10,000 publications from this institution
This paper gives several basic results on dynamic nonlinear networks from a geometric point of view. One of the main advantages of a geometric approach is that it is coordinate-free, i.e., results obtained by a geometric method do not depend on the particular choices of a tree, a loop matrix, state variables, etc. Therefore, the method is suitable for studying intrinsic properties of networks. It is shown that transversality of resistor constitutive relations and Kirchhoff space is a sufficient condition for the configuration space to be a submanifold. Main result of the paper states that a network is locally solvable, i.e., the dynamics of a network is well defined in the sense of Definition 3, if and only if, capacitor charges and inductor fluxes serve as a local coordinate system for the configuration space. In other words, if all the variables in a network are determined as functions of capacitor charges and inductor fluxes, at least locally, then the dynamics is well defined. Conversely, if the dynamics is well defined, then all the variables in a network are determined as functions of capacitor charges and inductor fluxes. Because of its coordinate-free property, the main result also says that if the dynamics is well defined in terms of some coordinate system, then it must be well defined in terms of capacitor charges and inductor fluxes. Conversely, if the dynamics is not well-defined in terms of capacitor charges and inductor fluxes, then there is no choice of variables in terms of which the dynamics is well defined in the sense of Definition 3. This shows that capacitor charges and inductor fluxes are the fundamental quantities in describing the dynamics of networks. Perturbation results are given which guarantee transversality and local solvability. Finally, several other perturbation results are given which guarantee eventual strict passivity of dynamic nonlinear networks. They explain why the voltage and current waveforms of almost every network of practical importance are eventually uniformly bounded.
Stablecoins and central bank digital currencies are on the horizon in Asia, and in some cases have already arrived. This paper provides new analysis and a critique of the use case for both forms of digital currency. It provides time-varying estimates of devaluation risk for the leading stablecoin, Tether, using data from the futures market. It describes the formidable obstacles to widespread use of central bank digital currencies in cross-border transactions, the context in which their utility is arguably greatest. The bottom line is that significant uncertainties continue to dog the region's digital currency initiatives.
An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
The synthesis of novel dendrimers functionalized with laser dyes both at the periphery and at the core, along with all relevant model compounds necessary for accurate photophysical studies, is described. The utilized synthetic strategy involves a modular approach in which a variety of peripheral and core moieties can be placed on a dendritic structure bearing electrophilic peripheral groups and a nucleophilic core. Specifically, the target macromolecules required functionalization with the laser dyes coumarin 2 (periphery) and coumarin 343 (core) due to the possibility of energy transfer from the former to the latter dye. In addition, the preparation of a novel, highly soluble and reactive hypermonomer utilized in the rapid and efficient synthesis of high-generation dye-labeled dendrimers and model compounds is outlined.
