A Non-Analytic Growth Bound for Laplace Transforms and Semigroups of Operators

Let f : \mathbbR₊ ? \mathbbC f : \mathbb{R}_{+} \longrightarrow \mathbb{C} be an exponentially bounded, measurable function. We introduce a growth bound z(f) \zeta(f) which measures the extent to which f f can be approximated by holomorphic functions. This growth bound is related to the location of the domain of holomorphy of the Laplace transform of f f far from the real axis. The denition extends to vector and operator-valued cases. For a C₀ C_{0} -semigroup T T of operators, z(T) \zeta(T) is closely related to the critical growth bound of T T .     

Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations

The main object of this paper is to investigate several general families of hyper-geometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.     

On the growth and approximation of entire functions represented by Laplace–Stieltjes’ transformation

In the present paper, we obtain the characterization of various growth parameters of an entire function F(s) represented by Laplace–Stieltjes transformation in terms of the rate of decrease of \(E_n ( {F,\beta } ),\)where \(E_n ( {F,\beta } )\) represents the error in approximating the function F(s) by exponential polynomials.     

Application of Doehlert design in optimizing the determination of degraded products of nerve agents by ion-pair liquid chromatography electrospray ionization tandem mass spectrometry

A qualitative method was developed for the determination of degraded products of nerve agents by using ion-pair liquid chromatography electrospray ionization tandem mass spectrometry (IP-LC-ESI-MS(n)). Generally, alkylphosphonic acids (APAs) and O-alkyl alkylphosphonic acids (AAPAs) give deprotonated molecular ion [M-H](-) in negative mode. Interestingly, first time we obtained the molecular radical anion [M](.-) of phosphonic acids in negative mode by using tri-n-butyl amine as an ion-pairing agent. We interpreted this observation as an indication of electrochemical reduction of phosphonic acids in electrospray needle. Three variables such as sheath gas flow, electrospray needle voltage and pH of the mobile phase were investigated to enhance the molecular radical anion [M](.-) signal of each analyte. The Doehlert design was used to obtain the region in which the optimum value of such variables is simultaneously achieved. Limit of detection achieved was 0.5 microg mL(-1) for AAPAs and 10 microg mL(-1) for APAs. Excellent precision was observed with less than 8.61% RSD. Finally, the method was applied for the detection of ethyl methylphosphonic in aqueous extract of soil sample.     

Development and validation of rapid ion-pair RPLC method for simultaneous determination of certain B-complex vitamins along with vitamin C

A rapid, simple, and accurate ion-pair RPLC method has been developed for simultaneous analysis of vitamin C and major B-complex vitamins. An RP C18 column thermostated at 30 degrees C was used with gradient elution of mobile phase comprising 10 mM potassium dihydrogen phosphate buffer (containing 3 mM sodium hexane-1-sulfonate, adjusted to pH 2.80 with o-phosphoric acid) and methanol at a flow rate of 1.0 mL/min to achieve the best possible separation and resolution of all vitamins in about 11.00 min. The detection was performed at 274 nm. The method has been implemented successfully for simultaneous determination of vitamins present in 12 multivitamin/multimineral pharmaceutical preparations, as well as in human urine. Typical validation characteristics were evaluated in accordance with International Conference on Harmonization guidelines. Good linearity over the investigated concentration levels was observed. Intraday repeatability was < or = 2.0%, and interday variation was < or = 2.6%, for all vitamins. The method can be used for assay of these vitamins over a wide concentration range with good precision and accuracy; hence, it would be appropriate for routine QC as well as in clinical analysis.     

Crystal Structure of Mononuclear Non-Heme Nikel(II) Octahedral Complex: [Ni(bqenH<Subscript>2</Subscript>)(bpy)](ClO<Subscript>4</Subscript>)<Subscript>2</Subscript>·0.125H<Subscript>2</Subscript>O

The crystal structure of a mononuclear Ni(II) complex [Ni(bqenH₂)(bpy)](ClO₄)₂·0.125H₂O 1 (where bqenH₂ is N,N′-bis(8-quinolyl)ethane-1,2-diamine, bpy = 2,2′-bipyridine) is reported here. The crystallographic data for 1 are as follows: monoclinic crystal system, P2_1/n space group, a = 17.3255(11), b = 10.6110(7), c = 34.328(2) Å, α = 90°, β = 93.9480(13)°, γ = 90°, V = 6295.8(7) ų, Z = 4, d_x = 1.541 mg/m³. The nickel(II) ion coordinates four N atoms of the tetradentate ligand bqenH₂ and two N atoms of the auxiliary bidentate 2,2′-bipyridine ligand, resulting in a slightly distorted NiN6 octahedron with two perchlorates serving as charge balancing counter anions. The overall structure of 1 is stabilized by the presence of water of crystallization in the crystal lattice. The crystal structure shows two symmetrically identical octahedral NiN6 units in its asymmetric unit. The extensive hydrogen bonding network resulting in a supramolecular architecture is observed due to the N–H?O, O–H?O, O–H?Cl, and N–H?Cl interactions.     

The complexes of aluminium,gallium, and indium with calmagite: Evaluation of stepwise stability constants

Summary Calmagite [1-(1-hydroxy-4-methyl-2-phenyl azo)-2-naphthol sulphonic acid], dissociates in two steps. It forms violet complexes with Al³⁺, Ga³⁺ and In³⁺. The stepwise proton-ligand stability constants of calmagite and stepwise metal-ligand stability constants of these complexes were evaluated by potentiometric titration technique ofBjerrum andIrving andRossotti. The order of the stabilities of complexes is In³⁺ > Ga³⁺ > > Al³⁺.

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Zusammenfassung Camalgit [1-(1-Hydroxy-4-methyl-2-phenylazo)-2-naphtholsulfonsäure] dissoziiert in zwei Stufen und bildet violette Komplexe mit Al(III), Ga(III) und In(III). Die Konstanten der Dissoziationsstufen der freien Säure und die der Metallkomplexe wurden potentiometrisch nachBjerrum bzw.Irving undRossotti ermittelt. Die Stabilität der Komplexe nimmt in der Reihe In(III) > Ga(III) > Al(III) ab.

     

Organotellurium derivatives : IV. Synthesis of some diaryltellurium dihalides and pseudohalides

Iodine monohalides (ICl, IBr), cyanogen halides (CNBr, CNI) and thiocyanogen (SCN)₂ add oxidatively to diaryltellurium(II), R₂Te (R = Ph, p-Ch₃OC₆H₄) under mild conditions ( °C). The resulting organotellurium(IV) derivatives react metathetically with silver pseudohalides to yield several new diaryltellurium(IV) pseudohalide derivatives.