Analytical evaluation of the plasma dispersion function for a Fermi-Dirac distribution

An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.

A Particle Interacting with V-shaped Potential Decorated by a Dirac Delta Function Interaction at Center

The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.

Solution of Dirac Equation with Killingbeck Potential by Using Wave Function Ansatz Method under Spin Symmetry Limit

The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.

Literary Text Translation from Functional Perspective

Functional linguistics has become the most influential linguistic theory in the field of translation study since the last de cade of 20th century.However,for the complexity of the context,it is uncommon and insufficient to explore literary texts.Draw ing a general picture of literary text translation from functional perspectives aims to probe into the functional modes of translation.

ON GROUND STATE SOLUTIONS FOR SUPERLINEAR DIRAC EQUATION

This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.

Bacillus licheniformis PF9 improves barrier function and alleviates inflammatory responses against enterotoxigenic Escherichia coli F4 infection in the porcine intestinal epithelial cells

Background:Enterotoxigenic Escherichia coli(ETEC)F4 commonly colonizes the small intestine and releases enterotoxins that impair the intestinal barrier function and trigger inflammatory responses.Although Bacillus licheniformis(B.licheniformis)has been reported to enhance intestinal health,it remains to be seen whether there is a functional role of B.licheniformis in intestinal inflammatory response in intestinal porcine epithelial cell line(IPEC-J2)when stimulated with ETEC F4.Methods:In the present study,the effects of B.licheniformis PF9 on the release of pro-inflammation cytokines,cell integrity and nuclear factor-κB(NF-κB)activation were evaluated in ETEC F4-induced IPEC-J2 cells.Results:B.licheniformis PF9 treatment was capable of remarkably attenuating the expression levels of inflammation cytokines tumor necrosis factor-α(TNF-α),interleukin(IL)-8,and IL-6 during ETEC F4 infection.Furthermore,the gene expression of Toll-like receptor 4(TLR4)-mediated upstream related genes of NF-κB signaling pathway has been significantly inhibited.These changes were accompanied by significantly decreased phosphorylation of p65 NF-κB during ETEC F4 infection with B.licheniformis PF9 treatment.The immunofluorescence and western blotting analysis revealed that B.licheniformis PF9 increased the expression levels of zona occludens 1(ZO-1)and occludin(OCLN)in ETEC F4-infected IPEC-J2 cells.Meanwhile,the B.licheniformis PF9 could alleviate the injury of epithelial barrier function assessed by the trans-epithelial electrical resistance(TEER)and cell permeability assay.Interestingly,B.licheniformis PF9 protect IPEC-J2 cells against ETEC F4 infection by decreasing the gene expressions of virulence-related factors(including luxS,estA,estB,and elt)in ETEC F4.Conclusions:Collectively,our results suggest that B.licheniformis PF9 might reduce inflammation-related cytokines through blocking the NF-κB signaling pathways.Besides,B.licheniformis PF9 displayed a significant role in the enhancement of IPEC-J2 cell integrity.

MiR-19a-3p regulates the Forkhead box F2-mediated Wnt/β-catenin signaling pathway and affects the biological functions of colorectal cancer cells

BACKGROUND Colorectal cancer(CRC)is one of the most common malignancies worldwide.AIM To explore the expression of microRNA miR-19a-3p and Forkhead box F2(FOXF2)in patients with CRC and the relevant mechanisms.METHODS Sixty-two CRC patients admitted to the hospital were enrolled into the study group,and sixty healthy people from the same period were assigned to the control group.Elbow venous blood was sampled from the patients and healthy individuals,and blood serum was saved for later analysis.MiR-19a-3p mimics,miR-19a-3p inhibitor,miR-negative control,small interfering-FOXF2,and short hairpin-FOXF2 were transfected into HT29 and HCT116 cells.Then quantitative polymerase chain reaction was performed to quantify the expression of miR-19a-3p and FOXF2 in HT29 and HCT116 cells,and western blot(WB)analysis was conducted to evaluate the levels of FOXF2,glycogen synthase kinase 3 beta(GSK-3β),phosphorylated GSK-3β(p-GSK-3β),β-catenin,p-β-catenin,α-catenin,Ncadherin,E-cadherin,and vimentin.The MTT,Transwell,and wound healing assays were applied to analyze cell proliferation,invasion,and migration,respectively,and the dual luciferase reporter assay was used to determine the correlation of miR-19a-3p with FOXF2.RESULTS The patients showed high serum levels of miR-19a-3p and low levels of FOXF2,and the area under the curves of miR-19a-3p and FOXF2 were larger than 0.8.MiR-19a-3p and FOXF2 were related to sex,tumor size,age,tumor-nodemetastasis staging,lymph node metastasis,and differentiation of CRC patients.Silencing of miR-19a-3p and overexpression of FOXF2 suppressed the epithelialmesenchymal transition,invasion,migration,and proliferation of cells.WB analysis revealed that silencing of miR-19a-3p and FOXF2 overexpression significantly suppressed the expression of p-GSK-3β,β-catenin,N-cadherin,and vimentin;and increased the levels of GSK-3β,p-β-catenin,α-catenin,and Ecadherin.The dual luciferase reporter assay confirmed that there was a targeted correlation of miR-19a-3p with FOXF2.In addition,a rescue experiment revealed that there were no differences in cell proliferation,invasion,and migration in HT29 and HCT116 cells co-transfected with miR-19a-3p-mimics+sh-FOXF2 and miR-19a-3p-inhibitor+si-FOXF2 compared to the miR-negative control group.CONCLUSION Inhibiting miR-19a-3p expression can upregulate the FOXF2-mediated Wnt/β-catenin signaling pathway,thereby affecting the epithelial-mesenchymal transition,proliferation,invasion,and migration of cells.Thus,miR-19a-3p is likely to be a therapeutic target in CRC.

F-53B胁迫下污水厌氧处理系统及微生物群落的响应

通过构建厌氧反应体系,评估低浓度(1mg/L)和高浓度(10mg/L)氯化多氟醚磺酸盐(F-53B)胁迫下,厌氧处理系统出水水质、污泥性状和细菌群落的响应特征.结果表明,在F-53B的胁迫下,COD、氮(TN、NH_(4)^(+)-N)和磷(TP、PO_(4)^(3-)-P)在出水中的含量会升高,而污泥相对生物量(MLVSS/MLSS)则出现下降,且F-53B的浓度越高影响越大.高通量测序分析发现,相较于对照组(0mg/L F-53B),仅高浓度F-53B胁迫下细菌群落的多样性(ACE、Chao1和PD指数)出现了显著下降.同时,研究还发现,随着高浓度F-53B暴露时间的延长,厚壁菌门的相对丰度逐渐增大,而变形菌门、拟杆菌门和硝化螺旋菌门的相对丰度逐渐降低.此外,基于FAPROTAX功能预测分析发现,F-53B胁迫下微生物表现出更低的氮(N)代谢潜力和更高的化能异养和发酵能力.冗余分析(RDA)表明,厚壁菌门主要受F-53B的正向影响,并与TN和NH_(4)^(+)-N呈正相关;而变形菌门受F-53B的负向影响,并与COD、TP和PO_(4)^(3-)-P呈正相关.揭示了新型氟化物—F-53B对污水厌氧处理系统的胁迫机制.

A MAXIMAL FUNCTION CHARACTERIZATION 0F HARDY SPACES ON SPACES OF HOMOGENEOUS TYPE

A new maximal function is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces.

Density functional calculations on the geometric structure and properties of the 3d transition metal atom doped endohedral fullerene M@C_(20)F_(20)(M=Sc-Ni)

This paper uses the generalised gradient approximation based on density functional theory to analyse the geometric structure and properties of the 3d transition metal atom doped endohedral fullerene M@C20F20 （M = Sc-Ni）. The geometric optimization shows that the cage centre is the most stable position for M, forming the structure named as M@C20F20-4. The inclusion energy, zero-point energy, and energy gap calculations tell us that Ni@C20F20-4 should be thermodynamically and kinetically stablest. M@C20F20-4 （M = Sc-Co） possesses high magnetic moments varied from 1 to 6 μB, while Ni@C20F20-4 is nonmagnetic. The Ni-C bond in Ni@C20F20-4 contains both the covalent and ionic characters.

Fluid State of Dirac Quantum Particles

In our previous works, we suggest that quantum particles are composite physical objects endowed with the geometric and topological structures of their corresponding differentiable manifolds that would allow them to imitate and adapt to physical environments. In this work, we show that Dirac equation in fact describes quantum particles as composite structures that are in a fluid state in which the components of the wavefunction can be identified with the stream function and the velocity potential of a potential flow formulated in the theory of classical fluids. We also show that Dirac quantum particles can manifest as standing waves which are the result of the superposition of two fluid flows moving in opposite directions. However, for a steady motion a Dirac quantum particle does not exhibit a wave motion even though it has the potential to establish a wave within its physical structure, therefore, without an external disturbance a Dirac quantum particle may be considered as a classical particle defined in classical physics. And furthermore, from the fact that there are two identical fluid flows in opposite directions within their physical structures, the fluid state model of Dirac quantum particles can be used to explain why fermions are spin-half particles.

Molecule functionalization to facilitate electrocatalytic oxygen reduction on graphdiyne

Chemical doping is verified to be a promising strategy to regulate local electron distribution and further promote the poor intrinsic catalytic activity of graphdiyne.However,the current doping approach still faces problems such as precise doping for creating active sites and the destruction of graphdiyne skeleton calling for high temperature.Here,we achieved charge redistribution on graphdiyne surface through molecule functionalization.A p-type molecule–F4 TCNQ(2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodime thane)was introduced and the site-defined functionalization was accomplished.Theoretical calculations showed that the charge transfer ability is improved and graphdiyne becomes positively charged.The oxygen reduction electrocatalysis was conducted as a proof of principle,where the electronic states of sp hybridized C active site was tuned toward favorable reaction intermediates’adsorption.Such work from both theoretical prediction and experimental validation,found that molecule functionalization is effective to promote the electrocatalytic oxygen reduction,which creates new possibilities for graphdiyne’s applications in different electrochemical reactions.

GRADIENT ESTIMATES FOR POSITIVE SMOOTH f-HARMONIC FUNCTIONS

For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below, generalizing the classical ones of Yau （i.e., when ： is constant）.

A simple rule for finding Dirac cones in bilayered perovskites

A simple rule for finding Dirac cone electronic states in solids is proposed, which is neglecting those lattice atoms inert to particular electronic bands, and pursuing the two-dimensional(2D) graphene-like quasi-atom lattices with s-and pbindings by considering the equivalent atom groups in the unit cell as quasi-atoms.Taking CsPbBr3 and Cs3Bi2Br9 bilayers as examples, we prove the effectiveness and generality of this rule with the density functional theory(DFT) calculations.We demonstrate that both bilayers have Dirac cones around the Fermi level and reveal that their corresponding Fermi velocities can reach as high as^0.2 × 10^6 m/s.This makes these new 2D layered materials very promising in making new ultra-fast ionic electronic devices.

Approximate analytical solution of the Dirac equation with q-deformed hyperbolic Poschl–Teller potential and trigonometric Scarf II non-central potential

An approximate solution of the Dirac equation for a spin-1/2 particle under the influence of q-deformed hyperbolic P ¨oschl–Teller potential combined with trigonometric Scarf II non-central potential is studied analytically. It is assumed that the scalar potential equals the vector potential in order to obtain analytical solutions. Both radial and angular parts of the Dirac equation are solved using the Nikiforov–Uvarov method. A relativistic energy spectrum and the relation between quantum numbers can be obtained using this method. Several quantum wave functions corresponding to several states are also presented in terms of the Jacobi Polynomials.

A Distributional Representation of Gamma Function with Generalized Complex Domian

In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma function can be defined over a space of complex test functions of slow growth denoted by Z. Some properties of gamma function are discussed by using the properties of delta function.

动力系统中F-传递性与F-混合性的一个注记

对一维动力系统的混合性及传递性进行了一般性讨论。设(I,f)是一个拓扑动力系统(简称动力系统或系统),其中I为紧致度量空间(度量为d),f:X→X是连续映射。基于Furstenberg族,研究了一维动力系统(I,f)和它的泛函包络系统(L^(1)(I,I),H_(f))的一些性质,在前人研究的混合性和传递性的基础上,引进了F–混合与F–传递的概念,并证明了如果(I,f)是F–混合的,则(L^(1)(I,I),H_(f))是F–传递的。

Long-range adsorbate interactions mediated by two-dimensional Dirac fermions

We provide here an analytical formalism to describe the indirect interaction between adsorbed atom or molecule pairs mediated by two-dimensional(2D)Dirac fermions.We show that in contrast to the case of traditional 2D electron gas,in the 2D Dirac system,the long-range interaction behaves as 1/r^(3) decaying Friedel oscillation.This analytical formalism is fully consistent with a tight-binding numerical calculation of honeycomb lattices.Our formalism is suitable for the realistic 2D Dirac materials,such as graphene and surface states of three-dimensional topological insulators.

Interpolation of Generalized Functions Using Artificial Neural Networks

In this paper we employ artificial neural networks for predictive approximation of generalized functions having crucial applications in different areas of science including mechanical and chemical engineering, signal processing, information transfer, telecommunications, finance, etc. Results of numerical analysis are discussed. It is shown that the known Gibb’s phenomenon does not occur.

Solution of the Dirac equation with the ring-shaped oscillator potential

The ring-shaped oscillator potential, obtained by replacing the Coulomb part of the Hartmann potential by a harmonic oscillator term, was investigated. Under the equal vector potential and scalar potential, the Dirac equation was solved in spherical coordinate. The exact energy spectrum of the bound states was presented as a solution to the confluent hypergeometric equation by boundary conditions. Furthermore, the normalized angular and radial wave functions were presented.