Numerical analysis of buoyant flow in a hemispherical enclosure at high Rayleigh numbers

A numerical analysis is presented for buoyancy driven flow of a Newtonian fluid contained in a two dimensional (R, ) hemispherical enclosure for high Rayleigh (Ra) numbers. It is assumed that the flow is driven by the uniformly distributed internal heat sources within the enclosure. All walls of the cavity are maintained at a constant temperature. Finite volume based SIMPLER algorithm has been used for the present analysis. Discretised governing equations, in primitive variables, are solved by a combination of Three Diagonal Matrix Algorithm (TDMA) and Point Successive Overrelaxation (PSOR) method. A benchmark solution prepared for a Ra number range of 10⁷ to 10¹² and Prandtl (Pr) number 7.0, shows an excellent agreement with the experimental results obtained from the open literature.     

Gomory integer programs

 The set of all group relaxations of an integer program contains certain special members called Gomory relaxations. A family of integer programs with a fixed coefficient matrix and cost vector but varying right hand sides is a Gomory family if every program in the family can be solved by one of its Gomory relaxations. In this paper, we characterize Gomory families. Every TDI system gives a Gomory family, and we construct Gomory families from matrices whose columns form a Hilbert basis for the cone they generate. The existence of Gomory families is related to the Hilbert covering problems that arose from the conjectures of Seb?. Connections to commutative algebra are outlined at the end. Received: May 17, 2001 / Accepted: February 7, 2002 Published online: April 24, 2003 RID="⋆" ID="⋆" Research partially supported by NSF grant DMS-0100141.     

Geometric Dynamics

A kinematic differential system on a Riemann (or semi-Riemann) manifold induces a Lorentz-Udrite world-force law, i.e., any local group with one parameter (any local flow) on a Riemann (or semi-Riemann) manifold induces the dynamics of the given vector field or of an associated particle, which will be called geometric dynamics.The cases of Riemann-Jacobi or Riemann-Jacobi-Lagrange structures are imposed by the behavior of an external tensor field of type (1,1). The case of the Finsler-Jacobi structure appears if the initial metric is chosen such that the energy of the given vector field is constant (Sec. 1). At the end of Sec. 1 are formulated open problems regarding some extensions of geometric dynamics.Adequate structures on the tangent bundle describe the geometric dynamics in the Hamilton language (Sec. 2).Section 3 proves the existence of a Finsler-Jacobi structure induced by an almost contact metric structure.The theory is applied to electromagnetic dynamical systems (the starting point of our theory), offering new principles of unification of the gravitation and the electromagnetism. Also, here, one enounces open problems regarding the geometric dynamics induced by the electric intensity and magnetizing force (Sec. 4).From the geometrical point of view, we create a wider class of Riemann-Jacobi, Riemann-Jacobi-Lagrange, or Finsler-Jacobi manifolds ensuring that all trajectories of a given vector field are geodesics. Having T₁M²ⁿ⁺¹ in mind, the problem of creating a wider class of Riemannian manifolds, in which there exists a vector field such that (1) all trajectories of the vector field are geodesics; (2) the flow defined by is incompressible; (3) the condition which corresponds to the property that is the associate vector field of the contact structure is satisfied;was studied intensively by S. Sasaki. The results were not satisfactory, but Sasaki discovered (, , )-structures [10].AMS Subject Classification (1991): 70H35, 53C22, 58F25, 83C22     

On the mechanism of the N,N‐dimethyl amination of Grignard reagents: a kinetic study

A direct kinetic study is reported for the electrophilic amination of substituted phenylmagnesium bromides with N,N‐dimethyl O‐(mesitylenesulfonyl)hydroxylamine in THF. Rate data, Hammett relationship, and activation entropy are consistent with a S_N2 displacement involving the attack of carbanions to sp³N in the amination reagent (AR). Copyright © 2007 John Wiley & Sons, Ltd.     

The Determination of Protonation Constants of Some Amino Acids and Their Esters by Potentiometry in Different Media

In this study, stoichiometric protonation constants of L-tyrosine, L-cysteine, L-tryptophane, L-lysine, and L-histidine, and their methyl and ethyl esters in water and ethanol–water mixtures of 30, 50, and 70% ethanol (v/v), were determined potentiometrically using a combined pH electrode system calibrated as the concentration of hydrogen ion. Titrations were performed at 25^∘C and the ionic strength of the medium was maintained at 0.10 mol⋅L⁻¹ using sodium chloride. Protonation constants were calculated by using the BEST computer program. The effect of solvent composition on the protonation constants is discussed. The log₁₀ K₂ values of esters generally decreased with increasing ethanol content. However, the log₁₀ K₁ values of the esters of L-tyrosine, L-cysteine, and L-tryptophane were found to increase with increasing ethanol content in contrast those of L-lysine and L-histidine esters.     

Strong convergence of a proximal point algorithm with bounded error sequence

Given any maximal monotone operator ${A: D(A)\subset H \rightarrow 2^H}$ in a real Hilbert space H with ${A^{-1}(0) \ne \emptyset}$ , it is shown that the sequence of proximal iterates ${x_{n+1}=(I+\gamma_n A)^{-1}(\lambda_n u+(1-\lambda_n)(x_n+e_n))}$ converges strongly to the metric projection of u on A ^?1(0) for (e _n ) bounded, ${\lambda_n \in (0,1)}$ with ${\lambda_n \to 1}$ and γ _n  > 0 with ${\gamma_n \to\infty}$ as ${n \to \infty}$ . In comparison with our previous paper (Boikanyo and Moro?anu in Optim Lett 4(4):635–641, 2010), where the error sequence was supposed to converge to zero, here we consider the classical condition that errors be bounded. In the case when A is the subdifferential of a proper convex lower semicontinuous function ${\varphi :H \to (-\infty,+ \infty]}$ , the algorithm can be used to approximate the minimizer of φ which is nearest to u.     

Functional copolymer/organo‐MMT nanoarchitectures. XIX. Nanofabrication and characterization of poly(MA‐alt‐1‐octadecene)‐g‐PLA layered silicate nanocomposites with nanoporous core–shell morphology

Novel bioengineering functional copolymer‐g‐biopolymer‐based layered silicate nanocomposites were fabricated by catalytic interlamellar bulk graft copolymerization of L‐lactic acid (LA) monomer onto alternating copolymer of maleic anhydride (MA) with 1‐octadecene as a reactive matrix polymer in the presence of preintercalated LA…organo‐MMT clay (reactive ODA‐MMT and non‐reactive DMDA‐MMT) complexes as nanofillers and tin(oct)₂ as a catalyst under vacuum at 80°C. To characterize the functional copolymer layered silicate nanocomposites and understand the mechanism of in situ processing, interfacial interactions and nanostructure formation in these nanosystems, we have utilized a combination of variuous methods such as FT‐IR spectroscopy, X‐ray diffraction (XRD), dynamic mechanical (DMA), thermal (DSC and TGA‐DTG), SEM and TEM morphology. It was found that in situ graft copolymerization occurred through the following steps: (i) esterification of anhydride units of copolymer with LA; (ii) intercalation of LA between silicate galleries; (iii) intercalation of matrix copolymer into silicate layers through in situ amidization of anhydride units with octadecyl amine intercalant; and (iv) interlamellar graft copolymerization via in situ intercalating/exfoliating processing. The main properties and observed micro‐ and nanoporous surface and internal core–shell morphology of the nanocomposites significantly depend on the origin of MMT clays and type of in situ processing (ion exchanging, amidization reaction, strong H‐bonding and self‐organized hydrophobic/hydrophilic interfacial interactions). This developed approach can be applied to a wide range of anhydride‐containing copolymers such as random, alternating and graft copolymers of MA to synthesize new generation of polymer‐g‐biopolymer silicate layered nanocomposites and nanofibers for nanoengineering and nanomedicine applications. Copyright © 2014 John Wiley & Sons, Ltd.     

Synthesis of N,N‐Dimethylamines via Barbier–Grignard‐Type Electrophilic Amination

Aryl Grignard reagents react with N,N‐dimethyl O‐(mesitylenesulfonyl)hydroxylamine in THF under Barbier conditions at room temperature and give N,N‐dimethylanilines with high yields in a 2‐h reaction. The amination yield of in situ Grignard reagents were not lower than those of preformed aryl Grignard reagents. In situ cycloalkyl‐, allyl‐, and benzylmagnesium bromides did not react with N,N‐dimethyl O‐(mesitylenesulfonyl)hydroxylamine, except that amination of in situ n‐hexylmagnesium bromide resulted in a medium yield. Grignard–Barbier‐type amination of aryl bromides with N,N‐dimethyl O‐(mesitylenesulfonyl)hydroxylamine provides a new alternative route for the synthesis of N,N‐dimethylanilines.     

Development of a Diamond Nanoparticles-based Nanosensor for Detection and Determination of Antiviral Drug Favipiravir

This study developed a nanosensor for the detection and determination of favipiravir, a presumed drug that has potential therapeutic efficacy in treating COVID-19 patients, from tablets and serum samples. This nanosensor was obtained by adding the optimum amount of diamond nanoparticles into carbon paste. For the determination of favipiravir adsorptive stripping differential pulse (AdSDPV) and adsorptive stripping square wave voltammetry (AdSSWV) were used. Limit of detection values were found as 4.83×10⁻⁹ M and 2.44×10⁻⁷ M for bulk and 5.18×10⁻⁸ M and 4.38×10⁻⁸ M for serum samples using AdSDPV and AdSSWV, respectively. Recovery studies made of the tablet and serum produced satisfactory results.