Generators and normal forms of Richard Thompson’s group F and the four-color theorem

We use a result of Kauffman to explore the connection between Richard Thompson’s Group F and the four-color theorem.     

Highly efficient water‐soluble visible light photoinitiators

The monoacylphosphineoxide (MAPO) salts Na‐TPO and Li‐TPO and the bisacylphosphineoxide (BAPO) salts BAPO‐ONa and BAPO‐OLi define an important and in the latter case a new class of water‐soluble photoinitiators (PIs) for radical polymerization. These compounds showed excellent water‐solubility of at least 29 g/L for Na‐TPO and up to 60 g/L for BAPO‐ONa in deionized water, thus exceeding the solubility of the state of the art PI for water‐based systems Irgacure 2959 ( I2959 ) 6‐ to 12‐fold. However, biocompatibility, storage stability, and reactivity were equally important to replace the state of the art compounds. Concerning these properties, the MAPO and BAPO salts were at least in the same range (biocompatibility, stability) or showed even better results (reactivity) and had the additional advantage of visible light initiation. Na‐TPO and Li‐TPO achieved double bond conversions of an aqueous solution of N‐acryloylmorpholine over 97% with broad band irradiation (320–500 nm), Li‐TPO showed additionally very good biocompatibility (LC₅₀ = 3.1 mmol/L) and BAPO‐OLi showed highest reactivity with visible light irradiation. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 473–479     

Arrangements on Parametric Surfaces I: General Framework and Infrastructure

We introduce a framework for the construction, maintenance, and manipulation of arrangements of curves embedded on certain two-dimensional orientable parametric surfaces in three-dimensional space. The framework applies to planes, cylinders, spheres, tori, and surfaces homeomorphic to them. We reduce the effort needed to generalize existing algorithms, such as the sweep line and zone traversal algorithms, originally designed for arrangements of bounded curves in the plane, by extensive reuse of code. We have realized our approach as the Cgal package Arrangement_on_surface_2. We define a compact and modular interface for our framework; for a given application a required small subset of the interface can be identified. Then, only this subset must be implemented. A companion paper describes concretizations for several types of surfaces and curves embedded on them, and applications. This is the first implementation of a generic algorithm that can handle arrangements on a large class of parametric surfaces.     

The structural development of linear canonical transforms

Physics of Atomic Nuclei - We consider that the simultaneous development of the theory of linear canonical integral transforms among two quite distinct scientific communities, provides an...     

Chaotic dynamics of resistively coupled DC-driven distinct Josephson junctions and the effects of circuit parameters

Two distinct Josephson junctions (JJs) connected with a constant coupling resistance R_cp are theoretically considered to investigate the overall dynamics below and above the critical current I_c. The circuit model of the device is driven by two DC current sources, I₁ and I₂. Each junction is characterized by a nonlinear resistive–capacitive junction (NRCSJ). Having constructed the circuit model, time-dependent simulations are carried out for a variety of control parameter sets. Common techniques such as bifurcation diagrams, two-dimensional attractors and Lyapunov exponents are applied for the determination of chaotic as well as periodic dynamics of the superconducting junction devices. According to the findings, two states (namely superconducting and ordinary conducting) are determined as functions of the source currents. The chaotic current which flows through R_cp exhibits a very rich behavior depending on the source currents I₁ and I₂ and junction capacitances C₁ and C₂. The device characteristics are summarized by a number of three-dimensional phase diagrams in the parameter space. In addition, for certain parameters, hyper-chaotic cases with two positive Lyapunov exponents are encountered. In contrast to earlier studies claiming the need for a sinusoidal feeding current for generating a chaotic signal, our circuitry can easily generate one via a DC source.     

Port-Hamiltonian representation for pdes with second-order derivatives in the energy density

In this contribution we consider a port-Hamiltonian setting for partial differential equations. A crucial property of this system class is the property to be able to link a power balance relation to the structure of the equations. However, one has to take into account also the effects of energy flows via the boundary. This is straightforward when the Hamiltonian depends on derivative variables of first order, e.g. by using integration by parts. If second-order derivatives appear then integration by parts cannot be used without due care, thus we suggest an approach by using the so-called Cartan-form. We visualize the derivation of a power balance relation by using the Kirchhoff plate as an example. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)