Phase Transition in Modified Newtonian Dynamics (MONDian) Self-Gravitating Systems

We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system.     

Numerical solution of nonlinear integral equations using alternative Legendre polynomials

In this paper, the operational matrices of integration and the product for the alternative Legendre polynomials (ALPs) are first derived. Then, using these operational matrices and the collocation method, the nonlinear Volterra–Fredholm–Hammerstein integral equations are reduced to a set of nonlinear algebraic equations with unknown ALP coefficients. Some error estimations are provided and the efficiency and accuracy is verified by applying the method to some examples chosen from other literature.     

An unusual (10,3)-a racemic twofold interpenetrating network assembled from isolable tris(cyclopentadienyl)manganate and cesocene building blocks

The syntheses and X-ray crystal structures of [([18]crown-6)2Cs](+)-[Cp3Mn]- (1), [([18]crown-6)2Cs](+)-[Cp'3Mn]- (2), [CsCp'] (3), [(CsCp')2-([18]crown-6)] (4), and Cs[MnCp3] (5), and the synthesis of Cs[MnCp'3] (6) are reported (Cp' = C5H4Me). The anions [Cp3Mn]- (1-) and [Cp'3Mn]- (2-) are characterized by eta 2 coordination of all three Cp or Cp' rings. Measurements of the magnetic susceptibilities chi M resulted in values of mu eff = 6.20 microB (300 K), mu eff = 6.33 microB (301 K), and mu eff = 5.83 microB (300 K) for 1, 2, and 5, respectively, which are indicative of high-spin d5-Mn2+ centers. Density functional calculations illustrate that the coordination mode of 1- is characteristic for its sextet electronic ground state. Compound 3 forms infinite chains of cesocene-type sandwiches in the solid state, which are broken up into small subunits by the addition of crown ether to form 4. Compound 5 is a rare example of a (10,3)-a racemic interpenetrating network that crystallizes in the orthorhombic space group Pbca.     

Synthesis of benzoxazinone derivatives: a new route to 2 (N phthaloylmethyl)-4H-3,1-benzoxazin-4-one

A new method has been designed to prepare the known benzoxazinone derivative 2-(N-phthaloylmethyl)-4H-3,1-benzoxazin-4-one (4). The acyl chloride derivative N-phthaloylglycine reacts with anthranilic acid in chloroform, in the presence of triethylamine, to give an intermediate that is then reacted with cyanuric chloride, used as a cyclization agent, to produce the benzoxazinone derivative.     

Experimental and modeling investigation of thorium biosorption by orange peel in a continuous fixed-bed column

In this research work process parameters and breakthrough modeling of thorium biosorption on orange peel in a fixed-bed column has been studied. Some experiments have been done with sorbent diameter, flow rate, bed height and feed inlet concentration. Breakthrough point decreased with decreasing the bed height, increasing feed inlet concentration and increasing flow rate. Meanwhile, sorption capacity increased with decreasing bed height and flow rate. The highest sorption capacity, 87.7 mg/g, occurred in a 0.4–0.8 mm sorbent diameter. The experimental results were fitted by models of Thomas, Yoon–Nelson and Modified Dose–Response (MDR). The MDR model showed better results.     

Liquid Phase Selective Oxidation of Alcohols over VPO Catalysts Supported on Mesoporous Hexagonal Molecular Sieves (HMS)

The vanadium phosphorous oxide (VPO) catalysts, supported on mesoporous hexagonal molecular sieves (HMS) with different vanadium loadings, were prepared by precipitation method on organic phase. Techniques such as XRD, BET and SEM, were used for characterization of the catalyst. The bulk VPO catalyst contains vanadyl pyrophosphate phase ((VO)₂P₂O₇), and a small amount of VOPO₄. The high surface area, large pore volume and pore size of HMS in VPO/HMS samples, provide an excellent dispersion of same phase of VPO compound on the support surface. Oxidation of various alcohols was studied in the liquid phase over VPO/HMS catalyst, using tert‐butylhydroperoxide (TBHP) as an oxidant. The activity of VPO/HMS samples were considerably increased with respect to bulk VPO catalyst. At 90 °C, the obtained activities were 0.567 and 6.545 g_pro.g^?1_VPOh^?1 over the bulk VPO and 20 wt% VPO/HMS catalysts, respectively. The effects of substrates, reaction time, reaction temperature, solvents, catalyst recycling and leaching of VPO in liquid phase reaction were also investigated. The following order has been observed for the percentage of conversions of alcohols: Benzylic alcohol > Secondary alcohol ～ Primary alcohol. The kinetic of benzyl alcohol oxidation using excess TBHP over VPO/HMS catalyst was investigated at temperatures of 27, 60 and 90 °C, and followed a pseudo‐first order with respect to benzyl alcohol.     

Generating strong defining hyperplanes of the production possibility set in data envelopment analysis

In data envelopment analysis (DEA), identification of the strong defining hyperplanes of the empirical production possibility set (PPS) is important, because they can be used for determining rates of change of outputs with change in inputs. Also, efficient hyperplanes determine the nature of returns to scale. The present work proposes a method for generating all linearly independent strong defining hyperplanes (LISDHs) of the PPS passing through a specific decision making unit (DMU). To this end, corresponding to each efficient unit, a perturbed inefficient unit will be defined and, using at most m+s linear programs, all LISDHs passing through the DMU will be determined, where m and s are the numbers of inputs and outputs, respectively.