n-dimensional array languages and description of crystal symmetry—I

Following the general linguistic approach proposed by Narasimhan to pattern recognition we proposed two generative models,viz., the matrix models and the more powerful two-dimensional array models. In this paper we generalize the matrix models ton-dimensions and establish that then-dimensional matrix models are closed under union, concatenation, Kleene closure, ∈-free homomorphism, inverse homomorphism and intersection with regular matrices. Symmetry operations such as translation, reflection and half-turn are examined.     

Synthesis and characterization of activated carbon–ethylenediamine–cobalt(II) tetracarboxyphthalocyanine conjugate for catalytic oxidation of ascorbic acid

We report on the synthesis and characterization of activated carbon–ethylenediamine–cobalt(II) tetracarboxyphthalocyanine conjugate (AC–CONHCH₂CH₂NH₂–CoPc) and its electrocatalytic behavior for oxidation of ascorbic acid. Ultraviolet–visible (UV–Vis), Fourier-transform infrared (FTIR), and electrochemical impedance spectroscopies, and cyclic and square-wave voltammetry were used to characterize the electrode modifiers and modified glassy carbon electrode. The limit of detection was found to be 0.26 µm using 3δ notation. The linear dynamic range was from 1.5 × 10^?4 to 1 × 10^?2 M with electrode sensitivity of 0.01 A mol^?1 L cm^?2. A Tafel slope of 200.8 mV decade^?1 was found. The concentration of ascorbic acid in the tablet was 0.034 M. Oxalic acid showed no interference in ascorbic acid determination.     

Equal matrix languages and Kleene closure

It is shown that the family of equal matrix languages (EML) which intersects the family of context-sensitive and context-free languages is not closed under Kleene closure, intersection and complementation. The family of bounded EML whose generative power lies between that of bounded context-sensitive languages and bounded context-free languages is shown to be a class of unambiguous languages. Operations that preserve unambiguity and certain decidability questions are discussed.     

Simple proof of the Lagrange multiplier rule for the fixed endpoint problem in the calculus of variations

A new simple proof of the Lagrange multiplier rule is presented in this paper. The approach used involves simple analytical techniques that are very easy to follow and does not involve theorems on imbeddability in a one-parameter family of curves or matrix-rank analysis as do most of the existing techniques. The proof is here developed for the fixed-endpoint problem in a three-dimensional space.     

Surface-enhanced Raman spectral measurements of 5-fluorouracil in saliva

The ability of surface-enhanced Raman spectroscopy (SERS) to measure 5-fluorouracil (5-FU) in saliva is presented. The approach is based on the capacity of Raman spectroscopy to provide a unique spectral signature for virtually every chemical, and the ability of SERS to provide microg/mL sensitivity. A simple sampling method, that employed 1-mm glass capillaries filled with silver-doped sol-gels, was developed to isolate 5-FU from potential interfering chemical components of saliva and simultaneously provide SERSactivity. The method involved treating a 1 mL saliva sample with 1 mL of acetic acid, drawing 10 microL of sample into a SERS-active capillary by syringe, and then measuring the SER spectrum. Quality SER spectra were obtained for samples containing as little as 2 microg of 5-FU in 1 mL saliva. The entire process, the acid pretreatment, extraction and spectral measurement, took less than 5 minutes. The SERS of 5-fluorouridine and 5-fluoro-2'-deoxyuridine, two major metabolites of 5-FU, were also measured and shown to have unique spectral peaks. These measurements suggest that disposable SERS-active capillaries could be used to measure 5-FU and metabolite concentrations in chemotherapy patient saliva, thereby providing metabolic data that would allow regulating dosage. Tentative vibrational mode assignments for 5-FU and its metabolites are also given.     

Process Optimisation Studies and Aminonitrile Substrate Evaluation of Rhodococcus erythropolis SET1, A Nitrile Hydrolyzing Bacterium

A comprehensive series of optimization studies including pH, solvent and temperature were completed on the nitrile hydrolyzing Rhodococcus erythropolis bacterium SET1 with the substrate 3-hydroxybutyronitrile. These identified temperature of 25 °C and pH of 7 as the best conditions to retain enantioselectivity and activity. The effect of the addition of organic solvents to the biotransformation mixture was also determined. The results of the study suggested that SET1 is suitable for use in selected organo-aqueous media at specific ratios only. The functional group tolerance of the isolate with unprotected and protected β-aminonitriles, structural analogues of β-hydroxynitriles was also investigated with disappointingly poor isolated yields and selectivity obtained. The isolate was further evaluated with the α- aminonitrile phenylglycinonitrile generating acid in excellent yield and ee (>99 % (S) – isomer and 50 % yield). A series of pH studies with this substrate indicated pH 7 to be the optimum pH to avoid product and substrate degradation.     

Atomistic simulation reveals structural mechanisms underlying D614G spike glycoprotein-enhanced fitness in SARS-COV-2

D614G spike glycoprotein (sgp) mutation in rapidly spreading severe acute respiratory syndrome coronavirus-2 (SARS-COV-2) is associated with enhanced fitness and higher transmissibility in new cases of COVID-19 but the underlying mechanism is unknown. Here, using atomistic simulation, a plausible mechanism has been delineated. In G614 sgp but not wild type, increased D(G)614-T859 Cα-distance within 65 ns is interpreted as S1/S2 protomer dissociation. Overall, ACE2-binding, post-fusion core, open-state and sub-optimal antibody-binding conformations were preferentially sampled by the G614 mutant, but not wild type. Furthermore, in the wild type, only one of the three sgp chains has optimal communication route between residue 614 and the receptor-binding domain (RBD); whereas, two of the three chains communicated directly in G614 mutant. These data provide evidence that D614G sgp mutant is more available for receptor binding, cellular invasion and reduced antibody interaction; thus, providing framework for enhanced fitness and higher transmissibility in D614G SARS-COV-2 mutant.     

Water hyacinth modified carbon paste electrode for simultaneous electrochemical stripping analysis of Cd (II) and Pb (II)

In this study, we demonstrated a highly sensitive electrochemical sensor for the simultaneous detection of Pb (II) and Cd (II) in aqueous solution using carbon paste electrode modified with Eichhornia crassipes powder by square wave anodic stripping voltammetry. The effect of modifier composition, pH, preconcentration time, reduction potential and time, and type of supporting electrolyte on the determination of metal ions were investigated. Pre-concentration on the modified surface was performed at open circuit. The modified electrode exhibited well-defined and separate stripping peaks for Pb (II) and Cd (II). Under optimum experimental conditions, a linear range for both metal ions was from 10 to 5000 μg L^?1 with the detection limits of 4.9 μg L^?1, 2.1 μg L^?1 for Cd(II) and Pb (II), respectively. The modified electrode was found to be sensitive and selective when applied to determine trace amounts of Cd (II) and Pb (II) in natural water samples.     

Contributions to the calculus of variations

In this paper, the theory of the calculus of variations for the simplest problem is reviewed. Simpler proofs are given for the classical conditions and a new necessary condition is presented which allows strong, necessary, and sufficient conditions to be stated for the first time.The major part of this research was conducted in the Department of Electrical Engineering, University of the West Indies, St. Augustine, Trinidad, West Indies. The author is indebted to Dr. B. Bhatt for interesting discussions.     

Solvent‐free Synthesis,Characterization and Solvent‐Vapor Interaction of Zinc(II) and Copper(II) Coordination Polymers containing Nitrogen‐donor Ligands

Coordination polymers of [Zn(INA)₂] ( 1 ) (INA = isonicotinate), [Cu₂(mal)₂(H₂O)₂(bipy)] ( 2 ) (mal = malonate, bipy = 4,4‐bipyridine), and [Zn₂(OAC)₄(bipy)₂] ( 3 ) (OAC = acetate) were prepared using mechanochemical grinding and heating methods. The materials were characterized with elemental analysis, FT‐IR spectroscopy, TGA, SEM, EI‐MS, BET, and PXRD. Comparison of PXRD patterns of the materials with patterns simulated from single‐crystal X‐ray diffraction data allowed identification of the products. Compared to conventional synthetic techniques such as solvothermal/hydrothermal solvent‐based methods, solvent‐free method was found to be simple, highly efficient, and environmentally friendly especially for the preparation of these coordination polymers on a large scale. Solvent‐vapor interaction properties of 1 , 2 , and 3 were investigated by exposure of the compounds to water and methanol at room temperature.