The tangential k-Cauchy-Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group

The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.

ABOUT THE INVERSION FORMULA ON THE LIE GROUP SL (2, R)

Harish-Chandra have got a Fourier inversion formula for C-c(infinity)(SL (2, R)). In this paper, we give a discussion on approximation identity kernels on SL(2, R) and get some properties of their Fourier transforms, and then, making use of these properties and Harish-Chandra's result, we prove that the Fourier inversion formula obtained by Harish-Chandra is also valid for C-o(3)(SL,2, R)).

THE DECOMPOSITION OF THE REPRESENTATIONS Tv AND THE PLANCHEREL FORMULA FOR THE UNIVERSAL COVERING GROUP OF 517(1,1)

The decomposition of the representations T0(v∈R) ore considered here. The Plancherel formula for the universal covering group of SU(1,1) is also deduced.

指数有界双连续n阶m次积分C群的指数公式

利用经典算子半群理论中的研究方法,基于指数有界双连续n阶m次积分C群和预解式的定义,给出指数有界双连续n阶m次积分C群与其预解式间积分的表示关系,得到指数有界双连续n阶m次积分C群的指数公式,从而推广了n阶m次积分C半群的相关结果,丰富了算子半群理论的研究内容.

自拟通便方治疗慢性功能性便秘的疗效及对胃肠道功能和腹部肌群肌电图指标的影响

目的观察自拟通便方治疗慢性功能性便秘的疗效及对胃肠道功能和腹部肌群肌电图指标的影响。方法依据治疗方案不同将2021年1月至2023年4月期间在抚州市东乡区中医院消化内科就诊的70例慢性功能性便秘患者分为对照组与观察组,各35例。对照组服用乳果糖溶液,在此基础上观察组给予自拟通便方治疗,连续治疗2周。观察两组临床疗效、症状积分、胃肠功能改善时间、腹部肌群肌电图指标及生活质量情况。结果观察组治疗总有效率(94.29%)较对照组(77.14%)高(P<0.05);治疗后两组症状积分降低,且观察组较对照组低(P<0.001);观察组肠鸣音恢复时间、肛门首次排气时间、首次自主排便时间较对照组短(P<0.01);治疗后两组10 s松弛压力(10SR)降低,净压力(NET)、3 s收缩幅度(FSC)、10 s收缩幅度(10SC)提高,且观察组改善更显著(P<0.01);治疗后两组生存质量量表(PAC-QOL)评分降低,且观察组较对照组低(P<0.001)。结论自拟通便方治疗慢性功能性便秘疗效显著,可有效促进胃肠功能恢复及腹部肌群肌电图指标的改善,提升患者生活质量。

驻马店城市应急供水水源地规划及评价

规划及评价城市应急供水水源地是城市地质调查的重要内容。在驻马店城市地质调查工作中,对城市应急供水水源地进行了规划及评价。规划四水厂片区和三水厂片区两处地下水应急供水水源地。四水厂片区,布井14眼,日开采量30 960 m^(3)/d,开采180 d,最大降深值为35.93 m;三水厂片区,布井6眼,日开采量8 640 m^(3)/d,开采180 d,最大降深值为43.05 m。加上井损,最大降深值分别为40.99 m、45.81 m。两片区中深层含水层顶板埋深分别大于90 m、大于79 m,地下水最大动水位分别在71 m、75.81 m,均小于含水层顶板埋深,不会出现含水层疏干以及破坏性开采。

Mechanical mechanism of overlying strata breaking and development of fractured zone during close-distance coal seam group mining

This study mainly investigates the mechanical mechanism of overlying strata breaking and the development of fractured zones during close-distance coal seam group mining in the Gaojialiang coal mine.First,a mechanical model for the second"activation"of broken overlying strata is established,and the related mechanical"activation"conditions are obtained.A recursive formula for calculating the separation distance of overlying strata is deduced.Second,a height determining method for predicting the height of fractured zones during close-distance coal seam group mining is proposed based on two values,namely,the separation distance and ultimate subsidence value of overlying strata.This method is applied to calculate the fractured zone heights in nos.20107 and 20307 mining faces.The calculated results are almost equal to the field observation results.Third,a modified formula for calculating the height of a waterflowing fractured zone is proposed.A comparison of the calculated and observed results shows that the errors are small.The height determining method and modified formula not only build a theoretical foundation for water conservation mining at the Gaojialiang coal mine,but also provide a reference for estimating the height of water-flowing fractured zones in other coal mines with similar conditions.

Analysis of high-frequency local coupling instability induced by multi- transmitting formula - P-SV wave simulation in a 2D waveguide

Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain. That is, the two schemes support common wave solutions with group velocity pointed into the computation domain. The key to eliminate local coupling instability is to avoid such wave solutions. For lumped-mass finite element simulation of P-SV wave motion in a 2D waveguide, an approach for stable implementation of high order multi-transmitting formula is provided. With a uniform rectangular mesh, it is proven and validated that high-freqaency local coupling instability can be eliminated by setting the ratio of the element size equal to or greater than x/2 times the ratio of the P wave velocity to the S wave velocity. These results can be valuable for dealing instability problems induced by other absorbing boundary conditions.

On fundamental solution for powers of the sub-Laplacian on the Heisenberg group

We discuss the fundamental solution for m-th powers of the sub-Laplacian on the Heisenberg group. We use the representation theory of the Heisenberg group to analyze the associated m-th powers of the sub-Laplacian and to construct its fundamental solution. Besides, the series representation of the fundamental solution for square of the sub-Laplacian on the Heisenberg group is given and we also get the closed form of the fundamental solution for square of the sub-Laplacian on the Heisenberg group with dimension n = 2, 3, 4.

Multi-attribute group decision making method under 2-dimension uncertain linguistic variables

A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their fuzzy subjective evaluation information.Firstly,in order to measure the 2DULVs more accurately,a new method is proposed to compare two 2DULVs,called a score function,while a new function is defined to measure the distance between two 2DULVs.Secondly,two optimization models are established to determine the weight of experts and attributes based on the new distance formula and a weighted average operator is used to determine the comprehensive evaluation value of each alternative.Then,a score function is used to determine the ranking of the alternatives.Finally,the effectiveness of the proposed method is proved by an illustrated example.

Classical Fourier Analysis over Homogeneous Spaces of Compact Groups

This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.

A Restriction Theorem on the Reduced Product Heisenberg Group

In this paper,we give the Plancherel formula on the reduced product Heisenberg group,and obtain a restriction theorem on this group.

Vacuum Solutions of Classical Gravity on Cyclic Groups from Noncommutative Geometry

Based on the observation that the moduli of a link variable on a cyclic group modify Connes' distance on this group, we construct several action functionals for this link variable within the framework of noncommutative geometry. After solving the equations of motion, we find that one type of action gives nontrivial vacuum solution for gravity on this cyclic group in a broad range of coupling constants and that such a solution can be expressed with Chebyshev's polynomials.

温阳散寒活血法治疗下肢动脉硬化闭塞症疗效及血清hsCRP、TNF-α、IL-6的影响

目的:探讨温阳散寒活血法治疗下肢动脉硬化闭塞症(ASO)疗效及血清超敏C反应蛋白(hsCRP)、肿瘤坏死因子-α(TNF-α)、白介素-6(IL-6)的影响。方法:选取2018年1月~2020年12月河北省沧州中西医结合医院收治的180例ASO患者,根据随机数字表法分为两组,对照组(n=90)接受常规西医治疗,观察组(n=90)在常规西医治疗基础上接受自拟脉管炎Ⅰ号组方熏洗治疗。比较两组患者临床疗效和治疗14d、28d后中医证候积分、间歇性跛行距离、踝肱指数、足背动脉血流量和血清hsCRP、TNF-α、IL-6水平及不良反应发生情况。结果:观察组临床治疗总有效率明显高于对照组(P<0.05)。治疗后14d、28d观察组中医证候积分和血清hsCRP、TNF-α、IL-6水平明显低于对照组,间歇性跛行距离、踝肱指数、足背动脉血流量明显高于对照组(P<0.05)。两组患者不良反应发生率比较无差异(P>0.05)。结论:自拟脉管炎Ⅰ号组方熏洗治疗ASO疗效显著,可有效改善下肢缺血症状,延长间歇性跛行距离,调节血清hsCRP、TNF-α、IL-6水平,且安全性高,值得推广。

爆破振动对露天矿山永久边坡稳定性的影响分析

为研究爆破振动对露天矿山永久边坡稳定性的影响,以卡莫亚-卡兹比兹矿群中的3个矿坑作为研究对象,对比爆破振动对于不同岩性边坡稳定性的影响。通过选择爆破测振仪并设置测振仪参数,通过振动监测得到测点的爆破振动速度,对爆破振动速度、最大一段起爆药量以及测点到爆源中心距离等数据进行整理,并按照乘幂函数进行回归分析,得出各矿爆破振动速度v与3 Q/R的趋势线,进而得到对应矿坑的爆破振动公式,根据振动公式来预测爆破振动。为得出测点到爆源中心距离和最大一段起爆药量对边坡振动速度的影响大小,把距离与药量作为影响因子,把爆破振动速度作为因变量,并根据各矿拟合得出的爆破振动公式分别计算振动速度,制定九组实验方案;采用SPSS软件进行方差分析,得出测点到爆源中心距离这一因素对于爆破振动速度敏感性较高,对于矿坑边坡振动的影响较大;因此对于卡兹、东二软岩边坡,采取预留2~3排孔作为非爆破区域,采用机械挖掘修坡;对于南二中硬岩石边坡,采用提前进行预裂爆破来减弱爆破振动对边坡稳定性的影响。该研究成果对于刚果(金)其他相同地质条件的露天铜钴矿爆破施工有借鉴及应用的价值。

关于贝叶斯公式及其实际应用

贝叶斯公式是概率论中的一个著名公式,主要用于对诱发某结果的最可能原因进行概率推理,本文通过对贝叶斯公式进行了分析证明,同时阐述了它在疾病诊断、产品检验和信号估计方面的应用。

基于模拟测算法的森林合理年伐量确定与应用

森林合理年伐量的科学测算是优化森林结构和实现森林资源可持续发展的关键。以贵州省国有浪风关林场为例,采用模拟测算法确定马尾松用材林的合理年伐量,并与传统公式法进行对比。结果表明:1)基于模拟测算法确定30 a为马尾松用材林的最优经理期和轮伐期,合理年伐面积为19.88 hm^(2),年伐蓄积为4807.11 m^(3)。2)在未来30 a的模拟经营过程中,龄组结构逐渐趋于稳定,中龄林和近熟林面积占比逐渐减小,幼龄林和成过熟林面积占比逐渐增大,模拟经营后的马尾松用材林成过熟林面积占比可稳定处于42.86%,龄组结构呈理想分布。3)与传统公式法相比,模拟测算法具有更加科学的测算机理、更加灵活的适应能力、更加精准的测算过程和更加客观的测算结果。采用模拟测算法来确定森林合理年伐量,能够为指导森林经营和实现森林资源的永续利用提供科学的参考依据。

C半群和双参数C半群的指数公式

根据C半群与双参数C半群的关系以及C0半群的指数公式,给出了C半群和双参数C半群的指数公式.

考虑检验错误的集团抽样检验接收概率函数

本文给出存在集团检验误差时的集团抽样检验接受概率计算公式,该公式可用于设计抽样方案、分析集团检验错误对抽样方案的影响.采用计算机模拟抽样检验的方法对给出的公式加以验证,证明了该所给公式的正确性.同时通过对集团检验错误存在与否的抽样检验特征(OC)曲线的比较,指出:以往的集团抽样检验方案设计,都是在假设无检验误差前提下设计的,在抽样检验中,若存在检验错误,会严重影响抽样检验的接收概率,使抽样检验结果不能客观地反映检验批的质量.

分支水平井产能公式研究进展

分析了分支水平井的7个典型产能公式.对比发现,王卫红公式、李?公式均为程林松公式的特例;蒋廷学公式比程林松公式更加准确.通过理论分析和实例运算,验证了齐成伟公式在外部渗流阻力部分的重要突破.进一步分析发现,齐成伟公式的外部渗流阻力部分自相容,科学严谨.最后,考虑到各种附加阻力,得出了完整的产能公式.