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.

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 Fixed Point Theorem and the Iterative Approximation of Modified Cauchy Integral Operator of Regular Functions

In the first part of this paper, we discuss the Holder continuity of the cauchy integral operator for regular functions and the relation between ‖T{f}‖α and ‖f‖α. In the second part of this paper, we introduce the modified cauchy integral operator T^- for regular functions. Firstly, we prove that the operator T^- has a unique fixed point by the Banach＇s Contraction Mapping Principle. Secondly, we give the Mann iterative sequence, and then we show the iterative sequence strongly converges to the fixed point of the operator T^-.

A Laurent Expansion and Residue Theorems of k-Regular Functions in Clifford Analysis

In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness, give the definitions of k-poles, isolated and essential singular points and removable singularity, discuss some properties, and further obtain the residue theorems.

The Similarity Transformation of Regularizing Functionals and Simularity Property of Their Fourier Transformations

Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.

Kernel matrix learning with a general regularized risk functional criterion

Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.

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.

Correlation between Residual Renal Function and Hypertension in Regular Haemodialysis Patients

Objective: To evaluate the correlation between residual renal function and hypertension in regular haemodialysis patients. Background: Initiating chronic dialysis treatment gives end-stage renal disease patients a new lease on life. However, the annual mortality rate in dialysis patients is ~20% and quality of life is substantially reduced. Patients and Methods: This study was carried out on a reasonable number of subjects on regular haemodialysis divided into two groups. All were given informed consent and, the study was approved by the ethics committee of Menoufia University. Results: There was significant relation between presence of residual renal function and hypertension in patients with ESRD on regular haemodialysis, but the relation between residual renal function and control of hypertension is not statistically significant. 40% of group 1 were hypertensive, 66.7% of group 2 patients were hypertensive, the interdialytic weight gain mean was 1.42 in group 1 and 2.37 in group 2. Control of hypertension was achieved in 63.6% of group 1 patients by one drug, 27.3% patients by 2 drugs;however 9.1% of patients need 3 drugs to control their blood pressure, while in group 2 40% of patients were controlled by one drug, 45% with 2 drugs and 15% need 3 drugs to control blood pressure. Conclusion: There is significant relation between presence of residual renal function and hypertension in patients with ESRD on regular haemodialysis, but the relation between residual renal function and control of hypertension is not statistically significant.

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 a -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 function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.

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.

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.

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。

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。

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.

与弱正则高原平衡函数相关的线性码

运用两个弱正则高原平衡函数,设计适当的定义集,构造基于定义集的多种线性码.利用Walsh变换与指数和的性质确定线性码的重量分布.这些线性码都具有较少的非零重量,可应用于秘密共享方案和结合方案等领域.

基于ST-UNet和目标特征的混凝土裂缝检测

混凝土裂缝对结构承载能力、耐久性和防水性有负面影响,因此早期裂缝检测具有重要意义.大数据和深度学习的快速发展,为裂缝智能检测提供了有效的方法.针对裂缝检测过程中图像正负样本不平衡,裂缝区域色彩深沉和低亮度的特点,提出一种基于ST-UNet(Swin Transformer U-Net)和目标特征的裂缝检测方法.该算法在网络中引入CBAM注意力机制,使网络更加关注图像中对裂缝检测起决定作用的像素区域,增强裂缝图像的特征表达能力;使用Focal+Dice混合损失函数代替单一交叉熵损失函数,处理样本图像正负样本分布不均的问题;设计APSD正则化项优化损失函数,针对裂缝区域色彩深沉、低亮度的问题,降低检测的漏检率与误检率.裂缝检测结果表明:IoU指标提升22%,Dice指数提升17%,该算法是有效可行的.

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.

全程优质护理模式联合规则性呼吸训练在肺癌患者术后康复中的效果

目的探讨肺癌患者应用全程优质护理模式联合规则性呼吸训练的效果。方法选取河南省胸科医院2021年1月至2022年8月收治的76例肺癌患者,随机分为对照组和观察组,各38例。对照组采用常规护理干预,观察组采用全程优质护理模式联合规则性呼吸训练。比较两组术后临床指标、干预前后心理状态、肺功能及并发症情况。结果观察组临床指标改善优于对照组,差异有统计学意义(P<0.05)。干预后,两组焦虑自评量表(SAS)评分、抑郁自评量表(SDS)评分均有所降低,且观察组低于对照组,差异有统计学意义(P<0.05)。干预后,两组用力肺活量(FVC)、第一秒肺活量(FEV_(1))、最大通气量(MVV)指数均有所提升,观察组高于对照组,差异有统计学意义(P<0.05)。观察组并发症发生率(5.26%)低于对照组(26.32%),差异有统计学意义(P<0.05)。结论全程优质护理联合规则性呼吸训练可加快肺癌患者康复,改善心理状态和肺功能,降低并发症发生率。