The newtonian limit of hermitian gravity

We construct the gauge invariant potentials of Hermitian Gravity [1] and derive the linearized equations of motion they obey. A comparison reveals a striking similarity to the Bardeen potentials of general relativity. We then consider the response to a point particle source, and discuss in what sense the solutions of Hermitian Gravity reduce to the Newtonian potentials. In a rather intriguing way, the Hermitian Gravity solutions exhibit a generalized reciprocity symmetry originally proposed by Born in the 1930s. Finally, we consider the trajectories of massive and massless particles under the influence of a potential. The theory correctly reproduces the Newtonian limit in three dimensions and the nonrelativistic acceleration equation. However, it differs from the light deflection calculated in linearized general relativity by 25 %. While the specific complexification of general relativity by extension to Hermitian spaces performed here does not agree with experiment, it does possess useful properties for quantization and is well-behaved around singularities as described in [1]. Another form of complex general relativity may very well agree with experimental data.     

Canonical models of arithmetic (1; e)-curves

The Fuchsian groups of signature (1; e) are the simplest class of Fuchsian groups for which the calculation of the corresponding quotient of the upper half plane presents a challenge. This paper considers the finite list of arithmetic (1; e)-groups. We define canonical models for the associated quotients by relating these to genus 1 Shimura curves. These models are then calculated by applying results on the ${\mathfrak{p}}$ -adic uniformization of Shimura curves and Hilbert modular forms.     

Investigation of design parameters in ultrasound reactors with confined channels

This paper presents a three-dimensional numercial simulation of sonochemical degradation upon cavitational activity. The model relates the simulation of the acoustic pressure distribution to the sonochemical reaction rate. As a case study, the thermal degradation of carbon tetrachloride during sonication is studied in a tubular milliscale reactor. The model is used to optimize the reactor diameter, ultrasound frequency and power dissipated to the ultrasound transducers. The results indicate that multiple transducers at a moderate power level are more efficient than one transducer with high power level. Furthermore, the average cavity volume fraction is proposed as a reaction independent parameter to estimate the optimal reactor design. Within the results obtained in this paper, it appears possible to optimise reactor design based on this parameter.     

Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

We consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.     

先进ATHENATM选用策略与对准功能

基于先进科技对准规格的减缩,对准仪量测数据的应用也变得更为重要。不同对准策略的选择所引起的结果,对全部对准预算有很重要的影响。介绍两个主要科技研发项目:先进对准配套和对准标的设计。     

Monomeric Copper(II) Sites Supported on Alumina Selectively Convert Methane to Methanol

Monomeric Cu^II sites supported on alumina, prepared using surface organometallic chemistry, convert CH₄ to CH₃OH selectively. This reaction takes place by formation of CH₃O surface species with the concomitant reduction of two monomeric Cu^II sites to Cu^I, according to mass balance analysis, infrared, solid‐state nuclear magnetic resonance, X‐ray absorption, and electron paramagnetic resonance spectroscopy studies. This material contains a significant fraction of Cu active sites (22 %) and displays a selectivity for CH₃OH exceeding 83 %, based on the number of electrons involved in the transformation. These alumina‐supported Cu^II sites reveal that C?H bond activation, along with the formation of CH₃O‐ surface species, can occur on pairs of proximal monomeric Cu^II sites in a short reaction time.     

Furanosyl Oxocarbenium Ion Conformational Energy Landscape Maps as a Tool to Study the Glycosylation Stereoselectivity of 2-Azidofuranoses, 2-Fluorofuranoses and Methyl Furanosyl Uronates

The 3D shape of glycosyl oxocarbenium ions determines their stability and reactivity and the stereochemical course of S_N1 reactions taking place on these reactive intermediates is dictated by the conformation of these species. The nature and configuration of functional groups on the carbohydrate ring affect the stability of glycosyl oxocarbenium ions and control the overall shape of the cations. We herein map the stereoelectronic substituent effects of the C2-azide, C2-fluoride and C4-carboxylic acid ester on the stability and reactivity of the complete suite of diastereoisomeric furanoses by using a combined computational and experimental approach. Surprisingly, all furanosyl donors studied react in a highly stereoselective manner to provide the 1,2-cis products, except for the reactions in the xylose series. The 1,2-cis selectivity for the ribo-, arabino- and lyxo-configured furanosides can be traced back to the lowest-energy ³E or E₃ conformers of the intermediate oxocarbenium ions. The lack of selectivity for the xylosyl donors is related to the occurrence of oxocarbenium ions adopting other conformations.     

Diterpene Biosynthesis in Actinomycetes: Studies on Cattleyene Synthase and Phomopsene Synthase

Three diterpene synthases from actinomycetes have been studied. The first enzyme from Streptomyces cattleya produced the novel compound cattleyene. The other two enzymes from Nocardia testacea and Nocardia rhamnosiphila were identified as phomopsene synthases. The cyclisation mechanism of cattleyene synthase and the EIMS fragmentation mechanism of its product were extensively studied by incubation experiments with isotopically labelled precursors. Oxidative transformations expanded the chemical space of these unique diterpenes.     

Bacterial Diterpene Biosynthesis

This Minireview summarises recent developments in the biosynthesis of diterpenes by diterpene synthases in bacteria. It is structured by the class of enzyme involved in the first committed step towards diterpenes, starting with type I diterpene synthases, followed by type II enzymes and the more recently discovered UbiA‐related diterpene synthases. A special emphasis lies on the reaction mechanisms of diterpene synthases that convert simple linear precursors through cationic cascades into structurally complex, usually polycyclic carbon skeletons with multiple stereogenic centres. A further main focus of this Minireview is a discussion of how these mechanisms can be unravelled. Downstream modifications to bioactive molecules are also covered.