Inequalities for a Polynomial and Its Derivative II

A well-known result of Rivlin states that if p(z) is a polynomial of degree n, such that p(z) ≠ 0 in |z| < 1, then max_{|z|=r < 1} |p(z)| ≤ ((r + 1)/2)ⁿ max_{|z| = 1} |p(z)|. In this paper, we consider the polynomial p(z) = a₀ + Σⁿ_{v = μ}a_υz^υ having all its zeros in |z| ≤ k > 1 and obtain a generalization of this result. Our result improves upon a result recently proved by Bidkham and Dewan (J. Math. Anal. Appl.166 (1992), 19-324).     

Photochemical Symthesisof Aporphines: (±)-Thaliporphime. (±)-N-Nethyllaurotetanineand(±)-Isoboldime

Aporphines, (±)-thaliporphine (1). (±)-N-methyllaurotetatine (2), and (±)-isoboldine (3) were synthesised using photochemical cyclization as the key step.     

Prediction of gas chromatographic retention times of esters of long chain alcohols and fatty acids

The linear free energy of solution (DeltaG) relationship (DeltaG=DeltaGo+zdeltaG) for compounds of different carbon atoms (z) in the same homologous series is expanded and modified to cover compounds with two different hydrocarbon side chains. The expanded equation is successfully used to predict the retention times (tR) of standard esters of long chain alcohols and fatty acids of different chain lengths in both isothermal and temperature-programmed gas chromatography (TPGC). Approximately 90% of the 125 predicted tR values have a difference of less than 1.00% from the actual tR and the highest difference is 1.26%. Two different temperature gradients in TPGC are tested. The expanded equation can be used to forecast the tR of TPGC with good accuracy. The highest difference is +/-1.40% and +/-1.00% for the temperature gradients of 2 degrees C and 4 degrees C/min, respectively. However, the increments in free energy per carbon atom (zdeltaG) of the alcohol and acid are approximately equal but have slightly different temperature sensitivities. Therefore, it is very difficult to separate esters of different acid and alcohol chain length but with the same total carbon numbers. Furthermore, the difference in temperature sensitivities for the acid and alcohol side chains renders them to be inversely eluted at different temperatures.     

Study on ion–solvent interactions of alkali metal salts in pure methanol and its binary mixtures with ethane-1,2-diol by a conductometric technique

Electrolytic conductivities of some sodium salts (NaI, NaSCN, CH₃COONa) have been studied in 0, 25, 50 and 75 mass% ethane-1,2-diol + methyl alcohol mixtures at 293.15, 298.15 and 303.15 K. The limiting molar conductivity (Λ°), the association constant (K_A) and the distance of closest approach of ion (R) have been evaluated using the Fuoss conductance equation (1978). The association constant (K_A) decreases with temperature while it tends to decrease in the order: 0 mass% > 25 mass% > 50 mass% > 75 mass% ethane-1,2-diol + methyl alcohol mixtures. Thermodynamic parameters ΔH°, ΔG° and ΔS° along with the Walden products (Λ°η) are obtained and discussed. The results have been interpreted in terms of ion–solvent interactions and structural changes in the mixed solvents.     

Some polynomial inequalities in the complex domain

Let

Heat transfer and flow characteristics of turbulent slot jet impingement on plane and ribbed surfaces

A computational study is carried out to assess the suitability of various RANS based turbulence models for slot jet impingement on flat and ribbed surfaces with various values of Reynolds number and jet to plate spacing. The com-puted results are compared with the reported experimental data. It was observed that none of the turbulence models considered predicted the heat transfer data accurately. However, some models predicted the experimental data with good trends, e.g., secondary peak and several spikes in Nusselt number for ribbed surface, with a precise computation of the stagnation point Nusselt number. Further, the effects of slot width, rib pitch and jet to ribbed surface spacing were investigated for jet impingement on a ribbed surface. It was observed that the local Nusselt number increased with slot width and rib to plate spacing. It was also observed that increasing Reynolds number had a positive effect on the local heat transfer. With increasing rib pitch the local Nusselt number increased near the stagnation zone but de-creased downstream. The observed flow pattern was different for jet impingement on a ribbed surface than that on a flat surface.     

Use of ion-exchange chromatography coupled with TLC-laser scanning densitometry for the quantitation of fumonisin B(1)

A simple TLC-Laser scanning densitometric (TLC-LSD) method was developed for the quantitation of fumonisin B(1) (FB(1)) isolated from solid media cultures (corn) and liquid media cultures of toxigenic Fusarium moniliforme strains (F. moniliforme MRC 826, F. moniliforme 4223 and F. moniliforme 2927)). FB(1) was isolated from the cultures by solvent extraction (methanol:water, 3:1) and purified in a single step by ion-exchange chromatography using Dowex-1. FB(1) in the purified extracts was detected by TLC analysis using p-anisaldehyde as a post-chromatographic derivatizing agent. The major toxin identified was FB(1) (R(f) 0.51) along with traces of FB(2) (R(f) 0.57) and FB(3) (R(f) 0.60) based on their comparison with the reference standard fumonisins. The sensitivity of the TLC-LSD method for the quantitation of FB(1) was found to be 500 ng g(-1). The linear regression analysis performed for the quantitation of FB(1) by the TLC-LSD method showed a correlation coefficient (r) value of 0.9. Spiking studies revealed the recovery of standard FB(1) (5 and 10 mug g(-1)) loaded on to Dowex-1 in the range of 87-96%. The purity of FB(1) purified from the cultures was determined by the two-dimensional TLC analysis. Two-dimensional TLC-analysis of the purified FB(1) revealed the purity to be greater than 85%. The method developed may find wide application in the environmental monitoring of the FB(1) contaminations in the various agricultural commodities and screening fumonisin producing toxigenic strains of F. moniliforme.     

Biosynthesis of isotetrandrine

The incorporation of (±)-coclaurine, (±)-N-methylcoclaurine, didehydro-N-methylcoclaurinium iodide, (+)-(S)-N-methylcoclaurine and (?)-(R)-N-methylcoclaurine into isotetrandrine in Cocculus laurifolius DC has been studied and specific utilization of (±)-, (+)-(S)- and (?)-R-N-methylcoclaurines and didehydro-N-methylcoclaurinium iodide demonstrated. The evidence supports intermolecular oxidative coupline of (+)-(S)- and (?)-(R)-N-methylcoclaurines to form isotetrandrine. Double labelling experiment with (±)-N- [¹⁴C] methyl [1 - ³H] coclaurine demonstrated that the hydrogen atom at the asymmetric centre in N-methylcoclaurine is retained in the bioconversion into isotetrandrine.