Differential Calculi on Commutative Algebras

A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in very much the same way we are used to from the geometrical arena underlying classical physical theories and models. In previous work, certain differential calculi on a commutative algebra exhibited relations with lattice structures, stochastics, and parametrized quantum theories. This motivated the present systematic investigation of differential calculi on commutative and associative algebras. Various results about their structure are obtained. In particular, it is shown that there is a correspondence between first order differential calculi on such an algebra and commutative and associative products in the space of 1-forms. An example of such a product is provided by the Ito calculus of stochastic differentials. For the case where the algebra A is freely generated by `coordinates' x^i, i=1,...,n, we study calculi for which the differentials dx^i constitute a basis of the space of 1-forms (as a left A-module). These may be regarded as `deformations' of the ordinary differential calculus on R^n. For n < 4 a classification of all (orbits under the general linear group of) such calculi with `constant structure functions' is presented. We analyse whether these calculi are reducible (i.e., a skew tensor product of lower-dimensional calculi) or whether they are the extension (as defined in this article) of a one dimension lower calculus. Furthermore, generalizations to arbitrary n are obtained for all these calculi.Comment: 33 pages, LaTeX. Revision: A remark about a quasilattice and Penrose tiling was incorrect in the first version of the paper (p. 14

Dutch disease-cum-financialization booms and external balance cycles in developing countries

We formally investigate the medium-to-long-run dynamics emerging out of a Dutch disease-cum-financialization phenomenon. We take inspiration from the most recent Colombian development pattern. The “pure” Dutch disease first causes deindustrialization by permanently appreciating the economy’s exchange rate in the long run. Financialization, i.e. booming capital inflows taking place in a climate of natural resource-led financial over-optimism, causes medium-run exchange rate volatility and macroeconomic instability. This jeopardizes manufacturing development even further by raising macroeconomic uncertainty. We advise the adoption of capital controls and a developmentalist monetary policy to tackle these two distinct but often intertwined phenomena

Influence of Deep Margin Elevation and preparation design on the fracture strength of indirectly restored molars

The objectives of this in-vitro study were to investigate the influence of Deep Margin Elevation (DME) and the preparation design (cusp coverage) on the fracture strength and repairability of CAD/CAM manufactured lithium disilicate (LS2) restorations on molars. Sound extracted human molars (n = 60) were randomly divided into 4 groups (n = 15) (inlay without DME (InoD); inlay with DME (IWD); onlay without DME (OnoD); onlay with DME (OnWD)). All samples were aged (1.2 × 106 cycles of 50N, 8000 cycles of 5–55 °C) followed by oblique static loading until fracture. Fracture strength was measured in Newton and the fracture analysis was performed using a (scanning electron) microscope. Data was statistically analyzed using two-way ANOVA and contingency tables. DME did not affect the fracture strength of LS2 restorations to a statistically significant level (p =.15). Onlays were stronger compared to inlays (p =.00). DME and preparation design did not interact (p =.97). However, onlays with DME were significantly stronger than inlays without DME (p =.00). More repairable fractures were observed among inlays (p =.00). Catastrophic, crown-root fractures were more prevalent in onlays (p =.00). DME did not influence repairability of fractures or fracture types to a statistically significant level (p &gt;.05). Within the limitations of this in-vitro study, DME did not statistical significantly affect the fracture strength, nor the fracture type or repairability of LS2 restorations in molars. Cusp coverage did increase the fracture strength. However, oblique forces necessary to fracture both inlays and onlays, either with or without DME, by far exceeded the bite forces that can be expected under physiological clinical conditions. Hence, both inlays and onlays are likely to be fracture resistant during clinical service.</p

A Comparative Review of Electrolytes for Organic-Material-Based Energy-Storage Devices Employing Solid Electrodes and Redox Fluids

Electrolyte chemistry is critical for any energy‐storage device. Low‐cost and sustainable rechargeable batteries based on organic redox‐active materials are of great interest to tackle resource and performance limitations of current batteries with metal‐based active materials. Organic active materials can be used not only as solid electrodes in the classic lithium‐ion battery (LIB) setup, but also as redox fluids in redox‐flow batteries (RFBs). Accordingly, they have suitability for mobile and stationary applications, respectively. Herein, different types of electrolytes, recent advances for designing better performing electrolytes, and remaining scientific challenges are discussed and summarized. Due to different configurations and requirements between LIBs and RFBs, the similarities and differences for choosing suitable electrolytes are discussed. Both general and specific strategies for promoting the utilization of organic active materials are covered.So solid storage : The use of organic redox‐active materials is a new tendency for rechargeable batteries, either as traditional solid‐state electrode materials in lithium‐ion batteries or as dissolved redox fluidic species in liquid electrolytes for redox flow batteries. The performance‐limiting scenarios and some illuminating improvements by formulating electrolytes are reviewed

Tailoring the Charge/Discharge Potentials and Electrochemical Performance of SnO₂ Lithium‐Ion Anodes by Transition Metal Co‐Doping

It has been shown that the introduction of several transition metal (TM) dopants into SnO2 lithium‐ion battery anodes can overcome the issues associated with the irreversible capacity loss from the conversion reaction of SnO2 and the aggregation of the metallic Sn particles formed upon lithiation. As the choice of the single dopant, however, plays a decisive role for the achievable energy density – precisely its redox potential – we investigate herein TM co‐doped SnO2, prepared by using a readily scalable continuous hydrothermal flow synthesis (CHFS) process, to tailor the dis‐/charge profile and by this the energy density. It is shown that the judicious choice of different elemental doping combinations in samples made via CHFS simultaneously improves the cycling performance and the full‐cell energy density. To support these findings, we realized a lithium‐ion full‐cell incorporating the best performing co‐doped SnO2 as negative electrode and high‐voltage LiNi0.5Mn1.5O4 (LNMO) as positive electrode–to the best of our knowledge, the first full‐cell based on such anode material in combination with LNMO as cathode active material

Noncommutative Geometry of Finite Groups

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more generally for Hopf algebras including quantum groups. A differential calculus is regarded as the most basic structure needed for the introduction of further geometric notions like linear connections and, moreover, for the formulation of field theories and dynamics on finite sets. Associated with each bicovariant first order differential calculus on a finite group is a braid operator which plays an important role for the construction of distinguished geometric structures. For a covariant calculus, there are notions of invariance for linear connections and tensors. All these concepts are explored for finite groups and illustrated with examples. Some results are formulated more generally for arbitrary associative (Hopf) algebras. In particular, the problem of extension of a connection on a bimodule (over an associative algebra) to tensor products is investigated, leading to the class of `extensible connections'. It is shown that invariance properties of an extensible connection on a bimodule over a Hopf algebra are carried over to the extension. Furthermore, an invariance property of a connection is also shared by a `dual connection' which exists on the dual bimodule (as defined in this work).Comment: 34 pages, Late

Clinical longevity of intracoronal restorations made of gold, lithium disilicate, leucite, and indirect resin composite:a systematic review and meta-analysis

OBJECTIVES: The aim of this systematic review and meta-analysis is to assess the comparative clinical success and survival of intracoronal indirect restorations using gold, lithium disilicate, leucite, and indirect composite materials.MATERIAL AND METHODS: This systematic review and meta-analysis were conducted following the Cochrane Handbook for Systematic Reviews of Interventions and PRISMA guidelines. The protocol for this study was registered in PROSPERO (registration number: CRD42021233185). A comprehensive literature search was conducted across various databases and sources, including PubMed/Medline, Embase, Cochrane Library, Web of Science, ClinicalTrials.gov, and gray literature. A total of 7826 articles were screened on title and abstract. Articles were not excluded based on the vitality of teeth, the language of the study, or the observation period. The risk difference was utilized for the analyses, and a random-effects model was applied. All analyses were conducted with a 95% confidence interval (95% CI). The calculated risk differences were derived from the combined data on restoration survival and failures obtained from each individual article. The presence of heterogeneity was assessed using the I2 statistic, and if present, the heterogeneity of the data in the articles was evaluated using the non-parametric chi-squared statistic (p &lt; 0.05).RESULTS: A total of 12 eligible studies were selected, which included 946 restorations evaluated over a minimum observation period of 1 year and a maximum observation period of 7 years. Results of the meta-analysis indicated that intracoronal indirect resin composite restorations have an 18% higher rate of failure when compared to intracoronal gold restorations over 5-7 years of clinical service (risk difference =  - 0.18 [95% CI: - 0.27, - 0.09]; p = .0002; I2 = 0%). The meta-analysis examining the disparity in survival rates between intracoronal gold and leucite restorations could not be carried out due to methodological differences in the studies.CONCLUSIONS: According to the currently available evidence, medium-quality data indicates that lithium disilicate and indirect composite materials demonstrate comparable survival rates in short-term follow-up. Furthermore, intracoronal gold restorations showed significantly higher survival rates, making them a preferred option over intracoronal indirect resin-composite restorations. Besides that, the analysis revealed no statistically significant difference in survival rates between leucite and indirect composite restorations. The short observation period, limited number of eligible articles, and low sample size of the included studies were significant limitations.CLINICAL SIGNIFICANCE: Bearing in mind the limitations of the reviewed literature, this systematic review and meta-analysis help clinicians make evidence-based decisions on how to restore biomechanically compromised posterior teeth.</p