QUATERNIONIC SLICE REGULAR FUNCTIONS AND QUATERNIONIC LAPLACE TRANSFORMS

The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involution,and that the intrinsic slice regular functions play a central role in the theory of slice regular functions.The relation between left slice regular functions,right slice regular functions and intrinsic slice regular functions is revealed.As an application,the classical Laplace transform is generalized naturally to quaternions in two different ways,which transform a quaternion-valued function of a real variable to a left or right slice regular function.The usual properties of the classical Laplace transforms are generalized to quaternionic Laplace transforms.

APPROXIMATION ANALYSES FOR FUZZY VALUED FUNCTIONS IN L_1(μ)-NORM BY REGULAR FUZZY NEURAL NETWORKS

By defining fuzzy valued simple functions and giving L1(μ) approximations of fuzzy valued integrably bounded functions by such simple functions, the paper analyses by L1(μ)-norm the approximation capability of four-layer feedforward regular fuzzy neural networks to the fuzzy valued integrably bounded function F : Rn → FcO(R). That is, if the transfer functionσ: R→R is non-polynomial and integrable function on each finite interval, F may be innorm approximated by fuzzy valued functions defined as to anydegree of accuracy. Finally some real examples demonstrate the conclusions.

The Theory of Higher-Order Types of Asymptotic Variation for Differentiable Functions. Part I: Higher-Order Regular, Smooth and Rapid Variation

Motivated by a general theory of finite asymptotic expansions in the real domain for functions f of one real variable, a theory developed in a previous series of papers, we present a detailed survey on the classes of higher-order asymptotically-varying functions where “asymptotically” stands for one of the adverbs “regularly, smoothly, rapidly, exponentially”. For order 1 the theory of regularly-varying functions (with a minimum of regularity such as measurability) is well established and well developed whereas for higher orders involving differentiable functions we encounter different approaches in the literature not linked together, and the cases of rapid or exponential variation, even of order 1, are not systrematically treated. In this semi-expository paper we systematize much scattered matter concerning the pertinent theory of such classes of functions hopefully being of help to those who need these results for various applications. The present Part I contains the higher-order theory for regular, smooth and rapid variation.

Estimation of Derivatives for Bounded Regular Vanishing Functions

In this paper, we mainly discuss the problem of estimating the n-th derivative for bounded regular vanishing functions. The estimation of the n-th derivative for the function is deduced by the 1-th and 2-th derivative.

Zeta Functions of the Complement and xyz-Transformations of a Regular Graph

Let Z(λ,G)denote the zeta function of a graph G.In this paper the complement G^Cand the G^(xyz)-transformation G^(xyz)of an r-regular graph G with n vertices and m edges for x,y,z∈{0,1,+,-},are considerd.The relationship between Z(λ,G)and Z(λ,G^C)is obtained.For all x,y,z∈{0,1,+,-},the explicit formulas for the reciprocal of Z(λ,G^(xyz))in terms of r,m,n and the characteristic polynomial of G are obtained.Due to limited space,only the expressions for G^(xyz)with z=0,and xyz∈{0++,+++,1+-}are presented here.

α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problems

In this paper, α -times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α -times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α + 1)-times abstract Cauchy problem and mild α -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine finction.The characterization of an exponentially botnded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.

THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions.In this paper,we present an equivalent characterization for the boundedness of the product operator C_(φ)D^(m) acting on Bloch-type spaces of slice regular functions.After that,an equivalent estimation for its essential norm is established,which can imply several existing results on holomorphic spaces.

The Ill-Posedness of Derivative Interpolation and Regularized Derivative Interpolation for Non-Bandlimited Functions

In this paper, the ill-posedness of derivative interpolation is discussed, and a regularized derivative interpolation for non-bandlimited signals is presented. The convergence of the regularized derivative interpolation is studied. The numerical results are given and compared with derivative interpolation using the Tikhonov regularization method. The regularized derivative interpolation in this paper is more accurate in computation.

Brain Functional Networks with Dynamic Hypergraph Manifold Regularization for Classification of End-Stage Renal Disease Associated with Mild Cognitive Impairment

The structure and function of brain networks have been altered in patients with end-stage renal disease(ESRD).Manifold regularization(MR)only considers the pairing relationship between two brain regions and cannot represent functional interactions or higher-order relationships between multiple brain regions.To solve this issue,we developed a method to construct a dynamic brain functional network(DBFN)based on dynamic hypergraph MR(DHMR)and applied it to the classification of ESRD associated with mild cognitive impairment(ESRDaMCI).The construction of DBFN with Pearson’s correlation(PC)was transformed into an optimization model.Node convolution and hyperedge convolution superposition were adopted to dynamically modify the hypergraph structure,and then got the dynamic hypergraph to form the manifold regular terms of the dynamic hypergraph.The DHMR and L_(1) norm regularization were introduced into the PC-based optimization model to obtain the final DHMR-based DBFN(DDBFN).Experiment results demonstrated the validity of the DDBFN method by comparing the classification results with several related brain functional network construction methods.Our work not only improves better classification performance but also reveals the discriminative regions of ESRDaMCI,providing a reference for clinical research and auxiliary diagnosis of concomitant cognitive impairments.

Regularization Methods to Approximate Solutions of Variational Inequalities

In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y0, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.

不确定电液伺服系统的时变输出约束自适应滤波控制

针对电液伺服系统位置跟踪控制中存在的输出约束和不确定性问题,提出一种基于正切型时变障碍Lyapunov函数的输出约束自适应滤波控制方法。构造具有时变约束边界的正切型时变障碍Lyapunov函数,通过时变边界函数的参数设置,使系统输出具有较好的瞬态和稳态性能;设计径向基函数(RBF)神经网络及权重自适应学习律,在线逼近由模型不确定性和未知干扰组成的复合干扰,并将逼近值用于反馈控制;采用二阶指令滤波反步法设计状态反馈控制律和误差补偿机制,避免反步设计中“计算爆炸”的问题,同时消除滤波误差,提高系统位置跟踪精度;依据Lyapunov稳定性理论证明闭环系统中所有误差信号的收敛性。仿真结果表明:系统的稳态误差在所提方法下约为3.48×10^(-8)m,相比于其他控制方法,跟踪误差始终约束在时变的约束边界内,跟踪精度和控制性能均得到提升。

基于GRACE星间重力位差的Slepian局部地表质量变化反演法

根据Slepian基函数在频域和空域的局部集中特性,建立了利用GRACE星间重力位差(GPD)估计局部地表质量变化的Slepian基函数反演模型及病态问题求解算法,并以亚马逊流域的陆地水储量变化(TWSC)反演为例,评估了反演方法的精度和有效性.首先,通过闭环数值模拟比较了Slepian基函数法(GPD SBF)、基于GPD的mascon方法(GPD Mascon)和球谐系数法(GPD SH)反演2005年亚马逊流域TWSC的性能,结果表明:Slepian基函数法通过限定信号的频域和空域范围,降低了反演过程中向下延拓带来的不确定性,有效削弱了法方程求解的病态性,其解算结果的稳定性明显优于GPD Mascon;GPD SBF的反演精度及可靠性总体上优于GPD Mascon和GPD SH,并且能够更好地恢复边缘区域的信号和减小泄漏误差的影响.其次,利用实测的GRACE GPD数据反演了2004—2015年亚马逊流域的TWSC时间序列,结果显示:GPDSBF相比GPDMascon反演的TWSC与官方mascon模型(CSR、JPL和GSFC RL06 mascon)更为一致,并且GPD SBF反演结果呈现出更多的空间细节和更好的信噪比.最后,利用不同GRACE反演结果计算的(TWSC的一阶导数)和水文气象数据(GPCP降水、ERA5蒸散发)由水量平衡方程估计了亚马逊流域Obidos水文站的月平均径流量,并采用测站的实测径流量进行检验,结果表明:GPD SBF和GPD Mascon估计的径流量与实测值扣除季节性信号后的差值STD分别为12.35 mm和14.54 mm,相关系数分别为0.71和0.69,并且GPD SBF和各种官方mascon模型估计的径流量与实测径流量更为接近.本文研究证明Slepian基函数法可削弱病态问题求解对正则化约束的依赖,其比传统的GPD Mascon解算精度和可靠性更高,为反演高精度、高分辨率的局部地表质量变化提供了一种新的解决方案.

腹腔镜规则性肝叶切除术对原发性肝癌患者肝功能、免疫功能、血清AFP、Hcy水平的影响

目的:探究腹腔镜规则性肝叶切除术对原发性肝癌(PLC)患者肝功能、免疫功能、血清甲胎蛋白(AFP)、同型半胱氨酸(Hcy)水平的影响。方法:回顾性分析2019年1月—2023年6月于贵州省人民医院接受手术治疗的200例PLC患者的临床资料,将行开腹手术的100例患者纳入对照组,行腹腔镜规则性肝叶切除术的100例患者纳入观察组。观察两组术后肝功能[总胆红素(TBIL)、白蛋白(ALB)、丙氨酸转移酶(ALT)、天冬氨酸氨基转移酶(AST)]、免疫功能(CD8^(+)、CD4^(+)、CD3^(+))、炎症因子[肿瘤坏死因子-α(TNF-α)、白细胞介素-6(IL-6)]及血清AFP、Hcy水平的变化情况。结果:术前,两组肝功能、免疫功能、炎症因子、血清AFP、Hcy水平比较,差异无统计学意义(P>0.05);术后1 d,两组ALB高于术前,TBIL、ALT、AST及术后5 d的AFP、Hcy均低于术前,且研究组ALB高于对照组,TBIL、ALT、AST、AFP、Hcy低于对照组,差异有统计学意义(P<0.05);术后5 d,对照组TNF-α、IL-6水平均高于术前,CD8^(+)、CD4^(+)、^(+)CD3水平均低于术前,差异有统计学意义(P<0.05),术后5 d,研究组TNF-α、IL-6水平均低于对照组,CD8^(+)、CD4^(+)、^(+)CD3水平均高于对照组,差异有统计学意义(P<0.05)。结论:PLC患者予以腹腔镜规则性肝叶切除术治疗可明显降低患者术后血清AFP、Hcy水平,降低炎症因子水平,提高免疫力,恢复肝功能。

2-D离散时滞系统的新时滞相关稳定性准则

研究了具有时变时滞的二维(two-dimensional,2-D)离散系统的时滞相关稳定性问题.所创建的Lyapunov-Krasovskii泛函(Lyapunov-Krasovskii functionals,LKFs)考虑在二次项和单项求和项中引入时滞相关矩阵,包含了更多的状态信息.同时在单项求和项中引入增广向量矩阵,并给出适用于2-D系统的多重辅助函数不等式和互凸组合不等式,用于处理LKFs差分,以便降低计算负担.然后,为具有时变时滞的2-D离散系统推导出保守性更小的稳定性准则.通过两个数值算例验证了所设计方法的有效性和优越性.

基于二次函数负定判据的LFC系统稳定性分析

基于改进的二次积分不等式和二次多项式不等式建立的稳定性条件,研究了基于负荷频率控制(LFC)的时滞电力系统稳定性问题。首先,搭建了包含PI参数的负荷频率时滞系统数学模型;然后,通过引入增广的Lyapunov-Krasovskii泛函,利用近年改进的二次积分不等式和二次多项式不等式的充分条件,成功导出了具有时变时滞的系统稳定性判据;最后,通过负荷频率系统模型的实例仿真,验证了所得稳定性判据优于现有的一些计算结果。

特高压换流站抗震韧性及震后修复策略快速评估方法

地震作用下特高压换流站中设备极易损坏,然而由于资源条件限制使得震后抢修效率较低,从而导致了大量经济损失。为寻求高效的震后修复策略,该文搭建一套基于功能状态模型的抗震韧性快速评估框架。从结构和电气两方面建立换流站系统的二维功能网络模型,并利用贝叶斯网络进行功能状态快速评估。为提高系统震后修复效率,提出一种生物启发式多目标优化算法,利用震后迭代模拟得到系统阶梯型功能时变函数。通过对一典型±800 kV特高压换流站进行抗震韧性分析,得到换流站系统的关键抢修设备及最优修复策略,证明了最优修复策略的有效性和必要性。该框架量化了特高压换流站的震后修复过程及抗震韧性水平,可为换流站系统的震后应急抢修提供参考。

河南省南水北调受水区浅层地下水埋深变化分析

南水北调中线工程运行后地下水大量压采,需定量评估河南省受水区地下水埋深的变化特征。利用河南省2000—2020年受水区342口浅层地下水监测井的平均埋深、枯水期最大埋深和丰水期最小埋深年数据,通过空间插值法、水位动态法分析11个地市地下水埋深的变化特征,采用径向基函数神经网络模型计算地下水埋深关键驱动因素的贡献度。同时,统计用水结构中地下水的占比进行分析论证。结果表明:空间上,调水压采的成效主要为埋深4~<8 m向0~<4 m转换,集中在淮河流域中南部和长江流域埋深较小的区域。时间上,调水后受水区地下水埋深恢复情况丰水期最小埋深>平均埋深>枯水期最大埋深,同时郑州等7个地市的三个地下水埋深指标均得到恢复。影响因素上,相较降水量,地下水开采量对地下水埋深的影响更大。用水结构上,用水总量及四个分类中地下水占比在调水后显著下降。

面向爆炸压力场的体绘制自动传输函数设计

直接体绘制广泛应用于可视化领域,其中传输函数决定了最终绘制的效果。大规模爆炸数据属于复杂的时变数据,其压力场的取值范围和分布会随时间剧烈变化。为了实现对冲击波传播特征的连续跟踪,提出了一种基于标量-时间梯度(scalar-temporal gradient,STG)二维空间的自动传输函数设计方法。结合爆炸过程中的物理规律,将STG空间划分为多种状态并总结了状态之间的转移规律。将冲击波的传播特征编码为一段一定长度的状态转移链(state transitions chain,STC),称为时变特征。传输函数中的颜色以时变特征为单位,基于完全状态转移链自动分配。传输函数中的不透明度采用基于压强变化速率的分段非线性曲线,凸显压强变化剧烈的特征。选取了两类典型的大规模爆炸场景对方法进行了验证,绘制结果中都包含了丰富的明显可区分的冲击波传播特征。结果表明,生成的传输函数在整个时间维度上都能稳定、准确地捕捉冲击波的传播特征。

基于正则模糊划分的模糊系统及其逼近性质

文中讨论了带有不同模糊基函数的模糊系统的逼近问题。首先,基于一维正则模糊划分和重叠函数建立多维正则模糊划分,以划分中的元素为模糊基函数设计模糊系统,应用Weierstrass逼近定理证明了该模糊系统是通用逼近器,给出了模糊系统的逼近误差界。其次,提出了多项式型、指数型和对数型模糊系统,并给出了带有隶属函数参数的逼近误差界。最后,通过数值实验对不同模糊系统的逼近能力进行了比较,实验结果进一步验证了理论分析的正确性。

用Tikhonov正则化方法同时反演对流扩散方程的对流速度和源函数

在给定两个附加观测数据的条件下,本文基于Tikhonov正则化方法研究了对流扩散方程的对流速度和源函数的同时反演问题.鉴于原问题是一个初始值非零的对流扩散方程,本文通过将初始值转化为源项得到了一个组合源项,首先将原问题转化为一个具有齐次条件的对流扩散问题.由于所得问题是不适定的,本文进而利用Tikhonov正则化方法构建了相应的极小化目标泛函,得到了问题最优解的存在性和应满足的必要条件.最后,对终端时刻较小的特殊情形,本文证明了最优解的唯一性和稳定性.