Modifications of the method of variation of parameters

AbstractIn spite of being a classical method for solving differential equations, the method of variation of parameters continues having a great interest in theoretical and practical applications, as in astrodynamics. In this paper we analyse this method providing some modifications and generalised theoretical results. Finally, we present an application to the determination of the ephemeris of an artificial satellite, showing the benefits of the method of variation of parameters for this kind of problems

Modification and physico-chemical properties of citrus pectin – Influence of enzymatic and acidic demethoxylation

Aim of the present study was to investigate the effect of the method of demethoxylation on the particle structure and techno-functional properties of pectins with different degree of methoxylation and distribution of free carboxyl groups. Two groups of model pectins, one with 57% and one with 42% degree of methoxylation have been prepared from one single commercial pectin. Modifications were performed by an acidic and two enzymatic methods using fungal and plant-derived pectin methyl esterases. Thermal stability was investigated by thermal analysis and water uptake was determined by a sorption and a capillary sucking method. The enzyme-treated pectins were thermally less stable than the acid-treated. The water uptake of enzyme-treated pectins was higher than in acid-treated samples in the sorption method and lower in the capillary sucking tests. The different behaviour is explained by differences in pH during demethoxylation and a co-occurring variation in sodium content. Both parameters affected intermolecular interactions of the pectin macromolecules in solution, which resulted in differences in the particle morphology. The effect of the distribution of free carboxyl groups (statistical or block-wise) on the techno-functional properties was more pronounced in high-methoxylated pectins than in low-methoxylated pectins

Doping of graphene by a Au(111) substrate: Calculation strategy within the local density approximation and a semiempirical van der Waals approach

We have performed a density functional study of graphene adsorbed on Au(111) surface using both a local density approximation and a semiempirical van der Waals approach proposed by Grimme, known as the DFT-D2 method. Graphene physisorbed on metal has the linear dispersion preserved in the band-structure, but the Fermi level of the system is shifted with respect to the conical points which results in a doping effect. We show that the type and amount of doping depends not only on the choice of the exchange-correlation functional used in the calculations, but also on the supercell geometry that models the physical system. We analyzed how the factors such as the in-plane cell parameter and interlayer spacing in gold influence the Fermi level shift and we found that even a small variation in these parameters may cause a transition from p-type to n-type doping. We have selected a reasonable set of model parameters and obtained that graphene is either undoped or at most slightly p-type doped on the clean Au(111) surface, which seems to be in line with experimental findings. On the other hand, modifications of the substrate lattice may induce larger doping up to 0.30-0.40 eV depending on the graphene-metal adsorption distance. The sensitivity of the graphene-gold interface to the structural parameters may allow to tune doping across the samples which could lead to possible applications in graphene-based electronic devices. We believe that the present remarks can be also useful for other studies based on the periodic DFT

Non-linear evolution of f(R) cosmologies I: methodology

We introduce the method and the implementation of a cosmological simulation of a class of metric-variation f(R) models that accelerate the cosmological expansion without a cosmological constant and evade solar-system bounds of small-field deviations to general relativity. Such simulations are shown to reduce to solving a non-linear Poisson equation for the scalar degree of freedom introduced by the f(R) modifications. We detail the method to efficiently solve the non-linear Poisson equation by using a Newton-Gauss-Seidel relaxation scheme coupled with multigrid method to accelerate the convergence. The simulations are shown to satisfy tests comparing the simulated outcome to analytical solutions for simple situations, and the dynamics of the simulations are tested with orbital and Zeldovich collapse tests. Finally, we present several static and dynamical simulations using realistic cosmological parameters to highlight the differences between standard physics and f(R) physics. In general, we find that the f(R) modifications result in stronger gravitational attraction that enhances the dark matter power spectrum by ~20% for large but observationally allowed f(R) modifications. More detailed study of the non-linear f(R) effects on the power spectrum are presented in a companion paper.Comment: 15 pages, 11 figure

In-vitro dissolution of vitreous silicate fibres according to EURIMA test guideline - Results of two Round Robins

The EURIMA (The European Insulation Manufacturers Association) test guideline "In-vitro acellular dissolution of man-made vitreous silicate fibres" provides a state-of-the-art method for measuring in-vitro dissolution rates relevant for evaluating the biopersistence of insulation wool fibres and other vitreous silicate fibres. Based on this guideline two Round Robins were conducted as well as specific investigations on the influence of selected test parameters. Nine and six laboratories, respectively, participated in the two Round Robins. The standard deviation between Kdis results obtained by different laboratories was slightly lower in the second Round Robin ranging from 24 to 61 % (highest for the low-soluble fibres). The relatively high inter-laboratory variation suggests that the equipment, setup and procedures should be specified in much more detail in a future test method. Key parameters to be kept constant are flow rate/surface area and liquid composition, and care should be taken to maintain constant conditions and eliminate outlier measurements. Α laboratory may use the method described in the guideline for quality assurance of maintained biosolubility and for development of alternative fibre modifications as the method is well suited for ranking different fibres with respect to dissolution coefficients within one laboratory. However, caution should be exercised when comparing values obtained by one laboratory to values obtained by another

Multicontrast MRI reconstruction with structure-guided total variation

Magnetic resonance imaging (MRI) is a versatile imaging technique that allows different contrasts depending on the acquisition parameters. Many clinical imaging studies acquire MRI data for more than one of these contrasts---such as for instance T1 and T2 weighted images---which makes the overall scanning procedure very time consuming. As all of these images show the same underlying anatomy one can try to omit unnecessary measurements by taking the similarity into account during reconstruction. We will discuss two modifications of total variation---based on i) location and ii) direction---that take structural a priori knowledge into account and reduce to total variation in the degenerate case when no structural knowledge is available. We solve the resulting convex minimization problem with the alternating direction method of multipliers that separates the forward operator from the prior. For both priors the corresponding proximal operator can be implemented as an extension of the fast gradient projection method on the dual problem for total variation. We tested the priors on six data sets that are based on phantoms and real MRI images. In all test cases exploiting the structural information from the other contrast yields better results than separate reconstruction with total variation in terms of standard metrics like peak signal-to-noise ratio and structural similarity index. Furthermore, we found that exploiting the two dimensional directional information results in images with well defined edges, superior to those reconstructed solely using a priori information about the edge location.Engineering and Physical Sciences Research Council (Grant ID: EP/H046410/1)This is the final version of the article. It first appeared from Society for Industrial and Applied Mathematics via http://dx.doi.org/10.1137/15M1047325

BayesPI - a new model to study protein-DNA interactions: a case study of condition-specific protein binding parameters for Yeast transcription factors

<p>Abstract</p> <p>Background</p> <p>We have incorporated Bayesian model regularization with biophysical modeling of protein-DNA interactions, and of genome-wide nucleosome positioning to study protein-DNA interactions, using a high-throughput dataset. The newly developed method (BayesPI) includes the estimation of a transcription factor (TF) binding energy matrices, the computation of binding affinity of a TF target site and the corresponding chemical potential.</p> <p>Results</p> <p>The method was successfully tested on synthetic ChIP-chip datasets, real yeast ChIP-chip experiments. Subsequently, it was used to estimate condition-specific and species-specific protein-DNA interaction for several yeast TFs.</p> <p>Conclusion</p> <p>The results revealed that the modification of the protein binding parameters and the variation of the individual nucleotide affinity in either recognition or flanking sequences occurred under different stresses and in different species. The findings suggest that such modifications may be adaptive and play roles in the formation of the environment-specific binding patterns of yeast TFs and in the divergence of TF binding sites across the related yeast species.</p

Analisis Pengaruh Parameter Mesin Bubut Konvensional Terhadap Kesilindrisan Permukaan Baja ST 42 Menggunakan Metode Box Behnken Design

The dimensional accuracy of the workpiece might be impacted by geometric variations that machines frequently experience. The geometric shape of the workpiece as a result of the machining process can be used to quantify machine quality and can take the form of cylindricality, smoothness, roundness, and other geometric shapes. The results of the workpiece surface's cylindricality will depend on machining parameters such engine rotation, feed speed, and feed depth. For the design of the research experiment and the data analysis, this study employs the Box Behnken Design in Response Surface Method that is figuring out the trial variation using 3 stages. The specimen used was ST 42 steel, and a DNMG 150404 carbide insert tool was used on a Pinacho L-1/260 conventional lathe to perform a total of 15 experimental modifications on the specimen. Furthermore, the cylindricity test was carried out using a dial indicator. The research results on the effect of parameters on surface cylindricity, namely engine speed with a Pvalue of 0.068, depth of feed with a Pvalue of 0.784, and feed speed with a Pvalue of 0.839, the three parameters were declared not to have a significant effect. The engine rotation parameter provides a contribution effect of 26.87%, the depth of feed is 0.52% and the feed speed is 0.28%

Pressure distribution and aerodynamic coefficients associated with heat addition to supersonic air stream adjacent to two-dimensional supersonic wing

The modifications in the pressure distributions and the aerodynamic coefficients associated with additions of heat to the two-dimensional supersonic in viscid flow field adjacetnt to the lower surface of of a 5-percent-thickness symmetrical circular-arc wing are presented in this report. The pressure distributions are obtained by the use of graphical method which gives the two-dimensional supersonic inviscid flow field obtained with moderate heat addition. The variation is given of the lift-drag ratio and of the aerodynamic coefficients of lift, drag, and moment with free stream Mach number, angle of attack, and parameters defining extent and amount of heat addition. The six graphical solutions used in this study included Mach numbers of 3.0 and 5.0 and angles of attack of 0 degrees and 2 degrees