GOPPA CODES FROMARTIN-SCHREIER FUNCTION FIELDS

A class of Goppa codes is constructed by using Artin-Schreier function fields, of which thenumber of prime divisors of degree olle is obtained for some cases, and their minimum distance,duallty and selfeduality are discussed. At laSt the sublield subcode of Artin-Schreier code isinvestigated, the true dimension under certain conditions is given and the covering radius andminimum distance are estimated.

Charge self-consistent dynamical mean field theory calculations incombination with linear combination of numerical atomic orbitalsframework based density functional theory

We present a formalism of charge self-consistent dynamical mean field theory(DMFT)in combination with densityfunctional theory(DFT)within the linear combination of numerical atomic orbitals(LCNAO)framework.We implementedthe charge self-consistent DFT+DMFT formalism by interfacing a full-potential all-electron DFT code with threehybridization expansion-based continuous-time quantum Monte Carlo impurity solvers.The benchmarks on several 3d,4fand 5f strongly correlated electron systems validated our formalism and implementation.Furthermore,within the LCANOframework,our formalism is general and the code architecture is extensible,so it can work as a bridge merging differentLCNAO DFT packages and impurity solvers to do charge self-consistent DFT+DMFT calculations.

Uncertainty-Aware Physical Simulation of Neural Radiance Fields for Fluids

This paper presents a novel framework aimed at quantifying uncertainties associated with the 3D reconstruction of smoke from2Dimages.This approach reconstructs color and density fields from 2D images using Neural Radiance Field(NeRF)and improves image quality using frequency regularization.The NeRF model is obtained via joint training ofmultiple artificial neural networks,whereby the expectation and standard deviation of density fields and RGB values can be evaluated for each pixel.In addition,customized physics-informed neural network(PINN)with residual blocks and two-layer activation functions are utilized to input the density fields of the NeRF into Navier-Stokes equations and convection-diffusion equations to reconstruct the velocity field.The velocity uncertainties are also evaluated through ensemble learning.The effectiveness of the proposed algorithm is demonstrated through numerical examples.The presentmethod is an important step towards downstream tasks such as reliability analysis and robust optimization in engineering design.

Long-term radiofrequency electromagnetic fields exposure attenuates cognitive dysfunction in 5×FAD mice by regulating microglial function

We have previously found that long-term effects of exposure to radiofrequency electromagnetic fields in 5xFAD mice with severe late-stage Alzheimer’s disease reduced both amyloid-βdeposition and glial activation,including microglia.To examine whether this therapeutic effect is due to the regulation of activated microglia,we analyzed mic roglial gene expression profiles and the existence of microglia in the brain in this study.5xFAD mice at the age of 1.5 months were assigned to sham-and radiofrequency electromagnetic fields-exposed groups and then animals were exposed to 1950 MHz radiofrequency electromagnetic fields at a specific absorption rate of 5 W/kg for 2 hours/day and 5 days/week for 6 months.We conducted behavioral tests including the object recognition and Y-maze tests and molecular and histopathological analysis of amyloid precursor protein/a myloid-beta metabolism in brain tissue.We confirmed that radiofrequency electromagnetic field exposure for 6 months ameliorated cognitive impairment and amyloid-βdeposition.The expression levels of Iba1(pan-microglial marker)and colony-stimulating factor 1 receptor(CSF1R;regulates microglial prolife ration)in the hippocampus in 5xFAD mice treated with radiofrequency electromagnetic fields were significantly reduced compared with those of the sham-exposed group.Subsequently,we analyzed the expression levels of genes related to mic rogliosis and microglial function in the radiofrequency electromagnetic fields-exposed group compared to those of a CSF1R inhibitor(PLX3397)-treated group.Both radiofrequency electromagnetic fields and PLX3397 suppressed the levels of genes related to microgliosis(Csf1r,CD68,and Ccl6)and pro-inflammatory cytokine interleukin-1β.N otably,the expression levels of genes related to mic roglial function,including Trem2,Fcgr1α,Ctss,and Spi1,were decreased after long-term radiofrequency electromagnetic field exposure,which was also observed in response to microglial suppression by PLX3397.These results showed that radiofrequency electromagnetic fields ameliorated amyloid-βpathology and cognitive impairment by suppressing amyloid-βdeposition-induced microgliosis and their key regulator,CSF1R.

Extremely low frequency electromagnetic fields promote cognitive function and hippocampal neurogenesis of rats with cerebral ischemia

Extremely low frequency electromagnetic fields(ELF-EMF) can improve the learning and memory impairment of rats with Alzheimer's disease, however, its effect on cerebral ischemia remains poorly understood.In this study, we established rat models of middle cerebral artery occlusion/reperfusion.One day after modeling, a group of rats were treated with ELF-EMF(50 Hz, 1 mT) for 2 hours daily on 28 successive days.Our results showed that rats treated with ELF-EMF required shorter swimming distances and latencies in the Morris water maze test than those of untreated rats.The number of times the platform was crossed and the time spent in the target quadrant were greater than those of untreated rats.The number of BrdU~+/NeuN~+ cells, representing newly born neurons, in the hippocampal subgranular zone increased more in the treated than in untreated rats.Up-regulation in the expressions of Notch1, Hes1, and Hes5 proteins, which are the key factors of the Notch signaling pathway, was greatest in the treated rats.These findings suggest that ELF-EMF can enhance hippocampal neurogenesis of rats with cerebral ischemia, possibly by affecting the Notch signaling pathway.The study was approved by the Institutional Ethics Committee of Sichuan University, China(approval No.2019255A) on March 5, 2019.

Characteristic analysis of scattering field in two-layer media by Green's function

The problem of three-dimensional(3D) acoustic scattering in a complex medium has aroused considerable interest of researchers for many years. An ultrasonic scattered field calculating technique is proposed to study the scattering echo from strongly scattered materials in a two-layer medium in this work. Firstly, with the high frequency stationary phase method,the Green's function of two-layer fluid media is derived. And then based on the idea of integral equation discretization,the Green's function method is extended to two-layer fluid media to derive the scattering field expression of defects in a complex medium. With this method, the scattering field of 3D defect in a two-layer medium is calculated and the characteristics of received echoes are studied. The results show that this method is able to solve the scattering P wave field of 3D defect with arbitrary shape at any scattering intensity in two-layer media. Considering the circumstance of waterimmersion ultrasonic non-destructive test(NDT), the scattering sound field characteristics of different types of defects are analyzed by simulation, which will help to optimize the detection scheme and corresponding imaging method in practice so as to improve the detection quality.

Flood Reduction Function of Paddy Rice Fields under Different Water Saving Irrigation Techniques

This study is conducted to investigate the function of paddy fields for flood reduction under different water saving irrigation techniques. A daily water balance component data including rainfall, percolation, and overflow through the paddy field levee were collected from experimental paddy rice fields during rainy season cultivation. Results show that paddy field was very effective in flood reduction. More than 40% of rainfall could be stored in the paddy fields. However, the effectiveness of paddy fields in flood reduction was highly depends on the WSI technique used. Semi dry cultivation technique was the most effective one in terms of flood reduction. It retained the rainfall up to 55.7% (365 mm) of the total rainfall (636 mm) without reducing the yield. In terms of flood volume reduction, the alternate wetting and drying performed similarly with traditional continuous flooding, i.e., 37.2% and 40.8%, respectively.

Construction Theory of Function on Local Fields

We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.

A FUNCTION MINIMIZATION CALCULATION OF CYCLONE 10 MAGNETIC FIELDS

By app(?)ing function minimization calculation method, two function expressions are used to simulate the magnetic field measured for cyclotron Cyclone 10 in azimuth and radius The numerical fitting curves are consistent with magnetic field measured. In most pl(?)es, the accuracies are several thousandth, except those errors to be pointed out in paper.

Rotating magnetic field inhibits Aβ protein aggregation and alleviates cognitive impairment in Alzheimer’s disease mice

Amyloid beta(Aβ)monomers aggregate to form fibrils and amyloid plaques,which are critical mechanisms in the pathogenesis of Alzheimer’s disease(AD).Given the important role of Aβ1-42 aggregation in plaque formation,leading to brain lesions and cognitive impairment,numerous studies have aimed to reduce Aβaggregation and slow AD progression.The diphenylalanine(FF)sequence is critical for amyloid aggregation,and magnetic fields can affect peptide alignment due to the diamagnetic anisotropy of aromatic rings.In this study,we examined the effects of a moderate-intensity rotating magnetic field(RMF)on Aβaggregation and AD pathogenesis.Results indicated that the RMF directly inhibited Aβamyloid fibril formation and reduced Aβ-induced cytotoxicity in neural cells in vitro.Using the AD mouse model APP/PS1,RMF restored motor abilities to healthy control levels and significantly alleviated cognitive impairments,including exploration and spatial and non-spatial memory abilities.Tissue examinations demonstrated that RMF reduced amyloid plaque accumulation,attenuated microglial activation,and reduced oxidative stress in the APP/PS1 mouse brain.These findings suggest that RMF holds considerable potential as a non-invasive,high-penetration physical approach for AD treatment.

Configuration of propagator method for calculation of electron velocity distribution function in gas under crossed electric and magnetic fields

This paper presents a self-contained description on the configuration of propagator method(PM)to calculate the electron velocity distribution function(EVDF) of electron swarms in gases under DC electric and magnetic fields crossed at a right angle. Velocity space is divided into cells with respect to three polar coordinates v,θ and f. The number of electrons in each cell is stored in three-dimensional arrays. The changes of electron velocity due to acceleration by the electric and magnetic fields and scattering by gas molecules are treated as intercellular electron transfers on the basis of the Boltzmann equation and are represented using operators called the propagators or Green’s functions. The collision propagator, assuming isotropic scattering, is basically unchanged from conventional PMs performed under electric fields without magnetic fields. On the other hand, the acceleration propagator is customized for rotational acceleration under the action of the Lorentz force. The acceleration propagator specific to the present cell configuration is analytically derived. The mean electron energy and average electron velocity vector in a model gas and SF6 were derived from the EVDF as a demonstration of the PM under the Hall deflection and they were in a fine agreement with those obtained by Monte Carlo simulations. A strategy for fast relaxation is discussed, and extension of the PM for the EVDF under AC electric and DC/AC magnetic fields is outlined as well.

CHAINS OF FUNCTION SPACES OVER EUCLIDIAN SPACES AND LOCAL FIELDS

The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function spaces' over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.

Higher-order crack tip fields for functionally graded material plate with transverse shear deformation

The crack tip fields are investigated for a cracked functionally graded material （FGM） plate by Reissner＇s linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson＇s ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner＇s plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner＇s effect when the in-homogeneity parameter approaches zero.

Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters

This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric functions have been presented.In virtue of quantum fields,we derive a series of infinite order nonlinear integrable equations,namely,universal character hierarchy,symplectic KP hierarchy and symplectic universal character hierarchy,respectively.In addition,the solutions of these integrable systems have been discussed.

Crack tip higher order stress fields for functionally graded materials with generalized form of gradation

A generalized form of material gradation applicable to a more broad range of functionally graded materials(FGMs) was presented.With the material model,analytical expressions of crack tip higher order stress fields in a series form for opening mode and shear mode cracks under quasi-static loading were developed through the approach of asymptotic analysis.Then,a numerical experiment was conducted to verify the accuracy of the developed expressions for representing crack tip stress fields and their validity in full field data analysis by using them to extract the stress intensity factors from the results of a finite element analysis by local collocation and then comparing the estimations with the existing solution.The expressions show that nonhomogeneity parameters are embedded in the angular functions associated with higher terms in a recursive manner and at least the first three terms in the expansions must be considered to explicitly account for material nonhomogeneity effects on crack tip stress fields in the case of FGMs.The numerical experiment further confirms that the addition of the nonhomogeneity specific terms in the expressions not only improves estimates of stress intensity factor,but also gives consistent estimates as the distance away from the crack tip increases.Hence,the analytical expressions are suitable for the representation of crack tip stress fields and the analysis of full field data.

The X-ray Background (Deep Fields, Luminosity Functions and Type-Ⅱ Quasars)

Deep X ray surveys have shown that the cosmic X ray background (XRB) is largely due to the accretion onto supermassive black holes, integrated over the cosmic time. These surveys have resolved more than 80% of the 0.1-10keV X ray background into discrete sources. Optical spectroscopic identifications show that the sources producing the bulk of the X ray background are a mixture of obscured (type 1) and unobscured (type 2) AGNs, as predicted by the XRB population synthesis models. A class of highly luminous type 2 AGN, so called QSO 2s, has been detected in the deepest Chandra and XMM Newton surveys. The new Chandra AGN redshift distribution peaks at much lower redshifts (z≈0.7) than that based on ROSAT data, indicating that Seyfert galaxies peak at significantly lower redshifts than QSOs.

Heun Functions Describing Fermions Evolving in Parallel Electric and Magnetic Fields

The present work deals with the behavior of fermions moving in a static magnetic induction and a time-harmonic electric field, both oriented along Oz. For the ultra-relativistic particles described by a Heun double confluent equation, we derive the corresponding wave functions and the conserved current density components.

Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

HALF-SPACE GREENS'S FUNCTION DUE TO A SPATIALLY HARMONIC LINE LOAD AND SCATTERED FIELDS IN THE FAR FIELD REGION

Half-space Green's function due to a spatially harmonic line load has been expressed as a sum of the full-space Green's functions and a 2-D integral representation of the reflected waves by the free surface of the half-space.By using the obtained half-space Green's function,an integral rep- resentation of the scattered waves by a cylindrical obstacle is then derived.Finally,by analyzing the far-zone behavior of the integrands of the integral representation.the far-field pattern of the scattered waves in a half-space obtained.

代数函数域的一些Artin-Schreier型扩张相伴的Riemann-Roch空间

阐明给定代数函数域上一些除子的Riemann-Roch空间是代数几何码构造的基础.给出代数函数域的一些Artin-Schreier型扩张的Riemann-Roch空间的一组基,并应用于编码理论,得到F_(16)上参数分别是[54,43,5],[54,41,7],[54,40,8]的代数几何码.