Computing the algebraic relations of C-finite sequences and multisequences

We present an algorithm for computing generators for the ideal of algebraic relations among sequences which are given by homogeneous linear recurrence equations with constant coefficients. Knowing these generators makes it possible to use Gröbner basis methods for carrying out certain basic operations in the ring of such sequences effectively. In particular, one can answer the question whether a given sequence can be represented in terms of other given sequences.     

青霉素钾,青霉素亚砜和青霉素砜的薄层色谱法分离和鉴别

用薄层色谱法分离和鉴别青霉素钾、青霉素亚砜、青霉素砜，斑点清晰，重现性好，可作为中间体的检测。     

Fractionation of soybean phospholipids by high-performance liquid chromatography with an evaporative light-scattering detector

Phosphatidylcholine (PC) and phosphatidylethanolamine (PE) from 23 soybean lines with a wide range of fatty acid compositions were resolved into seven fractions by high-performance liquid chromatography (HPLC). Fraction identities were assigned from fatty acid compositions determined by gas chromatography (GC). A mass detector, i.e., an evaporative light-scattering detector, was used for HPLC quantification. The detector response was a power function of PC and PE concentrations. Various correction methods were applied to the detector response to obtain the best agreement between phospholipid (PL) fatty acid compositions determined by GC and that calculated from the corrected HPLC fraction percentages. The corrected HPLC fraction composition also was compared with that calculated from stereospecific distribution data using a 1-random-2-random hypothesis. Correlation between PL-fatty acid and HPLC-fraction percentages showed that genetic modification of soybean oil composition caused changes in PL species, which alter physical properties and may alter the physiological functions of PL in biomembranes.     

Uncharted islands of chatter instability in milling

This paper provides conclusive evidence that isolated islands of chatter vibration can exist in milling processes. Investigations show these islands are induced by the tool helix angle and act to separate regions of period-doubling and quasi-periodic behavior. Modeling efforts develop an analytical force model with three piecewise continuous regions of cutting that describe helix angle tools. Theoretical results examine the asymptotic stability trends for several different radial immersions and helix angles. In addition, new results are shown through the implementation of a temporal finite element analysis approach for delay equations written in the form of a state space model. Predictions are validated by a series of experimental tests that confirm the isolated island phenomenon.     

A new discretization of space for the solution of multi-dimensional population balance equations

In this work, a novel radial grid is combined with the framework of minimal internal consistency of discretized equations of Chakraborty and Kumar [2007. A new framework for solution of multidimensional population balance equations. Chemical Engineering Science 62, 4112-4125] to solve n-dimensional population balance equations (PBEs) with preservation of (n+1) instead of 2ⁿ properties required in direct extension of the 1-d fixed pivot technique of Kumar and Ramkrishna [1996a. On the solutions of population balance equation by discretization-I. A fixed pivot technique. Chemical Engineering Science 51, 1311-1332]. The radial grids for the solution of 2-d PBEs are obtained by intersecting arbitrarily spaced radial lines with arcs of arbitrarily increasing radii. The quadrilaterals obtained thus are divided into triangles to represent a non-pivot particle in 2-d space through three surrounding pivots by preserving three properties, the number and the two masses of the species that constitute the newly formed particle. Such a grid combines the ease of generating and handling a structured grid with the effectiveness of the framework of minimal internal consistency. A new quantitative measure to supplement visual comparison of two solutions is also introduced. The comparison of numerical and analytical solutions of 2-d PBEs for a number of uniform and selectively refined radial grids shows that the quality of solution obtained with radial grids is substantially better than that obtained with the direct extension of the 1-d fixed pivot technique to higher dimensions for both size independent and size dependent aggregation kernels. The framework of Chakraborty and Kumar combined with the proposed 2-d radial grid, which offers flexibility and achieves both reduced numerical dispersion and the ease of implementation, appears as an effective extension of the widely used 1-d fixed pivot technique to solve 2-d PBEs.     

A boundary meshless method using Chebyshev interpolation and trigonometric basis function for solving heat conduction problems

A boundary meshless method has been developed to solve the heat conduction equations through the use of a newly established two‐stage approximation scheme and a trigonometric series expansion scheme to approximate the particular solution and fundamental solution, respectively. As a result, no fundamental solution is required and the closed form of approximate particular solution is easy to obtain. The effectiveness of the proposed computational scheme is demonstrated by several examples in 2D and 3D. We also compare our proposed method with the finite‐difference method and the other meshless method showed in ?arler and Vertnik (Comput. Math. Appl. 2006; 51 :1269–1282). Excellent numerical results have been observed. Copyright © 2007 John Wiley & Sons, Ltd.     

The role of continuity in residual-based variational multiscale modeling of turbulence

This paper examines the role of continuity of the basis in the computation of turbulent flows. We compare standard finite elements and non-uniform rational B-splines (NURBS) discretizations that are employed in Isogeometric Analysis (Hughes et al. in Comput Methods Appl Mech Eng, 194:4135–4195, 2005). We make use of quadratic discretizations that are C ⁰-continuous across element boundaries in standard finite elements, and C ¹-continuous in the case of NURBS. The variational multiscale residual-based method (Bazilevs in Isogeometric analysis of turbulence and fluid-structure interaction, PhD thesis, ICES, UT Austin, 2006; Bazilevs et al. in Comput Methods Appl Mech Eng, submitted, 2007; Calo in Residual-based multiscale turbulence modeling: finite volume simulation of bypass transition. PhD thesis, Department of Civil and Environmental Engineering, Stanford University, 2004; Hughes et al. in proceedings of the XXI international congress of theoretical and applied mechanics (IUTAM), Kluwer, 2004; Scovazzi in Multiscale methods in science and engineering, PhD thesis, Department of Mechanical Engineering, Stanford Universty, 2004) is employed as a turbulence modeling technique. We find that C ¹-continuous discretizations outperform their C ⁰-continuous counterparts on a per-degree-of-freedom basis. We also find that the effect of continuity is greater for higher Reynolds number flows.     

高效液相色谱定量分析煤衍生重质产品

针对煤衍生重质产品的组分分析，以高效液相色谱（HPLC）研究了其定量问题。首先，建立高分辨的色谱分离体系，使组分得以好的分离和定性。对各分离组分定量测定采用了外标法和外标-定量因子法。实验表明准确定量的技术关键在于：溶解样品溶剂的合理选择；配制样品溶液浓度的正确控制；配制样品溶液的进一步处理技术。     

Chemical composition and antimicrobial activities of essential oil from the peel of bingtang sweet orange (Citrus sinensis Osbeck)

The chemical composition of the essential oil obtained from the peel of Bingtang sweet orange ( Citrus sinensis Osbeck) was analysed by gas chromatography and gas chromatography/mass spectrometry (GC/MS). Twenty-seven components were identified. The monoterpenes and sesquiterpene hydrocarbons with 96.03% (w/w) of the total oil were the principal compound groups. Among which, limonene was observed dominant (77.49%), followed by myrcene (6.27%), α-farnesene (3.64%), γ-terpinene (3.34%), α -pinene (1.49%), sabinene (1.29%) and other minor components. Results by disc diffusion method and minimum inhibitory concentration (MIC) determination method showed that the essential oil had a wide spectrum of antimicrobial activities against Staphylococcus aureus , Penicillium chrysogenum , Bacillus subtilis, Escherichia coli and Saccharomyces cerevisiae , with their inhibition zones ranging from 14.57 mm to 23.37 mm and the MIC ranging from 4.66 μL mL⁻¹ to 18.75 μL mL⁻¹.     

Partial-differential-equation-constrained amplitude-based shape detection in inverse acoustic scattering

In this article we discuss a formal framework for casting the inverse problem of detecting the location and shape of an insonified scatterer embedded within a two-dimensional homogeneous acoustic host, in terms of a partial-differential-equation-constrained optimization approach. We seek to satisfy the ensuing Karush–Kuhn–Tucker first-order optimality conditions using boundary integral equations. The treatment of evolving boundary shapes, which arise naturally during the search for the true shape, resides on the use of total derivatives, borrowing from recent work by Bonnet and Guzina [1–4] in elastodynamics. We consider incomplete information collected at stations sparsely spaced at the assumed obstacle’s backscattered region. To improve on the ability of the optimizer to arrive at the global optimum we: (a) favor an amplitude-based misfit functional; and (b) iterate over both the frequency- and wave-direction spaces through a sequence of problems. We report numerical results for sound-hard objects with shapes ranging from circles, to penny- and kite-shaped, including obstacles with arbitrarily shaped non-convex boundaries. Partial support for this work was provided by the US National Science Foundation under grant award CMS-0348484.