Deep brain implantable microelectrode arrays for detection and functional localization of the subthalamic nucleus in rats with Parkinson’s disease

The subthalamic nucleus(STN)is considered the best target for deep brain stimulation treatments of Parkinson’s disease(PD).It is difficult to localize the STN due to its small size and deep location.Multichannel microelectrode arrays(MEAs)can rapidly and precisely locate the STN,which is important for precise stimulation.In this paper,16-channel MEAs modified with multiwalled carbon nanotube/poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate)(MWCNT/PEDOT:PSS)nanocomposites were designed and fabricated,and the accurate and rapid identification of the STN in PD rats was performed using detection sites distributed at different brain depths.These results showed that nuclei in 6-hydroxydopamine hydrobromide(6-OHDA)-lesioned brains discharged more intensely than those in unlesioned brains.In addition,the MEA simultaneously acquired neural signals from both the STN and the upper or lower boundary nuclei of the STN.Moreover,higher values of spike firing rate,spike amplitude,local field potential(LFP)power,and beta oscillations were detected in the STN of the 6-OHDA-lesioned brain,and may therefore be biomarkers of STN localization.Compared with the STNs of unlesioned brains,the power spectral density of spikes and LFPs synchronously decreased in the delta band and increased in the beta band of 6-OHDA-lesioned brains.This may be a cause of sleep and motor disorders associated with PD.Overall,this work describes a new cellular-level localization and detection method and provides a tool for future studies of deep brain nuclei.

How to Prove Riemann Conjecture by Riemann’s Four Theorems

Riemann (1859) had proved four theorems: analytic continuation ζ(s), functional equation ξ(z)=G(s)ζ(s)(s=1/2+iz, z=t−i(σ−1/2)), product expression ξ1(z)and Riemann-Siegel formula Z(z), and proposed Riemann conjecture (RC): All roots of ξ(z)are real. We have calculated ξand ζ, and found that ξ(z)is alternative oscillation, which intuitively implies RC, and the property of ζ(s)is not good. Therefore Riemann’s direction is correct, but he used the same notation ξ(t)=ξ1(t)to confuse two concepts. So the product expression only can be used in contraction. We find that if ξhas complex roots, then its structure is destroyed, so RC holds. In our proof, using Riemann’s four theorems is sufficient, needn’t cite other results. Hilbert (1900) proposed Riemann hypothesis (RH): The non-trivial roots of ζhave real part 1/2. Of course, RH also holds, but can not be proved directly by ζ(s).

On the Weyl’s Lemma for Triharmonic Functions

In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.

Evaluation of Generalized Error Function via Fast-Converging Power Series

A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders.

A hybrid method integrating Green's function Monte Carlo and projected entangled pair states

This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC.By leveraging PEPS’s proficiency in capturing quantum state entanglement and GFMC’s efficient parallel architecture,the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems.As a benchmark,we applied this approach to study the frustrated J_(1)–J_(2) Heisenberg model on a square lattice with periodic boundary conditions(PBCs).Compared with other numerical methods,our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy.This paper provides systematic and comprehensive discussion of the approach of our previous work[Phys.Rev.B 109235133(2024)].

Implementation of the Integrated Green’s Function Method for 3D Poisson’s Equation in a Large Aspect Ratio Computational Domain

The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.

基于Riemann-Liouville分数阶积分Bernstein-Kantorovich算子的逼近性质

文章构造一种基于Riemann-Liouville分数阶积分的Bernstein-Kantorovich算子。利用一阶、二阶光滑模、Peetre’-K泛函和Lipschitz型极大函数等工具研究该算子的近似性质。然后利用一阶、二阶和四阶中心矩对该算子建立Vorononskaja型渐进公式。该算子的构建使得在曲线曲面造型方面对于给定的函数将会有更小的近似误差。

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

A Set of Almost Automorphic Functions and Applications

For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.

Proof of Riemann Conjecture Based on Contradiction between Xi-Function and Its Product Expression

Riemann proved three results: analytically continue ζ(s) over the whole complex plane s =σ + it with a pole s =1;(Theorem A) functional equation ξ(t) = G(s0)ζ (s0), s0 =1/2 + it and (Theorem B) product expression ξ1(t) by all roots of ξ(t). He stated Riemann conjecture (RC): All roots of ξ (t) are real. We find a mistake of Riemann: he used the same notation ξ(t) in two theorems. Theorem B must contain complex roots;it conflicts with RC. Thus theorem B can only be used by contradiction. Our research can be completed on s0 =1/2 + it. Using all real roots rk and (true) complex roots zj = tj + iaj of ξ (z), define product expressions w(t), w(0) =ξ(0) and Q(t) > 0, Q(0) =1 respectively, so ξ1(t) = w(t)Q(t). Define infinite point-set L(ω) = {t : t ≥10 and |ζ(s0)| =ω} for small ω > 0. If ξ(t) has complex roots, then ω =ωQ(t) on L(ω). Finally in a large interval of the first module |z1|>>1, we can find many points t ∈ L(ω) to make Q(t) . This contraction proves RC. In addition, Riemann hypothesis (RH) ζ for also holds, but it cannot be proved by ζ.

高压管汇材料疲劳性能测试及P-S-N模型曲线的拟合

高压管汇作为压裂设备中的主要易损件之一,其失效危害较大。它的失效原因主要是疲劳、冲蚀、腐蚀或者材料缺陷引起的刺漏和爆裂,其中尤以疲劳失效最不可预估。目前,对于高压管汇材料的疲劳性能研究不够深入,为解决高压管汇材料疲劳寿命的准确描述问题,以某国产高压管汇材料为例,进行了一系列疲劳试验,并基于试验数据,采用多种分布模型和不同S-N模型进行拟合分析,得出综合评价拟合能力最强的P-S-N模型。结果表明,该材料在中长疲劳寿命区,Weibull三参数模型在7级应力水平下综合评价能力最好;在存活率分别为50%、90%、99%、99.9%时,指数S-N模型的拟合系数均大于0.98,拟合能力最好。得出的P-S-N模型曲线可以为高压管汇的疲劳寿命以及安全设计提供依据。

基于哨兵函数和S变换的风力机叶片材料损伤特性研究

利用声发射检测技术研究玻璃纤维增强环氧树脂复合材料的损伤特性,在此过程中,采用哨兵函数来表征该材料的损伤程度,并通过S变换和模糊C均值(FCM)聚类来分析声发射信号,从而获得材料的损伤特征。三点弯曲实验结束后对试件断口进行扫描电子显微镜(SEM)拍照来验证,可得:通过对SEM照片的分析得到基体开裂、纤维脱粘、分层破坏、纤维断裂4种损伤模式;对整个声发射事件进行哨兵函数分析,观察到试件在弯曲过程中哨兵函数曲线呈明显下降趋势;对依据哨兵函数划分的不同阶段的信号进行VMD降噪处理,然后采用S变换进行时频分析得到不同损伤的特征频率,最后采用FCM聚类进行验证。结果表明:哨兵函数值的突变可作为材料断裂的预警信号,材料损伤类型的识别可依据S变换的频率分布结果进行确定。

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green’s function method for neutron-rich Ca,Ni,Zr,and Sn isotopes

The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.

Green's functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials

In this paper,we obtain Green’s functions of two-dimensional(2D)piezoelectric quasicrystal(PQC)in half-space and bimaterials.Based on the elastic theory of QCs,the Stroh formalism is used to derive the general solutions of displacements and stresses.Then,we obtain the analytical solutions of half-space and bimaterial Green’s functions.Besides,the interfacial Green’s function for bimaterials is also obtained in the analytical form.Before numerical studies,a comparative study is carried out to validate the present solutions.Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force,the line dislocation,the line charge,and the phason line force.As a result,the coupling effect among the phonon field,the phason field,and the electric field is prominent,and the butterfly-shaped contours are characteristic in 2D PQCs.In addition,the changes of material parameters cause variations in physical quantities to a certain degree.

关于Riemann-Lebesgue引理的一个推广

通过“把Riemann-Lebesgue引理看做是在一个周期上可积的周期函数的一种性质”的这个角度,提出了亚周期函数的概念,并得到有界亚周期函数的刻画.

ON RIEMANN BOUNDARY VALUE PROBLEM FOR POLYANALYTIC FUNCTIONS ON THE REAL AXIS

In this article, Riemann boundary value problem with different factors for polyanalytic functions on the real axis is studied. The expression of solution and sufficient and necessary condition for solvability of the non-homogeneous Riemann boundary value problem are obtained.

RIEMANN BOUNDARY VALUE PROBLEMS FOR SOME K-REGULAR FUNCTIONS IN CLIFFORD ANALYSIS

In this paper,we study the R m（m〉0） Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C（Vn,n）.By using Plemelj formula,we get the solutions of R m（m〉0） Riemann boundary value problems for regular functions.Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions,we obtain the solutions of R m（m〉0） Riemann boundary value problems for harmonic functions and bi-harmonic functions.

Riemann theta function periodic wave solutions for the variable-coefficient mKdV equation

In this paper, a variable-coefficient modified Korteweg-de Vries （vc-mKdV） equation is considered. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function, then the one and two periodic wave solutions are presented~ and it is also shown that the soliton solutions can be reduced from the periodic wave solutions.

Neuroprotective effect of liraglutide and memantine in a rat model of Alzheimer’s disease

Objective:To assess the effect of memantine combined with liraglutide on aluminum chloride(AlCl_(3))and D-galactose(D-GAL)-induced neurotoxicity in rats.Methods:Male Wistar rats were divided into 5 groups of 5 animals each:the positive control,the negative control,the memantine-treated group,the liraglutide-treated group,and the combination group treated with memantine and liraglutide.AlCl_(3)and D-GAL were used to induce neurotoxicity.Behavioral tests,brain beta-amyloid protein,and oxidative stress biomarkers were evaluated.Results:The Morris water maze test indicated an enhanced memory in the combination group.Moreover,the combination treatment of liraglutide and memantine resulted in a remarkable reduction in the beta-amyloid protein level in the brain tissue.Neuronal inflammation and oxidative stress biomarkers were significantly reduced,and the levels of antioxidant parameters were enhanced.Conclusions:The combination of liraglutide and memantine exerts neuroprotective effects and enhances memory and cognitive functions in rats with Alzheimer’s disease.

Common Properties of Riemann Zeta Function, Bessel Functions and Gauss Function Concerning Their Zeros

The behavior of the zeros in finite Taylor series approximations of the Riemann Xi function (to the zeta function), of modified Bessel functions and of the Gaussian (bell) function is investigated and illustrated in the complex domain by pictures. It can be seen how the zeros in finite approximations approach to the genuine zeros in the transition to higher-order approximation and in case of the Gaussian (bell) function that they go with great uniformity to infinity in the complex plane. A limiting transition from the modified Bessel functions to a Gaussian function is discussed and represented in pictures. In an Appendix a new building stone to a full proof of the Riemann hypothesis using the Second mean-value theorem is presented.