On the convergence of the LJ search method

The convergence of the Luus-Jaakola search method for unconstrained optimization problems is established.Notation E _n Euclideann-space - f Gradient off(x) - ² f Hessian matrix - (·) ^T Transpose of (·) - I Index set {1, 2, ...,n} - [x _i1 ^*(j) ] Point around which search is made in the (j + 1)th iteration, i.e., [x _1l ^*(j) ,x _2l ^*(j) ,...,x _n1 ^*(j) ] - r _i ⁽ⁱ⁾ Range ofx _il ^*(i) in the (j + 1)th iteration - l ₁ min_i {r _i ⁽⁰⁾ } - l ₂ min_i {r _i ⁽⁰⁾ } - A _j Region of search in thejth iteration, i.e., {x E _n:x _il ^*(j-1) –0.5r _i ^(j-1) x _ix _il ^*(j-1) +0.5r _i ^(j-1) ,i I} - S _j Closed sphere with center origin and radius _j - Reduction factor in each iteration - 1– - (·) Gamma function Many discussions with Dr. S. N. Iyer, Professor of Electrical Engineering, College of Engineering, Trivandrum, India, are gratefully acknowledged. The author has great pleasure to thank Dr. K. Surendran, Professor, Department of Electrical Engineering, P.S.G. College of Technology, Coimbatore, India, for suggesting this work.     

Separation of rare earths by reverse phase partition chromatography

Journal of Radioanalytical and Nuclear Chemistry - Individual separation of rare earth isotopes from lanthanum to lutetium has been carried out using reverse phase partition chromatography and...     

Development and validation of LC‐MS/MS method for the estimation of β‐hydroxy‐β‐methylbutyrate in rat plasma and its application to pharmacokinetic studies

A simple, sensitive and specific high‐performance liquid chromatography mass spectrometry (LC‐MS/MS) method was developed and validated for the quantification of β‐hydroxy‐β‐methyl butyrate (HMB) in small volumes of rat plasma using warfarin as an internal standard (IS). The API‐4000 LC‐MS/MS was operated under the multiple reaction‐monitoring mode using the electrospray ionization technique. A simple liquid–liquid extraction process was used to extract HMB and IS from rat plasma. The total run time was 3 min and the elution of HMB and IS occurred at 1.48 and 1.75 min respectively; this was achieved with a mobile phase consisting of 0.1% formic acid in a water–acetonitrile mixture (15:85, v/v) at a flow rate of 1.0 mL/min on a Agilent Eclipse XDB C₈ (150 × 4.6, 5 µm) column. The developed method was validated in rat plasma with a lower limit of quantitation of 30.0 ng/mL for HMB. A linear response function was established for the range of concentrations 30–4600 ng/mL (r > 0.998) for HMB. The intra‐ and inter‐day precision values for HMB were acceptable as per Food and Drug Administration guidelines. HMB was stable in the battery of stability studies, viz. bench‐top, autosampler freeze–thaw cycles and long‐term stability for 30 days in plasma. The developed assay method was applied to a bioavailability study in rats. Copyright © 2012 John Wiley & Sons, Ltd.     

Convergence of Szász-Beta operators

In the present article we find the hypergeometric representation of the Szász-Beta operators and obtain the moments using confluent hypergeometric functions, which can be related to generalized Laguerre polynomials. Then we estimate a convergence result for functions having bounded derivatives.     

A Novel Synthesis of 5-Aryltropoxe Derivatives

The reaction of substituted arylboronic acids with 5-bromo-2-methoxytropone catalyzed by palladium(0) complex furnished 5-arylated tropone derivatives in good yield.     

Approximation by complex szász-durrmeyer operators in compact disks

In the present paper, we deal with the complex Szász-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.     

Thermal comparison and multi-objective optimization of single-stage aqua-ammonia absorption cooling system powered by different solar collectors

Journal of Thermal Analysis and Calorimetry - This paper presents the comprehensive thermodynamic modelling to compare the performance and optimization of single-stage NH3–H2O-type absorption...