Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Linear and nonlinear microrheology of dense colloidal suspensions

The length and time scales accessible to optical tweezers make them an ideal tool for the examination of colloidal systems. Embedded high-refractive-index tracer particles in an index-matched hard sphere suspension provide 'handles' within the system to investigate the mechanical behaviour. Passive observations of the motion of a single probe particle give information about the linear response behaviour of the system, which can be linked to the macroscopic frequency-dependent viscous and elastic moduli of the suspension. Separate 'dragging' experiments allow observation of a sample's nonlinear response to an applied stress on a particle-by particle basis. Optical force measurements have given new data about the dynamics of phase transitions and particle interactions; an example in this study is the transition from liquid-like to solid-like behaviour, and the emergence of a yield stress and other effects attributable to nearest-neighbour caging effects. The forces needed to break such cages and the frequency of these cage breaking events are investigated in detail for systems close to the glass transition.

A model of net amino acid absorption and utilization by the portal-drained viscera of the lactating dairy cow

A more complete understanding of amino acid ( AA) metabolism by the various tissues of the body is required to improve upon current systems for predicting the use of absorbed AA. The objective of this work was to construct and parameterize a model of net removal of AA by the portal-drained viscera (PDV). Six cows were prepared with arterial, portal, and hepatic catheters and infused abomasally with 0, 200, 400, or 600 g of casein daily. Casein infusion increased milk yield quadratically and tended to increase milk protein yield quadratically. Arterial concentrations of a number of essential AA increased linearly with respect to infusion amount. When infused casein was assumed to have a true digestion coefficient of 0.95, the minimum likely true digestion coefficient for noninfused duodenal protein was found to be 0.80. Net PDV use of AA appeared to be linearly related to total supply (arterial plus absorption), and extraction percentages ranged from 0.5 to 7.25% for essential AA. Prediction errors for portal vein AA concentrations ranged from 4 to 9% of the observed mean concentrations. Removal of AA by PDV represented approximately 33% of total postabsorptive catabolic use, including use during absorption but excluding use for milk protein synthesis, and was apparently adequate to support endogenous N losses in feces of 18.4 g/d. As 69% of this use was from arterial blood, increased PDV catabolism of AA in part represents increased absorption of AA in excess of amounts required by other body tissues. Based on the present model, increased anabolic use of AA in the mammary and other tissues would reduce the catabolic use of AA by the PDV.

Effects of volatile fatty acid supply on their absorption and on water kinetics in the rumen of sheep sustained by intragastric infusions

Three sheep fitted with a ruminal cannula and an abomasal catheter were used to study water kinetics and absorption of VFA infused continuously into the rumen. The effects of changing VFA concentrations in the rumen by shifting VFA infusion rates were investigated in an experiment with a 3 x 3 Latin square design. On experimental days, the animals received the basal infusion rate of VFA (271 mmol/h) during the first 2 h. Each animal then received VFA at a different rate (135, 394, or 511 mmol/h) for the next 7.5 h. Using soluble markers (polyethylene glycol and Cr-EDTA), ruminal volume, liquid outflow, apparent water absorption, and VFA absorption rates were estimated. There were no significant effects of VFA infusion rate on ruminal volume and water kinetics. As the VFA infusion rate was increased, VFA concentration and osmolality in the rumen were increased and pH was decreased. There was a biphasic response of liquid outflow to changes in the total VFA concentration in the rumen, as both variables increased together up to a total VFA concentration of 80.1 mM, whereas, beyond that concentration, liquid outflow remained stable at an average rate of 407 mL/h. There were significant linear (P = 0.003) and quadratic (P = 0.001) effects of VFA infusion rate on the VFA absorption rate, confirming that VFA absorption in the rumen is mainly a concentration-dependent process. The proportion of total VFA supplied that was absorbed in the rumen was 0.845 (0.822, 0.877, and 0.910 for acetate, propionate, and butyrate, respectively). The molar proportions of acetate, propionate, and butyrate absorbed were affected by the level of VFA infusion in the rumen, indicating that this level affected to a different extent the absorption of the different acids.

Net nutrient absorption and liver metabolism in lactating dairy cows fed supplemental dietary biotin

The effect of feeding supplemental biotin on net absorption and metabolism of nutrients by the portal-drained viscera (PDV; the gut, pancreas, spleen and associated fat) and liver of lactating dairy cows was measured. Three cows in early to mid-lactation catheterised for measurements of net nutrient absorption and metabolism by the PDV and liver were fed a total-mixed ration with or without supplemental biotin at 20 mg/day using a switch-back design (ABA v. BAB) with three 2-week periods. There were no effects of feeding biotin on dry matter intake (22.2 kg/day), milk yield (29.5 kg/day) or milk composition. There was also no effect of feeding biotin on net release of glucose by the liver, net liver removal of glucose precursors (propionate, alanine, lactate) or net liver release of p-hydroxybutyrate. Feeding biotin increased net PDV release of ammonia. Reasons for the response are not certain, but a numerical increase in net PDV release of acetate suggests that rumen or hindgut fermentation was altered. Results of the present study do not support the hypothesis that supplemental biotin increases liver glucose production in lactating dairy cows.

Syntheses of two new 1D and 3D networks of Cu(II) and Co(II) using malonate and urotropine as bridging ligands: Crystal structures and magnetic studies

Two new metal-organic based polymeric complexes, [Cu-4(O2CCH2CO2)(4)(L)].7H(2)O (1) and [CO2(O2CCH2CO2)(2)(L)].2H(2)O (2) [L = hexamethylenetetramine (urotropine)], have been synthesized and characterized by X-ray crystal structure determination and magnetic studies. Complex 1 is a 1D coordination polymer comprising a carboxylato, bridged Cu-4 moiety linked by a tetradentate bridging urotropine. Complex 2 is a 3D coordination polymer made of pseudo-two-dimensional layers of Co(II) ions linked by malonate anions in syn-anticonformation which are bridged by bidentate urotropine in trans fashion, Complex 1 crystallizes in the orthothombic system, space group Pmmn, with a = 14,80(2) Angstrom, b = 14.54(2) Angstrom, c = 7.325(10) Angstrom, beta = 90degrees, and Z = 4. Complex 2 crystallizes in the orthorhombic system, space group Imm2, a = 7.584(11) Angstrom, b = 15.80(2) Angstrom, c = 6.939(13) Angstrom, beta = 90.10degrees(1), and Z = 4. Variable temperature (300-2 K) magnetic behavior reveals the existence of ferro- and antiferromagnetic interactions in 1 and only antiferromagnetic interactions in 2. The best fitted parameters for complex 1 are J = 13.5 cm(-1), J = -18.1 cm(-1), and g = 2.14 considering only intra-Cu-4 interactions through carboxylate and urotropine pathways. In case of complex 2, the fit of the magnetic data considering intralayer interaction through carboxylate pathway as well as interlayer interaction via urotropine pathway gave no satisfactory result at this moment using any model known due to considerable orbital contribution of Co(II) ions to the magnetic moment and its complicated structure. Assuming isolated Co(II) ions (without any coupling, J = 0) the shape of the chi(M)T curve fits well with experimental data except at very low temperatures.

A preliminary investigation of the impact of catechol-O-methyltransferase genotype on the absorption and metabolism of green tea catechins

Purpose Green tea is thought to possess many beneficial effects on human health. However, the extent of green tea polyphenol biotransformation may affect its proposed therapeutic effects. Catechol-O-methyltransferase (COMT), the enzyme responsible for polyphenolic methylation, has a common polymorphism in the genetic code at position 158 reported to result in a 40% reduction in enzyme activity in in vitro studies. The current preliminary study was designed to investigate the impact of COMT genotype on green tea catechin absorption and metabolism in humans. Methods Twenty participants (10 of each homozygous COMT genotype) were recruited, and plasma concentration profiles were produced for epigallocatechin gallate (EGCG), epigallocatechin (EGC), epicatechin gallate (ECG), epicatechin (EC) and 4′-O-methyl EGCG after 1.1 g of Sunphenon decaffeinated green tea extract (836 mg green tea catechins), with a meal given after 60 min. Results For the entire group, EGCG, EGC, EC, ECG and 4′-O-methyl EGCG reached maximum concentrations of 1.09, 0.41, 0.33, 0.16 and 0.08 μM at 81.5, 98.5, 99.0, 85.5 and 96.5 min, respectively. Bimodal curves were observed for the non-gallated green tea catechins EGC and EC as opposed to single-peaked curves for the gallated green tea catechins EGCG and ECG. No significant parametric differences between COMT genotype groups were found. Conclusions In conclusion, the COMT Val(158/108)Met does not appear to have a dramatic influence on EGCG absorption and elimination. However, further pharmacokinetic research is needed to substantiate these findings.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.