A new viewpoint and model of neural signal generation and transmission: Signal transmission on myelinated neuron

Based on our previous work, we study the problem of neural signal transmission of myelinated neurons. We found that the transmembrane ion current at Ranvier's node acts as an energy supplement. In addition, the length of the myelin sheath has an upper limit of lT. Above this upper limit, the neural signal will not be effectively transmitted. In the range of normal physiological parameters, lT is on the order of mm. Finally, the effect of temperature on the transmission of nerve signals is investigated. temperatures that are too high and too low are not conducive to the conduction of nerve signals.

A primary model of decoherence in neuronal microtubules based on the interaction Hamiltonian between microtubules and plasmon in neurons

Microtubules(MTs) are part of the cellular cytoskeleton and they play a role in many activities, such as cell division and maintenance of cell shape. In recent years, MTs have been thought to be involved in storing and processing information.Several models have been developed to describe the information-processing ability of MTs. In these models, MTs are considered as a device that can transmit quantum information. However, MTs are affected by the "wet and warm" cellular environment, thus it is essential to calculate the decoherence time. Many researchers have attempted to calculate this parameter but the values that have been obtained vary markedly. Previous studies considered the cellular environment as a distant ion; however, this treatment is somewhat simplified. In this study, we develop a model to determine the decoherence time in neuronal MTs while considering the interaction effects of the neuronal fluid environment. The neuronal environment is considered as a plasmon reservoir. The coupling between MTs and neuronal environment occurs due to the interaction between dipoles and plasmon. The interaction Hamiltonian is derived by using the second quantization method, and the coupling coefficient is calculated. Finally, the decoherence time scale is estimated according to the interaction Hamiltonian.In this paper, the time scale of decoherence in MTs is approximately 1 fs-100 fs. This model may be used as a reference in other decoherence processes in biological tissues.

PREFACE

This special issue of Acta Mathematica Scientia is dedicated to the memory of ProfessorJia-Rong Yu on the occasion of his hundredth anniversary.Professor Jia-Rong Yu, born November 16, 1920, passed away on October 14, 2020, at theage of one hundred. He is known as the founder of the Sino-French Mathematical Center inWuhan University, and was the director of this center from 1980 to 1994. In 1991, thanks to hiscolossal investment in Franco-Chinese cooperation, he was made officer in the order of academicpalms by the French Government.

COMMUTATORS OF BMO FUNCTIONS AND SINGULAR INTEGRAL OPERATORS WITH NON-SMOOTH KERNELS ON SPACES OF HOMOGENEOUS TYPE OF FINITE MEASURE

Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p （X）, 1 〈 p 〈 ∞. We give a sufficient condition on the kernel k（x,y） of Tso thatwhen a function b ∈ BMO （X）,the commutator [b,T] （f）=T （b f）- bT （f） is bounded on spaces L^p for all p, 1 〈 p 〈 ∞.

IN MEMORIAM PROFESSOR DONGGAO DENG

Donggao Deng, professor of mathematics, the associate Editor of ATA,was born in June 8, 1935 in Rongqi Town, Shunde City, GuangdongProvince, China. He passed away by illness in Guangzhou on October21, 2007.

Hörmander型谱乘子的极大函数的有界性

在齐型空间(X,d,μ)中,假设L是L^(2)(X)上的一个非负自伴算子,其热核满足Gauss上、下界估计.给定N个具有一致估计的Hörmander型谱乘子m_(i),1 i N,本文应用Doob变换和Chang-Wilson-Wolff对二进鞅平方函数的exp(L^(2))估计,建立极大函数sup1≤i≤N|m_(i)(L)f|的L^(p)有界性,并给出L^(p)有界的最佳的上界估计√log(1+N).基于这个估计,本文给出乘子m的一类充分条件,其极大函数M_(m,L)f(x)=sup_(t>0)|m(t L)f(x)|在L^(p)(X)上是有界的.

Enhanced terahertz generation via plasma modulation on two bunches

Terahertz(THz)radiation finds important applications in various fields,making the study of THz sources significant.Among different approaches,electron accelerator-based THz sources hold notable advantages in generating THz radiation with narrow bandwidth,high brightness,high peak power,and high repetition rate.To further improve the THz radiation energy,the bunching factor of the free electron bunch train needs to be increased.We propose and numerically reveal that,by adding an additional short-pulse drive beam before the main beam as the excitation source of nonlinear plasma wake,the bunching factor of the main beam can be further increased to∼0.94,even though with a relatively low charge,low current,and relatively diffused electron beam.Two such electron beams with loose requirements can be easily generated using typical photoinjectors.Our work provides a way for a new THz source with enhanced radiation energy.

齐型空间上的指数平方类的刻画与应用

本文在齐型空间(X, d,μ)上建立与经典二进平方函数相联系的指数平方类的三个等价刻画,即指数平方可积性、好λ不等式及二进平方函数的Lp下界最佳估计.该工作推广了著名的Rn上ChangWilson-Wolff定理.作为应用,本文建立了非负Ricci曲率Riemann流形上与Laplace-Beltrami算子相联系的平方函数的L^p下界最佳估计.