On the dynamics of a class of rational Kolmogorov systems

In this paper we are intersted in studying the existence of a First integral and the non-existence of limit cycles of rational Kolmogorov systems of the form where P (x, y) , Q (x, y) , R (x, y) , S (x, y) are homogeneous polynomials of degree n, n, m, a respectively.     

Numerical Simulations of Fractional Systems: An Overview of Existing Methods and Improvements

An overview of the main simulation methods of fractional systems is presented. Based on Oustaloups recursive poles and zeros approximation of a fractional integrator in a frequency band, some improvements are proposed. They take into account boundary effects around outer frequency limits and simplify the synthesis of a rational approximation by eliminating arbitrarily chosen parameters.     

One pot Pd(OAc)2-catalysed 2,5-diarylation of imidazoles derivatives

The regioselective 2- or 5-arylation of imidazole derivatives with aryl halides using palladium catalysts has been described in recent years; whereas the arylation at both C2 and C5 carbons of imidazoles in high yields has not been performed. We found conditions allowing the access to these 2,5-diarylimidazoles via a one pot reaction. The choice of the base was found to be crucial to obtain these products in high yields. Using CsOAc as the base, DMA as the solvent and only 2 mol % of the phosphine-free Pd(OAc)₂ the catalyst, the target 2,5-diarylated imidazoles were obtained in moderate to good yields with a wide variety of aryl bromides. Substituents such as fluoro, trifluoromethyl, formyl, acetyl, propionyl, ester, nitro or nitrile on the aryl bromide were tolerated. Sterically congested aryl bromides or heteroaryl bromides can also be employed. Surprisingly the nature of the substituent at position 1 on the imidazole derivative exhibits a huge influence on the reaction.     

Study of mechanism retention of nonvolatile alkylphosphonic acids on unmodified selected polymer-based ion exchanger columns

The retention of alkylphosphonic acids (MPA, EPA, PPA, and BPA) and inorganic anions (Cl⁻, NO₃⁻, and SO₄²⁻) were studied on two anion exchangers, e.g., Dionex IonPac AS4A-SC (250 ± 4 mm I.D.) and Satisfaction P 4000-SAX (50 ± 4.6 mm I.D.) under isocratic elution conditions with evaporative light scattering detector. The plots of retention factors, k, of organic anions vs. the reciprocal of eluent ion concentration show good linearity. The major retention mechanisms are interpreted as ion exchange and some others interactions. The C effect of organic modifier added to the aqueous buffered mobile phase is also investigated.     

Sono-Transition-Metal Catalysis of One-Pot Three-Step Synthesis of Glycosyl-1,2,3-triazoles

As a continuation of our studies directed at the development of straightforward and sustainable methodologies, we describe herein an original example of a combined effect of ultrasonic activation and iron–copper dual catalysis that allows an efficient and ecofriendly one-pot, three-step route to a new series of nucleoside-substituted triazoles. The reactions were carried out under both conventional and ultrasonic irradiation conditions.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

Are the hyperharmonics integral? A partial answer via the small intervals containing primes

In a recent work, the authors have used Bertrand's postulate to give a partial answer to the conjecture of Mez? which says that the hyperharmonic numbers – iterations of partial sums of harmonic numbers – are not integers. In this Note, using small intervals containing prime numbers, we prove that a great class of hyperharmonic numbers are not integers.     

Synthesis and antitumor activity of puupehedione and related compounds

The first enantiospecific synthesis of bioactive marine puupehedione (2) and related compounds from (−)-sclareol (11) is reported. The antitumor activity of these compounds was assayed and compared with that of the natural products.