Optimal reparametrizations in the square root velocity framework

The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves, if the differ by a reparametrization leads to the quotient space of unparametrized curves. In this paper we study analytical and topological aspects of this construction for the class of absolutely continuous curves. We show that the square root velocity transform is a homeomorphism and that the action of the reparametrization semigroup is continuous. We also show that given two $C^1$-curves, there exist optimal reparametrizations realising the minimal distance between the unparametrized curves represented by them.

Liquid chromatographic-mass spectrometric method for determination of drug content uniformity of two commonly used dermatology medications in a split-tablet dosage form

Purpose: To develop and validate a simple, efficient and reliable Liquid chromatographic-mass spectrometric (LC-MS/MS) method for the quantitative determination of two dermatological drugs, Lamisil® (terbinafine) and Proscar® (finasteride), in split tablet dosage form. Methods: Thirty tablets each of the 2 studied medications were randomly selected. Tablets were weighed and divided into 3 groups. Ten tablets of each drug were kept intact, another group of 10 tablets were manually split into halves using a tablet cutter and weighed with an analytical balance; a third group were split into quarters and weighed. All intact and split tablets were individually dissolved in a water: methanol mixture (4:1), sonicated, filtered and further diluted with mobile phase. Optimal chromatographic separation and mass spectrometric detection were achieved using an Agilent 1200 HPLC system coupled with an Agilent 6410 triple quadrupole mass spectrometer. Analytes were eluted through an Agilent eclipse plus C8 analytical column (150 mm × 4.6 mm, 5 μm) with a mobile phase composed of solvent A (water) containing 0.1% formic acid and 5mM ammonium formate pH 7.5, and solvent B (acetonitrile mixed with water in a ratio A:B 55:45) at a flow rate of 0.8 mL min-1 with a total run time of 12 min. Mass spectrometric detection was carried out using positive ionization mode with analyte quantitation monitored by multiple reaction monitoring (MRM) mode. Results: The proposed analytical method proved to be specific, robust and adequately sensitive. The results showed a good linear fit over the concentration range of 20 - 100 ng mL-1 for both analytes, with a correlation coefficient (r2) ≥ 0.999 and 0.998 for finasteride and terbinafine, respectively. Following tablet splitting, the drug content of the split tablets fell outside of the proxy USP specification for at least 14 halves (70 %) and 34 quarters (85 %) of FIN, as well as 16 halves (80 %) and 37 quarters (92.5 %) of TBN. Mean weight loss, after splitting, was 0.58 and 2.22 % for FIN half- and quarter tablets, respectively, and 3.96 and 4.09 % for TBN half- and quarter tablets,respectively. Conclusion: The proposed LC-MS/MS method has successfully been used to provide precise drug content uniformity of split tablets of FIN and TBN. Unequal distribution of the drug on the split tablets is indicated by the high standard deviation beyond the accepted value. Hence, it is recommended not to split non-scored tablets especially, for those medications with significant toxicity

Properties of a method of fundamental solutions for the parabolic heat equation

We show that a set of fundamental solutions to the parabolic heat equation, with each element in the set corresponding to a point source located on a given surface with the number of source points being dense on this surface, constitute a linearly independent and dense set with respect to the standard inner product of square integrable functions, both on lateral- and time-boundaries. This result leads naturally to a method of numerically approximating solutions to the parabolic heat equation denoted a method of fundamental solutions (MFS). A discussion around convergence of such an approximation is included.

Applying Least Absolute Shrinkage Selection Operator and Akaike Information Criterion Analysis to Find the Best Multiple Linear Regression Models between Climate Indices and Components of Cow’s Milk

This study focuses on multiple linear regression models relating six climate indices (temperature humidity THI, environmental stress ESI, equivalent temperature index ETI, heat load HLI, modified HLI (HLI new), and respiratory rate predictor RRP) with three main components of cow’s milk (yield, fat, and protein) for cows in Iran. The least absolute shrinkage selection operator (LASSO) and the Akaike information criterion (AIC) techniques are applied to select the best model for milk predictands with the smallest number of climate predictors. Uncertainty estimation is employed by applying bootstrapping through resampling. Cross validation is used to avoid over-fitting. Climatic parameters are calculated from the NASA-MERRA global atmospheric reanalysis. Milk data for the months from April to September, 2002 to 2010 are used. The best linear regression models are found in spring between milk yield as the predictand and THI, ESI, ETI, HLI, and RRP as predictors with p-value < 0.001 and R2 (0.50, 0.49) respectively. In summer, milk yield with independent variables of THI, ETI, and ESI show the highest relation (p-value < 0.001) with R2 (0.69). For fat and protein the results are only marginal. This method is suggested for the impact studies of climate variability/change on agriculture and food science fields when short-time series or data with large uncertainty are available.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of-reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced-assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.