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1.
Dinatural transformations, which generalise the ubiquitous natural transformations to the case where the domain and codomain functors are of mixed variance, fail to compose in general; this has been known since they were discovered by Dubuc and Street in 1970. Many ad hoc solutions to this remarkable shortcoming have been found, but a general theory of compositionality was missing until Petri?, in 2003, introduced the concept of g-dinatural transformations, that is, dinatural transformations together with an appropriate graph: he showed how acyclicity of the composite graph of two arbitrary dinatural transformations is a sufficient and essentially necessary condition for the composite transformation to be in turn dinatural. Here we propose an alternative, semantic rather than syntactic, proof of Petri?'s theorem, which the authors independently rediscovered with no knowledge of its prior existence; we then use it to define a generalised functor category, whose objects are functors of mixed variance in many variables, and whose morphisms are transformations that happen to be dinatural only in some of their variables.We also define a notion of horizontal composition for dinatural transformations, extending the well-known version for natural transformations, and prove it is associative and unitary. Horizontal composition embodies substitution of functors into transformations and vice-versa, and is intuitively reflected from the string-diagram point of view by substitution of graphs into graphs.This work represents the first, fundamental steps towards a substitution calculus for dinatural transformations as sought originally by Kelly, with the intention then to apply it to describe coherence problems abstractly. There are still fundamental difficulties that are yet to be overcome in order to achieve such a calculus, and these will be the subject of future work; however, our contribution places us well in track on the path traced by Kelly towards a calculus of substitution for dinatural transformations. 相似文献
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Mateusz Pucilowski Mehdi Jangi Hesameddin Fatehi Kar Mun Pang Xue-Song Bai 《Proceedings of the Combustion Institute》2021,38(4):5597-5604
In this paper, the flame-wall interaction of reacting diesel spray under engine like conditions is investigated using large eddy simulations. The aim of this study is to understand the influence of the distance between the wall and the spray nozzle on the air entrainment rate, which is a key variable in formation/oxidation process of soot. Three experimental cases are investigated, a free jet case and two wall impingement cases with a distance from nozzle to wall of 30 mm and 50 mm, which are considered as characteristic wall impingement distances for light- and heavy-duty bores in diesel engines, respectively. The optical soot measurements imply a positive influence of wall on the rate of soot oxidation. Numerical simulations are employed to elucidate importance of different mechanisms for the air entrainment, i.e., air entrainment prior to flame lift-off position, enhanced mixing due to the wall impingement and enhanced mixing by the entrainment wave. The results show that oxidation process after the end of injection is driven by a different mixing mechanism depending on the distance to the wall. The 30 mm case resulted in a “mixing boost”, where the dominant mixing mechanism is the wall impingement vortex mixing, which gives rise to the fastest soot decay among the cases. The mixing in the 50 mm case is governed by a late wall impingement vortex mixing, giving rise to a low, but a constant air entrainment rate, i.e., a “mixing plateau”. The free jet case resulted in mixing governed by the entrainment wave mechanism. Both wall impingement cases have faster soot oxidation rate compared with the free jet case, but due to a different underlying mixing process. LES is shown to be able to replicate the line-of-sight measurements of natural OH* chemiluminescence and distribution of soot region from the optical soot diagnostics. 相似文献
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Contaminants of emerging concern (CEC) such as pharmaceuticals commonly found in urban and industrial wastewater are a potential threat to human health and have negative environmental impact. Most wastewater treatment plants cannot efficiently remove these compounds and therefore, many pharmaceuticals end up in aquatic ecosystems, inducing problems such as toxicity and antibiotic-resistance. This review reports the extent of pharmaceutical removal by individual processes such as bioreactors, advanced oxidation processes and membrane filtration systems, all of which are not 100% efficient and can lead to the direct discharge of pharmaceuticals into water bodies. Also, the importance of understanding biotransformation of pharmaceutical compounds during biological and ultrasound treatment, and its impact on treatment efficacy will be reviewed. Different combinations of the processes above, either as an integrated configuration or in series, will be discussed in terms of their degradation efficiency and scale-up capabilities. The trace quantities of pharmaceutical compounds in wastewater and scale-up issues of ultrasound highlight the importance of membrane filtration as a concentration and volume reduction treatment step for wastewater, which could subsequently be treated by ultrasound. 相似文献
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BackgroundT2-weighted, two-point Dixon fast-spin-echo (FSE) is an effective technique for magnetic resonance neurography (MRN) that can provide quantitative assessment of muscle denervation. Low signal-to-noise ratio and inadequate fat suppression, however, can impede accurate interpretation.PurposeTo quantify effects of principal component analysis (PCA) denoising on tissue signal intensities and fat fraction (FF) and to determine qualitative image quality improvements from both denoising and water-weighting (WW) algorithms to improve nerve conspicuity and fat suppression.Study typeProspective.SubjectsTwenty-one subjects undergoing MR neurography evaluation (11/10 male/female, mean age = 46.3±13.7 years) with 60 image volumes. Twelve subjects (23 image volumes) were determined to have muscle denervation based on diffusely elevated T2 signal intensity.Field strength/sequence3 T, 2D, two-point Dixon FSE.AssessmentQualitative assessment included overall image quality, nerve conspicuity, fat suppression, pulsation and ringing artifacts by 3 radiologists separately on a three-point scale (1 = poor, 2 = average, 3 = excellent). Quantitative measurements for FF and signal intensity relative to normal muscle were made for nerve, abnormal muscle and subcutaneous fat.Statistical testsLinear and ordinal regression models were used for quantitative and qualitative comparisons, respectively; 95% confidence intervals (CIs) and p-values for pairwise comparisons were adjusted using the Holm-Bonferroni method. Inter-rater agreement was assessed using Gwet's agreement coefficient (AC2).ResultsSimulations showed PCA-denoising reduced FF error from 2.0% to 1.0%, and from 7.6% to 3.1% at noise levels of 10% and 30%, respectively. In human subjects, PCA-denoising did not change signal levels and FF quantitatively. WW decreased fat signal significantly (−83.6%, p < 0.001). Nerve conspicuity was improved by WW (odds ratio, OR = 5.8, p < 0.001). Fat suppression was improved by both PCA (OR = 3.6, p < 0.001) and WW (OR = 2.2, p < 0.001). Overall image quality was improved by PCA + WW (OR = 1.7, p = 0.04).ConclusionsWW and PCA-denoising improved nerve conspicuity and fat suppression in MR neurography. Denoising can potentially provide improved accuracy of FF maps for assessing fat-infiltrated muscle. 相似文献
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Rational Design of Two-Dimensional Magnetic Chromium Borides Based on First-Principles Calculation 下载免费PDF全文
Two-dimensional(2D) magnetic materials have been experimentally recognized recently,however,the Curie temperatures(TC) of known 2D systems are quite low.Generally,magnetic systems can be seen as constituent magnetic elements providing spins and the non-magnetic elements providing frameworks to host the magnetic elements.Short bond lengths between the magnetic and non-magnetic elements would be beneficial for strong magnetic interactions and thus high TC.Based on this,we propose to combine the magnetic element Cr and the non-magnetic element boron to design novel 2D magnetic systems.Using our self-developed software package IM2 ODE,we design a series of chromium-boride based 2D magnetic materials.Nine stable magnetic systems are identified.Among them,we find that CrB4-Ⅰ,CrB4-Ⅱ and CrBs-Ⅰ with common structural units [CrB8] are ferromagnetic metals with estimated TC of 270 K,120 K and 110 K,respectively.On the other hand,five CrB3 phases with structural units [Cr2B12] are antiferromagnetic metals.Additionally,we also find one antiferromagnetic semiconductor CrB2-Ⅰ.Our work may open new directions for identifying 2D magnetic systems with high TC. 相似文献
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