Numerically stable,scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.     

Overtone spectroscopy of some benzaldehyde derivatives

Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm⁻¹ region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined. We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed in these distances is an indication of the substitution effect. It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the case of o-disubstituted benzenes it is only 80% of the para-substituted shift.     

Benzopentalenonaphthalenones from the intramolecular capture of a merocyanine derived from a naphthopyran

Novel, highly coloured benzopentalenonaphthalenones result from a cascade process initiated by the thermally-induced ring-opening of diarylmethanol substituted 2H-naphtho[1,2-b]pyrans in the presence of acid.     

EDTA-catalyzed synthesis of 3,4-dihydroquinoxalin-2-amine derivatives by a three-component coupling of one-pot condensation reactions in an aqueous medium

This paper describes a simple and efficient one-pot synthetic approach for the preparation of biologically interesting 3,4-dihydroquinoxalin-2-amine derivatives using EDTA-catalyzed three-component reactions of o-phenylenediamines, carbonyl compounds, and isocyanides in an aqueous medium. This method is of great value because of its environmentally benign character, high yields, and ease of handling.     

An efficient synthesis of dexlansoprazole employing asymmetric oxidation strategy

An alternative and scalable synthesis of dexlansoprazole ((R)-(+)-1); the (R)-enantiomer of Lansoprazole with an enantiomeric excess of >99.8% is presented.     

Influence of cross diffusions on mixed convection chemical reaction flow in a vertical channel with Navier slip: Homotopy approach

This paper is to examine the incompressible, laminar mixed convective Navier slip flow between vertical plates with cross diffusion effects. This research includes the first order chemical reaction also. The resulting equations with boundary conditions are reduced into dimensionless form using appropriate transformations. The series solutions are developed through a modern technique known as the homotopy analysis method. The convergent expressions of velocity components and temperature are derived. The influence of emerging parameters on fluid flow quantities have been presented graphically. Also, the nature of physical quantities are shown in tabular form.     

Polymer-coated cation-exchange stationary phases on the basis of silica

Summary The procedure of polymer coating of preferably inorganic porous particle support materials for LC has been applied to the preparation of a new type of weak cationexchange phases. A special copolymer of butadiene and maleic acid could be immobilized on silica by cross-linking effected with radical starters such as peroxides or γ-radiation. The chromatographic properties of such materials proved to be excellent regarding efficiency, ion-exchange capacity and selectivity, as well as chemical stability also in comparison to other, commercially available, materials. Test measurements were successfully performed with ionic or ionizable inorganic and organic solutes over the entire applicable pH-range of the mobile phase which also contained organic modifiers. A special feature of the new type of cation-exchange phase is the minor contribution of hydrophobic (lipophilic) interaction to the retention mechanism besides the actual ion-exchange process.     

Extremes of nuclear structure

With the advent of medium and large gamma detector arrays, it is now possible to look at nuclear structure at high rotational forces. The role of pairing correlations and their eventual breakdown, along with the shell effects have showed us the interesting physics for nuclei at high spins — superdeformation, shape co-existence, yrast traps, alignments and their dramatic effects on nuclear structure and so on. Nuclear structure studies have recently become even more exciting, due to efforts and possibilities to reach nuclei far off from the stability valley. Coupling of gamma ray arrays with ‘filters’, like neutron wall, charged particle detector array, gamma ray total energy and multiplicity castles, conversion electron spectrometers etc gives a great handle to study nuclei produced online with ‘low’ cross-sections. Recently we studied, nuclei in mass region 80 using an array of 8 germanium detectors in conjunction with the recoil mass analyser, HIRA at the Nuclear Science Centre and, most unexpectedly came across the phenomenon of identical bands, with two quasi-particle difference. The discovery of magnetic rotation is another highlight. Our study of light In nucleus, 107In brought us face to face with the ‘dipole’ bands. I plan to discuss some of these aspects. There is also an immensely important development — that of the ‘radioactive ion beams’. The availability of RIB, will probably very dramatically influence our ‘conventional’ concept of nuclear structure. The exotic shapes of these exotic nuclei and some of their expected properties will also be touched upon.