On a new simple method for evaluation of certain multiple definite integrals

This paper deals with a simple method of evaluation of certain multiple difinite integrals. This is followed by two main theorems concerning multiple difinite integrals. Some examples of applications are given.     

An Extension of Carlson's Inequality

An extension of Carlson's inequality is made by using the Euler-Maclaurin summation formula. The integral analogues of this inequality are also presented.     

Geometric constraints at the surfactant headgroup: effect on lipase activity in cationic reverse micelles

The primary objective of the present article is to understand how the geometric constraints at the surfactant head affect the lipase activity in the reverse micellar interface. To resolve this issue, surfactants were designed and synthesized, and activity was measured in /water/isooctane/n-hexanol reverse micellar systems at z ([alcohol]/[surfactant])=5.6, pH 6.0 (20 mM phosphate), 25 degrees C across a varying range of W0 ([water]/[surfactant]) using p-nitrophenylalkanoates as the substrate. It was observed that lipase activity increases from surfactants to with the increment in surface area per molecule (Amin) because of the substitution by the bulky tert-butyl group at the polar head. However, the activity was found to be similar for despite an enhancement in the hydrophilic moieties at the interface. This unchanged lipase activity is presumably due to the comparable surface area of to originating from the rigidity at the surfactant head. Noticeably, the enzyme activity improved from with the simultaneous increment of both the hydroxyl group and the flexibility of the headgroup whereas that for increased exclusively with the flexibility of the headgroup. The common parameter in both groups of surfactants and is the flexibility of the headgroup, which possibly enhance Amin and consequently the lipase activity. Thus, the geometric constraints at the surfactant headgroup play a crucial role in modulating the lipase activity profile probably because of the variation in interfacial area.     

The role of thiophosphoryl disulfide on the co‐cure of CR‐EPDM blends: effect of white fillers

Bis(diisopropyl) thiophosphoryl disulfide (DIPDIS) being a rubber accelerator has a definite role as a coupling agent in the silica filled polychloroprene rubber with ethylene propylene diene rubber (CR‐EPDM) blends. Diethylene glycol can further improve the beneficial effect of DIPDIS in silica filled CR‐EPDM blends. Two‐stage vulcanization technique further improves the physical properties of silica filled CR‐EPDM blends. The results have been compared with non‐reinforcing calcium carbonate filled systems. Scanning electron microscopy (SEM) studies further indicate the coherency and homogeneity in the silica filled CR‐EPDM blend vulcanizates obtained from this two‐stage process. Copyright © 2004 John Wiley & Sons, Ltd.     

Fullerene‐β‐Cyclodextrin Conjugate Based Electrochemical Sensing Device for Ultrasensitive Detection of p‐Nitrophenol

The article describes the use of a fullerene (C₆₀)‐β‐cyclodextrin conjugate, synthesized via 1,3‐dipolar cycloaddition, for the ultrasensitive electrochemical detection of p‐nitrophenol. This conjugate was successfully immobilized on the surface of a glassy carbon electrode and the developed device showed high activity towards p‐nitrophenol due to the synergetic effect of C₆₀, the latter becoming highly conductive upon reduction. The determination of p‐nitrophenol was performed by using square wave voltammetry over a concentration range from 2.8×10^?9 mol L^?1 to 4.2×10^?7 mol L^?1 and the detection limit was calculated to be 1.2×10^?9 mol L^?1.     

Real-time quantitative phase imaging with a spatial phase-shifting algorithm

This Letter reports on the use of a spatial phase-shifting algorithm in a fast, straightforward method of real-time quantitative phase imaging. The computation time for phase extraction is five times faster than a Fourier transform and twice as fast as a Hilbert transform. The fact that the phase extraction from an interferogram of 512 × 512 pixels takes less than 8.93 ms with a typical desktop computer suggests the proposed method can be readily applied to high-speed dynamic quantitative phase imaging. The proposed method of quantitative phase imaging is effective and sufficiently general for application to the dynamic phenomena of biological samples.     

G4 Sensing Pyridyl-Thiazole Polyamide Represses c-KIT Expression in Leukemia Cells

Specific sensing and functional tuning of nucleic acid secondary structures remain less explored to date. Herein, we report a thiazole polyamide TPW that binds specifically to c-KIT1 G-quadruplex (G4) with sub-micromolar affinity and ∼1 : 1 stoichiometry and represses c-KIT proto-oncogene expression. TPW shows up to 10-fold increase in fluorescence upon binding with c-KIT1 G4, but shows weak or no quantifiable binding to other G4s and ds26 DNA. TPW can increase the number of G4-specific antibody (BG4) foci and mark G4 structures in cancer cells. Cell-based assays reveal that TPW can efficiently repress c-KIT expression in leukemia cells via a G4-dependent process. Thus, the polyamide can serve as a promising probe for G-quadruplex recognition with the ability to specifically alter c-KIT oncogene expression.     

Synthesis of polymer microsphere-supported chiral pyrrolidine catalysts by precipitation polymerization and their application to asymmetric Michael addition reactions

Polymer microsphere-supported chiral pyrrolidine catalysts were successfully synthesized by a precipitation polymerization incorporating a methacrylate monomer bearing chiral N-Boc-pyrrolidine moiety, followed by removal of the N-Boc groups. The resulting polymeric catalysts were applied to the asymmetric Michael addition reactions of aldehydes with alkyl vinyl ketones. The effects of the comonomer, the molar ratios within the catalyst, the catalyst loading, the temperature, and the solvent on the catalytic performance were investigated in detail. The reactions were found to proceed smoothly in the absence of a solvent. A hydrophobic polystyrene-based chiral pyrrolidine catalyst exhibited high reactivity (up to 97% yield) and enantioselectivity (up to 95% ee) during these reactions. The catalyst could also be recovered and reused up to five times without significant loss of activity.     

Super Sensitization: Grand Charge (Hole/Electron) Separation in ATC Dye Sensitized CdSe,CdSe/ZnS Type‐I,and CdSe/CdTe Type‐II Core–Shell Quantum Dots

Ultrafast charge‐transfer dynamics has been demonstrated in CdSe quantum dots (QD), CdSe/ZnS type‐I core–shell, and CdSe/CdTe type‐II core–shell nanocrystals after sensitizing the QD materials by aurin tricarboxylic acid (ATC), in which CdSe QD and ATC form a charge‐transfer complex. Energy level diagrams suggest that the conduction and valence band of CdSe lies below the LUMO and the HOMO level of ATC, respectively, thus signifying that the photoexcited hole in CdSe can be transferred to ATC and that photoexcited ATC can inject electrons into CdSe QD, which has been confirmed by steady state and time‐resolved luminescence studies and also by femtosecond time‐resolved absorption measurements. The effect of shell materials (for both type‐I and type‐II) on charge‐transfer processes has been demonstrated. Electron injection in all the systems were measured to be <150 fs. However, the hole transfer time varied from 900 fs to 6 ps depending on the type of materials. The hole‐transfer process was found to be most efficient in CdSe QD. On the other hand, it has been found to be facilitated in CdSe/CdTe type‐II and retarded in CdSe/ZnS type‐I core–shell materials. Interestingly, electron injection from photoexcited ATC to both CdSe/CdTe type‐II and CdSe/ZnS type‐I core–shell has been found to be more efficient as compared to pure CdSe QD. Our observation suggests the potential of quantum dot core–shell super sensitizers for developing more efficient quantum dot solar cells.     

Quality evaluation and quantification of cucurbitacin E in different cultivars of Cucumis sativus L. fruit by a validated high-performance thin-layer chromatography method

Cucumis sativus L. of the Cucurbitaceae family, commonly known as cucumber, is commercially cultivated worldwide. The major phytoconstituents present in the Cucurbitaceae family are different curcurbitacins, principally cucurbitacin E. The content of cucurbitacin E differs within the species or cultivars due to factors like genetic variation and geographical location. The present study reports a simple and rapid quantitative analysis of cucurbitacin E in 5 different C. sativus cultivars by a validated high-performance thin-layer chromatography (HPTLC) method. The mobile phase contained petroleum ether, ethyl acetate and formic acid in the ratio of 40:60:0.5 (V/V). Cucurbitacin E was analyzed densitometrically and the absorbance wavelength was 254 nm. The method showed R_F spot = 0.79 ± 0.06, corresponding to cucurbitacin E in various samples. The calibration curve of standard cucurbitacin E showed good linear relationship in the concentration range of 2‒10 µg/spot with a correlation coefficient (r) > 0.99. The HPTLC method was validated in terms of sensitivity, linearity, accuracy, precision, and specificity as per the International Conference on Harmonization (ICH) guidelines. The present study revealed that the content of cucurbitacin E differs among the C. sativus cultivars. This method may be beneficial for addressing the quality-related aspects of C. sativus for food and pharmaceutical preparation.