Dynamic and wear characteristics of self-lubricating bearing cage: effects of cage pocket shape

34,354,966 active cases and 460,787 deaths because of COVID-19 pandemic were recorded on November 06, 2021, in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible (S), asymptomatic infected (A), clinically ill or symptomatic infected (I), quarantine (Q), isolation (J) and recovered (R), collectively termed as SAIQJR. The qualitative behavior of the model and the stability of biologically realistic equilibrium points are investigated in terms of the basic reproduction number. We performed sensitivity analysis with respect to the basic reproduction number and obtained that the disease transmission rate has an impact in mitigating the spread of diseases. Moreover, considering the non-pharmaceutical and pharmaceutical intervention strategies as control functions, an optimal control problem is implemented to mitigate the disease fatality. To reduce the infected individuals and to minimize the cost of the controls, an objective functional has been constructed and solved with the aid of Pontryagin’s maximum principle. The implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Extensive numerical simulations show that the implementation of intervention strategy has an impact in controlling the transmission dynamics of COVID-19 epidemic. Further, our numerical solutions exhibit that the combination of three controls are more influential when compared with the combination of two controls as well as single control. Therefore, the implementation of all the three control strategies may help to mitigate novel coronavirus disease transmission at this present epidemic scenario.

     

Numerical appoximation of a channel flow problem

Our object in this article is to describe some numerical schemes for the approximation of a Channel Flow problem, and to study the stability of the schemes. Discretization is performed by the combination of spectral methods and finite difference methods.     

Practical Synthesis of New β‐Diketone‐Connected Bipyridine and Its Conversion to Pyrazole‐Centered Bipyridine Ligand

Two new polydentate ligands, 1‐(6‐hydroxymethyl‐2‐pyridyl)‐3‐(2‐pyridyl)‐propane‐1,3‐dione (6) and 1,3‐bis(6‐hydroxymethyl‐2‐pyridyl)‐propane‐1, 3‐dione (8), have been synthesized starting from 2,6‐pyridinedicarboxylic acid by conventional esterification, reduction, and condensation reactions. They were further converted to two new polydentate ligands, 3‐(6‐hydroxymethyl‐2‐pyridyl)‐5‐(2‐pyridyl)‐1H‐pyrazole (7) and 3,5‐bis(6‐hydroxymethyl‐2‐pyridyl)‐1H‐pyrazole (9), by reaction with hydrazine hydrate. These four compounds were characterized by proton nuclear magnetic resonance (¹H NMR), electrospray ionization‐mass spectrum (ESI‐MS), infrared spectrum (IR), and elemental analyses. The structure of 9 was also determined by X‐ray diffraction.     

磺化壳聚糖的制备及其对生长因子活性的保护作用

以壳聚糖为基材,分别以氯磺酸、三甲胺.三氧化硫和丙磺酸内酯为磺化试剂,制备了3,6-O-磺化壳聚糖(OCS)、2-N-磺化壳聚糖(NCS)和2-N-磺丙基壳聚糖(PCS)3种磺化壳聚糖.采用红外光谱、核磁共振谱证明了磺化壳聚糖的结构,元素分析测定了磺化壳聚糖的磺化率.以组织修复过程中一种重要的活性因子——碱性成纤维细胞生长因子(bFGF)为目标因子,通过体外成纤维细胞培养实验,评价了不同磺化壳聚糖对bFGF活性的保护能力.结果显示,相对于未改性壳聚糖(CS),磺化壳聚糖对成纤维细胞的形态无显著影响.细胞活性检测结果显示,OCS和PCS对bFGF活性无明显的保护能力;NCS能有效提高bFGF促进成纤维细胞活性的能力,其对bFGF活性的保护能力可达肝素70%左右.磺化壳聚糖的bFGF活性保护能力不随磺化率的改变而变化.     

Chemoselective palladium-catalyzed deprotonative arylation/[1,2]-Wittig rearrangement of pyridylmethyl ethers

Control of chemoselectivity is one of the most challenging problems facing chemists and is particularly important in the synthesis of bioactive compounds and medications. Herein, the first highly chemoselective tandem C(sp³)–H arylation/[1,2]-Wittig rearrangement of pyridylmethyl ethers is presented. The efficient and operationally simple protocols enable generation of either arylation products or tandem arylation/[1,2]-Wittig rearrangement products with remarkable selectivity and good to excellent yields (60–99%). Choice of base, solvent, and reaction temperature play a pivotal role in tuning the reactivity of intermediates and controlling the relative rates of competing processes. The novel arylation step is catalyzed by a Pd(OAc)₂/NIXANTPHOS-based system via a deprotonative cross-coupling process. The method provides rapid access to skeletally diverse aryl(pyridyl)methanol core structures, which are central components of several medications.     

A high resolution NV/TVD Hermite polynomial upwind scheme for convection‐dominated problems

A high‐order convection‐bounded scheme is constructed by combining the total variational diminishing constraint and convection boundedness criterion condition in the normalized variable formulation. It employs the Hermite polynomial interpolation to design its characteristic line in the normalized variable diagram. Numerical results of the convection‐dominated problems with smooth or discontinuous initial distributions demonstrate the present scheme possesses high resolution and good robustness. Copyright © 2012 John Wiley & Sons, Ltd.