Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples：turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder （GL） model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.

Extremum of second-order directional derivatives

In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the formulae for the extremum of second-order directional derivatives are derived, and the directions corresponding to maximum and minimum are perpendicular to each other.

Derivations and 2-Local Derivations on the BMS-Weyl Algebra

Using the theory of derivations on finitely generated and graded Lie algebras, we determine that derivations of the BMS-Weyl algebra are all inner. On this basis, it is proved that every 2-local derivation of the BMS-Weyl algebra is a derivation.

A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

Characterizations of semihoops based on derivations

In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multiplicative derivations and show that every Boolean algebra is isomorphic to the algebra of all implicative derivations.Finally,we show that the sets of multiplicative and implicative derivations on bounded regular idempotent semihoops are in oneto-one correspondence.

Synthesis of Imidazole Derivatives for Their Second-order Nonlinear Optics

The design and the synthesis of two conjugated donor acceptor imidazole derivatives(1, 2) were carried out for second order nonlinear optics. The thermal properties, the transparency and second order nonlinear optical properties of the molecules were investigated. The experimental results indicate that a good nonlinearity transparency thermal stability trade off is achieved for them.

The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Catalytic Kinetic Determination of Micro Amounts of Oxalic Acid by Second-Order Derivative Oscillopolarography

It was found that micro amounts of oxalate showed a very strong catalytic effect on the slow reaction between K 2Cr 2O 7 and Orange Ⅳ in a diluted sulfuric acid medium in a water bath at 70 ℃ . Orange Ⅳ exhibited a sensitive second order derivative polarographic wave at -0 50 V( vs . SCE). This provides the basis for a sensitive and selective catalytic kinetic method for oxalate determination with second order derivative oscillopolarography. The effects of sulphuric acid, K 2Cr 2O 7, and orange Ⅳ concentrations, reaction temperature and reaction time were investigated. A calibration curve of oxalate in the range of 0 1-2 0 μg/mL was obtained by the fixed time procedure. The detection limit was 0 03 μg/ mL. The possible interference from co existing substances or ions was examined. The new method has a high sensitivity and a good selectivity compared to other existing methods for oxalic acid determination. It has been applied to the determination of micro amounts of oxalate in real urine samples with satisfactory results.

Transfer RNA-derived small RNA serves as potential non-invasive diagnostic marker and a novel therapeutic target for acute pancreatitis

Transfer RNA(tRNA)-derived fragments,a new type of tRNA-derived small RNA(tsRNA),can be cleaved from tRNA by enzymes to regulate target gene expression at the transcriptional and translational levels.tsRNAs are not only degradation fragments but also have biological functions,including those in immune inflammation,metabolic disorders,and cell death.tsRNA dysregulation is closely associated with multiple diseases,including various cancers and acute pancreatitis(AP).AP is a common gastrointestinal disease,and its incidence increases annually.AP development is associated with tsRNAs,which regulate cell injury and induce inflammation,especially pyroptosis and ferroptosis.Notably,serum tRF36 has the potential to serve as a non-invasive diagnostic biomarker and leads to pancreatic acinar cell ferroptosis causing inflammation to promote AP.We show the characteristics of tsRNAs and their diagnostic value and function in AP,and discuss the potential opportunities and challenges of using tsRNAs in clinical applications and research.

Fluorine-Mediated Benzothiadiazole Derivatives for Second-Order Nonlinear Optics

With increasing research interests in the field of light-matter interactions,various methods have been developed for regulating nonlinear optical(NLO)materials.However,the design and synthesis of organic molecular materials for second-order nonlinear optics remain a great challenge because of the strict requirement of the materials to possess a noncentrosymmetric structure.In this work,two benzothiadiazole(BTD)derivatives referred to as BTD-H and BTD-F were synthesized,and their NLO properties in the crystalline states were studied.It was found that introducing fluorine into the BTD backbone effectively tuned the crystal packing styles of BTD derivatives to a noncentrosymmetric system for effective second-order NLO responses.Such a strategy to induce the noncentrosymmetric structure by introducing the fluorine atoms and halogen interactions may provide guidance for future engineering of organic NLO molecular materials.

CALCULATION OF THE SECOND-ORDER OPTICAL SUSCEPTIBILITIES OF SOME BENZENE DERIVATIVE MOLECULES AND CRYSTALS

The microscopic and macroscopic second-order optical susceptibilities of ten benzene derivative molecules and three crystals were calculated and discussed,basing on the nonlinear optical active group theory.

Hypoxia-preconditioned bone marrow-derived mesenchymal stem cells protect neurons from cardiac arrest-induced pyroptosis

Cardiac arrest can lead to severe neurological impairment as a result of inflammation,mitochondrial dysfunction,and post-cardiopulmonary resuscitation neurological damage.Hypoxic preconditioning has been shown to improve migration and survival of bone marrow–derived mesenchymal stem cells and reduce pyroptosis after cardiac arrest,but the specific mechanisms by which hypoxia-preconditioned bone marrow–derived mesenchymal stem cells protect against brain injury after cardiac arrest are unknown.To this end,we established an in vitro co-culture model of bone marrow–derived mesenchymal stem cells and oxygen–glucose deprived primary neurons and found that hypoxic preconditioning enhanced the protective effect of bone marrow stromal stem cells against neuronal pyroptosis,possibly through inhibition of the MAPK and nuclear factor κB pathways.Subsequently,we transplanted hypoxia-preconditioned bone marrow–derived mesenchymal stem cells into the lateral ventricle after the return of spontaneous circulation in an 8-minute cardiac arrest rat model induced by asphyxia.The results showed that hypoxia-preconditioned bone marrow–derived mesenchymal stem cells significantly reduced cardiac arrest–induced neuronal pyroptosis,oxidative stress,and mitochondrial damage,whereas knockdown of the liver isoform of phosphofructokinase in bone marrow–derived mesenchymal stem cells inhibited these effects.To conclude,hypoxia-preconditioned bone marrow–derived mesenchymal stem cells offer a promising therapeutic approach for neuronal injury following cardiac arrest,and their beneficial effects are potentially associated with increased expression of the liver isoform of phosphofructokinase following hypoxic preconditioning.

Evaluating Wharton’s jelly-derived stem cell therapy in autism:Insights from a case study

Autism spectrum disorder(ASD)is a complex neurodevelopmental disorder affecting over 2%of the global population,marked by social communication deficits and repetitive behaviors.Kabatas et al explored the efficacy and safety of Wharton’s jelly-derived mesenchymal stem cell(WJ-MSC)therapy in a 4-year-old child with ASD.Using the childhood autism rating scale and Denver II develop-mental screening test,significant improvements were seen after six WJ-MSC sessions,with no adverse events over 2 years.Despite promising results,the study’s single-case design limits generalizability.Larger,multi-center trials are needed to validate the findings and assess long-term effects of WJ-MSC therapy in ASD.

Approximation of Derivative for a Singularly Perturbed Second-Order ODE of Robin Type with Discontinuous Convection Coefficient and Source Term

In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving numerical method is proposed. An e-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are presented, which are in agreement with the theoretical predictions.

Second-Order Raman Scattering from n- and p-Type 4H-SiC

The results of second-order Raman-scattering experiments on n- and p-type 4H-SiC are presented,covering the acoustic and the optical overtone spectral regions.Some of the observed structures in the spectra are assigned to particular phonon branches and the points in the Brillouin zone from which the scattering originates.There exists a doublet at 626/636cm -1 with energy difference about 10cm -1 in both n- and p-type 4H-SiC,which is similar to the doublet structure with the same energy difference founded in hexagonal GaN,ZnO, and AlN.The cutoff frequency at 1926cm -1 of the second-order Raman is not the overtone of the A 1(LO) peak of the n-type doping 4H-SiC,but that of the undoping one.The second-order Raman spectrum of 4H-SiC can hardly be affected by doping species or doping density.

Concept Derivation in the Conceptual Planning of Jiuzhouwa Eco-Wetland Park

Through analyzing problems exist in the conceptual planning of Jiuzhouwa Eco-Wetland Park, the derivation process and approach of its core concepts were discussed.

Anti-periodic solutions to a class of second-order evolution equations

In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.

Anti-interference beam pattern design based on second-order cone programming optimization

When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.

DERIVATION ALGEBRAS OF THE MODULAR LIE SUPERALGEBRAS W AND S OF CARTAN-TYPE

Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.

Design of PID controller with incomplete derivation based on differential evolution algorithm

To determine the optimal or near optimal parameters of PID controller with incomplete derivation, a novel design method based on differential evolution （DE） algorithm is presented. The controller is called DE-PID controller. To overcome the disadvantages of the integral performance criteria in the frequency domain such as IAE, ISE, and ITSE, a new performance criterion in the time domain is proposed. The optimization procedures employing the DE algorithm to search the optimal or near optimal PID controller parameters of a control system are demonstrated in detail. Three typical control systems are chosen to test and evaluate the adaptation and robustness of the proposed DE-PID controller. The simulation results show that the proposed approach has superior features of easy implementation, stable convergence characteristic, and good computational efficiency. Compared with the ZN, GA, and ASA, the proposed design method is indeed more efficient and robust in improving the step response of a control system.