Pattern Hit-and-Run for sampling efficiently on polytopes

Pattern Hit-and-Run (PHR) is a Markov chain Monte Carlo sampler for a target distribution that was originally designed for general sets embedded in a box. A specific set of interest to many applications is a polytope intersected with discrete or mixed continuous/discrete lattices. PHR requires an acceptance/rejection mechanism along a bidirectional walk to guarantee feasibility. We remove this inefficiency by utilizing the linearity of the constraints defining the polytope, so each iteration of PHR can be efficiently implemented even though the variables are allowed to be integer valued. Moreover, PHR converges to a uniform distribution in polynomial time for a class of discrete polytopes.     

Electroinitiated Polymerization of N-Vinylcarbazole by Direct Electron Transfer

Electroinitiated polymerization of N-vinylcarbazole has been accomplished by constant potential electrolysis. It was found that direct electron transfer from the monomer to the anode initiates the polymerization even at a potential as low as +0.95 V versus Ag^?/ Ag⁺. Dichloromethane was used as the solvent, and the electrolyte was tetrabutylammonium fluoroborate. Conversions as high as 86% were reached even when a microelectrode was used. Effects of electrode area, temperature, and electrode potential on polymerization were studied. Percent conversion was followed by cyclic voltammetry.     

Dipotassium maleate with boric acid

In the title compound, poly[(μ₃‐boric acid)‐μ₄‐maleato‐dipotassium], [K₂(C₄H₂O₄){B(OH)₃}]_n, there are two independent K⁺ cations, one bonded to seven O atoms (three from boric acid and four from maleate), and the other eight‐coordinate via three boric acid and four maleate O atoms and a weak η¹‐type coordination to the C=C bond of the maleate central C atoms. Hydrogen bonding links the boric acid ligands and maleate dianions, completing the packing structure.     

Isotherm,thermodynamic and kinetic studies of Sr<Superscript>2+</Superscript> adsorption on spherical TiO<Subscript>2</Subscript>/PAN composites

A spherical polyacrylonitrile–TiO₂ composite adsorbent was prepared and its strontium removal potential was investigated. The Langmuir equation fixed well the equilibrium data. The value of ∆H° = 8.943 kJ/mol and ∆G° = 6.291 kJ/mol at 298 K indicate that the adsorption of strontium onto TiO₂/PAN composite adsorbent is an endothermic and non-spontaneous reaction. The kinetic process was described by a pseudo-second-order rate model very well.     

Mirror duality in a Joyce manifold

Previously the two of the authors defined a notion of dual Calabi-Yau manifolds in a G₂ manifold, and described a process to obtain them. Here we apply this process to a compact G₂ manifold, constructed by Joyce, and as a result we obtain a pair of Borcea-Voisin Calabi-Yau manifolds, which are known to be mirror duals of each other.     

Speeding up Huff form of elliptic curves

This paper presents faster inversion-free point addition formulas for the curve \(y (1+ax^2) = cx (1+dy^2)\). The proposed formulas improve the point doubling operation count record (I, M, S, D, a are arithmetic operations over a field. I: inversion, M: multiplication, S: squaring, D: multiplication by a curve constant, a: addition/subtraction) from \(6\mathbf{{M}}+ 5\mathbf{{S}}\) to \(8\mathbf{{M}}\) and mixed addition operation count record from \(10\mathbf{{M}}\) to \(8\mathbf{{M}}\). Both sets of formulas are shown to be 4-way parallel, leading to an effective cost of \(2\mathbf{{M}}\) per either of the group operations.     

Synthesis of pyrimidine Schiff base transition metal complexes: characterization,spectral and electrochemical analyses,and photoluminescence properties

Research on Chemical Intermediates - This study includes the synthesis, characterization, electrochemical analysis and photoluminescence properties of a Schiff base ligand bearing a pyrimidine ring...     

MRI findings of intraosseous lipoma: case report

Intraosseous lipoma is one of the rarest benign bone tumors and usually presents in the fourth to fifth decades. Except for minor symptoms, they are usually asymptomatic. Metaphysis of long bones, especially proximal parts of femur and fibula, are involved in most cases. We present intraosseous lipoma to discuss the benefits of MRI and contrast-enhanced MRI findings for differential diagnosis.