Filters compatible with isomorphism testing

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.     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on 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 with a window size , 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 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.     

Geometric and operational optimization of 20-kHz probe-type sonoreactor for enhancing sonochemical activity

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.     

A rapid and sensitive bioanalytical LC–MS/MS method for the quantitation of a novel CDK5 inhibitor 20–223 (CP668863) in plasma: Application to in vitro metabolism and plasma protein-binding studies

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 (CL_int) 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.     

基于SWT方法的钢绞线索微动疲劳特性分析

为得到钢绞线索丝间接触区的应力场分布并预测微动疲劳裂纹萌生位置和微动疲劳寿命，本文利用参数化方法建立了精细化的钢绞线拉索有限元模型，包括整索模型和不同层丝间接触区域的局部精细化子模型．分析了钢绞线索在两种交变荷载工况下的应力场变化情况，并基于多轴疲劳SWT(Smith-Watson-Topper)临界平面法进行了疲劳特性分析和疲劳寿命预测．主要结论如下：钢绞线索内接触区边缘处的微动幅值较大，中心处几乎没有相对滑动，微动疲劳的初始裂纹萌生点位于接触区域边缘；经不同区域子模型分析比较，在轴向循环荷载作用下，外层钢丝的接触区域比内层钢丝更易发生微动疲劳损伤；在横向位移循环荷载作用下，同层钢丝因位置角度不同而产生了较大的疲劳特性差异，且相比轴向循环拉伸，该工况下最不利单丝的微动疲劳寿命更低；与非接触区域相比，接触区的疲劳寿命大幅降低，微动现象对钢绞线索的抗疲劳性能有明显降低作用．     

Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Corrigendum to “Maximal linear groups induced on the Frattini quotient of a p-group” [J. Pure Appl. Algebra 222 (10) (2018) 2931–2951]

We give a correction to Fig. 1 and supporting text published in the paper: ‘Maximal linear groups induced on the Frattini quotient of a p-group’, J. Pure Appl. Algebra 222 (10) (2018) 2931–2951.     

Regularity results of the thin obstacle problem for the p(x)-Laplacian

We study thin obstacle problems involving the energy functional with $p(x)$-growth. We prove higher integrability and Hölder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent $p(x)$ is Hölder continuous.