Synthesis of mono-O-alkylated homooxacalix[3]arene and a protection–deprotection strategy for homooxacalix[3]arene

The regioselective synthesis of mono-O-alkylated homooxacalix[3]arene is accomplished for the first time. The synthetic route relies on two key steps: (i) a facile protection of two OH groups at the lower rim of the homooxacalix[3]arene and (ii) the deprotection of 9- anthrylmethyl groups via the Pd/C-catalyzed hydrogenation under atmospheric hydrogen. An efficient protection- deprotection strategy for the functionalization of homooxacalix[ 3]arene is presented

Competing density-wave orders in a one-dimensional hard-boson model

We describe the zero-temperature phase diagram of a model of bosons, occupying sites of a linear chain, which obey a hard-exclusion constraint: any two nearest-neighbor sites may have at most one boson. A special case of our model was recently proposed as a description of a ``tilted'' Mott insulator of atoms trapped in an optical lattice. Our quantum Hamiltonian is shown to generate the transfer matrix of Baxter's hard-square model. Aided by exact solutions of a number of special cases, and by numerical studies, we obtain a phase diagram containing states with long-range density-wave order with period 2 and period 3, and also a floating incommensurate phase. Critical theories for the various quantum phase transitions are presented. As a byproduct, we show how to compute the Luttinger parameter in integrable theories with hard-exclusion constraints.Comment: 16 page

A Stackelberg game theoretic model for optimizing product family architecting with supply chain consideration

Planning of an optimal product family architecture (PFA) plays a critical role in defining an organization's product platforms for product variant configuration while leveraging commonality and variety. The focus of PFA planning has been traditionally limited to the product design stage, yet with limited consideration of the downstream supply chain-related issues. Decisions of supply chain configuration have a profound impact on not only the end cost of product family fulfillment, but also how to design the architecture of module configuration within a product family. It is imperative for product family architecting to be optimized in conjunction with supply chain configuration decisions. This paper formulates joint optimization of PFA planning and supply chain configuration as a Stackelberg game. A nonlinear, mixed integer bilevel programming model is developed to deal with the leader–follower game decisions between product family architecting and supply chain configuration. The PFA decision making is represented as an upper-level optimization problem for optimal selection of the base modules and compound modules. A lower-level optimization problem copes with supply chain decisions in accordance with the upper-level decisions of product variant configuration. Consistent with the bilevel optimization model, a nested genetic algorithm is developed to derive near optimal solutions for PFA and the corresponding supply chain network. A case study of joint PFA and supply chain decisions for power transformers is reported to demonstrate the feasibility and potential of the proposed Stackelberg game theoretic joint optimization of PFA and supply chain decisions

Unsigned state models for the Jones polynomial

It is well a known and fundamental result that the Jones polynomial can be expressed as Potts and vertex partition functions of signed plane graphs. Here we consider constructions of the Jones polynomial as state models of unsigned graphs and show that the Jones polynomial of any link can be expressed as a vertex model of an unsigned embedded graph. In the process of deriving this result, we show that for every diagram of a link in the 3-sphere there exists a diagram of an alternating link in a thickened surface (and an alternating virtual link) with the same Kauffman bracket. We also recover two recent results in the literature relating the Jones and Bollobas-Riordan polynomials and show they arise from two different interpretations of the same embedded graph.Comment: Minor corrections. To appear in Annals of Combinatoric

Superconductivity in MgB_2 doped with Ti and C

Measurements of the superconducting upper critical field, H_{c2}, and critical current density, J_c, have been carried out for MgB_2 doped with Ti and/or C in order to explore the problems encountered if these dopants are used to enhance the superconducting performance. Carbon replaces boron in the MgB_2 lattice and apparently shortens the electronic mean free path thereby raising H_c2. Titanium forms precipitates of either TiB or TiB_2 that enhance the flux pinning and raise J_c. Most of these precipitates are intra-granular in the MgB_2 phase. If approximately 0.5% Ti and approximately 2% C are co-deposited with B to form doped boron fibers and these fibers are in turn reacted in Mg vapor to form MgB_2, the resulting superconductor has H_{c2}(T=0) ~ 25 T and J_c ~ 10,000 A/cm**2 at 5 K and 2.2 T.Comment: 11 pages, 10 figure

Scaling laws for the 2d 8-state Potts model with Fixed Boundary Conditions

We study the effects of frozen boundaries in a Monte Carlo simulation near a first order phase transition. Recent theoretical analysis of the dynamics of first order phase transitions has enabled to state the scaling laws governing the critical regime of the transition. We check these new scaling laws performing a Monte Carlo simulation of the 2d, 8-state spin Potts model. In particular, our results support a pseudo-critical beta finite-size scaling of the form beta(infinity) + a/L + b/L^2, instead of beta(infinity) + c/L^d + d/L^{2d}. Moreover, our value for the latent heat is 0.294(11), which does not coincide with the latent heat analytically derived for the same model if periodic boundary conditions are assumed, which is 0.486358...Comment: 10 pages, 3 postscript figure

Diagonalization of the XXZ Hamiltonian by Vertex Operators

We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of affine U_q( sl(2) ). Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors. We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limit --- the $su(2)$-invariant Thirring model.Comment: 65 page

Hydrogen-bonded Silica Gels Dispersed in a Smectic Liquid Crystal: A Random Field XY System

The effect on the nematic to smectic-A transition in octylcyanobiphenyl (8CB) due to dispersions of hydrogen-bonded silica (aerosil) particles is characterized with high-resolution x-ray scattering. The particles form weak gels in 8CB creating a quenched disorder that replaces the transition with the growth of short range smectic correlations. The correlations include thermal critical fluctuations that dominate at high temperatures and a second contribution that quantitatively matches the static fluctuations of a random field system and becomes important at low temperatures.Comment: 10 pages, 4 postscript figures as separate file