THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

Pathological and therapeutic effects of extracellular vesicles in neurological and neurodegenerative diseases

Extracellular vesicles are released by all cell types and contain proteins,microRNAs,mRNAs,and other bioactive molecules.Extracellular vesicles play an important role in intercellular communication and in the modulation of the immune system and neuroinflammation.The cargo of extra cellular vesicles(e.g.,proteins and microRNAs)is altered in pathological situations.Extracellular vesicles contribute to the pathogenesis of many pathologies associated with sustained inflammation and neuroinflammation,including cance r,diabetes,hype rammonemia and hepatic encephalopathy,and other neurological and neurodegenerative diseases.Extracellular vesicles may cross the blood-brain barrier and transfer pathological signals from the periphery to the brain.This contributes to inducing neuroinflammation and cognitive and motor impairment in hyperammonemia and hepatic encephalopathy and in neurodegenerative diseases.The mechanisms involved are beginning to be unde rstood.For example,increased tumor necrosis factor a in extracellular vesicles from plasma of hype rammonemic rats induces neuroinflammation and motor impairment when injected into normal rats.Identifying the mechanisms by which extracellular vesicles contribute to the pathogenesis of these diseases will help to develop new treatments and diagnostic tools for their easy and early detection.In contrast,extra cellular vesicles from mesenchymal stem cells have therapeutic utility in many of the above pathologies,by reducing inflammation and neuroinflammation and improving cognitive and motor function.These extra cellular vesicles recapitulate the beneficial effects of mesenchymal stem cells and have advantages as therapeutic tools:they are less immunoge nic,may not diffe rentiate to malignant cells,cross the blood-brain barrier,and may reach more easily target organs.Extracellular vesicles from mesenchymal stem cells have beneficial effects in models of ischemic brain injury,Alzheimer's and Parkinson's diseases,hyperammonemia,and hepatic encephalopathy.Extracellular vesicles from mesenchymal stem cells modulate the immune system,promoting the shift from a pro-inflammato ry to an anti-inflammatory state.For example,extracellular vesicles from mesenchymal stem cells modulate the Th17/Treg balance,promoting the anti-inflammatory Treg.Extracellular vesicles from mesenchymal stem cells may also act directly in the brain to modulate microglia activation,promoting a shift from a pro-inflammatory to an anti-inflammatory state.This reduces neuroinflammation and improves cognitive and motor function.Two main components of extracellular vesicles from mesenchymal stem cells which contribute to these beneficial effects are transforming growth factor-βand miR-124.Identifying the mechanisms by which extracellular vesicles from mesenchymal stem cells induce the beneficial effects and the main molecules(e.g.,proteins and mRNAs)involved may help to improve their therapeutic utility.The aims of this review are to summarize the knowledge of the pathological effects of extracellular vesicles in different pathologies,the therapeutic potential of extra cellular vesicles from mesenchymal stem cells to recover cognitive and motor function and the molecular mechanisms for these beneficial effects on neurological function.

The Class of Atomic Exponential Basis Functions EFup_(n)(x,ω)-Development and Application

The purpose of this paper is to present the class of atomic basis functions(ABFs)which are of exponential type and are denoted by EFupn(x,ω).While ABFs of the algebraic type are already represented in the numerical modeling of various problems inmathematical physics and computationalmechanics,ABFs of the exponential type have not yet been sufficiently researched.These functions,unlike the ABFs of the algebraic type Fupn(x),contain the tension parameterω,which gives them additional approximation properties.Exponential monomials up to the nth degree can be described exactly by the linear combination of the functions EFupn(x,ω).The function EFupn for n=0 is called the“mother”ABF of the exponential type,i.e.,EFup0(x,ω)≡Eup(x,ω).In other words,the functions EFupn(x,ω)are elements of the linear vector space EUPn and retain all the properties of their“mother”function Eup(x,ω).Thus,this paper,in terms of its content and purpose,can be understood as a sequel of the article by Brajcic Kurbasa et al.,which shows the basic properties and application of the basis function Eup(x,ω).This paper presents,in an analogous way,the development and application of the exponential basis functions EFupn(x,ω).Here,for the first time,expressions for calculating the values of the functions EFupn(x,ω)and their derivatives are given in a form suitable for application in numerical analyses,which is shown in the verification examples of the approximations of known functions.

Thermodynamic Functions and Phase Transformation of Metal Nanocrystals

A model to calculate the thermodynamic functions of the pure metal nanocrystals has been developed, with the consideration of the effects of both the interfaces and the crystal in the nano-grain interior. As an example, the enthalpy, entropy and Gibbs free energy, as functions of the excess free volume at interfaces, temperature and grain size, are calculated for the Co nanocrystals. Furthermore, the characteristics of β-Co→α-Co phase transformation are studied, and the transformation temperatures at different levels of grain size, as well as the critical grain sizes at different temperatures, are predicted. The calculation results show that, the nano-grained β-Co （fcc） is thermodynamically stable at temperatures much lower than that for the conventional coarse-grained materials, and may also stably exist at room temperature when the grain size is reduced to be small enough. The present model is verified by comparisons between the experimental findings and the theoretical predictions.

The Transformation of Newly Compiled Chinese Genealogical Functions in the New Era

The cultural customs of compiling genealogy for 5,000 years are an integral part of the Chinese civilization.During the new socialist era,compiling new genealogy is a continuation and development of old genealogy,a cultural phenomenon adapting to social and public needs.The paper examines how Chinese genealogies transformed,and then explores how new genealogies have the new cultural function of serving the socialist era.The paper concludes with comments on how new compilations play a positive role in the construction of a harmonious society.

Zeta Functions of the Complement and xyz-Transformations of a Regular Graph

Let Z(λ,G)denote the zeta function of a graph G.In this paper the complement G^Cand the G^(xyz)-transformation G^(xyz)of an r-regular graph G with n vertices and m edges for x,y,z∈{0,1,+,-},are considerd.The relationship between Z(λ,G)and Z(λ,G^C)is obtained.For all x,y,z∈{0,1,+,-},the explicit formulas for the reciprocal of Z(λ,G^(xyz))in terms of r,m,n and the characteristic polynomial of G are obtained.Due to limited space,only the expressions for G^(xyz)with z=0,and xyz∈{0++,+++,1+-}are presented here.

Development of a rapid and efficient system for CR genes identification based on hairy root transformation in Brassicaceae

Many economically important crops and vegetables belonging to the cruciferous family are heavily endangered by clubroot disease caused by Plasmodiophora brassicae infection.Breeding of clubroot resistant cultivars based on mapping and cloning of resistant genes is commonly regarded as the most cost-effective and efficient way to fight against this disease.The traditional way of R gene functional validation requires stable transformation that is both time-and labor-consuming.In this study,a rapid and efficient hairy-root transgenic protocol mediated by Agrobacterium rhizogenes was developed.The transformation positive rate was over 80%in Brassica napus showed by GUS reporter gene and this transformation only took 1/6 of the time compared with stable transformation.The system was applicable to different B.napus varieties and other cruciferous crops including Brassica rapa and Brassica oleracea.In particular,two known CR genes,CRA3.7.1 and CRA8.2.4 were used respectively,as example to show that the system works well for CR gene study combined with subsequent P.brassicae infection in B.napus.Most importantly,it works both in over-expression that led to disease resistance,as well as in RNAi which led to disease susceptible phenotype.Therefore,this system can be used in batch-wise identification of CR genes,and also offered the possibility of manipulating key genes within the P.brassicae genome that could improve our knowledge on host-pathogen interaction.

Biofilm formation under high temperature causes the commensal bacteria Bacillus cereus WPySW2 to shift from friend to foe in Neoporphyra haitanensis in vitro model

Although biofilm formation may promote growth,biofilms are not always beneficial to their hosts.The biofilm formation characteristics of Bacillus cereus WPySW2 and its changes at different temperatures were studied.Results show that B.cereus WPySW2 promoted the growth of Neoporphyra haitanensis(an economically cultivated seaweed)at 20℃ but accelerated algal rot at 28℃.Thicker B.cereus WPySW2 biofilms covered the surface of N.haitanensis thalli at 28℃,which hindered material exchange between the algae and surrounding environment,inhibited algal photosynthesis and respiration,and accelerated algal decay.Compared with planktonic bacteria,mature biofilm cells had lower energy consumption and metabolic levels.The biofilm metabolic characteristics of B.cereus WPySW2 changed significantly with temperature.High temperature accelerated biofilm maturation,which made it thicker and more stable,allowing the bacteria to easily adapt to environmental changes and obtain greater benefits from their host.High temperature did not affect the production or increased the abundance of toxic metabolites,indicating that the negative effects of B.cereus WPySW2 on algae were not caused by toxins.This study shows that increased temperature can transform a harmless bacterium into a detrimental one,demonstrating that temperature may change the ecological function of phycospheric bacteria by affecting their morphology and metabolism.

Cross-sectional warping and precision of the first-order shear deformation theory for vibrations of transversely functionally graded curved beams

The warping may become an important factor for the precise transverse vibrations of curved beams.Thus,the first aim of this study is to specify the structural design parameters where the influence of cross-sectional warping becomes great and the first-order shear deformation theory lacks the precision necessary.The outof-plane vibrations of the first-order shear deformation theory are compared with the warping-included vibrations as the curvature and/or thickness increase for symmetric and asymmetric transversely-functionally graded(TFG)curved beams.The second aim is to determine the influence of design parameters on the vibrations.The circular/exact elliptical beams are formed via curved mixed finite elements(MFEs)based on the exact curvature and length.The stress-free conditions are satisfied on three-dimensional(3D)constitutive equations.The variation of functionally graded(FG)material constituents is considered based on the power-law dependence.The cross-sectional warping deformations are defined over a displacement-type FE formulation.The warping-included MFEs(W-MFEs)provide satisfactory 3D structural characteristics with smaller degrees of freedom(DOFs)compared with the brick FEs.The Newmark method is used for the forced vibrations.

Breakdown Voltage Prediction by Utilizing the Behavior of Natural Ester for Transformer Applications

This research investigates the dielectric performance of Natural Ester(NE)using the Partial Differential Equation(PDE)tool and analyzes dielectric performance using fuzzy logic.NE nowadays is found to replace Mineral Oil(MO)due to its extensive dielectric properties.Here,the heat-tolerant Natural Esters Olive oil(NE1),Sunflower oil(NE2),and Ricebran oil(NE3)are subjected to High Voltage AC(HVAC)under different electrodes configurations.The break-down voltage and leakage current of NE1,NE2,and NE3 under Point-Point(P-P),Sphere-Sphere(S-S),Plane-Plane(PL-PL),and Rod-Rod(R-R)are measured,and survival probability is presented.The electricfield distribution is analyzed using the Partial Differential Equation(PDE)tool.NE shows better HVAC with stand capacity under all the electrodes configuration,especially in the S-S shape geometry.The exponential function is developed for the oils under different elec-trode geometry;NE shows a higher survival probability.Likewise,the most influ-ential dielectric properties such as breakdown voltage,kinematic viscosity,and water content are used to develop a Mamdani-based control system model that combines two variables to produce the surface model.The surface model indi-cates that the NE subjected for investigation is less susceptible to moisture effect and higher kinematic viscosity.Based on the surface models of PDE and fuzzy,it is concluded that NE possesses a high survival rate since its breakdown voltage does not react to changes in water content.Hence the application of NE in the transformer application is highly safe and possesses extended life.

Identification of potential biomarkers for idiopathic pulmonary fibrosis and validation of TDO2 as a potential therapeutic target

BACKGROUND Idiopathic pulmonary fibrosis(IPF)is a progressive interstitial lung disease with a high mortality rate.On this basis,exploring potential therapeutic targets to meet the unmet needs of IPF patients is important.AIM To explore novel hub genes for IPF therapy.METHODS Here,we used public datasets to identify differentially expressed genes between IPF patients and healthy donors.Potential targets were considered based on multiple bioinformatics analyses,especially the correlation between hub genes and carbon monoxide diffusing capacity of carbon monoxide,forced vital capacity,and patient survival rate.The mRNA levels of the hub genes were determined through quantitative real-time polymerase chain reaction.RESULTS We found that TDO2 was upregulated in IPF patients and predicted poor prognosis.Surprisingly,single-cell RNA sequencing data analysis revealed significant enrichment of TDO2 in alveolar fibroblasts,indicating that TDO2 may participate in the regulation of proliferation and survival.Therefore,we verified the upregulated expression of TDO2 in an experimental mouse model of transforming growth factor-β(TGF-β)-induced pulmonary fibrosis.Furthermore,the results showed that a TDO2 inhibitor effectively suppressed TGF-β-induced fibroblast activation.These findings suggest that TDO2 may be a potential target for IPF treatment.Based on transcription factors-microRNA prediction and scRNA-seq analysis,elevated TDO2 promoted the IPF proliferation of fibroblasts and may be involved in the P53 pathway and aggravate ageing and persistent pulmonary fibrosis.CONCLUSION We provided new target genes prediction and proposed blocking TGF-βproduction as a potential treatment for IPF.

Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation

By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.

Exact Traveling Wave Solutions for the System of Shallow Water Wave Equations and Modified Liouville Equation Using Extended Jacobian Elliptic Function Expansion Method

In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.

Comprehensive Reliability Allocation Method for CNC Lathes Based on Cubic Transformed Functions of Failure Mode and Effects Analysis

Reliability allocation of computerized numerical controlled（CNC）lathes is very important in industry.Traditional allocation methods only focus on high-failure rate components rather than moderate failure rate components,which is not applicable in some conditions.Aiming at solving the problem of CNC lathes reliability allocating,a comprehensive reliability allocation method based on cubic transformed functions of failure modes and effects analysis（FMEA）is presented.Firstly,conventional reliability allocation methods are introduced.Then the limitations of direct combination of comprehensive allocation method with the exponential transformed FMEA method are investigated.Subsequently,a cubic transformed function is established in order to overcome these limitations.Properties of the new transformed functions are discussed by considering the failure severity and the failure occurrence.Designers can choose appropriate transform amplitudes according to their requirements.Finally,a CNC lathe and a spindle system are used as an example to verify the new allocation method.Seven criteria are considered to compare the results of the new method with traditional methods.The allocation results indicate that the new method is more flexible than traditional methods.By employing the new cubic transformed function,the method covers a wider range of problems in CNC reliability allocation without losing the advantages of traditional methods.

Filtering Function Method for the Cauchy Problem of a Semi-Linear Elliptic Equation

A Cauchy problem for the semi-linear elliptic equation is investigated. We use a filtering function method to define a regularization solution for this ill-posed problem. The existence, uniqueness and stability of the regularization solution are proven;a convergence estimate of H?lder type for the regularization method is obtained under the a-priori bound assumption for the exact solution. An iterative scheme is proposed to calculate the regularization solution;some numerical results show that this method works well.

On the Approximation of an Analytic Function Represented by Laplace-Stieltjes Transformation

In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of E;（F,β） where E;（F,β） is the error in approximating of the function F（s） by definite integral polynomials in the half plane Res≤β<α.

Surface Effects on the Scatter of SH-Wave by a Shallow Buried the Elliptical Hole

The methods of complex function, multi-polar coordinate system, and conformal mapping are used to solve dynamic stress concentration factor. The surface elasticity theory is applied to obtain the stress boundary conditions on the surface. The effects of frequency and the ration of the major and minor axis of the ellipse on the dynamic stress concentration factor around the elliptical nano-hole are discussed in detail. When the size of elliptical hole shrinks to nanometers, the numerical results show that the surface effect has a significant effect on the scattering of SH-wave.

The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term

By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of Korteweg de Vries （KdV） equations with variable coefficients and a KdV equation with a forcible term are constructed with the help of symbolic computation system Mathematica, where the new solutions are also constructed.

The Functional Gradient Description Method of Space Coordinate Transformation

The 3-dimension coordinate datum transformation is very important in geomatics.Generally,there are small angle coordinate transformation model (i.e.,Bursa model,et al) and large angle coordinate transformation model (i.e.,Rodrigo matrix model,et al).However,these papers only focus on the fixed and static situation regardless of the small or large angle.This paper proposes the conception of coordinate transformation gradient field,which can realize the space coordinate transformation from small angle to arbitrary angle,and from static to dynamical.Based on the equivalent characteristics of the unit quaternion rotation matrix and the Rodrigo matrix,through studying the mathematical relationship between the spatial coordinate transformation and the functional gradient,we derive a functional gradient expression of the arbitrary transformation formula in space.The study shows that the essence of spatial coordinate transformation is a kind of potential field mathematically.This potential field conception can unify all the space coordinate transformations.It is the theoretical foundation for the further study of time continuous space coordinate transformation,and this study gives a new solution for the attitude determination of motion carriers.