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1.
Like the lower central series of a nilpotent group, filters generalize the connection between nilpotent groups and graded Lie rings. However, unlike the case with the lower central series, the associated graded Lie ring may share few features with the original group: e.g. the associated Lie ring can be trivial or arbitrarily large. We determine properties of filters such that every isomorphism between groups is induced by an isomorphism between graded Lie rings.  相似文献   
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3.
We consider the random‐cluster model (RCM) on 20931:rsa20931-math-0001" class="section_image" src="/cms/asset/71c29033-1df3-4b3f-9b2c-7959dd816ed1/rsa20931-math-0001.png"> with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at 20931:rsa20931-math-0002" class="section_image" src="/cms/asset/47cfc3e0-c030-4319-b15e-e9509a24362b/rsa20931-math-0002.png"> with a window size 20931:rsa20931-math-0003" class="section_image" src="/cms/asset/5297e6dd-c5e8-43c3-ad45-081d228be32a/rsa20931-math-0003.png">, where λ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp 20931:rsa20931-math-0004" class="section_image" src="/cms/asset/c5656f2a-5086-4fa9-8ca8-e306bb2dab39/rsa20931-math-0004.png"> mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.  相似文献   
4.
20(R)-panaxadiol (PD) was metabolised by the fungus Aspergillus niger AS 3.3926 to its C-3 carbonylated metabolite and five other hydroxylated metabolites (1–6). Their structures were elucidated as 3-oxo-20(R)-panaxadiol (1), 3-oxo-7β-hydroxyl- 20(R)-panaxadiol (2), 3-oxo-7β,23α-dihydroxyl-20(R)-panaxadiol (3), 3,12-dioxo- 7β,23β-dihydroxyl-20(R)-panaxadiol (4), 3-oxo-1α,7β-dihydroxyl-20(R)-panaxadiol (5) and 3-oxo-7β,15β-dihydroxyl-20(R)-panaxadiol (6) by spectroscopic analysis. Among them, compounds 26 were new compounds. Pharmacological studies revealed that compound 6 exhibited significant anti-hepatic fibrosis activity.  相似文献   
5.
The use of a 20-kHz probe-type sonicator irradiating downward in a 500 mL vessel was optimized for the enhancement of the sonochemical activity in terms of the geometric and operational factors. These factors included the probe immersion depth (the vertical position of the probe), input power, height of the liquid from the bottom, horizontal position of the probe, and thickness of bottom plate The sonochemical oxidation reactions were investigated both quantitatively and qualitatively using calorimetry, KI dosimetry, and luminol (Sonochemiluminescence, SCL) techniques. The sonochemical activity was very positively affected by the vertical boundaries. The highest sonochemical activity was obtained when the probe was placed close to the bottom of the vessel (immersion depth of 60 mm), with a high input power (input power of 75%), and optimal liquid height condition (liquid height of 70 mm). The SCL image analysis showed that the cavitational activity zone gradually expanded around the probe body and changed into a circular shape as the experimental conditions were optimized, and consequently the sonochemical activity increased. The formation of a large bright circular-shaped activity zone could be attributed to the strong reflections of the ultrasound firstly, at the vessel bottom and secondly, at the liquid surface. On the other hand, the cavitational activity zone and the sonochemical activity were negatively affected by the horizontal boundaries when the probe was placed close to the side wall of the vessel. In addition, it was found that the sonochemical activity was also significantly affected by the thickness of the support plate owing to the reflection and transmission of the ultrasound at the boundary between the liquid and the solid media.  相似文献   
6.
A rapid, selective, and sensitive liquid chromatography coupled with tandem mass spectrometry (MS/MS) method was developed and validated for the quantitation of the novel CDK5 inhibitor ‘20–223' in mouse plasma. Separation of analytes was achieved by a reverse-phase ACE Excel C18 column (1.7 μm, 100 × 2.1 mm) with gradient elution using 0.1% formic acid (FA) in methanol and 0.1% FA as the mobile phase. Analytes were monitored by MS/MS with an electrospray ionization source in the positive multiple reaction monitoring mode. The MS/MS response was linear over the concentration range 0.2–500 ng/mL for 20–223. The within- and between-batch precision were within the acceptable limits as per Food and Drug Administration guidelines. The validated method was successfully applied to plasma protein binding and in vitro metabolism studies. Compound 20–223 was highly bound to mouse plasma proteins (>98% bound). Utilizing mouse S9 fractions, in vitro intrinsic clearance (CLint) was 24.68 ± 0.99 μL/min/mg protein. A total of 12 phase I and II metabolites were identified with hydroxylation found to be the major metabolic pathway. The validate method required a low sample volume, was linear from 0.2 to 500 ng/mL, and had acceptable accuracy and precision.  相似文献   
7.
We categorify the notion of an infinitesimal braiding in a linear strict symmetric monoidal category, leading to the notion of a (strict) infinitesimal 2-braiding in a linear symmetric strict monoidal 2-category. We describe the associated categorification of the 4-term relations, leading to six categorified relations. We prove that any infinitesimal 2-braiding gives rise to a flat and fake flat 2-connection in the configuration space of n particles in the complex plane, hence to a categorification of the Knizhnik–Zamolodchikov connection. We discuss infinitesimal 2-braidings in a certain monoidal 2-category naturally assigned to every differential crossed module, leading to the notion of a symmetric quasi-invariant tensor in a differential crossed module. Finally, we prove that symmetric quasi-invariant tensors exist in the differential crossed module associated to Wagemann's version of the String Lie-2-algebra. As a corollary, we obtain a more conceptual proof of the flatness of a previously constructed categorified Knizhnik–Zamolodchikov connection with values in the String Lie-2-algebra.  相似文献   
8.
The Weitzenböck curvature operators are the curvature terms of order zero that appear in the well‐known classical Weitzenböck formula. In this paper, we use the formalism of double forms to prove a simple formula for these operators and to study their geometric properties.  相似文献   
9.
We formulate a definition of isometric action of a compact quantum group (CQG) on a compact metric space, generalizing Banica's definition for finite metric spaces. For metric spaces (X,d)(X,d) which can be isometrically embedded in some Euclidean space, we prove the existence of a universal object in the category of the compact quantum groups acting isometrically on (X,d)(X,d). In fact, our existence theorem applies to a larger class, namely for any compact metric space (X,d)(X,d) which admits a one-to-one continuous map f:X→Rnf:XRn for some n   such that d0(f(x),f(y))=?(d(x,y))d0(f(x),f(y))=?(d(x,y)) (where d0d0 is the Euclidean metric) for some homeomorphism ?   of R+R+.  相似文献   
10.
We define two transforms of non‐conformal harmonic maps from a surface into the 3‐sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between harmonic maps into the 3‐sphere, H‐surfaces in Euclidean 3‐space and almost complex surfaces in the nearly Kähler manifold 201400271:mana201400271-math-0001" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/364b964d-395f-43d0-bb89-6e35ab316007/mana201400271-math-0001.png">. As a consequence we can construct sequences of H‐surfaces and almost complex surfaces.  相似文献   
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