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.

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.

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.

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.

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.

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.

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.

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.

Functions of Allusions from Leppihalme’s model

The general function of allusions is often thought to add clarity and significance to ideas and descriptions.However,it would be difficult to establish an exhaustive list of mutually exclusive category

SOME INEQUALITIES OF HERMITE-HADAMARD TYPE FOR s-CONVEX FUNCTIONS

In this paper several inequalities of the left-hand side of Hermite-Hadamard’s inequality are obtained for s-convex functions.

Analysis of chaos behaviors of a bistable piezoelectric cantilever power generation system by the second-order Melnikov function

By applying the second order Melnikov function, the chaos behaviors of a bistable piezoelectric cantilever power generation system are analyzed. Firstly, the conditions for emerging chaos of the system are derived by the second order Melnikov function. Secondly, the effects of each item in chaos threshold expression are analyzed. The excitation frequency and resistance values, which have the most influence on chaos threshold value, are found. The result from the second order Melnikov function is more accurate compared with that from the first order Melnikov function. Finally, the attraction basins of large amplitude motions under different exciting frequency, exciting amplitude, and resistance parameters are given.

Green's functions for uniformly distributed loads acting on an inclined line in a poroelastic layered site

Based on one type of practical Biot＇s equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green＇s functions were derived for unitformly distributed loads acting on an inclined line in a poroelastie layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green＇s functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.

Integral Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>s</i>-Convex

In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.

ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.

GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM

The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space,and the singular kinetic waves which become smooth for all(t,x,v)when t>0.Furthermore,we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function.

Quantifyingα-diversity as a continuous function of location——a case study of a temperate forest

α-diversity describes species diversity at local scales.The Simpson’s and Shannon-Wiener indices are widely used to characterizeα-diversity based on species abundances within a fixed study site(e.g.,a quadrat or plot).Although such indices provide overall diversity estimates that can be analyzed,their values are not spatially continuous nor applicable in theory to any point within the study region,and thus they cannot be treated as spatial covariates for analyses of other variables.Herein,we extended the Simpson’s and Shannon-Wiener indices to create point estimates ofα-diversity for any location based on spatially explicit species occurrences within different bandwidths(i.e.,radii,with the location of interest as the center).For an arbitrary point in the study region,species occurrences within the circle plotting the bandwidth were weighted according to their distance from the center using a tri-cube kernel function,with occurrences closer to the center having greater weight than more distant ones.These novel kernel-basedα-diversity indices were tested using a tree dataset from a 400 m×400 m study region comprising a 200 m×200 m core region surrounded by a 100-m width buffer zone.Our newly extendedα-diversity indices did not disagree qualitatively with the traditional indices,and the former were slightly lower than the latter by<2%at medium and large band widths.The present work demonstrates the feasibility of using kernel-basedα-diversity indices to estimate diversity at any location in the study region and allows them to be used as quantifiable spatial covariates or predictors for other dependent variables of interest in future ecological studies.Spatially continuousα-diversity indices are useful to compare and monitor species trends in space and time,which is valuable for conservation practitioners.

Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain

Green＇s functions for Blot＇s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green＇s functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term ＂decoupling coefficient＂ for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green＇s functions. The correct- ness of the solution is demonstrated by numerically comparing the current solution with Cheng＇s previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green＇s functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method （BEM） and other applications.

TIME-HARMONIC DYNAMIC GREEN'S FUNCTIONS FOR ONE-DIMENSIONAL HEXAGONAL QUASICRYSTALS

Quasicrystals have additional phason degrees of freedom not found in conventional crystals. In this paper, we present an exact solution for time-harmonic dynamic Green＇s function of one-dimensional hexagonal quasicrystals with the Laue classes 6/mh and 6/mhmm. Through the introduction of two new functions φ and ψ, the original problem is reduced to the determination of Green＇s functions for two independent Helmholtz equations. The explicit expressions of displacement and stress fields are presented and their asymptotic behaviors are discussed. The static Green＇s function can be obtained by letting the circular frequency approach zero.