A Free Energy Model for Curved Surfaces and Curved Thin Films in Emulsions

The formulation of surface thermodynamics for flat surfaces has been done so as to be free of the Gibbs surface construction. The advantage of these formulations is that it allows the choice of thermodynamic field variables that is more general than the traditional construction. However, a generalization to curved surfaces including thin films that exist in emulsion structures has not been published. The Hansen-Cahn construction is developed in a setting that allows curvature terms to be added to the free energy expression. The Laplace equation extended to include bending elasticity and spontaneous bending elasticity is derived by computing functional derivatives of the free energy. Results for both single interfaces and double interfaces are reported. Stability conditions for profile fluctuations are developed to include these additional properties.     

Denominators for the Poincaré series of invariants of matrices with involution

The goal of this paper is to study some Poincaré series associated to the invariants of the symplectic and odd orthogonal groups. These series turn out to be rational functions and our main results will describe the denominators. This work will generalize some known results on the invariants of the general linear groups. In addition to whatever intrinsic interest we hope our results may have, the subject involves an interesting interplay of invariant theory and complex variables. The first author gratefully acknowledges Support from DePaul University Research Council. The second author was supported in part by the Israel Science Foundation, founded by the Israel Academy of Sciences and Humanities, and by an Internal Research Grant from Bar-Ilan University.     

The conjugacy character ofS n tends to be regular

Consider the regular and the conjugacy characters ofS _n as vectors in Euclidean space, with the standard inner product. Asn grows, the angle between them tends to zero and the ratio of their lengths tends to one. The two characters have therefore asymptotically similar decompositions into irreducible components.     

Synthesis of side chain liquid crystalline copolymers and characterization of their polar structure

A series of side chain liquid crystalline copolymers having different spacer lengths, copolymer compositions, and chromophore types were synthesized and characterized both in the bulk and at the gas‐water interface. Liquid crystalline properties were identified by differential scanning calorimetry (DSC), optical microscopy, and X‐ray diffraction (XRD). Copolymer with spacer lengths 4, 5, 10, and 11 showed smectic A (S_A) phases with a bâtonnet texture. The liquid crystalline (LC) phase stabilized as the spacer increased. Copolymers with different compositions were investigated both as monolayers and transferred films. The isotherms suggest nanodomain formation at the gas‐water interface in copolymers with high nitrobiphenyl (NBP) content. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1057–1070, 1999     

The effect of angle on the strain of scarf lap joints subjected to tensile loads

In this paper, the mechanical behavior of the scarf lap joints (SLJs) bonded with adhesive (Vinylester Atlac 580) under a tensile load was analyzed. The effects of scarf angle at the interface strain distributions of SLJs were examined. The stress analyses were performed via three dimensional Finite Element Method (3D-FEM). The 3D-FEM code employed was Ansys (12.0). Experimental results were compared with the 3D-FEM results and were found quite reasonable. The results indicated that the maximum values of the normalized ε_x strain values were determined at θ = 60° in all joints.     

Counting colorful multi-dimensional trees

LetV be a disjoint union ofr finite setsV ₁,...,V _r (colors). A collectionT of subsets ofV iscolorful if each member ifT contains at most one point of each color. Ak-dimensional colorful tree is a colorful collectionT of subsets ofV, each of sizek+1, such that if we add toT all the colorful subsets ofV of sizek or less, we get aQ-acyclic simplicial complex _T We count (using the Binet-Cauchy theorem) thek-dimensional colorful trees onV (for allk), where each treeT is counted with weight . The result confirms, in a way, a formula suggested by Bolker. (fork-r–1). It extends, on one hand, a result of Kalai on weighted counting ofk-dimensional trees and, on the other hand, enumeration formulas for multi-partite (1-dimensional) trees. All these results are extensions of Cayley's celebrated treecounting formula, now 100 years old.     

Functionalized diacetylenes for nonlinear optical applications: Synthesis,characterization, and the properties of their monolayers

Synthesis and characterization of DA(8/1)OMe (14-{4′-[(methoxy)methoxy] biphenyl}-10,12-tetradecadiynoic acid) and DA(8/1)NBP (14-{4′-[(nitro)methoxy] biphenyl}-10,12-tetradecadiynoic acid ) are presented. Monolayers of DA(8/1)OMe at gas-water interface were investigated. It does not form a stable monolayer nor does it undergo polymerization at the gas-water interface. However, the Ba²⁺ and Cd²⁺ salts formed stable monolayer that polymerized. Polymerization was confirmed by Raman spectroscopy. The diacetylene analog with the more polar tail group, DA(8/1)NBP, does not form a monolayer and undergo polymerization regardless of the subphase condition. A mixed monolayer of DA(8/1)OMe and DA(8/1)NBP forms a true monolayer if the composition of DA(8/1)NBP is 50% or less. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1771–1779, 1999     

Optimizing a Multi-Stage Production Process

When articles are made by a sequence of processes, it is often necessary to make discrete batches for each process. These may not be the same size for each stage in the sequence. Two procedures are given for determining the optimum batch sizes, i.e. the batch sizes giving the lowest total for the set-up and investment costs.     

Extreme positive operators on minimal and almost minimal cones

Fiedler and Pták called a cone minimal if it is n-dimensional and has n+1 extremal rays. We call a cone almost minimal if it is n-dimensional and has n+2 extremal rays. Duality properties stemming from the use of Gale pairs lead to a general technique for identifying the extreme cone-preserving (positive) operators between polyhedral cones. This technique is most effective for cones with dimension not much smaller than the number of their extreme rays. In particular, the Fiedler-Pták characterization of extreme positive operators between minimal cones is extended to the following cases: (i) operators from a minimal cone to an arbitrary polyhedral cone, (ii) operators from an almost minimal cone to a minimal cone.     

Equi-distribution over descent classes of the hyperoctahedral group

A classical result of MacMahon shows that the length function and the major index are equi-distributed over the symmetric group. Foata and Schützenberger gave a remarkable refinement and proved that these parameters are equi-distributed over inverse descent classes, implying bivariate equi-distribution identities. Type B analogues of these results, refinements and consequences are given in this paper.