Calculation of bounds on variables satisfying nonlinear inequality constraints

Existing techniques for solving nonconvex programming problems often rely on the availability of lower and upper bounds on the problem variables. This paper develops a method for obtaining these bounds when not all of them are availablea priori. The method is a generalization of the method of Fourier which finds bounds on variables satisfying linear inequality constraints. First, nonlinear inequality constraints are converted to equivalent sets of separable constraints. Generalized variable elimination techniques are used to reduce these to constraints in one variable. Bounds on that variable are obtained and an inductive process yields bounds on the others.Research Sponsored by the Office of Naval Research Grant N00014-89-J-1537.     

Effect of pressure on turnover behaviour inI–V characteristic curves in GeTeSe chalcogenide glass

Summary Thick layers of GeTeSe chalcogenide glass have been prepared and subjected to conduction measurements under the effect of both temperature and pressure. The results of theI–V characteristics exhibit transition from high-resistance state to differential negative resistance state through a turnover point. The application of uniaxial pressure shows the similar effect of temperature on that behaviour. Both current and voltage at the turnover point depend on pressure and ambient temperature. The rise of temperature in the conduction path due to joule heating and application of uniaxial pressure as well as the reduction in the energy gap width (β=2.87·10⁻¹²eV/N m⁻²) are estimated and discussed at the turnover point. This behaviour is explained according to the orientation of dipoles randomly dispersed in viscous amorphous matrix.     

Highest weight representations of Euclidean Kac-Moody algebras spanned by the principal subalgebra action

The aim of this Letter is to characterize the representations of Euclidean Ka-Moody with highest weight, spanned by the principal subalgebra action on a highest-weight vector.We conjecture that, modulo the Dynkin diagram automorphisms, only the basic representations have this property. This is proved for A _infn ^sup(1) , D _inf4 ^sup(1) , and A _inf2 ^sup(2) .     

Blowing up solutions for Neumann problem with critical nonlinearity on the boundary

Let G be a transitive permutation group on a finite set of size at least 2. By a well known theorem of Fein, Kantor and Schacher, G contains a derangement of prime power order. In this paper, we study the finite primitive permutation groups with the extremal property that the order of every derangement is an r-power, for some fixed prime r. First we show that these groups are either almost simple or affine, and we determine all the almost simple groups with this property. We also prove that an affine group G has this property if and only if every two-point stabilizer is an r-group. Here the structure of G has been extensively studied in work of Guralnick and Wiegand on the multiplicative structure of Galois field extensions, and in later work of Fleischmann, Lempken and Tiep on \({r'}\)-semiregular pairs.     

New strategy for the biosorption of atrazine after magnetic solid‐phase extraction from water followed by high‐performance liquid chromatography analysis

We describe a rapid and simple microextraction of atrazine from water samples. This method is based on the use of magnetic nanoparticles as sorbents and bioaggregates that are applied to the extraction and preconcentration of atrazine. The resulting magnetic nanoparticles possess a fast adsorption kinetics and high adsorption capacity. Bioaggregates made up of rhaminolipid biosurfactant were assessed as a new strategy for the sample treatment. The extractant was obtained from magnetic nanoparticles using the magnetic solid‐phase extraction method. Then the target analyte was rapidly transferred from the sorbent surface to bioaggregates, which have a low toxicity and are green and ecofriendly. Finally, the extract is centrifuged and transferred to micro‐syringe for analysis by high‐performance liquid chromatography. Experimental parameters affecting the extraction efficiency were studied and optimized. Under optimum conditions the enrichment factor was 268. The linear dynamic range and limit of detection were 0.1–50 and 0.033 μg/L, respectively. The relative standard deviation for six replicate measurements was 5.3%. The results demonstrate good applicability of biosorption‐assisted magnetic solid‐phase extraction method for the determination of atrazine from water samples.     

Synthesis and structural characterization of the dinuclear tetrakis(guanidino) bis(2-cyanoguanidine)dicopper(II) complex

The synthesis and crystal structure of a new dinuclear complex Cu₂(C₂H₄N₄)₂ (CH₃N₃)₄ are reported. It crystallizes in the monoclinic system of space group P2₁/c, with a = 8,459(1) Å, b = 15,481(3) Å, c = 8,714(2) Å, = 110,60(1)°, and Z = 2. The centrosymmetric molecular structure of Cu₂(C₂H₄N₄)₂(CH₃N₃)₄ comprises a tetrakis(guanidino)-bridged dinuclear copper(II) core with axially located cnge moities.