Spectral asymptotics and basis properties of fourth order differential operators with regular boundary conditions

In this paper, we consider the problem where λ is a spectral parameter; q(x) ∈ L₁(0,1) is complex‐valued function; α_s, s = 1,2,3, are arbitrary complex constants that satisfy α₂ = α₁ + α₃ and σ = 0,1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem are established. It is proved that all the eigenvalues, except for finite number, are simple and the system of root functions of this spectral problem forms a basis in the space L_p(0,1), 1 < p < ∞ , when ; moreover, this basis is unconditional for p = 2. We note that the considered problem was previously investigated in the condition of α₂ ≠ α₁ + α₃. Copyright © 2013 John Wiley & Sons, Ltd.     

Effect of amine catalysts on preparation of nanometric SiO<Subscript>2</Subscript> particles and antireflective films via sol–gel method

SiO₂ sols were prepared by hydrolysis and condensation reactions of tetraethyl orthosilicate through a one step acid or a two step acid + base catalysis process, in the presence of nitric acid and four different base catalyzers, namely trimethylamine, triethylamine, tripropylamine and tributylamine. Hydrolysis of TEOS was followed by FT-IR analyses. Particle size distributions of the sols were evaluated after predetermined durations in 1–22 days. Particle growth was seen to be faster in amine catalyzed systems than in one step acid catalyzed system. The highest rate of growth was in triethylamine catalyzed system. Glass substrates were dip coated with the prepared SiO₂ sols. Effect of sol aging duration on film thickness and on light transmittance properties of the films was investigated with respect to type of base catalyst. Thicknesses of the films which were measured to be in the range of 100–400 nm, were seen to increase with aging duration of the sols. Triethylamine catalyzed system presented the highest film thickness. Films obtained from one step acid catalyzed system presented an increase of 4.8%; whereas acid + base catalyzed films provided an increase in the light transmittance of 5.7% in the first 4 days of aging. Surfaces of films were examined by FESEM and AFM. The antireflective character of the films was verified by diffuse reflectance analyses.     

Swelling of <Emphasis Type="Italic">N</Emphasis>-vinylcaprolactam-dodecyl methacrylate gel in {heptane + toluene} mixtures

A copolymer gel has been synthesized from N-vinylcaprolactam and dodecyl methacrylate in ethanol using the free radical cross-linking polymerization method. Characterizations of the gel were performed by scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and thermal gravimetric analysis (TGA) techniques. Swelling behavior of the gel was investigated in heptane, toluene, and their binary mixtures with different compositions. Swelling value in toluene is higher than that in heptane and swelling value increases with the increasing initial content of toluene in the binary mixture with heptane. The swelling values are correlated by the first- and second-order differential equations, and the best model correlating the experimental results is a second-order one. Diffusion coefficients have also been calculated for heptane and toluene at each concentration by power-law and first-order equations. While the diffusion mechanism of the gel in heptane is a Fickian one, the gel swelled in toluene exhibits a non-Fickian character. Diffusion mechanisms of the gels in binary mixtures are much more complicated. Because of the higher swelling degree in toluene compared to that in heptane, selectivity of the gel in different {heptane + toluene} mixtures with selectivity close to 1 has also been taken into consideration.     

Swelling behaviors of poly(dodecyl methacrylate-co-methyl eugenol) and poly(dodecyl methacrylate-co-methyl chavicol) gels in essential oil components

Poly(dodecylmethacrylate-co-methyleugenol) P(DDMA-co-Meu) and poly(dodecylmethacrylate-co-methylchavicol) P(DDMA-co-Mch) gels were synthesized in ethanol using free radical cross-linking polymerization method at 60 °C for 24 h in the presence of azobisisobutyronitrile (AIBN) and triethylene glycol dimethacrylate (TEGDMA) as initiator and cross-linker, respectively. Scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR) were used to characterize the gels. These gels were used to investigate swelling behaviors in linalool and methyl eugenol, in essential oil mixture of phenyl propanoid and terpenoid, and also in various solvents. While the equilibrium swelling values (ESV) of both gels were higher in linalool than in methyl eugenol, the result was vice versa in the case of essential oil mixture. ESVs of both gels were also obtained in various solvents with different functional groups and the highest ESV of both gels were obtained in toluene, and the lowest ESV of P(DDMA-co-Meu) and P(DDMA-co-Mch) was in methanol and in ethylene glycol, respectively. While P(DDMA-co-Meu) is sensitive to carbon number change in alcohol, P(DDMA-co-Mch) is less sensitive. In the case of esters, increase of carbon number in functional group causes a more significant change in ESV than an increase of carbon number in aliphatic chain. Experimental results were correlated by the first-order and second-order models. The second-order model was more suitable than the other. While P(DDMA-co-Meu) gel swelled in linalool exhibits a Fickian diffusion character, the diffusion mechanism of the gel in methyl eugenol is a non-Fickian one. In the case of P(DDMA-co-Mch), the result is vice versa.     

The synthesis and characterization of copper(II)–<Emphasis Type="Italic">p</Emphasis>-aminosalicylate complexes with diamine ligands

The complexes were synthesized by the reaction between sodium salt of p-aminosalicylic acid (PAS) and Cu(II) for 1 and corresponding ethylenediamine (en) or its derivatives for 2–6. The complexes were characterized by using elemental analyses, FT-IR, UV–Vis, magnetic moment measurements, and thermal analyses techniques. In complex 1[Cu₂(PA)₄(H₂O)₂], two Cu(II) ions were found as bridged by four μ-O:O′ p-aminosalicylato (PA) ligands, forming a cage structure, and two aqua ligands to form dinuclear square-pyramidal geometry around Cu(II) ions. In the complexes 2–6, the PA (anionic form of p-aminosalicylic acid) coordinated to Cu(II) ions as monodentate manner by using its oxygen atom of deprotonated carboxylic acid and ethylenediamine derivatives coordinated to the Cu(II) ions in bidentate manner to form mononuclear octahedral complexes [Cu(PA)₂(L)₂] (L = ethylendiamine, N,N-dimethylethylendiamine, N,N′-dimethylethylendiamine, N,N,N′,N′-tetramethylethylendiamine, and 1,3-propanediamine, for complexes 2, 3, 4, 5, and 6, respectively). In all the complexes OH and NH₂ groups of PA ligands were not coordinated to metals.     

On a generalization of semisimple modules

Let R be a ring with identity. A module \(M_R\) is called an r-semisimple module if for any right ideal I of R, MI is a direct summand of \(M_R\) which is a generalization of semisimple and second modules. We investigate when an r-semisimple ring is semisimple and prove that a ring R with the number of nonzero proper ideals \(\le \)4 and \(J(R)=0\) is r-semisimple. Moreover, we prove that R is an r-semisimple ring if and only if it is a direct sum of simple rings and we investigate the structure of module whenever R is an r-semisimple ring.     

Hubbing and routing in postal delivery systems

We consider the combined hubbing and routing problem in postal delivery systems and develop an iterative two-stage solution procedure for the problem. In the first stage, hub locations are determined and postal offices are multiply allocated to the hubs. The second stage gives the routes in hub regions that alter the distances between points used in the hub-location problem. The procedure then iterates between two stages by updating the distances used in hubbing in order to produce a route-compatible hub configuration. Computational experience is reported for the test problems taken from the literature. For a case study Turkish postal delivery system data are utilized. As the case study is applied on a road network, a final stage, seeking improvements based on special structures in the routed network, is appended to the two-stage solution procedure.     

Inventory control with an order-time constraint: optimality,uniqueness and significance

This paper analyzes a stochastic inventory problem with an order-time constraint that restricts the times at which a manufacturer places new orders to a supplier. This constraint stems from the limited upstream capacity in a supply chain, such as production capacity at a supplier or transportation capacity between a supplier and a manufacturer. Consideration of limited upstream capacity extends the classical inventory literature that unrealistically assumes infinite supplier/transporter capacity. But this consideration increases the complexity of the problem. We study the constraint under a Poisson demand process and allow for a fixed ordering cost. In presence of the constraint, we establish the optimality of an (s,S) policy under both the discounted and average cost objectives. Under the average cost objective, we show the uniqueness of the order-up-to level S. We numerically compare our model with the classical unconstrained model. We report significant savings in costs that can be achieved by using our model when the order time is constrained.     

Synthesis,characterization, duplex-DNA interactions,and anticancer activities of novel octahedral [Ni(phen)2(dppz-idzo)]2+ and [Co(phen)2(dppz-idzo)]3+ complexes

Two new octahedral [Ni(phen)₂(dppz-idzo)]²⁺ and [Co(phen)₂(dppz-idzo)]³⁺ complexes have been synthesized and characterized by CHN analysis, electrospray ionization-MS, nuclear magnetic resonance, and UV–Vis spectra. The DNA-binding ability of these complexes was spectrophotometrically, hydrodynamically, and electrophoretically evaluated which indicated that they strongly intercalate into the DNA double helix, and that both induced severe DNA damage in the presence of peroxide. The complexes also showed strong antiproliferative effect against HepG2 and MDA-MB-231 cells. By contrast, they were found to be inactive against the MCF-7 cell line. The ligand itself was found to be inactive against the cells tested.