A note on mixed summation-integral-type operators

Very recently Deo, in the paper “Simultaneous approximation by Lupas operators with weighted function of Szasz operators” [J. Inequal. Pure Appl. Math., 5, No. 4 (2004)] claimed to introduce the integral modifications of Lupas operators. These operators were first introduced in 1993 by Gupta and Srivastava. They estimated the simultaneous approximation for these operators and called them Baskakov-Szasz operators. There are several misprints in the paper by Deo. This motivated us to perform subsequent investigations in this direction. We extend the study and estimate a saturation result in simultaneous approximation for the linear combinations of these summation-integral-type operators. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1135–1139, August, 2007.     

Polyoxometalate-Engineered Building Blocks with Gold Cores for the Self-Assembly of Responsive Water-Soluble Nanostructures

The controlled assembly of gold nanoparticles (AuNPs) with the size of quantum dots into predictable structures is extremely challenging as it requires the quantitatively and topologically precise placement of anisotropic domains on their small, approximately spherical surfaces. We herein address this problem by using polyoxometalate leaving groups to transform 2 nm diameter gold cores into reactive building blocks with hydrophilic and hydrophobic surface domains whose relative sizes can be precisely tuned to give dimers, clusters, and larger micelle-like organizations. Using cryo-TEM imaging and ¹H DOSY NMR spectroscopy, we then provide an unprecedented “solution-state” picture of how the micelle-like structures respond to hydrophobic guests by encapsulating them within 250 nm diameter vesicles whose walls are comprised of amphiphilic AuNP membranes. These findings provide a versatile new option for transforming very small AuNPs into precisely tailored building blocks for the rational design of functional water-soluble assemblies.     

Existence of unimodular elements in a projective module

(1) Let R be an affine algebra over an algebraically closed field of characteristic 0 with $\dim (R)=n$. Let P be a projective $A=R[T_1,?,T_k]$-module of rank n with determinant L. Suppose I is an ideal of A of height n such that there are two surjections $\alpha :P?I$ and $?:L\oplus A^{n?1}?I$. Assume that either (a) $k=1$ and $n\ge 3$ or (b) k is arbitrary but $n\ge 4$ is even. Then P has a unimodular element (see 4.1, 4.3).(2) Let R be a ring containing $\mathbb{Q}$ of even dimension n with height of the Jacobson radical of $R\ge 2$. Let P be a projective $R[T,T^{?1}]$-module of rank n with trivial determinant. Assume that there exists a surjection $\alpha :P?I$, where $I?R[T,T^{?1}]$ is an ideal of height n such that I is generated by n elements. Then P has a unimodular element (see 3.4).     

Comparison of stability and control characteristics of two twin-lift helicopter configurations

The stability and control characteristics of two twin-lift helicopter configurations are analyzed in this paper. In order to address the issue of configuration selection from a handling qualities viewpoint, their open-and closed-loop characteristics are compared. The two twin-lift configurations considered are the twin-lift with spreader bar and twin-lift without spreader bar. The nonlinear models describing the dynamics of these two configurations in the lateral/vertical plane are derived. The open-loop characteristics of the two systems are compared by linearizing the nonlinear models about a symmetric hovering equilibrium condition. The closed-loop characteristics of the two systems are compared using nonlinear controllers based on feedback linearization schemes. The performance of the resulting closed-loop systems in carrying out a typical twin-lift mission is evaluated through nonlinear simulation. Also, the effects of helicopter performance degradation and measurement errors on the overall system performance are discussed.[B] Matrix multiplying the control vector in the nonlinear model[B₁] Matrix multiplying the control vector in the linear model[C] Matrix defining vector of variables to be controlled[C₁] Damping matrixC_ijElement of the damping matrix e Parameter used in the linear model = M ₁ h ₁/I ₁=M ₂ h ₂/I ₂,/ft{f} Vector independent of controls in the nonlinear model g Acceleration due to gravity, ft/sec² h₁, h₂Distance of tether attachment point to the center of gravity for helicopters 1 and 2, ft h Parameter used in the linear model, =h ₁=h ₂, ft h Distance between rotor hub and the helicopter center of gravity, ft h h/l H Distance of the load from the spreader bar c.g., ftH₁, H₂Length of tethers 1 and 2, ftI_RMass moment of inertia of spreader bar, slug-ft² I₁, I₂Roll moments of inertia of helicopters 1 and 2, slug-ft² k Non-dimensional hub control moment coefficientK_DDerivative gainsK_IIntegral gainsK_PProportional gains[K_i] Stiffness matrixK_ijElement of the stiffness matrix l Parameter used in the linear model, =H ₁=H ₂, ft L Spreader bar length, ftNomenclature     

Borazine as a sensor for fluoride ion: a computational and experimental study

The computational and experimental studies have revealed that even simple molecule like borazine can act as a sensor for fluoride ions. This study further reported the various binding modes of analytes using quantum chemical calculations and the nature of such interactions have been examined using electron density surface analysis. Total charge transfer analysis (q_CT) correlates well with the binding affinities of analytes with the borazine receptor.     

Methotrexate intercalated ZnAl-layered double hydroxide

The anticancerous drug methotrexate (MTX) has been intercalated into an ZnAl-layered double hydroxide (LDH) using an anion exchange technique to produce LDH-MTX hybrids having particle sizes in the range of 100-300 nm. X-ray diffraction studies revealed increases in the basal spacings of ZnAl-LDH-MTX hybrid on MTX intercalation. This was corroborated by the transmission electron micrographs, which showed an increase in average interlayer spacing from 8.9 Å in pristine LDH to 21.3 Å in LDH-MTX hybrid. Thermogravimetric analyses showed an increase in the decomposition temperature for the MTX molecule in the LDH-MTX hybrid indicating enhanced thermal stability of the drug molecule in the LDH nanovehicle. The cumulative release profile of MTX from ZnAl-LDH-MTX hybrids in phosphate buffer saline (PBS) at pH 7.4 was successfully sustained for 48 h following Rigter-Peppas model release kinetics via diffusion.     

Multiresidue analysis of multiclass plant growth regulators in grapes by liquid chromatography/tandem mass spectrometry

A selective and rapid multiresidue analysis method is presented for simultaneous estimation of 12 plant growth regulators (PGRs), namely, auxins (indol-3-acetic acid, indol-3-butyric acid, and naphthyl acetic acid), cytokinins (kinetin, zeatin, and 6-benzyladenine), gibberellic acid (GA3), abscisic acid, and synthetic compounds, namely, forchlorfenuron, paclobutrazole, isoprothiolane, and 2,4-dichlorophenoxy acetic acid (2,4-D) in bud sprouts and grape berries at the development stages of 2-3 and 6-8 mm diameters, which are the critical phases when exogenous application of PGRs may be necessary to achieve desired grape quality and yield. The sample preparation method involved extraction of plant material with acidified methanol (50%) by homogenization for 2 min at 15000 rpm. The pH of the extract was enhanced up to 6 by adding ammonium acetate, followed by homogenization and centrifugation. The supernatant extract was cleaned by SPE on an Oasis HLB cartridge (200 mg, 6 cc). The final extract was measured directly by LC/MS/MS with electrospray ionization in positive mode, except for 2,4-D, GA3, and abscisic acid extracts, which required analysis in negative mode. Quantification by multiple reaction monitoring (MRM) was supported with full-scan mass spectrometric confirmation using "information-dependent acquisition" triggered with MRM to "enhanced product ionization" mode of the hybrid quadrupole-ion trap mass analyzer. The LOQ of the test analytes varied between 1 and 10 ng/g with associated recoveries of 80-120% and precision RSD <25% (n = 8). Significant matrix-induced signal suppression was recorded when the responses for pre- and postextraction spikes of analytes were compared; this could be resolved by using matrix-matched calibration standards. The method could successfully be applied in analyzing incurred residue samples and would, therefore, be useful in precisely deciding the necessity and dose of exogenous applications of PGRs on the basis of measured endogenous levels.     

Thiacalix[4]arene based reconfigurable molecular switches: set-reset memorized sequential device

The fluorescent chemosensors 3, 5 and 7 based on thiacalix[4]arene bearing naphthyl groups have been designed and synthesized. The optical chemosensor 3 based on a thiacalix[4]arene of cone conformation behaves as "turn-on" optical chemosensor for Fe(3+) and F(-) ions. However, chemosensors 5 and 7 based on a thiacalix[4]arene of 1,3-alternate conformation demonstrate "turn-on" optical behaviour for Hg(2+), F(-) ions (with receptor 5 as turn-on for K(+) ions also) and "turn-off" behaviour for Fe(3+) ions. The simultaneous presence of Fe(3+) and Hg(2+) or K(+) or F(-) ions results in formulation of reversible "on-off" switches. Various molecular logic gates developed in response to molecular switching between these chemical inputs have been integrated into sequential logic circuits with memory function in a feedback loop which mimics "set-reset" molecular level information processing device.     

Optical chemosensor for Ag+, Fe3+, and cysteine: information processing at molecular level

A thiacalix[4]arene based chemosensor 3 bearing two pyrene groups has been synthesized which demonstrates ratiometric sensing with Ag(+) and fluorescence quenching with Fe(3+) ions in mixed aqueous media. The 'in situ' prepared Ag(+) and Fe(3+) complexes showed high selectivity toward cysteine. The molecular switching between three chemical inputs (Ag(+), Fe(3+), cysteine) results in various molecular logic gates which have been integrated sequentially to generate a sequential information processing device.