Differentiable spaces that are subcartesian

We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows.     

The full basis theorem does not imply analytic wellordering

A finite support product of s="true">s="true">s="true">ωs="true">s="true">1sub> clones of Jensen's minimal sup is="true">s="true">s="true">Πs="true">s="true">2s="true">s="true">1subsup> singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals.     

Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

A unified theory for brittle and ductile shear mode fracture

A unified theory captures both brittle and ductile fracture. The fracture toughness is proportional to the applied stress squared and the length of the crack. For purely brittle solids, this criterion is equivalent to Griffith's theory. In other cases, it provides a theoretical basis for the Irwin-Orowan formula. For purely ductile solids, the theory makes direct contact with the Bilby-Cottrell-Swinden model. The toughness is highest in ductile materials because the shielding dislocations in the plastic zone provide additional resistance to crack growth. This resistance is the force opposing dislocation motion, and the Peach-Koehler force overcomes it. A dislocation-free zone separates the plastic zone from and the tip of the crack. The dislocation-free zone is finite because molecular forces responsible for the cohesion of the surfaces near the crack tip are not negligible. At the point of crack growth, the length of the dislocation-free zone is constant and the shielding dislocations advance in concert. As in Griffith's theory, the crack is in unstable equilibrium. The theory shows that a dimensionless variable controls the elastoplastic behaviour. A relationship for the size of the dislocation-free zone is derived in terms of the macroscopic and microscopic parameters that govern the fracture.     

Sustainability of ride-hailing services in China’s mobility market: A simulation model of socio-technical system transition

As a symbol of sharing economy, ride-hailing services have spread to Asia, where various forms of services have been established according to the existing socio-technical regimes, including legal, policy, and environmental concerns. China, in particular, has accepted ride-hailing services by revising existing institutions. This study analyzes China’s acceptance of ride-hailing services in the socio-technical system context set up for legacy services. Simulation modeling, combined with transition theory and an agent-based model, is used to analyze the data. This study calculates consumer disutility based on mobility market share, reflecting consumer preference, and predicts the sustainability of ride-hailing services. The simulation results conclude that legalization and socio-technical context are of importance for sustainable mobility.     

Pure tetrahedral quadruple systems with index two

An oriented tetrahedron defined on four vertices is a set of four cyclic triples with the property that any ordered pair of vertices is contained in exactly one of the cyclic triples. A tetrahedral quadruple system of order $n$ with index $\lambda$, denoted by , is a pair , where $X$ is an $n$‐set and is a set of oriented tetrahedra (blocks) such that every cyclic triple on $X$ is contained in exactly $\lambda$ members of . A is pure if there do not exist two blocks with the same vertex set. When $\lambda =1$, the spectrum of a pure TQS has been completely determined by Ji. In this paper, we show that there exists a pure if and only if and $n\ge 7$. A corollary is that a simple also exists if and only if and $n\ge 7$.     

Design and validation of robotic bionic eye with multiple flexible ropes parallel mechanism inspired by oculomotor law

Producing a stable and agile bionic eye for visual image acquisition in robotics is a challenging task. In this paper, we design a bionic eye with mirror-symmetric distribution and cross-connection of flexible ropes. This mechanism is based on oculomotor law and the physiological structure of the extraocular muscles (EOMs). Specifically, the basic structural parameters are determined by Listing’s law, and the unique connection of the flexible ropes can realize the functions of the recti and oblique muscles. Furthermore, to mimic the trochlea structure, a pulley mechanism is constructed to permit the free movement of the flexible ropes. Through simulation and physical experiments, it is demonstrated that the bionic eye mechanism can move with agility under the structural parameters. The experimental results indicate that the proposed bionic eye mechanism has a superior motion accuracy of 2.798 mm, which is 6.7% of the maximum motion distance, and the repeatable accuracy of the mechanism can up to 0.210 mm.     

Synthesis of diisocyanides with phenolic groups and their polymerization to helically chiral poly(quinoxaline‐2,3‐diyl)s

The development of synthetic routes which lead to five new diisocyanide monomers with one or two phenolic groups is described. Their polymerization behavior is studied with Pd‐ and Ni‐based initiators, as well as under microwave irradiation. The polymerizability is mainly dominated by steric effects as is concluded from experiments using different protecting groups. Chiroptical properties of these new polymers are studied by CD‐spectroscopy. After deprotection, helically chiral poly(quinoxalin‐2,3‐diyl)s are obtained which display a Brønsted function attached to a stereolabile biaryl axis whose configuration should be influenced by the chiral polymer backbone. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1320–1329     

Buffering effects on the solution behavior and hydrolytic degradation of poly(β-amino ester)s

With a vast, synthetically accessible compositional space and highly tunable hydrolysis rates, poly(β-amino ester)s (PBAEs) are an attractive degradable polymer platform. Leveraging PBAEs in a wide range of applications hinges on the ability to program degradation, which, thus far, has been frustrated by multiple confounding phenomena contributing to the degradation of these charged polyesters. Basic conditions accelerate hydrolysis, yet reduce solubility, limiting water access to amines and esters. Further, the high buffering capacity of PBAEs can render buffers ineffective at controlling solution pH. To unify understanding of PBAE degradation and solution properties, this study examines PBAE hydrolysis as a function of pH and buffer concentration as well as polymer hydrophobicity. At low buffer concentrations, the PBAE amines and the acid produced during hydrolysis control solution pH. Meanwhile, at high buffer concentrations that afford relatively constant pH, hydrolysis rate increases with pH, despite the reduced PBAE solubility. Increasing the hydrophobic content of PBAEs eventually hinders the capacity of the polymer to accept protons from solution, limiting the pH increase and slowing hydrolysis. These studies showcase the role of buffering on the pH-dependent degradation and solution properties of PBAEs, providing guidance for programming degradation in applications ranging from drug delivery to thermosets.