A Lagrangian representation of tangles

We construct a functor from the category of oriented tangles in R³ to the category of Hermitian modules and Lagrangian relations over Z[t,t^-1]. This functor extends the Burau representations of the braid groups and its generalization to string links due to Le Dimet.     

The Generalized Uncertainty Principle

The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit of the measurement precision of incompatible observables. Here it is shown that the traditional uncertainty relation in fact belongs to the leading order approximation of a generalized uncertainty relation. That is, the leading order linear dependence of observables gives the Heisenberg type of uncertainty relations, while higher order nonlinear dependence may reveal more different and interesting correlation properties. Applications of the generalized uncertainty relation and the high order nonlinear dependence between observables in quantum information science are also discussed.     

Synthesis and characterization of poly(thioether ether sulfone imide)s derived from isomeric bis(chlorophthalimide)s and bis(4-mercaptophenyl) sulfone

A series of isomeric bis(chlorophthalimide)s (BCPIs) were conveniently prepared from 3-chlorophthalic anhydride, 4-chlorophthalic anhydride, and mixtures thereof. Polymerization of BCPIs with bis(4-mercaptophenyl) sulfone (BMPS) proceeded smoothly in the presence of tributylamine, from which a class of isomeric poly(thioether ether sulfone imide)s (PTESIs) with inherent viscosities of 0.45-0.82 dL/g were obtained. The solubility, thermal stability, and mechanical properties of these polymers were characterized. Compared to the PTESIs derived from single BCPIs, i.e., 3,3′-, 3,4′-, or 4,4′-BCPIs, the PTESIs derived from mixed BCPIs showed better solubility and higher storage modulus. These PTESIs also demonstrated good thermal stability, giving only 5% weight loss at temperature of 490 °C in nitrogen atmosphere. The glass transition temperatures (T_gs) of these isomeric PTESIs were between 242 and 265 °C, and were increased with increasing of the ratio of 3-chlorophthalimide unit in the polymer backbone.     

Interface model for non-equilibrium evaporation

A microscopic interface condition for condensing/evaporating interfaces is developed by combining a velocity dependent condensation probability [T. Tsuruta, H. Tanaka, T. Masuoka, Int. J. Heat Mass Transfer 42 (1999) 4107] and Maxwell type interface conditions with accommodation. Using methods from kinetic theory, macroscopic interface conditions for mass and energy transport across the phase boundary are derived. This model only applies to simple substances, where diffusive effects in the bulk phases are not present. The results are compared to classical non-equilibrium thermodynamics. The interface conditions are considered for the limit of small deviation from equilibrium, and the corresponding Onsager coefficients are computed. These results are useful as boundary conditions for non-equilibrium evaporation and condensation problems, as done previously by our group [M. Bond, H. Struchtrup, Phys. Rev. E 70 (2004) 061605].     

Thermodynamic potentials and thermodynamic relations in nonextensive thermodynamics

The generalized Gibbs free energy and enthalpy are derived in the framework of nonextensive thermodynamics by using the concept of the physical temperature and the physical pressure. Some relations of the thermodynamical potentials are changed due to the difference between the physical temperature and the inverse of Lagrange multiplier. We derive the thermodynamical relation between the heat capacities at a constant volume and at a constant pressure using the generalized thermodynamical potential. We find that it has a different form from the traditional one in Gibbs thermodynamics. But, the expressions of the heat capacities in this framework using the generalized thermodynamical potentials are still the same as the traditional one.     

Legendre-transform structure derived from quantum theorems

By recourse to (i) the Hellmann-Feynman theorem and (ii) the virial one, the information-optimizing principle based on Fisher’s information measure uncovers a Legendre-transform structure associated with Schrödinger’s equation, in close analogy with the structure that lies behind the standard thermodynamical formalism. The present developments provide new evidence for the information theoretical links based on Fisher’s measure that exist between Schrödinger’s equation, on the one hand, and thermodynamics/thermostatistics on the other hand.     

Decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance

A problem of decision making under uncertainty in which the choice must be made between two sets of alternatives instead of two single ones is considered. A number of choice rules are proposed and their main properties are investigated, focusing particularly on the generalizations of stochastic dominance and statistical preference. The particular cases where imprecision is present in the utilities or in the beliefs associated to two alternatives are considered.     

A combinatorial proof of the Kronecker–Weber Theorem in positive characteristic

In this paper we present a combinatorial proof of the Kronecker–Weber Theorem for global fields of positive characteristic. The main tools are the use of Witt vectors and their arithmetic developed by H.L. Schmid. The key result is to obtain, using counting arguments, how many p-cyclic extensions exist of fixed degree and bounded conductor where only one prime ramifies. We then compare this number with the number of subextensions of cyclotomic function fields of the same type and verify that these two numbers are the same.     

Criterion for judging satisfaction of consistency conditions in rate-dependent constitutive relations

Based on irreversible thermodynamics, the criterion for judging the satisfaction of consistency conditions in rate-dependent constitutive relationship is deduced by introducing four basic hypotheses. Formulas for solving internal variables are given. It makes the rate-dependent model applicable no matter whether the consistency conditions can be satisfied or not. This research was funded by the National Natural Science Foundation of China (No. 59739180) and the Foundation of National Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology (No. 9701).     

Thiol‐ene photopolymerization for efficient curing of vinyl esters

Monomers for radical photopolymerization based on vinyl esters (VEs) have recently been identified as suitable alternatives to (meth)acrylates on account of their low irritancy and cytotoxicity. The drawback of most VEs with abstractable hydrogens is their relatively low reactivity compared with (meth)acrylates. Within this article, we proved by photo‐differential scanning calorimetry measurements and real‐time Fourier transform infrared spectroscopy that the thiol‐ene concept is able to improve the photoreactivity of these VEs to a large extent to a level between those of acrylates and methacrylates. Other VEs have now a reactivity of at least the level of similar acrylates. Mechanical properties as determined by Dynamic Mechanical Analysis and Charpy impact tests showed significant toughening of these materials. Furthermore, we were able to confirm low toxicity of all components by osteoblast cell culture experiments. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013