Enveloping Σ-C *-algebra of a smooth Frechet algebra crossed product by ℝ,K-theory and differential structure inC *-algebras

Given anm-tempered strongly continuous action α of ℝ by continuous^*-automorphisms of a Frechet^*-algebraA, it is shown that the enveloping ↡-C ^*-algebraE(S(ℝ, A^∞, α)) of the smooth Schwartz crossed productS(ℝ,A ^∞, α) of the Frechet algebra A^∞ of C^∞-elements ofA is isomorphic to the Σ-C ^*-crossed productC ^*(ℝ,E(A), α) of the enveloping Σ-C ^*-algebraE(A) ofA by the induced action. WhenA is a hermitianQ-algebra, one getsK-theory isomorphismRK _*(S(ℝ, A^∞, α)) =K ^*(C ^*(ℝ,E(A), α) for the representableK-theory of Frechet algebras. An application to the differential structure of aC ^*-algebra defined by densely defined differential seminorms is given.     

Stinespring representability and Kadison’s Schwarz inequality in non-unital Banach star algebras and applications

A completely positive operator valued linear map ϕ on a (not necessarily unital) Banach *-algebra with continuous involution admits minimal Stinespring dilation iff for some scalark > 0, ϕ(x)*ϕ(x) ≤ kϕ(x*x) for allx iff ϕ is hermitian and satisfies Kadison’s Schwarz inequality ϕ(h) ² ≤ kϕ(h ²) for all hermitianh iff ϕ extends as a completely positive map on the unitizationA _e of A. A similar result holds for positive linear maps. These provide operator state analogues of the corresponding well-known results for representable positive functionals. Further, they are used to discuss (a) automatic Stinespring representability in Banach *-algebras, (b) operator valued analogue of Bochner-Weil-Raikov integral representation theorem, (c) operator valued analogue of the classical Bochner theorem in locally compact abelian groupG, and (d) extendability of completely positive maps from *-subalgebras. Evans’ result on Stinespring respresentability in the presence of bounded approximate identity (BAI) is deduced. A number of examples of Banach *-algebras without BAI are discussed to illustrate above results.     

On Interacting Systems of Hilbert-Space-Valued Diffusions

A nonlinear Hilbert-space-valued stochastic differential equation where L ^-1 (L being the generator of the evolution semigroup) is not nuclear is investigated in this paper. Under the assumption of nuclearity of L ^-1 , the existence of a unique solution lying in the Hilbert space H has been shown by Dawson in an early paper. When L ^-1 is not nuclear, a solution in most cases lies not in H but in a larger Hilbert, Banach, or nuclear space. Part of the motivation of this paper is to prove under suitable conditions that a unique strong solution can still be found to lie in the space H itself. Uniqueness of the weak solution is proved without moment assumptions on the initial random variable. A second problem considered is the asymptotic behavior of the sequence of empirical measures determined by the solutions of an interacting system of H -valued diffusions. It is shown that the sequence converges in probability to the unique solution Λ ₀ of the martingale problem posed by the corresponding McKean—Vlasov equation. Accepted 4 April 1996     

Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions

In this paper, we obtain some common fixed point theorems for occasionally weakly compatible mappings on a set X together with the function d:X×X→[0,∞) without using the triangle inequality and assuming symmetry only on the set of points of coincidence.     

The solution heat and conductance of some azomethines nonaqueous solutions at 308.15 K

Some new azomethines have been synthesized and their characterization was done by IR, ¹H NMR, mass spectra and CHN analysis. Further, some physicochemical properties such as heat of solution and conductance have been studied for these synthesized compounds in different solvents at 308.15 K. The heat of solution was also determined at different temperatures.     

Analysis of urinary stone constituents using powder X-ray diffraction and FT-IR

Constituents of urinary stones obtained from various patients from western part of India, which is a highly urinary stone disease-prone area, have been analysed. Eight stones from four patients were collected through urologists and have been analysed using powder X-ray diffraction and FT-IR. Thermogravimetric analysis (TGA) and scanning electron microscopic (SEM) image of selected samples were also carried out. The analysis revealed that calcium oxalate monohydrate, which is also known as whewellite, is the common constituent of all of the stones, particularly at the initial stage of stone formation. However, multi phases viz. whewellite phase, and hydroxyl and carbonate apatite phases are also detected in the case of third and fourth patients, from where multiple stones were obtained. Interestingly, in these mixed phase stones the concentration of whewellite decreases with increasing the concentration of apatite phases. Thermal behaviour of the whewellite phase was studied by TGA and variable temperature XRD analysis. Morphology of the whewellite and apatite phases, examined by SEM image, has also been reported.     

Existence of spectral well-behaved ∗-representations

There are several cases, where an m^∗-seminorm p is defined on a ∗-subalgebra of a given ∗-algebra A. This may lead to the construction of an unbounded ∗-representation of A. Such m^∗-seminorms are called unbounded. Given an unbounded m^∗-seminorm p of a ∗-algebra A, the concept of a p-spectral ∗-representation of A is introduced and studied in connection to well-behaved ∗-representations. More precisely, the existence of (p-) spectral well-behaved ∗-representations is investigated on ∗-algebras and locally convex ∗-algebras in terms of certain properties of Pták function, closely related to hermiticity and C^∗-spectrality of the ∗-subalgebras on which this function is defined. Various examples in diverse classes of locally convex algebras illuminate the elaborated results.     

Influence of pH and organic modifiers on the dissociation constants of selected drugs using reversed‐phase thin‐layer chromatography: Comparison with other techniques and computational tools

Knowledge of the acid–base dissociation constants of drugs is the key to understanding their biopharmaceutical characteristics. In the present work, the effect of pH and organic modifiers (acetonitrile and methanol) was investigated in the determination of dissociation constants (pK_a) of nine representative drugs (atenolol, betahistine, clarithromycin, deferiprone, diclofenac, ibuprofen, metoprolol, naproxen and propranolol) using reversed‐phase thin‐layer chromatography. Mobile phase consisting of various buffers and methanol–acetonitrile (10, 20, 30, 40, 50 and 60%, v/v) was used to evaluate the retention pattern on reversed‐phase plates. Compared with methanol, acetonitrile gave better results for the experimentally determined pK_a values by extrapolation to zero organic modifier volume fractions. To assess the effectiveness of the developed method the results were correlated using principal component analysis and hierarchical cluster analysis. The calculated values of the aqueous dissociation constant were compared with those reported previously using potentiometry and capillary electrophoresis and also with different computational platforms like ACD/Lab, ChemAxon and Jchem calculator. The results obtained by the RPTLC method were in good agreement with potentiometric methods for pK_a determination.     

Diorganotin(IV) complexes of 2-chloridophenylacetohydroxamic acid as prospective antimicrobials: synthesis,characterization, and biological properties

New diorganotin(IV) complexes [Me₂Sn(2-ClC₆H₄CH₂CONHO)₂] (1) and [n-Bu₂Sn(2-ClC₆H₄CH₂CONHO)₂] (2) have been synthesized by reactions of Me₂SnCl₂ and n-Bu₂SnCl₂ with potassium 2-chloridophenylacetohydroxamate (2-ClPhAHK = 2-ClC₆H₄CH₂CONHOK) in 1:2 molar ratio in MeOH+C₆H₆ solvent medium and characterized by elemental analyses, molar conductivity, molecular weight determinations and spectroscopic techniques (IR, ¹H, ¹³C, and ¹¹⁹Sn NMR) and mass spectrometry. Bonding through carbonyl and hydroxamic oxygens (O,O coordination) and distorted-octahedral geometry around tin is proposed. The electrochemical behavior of 1 and 2 studied by cyclic voltammetry shows quasi-reversible reductions. Thermal behavior of 1 and 2 in N₂ shows decomposition in one step affording SnO as the residue. The in vitro antimicrobial activity assay against pathogenic Gram-negative bacteria viz. Salmonella typhi, Escherichia coli; Gram-positive Bacillus cereus and Staphylococcus aureus and fungi Aspergillus niger and Alternaria alternata by MIC method revealed their significant antimicrobial potential relative to the respective standard Chloramphenicol and Nystatin drugs.     

Alternative transparent conducting electrode materials for flexible optoelectronic devices

Transparent Conductive Electrode (TCE) is an essential part of the optoelectronic and display devices such as Liquid Crystal Displays (LCDs), Solar Cells, Light Emitting Diodes (LEDs), Organic Light Emitting Diodes (OLEDs) and touch screens. Indium Tin Oxide (ITO) is a commonly used TCE in these devices because of its high transparency and low sheet resistance. However, scarcity of indium and brittle nature of ITO limit its use in future flexible electronics. In order to develop flexible optoelectronic devices with improved performance, there is a requirement of replacing the ITO with a better alternate TCE. In this work, several alternative TCEs including transparent conductive oxides, carbon nanotubes, conducting polymers, metal nanowires, graphene and composites of these materials are studied with their properties such as sheet resistance, transparency and flexibility. The advantage and current challenges of these materials are also presented in this work.