On the solution of a class of the reduced wave equation and the Riccati differential equation

In this paper we present an “iteration” technique for a class of differential equation having the form z^″=λz, where λ is a function in C^∞. We show that we can construct not only the general solution of the reduced wave equation but also the general solution of the Riccati differential equation by using this iteration technique if the given function λ is satisfies the condition

     

Around Jensen’s inequality for strongly convex functions

In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen type and Jensen–Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen’s operator inequality for strongly convex functions. As a corollary, we improve the Hölder-McCarthy inequality under suitable conditions. More precisely we show that if \(Sp\left( A \right) \subset \left( 1,\infty \right) \), then

$$\begin{aligned} {{\left\langle Ax,x \right\rangle }^{r}}\le \left\langle {{A}^{r}}x,x \right\rangle -\frac{{{r}^{2}}-r}{2}\left( \left\langle {{A}^{2}}x,x \right\rangle -{{\left\langle Ax,x \right\rangle }^{2}} \right) ,\quad r\ge 2 \end{aligned}$$

and if \(Sp\left( A \right) \subset \left( 0,1 \right) \), then

$$\begin{aligned} \left\langle {{A}^{r}}x,x \right\rangle \le {{\left\langle Ax,x \right\rangle }^{r}}+\frac{r-{{r}^{2}}}{2}\left( {{\left\langle Ax,x \right\rangle }^{2}}-\left\langle {{A}^{2}}x,x \right\rangle \right) ,\quad 0<r<1 \end{aligned}$$

for each positive operator A and \(x\in \mathcal {H}\) with \(\left\| x \right\| =1\).

     

An algorithm for the estimation of a regression function by continuous piecewise linear functions

The problem of the estimation of a regression function by continuous piecewise linear functions is formulated as a nonconvex, nonsmooth optimization problem. Estimates are defined by minimization of the empirical L ₂ risk over a class of functions, which are defined as maxima of minima of linear functions. An algorithm for finding continuous piecewise linear functions is presented. We observe that the objective function in the optimization problem is semismooth, quasidifferentiable and piecewise partially separable. The use of these properties allow us to design an efficient algorithm for approximation of subgradients of the objective function and to apply the discrete gradient method for its minimization. We present computational results with some simulated data and compare the new estimator with a number of existing ones.     

The catalytic performances of silica supported aluminum,gallium and indium for the <Emphasis Type="Italic">tert</Emphasis>-butylation of aromatics

RHA-Al, RHA-Ga and RHA-In catalysts were synthesized by the direct incorporation of aluminum, gallium and indium ions, respectively, into rice husk ash (RHA) silica at room temperature using the sol–gel method. The prepared catalysts were characterized by physicochemical methods, viz. N₂-adsorption, XRD, FT-IR, SEM-EDX, ICP-MS and Solid-state NMR. These catalysts were used to study the tert-butylation of benzene (Bz) and some substituted benzenes with tert-butyl chloride (TBC). The reaction was proposed to proceed initially through the radical mechanism and subsequently the tert-butyl cation was formed, which in turn attacks the benzene ring for the formation of tert-butyl benzene (TBB) and di-tert-butyl benzene (DTBB) via the S_N1 mechanism (main reaction). However, a proton elimination reaction (side reaction) also occurred, resulting in the formation of isobutene dimers (IBD) and isobutene trimers (IBT). The extent of these side products were found to decrease significantly with time, indicating the reversibility of the oligomerization reactions. The catalysts were stable against leaching and were reusable several times but with observable drop in catalytic activity. RHA-Ga lost almost 20% of its activity after each run, whereas, RHA-In was stable until the 3rd run and then lost ~13% of its activity at the 5th run. The deactivation was suggested to be induced by the poisoning effect of the bulky side products.     

New approaches to due date assignment in job shops

In this study, two new approaches for due date assignment in job shops are evaluated. Proposed approaches use statistical prediction techniques for dynamic prediction of job flowtimes in a job shop environment as the job arrives to the shop floor. Primary objective of this research is to compare the performance of the proposed due date assignment model (PDDAM) with several conventional due date assignment models (CDDAM). For this purpose, simulation models are developed and comparisons of the PDDAM and CDDAM are made in terms of the mean absolute percent error (MAPE), mean percent error (MPE) and mean tardiness (MT). Simulation experiments showed that for many test conditions, PDDAM dominates CDDAM. Therefore, case by case findings are summarized in the paper.     

Ni(II) ion-imprinted solid-phase extraction and preconcentration in aqueous solutions by packed-bed columns

Solid-phase extraction (SPE) columns packed with materials based on molecularly imprinted polymers (MIPs) were used to develop selective separation and preconcentration for Ni(II) ion from aqueous solutions. SPE is more rapid, simple and economical method than the traditional liquid-liquid extraction. MIPs were used as column sorbent to increase the grade of selectivity in SPE columns. In this study, we have developed a polymer obtained by imprinting with Ni(II) ion as a ion-imprinted SPE sorbent. For this purpose, NI(II)-methacryloylhistidinedihydrate (MAH/Ni(II)) complex monomer was synthesized and polymerized with cross-linking ethyleneglycoldimethacrylate to obtain [poly(EGDMA-MAH/Ni(II))]. Then, Ni(II) ions were removed from the polymer getting Ni(II) ion-imprinted sorbent. The MIP-SPE preconcentration procedure showed a linear calibration curve within concentration range from 0.3 to 25 ng/ml and the detection limit was 0.3 ng/ml (3 s) for flame atomic absorption spectrometry (FAAS). Ni(II) ion-imprinted microbeads can be used several times without considerable loss of adsorption capacity. When the adsorption capacity of nickel imprinted microbeads were compared with non-imprinted microbeads, nickel imprinted microbeads have higher adsorption capacity. The K_d (distribution coefficient) values for the Ni(II)-imprinted microbeads show increase in K_d for Ni(II) with respect to both K_d values of Zn(II), Cu(II) and Co(II) ions and non-imprinted polymer. During that time K_d decreases for Zn(II), Cu(II) and Co(II) ions and the k′ (relative selectivity coefficient) values which are greater than 1 for imprinted microbeads of Ni(II)/Cu(II), Ni(II)/Zn(II) and Ni(II)/Co(II) are 57.3, 53.9, and 17.3, respectively. Determination of Ni(II) ion in sea water showed that the interfering matrix had been almost removed during preconcentration. The column was good enough for Ni determination in matrixes containing similar ionic radii ions such as Cu(II), Zn(II) and Co(II).     

Clouding behavior of nonionic–cationic and nonionic–anionic mixed surfactant systems in presence of carboxylic acids and their sodium salts

The study is focused on evaluation of clouding phenomena of the aqueous single nonionic surfactant system Triton X-100 (TX-100) and its mixed systems with anionic aerosol-OT (AOT) and cationic dodecylpyridinium chloride (DPC) in presence of hydrophobic ions furnished by sodium salts of carboxylic acids, viz., sodium ethanoate, sodium propanoate, sodium butanoate, and sodium hexanoate and the respective carboxylic acids [ethanoic acid, propanoic acid, butanoic acid, and hexanoic acid]. The influence of salts on the cloud point (CP) has been explained on the basis of salt effect as well as the solubilization of higher alkyl chain hydrophobic ions furnished by these salts. Moreover, the co- and counterion effect has been taken into account to explain the variation of the CP in the mixed systems. However, the effect of acids on CP has been explained in the light of their aqueous solubility and their partitioning ability between octanol and water as reflected by their K _OW values.     

Reactions of α,β-unsaturated ketones with cyanoacetamide

3-Aryl-1-phenyl-2-propen-1-ones Ia-f and aroylphenylacetylenes Va-d reacted under reflux for 3 hours with cyanoacetamide in the presence of sodium ethoxide to give the corresponding 4-aryl-3-cyano-6-phenyl-2-(1H)pyridones VI. However, when ketones Ia-e were refluxed with cyanoacetamide for one hour in the presence of sodium ethoxide or piperidine, they gave the corresponding 4-aryl-3-cyano-3,4-dihydro-6-phenyl-2-(1H)pyridones IIIa-e, which upon heating with selenium gave the corresponding 2-pyridones VI. The structures of the products are based on chemical and spectroscopic evidence.     

Enantioseparation of aromatic amino acids using CEC monolith with novel chiral selector,N‐methacryloyl‐l‐histidine methyl ester

A new type of polymethacrylate‐based monolithic column with chiral stationary phase was prepared for the enantioseparation of aromatic amino acids, namely d ,l ‐phenylalanine, d ,l ‐tyrosine, and d ,l ‐tryptophan by CEC. The monolithic column was prepared by in situ polymerization of butyl methacrylate (BMA), N‐methacryloyl‐l ‐histidine methyl ester (MAH), and ethylene dimethacrylate (EDMA) in the presence of porogens. The porogen mixture included DMF and phosphate buffer. MAH was used as a chiral selector. FTIR spectrum of the polymethacrylate‐based monolith showed that MAH was incorporated into the polymeric structure via in situ polymerization. Some experimental parameters including pH, concentration of the mobile phase, and MAH concentration with regard to the chiral CEC separation were investigated. Single enantiomers and enantiomer mixtures of the amino acids were separately injected into the monolithic column. It was observed that l ‐enantiomers of aromatic amino acids migrated before d ‐enantiomers. The reversal enantiomer migration order for tryptophan was observed upon changing of pH. Using the chiral monolithic column (100 μm id and 375 μm od), the best chiral separation was performed in 35:65% ACN/phosphate buffer (pH 8.0, 10 mM) with an applied voltage of 12 kV in CEC. SEM images showed that the chiral monolithic column has a continuous polymeric skeleton and large through‐pore structure.     

Synthesis,spectral and biological studies of organotin(IV) complexes of heteroscorpionate

A heteroscorpionate ligand, potassium hydrobis(benzoato)(salicylaldehyde)borate (KL), has been synthesized. This was converted into organotin complexes R₂SnL₂ and R₃SnL complexes by mixing and stirring with a methanolic solution/suspension of organotin chloride. The ligand and its complexes were characterized by elemental analyses and spectral studies (IR, ¹H NMR, ¹³C NMR, ESI mass spectra and Thermo gravimetric analysis (TGA)). Antibacterial and antifungal studies of these compounds were evaluated by the disc diffusion method at variable concentration against three species of bacteria (Staphylococcus aureus, Klebsiella pneumonia and Bacillius subtillis) and two species of fungi (Asperjillius fiavus and Candida albicans). It was found that triorganotin derivatives (R₃SnL) of the ligand were more effective as compared with diorganotin derivatives (R₂SnL₂). The organotin complexes of borates were tested for their algicidal activity on the cyanobacterial strains Aulosira fertilissma, Anabaena species, Anabaena variabilis and Nostoc muscorum and showed high to moderate toxicity towards the above species. The ligand and its complexes were also tested for its pH effect on soil in vitro for a duration of more than one month and it was found that they are able to kill pests without damaging the soil quality. Copyright © 2006 John Wiley & Sons, Ltd.