Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Investigation of mononuclear,dinuclear, and trinuclear transition metal (II) complexes derived from an asymmetric Salamo‐based ligand possessing three different coordination modes

A new asymmetric Salamo‐based ligand H₂L was synthesized using 3‐tert‐butyl‐salicylaldehyde and 6‐methoxy‐2‐[O‐(1‐ethyloxyamide)]‐oxime‐1‐phenol. By adjusting the ratio of the ligand H₂L and Cu (II), Co (II), and Ni (II) ions, mononuclear, dinuclear, and trinuclear transition metal (II) complexes, [Cu(L)], [{Co(L)}₂], and [{Ni(L)(CH₃COO)(CH₃CH₂OH)}₂Ni] with the ligand H₂L possessing completely different coordination modes were obtained, respectively. The optical spectra of ligand H₂L and its Cu (II), Co (II) and Ni (II) complexes were investigated. The Cu (II) complex is a mononuclear structure, and the Cu (II) atom is tetracoordinated to form a planar quadrilateral structure. The Co (II) complex is dinuclear, and the two Co (II) atoms are pentacoordinated and have coordination geometries of distorted triangular bipyramid. The Ni (II) complex is a trinuclear structure, and the terminal and central Ni (II) atoms are all hexacoordinated, forming distorted octahedral geometries. Furthermore, optical properties including UV–Vis, IR, and fluorescence of the Cu (II), Co (II), and Ni (II) complexes were investigated. Finally, the antibacterial activities of the Cu (II), Co (II), and Ni (II) complexes were explored. According to the experimental results, the inhibitory effect was found to be enhanced with increasing concentrations of the Cu (II), Co (II), and Ni (II) complexes.     

Thermally Crosslinkable and Chemically Modifiable Aromatic Polyesters Possessing Pendant Propargyloxy Groups

New aromatic (co)polyesters containing pendant propargyloxy groups were synthesized by phase transfer‐catalyzed interfacial polycondensation of 5‐(propargyloxy)isophthaloyl chloride (P‐IPC) and various compositions of P‐IPC and isophthaloyl chloride with bisphenol A. FTIR and NMR spectroscopic data, respectively, revealed successful incorporation of pendant propargyloxy groups into (co)polyesters and formation of (co)polyesters with desired compositions. (Co)polyesters exhibited good solubility in common organic solvents such as chloroform, dichloromethane, and tetrahydrofuran and could be cast into transparent, flexible, and tough films from chloroform solution. Inherent viscosities and number average molecular weights of (co)polyesters were in the range 0.77–1.33 dL/g and 43,600–118,000 g/mol, respectively, indicating the achievement of reasonably high‐molecular weights. The 10% weight loss temperatures of (co)polyesters were in the range 390–420 °C, demonstrating their good thermal stability. (Co)polyesters exhibited T_g in the range 146–170 °C and T_g values decreased with increase in mol % incorporation of P‐IPC. The study of non‐isothermal curing by DSC indicated thermal crosslinking of (co)polyesters via propargyloxy groups. The utility of pendant propargyloxy group was demonstrated by post‐modification of the selected copolyester with 1‐(4‐azidobutyl)pyrene, 9‐(azidomethyl)anthracene, and azido‐terminated poly(ethyleneglycol) monomethyl ether via copper(I)‐catalyzed Huisgen 1,3‐dipolar cycloaddition reaction. FTIR and ¹H NMR spectra confirmed that click reaction was quantitative. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 588–597     

Pentapnictogen heterocyclic monoanions: Structure,stability, and aromaticity

Inorganic planar ring-shape molecules with 4n + 2 π electrons are always the focus of experimental synthesis and theoretical research due to their potential aromaticity and stability. In this work, the whole series of five-membered heterocycle monoanions X _nY_5-n⁻ (X, Y = group 15 elements; n = 1-4) were thoroughly investigated by means of density functional theory calculations. They all have large formation energies and HOMO-LUMO gap energies, suggesting the potential thermodynamic and kinetic stability. Their aromaticities are comparable to that of typical aromatic hydrocarbons. Their thermal stabilities were firmly established by the ab initio molecular dynamics simulations. As most of them are predicted for the first time, their various spectra were simulated for experimental characterization. Furthermore, we demonstrate that these five-membered cyclic anions can be employed as η⁵-ligand to construct novel all-inorganic metallocenes, which may serve as the building blocks of low-dimensional nanomaterials.     

Arbitrage‐free call option surface construction using regression splines

In this work, we suggest a novel quadratic programming‐based algorithm to generate an arbitrage‐free call option surface. The empirical performance of the proposed method is evaluated using S&P 500 Index call options. Our results indicate that the proposed method provides a more precise fit to observed option prices than other alternative methodologies. Copyright © 2014 John Wiley & Sons, Ltd.     

Amphiphilic block copolymer self‐assemblies of poly(NVP)‐b‐poly(MDO‐co‐vinyl esters): Tunable dimensions and functionalities

Functional, degradable polymers were synthesized via the copolymerization of vinyl acetate (VAc) and 2‐methylene‐1,3‐dioxepane (MDO) using a macro‐xanthate CTA, poly(N‐vinylpyrrolidone), resulting in the formation of amphiphilic block copolymers of poly(NVP)‐b‐poly(MDO‐co‐VAc). The behavior of the block copolymers in water was investigated and resulted in the formation of self‐assembled nanoparticles containing a hydrophobic core and a hydrophilic corona. The size of the resultant nanoparticles was able to be tuned with variation of the hydrophilic and hydrophobic segments of the core and corona by changing the incorporation of the macro‐CTA as well as the monomer composition in the copolymers, as observed by Dynamic Light Scattering, Static Light Scattering, and Transmission Electron Microscopy analyses. The concept was further applied to a VAc derivative monomer, vinyl bromobutanoate, to incorporate further functionalities such as fluorescent dithiomaleimide groups throughout the polymer backbone using azidation and “click” chemistry as postpolymerization tools to create fluorescently labeled nanoparticles. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2699–2710     

Azobenzene‐Functionalized Cage Silsesquioxanes as Inorganic–Organic Hybrid,Photoresponsive, Nanoscale,Building Blocks

Mono‐ and octa‐azobenzene‐functionalized cage silsesquioxanes were easily synthesized by the reaction of 4‐bromoazobenzene with monovinyl‐substituted octasilsesquioxane and cubic octavinylsilsesquioxane through the Heck coupling reaction. Excited‐state energies obtained from time‐dependent density functional theory (TDDFT) and the CAM‐B3LYP functional correlate very well with experimental trans–cis photoisomerization results from UV/Vis spectroscopy. These azobenzene‐functionalized cages exhibit good thermal stability and are fluorescent with maximum emission at approximately 400 nm, making them potential materials for blue‐light emission.     

Crosslinking network of bio‐based bis‐functional epoxides derived from trans‐limonene oxide

The thiol‐ene reaction between trans‐limonene oxide (trans‐LO) and ethane‐1,2‐dithiol in the presence of triethylborane affords a bio‐based bis‐functional epoxide (bis‐trans‐LO). The crosslinking reaction of bis‐trans‐LO with branched polyethyleneimine (BPEI; M_n = 600; BPEI₆₀₀) at a feed ratio of bis‐trans‐LO/BPEI₆₀₀ = 57/43 (wt/wt) yields the corresponding network polymer with T_d10 (10% thermal decomposition temperature) of 304.7 °C in 98% yield. In contrast, negligible amounts of network polymer are obtained by the reaction of bis‐LO (bis‐functional epoxide derived from cis and trans‐LO) and BPEI₆₀₀ regardless of the feed ratio. The mechanical strengths as measured by direct tensile tests of the network polymers derived from bis‐trans‐LO and BPEI_600,1800 (M_n = 600 and 1800) were approximately 16 and 11 times higher than that of bis‐LO and BPEI₁₈₀₀, respectively. The tensile shear strengths of the metal‐to‐metal adhesive bonds induced by bis‐trans‐LO and BPEI_600,1800 were 9.5 and 14.1 MPa, respectively. DMA revealed that the storage modulus of the network polymer derived from bis‐trans‐LO and BPEI₁₈₀₀ in the rubber region was higher than that of the material prepared from bis‐LO and BPEI₁₈₀₀, indicating higher crosslink density of the bis‐trans‐LO/BPEI₁₈₀₀ system. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2466–2473     

o-Trityl phenoxy-imino vanadium (III) complexes: synthesis,characterization, and catalysis on ethylene (co)polymerization

Several phenoxy-imine ligands bearing o-trityl group in phenoxy moiety RN=CHArOH (Ar = C₆H₂(CPh₃)^tBu, R = 2,6-Me₂C₆H₃ ( L ₁ H ); 2,6-ⁱPr₂C₆H₃ ( L ₂ H ); 3,5-(CF₃)₂C₆H₃ ( L ₃ H ); 3,5-(OMe)₂C₆H₃ ( L ₄ H ); CHPh₂ ( L ₅ H ); CPh₃ ( L ₆ H )) were synthesized and characterized by¹H NMR and ¹³C NMR spectroscopy. The vanadium complexes based on these ligands LVCl₂(THF)₂ ( 1–6 ) were synthesized via conventional transmetalation reaction in moderate to high yields. Complexes 1–6 were fully characterized by FT-IR, elemental analyses and the molecular structures of 1 , 2 ·H₂O, (2 ·H₂O ) ₂ (μ-Cl) ₂ , 4 , and 5 were confirmed by X-ray crystallographic analysis in which the six-coordinated vanadium centers are in a typical octahedral geometry. Upon activation with Et₂AlCl in toluene, complexes 1–6 showed high activities in ethylene polymerization affording polymers with moderate molecular weight (5.9–11.8 × 10⁴ Da). Moreover, in hexane or CH₂Cl₂, 1–6 /Et₂AlCl exhibited enhanced activities. When activated with MAO or MMAO in toluene, these complexes showed relatively low activities but afforded polymers with ultra-high molecular weight (up to 3.30 × 10⁶ Da). 1–6 /Et₂AlCl also showed high activities in ethylene/1-hexene copolymerization at room temperature giving moderate molecular-weight polymers (6.5–11.4 × 10⁴ Da) with co-monomer incorporation being of 6.0 ~ 7.8%.     

Purcell Effect and Nonlinear Behavior of the Emission in a Periodic Structure Composed of InAs Monolayers Embedded in a GaAs Matrix

Enhancement of spontaneous emission in a resonant Bragg quantum well (QW) structure with 60 periods of triple InAs monolayers embedded in a GaAs matrix is studied experimentally and theoretically. From measurements of the time‐resolved photoluminescence, besides the QW exciton at 1.47 eV, a specific super‐radiant (SR) emission demonstrating nonlinear properties is found. The SR mode shows a near‐quadratic dependence of intensity on excitation power, while its energy position follows the Bragg condition. It is revealed that the SR mode shows a peculiar non‐monotonic dependence of intensity on direction, with a maximum observed at approximately 40°. The enhancement in the SR emission at a specific direction is correlated well with suggested theoretical consideration of the modal Purcell factor for periodic quantum well structures.