Convergence rate of block-coordinate maximization Burer–Monteiro method for solving large SDPs

Mathematical Programming - Semidefinite programming (SDP) with diagonal constraints arise in many optimization problems, such as Max-Cut, community detection and group synchronization. Although...     

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.     

Uniform convergence and numerical computation of the Hubbell radiation rectangular source integral

In this paper, we investigate uniform convergence of the improper Hubbell radiation rectangular source (HRS) integral H(a,b). We prove that HRS integral H(a,b) is uniform convergent in the domain D?{(a,b)∈[0,A]×[0,∞)} for any positive finite number A. Then we give an accurate and efficient computation algorithm for the HRS integral.     

Crystal structure and conformational analysis of 1-[N-(2-bromophenyl)]naphthaldimine

1-[N-(2-bromophenyl)]naphthaldimine (C₁₇H₁₂NOBr) (1) was synthesised and its crystal structure was determined. The compound 1 is orthorhombic, space group P2₁2₁2₁ with a=12.653(2), b=13.7311(14), Z=4, R=0.032 for 499 reflections I>2σ(I)]. There is an intramolecular hydrogen bond of distance 2.473(3) Å between the hydroxyl oxygen atom and imine nitrogen atom, the hydrogen atom essentially being bonded to the oxygen atom. Minimum energy conformation was calculated as a function of torsion angle θ (C10-C11-N1-C12) varied every 5 degrees. The optimized geometry of the crystal structure corresponding to the non-planar conformation is the most stable conformation in all calculations. The results strongly indicate that the minimum energy conformation is primarily determined by hydrogen-hydrogen repulsions between the ortho-hydrogen atoms on the aldehyde rings. Complementary IR, ¹H NMR and UV measurements in solution and in the solid state were carried out.     

A generalization of the Holditch Theorem for the planar homothetic motions

In this paper, under the one-parameter closed planar homothetic motion, a generalization of Holditch Theorem is obtained by using two different line segments (with fixed lengths) whose endpoints move along two different closed curves.This revised version was published online in April 2005 with a corrected missing date string.     

From a theoretical concept to biochemical reactions: strain-induced bond localization (SIBL) in oxidation of vitamin E

The regioselectivity of the oxidation of alpha-tocopherol (the main component of vitamin E) to an ortho-quinone methide (oQM) has been explained in the literature mostly by the ill-defined term "Mills-Nixon effect". In this paper we describe the preparation of eleven alpha-tocopherol derivatives, different from each other by the sum of annulation angles, but keeping the electronic factors unchanged. These compounds underwent Ag(2)O oxidation, forming two isomeric oQMs that were trapped by vinylmethyl ether. It was found that the isomeric product ratio changes smoothly as a function of the annulation angles, not abruptly from one regioisomer to the other on going from five- to six- and seven-membered rings, as predicted by the Mills-Nixon effect. The relative amounts of the products were determined at four different temperatures, and assuming that the product ratio represents the relative rates ratio, the relative enthalpy of activations could be obtained. Theoretically (at B3LYP/6-31G* theoretical level) four different intermediates were considered. Each of these underwent angular angles deformations to model the two regioisomers. At each deformation angle the energy difference between the two intermediates models was correlated to the experimental data for each of the four intermediates. It was found that the angle-deformed lithium (6-methyl-2-benzylium)phenolate correlated best (R>0.994) to the experimental data. This study confirms that the regioselectivity of the two isomeric oQMs in the oxidation of alpha-tocopherol and related compounds is simply a function of angular strain, best explained by the SIBL (strain-induced bond localization) model. In addition, this study provides evidence that the highest energy intermediate in the oxidation of vitamin E is a phenolate-benzyl cation.     

N‐(p‐Chloro­phenyl)‐3,3‐di­phenyl‐4‐(β‐phenyl­styryl)azetidin‐2‐one

In the title compound, C₃₅H₂₆ClNO, the four‐membered β‐lactam ring is essentially planar, with a maximum deviation of 0.012 (1) Å for the N atom. The C—C bond lengths in the β‐lactam ring are 1.591 (2) and 1.549 (2) Å. The two phenyl rings attached to the β‐lactam ring are nearly perpendicular to each other [83.2 (1)°].     

One‐step synthesis of block‐graft copolymers via simultaneous reversible‐addition fragmentation chain transfer and ring‐opening polymerization using a novel macroinitiator

One‐step synthesis of block‐graft copolymers by reversible addition‐fragmentation chain transfer (RAFT) and ring‐opening polymerization (ROP) by using a novel initiator was reported. Block‐graft copolymers were synthesized in one‐step by simultaneous RAFT polymerization of n‐butylmethacrylate (nBMA) and ROP of ε‐caprolacton (CL) in the presence of a novel macroinitiator (RAFT‐ROP agent). For this purpose, first epichlorohydrin (EPCH) was polymerized by using H₂SO₄ via cationic ring‐opening mechanism. And then a novel RAFT‐ROP agent was synthesized by the reaction of potassium ethyl xanthogenate and polyepichlorohydrin (poly‐EPCH). By using the RAFT‐ROP agent, poly[CL‐b‐EPCH‐b‐CL‐(g‐nBMA)] block‐graft copolymers were synthesized. The principal parameters such as monomer concentration, initiator concentration, and polymerization time that affect the one‐step polymerization reaction were evaluated. The block lengths of the block‐graft copolymers were calculated by using ¹H‐nuclear magnetic resonance (¹H NMR) spectrum. The block length could be adjusted by varying the monomer and initiator concentrations. The characterization of the products was achieved using ¹H NMR, Fourier‐transform infrared spectroscopy, gel‐permeation chromatography, thermogravimetric analysis, differential scanning calorimetry, elemental analysis, and fractional precipitation (γ) techniques. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2651–2659     

A model for the bulk viscosity of a non-Newtonian fluid

A model for the bulk viscosity of a non-Newtonian fluid is presented. An elementary two-phase cell containing an incompressible non-Newtonian fluid and a gas bubble is compared with a one-phase cell consisting of a corresponding compressible non-Newtonian fluid. The rates of work of both cells are set equal to one another. The deformation histories of both cells are represented by the density history. From the extra stress an expression for the bulk viscosity of the compressible non-Newtonian fluid is derived. The material data are expressed in terms of the known properties of the two-phase flow.