Quartic Thue equations

We will give upper bounds upon the number of integral solutions to binary quartic Thue equations. We will also study the geometric properties of a specific family of binary quartic Thue equations to establish sharper upper bounds.     

A note on “A new method for solving fully fuzzy linear programming problems”

This note shows that solving fully fuzzy linear programming (FFLP) model presented by Kumar et al. [A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Appl. Math. Model. 35 (2011) 817–823] needs some corrections to make the model well in general. A new version is provided in this note. A simple example is also presented to demonstrate the new form.     

Synthesis and Characterization of Ligand-Linked Pt Nanoparticles: Tunable,Three-Dimensional,Porous Networks for Catalytic Hydrogen Sensing

Porous networks of Pt nanoparticles interlinked by bifunctional organic ligands have shown high potential as catalysts in micro-machined hydrogen gas sensors. By varying the ligand among p-phenylenediamine, benzidine, 4,4‘‘-diamino-p-terphenyl, 1,5-diaminonaphthalene, and trans-1,4-diaminocyclohexane, new variants of such networks were synthesized. Inter-particle distances within the networks, determined via transmission electron microscopy tomography, varied from 0.8 to 1.4 nm in accordance with the nominal length of the respective ligand. While stable structures with intact and coordinatively bonded diamines were formed with all ligands, aromatic diamines showed superior thermal stability. The networks exhibited mesoporous structures depending on ligand and synthesis strategy and performed well as catalysts in hydrogen gas microsensors. They demonstrate the possibility of deliberately tuning micro- and mesoporosity and thereby transport properties and steric demands by choice of the right ligand also for other applications in heterogeneous catalysis.     

Green synthesis and chemical characterization of silver nanoparticles obtained using Allium saralicum aqueous extract and survey of in vitro antioxidant,cytotoxic, antibacterial and antifungal properties

Allium saralicum R.M. Fritsch has been used in Iranian traditional medicine as a remedial supplement for microbial diseases. This paper reports the green synthesis, chemical characterization and antioxidant, cytotoxic, antibacterial and antifungal properties of silver nanoparticles obtained using aqueous extract of A. saralicum leaves. In this synthesis, no surfactants or stabilizers were used. For characterization, UV–visible spectroscopy, transmission electron microscopy, X‐ray diffraction, energy‐dispersive X‐ray spectroscopy and field emission scanning electron microscopy were used. 2,2‐Diphenyl‐1‐picrylhydrazyl was used in experiments to assess the antioxidant potential of the silver nanoparticles, which revealed an impressive prevention in comparison with butylated hydroxytoluene. The synthesized silver nanoparticles at low doses (1–250 μg dl^?1) did not show marked cytotoxic activity (against cervical cancer cells (Hela), breast cancer cells (MCF‐7) and human embryonic kidney cells (HEK‐293)). Agar diffusion tests were applied to determine the antibacterial and antifungal characteristics. Compared with all standard antimicrobials, the silver nanoparticles showed higher antibacterial and antifungal activities (p ≤ 0.01). Also, the silver nanoparticles inhibited the growth of all bacteria and fungi at concentrations of 31–250 μg ml^?1, and destroyed them at concentrations of 31–500 μg ml^?1 (p ≤ 0.01). Because the silver nanoparticles obtained using aqueous extract of A. saralicum leaves have antioxidant, non‐cytotoxic, antifungal and antibacterial potentials, they can be used as a medical supplement or drug.     

Reaction between alkyl isocyanides and 3-formylchromones in the presence of monocyclic unsaturated acyl compounds: Competition between Friedel-Crafts acylation and Diels-Alder cycloaddition

The highly reactive alkylaminofurochromenone intermediate, produced from the reaction between 3-formylchromones and alkyl isocyanides, was trapped by monocyclic unsaturated acyl compounds such as maleic anhydride or maleimide derivatives to yield new types of organic fluorophores 4-(alkylamino)-1H-furo[3,4-b]xanthene-1,3,10-triones or 4-(alkylamino)chromeno[2,3-f]isoindole-1,3,10(2H)-triones, which exhibited strong sky blue emission in solution. The reaction is very simple from an experimental point-of-view and allows the creation of a fused benzene ring with concomitant formation of three new C–C bonds in a single operation.     

On the Littlewood cyclotomic polynomials

In this article, we study the cyclotomic polynomials of degree N−1 with coefficients restricted to the set {+1,−1}. By a cyclotomic polynomial we mean any monic polynomial with integer coefficients and all roots of modulus 1. By a careful analysis of the effect of Graeffe's root squaring algorithm on cyclotomic polynomials, P. Borwein and K.K. Choi gave a complete characterization of all cyclotomic polynomials with odd coefficients. They also proved that a polynomial p(x) with coefficients ±1 of even degree N−1 is cyclotomic if and only if p(x)=±Φp₁(±x)Φp₂(±xp₁)?Φpr(±xp₁p₂?pr−1), where N=p₁p₂?pr and the pi are primes, not necessarily distinct. Here is the pth cyclotomic polynomial. Based on substantial computation, they also conjectured that this characterization also holds for polynomials of odd degree with ±1 coefficients. We consider the conjecture for odd degree here. Using Ramanujan's sums, we solve the problem for some special cases. We prove that the conjecture is true for polynomials of degree α²pβ−1 with odd prime p or separable polynomials of any odd degree.     

Silica-bonded S-sulfonic acid as a recyclable catalyst for chemoselective synthesis of 1,1-diacetates

A simple and efficient procedure for the preparation of silica-bonded S-sulfonic acid (SBSSA) by reaction of 3-mercaptopropylsilica (MPS) and chlorosulfonic acid in chloroform is described. This solid acid is employed as a recyclable catalyst for the synthesis of 1,1-diacetates from aromatic aldehydes and acetic anhydride under mild and solvent-free conditions at room temperature.     

Direct electrical measurement of the conversion of metal acetates to metal sulfides by hydrogen sulfide

Copper acetate and related metal salt films react directly with hydrogen sulfide at room temperature to form metal sulfides, resulting in conductivity changes as large as 108. The observed changes in conductivity are related to the solubility product constant (Ksp) and the difference in conductivity between the metal salt and the resulting metal sulfide. A smaller Ksp indicates a more stable metal sulfide and, therefore, greater metal salt reactivity. Polyaniline nanofiber/metal salt composites were also examined and show metal sulfide conversion with changes in resistance up to 106. The direct electrical measurement of the conversion of metal salt to metal sulfide has the potential to be the basis of a new type of sensitive, thin-film chemical sensor.     

Competitive modes for the Baier–Sahle hyperchaotic flow in arbitrary dimensions

In this article, the stretch-twist-fold (STF) flow is numerically studied using phase portraits, sensitive dependence on initial conditions, Lyapunov exponents, power spectrum, and the Poincaré map. The stretch-twist-fold flow is a two-parameter family of Stokes flows defined in a unit sphere that is associated with the fluid particle motion that naturally arises in the dynamo theory, which proposes a mechanism by which celestial bodies, such as earth and sun can maintain and amplify the magnetic field continuously. For this continuous growth of magnetic field, scientists are interested to invent new tools for the nonfuel consumption magnetism propulsion for the low earth orbit of spacecrafts or satellites. General properties of a chaotic dynamical system reference to the stretch-twist-fold flow model are addressed and numerical solutions are generated to explain some of these properties. Analytically, we studied the local behavior at equilibrium points. The predictability of chaos in the STF flow with the numerical calculation of Lyapunov exponents and Poincaré map is presented in this paper.