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.     

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.

---

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.

     

Dynamic contact angle and spreading rate measurements for the characterization of the effect of dentin surface treatments

A new methodology capable of providing reliable and reproducible contact angle (theta) data has been employed to study the effect of clinical treatments grinding, acid etching, and deproteinization on medial dentin tissue. It is based on the application of the ADSA-CD algorithm to the determination of low-rate dynamic contact angles, obtained from slowly growing drops, and on contact angle measurement, as well as spreading behavior analysis, during the relaxation of the system (water on treated dentin) after initial drop growth. The theta data obtained were substantially more reproducible than those obtained with classical methods. A net effect of the treatment on theta was found, increasing dentin wettability: theta (polished) >theta (etched) >theta (deproteinized). The spreading rates correlate with the angles and are adequate for the dentin surface characterization. ANOVA and SNK tests show that for advancing contact angles the means corresponding to all treatments are significantly different. In the relaxing phase, mean angle and spreading rates on polished dentin differ significantly from those on etched and deproteinized dentin, but the latter do not differ significantly from each other.     

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.