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).     

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.     

A question in the theory of saturated formations of finite soluble groups

This paper examines the following question. If and are saturated formations then is defined to be the class of all soluble groups whose belong to . In general is a formation, but need not be a saturated formation. Here the smallest saturated formation containing is studied.     

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.     

Liquid-Phase Selective Oxidation of Propane on Silica-Supported Nafion Catalysts

The liquid-phase partial oxidation of propane in the presence of the Fen+/H2O2 Fenton system at 70℃ and 1.4 atm on silica supported Nafion catalysts has been investigated. The reaction proceeds via a radical reaction path the efficiency of which is improved by silica-supported Nafion catalysts. Because of the direct relationship between reaction rate and concentration of sulphonic acid sites of Nafion catalysts, it is inferred that the active phase enahnces the kinetics of propane conversion by promoting the rate of active radicals generation.     

Reaction of 6-aminopyrimidin-4-ones with diethyl ethoxymethylenemalonate in several media: Synthesis of pyrido[2,3-d]pyrimidines

Reactions of 6-amino-3,4-dihydro-2-methoxy-4-oxopyrimidine 1 and its 3-methyl derivative 2 , with diethyl ethoxymethylenemalonate (EMME) are discussed in this paper. These reactions have been carried out in the following media: under fusion, ethanol, sodium methoxide/methanol, sodium ethoxide:ethanol and acetic acid media. In acetic medium, mixtures of products proceeding from C-alkylation and N-alkylation were obtained, while in the remaining conditions only products of N-alkylation were obtained.