Regularity of ideals and their radicals

In this paper we compare the regularityreg I of a homogeneous idealI⊂K[x ₁,...,x _n] with that of its radical. We prove that regI ≥ reg ifR/I is a BuchsbaumR-module or ifI is a monomial ideal. We also prove the same result when defines a non-singular curve inP ³ under some additional hypotheses     

Separation, identification, and quantification of selected withanolides in plant extracts of Withania somnifera by HPLC-UV(DAD)--positive ion electrospray ionisation-mass spectrometry

This paper describes a method for separation, identification, and quantification of selected withanolides in Withania somnifera plant extracts by HPLC-UV(DAD)-Mass Spectrometry (HPLC-MS). Withaferin-A (WS-3), 12-deoxywithastramonolide (WS-12DS), Withanolide A (WS-1), and Withanone (WS-2) were used as external standards. The compounds were isolated from Withania somnifera by repeated column chromatography of the root extract and their identity was established by 1H- and 13C-NMR and mass spectral data. The compounds were chromatographed on a Merck (250 x 4.6 mm ID, 5 microm) column and analyzed by Electrospray Ionization on a mass spectrometer in Selected Ion Mode (SIM). For quantification, [M + Na]+ ions were monitored. Linear calibration curves were obtained in the concentration range of 1.50 microg/mL to 6.5 microg/mL. The method was applied successfully to the detection and quantification of the said withanolides in a number of samples.     

β-(Methoxy-(substitutedphenyl)-methyl)-γ-butyrolactones: A short synthesis from cinnamyl acetate

A simple and short synthesis has been revealed for the preparation of (±) β-(Methoxy-(substitutedphenyl)-methyl)-γ-butyrolactones. The reaction of cinnamyl acetate with Mn(OAc)₃ · 2H₂O in boiling acetic acid containing acetic anhydride gave the products 2 and 3, which further cyclized in 3% H₂SO₄/CH₃OH to afford the butyrolactones (8a–e), which are intermediates of lignin, in good to moderate yields.     

Thin-Layer Chromatographic Enantioseparation of (RS)-Etodolac Using Indirect Approach

JPC – Journal of Planar Chromatography – Modern TLC - Enantioseparation of (RS)-etodolac was achieved by an indirect approach. Extraction of the drug (RS)-etodolac (Etd) was done from...     

Synthesis of Novel Drug‐Like Small Molecules Based on Quinoxaline Containing Amino Substitution at C‐2

A series of novel “drug‐like” small molecules based on quinoxaline containing amino substitution at C‐2 were synthesized. All these molecules were prepared either via the reaction of 2‐phenyl‐3‐(piperazin‐1‐yl)quinoxaline with acyl bromides or benzyl bromides or various carboxylic acids or via the reaction of 2‐chloro‐3‐phenylquinoxaline with various amines. The structures of these novel compounds were confirmed by spectral analysis. The strategy used is simple and efficient and afforded good yields of quinoxaline derivatives.     

Augmentation of heat transfer by twisted tape inserts during condensation of R-134a inside a horizontal tube

An experimental investigation has been carried out to find the heat transfer coefficient during condensation of R-134a vapor inside a horizontal tube. Experiments were conducted for the condensation of R-134a inside a plain tube and tubes with different twisted tape inserts. Twisted tapes with different twisted ratios of 6, 9, 12 and 15 were inserted in the refrigerant side, one by one, in the full length of test-condenser. For each inserted tube and the plain tube, test runs were carried out for the mass velocities of 92, 110, 128 and 147 kg/s-m². An empirical correlation has also been developed to predict the enhanced heat transfer coefficient.     

Implicit boundary method for determination of effective properties of composite microstructures

A method that uses a structured grid to perform micromechanical analysis for determining effective properties of a composite microstructure is presented. This approach eliminates the need for constructing a mesh that has nodes along the interfaces between constituent materials of the composite. Implicit boundary method is used to ensure that interface conditions are satisfied at the material boundaries. In this method, solution structures for test and trial functions are constructed using approximate step functions such that the interface conditions are satisfied, even if there are no nodes on the material interface boundary. Since a structured grid does not conform to the geometry of the analysis domain, the geometry of the microstructure is defined independently using equations of the interface boundary curves/surfaces. Structured grids that overlap the geometry are easy to generate, and the elements in the grid are regular shaped and undistorted. A numerical example is presented to demonstrate that the proposed solution structure accurately models the solution across material interface, and convergence analysis is performed to show that the method converges as the grid density is increased. Fiber reinforced microstructures are analyzed to compute the effective elastic properties using both 2D and 3D models to show that the results match closely with the ones available in the literature.     

Detection of turbulent/non-turbulent interface for an axisymmetric turbulent jet: evaluation of known criteria and proposal of a new criterion

In this paper, we evaluate several criteria for the detection of turbulent/non-turbulent interface using direct numerical simulation and particle image velocimetry data of an axisymmetric turbulent jet. The possibility of identifying the interface from information available in wholefield velocity data alone is also explored. The present results using a Concentration thresholding technique compare well against available results obtained using a similar detection criterion. It is noted that Concentration and Vorticity criteria are difficult to apply with standard PIV data and therefore a new criterion based on azimuthal vorticity and streamwise velocity—quantities available from such data, is proposed. The proposed criterion scores over previously employed criteria in terms of its simplicity of evaluation, and can possibly be applied to other flows not tested here. The instantaneous location of the interface as detected from the different criteria differs substantially. However, the conditionally averaged streamwise velocity, azimuthal vorticity, and Reynolds shear stress across the interface obtained from the new criterion, as well as from the previous criteria, agree reasonably well against available results. The present work further suggests that different criteria, even with slightly sub-optimal threshold value, can provide quantitatively similar ensemble-averaged results.     

Analysis of radial segregation of granular mixtures in a rotating drum

This paper considers the segregation of a granular mixture in a rotating drum. Extending a recent kinematic model for grain transport on sandpile surfaces to the case of rotating drums, an analysis is presented for radial segregation in the rolling regime, where a thin layer is avalanching down while the rest of the material follows rigid body rotation. We argue that segregation is driven not just by differences in the angle of repose of the species, as has been assumed in earlier investigations, but also by differences in the size and surface properties of the grains. The cases of grains differing only in size (slightly or widely) and only in surface properties are considered, and the predictions are in qualitative agreement with observations. The model yields results inconsistent with the assumptions for more general cases, and we speculate on how this may be corrected. Received 4 June 1999 and Received in final form 28 September 1999