Recursion-transform method and potential formulae of the m×n cobweb and fan networks

In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.

Microwave absorption properties regulation and bandwidth formula of oriented Y_(2)Fe_(17)N_(3-δ)@SiO_(2)/PU composite synthesized by reduction-diffusion method

As concepts closely related to microwave absorption properties,impedance matching and phase matching were rarely combined with material parameters to regulate properties and explore related mechanisms.In this work,reduction–diffusion method was innovatively applied to synthesize rare earth alloy Y_(2)Fe_(17).In order to regulate the electromagnetic parameters of absorbers,the Y_(2)Fe_(17)N_(3-δ)particles were coated with silica(Y_(2)Fe_(17)N_(3-δ)@SiO_(2))and absorbers with different volume fractions were prepared.The relationship between impedance matching,matching thickness,and the strongest reflection loss peak(RLmin)was presented obviously.Compared to the microwave absorption properties of Y_(2)Fe_(17)N_(3-δ)/PU absorber,Y_(2)Fe_(17)N_(3-δ)@SiO_(2)/PU absorbers are more conducive to the realization of microwave absorption material standards which are thin thickness,light weight,strong absorbing intensity,and broad bandwidth.Based on microwave frequency bands,the microwave absorption properties of the absorbers were analyzed and the related parameters were listed.As an important parameter related to perfect matching,reflection factor(√ε_(r)/μ_(r))was discussed combined with microwave amplitude attenuation.According to the origin and mathematical model of bandwidth,the formula of EAB(RL<-10 dB)was derived and simplified.The calculated bandwidths agreed well with experimental results.

A GENERALIZED GAUSS-TYPE QUADRATURE FORMULA AND ITS APPLICATIONS TO PSEUDOSPECTRAL METHOD

A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.

On Relations between the General Recurrence Formula of the Extension of Murase-Newton’s Method (the Extension of Tsuchikura*-Horiguchi’s Method) and Horner’s Method

In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.

A Nonstationary Halley’s Iteration Method by Using Divided Differences Formula

This paper presents a new nonstationary iterative method for solving non linear algebraic equations that does not require the use of any derivative. The study uses only the Newton’s divided differences of first and second orders instead of the derivatives of (1).

Application of Series Formula Method in Optimization Arrangement of Webs

The expressions of the internal forces of the webs under the vertical loads of the simply supported beam type trusses with vertical and horizontal webs and without vertical webs are studied through the mathematical formula method. The variations of internal forces under different angles and spacings of the webs are simulated. The law of the optimal arrangement of the webs of the parallel-string simple-beam truss is obtained: under the condition that the rigidity of the rod is allowed, the form of no vertical web-type truss and reducing the span distance and inclination of the side span are advisable, which can save materials and reduce the weight as well. This method can be applied to the calculation of internal forces for arbitrary loads and truss forms.

The Convergences Comparison between the Halley’s Method and Its Extended One Based on Formulas Derivation and Numerical Calculations

The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s method we give definition of function by variable transformation in Section 1. In Section 4 we do the numerical calculations of Halley’s method and extended one for elementary functions, compare these convergences, and confirm the theory. Under certain conditions we can confirm that the extended Halley’s method has better convergence or better approximation than Halley’s method.

Study on the accuracy of glomerular filtration rate formulas by double plasma method as "gold standard"

Objective: To evaluate the accuracy of glomerular filtration rate formula by comparising the CKD-EPI 2009 formula and the modified Modified MDRD formula with the 99mTc-DTPA double-phase plasma method as "gold standard" respectively. Methods: Totally 166 patients diognosed as chronic kidney disease (CKD) were enrolled. The 99mTc-DTPA double-plasma method (rGFR) was used as the "gold standard". The CKD-EPI 2009 formula and the modified MDRD formula were used to calculate eGFR. Statistical software was used to analyze the correlation between the calculated values of the two formulas and the gold standard value and the bias. Then we evaluated the accuracy of the two GFR formulas. Results: Among the CKD stage 1 patients, the bias of the CKD-EPI 2009 formula was smaller than that of the Modified MDRD formula (13.9911.45;20.1815.90);both formulas were weakly correlated with the gold standard (correlation coefficients were 0.216, 0.229, P<0.01, respectively);The probability that the bias of the calculated value of the CKD-EPI 2009 formula less than 15%, 30%, and 50% of the gold standard value is smaller. Among the CKD stage 2 patients, the bias of the CKD-EPI 2009 formula was smaller than that of the Modified MDRD formula (12.748.45;15.6811.01);both formulas were moderately correlated with the gold standard (correlation coefficients were 0.568, 0.581, P<0.01, respectively);The probability that the bias of the calculated value of the CKD-EPI 2009 formula less than 15%, 30%, and 50% of the gold standard value is smaller. Among the CKD stage 3 patients, the bias of the CKD-EPI 2009 formula was smaller than that of the Modified MDRD formula (12.6410.27;12.8810.97), and both formulas were strongly correlated with the gold standard (correlation coefficients were 0.664, 0.670, P<0.01, respectively);The probability that the bias of the calculated value of the Modified MDRD formula less than 15%, 30%, and 50% of the gold standard value is smaller. Among the CKD stage 4 to 5 patients, the bias of the CKD-EPI 2009 formula was smaller than that of the Modified MDRD formula (5.585.36;5.945.20);The CKD-EPI 2009 formula and the Modified MDRD formula were strongly correlated with the gold standard (correlation coefficient r was 0.808. 0.802, P<0.01, respectively);The probability of the bias of the calculated value of the CKD-EPI 2009 formula less than 15%, 30%, and 50% of the gold standard value is smaller. In patients with decreased renal function with GFR <60 ml/min, the sensitivity and positive predictive value of the CKD-EPI 2009 formula for the diagnosis of "decreased renal function"were higher, and the specificity was comparable. Conclusion: 1. When the renal function is only slightly decreased, the accuracy of the two formulas is not good. In this condition, the CKD-EPI 2009 formula is more accurate and recommended. 2. It is necessary to further improve the current formulas especialy when it comes to value the slightly declined renal function;3. When we try to identify the stage of CKD patients, only based on eGFR may cause misclassification, it is recommended to combine the cause-GFR-albuminuria staging to assess the stage of CKD;4. The current formulas have limitations.in the case that requires a highly accurate assessment of GFR, the 99mTc-DTPA dual plasma method is recommended.

The Formulas to Compare the Convergences of Newton’s Method and the Extended Newton’s Method (Tsuchikura-Horiguchi Method) and the Numerical Calculations

This paper gives the extension of Newton’s method, and a variety of formulas to compare the convergences for the extension of Newton’s method (Section 4). Section 5 gives the numerical calculations. Section 1 introduces the three formulas obtained from the cubic equation of a hearth by Murase (Ref. [1]). We find that Murase’s three formulas lead to a Horner’s method (Ref. [2]) and extension of a Newton’s method (2009) at the same time. This shows originality of Wasan (mathematics developed in Japan) in the Edo era (1603-1868). Suzuki (Ref. [3]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 2 gives the relations between Newton’s method, Horner’s method and Murase’s three formulas. Section 3 gives a new function defined such as .

Superposition formulas of multi-solution to a reduced(3+1)-dimensional nonlinear evolution equation

We gave the localized solutions,the interaction solutions and the mixed solutions to a reduced(3+1)-dimensional nonlinear evolution equation.These solutions were characterized by superposition formulas of positive quadratic functions,the exponential and hyperbolic functions.According to the known lump solution in the outset,we obtained the superposition formulas of positive quadratic functions by plausible reasoning.Next,we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory.These two kinds of solutions contained superposition formulas of positive quadratic functions,which were turned into general ternary quadratic functions,the coefficients of which were all rational operation of vector inner product.Then we obtained linear superposition formulas of exponential and hyperbolic function solutions.Finally,for aforementioned various solutions,their dynamic properties were showed by choosing specific values for parameters.From concrete plots,we observed wave characteristics of three kinds of solutions.Especially,we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.

A New Extrapolation Economy Cascadic Multigrid Method for Image Restoration Problems

In this paper, a new extrapolation economy cascadic multigrid method is proposed to solve the image restoration model. The new method combines the new extrapolation formula and quadratic interpolation to design a nonlinear prolongation operator, which provides more accurate initial values for the fine grid level. An edge preserving denoising operator is constructed to remove noise and preserve image edges. The local smoothing operator reduces the influence of staircase effect. The experiment results show that the new method not only improves the computational efficiency but also ensures good recovery quality.

退耕还林地生态环境损害评估案例分析及应用

近年来,随着我国经济的高速发展,林地生态环境损害事件日益增加。不同类型的生态系统或同一生态系统在不同区域所提供的生态服务功能侧重均不同,鉴定评估林地生态系统的环境损害价值时应选用不同的测算方法。通过阐述理论公式法和实际监测法的原理和适用范围及其在生态环境损害评估中的应用,并对量化过程中参数的选取原则与方法进行说明。结合案例分析非法占用退耕还林地导致的生态环境损害范围和程度,计算出2012年~2019年的生态环境损害价值量为205万元。研究退耕还林地生态环境损害典型案例,并将其推广应用于小规模普通林地,对林地生态环境损害案件的鉴定评估环节具有重要引领作用。

地下水型饮用水水源补给区划分——以辽宁省沈阳市北部某地区饮用水水源为例

选择辽宁省沈阳市北部某地区集中式地下水型饮用水水源作为研究区,收集其地形地貌、水源所属地下水含水系统的地质和水文地质概况等相关信息进行分析。选择公式法,根据含水层岩性,采取经验值参数,以水源开采井保护区外为基准,以15 a(5475 d)为地下水质点迁移时间,计算得出补给区面积为40.18 km^(2)。鉴于补给区边界部分横跨村庄,在补给区定界过程中,将横跨村庄纳入补给区范围内,切实加强补给区安全防护。并从补给区环境管理方面提出对策和建议。

国医大师张大宁教授以膏方辨治阴虚型慢性肾脏病经验总结

慢性肾脏病逐渐成为临床最常见的慢性疾病之一,严重影响了人民群众的身体健康,国医大师张大宁教授作为中医肾脏病的奠基人,在长期的临床实践中,最早提出了“肾虚血瘀论”并首创“补肾活血法”,同时将补肾活血法融入膏方之中来治疗阴虚型慢性肾脏病。文章总结了张大宁教授利用膏方治疗慢性肾脏病的经验,供读者参考。

二维层状盆地地震动附加放大特征研究:SV波入射

发展了一种基于谱元法和多次透射边界的平面SV波入射下二维复杂场地波动数值模拟方法。基于该方法,模拟分析了31条地震波输入下二维典型层状沉积盆地中的各场点相比其对应的一维土层模型的模拟地震动的附加放大特征,分析了放大系数对于输入地震波的敏感性。结果表明,该方法具有较高精度和良好的高频稳定性。不同地震波输入下,盆地地面运动及其放大特征存在较大差别。水平分量上平均反应谱放大系数的较大值(最大1.2左右)集中在盆地边缘区域及周期等于0.5倍~0.7倍自振周期附近,垂直分量上较大放大系数(最大0.9左右)紧邻盆地角点且周期为0.3倍自振周期处。同时,盆地对不同周期地震动的放大特征,以及不同位置点的谱放大系数随周期的变化规律均表现出明显不同,相对短周期地震动的盆地边缘效应最为强烈,而相对长周期地震动的放大作用明显减弱。此外,盆地边缘区域的放大系数对输入波最为敏感,不同地震波输入下放大系数值在较大范围内变化;而盆地中间区域的放大系数对输入波不敏感,其值的变化范围相对较小。

三维二十面体准晶弹性半平面周期接触问题研究

借助平面弹性复变方法,研究了周期刚性压头作用下三维二十面体准晶弹性半平面的周期有限摩擦和周期粘结接触问题.从应力、位移分量的复变函数形式表达式出发,利用半平面Hilbert核积分公式、Plemelj公式,得到两类周期接触问题的解答.针对周期有限摩擦接触问题,得到了三类周期刚性压头(直水平、直倾斜和圆形基底)作用在准晶体半平面上接触应力的封闭解.针对半平面周期粘结接触问题,求得接触边界上作用周期尖劈形位移时接触应力的显式解答.当不考虑相位子场的作用时,文中求得的理论结果可退化到正交各向异性材料平面弹性周期接触问题的对应结果.数值算例说明准晶弹性常数对接触应力分布规律及大小的影响.本文结论可为分析准晶材料压痕实验结果及准晶材料性能提供一定理论依据.

大庆油田长垣地区萨零组横波速度预测方法研究

萨零组是大庆油田萨尔图油层组顶部发育的一个沉积单元,含油面积广,油气资源丰富。萨零组储层致密、物性差、一直未动用,为了对大庆油田长垣地区萨零组进行高质量勘探开发,急需开展萨零组储层横波速度预测方法的研究。根据萨零组在平面上的分布特征,将长垣地区由南到北分5个区块,以67口井Xmac测井曲线和全波声波测井资料为基础,采用最小二乘法,分别进行线性关系和二次多项式关系拟合,得到长垣地区不同区块的纵横波速度经验公式。线性关系拟合的相关指数比二次多项式关系拟合的相关指数小,二次多项式关系预测值更接近实测值,应用不同区块的经验公式可以预测出横波速度,弥补了萨零组横波速度资料少的问题,对于提高垂向应力解释精度、判断压后裂缝形态等方面具有参考价值。

郑州市暴雨强度公式计算与对比分析

为真实客观地反映郑州市近年来暴雨特征变化,进一步优化郑州市暴雨强度公式,选取2000~2022年11个降雨历时的年最大暴雨量,采用最小二乘法、遗传算法、拟牛顿法优化了郑州市暴雨强度公式参数,并与郑州市2002年暴雨强度公式以及2023年暴雨强度公式进行对比分析。结果表明,郑州市暴雨强度公式在指数分布中采用拟牛顿法拟合误差最小,最终确定的优化参数A1为11.312、C为2.968、b为19.8、n为0.900;在不同重现期暴雨条件下,优化公式相对于2002年公式呈现出完全不同的极值分布情况,即“大的更大、小的更小”,而与2023年公式的雨强相差较小;在不同降雨情景管网水力运行特征中,优化公式与2023年公式的模拟结果高度一致,两者在预测郑州市内涝情况整体上具有相似的准确性和可靠性,对城市排水防涝具有一定的指导作用。

充气式橡胶坝的模型试验及有限差分研究

橡胶坝的挡水性能优越,兼具实用性与景观性,被广泛用在城市河流挡水闸坝和溢流坝等领域。充气式橡胶坝相比充水橡胶坝,安装和拆卸更为方便,但目前充气式橡胶坝采用查表法进行粗略设计,过程复杂且存在误差。鉴于此,设计大比尺模型试验测试充气式橡胶坝在充气、挡水条件下的坝袋截面形状和袋体张拉力分布特点。基于有限差分软件建立充气式橡胶坝的力学模型,通过大比尺模型试验和现行设计规范验证了该模型的准确性。分析充气式橡胶坝在挡水过程中横截面几何形状及尺寸、张拉力与上游水位及内部气压之间的关系。结果表明:坝袋宽度B、接地宽度b随上游水位增大呈非线性增加;坝袋高度H、横截面面积A随上游水位增大呈非线性减小。设计工况下,坝袋高度H、横截面面积A随气压增加呈非线性增大,坝袋宽度B、接地宽度b随气压增大呈非线性减小;坝袋张拉力与气压呈正比关系。基于Chapman-Richard曲线模型对设计工况下的几何尺寸、张拉力与内部气压间的关系进行拟合,提出橡胶坝简化设计计算公式,可用于充气式橡胶坝的设计计算。

祛湿通脉法治疗类风湿关节炎的研究与应用概况

基于类风湿关节炎患者“风湿瘀阻,筋伤骨损”的病机特点,提出“祛风除湿,通利血脉,畅通经络,健脾补肾,强筋壮骨”的治法,简称“祛湿通脉法”。在“祛湿通脉法”治疗原则的指导下,可根据正邪虚实,选用经验方如昆断益母方、南续益母颗粒、三藤舒筋方以及经方如桂枝芍药知母汤、黄芪桂枝五物汤、半夏泻心汤等进行随症加减的中药治疗,并可配合膏方、外治法、功能锻炼等,从而构建具有中医药优势的类风湿关节炎防治体系。该课题组所开展的系列临床和实验研究结果表明,“祛湿通脉法”治疗类风湿关节炎具有增效减毒的作用,是发挥中医药优势以防治类风湿关节炎的理论创新。