Gelatinisation of starch in mixtures of sugars. II. Application of differential scanning calorimetry

Differential scanning calorimetry was used to investigate the effect of mixtures of glucose and fructose, and five types of honeys on starch gelatinisation. At a 1:1 starch:water ratio, glucose generally increased the enthalpy (DeltaH(gel)) and temperatures (T-onset, T-peak and T-end) of gelatinisation more than fructose. Upon mixing, DeltaH(gel) of the low-temperature endotherm decreased in comparison to the sole sugars, but was fairly constant (7.7 +/- 0.33 J/g dry starch). DeltaH(gel) of the high-temperature endotherm increased with the fructose content. For both endotherms, the gelatinisation temperatures were unchanged (CV less than or equal to 3%) for the mixtures. With the honeys (moisture, 14.9-18.0%; fructose, 37.2-44.0%; glucose, 28.3-31.9%) added at 1.1-4.4 g per g dry starch, the enthalpy and temperatures of gelatinisation did not vary significantly (CV less than or equal to 6%). Typical thermograms are presented, and the results are interpreted in the light of the various proposed mechanisms for starch gelatinisation in sugar-water systems, total sugar content and possible sugar-sugar interactions. The thermograms were broader in the presence of the sugars and honeys, and a biphasic character was consistently exhibited. The application of an exponential equation to the gelatinisation temperatures of the starch-honey mixtures revealed an opposing influence of fructose and glucose during gelatinisation. The mechanism of starch gelatinisation may be better understood if techniques could be perfected to quantify breakage and formation of hydrogen bonds in the starch granules, and suggested techniques are discussed. (C) 2004 Elsevier Ltd. All rights reserved.

On the Schrodinger equation involving a critical Sobolev exponent and magnetic field

We consider the semilinear Schrodinger equation -Delta(A)u + V(x)u = Q(x)vertical bar u vertical bar(2* -2) u. Assuming that V changes sign, we establish the existence of a solution u not equal 0 in the Sobolev space H-A,V(1) + (R-N). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator -Delta(A).

Sharp Sobolev inequality involving a critical nonlinearity on a boundary

We consider the solvability of the Neumann problem for the equation -Delta u + lambda u = 0, partial derivative u/partial derivative v = Q(x)vertical bar u vertical bar(q-2)u on partial derivative Omega, where Q is a positive and continuous coefficient on partial derivative Omega, lambda is a parameter and q = 2(N - 1)/(N - 2) is a critical Sobolev exponent for the trace embedding of H-1(Omega) into L-q(partial derivative Omega). We investigate the joint effect of the mean curvature of partial derivative Omega and the shape of the graph of Q on the existence of solutions. As a by product we establish a sharp Sobolev inequality for the trace embedding. In Section 6 we establish the existence of solutions when a parameter lambda interferes with the spectrum of -Delta with the Neumann boundary conditions. We apply a min-max principle based on the topological linking.

Specific heat capacity of Australian honeys from 35 to 165C as a function of composition using differential scanning calorimetry

Modulated temperature differential scanning calorimetry was used to investigate the specific heat capacity (C-p) of 10 Australian honeys within the processing and handling temperatures. The values obtained were found to be different from the literature values at certain temperatures, and are not predictable by the additive model. The C-p of each honey exhibited a cubic relationship (P < 0.001) with the temperature (T, C). In addition, the moisture (M, %), fructose (F, %) and glucose (G, %) contents of the honeys influenced their C-p. The following equation (r(2) = 0.92) was proposed for estimating C-p of honey, and is recommended for use in the honey industry and in research: C = 996.7 + 1.4 x 10(-3)T + 5.6 x 10(-5)T(2) - 2.4 x 10(-7)T(3) - 56.5M - 25.8F - 31.0G + 1.5(M * F) + 1.8(M * G) + 0.8(F * G) - 4.6 x 10(-2) (M * F * G).

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Student Difficulties with units in differential equations in modelling contexts

First-year undergraduate engineering students' understanding of the units of factors and terms in first-order ordinary differential equations used in modelling contexts was investigated using diagnostic quiz questions. Few students appeared to realize that the units of each term in such equations must be the same, or if they did, nevertheless failed to apply that knowledge when needed. In addition, few students were able to determine the units of a proportionality factor in a simple equation. These results indicate that lecturers of modelling courses cannot take this foundational knowledge for granted and should explicitly include it in instruction.

Integration of the Manakov-PMD Equation with Precomputed M(w) Matrices for PMD Simulation

A novel direct integration technique of the Manakov-PMD equation for the simulation of polarisation mode dispersion (PMD) in optical communication systems is demonstrated and shown to be numerically as efficient as the commonly used coarse-step method. The main advantage of using a direct integration of the Manakov-PMD equation over the coarse-step method is a higher accuracy of the PMD model. The new algorithm uses precomputed M(w) matrices to increase the computational speed compared to a full integration without loss of accuracy. The simulation results for the probability distribution function (PDF) of the differential group delay (DGD) and the autocorrelation function (ACF) of the polarisation dispersion vector for varying numbers of precomputed M(w) matrices are compared to analytical models and results from the coarse-step method. It is shown that the coarse-step method achieves a significantly inferior reproduction of the statistical properties of PMD in optical fibres compared to a direct integration of the Manakov-PMD equation.

Towards the in silico identification of class II restricted T-cell epitopes:a partial least squares iterative self-consistent algorithm for affinity prediction

Motivation: The immunogenicity of peptides depends on their ability to bind to MHC molecules. MHC binding affinity prediction methods can save significant amounts of experimental work. The class II MHC binding site is open at both ends, making epitope prediction difficult because of the multiple binding ability of long peptides. Results: An iterative self-consistent partial least squares (PLS)-based additive method was applied to a set of 66 pep- tides no longer than 16 amino acids, binding to DRB1*0401. A regression equation containing the quantitative contributions of the amino acids at each of the nine positions was generated. Its predictability was tested using two external test sets which gave r pred =0.593 and r pred=0.655, respectively. Furthermore, it was benchmarked using 25 known T-cell epitopes restricted by DRB1*0401 and we compared our results with four other online predictive methods. The additive method showed the best result finding 24 of the 25 T-cell epitopes. Availability: Peptides used in the study are available from http://www.jenner.ac.uk/JenPep. The PLS method is available commercially in the SYBYL molecular modelling software package. The final model for affinity prediction of peptides binding to DRB1*0401 molecule is available at http://www.jenner.ac.uk/MHCPred. Models developed for DRB1*0101 and DRB1*0701 also are available in MHC- Pred

Solving Differential Equations by Parallel Laplace Method with Assured Accuracy

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30

A Dichotomy for Ordinary Differential Equations in a Banach Space

A dichotomysimilar property for a class of homogeneous differential equations in an arbitrary Banach space is introduced. By help of them, existence of quasi bounded solutions of the appropriate nonhomogeneous equation is proved.

Properties of Lp (K)-Solutions of Linear Nonhomogeneous Impulsive Differential Equations with Unbounded Linear Operator

Sufficient conditions for the existence of Lp(k)-solutions of linear nonhomogeneous impulsive differential equations with unbounded linear operator are found. An example of the theory of the linear nonhomogeneous partial impulsive differential equations of parabolic type is given.

Nonlinear Time-Fractional Differential Equations in Combustion Science

MSC 2010: 34A08 (main), 34G20, 80A25

Differential acid-base regulation in various gills of the green crab Carcinus maenas: Effects of elevated environmental pCO2

Euryhaline decapod crustaceans possess an efficient regulation apparatus located in the gill epithelia, providing a high adaptation potential to varying environmental abiotic conditions. Even though many studies focussed on the osmoregulatory capacity of the gills, acid-base regulatory mechanisms have obtained much less attention. In the present study, underlying principles and effects of elevated pCO2 on acid-base regulatory patterns were investigated in the green crab Carcinus maenas acclimated to diluted seawater. In gill perfusion experiments, all investigated gills 4-9 were observed to up-regulate the pH of the hemolymph by 0.1-0.2 units. Anterior gills, especially gill 4, were identified to be most efficient in the equivalent proton excretion rate. Ammonia excretion rates mirrored this pattern among gills, indicating a linkage between both processes. In specimen exposed to elevated pCO2 levels for at least 7 days, mimicking a future ocean scenario as predicted until the year 2300, hemolymph K+ and ammonia concentrations were significantly elevated, and an increased ammonia excretion rate was observed. A detailed quantitative gene expression analysis revealed that upon elevated pCO2 exposure, mRNA levels of transcripts hypothesized to be involved in ammonia and acid-base regulation (Rhesus-like protein, membrane-bound carbonic anhydrase, Na+/K+-ATPase) were affected predominantly in the non-osmoregulating anterior gills.

The larvae of congeneric gastropods showed differential responses to the combined effects of ocean acidification, temperature and salinity

The tolerance and physiological responses of the larvae of two congeneric gastropods, the intertidal Nassarius festivus and subtidal Nassarius conoidalis, to the combined effects of ocean acidification (PCO2 at 380, 950, 1250 ppm), temperature (15, 30 degrees C) and salinity (10, 30 psu) were compared. Results of three-way ANOVA on cumulative mortality after 72-h exposure showed significant interactive effects in which mortality increased with pCO(2) and temperature, but reduced at higher salinity for both species, with higher mortality being obtained for N. conoidalis. Similarly, respiration rate of the larvae increased with temperature and pCO(2) level for both species, with a larger percentage increase for N. conoidalis. Larval swimming speed increased with temperature and salinity for both species whereas higher pCO(2) reduced swimming speed in N. conoidalis but not N. festivus. The present findings indicated that subtidal congeneric species are more sensitive than their intertidal counterparts to the combined effects of these stressors. (c) 2014 Elsevier Ltd. All rights reserved.