Wandering Subspaces of the Bergman Space and the Dirichlet Space Over {{\mathbb{D}^{n}}}

Doubly commuting invariant subspaces of the Bergman space and the Dirichlet space over the unit polydisc \({\mathbb{D}^n}\) (with \({n \geq 2}\) ) are investigated. We show that for any non-empty subset \({\alpha=\{\alpha_1,\ldots,\alpha_k\}}\) of \({\{1,\ldots,n\}}\) and doubly commuting invariant subspace \({\mathcal{S}}\) of the Bergman space or the Dirichlet space over \({\mathbb{D}^n}\) , restriction of the multiplication operator tuple on \({\mathcal{S}, M_{\alpha}|_\mathcal{S}:=(M_{z_{\alpha_1}}|_\mathcal{S},\ldots, M_{z_{\alpha_k}}|_\mathcal{S})}\) , always possesses generating wandering subspace of the form $$\bigcap_{i=1}^k(\mathcal{S}\ominus z_{\alpha_i}\mathcal{S})$$ .     

Morphology and bilayer integrity of small liposomes during aerosol generation by air-jet nebulisation

Small liposome suspensions (hydrodynamic diameter, 80–130 nm) were nebulised, and the resulting changes in morphology and bilayer integrity were found to be related to surface properties controlled by bilayer composition. Four separate liposome compositions (or liposome types) were investigated using three different phospholipids with unique properties. Morphological changes were studied using light scattering and imaging of liposomes before and after nebulisation, and structural integrity was investigated on the basis of the retention of an encapsulated dye (probe molecule). Nebulisation generated droplets contained liposomes. The liposome particles generated on droplet evaporation had a hollow structure as evidenced by electron imaging, indicating that the lipid bilayer does not collapse on evaporation. The particles of all compositions had mobility diameters between 50 and 90 nm, 1.4–1.6 times smaller than their diameters (hydrodynamic) measured before nebulisation, implying considerable volume shrinkage. Liposomes that had polymer-conjugated lipids covering their external surface underwent aggregation during nebulisation, evidenced by increased diameter after nebulisation. Incorporation of charged lipids reduced nebulisation-induced aggregation, but induced greater membrane rupture during aerosol generation, causing leakage of encapsulated probe molecules. Incorporation of both cholesterol and charged lipids prevented aggregation, but also preserved bilayer integrity, evidenced by the maximum retention of encapsulated dye observed in these conditions (>85%). The findings suggest that liposome bilayer composition can be manipulated to improve the efficiency of liposome aerosol delivery.     

Applicability and effectiveness of classifications models for achieving the twin objectives of growth and outreach of microfinance institutions

Measuring performance of microfinance institutions (MFIs) is challenging as MFIs must achieve the twin objectives of outreach and sustainability. We propose a new measure to capture the performance of MFIs by placing their twin achievements in a 2 × 2 grid of a classification matrix. To make a dichotomous classification, MFIs that meet both their twin objectives are classified as ‘1’ and MFIs who could not meet their dual objectives simultaneously are designated as ‘0’. Six classifiers are applied to analyze the operating and financial characteristics of MFIs that can offer a predictive modeling solution in achieving their objectives and the results of the classifiers are comprehended using technique for order preference by similarity to ideal solution to identify an appropriate classifier based on ranking of measures of performance. Out of six classifiers applied in the study, kernel lab-support vector machines achieved highest accuracy and lowest classification error rate that discriminates the best achievement of the MFIs’ twin objective. MFIs can use both these steps to identify whether they are on the right path to attaining their multiple objectives from their operating characteristics.     

Radioanalytical separation and size-dependent ion exchange property of micelle-directed titanium phosphate nanocomposites

Nanocomposite titanium-phosphate (TiP) of different sizes was synthesized using Triton X-100 (polyethylene glycol-p-isooctylphenyl ether) surfactant. The materials were characterized by FTIR and powdered X-ray diffraction (XRD). The structural and morphological details of the material were obtained by scanning electron microscopy (SEM) and transmission electron microscopy. The SEM study was followed by energy dispersive spectroscopic analysis for elemental analysis of the sample. The important peaks of the XRD spectra were analyzed to determine the probable composition of the material. The average size distribution of the particles was determined by dynamic light scattering method. Ion exchange capacity was measured for different metal ions with sizes of the TiP nanocomposite and size-dependent ion exchange property of the material was investigated thoroughly. The nanomaterial of the smallest size of around 43 nm was employed to separate carrier-free ^137mBa from ¹³⁷Cs in column chromatographic technique using 1.0 M HNO₃ as eluting agent at pH 5.     

Photophysical and theoretical insights on non-covalently linked fullerene-zinc phthalocyanine complexes

The photo-physical aspects of non-covalently linked assemblies of a series of fullerenes, namely, C60, C70, tert-butyl-(1,2-methanofullerene)-61-carboxylate (1) and [6,6]-phenyl C70 butyric acid methyl ester (2) with a designed zinc phthalocyanine (ZnPc), viz., zinc-1,4,8,11,15,18,22,25-octabutoxy-29H,31H-phthalocyanine (3) in toluene medium are studied employing absorption spectrophotometric, steady state and time resolved fluorescence spectroscopic measurements. Of central interest in these investigations is the preferential binding of various fullerenes with ZnPc in toluene. The ground state interaction between fullerenes and 3 is first evidenced from UV-Vis measurements. Steady state fluorescence experiment reveals efficient quenching of the excited singlet state of 3 in presence of both underivatized and derivatized fullerenes. K values for the complexes of C60, C70, 1 and 2 with 3 are determined to be 6500, 22,230, 47,800 and 54,770 dm3 mol(-1), respectively. The magnitude of K suggests that 3 preferentially binds C70 and derivatized C70 in comparison to C60 and 1. Time resolved emission measurements establish that C(70)-3 and 2-3 complexes are stabilized much more in comparison to C(60)-3 and 1-3 systems in terms of charge separation process. Semi empirical calculations employing third parametric method substantiate the strong binding of C70 and its derivative with 3 in terms of heat of formation values of the respective complexes, and at the same time, determine the orientation of bound guest (here fullerenes) with the molecular plane of 3.     

A LASER FLASH PHOTOLYSIS STUDY OF PYRENE-1-ALDEHYDE. INTERSYSTEM CROSSING EFFICIENCY, PHOTOREACTIVITY AND TRIPLET STATE PROPERTIES IN VARIOUS SOLVENTS

Abstract— Triplet-and singlet-related photoprocesses of pyrene-1-aldehyde (PA) in various solvents have been investigated in detail using 337.1 and 355 nm laser flash photolysis in conjunction with time-correlated determination of fluorescence lifetimes (τ_F) and steady-state photochemical and absorption-emission spectral measurements. In benzene, the lowest triplet of PA (43 < E_T < 46 kcal/mol) has a lifetime of about 50 µs (τ_T) and displays the absorption maximum at 443 nm with a maximum extinction coefficient (ε_max) of 21000 M ^-1cm^-1; the corresponding ketyl radical has a sharp absorption maximum at 428 nm (ε_max≥ 25000 M ^-1cm^-1). The quantum yields (φ_T) of lowest triplet occupation are high in nonprotic solvents (0.6–0.8), decrease in protic solvents (alcohols) as the polarity of the latter is increased, and maintain a complementary relationship with the quantum yields (φ_F) of fluorescence. Quantum yields (φ_PC) of loss of PA due to photoreactions in some solvents have also been determined under conditions of steady irradiation at 366 nm; φ_PC is in the range 0.1–0.2 in electron-rich olefinic solvents such as cyclohexene and tetramethylethylene. These results concerning τ_F, τ_T, φ_F. φ_T and φ_PC as well as the effects of 1,2,4-trimethoxybenzene and 2,5-dimethyl-2,4-hexadiene as quenchers for fluorescence, triplet yield, and photochemistry are discussed in the light of possible state orders for PA in polar and nonpolar environments.     

Photoluminescence of 2-(2′-hydroxy-5′-methylbenzoyl)-1,5-diphenylpyrrole in aqueous and β-cyclodextrin environments: manifestation of open and closed conformers

Steady-state fluorometric studies have been performed on 2-(2′-hydroxy-5′-methylbenzoyl)-1,5-diphenylpyrrole (HMBDPP) in aqueous and aqueous β-cyclodextrin (β-CD) environments at ambient temperature. The fluorophore mostly shows a single emission in aqueous solution. Addition of β-CD to the aqueous solution of the fluorophore results in the development of another emission band at higher energy. The difference in the fluorometric behaviour is assigned to a remarkable change in the polarity of the microenvironment within the supramolecular structural environment compared to that of the bulk aqueous phase. Semi-empirical calculation (AM1-SCI) rules out the possibility of intramolecular proton transfer reaction in any of the S₀, S₁ and T₁ states of the fluorophore. It is proposed that HMBDPP exists mostly in the intermolecularly hydrogen-bonded form (open conformer) in aqueous solution while within β-CD environment, it is the intramolecularly hydrogen-bonded form (closed conformer) that predominates.     

A route for bulk separation of semiconducting from metallic single-wall carbon nanotubes

Substantial separation of single-wall carbon nanotubes (SWNTs) according to type (metallic versus semiconducting) has been achieved for HiPco and laser-ablated SWNTs. We presently argue that stable dispersions of SWNTs with octadecylamine (ODA) in tetrahydrofuran (THF) originate from the physisorption and organization of ODA along the SWNT sidewalls in addition to the originally proposed zwitterion model. Furthermore, the reported affinity of amine groups for semiconducting SWNTs, as opposed to their metallic counterparts, contributes additional stability to the physisorbed ODA. This provides a venue for the selective precipitation of metallic SWNTs upon increasing dispersion concentration, as indicated by Raman investigations.