A Hybrid Algorithm Based on Optimal Quadratic Spline Collocation and Parareal Deferred Correction for Parabolic PDEs

Parareal is a kind of time parallel numerical methods for time-dependent systems. In this paper, we consider a general linear parabolic PDE, use optimal quadratic spline collocation (QSC) method for the space discretization, and proceed with the parareal technique on the time domain. Meanwhile, deferred correction technique is also used to improve the accuracy during the iterations. In fact, the optimal QSC method is a correction of general QSC method. Along the temporal direction we embed the iterations of deferred correction into parareal to construct a hybrid method, parareal deferred correction (PDC) method. The error estimation is presented and the stability is analyzed. To save computational cost, we find out a simple way to balance the two kinds of iterations as much as possible. We also argue that the hybrid algorithm has better system efficiency and costs less running time. Numerical experiments by multicore computers are attached to exhibit the effectiveness of the hybrid algorithm

Role of the IgM Fc Receptor in Immunity and Tolerance

Immunoglobulin (Ig) M is the first antibody isotype to appear during evolution, ontogeny and immune responses. IgM not only serves as the first line of host defense against infections but also plays an important role in immune regulation and immunological tolerance. For many years, IgM is thought to function by binding to antigen and activating complement system. With the discovery of the IgM Fc receptor (FcμR), it is now clear that IgM can also elicit its function through FcμR. In this review, we will describe the molecular characteristics of FcμR, its role in B cell development, maturation and activation, humoral immune responses, host defense, and immunological tolerance. We will also discuss the functional relationship between IgM-complement and IgM-FcμR pathways in regulating immunity and tolerance. Finally, we will discuss the potential involvement of FcμR in human diseases

Mechanistic study of visible light-driven CdS or g-C₃N₄-catalyzed C–H direct trifluoromethylation of (hetero)arenes using CF₃SO₂Na as the trifluoromethyl source

The mild and sustainable methods for C–H direct trifluoromethylation of (hetero)arenes without any base or strong oxidants are in extremely high demand. Here, we report that the photo-generated electron-hole pairs of classical semiconductors (CdS or g-C3N4) under visible light excitation are effective to drive C–H trifluoromethylation of (hetero)arenes with stable and inexpensive CF3SO2Na as the trifluoromethyl (TFM) source via radical pathway. Either CdS or g-C3N4 propagated reaction can efficiently transform CF3SO2Na to [rad]CF3 radical and further afford the desired benzotrifluoride derivatives in moderate to good yields. After visible light initiated photocatalytic process, the key elements (such as F, S and C) derived from the starting TFM source of CF3SO2Na exhibited differential chemical forms as compared to those in other oxidative reactions. The photogenerated electron was trapped by chemisorbed O2 on photocatalysts to form superoxide radical anion (O2[rad]−) which will further attack [rad]CF3 radical with the generation of inorganic product F− and CO2. This resulted in a low utilization efficiency of [rad]CF3 (&lt;50%). When nitro aromatic compounds and CF3SO2Na served as the starting materials in inert atmosphere, the photoexcited electrons can be directed to reduce the nitro group to amino group rather than being trapped by O2. Meanwhile, the photogenerated holes oxidize SO2CF3− into [rad]CF3. Both the photogenerated electrons and holes were engaged in reductive and oxidative paths, respectively. The desired product, trifluoromethylated aniline, was obtained successfully via one-pot free-radical synthesis.</p

A Hybrid Algorithm Based on Optimal Quadratic Spline Collocation and Parareal Deferred Correction for Parabolic PDEs

Parareal is a kind of time parallel numerical methods for time-dependent systems. In this paper, we consider a general linear parabolic PDE, use optimal quadratic spline collocation (QSC) method for the space discretization, and proceed with the parareal technique on the time domain. Meanwhile, deferred correction technique is also used to improve the accuracy during the iterations. In fact, the optimal QSC method is a correction of general QSC method. Along the temporal direction we embed the iterations of deferred correction into parareal to construct a hybrid method, parareal deferred correction (PDC) method. The error estimation is presented and the stability is analyzed. To save computational cost, we find out a simple way to balance the two kinds of iterations as much as possible. We also argue that the hybrid algorithm has better system efficiency and costs less running time. Numerical experiments by multicore computers are attached to exhibit the effectiveness of the hybrid algorithm

Study on Kinetics of Transformation in Medium Carbon Steel Bainite at Different Isothermal Temperatures

Ultra-fine carbide-free bainitic (UCFB) steel, also known as nano-bainite (NB) steel, is composed of bainitic ferrite laths with nanoscale thickness and carbon-rich film-like retained austenite located between laths. The bainite transformation kinetic model can accurately describe the bainite transformation kinetics in conventional austempering (CA) processes based on the shear mechanism combined with the dilatometer test. UCFB steels with medium and high carbon composition are designed in this work to systematically study the transformation kinetics of bainite, and the evolution of its microstructure and properties, and reveal the influence of heat treatment processes on the microstructure and properties the UCFB steels. The results show that the activation energy for BF nucleation decreases during the CA process and isothermal transformation temperature decreases. The bainite transformation is first nucleated at the grain boundaries, and then nucleated at the newly formed bainitic ferrite/austenite interface

Investigation of the sustained-release mechanism of hydroxypropyl methyl cellulose skeleton type Acipimox tablets

In this study, we investigate the production of hypolipidemic agents in the form of Acipimox sustained-release tablets, using a wet pelleting process. The purpose of this research is to reduce the total intake time for patients and to lower the initial dose in such that the adverse reactions could be reduced. This study adopts the single-factor method and orthogonal experiments by using hydroxypropyl methyl cellulose (HPMC K15M) as the main sustained-release prescription composition. The final prescription is Acipimox 20%, HPMC K15M 26.67%, sodium carboxymethyl cellulose 30%, polyethylene glycol (PEG 6000) 1%, ethyl cellulose 16.6%, lactose 4.67% and magnesium stearate 1%. The dissolution of tablets reached 85.88% in 8 h. The difference in the weight, hardness and friability of the tables met the requirements in the Chinese Pharmacopoeia; to test the stability, a temperature and illumination accelerated test method was used, the results indicate that the Acipimox sustained-release tablets should be sealed and stored in a dark, cool area. A preliminary study on the tablets’ releasing mechanism showed that their release curve fitted the Higuchi model (the formula is Mt/M∞ = 31.137 t1/2–3.605 (R2 = 0.9903)). The Acipimox tablets’ release principle is dominated by the diffusion mechanism

Output feedback control for set stabilization of Boolean control networks

In this paper, the output feedback set stabilization problem for Boolean control networks (BCNs) is investigated with the help of the semi-tensor product (STP) tool. The concept of output feedback control invariant (OFCI) subset is introduced, and novel methods are developed to obtain the OFCI subsets. Based on the OFCI subsets, a technique, named spanning tree method, is further introduced to calculate all possible output feedback set stabilizers. An example concerning lac operon for the bacterium Escherichia coli is given to illustrate the effectiveness of the proposed method. This technique can also be used to solve the state feedback (set) stabilization problem for BCNs. Compared with the existing results, our method can dramatically reduce the computational cost when designing all possible state feedback stabilizers for BCNs

Study on Seismic Response in Deeply Deposited Saturated Liquefiable Soil Reinforced by Using Subarea Long-Short Gravel Piles

To avoid large deformation, resulting from liquefaction, in inclined and deeply deposited liquefiable soil, it is necessary to design economical and reasonable reinforcement schemes. A reinforcement scheme employing subarea long-short gravel piles was proposed, and it was successfully applied in the embankment construction of the Aksu-kashgar highway. To reveal its underlying mechanism and effect on the seismic performance of the highway, the dynamic responses of natural foundation and two kinds of reinforced foundations were analyzed and compared under this scheme, using the program FEMEPDYN. Results showed that both the seismic subsidence and the excess pore pressure ratios were far less in the foundation reinforced with isometric gravel piles and in the foundation reinforced with subarea long-short gravel piles, compared with that in natural foundation. Therefore, the potential hazards of liquefaction were overcome in these two kinds of reinforced foundations. Furthermore, it was obvious that the shielding region only formed within the foundation reinforced with subarea long-short gravel piles. With the shielding effect, the proposed reinforcement scheme employing subarea long-short gravel piles not only eliminated liquefaction in deeply deposited liquefiable soil, but it also demonstrated an outstanding advantage in that the total length of gravel piles used was greatly reduced compared to the total length in the isometric gravel piles scheme and the interphase long-short gravel piles