat cultivars contain major dwarfing genes, but their effects on root growth are unclear. Near-isogenic lines (NILs) containing Rht-B1b, Rht-D1b, Rht-B1c, Rht8c, Rht-D1c, and Rht12 were used to characterize the effects of semi-dwarfing and dwarfing alleles on root growth of 'Mercia' and 'Maris Widgeon' wheat cultivars. Wheat seedlings were grown in gel chambers, soil-filled columns, and in the field. Roots were extracted and length and dry mass measured. No significant differences in root length were found between semi-dwarfing lines and the control lines in any experiment, nor was there a significant difference between the root lengths of the two cultivars grown in the field. Total root length of the dwarf lines (Rht-B1c, Rht-D1c, and Rht12) was significantly different from that of the control although the effect was dependent on the experimental methodology; in gel chambers root length of dwarfing lines was increased by; 40% while in both soil media it was decreased (by 24-33%). Root dry mass was 22-30% of the total dry mass in the soil-filled column and field experiments. Root length increased proportionally with grain mass, which varied between NILs, so grain mass was a covariate for the analysis of variance. Although total root length was altered by dwarf lines, root architecture (average root diameter, lateral root: total root ratio) was not affected by reduced height alleles. A direct effect of dwarfing alleles on root growth during seedling establishment, rather than a secondary partitioning effect, was suggested by the present experiments.

The long-term effect of active immunization against inhibin in goats

This experiment addresses the long-term effect of active immunization of goats against a recombinant ovine inhibin alpha subunit (roIHN-alpha). In late anestrus 100 mu g of roINH-alpha was administered to 40 pluriparous Boer goat does, followed, 4 weeks later, by a booster injection. Weekly blood samples were drawn to monitor the inhibin binding capacity with the aid of a radio-tracer binding assay. From the onset until 48 h after the end of each estrus, follicular development and ovulation rate were monitored at 24 h intervals by transrectal ultrasonography. Beginning in August and continuing into January, does were mated at every other estrus, and submitted to transcervical embryo collection. Seven months after the first immunization, the does were mated again and permitted to carry to term. All immunized does produced inhibin antibodies, an elevated titre being first detected 2 weeks after primary immunization. Maximum titres were reached after 6 weeks, i.e. 2 weeks after the booster injection. Thereafter, in the course of the following 32 weeks, the titre subsided gradually. The does started cycling by mid-August. At that stage the average number of follicles more than 4 mm in diameter, ovulations and total embryos and ova recovered were 14.7 (+/- 2.3), 5.3 (+/- 0.7) and 4.4 (+/- 1.0), respectively. A steady decline followed and in January the corresponding means were: 5.2 (+/- 0.6) follicles, 3.1 (+/- 0.6) ovulations and 1.2 (+/- 0.4) embryos and ova recovered. When mated toward the end of the breeding season, 85% of the does became pregnant to the first mating and 73% went to term. Healthy kids were born, the average litter size being 2.2 (+/- 0.1). In conclusion, immunization of goats against a recombinant inhibin alpha-subunit proved to be a practicable means of producing embryos for transfer purposes. After about half a year, when the inhibin antibody titre has subsided, it is possible to return the does to the breeding flock without risking complications with normal breeding activity. (c) 2009 Elsevier Inc. All rights reserved.

Monthly average temperature modelling

This research is associated with the goal of the horticultural sector of the Colombian southwest, which is to obtain climatic information, specifically, to predict the monthly average temperature in sites where it has not been measured. The data correspond to monthly average temperature, and were recorded in meteorological stations at Valle del Cauca, Colombia, South America. Two components are identified in the data of this research: (1) a component due to the temporal aspects, determined by characteristics of the time series, distribution of the monthly average temperature through the months and the temporal phenomena, which increased (El Nino) and decreased (La Nina) the temperature values, and (2) a component due to the sites, which is determined for the clear differentiation of two populations, the valley and the mountains, which are associated with the pattern of monthly average temperature and with the altitude. Finally, due to the closeness between meteorological stations it is possible to find spatial correlation between data from nearby sites. In the first instance a random coefficient model without spatial covariance structure in the errors is obtained by month and geographical location (mountains and valley, respectively). Models for wet periods in mountains show a normal distribution in the errors; models for the valley and dry periods in mountains do not exhibit a normal pattern in the errors. In models of mountains and wet periods, omni-directional weighted variograms for residuals show spatial continuity. The random coefficient model without spatial covariance structure in the errors and the random coefficient model with spatial covariance structure in the errors are capturing the influence of the El Nino and La Nina phenomena, which indicates that the inclusion of the random part in the model is appropriate. The altitude variable contributes significantly in the models for mountains. In general, the cross-validation process indicates that the random coefficient model with spatial spherical and the random coefficient model with spatial Gaussian are the best models for the wet periods in mountains, and the worst model is the model used by the Colombian Institute for Meteorology, Hydrology and Environmental Studies (IDEAM) to predict temperature.

API-CALC 1.0: a computer program for calculating the average probability of identity allowing for substructure, inbreeding and the presence of close relatives

Individual identification via DNA profiling is important in molecular ecology, particularly in the case of noninvasive sampling. A key quantity in determining the number of loci required is the probability of identity (PIave), the probability of observing two copies of any profile in the population. Previously this has been calculated assuming no inbreeding or population structure. Here we introduce formulae that account for these factors, whilst also accounting for relatedness structure in the population. These formulae are implemented in API-CALC 1.0, which calculates PIave for either a specified value, or a range of values, for F-IS and F-ST.

Changes in milk composition and processing properties during the spring flush period

The period, known to UK farmers and processors as the "spring flush", when the cows' diet changes from dry feed to spring pasture, has long been established as a time of change in milk properties and processing characteristics. Although it is believed to be a time when problems in processing are most likely to occur (e.g. milk that does not form clots or forms weak gels during cheesemaking), there is little evidence in the literature of detailed changes in milk composition and their impact on product manufacture. In this study, a range of physicochemical properties were analysed in milk collected from five commercial dairy herds before, during and after the spring flush period of 2006. In particular, total and ionic calcium contents of milk were studied in relation to other parameters including rennet clotting, acid gel properties, heat coagulation, alcohol stability, micelle size and zeta potential. Total divalent cations were significantly reduced from 35.4 to 33.4 mmol.L-1 during the study, while ionic calcium was reduced from 1.48 to 1.40 mmol.L-1 over the same period. Many parameters varied significantly between the sample dates. However, there was no evidence to suggest that any of the milk samples would have been unsuitable for processing - e.g. there were no samples that did not form clots with chymosin within a reasonable time or formed especially weak rennet or acid gels. A number of statistically significant correlations were found within the data, including ionic calcium concentration and pH; rennet clotting time (RCT) and micelle diameter; and RCT and ethanol stability. Overall, while there were clear variations in milk composition and properties over this period, there was no evidence to support the view that serious processing problems are likely during the change from dry feed to spring pasture.

The role of terminal tyrosine residues in the formation of tripeptide nanotubes: a crystallographic insight

Terminally protected acyclic tripeptides containing tyrosine residues at both termini self-assemble into nanotubes in crystals through various non-covalent interactions including intermolecular hydrogen bonds. The nanotube has an average internal diameter of 5 angstrom (0.5 nm) and the tubular ensemble is developed through the hydrogen-bonded phenolic-OH side chains of tyrosine (Tyr) residues [Org. Lett. 2004, 6, 4463]. We have synthesized and studied several tripeptides 3-6 to probe the role of tyrosine residues in nanotube structure formation. These peptides either have only one Tyr residue at N- or C-termini or they have one or two terminally located phenylalanine (Phe) residues. These tripeptides failed to form any kind of nanotubular structure in the solid state. Single crystal X-ray diffraction studies of these peptides 3-6 clearly demonstrate that substitution of any one of the terminal Tyr residues in the Boc-Tyr-X-Tyr-OMe (X=VaI or Ile) sequence disrupts the formation of the nanotubular structure indicating that the presence of two terminally located Tyr residues is vital for nanotube formation. (c) 2006 Elsevier Ltd. All rights reserved.

A new motif in the formation of peptide nanotubes: the crystallographic signature

Terminally protected acyclic tripeptides Boc-Tyr(1)-Val(2)-Tyr(3)-OMe 1 and Boc-Tyr(1)-lle(2)-Tyr(3)-OMe 2 self-assemble into nanotubes in crystals through various noncovalent interactions with an average internal diameter of 5 Angstrom (0.5 nm), and the tubular ensemble is developed through the hydrogen-bonded side chains of tyrosine residues. The inside of the hollow nanotubular structures is hydrophilic; however, no solvent molecules have been crystallographically detected.

Calcium removal from milk by ion exchange

Calcium removal, using Duolite C433 ion exchange resin, was faster from permeate than from milk. Almost all calcium could be removed, suggesting a fairly rapid conversion from both soluble calcium phosphate and from micellar calcium to ionic calcium. Calcium reduction from milk is accompanied by an increase in pH, a reduction in ionic calcium, an increase in ethanol stability and an increase in the rennet coagulation time. There is a gradual increase in the average casein micelle size with calcium removal, up to a point where the micelle size increases dramatically. Zeta potential becomes more negative with calcium removal. At higher levels of calcium removal, the changes are not reversible, on reducing pH to its original value. For goat's milk, over the range 0-20% total calcium removal, relatively small reductions in total calcium gave rise to proportionally larger reductions in ionic calcium in a ratio of about 1:3.2.

The effect of vessel diameter on time dependent gas hold-up variations in highly viscous impeller agitated liquids

Time dependent gas hold-up generated in the 0.3 and 0.6 m diameter vessels using high viscosity castor oil and carboxy methyl cellulose (CMC) solution was compared on the basis of impeller speed (N) and gas velocity (V-G). Two types of hold-up were distinguished-the hold-up due to tiny bubbles (epsilon(ft)) and total hold-up (epsilon(f)), which included large and tiny bubbles. It was noted that vessel diameter (i.e. the scale of operation) significantly influences (i) the trends and the values of epsilon(f) and epsilon(ft), and (ii) the values of tau (a constant reflecting the time dependency of hold-up). The results showed that a scale independent correlation for gas hold-up of the form epsilon(f) or epsilon(ft) = A(N or P-G/V)(a) (V-G)(b), where "a" and "b" are positive constants is not appropriate for viscous liquids. This warrants further investigations into the effect of vessel diameter on gas hold-up in impeller agitated high viscosity liquids (mu or mu(a) > 0.4 Pa s). (C) 2003 Elsevier B.V. All rights reserved.

High pressure induced water uptake characteristics of Thai glutinous rice

Glutinous rice (or sticky rice) has to be soaked in water over an extended period of time before cooking. Soaking provides some of the water needed for starch gelatinisation to occur during cooking. The extent of water uptake during soaking is known to be influenced by temperature. This paper explores the use of very high pressures up to 600 MPa to accelerate water uptake kinetics during soaking. Changes occurring in length, diameter and moisture content were determined as a function of soaking time, pressure and temperature. The results show that length and diameter are positively correlated with all three parameters. However, the expansion ratios are not very high: the maximum length expansion ratio observed was 1.2, while the maximum diameter expansion ratio was 1. 1. Given these low values, it was possible to model water uptake kinetics by using the well-known Fickian model applied to a finite cylinder, assuming uniform average dimensions and effective diffusion coefficient. The results showed that the overall rates of water uptake and the equilibrium moisture content increased with pressure and temperature. The effective diffusion coefficient, on the other hand, did not follow the same trend. Temperature influenced the effective diffusion coefficient below 300 MPa, but had a marginal effect at higher pressures. Moreover, the effective diffusion coefficient increased with temperature between 20 and 50 degrees C, but dropped at higher temperatures. This drop can be attributed to the gelatinisation of starch, which restricts the transport of water. Regardless, it is possible to increase the quantity of water absorbed by rice and the rate at which it is absorbed, by using high pressures and temperatures. (c) 2004 Elsevier Ltd. All rights reserved.

Diameter of parallelogramic honeycomb torus

The determination of the diameter of an interconnection network is essential in evaluating the performance of the network. Parallelogramic honeycomb torus is an attractive alternative to classical torus network due to smaller vertex degree, and hence, lower implementation cost. In this paper, we present the expression for the diameter of a parallelogramic, honeycomb torus, which extends a known result about rhombic: honeycomb torus. (c) 2005 Elsevier Ltd. All rights reserved.