Fractional damping enhances chaos in the nonlinear Helmholtz oscillator

Nonlinear Dynamics - The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional-order damping. For that...     

From dilute to dense self-avoiding walks on hypercubic lattices

A field-theoretic representation is presented to count the number of configurations of a single self-avoiding walk on a hypercubic lattice ind dimensions with periodic boundary conditions. We evaluate the connectivity constant as a function of the fractionf of sites occupied by the polymer chain. The meanfield approximation is exact in the limit of infinite dimensions, and corrections to it in powers ofd ^–1 can be systematically evaluated. The connectivity constant and the site entropy calculated throughout second order compare well with known results in two and three dimensions. We also find that the entropy per site develops a maximum atf1–(2d)^–1. Ford=2 (d=3), this maximum occurs atf~0.80 (f~0.86) and its value is about 50% (30%) higher than the entropy per site of a Hamiltonian walk (f=1).     

Capillary zone electrophoretic separation and determination of imidazolic antifungal drugs

Capillary zone electrophoresis (CZE) was adapted to the simultaneous determination of a mixture of three imidazolic antifungal drugs. Separation was achieved by using a fused-silica capillary column with an acetic acid-Tris buffer at pH 5.18 and UV detection at 196 nm. Several electrophoretic parameters were investigated: pH and buffer concentration, applied voltage, temperature and injection conditions. The optimized CZE method was applied to the individual determination of ketoconazole, clotrimazole and econazole in pharmaceutical forms, after a previous single extraction step in methanol, with recoveries of 98.00, 99.96 and 99.58% respectively. The antifungal drugs can be determined at a concentration level lower than 1.0 x 10(-7) M.     

A family of (n−1)! Diagonal polynomial orders ofN n

Letn>0 be an element of the setN of nonnegative integers, and lets(x)=x ₁+...+x _n , forx=(x ₁, ...,x _n ) N _n . Adiagonal polynomial order inN _n is a bijective polynomialp:N _n N (with real coefficients) such that, for allx,y N _n ,p(x)<p(y) whenevers(x)<s(y). Two diagonal polynomial orders areequivalent if a relabeling of variables makes them identical. For eachn, Skolem (1937) found a diagonal polynomial order. Later, Morales and Lew (1992) generalized this polynomial order, obtaining a family of 2 ^n–2 (n>1) inequivalent diagonal polynomial orders. Here we present, for eachn>0, a family of (n – 1)! diagonal polynomial orders, up to equivalence, which contains the Morales and Lew diagonal orders.     

Synthesis of 5-glycopyranosylamino-pyrano[2,3-d]pyrimidin-2-one derivatives

Summary Three series of 3-substituted 5-glycopyranosylamino pyrano[2,3-d]pyrimidin-2-one derivatives,3 a–c,4 a–c, and5 a–c have been prepared by treatment of the corresponding 1,4-dihydro-6-glycopyranosylamino pyrimidin-4-ones1 a–c with malonic, methyl malonic and ethyl malonic acids, respectively.

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Synthese von Derivaten des 5-Glucopyranosylaminopyrano[2,3-d]pyrimidin-2-on

Zusammenfassung Es wurden drei Serien von 3-substituierten 5-Glucopyranosylaminopyrano[2,3-d]pyrimidin-2-onen (3 a–c,4 a–c und5 a–c) mittels Behandlung der entsprechenden 1,4-Dihydro-6-glucopyranosylamino-pyrimidin-4-one (1 a–c) mit Malon-, Methylmalon- bzw. Ethylmalonsäure dargestellt.

     

The reaction of aromatic α,β-unsaturated ketones with 4,5-diamino-1,6-dihydropyrimidin-6-ones

The reaction of 4,5-diamino-1,6-dihydropyrimidin-6-ones 1 with one equivalent of the chalcones 2 leads in an acidic medium to the formation of the 2,4-diaryl-2,3,6,7-tetrahydro-1H-pyrimido[4,5-b][1,4]diazepin-6-ones 3a-m . The structure elucidation of the products is based on detailed nmr investigations including selective ¹³C[¹H] decoupling experiments.     

Synthesis of 4-aryl-2,3,6,7-tetrahydro-1H-pyrimido[4,5-b][1,4]-diazepin-6-ones from 4,5-diamino-1H-pyrimidin-6-ones and 1-aryl-3-(dimethylamino)-1-propanones

The reaction of 1-aryl-3-(dimethylamino)-1-propanones 1 with one equivalent of 4,5-diamino-1H-pyrimidin-6-ones 2 , in acidic medium, leads to the formation of 4-aryl-2,3,6,7-tetrahydro-1H-pyrimido[4,5-b]-[1,4]diazepin-6-ones 3 . The structure elucidation of the products is based on detail nmr analysis of experiments such as ¹³C, ¹H and DEPT including selective ¹³C{¹H} decoupling experiments.