Some stochastic $${\varvec{}}$$-divergences in information theory

In this paper, we introduce the concept of stochastic HH-divergences based on convex stochastic processes. As an application, we propose some inequalities related to stochastic HH-divergences for convex stochastic processes. Our result extends HH-divergence in the class of f-divergence to the class of convex stochastic processes.     

Exact arithmetic on the Stern–Brocot tree

In this paper we present the Stern–Brocot tree as a basis for performing exact arithmetic on rational numbers. There exists an elegant binary representation for positive rational numbers based on this tree [Graham et al., Concrete Mathematics, 1994]. We will study this representation by investigating various algorithms to perform exact rational arithmetic using an adaptation of the homographic and the quadratic algorithms that were first proposed by Gosper for computing with continued fractions. We will show generalisations of homographic and quadratic algorithms to multilinear forms in n variables. Finally, we show an application of the algorithms for evaluating polynomials.     

Metal- and Solvent-Free Transesterification and Aldol Condensation Reactions by a Homogenous Recyclable Basic Ionic Liquid Based on the 1,3,5-Triazine Framework

A new recyclable basic ionic liquid was introduced as an efficient catalyst for aldol condensation and transesterification reactions under environmentally friendly conditions. The catalyst was prepared based on methyl imidazolium moieties bearing hydroxide counter anions via the Hofmann elimination on a 1,3,5-triazine framework. The ionic liquid with two functionalities including anion stabilizer and high basicity, was used as an efficient catalyst for aldol condensation as well as transesterification reaction of a variety of alkyl benzoates. All reactions were performed in the absence of any external reagent, co-catalyst, or solvent, in line with environmental protection. The kinetics isotope effect (KIE) was conducted for the transesterification reaction to elucidate the mechanism and rate determining step (RDS). It worth noted that, the homogeneous catalyst could be recycled from the reaction mixture and reused for several consecutive runs with insignificant drop of basicity and conversion.     

Mg-catalyzed one-pot preparation of benzimidazoles and spirooxindoles by an immobilized chlorophyll b on magnetic nanoparticles

Chlorophyll b was extracted from Heliotropium europaeum plant, then immobilized on magnetic nanoparticles (Fe₃O₄@SiO₂@Chl-Mg) and found as an efficient and green catalyst for the preparation of a variety of benzimidazoles and spirooxindoles in mild conditions. The catalyst was fully characterized by Fourier-transform infrared (FTIR), ultraviolet–visible (UV–vis) spectroscopy, X-ray diffraction (XRD), energy-dispersive X-ray spectroscopy (EDX), thermogravimetric (TGA), vibrating sample magnetometer (VSM), transmission electron microscopy (TEM), and dynamic light scattering (DLS) analyses. To prove the catalytic influence of Mg over the reactions, the catalytic activity of the demetalated chlorophyll b as well as some other control experiments was investigated. High to excellent yields were achieved for all entries, whether benzimidazole or spirooxindole derivatives at short reaction times. The catalyst could be recovered and reused for several consecutive runs by a simple external magnetic field without any considerable reactivity loss. The properties of the recovered catalyst were investigated by various analyses. Finally, the reasonable mechanisms were proposed for the reactions based on the literature.     

Fe3O4@SiO2 nanoparticles–functionalized Cu(II) Schiff base complex with an imidazolium moiety as an efficient and eco-friendly bifunctional magnetically recoverable catalyst for the Strecker synthesis in aqueous media at room temperature

Cu(II) Schiff base complex supported on Fe₃O₄@SiO₂ nanoparticles was employed as a magnetic nanocatalyst (nanocomposite) with a phase transfer functionality for the one-pot preparation of α-aminonitriles (Strecker reaction). The desired α-aminonitriles were obtained from the reaction of aromatic or aliphatic aldehydes, aniline or benzyl amine, NaCN, and 1.6 mol% of the catalyst in water at room temperature and good to excellent yields were obtained for all substrates. The catalyst was characterized analytically and instrumentally including Fourier-transform infrared spectroscopy, X-ray diffraction, thermogravimetric, nuclear magnetic resonance, energy-dispersive X-ray spectroscopy, inductively coupled plasma spectroscopy, vibrating-sample magnetometry analysis, dynamic light scattering, Brunauer–Emmett–Teller surface area, field emission scanning electron microscopy, and transmission electron microscopy analyses. The reaction mechanism was investigated, in which the performance of the catalyst as a phase transition factor seems to be probable. The catalyst showed high activity, high turnover frequency (TOF)s, significant selectivity, and fast performance toward the Strecker synthesis. The nanocatalyst can be readily and quickly separated from the reaction mixture with an external magnet and can be reused for at least seven successive reaction cycles without significant reduction in efficiency.     

Mixed convection enhancement by using optimized porous media and nanofluid in a cavity with two rotating cylinders

Journal of Thermal Analysis and Calorimetry - Mixed convection inside a square cavity with internal rotating heater and cooler is analyzed numerically by simultaneous application of porous media...     

Heat transfer enhancement in a counter-flow sinusoidal parallel-plate heat exchanger partially filled with porous media using metal foam in the channels’ divergent sections

Journal of Thermal Analysis and Calorimetry - This is a numerical study of heat transfer and flow in a counter-flow sinusoidal parallel-plate heat exchanger using metal foam in the channels’...     

Heterocyclic Synthesis with Enamines: Convenient Syntheses of Polyfunctionally Substituted Pyrazole,Pyridine, Pyrimidine and Pyrazolo[3,4-d]pyrimrdine Derivatives

Facile syntheses of pyrazole, pyridine, pyrimidine and pyrazolo[3,4-d]pyrimidine derivatives have been achieved by the reaction of β-enamino nitrile 2a with hydrazines, phenyl isothiocyanate, thiourea and active methylene reagents. The β-enamino ketone 2e with the same reagents affords 3,5-dimethyl heterocyclic ring systems.