Spontaneous generation of optical activity in urea inclusion compounds vis-a-vis current theories

A novel test of recent theories of the origin of optical activity has been designed based on the inclusion of certain alkyl 2-methylhexanoates into urea channels.

Solution of a System of Generalized Abel Integral Equations Using Fractional Calculus

A method is presented for obtaining useful closed form solution of a system of generalized Abel integral equations by using the ideas of fractional integral operators and their applications. This system appears in solving certain mixed boundary value problems arising in the classical theory of elasticity.

Homogeneous precipitation from solution by urea hydrolysis: a novel chemical route to the a-hydroxides of nickel and cobalt

Homogeneous precipitation from solution by hydrolysis of urea at elevated temperatures (T=120 degrees C) yields novel ammonia-intercalated alpha-type hydroxide phases of the formula M(OH)(x)(NH3)(0.4)(H2O)(y)(NO3)(2-x) where x=2, y=0.68 for M=Ni and x=1.85, y=0 for M=Co. These triple-layered hexagonal phases (a=3.08+/-0.01 Angstrom, c=21.7+/-0.05 Angstrom) are more crystalline than similar phases obtained by chemical precipitation or electrosynthesis. This method can be adapted as a convenient chemical route to the bulk synthesis of alpha-hydroxides.

Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

Fractional power dependence of rate on activation energy for reactions with very low internal barriers

The dynamics of reactions with low internal barriers are studied both analytically and numerically for two different models. Exact expressions for the average rate,kI, are obtained by solving the associated first passage time problems. Both the average rate constant, kI, and the numerically calculated long-time rate constant, kL, show a fractional power law dependence on the barrier height for very low barriers. The crossover of the reaction dynamics from low to high barrier is investigated.

Effect of varying the proportion of molasses in the diet on intake, digestion and microbial protein production by steers

The present experiment was conducted to determine the efficiency of microbial protein production in the rumen and intake by cattle fed high-molasses diets. Intake and microbial crude protein (MCP) production were measured along with the concentration of rumen ammonia-nitrogen (N) and volatile fatty acids (VFA), pH and the rate of digestion of roughage in the rumen. Eight Brahman crossbred steers weighing 211 ± 19.3 (± s.d.) kg were used in a double 4 × 4 Latin square design. Steers were allocated to one of four total mixed rations: control (pangola hay only), 25M (25% molasses/urea mix + 75% hay), 50M (50% molasses/urea + 50% hay), and 75M (75% molasses/urea + 25% hay). The production and efficiency of production of MCP (EMCP) of the diet increased quadratically as the level of molasses in the diet increased. The EMCP from the molasses/urea mix was estimated as 166 g MCP/kg digestible organic matter (DOM), a relatively high value. Intake of dry matter (DM) and DOM increased quadratically, reaching a peak when molasses was ~50% (as fed) of the ration. Digestibility of DM increased quadratically and that of neutral detergent fibre decreased linearly with increasing level of molasses in the diet. Molasses inclusion in the diet had no effect on rumen pH, ammonia and VFA concentration in the rumen fluid, plasma urea-N, urine pH or ruminal fractional outflow rate of ytterbium-labelled particles and Cr-EDTA. It was concluded that a diet with a high level of molasses (>50%) and supplemented with adequate N had high EMCP, and that low MCP production was not a factor limiting intake or performance of cattle consuming high-molasses diets.

Effect of varying the proportion of molasses in the diet on intake, digestion and microbial protein production by steers

The present experiment was conducted to determine the efficiency of microbial protein production in the rumen and intake by cattle fed high-molasses diets. Intake and microbial crude protein (MCP) production were measured along with the concentration of rumen ammonia-nitrogen (N) and volatile fatty acids (VFA), pH and the rate of digestion of roughage in the rumen. Eight Brahman crossbred steers weighing 211 ± 19.3 (± s.d.) kg were used in a double 4 x 4 Latin square design. Steers were allocated to one of four total mixed rations: control (pangola hay only), 25M (25% molasses/urea mix + 75% hay), 50M (50% molasses/urea + 50% hay), and 75M (75% molasses/urea + 25% hay). The production and efficiency of production of MCP (EMCP) of the diet increased quadratically as the level of molasses in the diet increased. The EMCP from the molasses/urea mix was estimated as 166 g MCP/kg digestible organic matter (DOM), a relatively high value. Intake of dry matter (DM) and DOM increased quadratically, reaching a peak when molasses was ∼50% (as fed) of the ration. Digestibility of DM increased quadratically and that of neutral detergent fibre decreased linearly with increasing level of molasses in the diet. Molasses inclusion in the diet had no effect on rumen pH, ammonia and VFA concentration in the rumen fluid, plasma urea-N, urine pH or ruminal fractional outflow rate of ytterbium-labelled particles and Cr-EDTA. It was concluded that a diet with a high level of molasses (>50%) and supplemented with adequate N had high EMCP, and that low MCP production was not a factor limiting intake or performance of cattle consuming high-molasses diets.

Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Water stress induced alterations in ornithine aminotransferase of ragi (Eleusine coracana): Protection by proline against heat inactivation and denaturation by urea and guanidinium chloride

Water stress resulted in a specific response leading to a large and significant increase (80-fold) in free proline content of ragi (Eleusine coracana) leaves and seedlings. L-Proline protected ornithine aminotransferase, an enzyme in the pathway for proline biosynthesis, isolated from normal and stressed ragi leaves against heat inactivation and denaturation by urea and guanidinium chloride. The protection of the stressed enzyme by L-proline was much more complete than that of the enzyme isolated from normal leaves. While L-ornithine, one of the substrates, protected the stressed enzyme against inactivation, it enhanced the rate of inactivation of the normal enzyme. α-Ketoglutarate protected both the normal and stressed enzyme against inactivation and denaturation. These results support the suggestion that ornithine aminotransferase has undergone a structural alteration during water stress. In view of the causal relationship between elevated temperature and water stress of plants under natural conditions, the protection afforded by proline against inactivation and denaturation of the enzyme from stressed leaves assumes significance. These results provide an explanation for a possible functional importance of proline accumulation during water stress.

A comprehensive study of interference and clearance fit pins in large plates

Pin joints in structures are designed for interference, push or clearance fits. That is, the diameter of the pin is made greater than, equal to or less than the hole diameter. Consider an interference fit pin in a plate subjected to a continuously increasing in-plane load.

Annual nitrogen dynamics and urea fertilizer recoveries from a dairy pasture using 15N; effect of nitrification inhibitor DMPP and reduced application rates

Direct nitrogen (N) losses from pastures contribute to the poor nitrogen use efficiency of the dairy industry, though the exact fate of applied N and the processes involved are largely unknown. Nitrification inhibitors such as DMPP can potentially increase fertilizer N use efficiency (NUE), though few studies globally have examined the effectiveness of DMPP coated urea in pastures. This study quantified the NUE of DMPP combined with reduced application rates, and the effect on N dynamics and plant–soil interactions over an annual ryegrass/kikuyu rotation in Queensland, Australia. Labeled 15N urea and DMPP was applied over 7 winter applications at standard farmer (45 kg N ha−1) and half (23 kg N ha−1) rates. Fertilizer recoveries and NUE were calculated over 13 harvests, and the contribution of fertilizer and soil N estimated. Up to 85% of the annual N harvested was from soil organic matter. DMPP at the lower rate increased annual yields by 31% compared to the equivalent urea treatment with no difference to the high N rates. Almost 40% of the N added at the conventional fertilizer application rate as urea was lost to the environment; 80 kg N ha−1 higher than the low DMPP. Combining the nitrification inhibitor DMPP with reduced fertilizer application rates shows substantial potential to reduce N losses to the environment while sustaining productivity in subtropical dairy pastures.

Beyond fractional derivatives: local approximation of other convolution integrals

Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs O(t(2)) computations owing to the repeated evaluation of integrals over intervals that grow like t. Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled in finite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives (Singh & Chatterjee 2006 Nonlinear Dyn. 45, 183-206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with O(t) computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e. g. in stability analyses.

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7T

PURPOSE To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.