Gap functions and error bounds for quasi variational inequalities

The paper aims to obtain new local/global error bounds for quasi variational inequality problems in terms of the regularized gap function and the D-gap function. These bounds provide effective estimated distances between a specific point and the exact solution of quasi variational inequality problem.     

Analysis of 226Ra, 232Th and 40K in soil samples for the assessment of the average effective dose

The activity concentrations of the natural radionuclides namely ²³⁸Ra, ²³²Th and ⁴⁰K are measured for soil samples collected from different locations of Faridkot and Mansa districts of Punjab. HPGe detector, based on high-resolution gamma spectrometry system is used for the measurement of activity concentration. The range of activity concentrations of ²²⁶Ra, ²³²Th and ⁴⁰K in the soil from the studied areas varies from 21.42 Bq kg⁻¹ to 40.23 Bq kg⁻¹, 61.01 Bq kg⁻¹ to 142.34 Bq kg⁻¹ and 227.11 Bq kg⁻¹ to 357.13 Bq kg⁻¹ with overall mean values of 27.17 Bq kg⁻¹, 95.22 Bq kg⁻¹ and 312.76 Bq kg⁻¹, respectively. Radium equivalent activities are calculated for the analyzed samples to assess the radiation hazards arising due to the use of these soil samples in the construction of dwellings. The absorbed dose rate calculated from activity concentration of ²²⁶Ra, ²³²Th and ⁴⁰K ranges between 9.87 and 18.55, 38.01 and 88.68 and 9.40 and 14.79 nGy h⁻¹, respectively. The total absorbed dose in the study area ranges from 61.10 nGy h⁻¹ to 112.86 nGy h⁻¹ with an average value of 84.80 nGy h⁻¹. The calculated values of external hazard index (H _ex) for the soil samples of the study area range from 0.36 to 0.68. Since these values are lower than unity, according to the Radiation Protection 112 (European Commission, 1999) report, soil from these regions is safe and can be used as construction material without posing any significant radiological threat to population. The corresponding average annual effective dose for indoor and outdoor measured in the study area are 0.42 mSv and 0.10 mSv respectively.      

The Young Julian Schwinger. II. Julian Schwinger at Columbia University

In this series of articles the life and work of the young Julian Schwinger are explored. In this second article in the series, Schwinger's work at Columbia University, up to the completion of his doctorate and a little after, is discussed. Schwinger soon matured into a brilliant theoretical physicist.     

Optimality Conditions and Duality Involving Arcwise Connected and Generalized Arcwise Connected Functions

Some properties of arcwise connected functions in terms of their directional derivatives are investigated. These properties are then utilized to establish necessary and sufficient optimality conditions for scalar-valued nonlinear programming problems. Mond–Weir type duality results are also proved.     

Studies on the valence electronic structure of Fe and Ni in Fe x Ni1−x alloys

K _β-to-K _α X-ray intensity ratios of Fe and Ni in pure metals and in Fe _x Ni_1−x alloys (x=0.20, 0.50, 0.58) exhibiting similar crystalline structure have been measured following excitation by 59.54 keV γ-rays from a ²⁴¹Am point source, to understand as to why the properties of permalloy Fe_0.2Ni_0.8 is distinct from other alloy compositions. It is observed that the valence electronic structure of Fe_0.2Ni_0.8 alloy is totally different from other alloys which may be attributed to its special magnetic properties.     

Studies on fused β-lactams : synthesis of novel 1-aza-analogs of cepham

Stereospecific synthesis of some 1-aza-analogs of cepham (V) have been accomplished using appropriate β-methylthio-β-lactams (IV) as precursors. The possible single step removal of the thiomethyl as well as benzyloxycarbonyl groups using Ni [H] converted VI into the novel 1-aza cepham (VII).     

Stereospecific synthesis of some polycyclic cis-β-lactams

Amides 1 on reaction with P₂S₅ in pyridine give thioamides 2 which on treatment with methyl iodide afford the corresponding 1-methylthio-3,4-dihydroisoquinolines 3. Annelation of these imines with phenoxyacetyl chloride in the presence of triethylamine furnish 6-methylthio-7-phenoxy-2',3' - dimethoxybenzo[a]octem 4a and 6-methylthio-7-phenoxy-2,3-methylenedioxybenzo[a]octem 4b respectively. Desulphurisation of these β-methylthio-β-lactams with Raney nickel yield the novel polycyclic cis-β-lactams 5a and 5b.     

Schiff base of 0-methylthioaniline and salicylaldehyde and its metal chelates

The Schiff base salicylideneamino-o-methylthiobenzene (I), CH₃S?C₆H₄?N=CH?C₆H₄?OH (SMeNOH), has been synthesized and its complexes of the type CuX(SMeNO) whereX=Cl, Br, NO₃, CNS, and ClO₄, CuX′(SMeNOH) whereX′=SO₄ and (BF₄)₂, NiX″ ₂(SMeNOH) whereX″=Cl and Br, NiNO₃(SMeNO) andM(SMeNO) ₂ whereM=Cu, Ni and Co, have been prepared and characterised through infrared, magnetic moment and conductance measurements.