General calculation formulas and recurrence relations of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0

In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.

SOME RECURRENCE FORMULAS FOR BOX SPLINES AND CONE SPLINES

A degree elevation formula for multivariate simplex splines was given by Micchelli [6] and extended to hold for multivariate Dirichlet splines in [8]. We report similar formulae for multivariate cone splines and box-splines. To this end, we utilixe a relation due to Dahmen and Micchelli [4] that connects box splines and cone splines and a degree reduction formula given by Cohen , Lyche, and Riesenfcld in [2].

Explicit expressions and recurrence formulas of radial average value for N-dimensional hydrogen atom

In this paper, two recurrence formulas for radial average values of N-dimensional hydrogen atom are derived. Explicit expressions for <n rJ N-2 |r s|n rJ N-2 > are given for 3≥s≥-6. These results can be applied to discuss average value of centrifugal potential energy and other physical quantities. The relevant results of the usual hydrogen atom are contained in more general conclusion of this paper as special cases.

Therapeutic and recurrence-preventing effects of Qi-Replenishing and Blood-Activating Formula in rats with acetic acid-induced gastric ulcer

Objective:To explore the therapeutic and recurrence-preventing effects of Qi-Replenishing and Blood-Activating Formula in rats with acetic acid-induced gastric ulcer.Methods:A total of 138 SD rats were selected to make rat models with gastric ulcer induced by acetic acid(24 rats with sham operation served as sham operation group),and were randomly divided into model group(n=30),western medicine group(n=30),traditional Chinese medicine(TCM) group(n=24) and combination group(combined western medicine and TCM group,n=30).Western medicine group was gavaged with omeprazole in the morning and with iso-volumetric distilled water in the afternoon;TCM group and TCM sham operation group were gavaged with iso-volumetric distilled water in the morning and with Qi-Replenishing and Blood-Activating Formula in the afternoon;combination group was gavaged with omeprazole in the morning and with Qi-Replenishing and Blood-Activating Formula in the afternoon;sham operation group and model group were gavaged with iso-volumetric distilled water both in the morning and afternoon.Ulcer indexes and degree of mucosal degree in rats at different time points after gavage were observed.Twentyeight days after gavage,interleukin(IL)-1β was given to induce ulcer recurrence so as to observe the recurrent severity and rate of ulcer in each group.Results:Compared with model group and western medicine group,treatment in combination group could prominently reduce the ulcer index of rats with peptic ulcer,and increase the healing rate and inhibition rate of peptic ulcer.After IL-1β-induced ulcer recurrence,combination group was significantly superior to model group and western medicine group in ulcer recurrent rate[50%(3/6) vs.100%(6/6)]and severity.Conclusions:Basic acid-suppression therapy combined with Qi-Replenishing and BloodActivating Formula can effectually improve the ulcer healing quality and reduce ulcer recurrence.

LEIBNIZ′FORMULA OF GENERALIZED DIFFERENCE WITH RESPECT TO A CLASS OF DIFFERENTIAL OPERATORS AND RECURRENCE FORMULA OF THEIR GREEN′S FUNCTION

In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.

A Formula of Solution for a Class of Homogeneous Recurrence of Variable Coefficients with Two Indices

In this paper, we obtain an explicit formula of general solution for a class of the homogeneous recurrence of variable coefficients with two indices.

A Formula of General Solution for a Class of Homogeneous Trinomial Recurrence of Variable Coefficients with Two Indices

In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices. It provides a concrete and applicable model to solve the relevant problem with computer.

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.

Mechanism and Research Progress of Fuyang Huoxue Jiedu Formula against Recurrence of Ulcerative Colitis

By introducing the composition and modern pharmacology of Fuyang Huoxue Jiedu Formula,the paper further explored the mechanism and research progress of Fuyang Huoxue Jiedu Formula against recurrence of ulcerative colitis(UC).The formula can effectively improve the TCM syndromes of UC patients,reduce the recurrence rate,and improve clinical efficacy and patients’quality of life.

Long Dan Xie Gan Formula Granule Promotes Pro-Inflammatory Cytokine Expression in Female Guinea Pigs with Recurrent Genital Herpes

Objective To explore the effects of Long Dan Xie Gan formula granule(LDXGFG)on regulation of pro-inflammatory cytokines in female guinea pigs with recurrent genital herpes(herpes simplex virus 2,HSV-2).Methods Levels of pro-inflammatory cytokines in blood of HSV-2-infected guinea pigs,including IL-6,IL-8,IL-10,IL-12,IFN-α,IFN-β,IFN-γ,and TNF-α,were detected by ELISA;corresponding gene expression levels in tissues were detected by real-time PCR.Results IL-6,IL-10,IL-12,IFN-α,IFN-γand TNF-αdecreased significantly in both blood and diseased tissues after infection with recurrent genital herpes.Upon feeding LDXGFG to HSV-2-infected guinea pigs,IL-6,IL-10,IL-12,IFN-α,IFN-γand TNF-αdemonstrated significant increases,similar to the effects of acyclovir(ACV).LDXGFG promoted the expression of pro-inflammatory cytokines in blood and tissue,with a stronger effect than ACV.Moreover,LDXGFG demonstrated broader effects than ACV.Conclusion The present results suggest that LDXGFG can serve as an alternative,inexpensive,and long-term treatment for HSV-2 infection.

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.

Mechanism of treating recurrent abortion with “Peiyuan Bushen Antai formula” based on network pharmacology and molecular docking

Objective:To study the effective compound action target signal pathway of Peiyuan bushenan taifang(PYBSATF)has achieved good clinical efficacy in the treatment of recurrent spontaneous abortion(RSA),but its mechanism has not been clarified because of its complex components.In this study,network pharmacology is applied to study the effective compounds,targets and signal pathways of PYBSATF in the treatment of RSA,so as to reveal its pharmacological mechanism of action in the treatment of recurrent spontaneous abortion.Methods:The Traditional Chinese Medicine Systems Pharmacology database(TCMSP)and CNKI are used to obtain the main compounds and drug action targets of PYBSATF.Genecards and the Online Mendelian Inheritance of Man databases(OMIM)are searched to collect the known genes related to RSA,so as to construct compound-target network and screen out the common target proteins and main active compounds.We also use string database to construct a visual protein-protein interaction network(PPI).Cluster Profiler and R software were used to analyze the common targets of drugs and diseases for GO function analysis and KEGG pathway enrichment analysis.Finally,the compound and the protein sequences were conducted according to the node parameters,so that the core protein and core compounds are used to perform molecular docking.Results:186 potential active components and 65 predicted action targets of PYBSATF were screened out.At the same time,1658 genes were also screened out to be closely related to RSA,among which 65genes overlaped with PYBSATF targets and were considered to be related to way of treatment.PPI network showed that VEGFA,IL6,EGFR,MAPK8 and ESR1were the core targets of PYBSATF for the treatment of RSA.GO and KEGG enrichment analysis obtained 93 biological processes of cells(P<0.01)and 87 signaling pathways(P<0.01).PYBSATF played a pharmacological role through a variety of pathways including anti-inflammatory,anti-apoptosis,promoting proliferation and angiogenesis.Molecular docking showed that most active components and key targets of PYBSATF had strong efficiency.Conclusion:Through the study of network pharmacology,it predicted that PYBSATF might treat RSA through multiple targets and multiple signal pathways.Significantly,the predictive targets may be potential targets for treatment of RSA.

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 .

补肾化瘀方加减对肾虚血瘀型子宫内膜异位症术后复发的预防作用与机制研究

[目的]探讨补肾化瘀方加减对肾虚血瘀型子宫内膜异位症术后复发的预防作用与机制。[方法]选择于2019年1月—2021年1月在衡水市第四人民医院治疗的子宫内膜异位症患者320例,按随机数字表法随机分组,常规西医组160例,给予患者常规西医治疗,补肾化瘀方组160例,在常规西医治疗同时给予患者补肾化瘀方加减治疗,治疗前后检测两组患者血清性激素[促黄体生成素(LH)、孕激素(P)、雌激素(E2)],肿瘤坏死因子-α(TNF-α),血管内皮生长因子(VEGF),抗子宫内膜抗体(EMAb)水平,通过语言描述评分法(VRS)评价患者痛经及非经期盆腔痛情况,给予患者中医证候评分,比较两组临床疗效,记录两组患者2年复发率及治疗期间两组患者不良反应发生情况。[结果]补肾化瘀方组患者痛经及非经期盆腔痛评分低于常规西医组(P<0.05),补肾化瘀方组TNF-α、VEGF、EMAb水平较常规西医组低(P<0.05),补肾化瘀方组患者LH、P、E2含量较常规西医组明显低(P<0.05),补肾化瘀方组患者中医证候评分较常规西医组明显降低(P<0.05),补肾化瘀方组患者总有效率(97.50%)较常规西医组(88.13%)高(P<0.05),常规西医组2年复发率为12.90%,补肾化瘀方组2年复发率为3.21%,两组2年复发率比较,差异有统计学意义(P<0.05),补肾化瘀方组开始复发时间长于常规西医组(P<0.05);治疗期间两组患者均无明显不良反应发生。[结论]补肾化瘀方加减治疗肾虚血瘀型子宫内膜异位症术后疗效显著,可有效缓解患者痛经及非经期盆腔痛,降低复发率,其作用机制可能与其抑制机体炎症,降低VEGF、EMAb水平,改善性激素水平有关。

中医药预防大肠息肉术后复发证型证素分布及用药规律研究

目的:探讨近二十年各医家预防大肠息肉术后复发证型证素分布及用药规律,为中医药预防大肠息肉术后复发提供新的思路。方法:以各医家处方为切入点,提取处方涉及的证候类型、病位证素、病性证素及药物组成,基于中医传承辅助平台(V2.5)软件,运用关联规则、系统熵聚类等一系列高级的数据挖掘方法,总结处方的证型证素分布、用药频次、性味、归经、药物相关性以及聚类情况。结果:共收集到数据库相关文献所载预防大肠息肉复发的处方105首,涉及中医证型30种,中药186味。其中核心药物组合139对,潜在常用药对157对,新处方3首。结论:脾胃虚弱是大肠息肉的核心病机,治疗当以健脾益胃为基础,根据不同患者血瘀、湿阻、痰凝、热毒等的差异,佐以活血、祛湿、化痰、清热之法,标本兼治,方获良效。

磺达肝癸钠联合寿胎丸加减方治疗肾虚血瘀型抗心磷脂抗体阳性复发性流产的临床效果

目的探讨磺达肝癸钠联合寿胎丸加减方治疗肾虚血瘀抗心磷脂抗体阳性复发性流产(RSA)的效果。方法选取2021年1月至12月江西省妇幼保健院收治的105例RSA患者作为研究对象,按随机数字表法分为单纯中药组、对照组和观察组,各35例。单纯中药组用寿胎丸加减方,对照组用依诺肝素+寿胎丸加减方,观察组用磺达肝癸钠+寿胎丸加减方。观察三组的疗效、抗心磷脂抗体转阴率、凝血指标及不良反应。结果观察组和对照组患者孕12周时总有效率均高于单纯中药组,差异有统计学意义(P<0.017),但观察组和对照组患者总有效率比较,差异无统计学意义(P>0.017)。观察组和对照组抗心磷脂抗体转阴率高于单纯中药组,差异有统计学意义(P<0.017);观察组患者抗心磷脂抗体转阴率高于对照组,差异有统计学意义(P<0.017);三组抗心磷脂抗体转阴率比较,差异有统计学意义(P<0.05)。三组患者孕12周时血清D-二聚体水平、凝血指数和最大振幅均低于本组治疗前,且观察组和对照组患者指标低于单纯中药组,差异有统计学意义(P<0.05);但观察组和对照组患者凝血相关指标比较,差异无统计学意义(P>0.05)。治疗期间,单纯中药组无不良反应发生;观察组患者注射部位皮肤反应、转氨酶升高发生率低于对照组,差异有统计学意义(P<0.05)。结论磺达肝癸钠联合寿胎丸加减方治疗肾虚血瘀抗心磷脂抗体阳性RSA患者的效果显著,可有效改善临床症状、凝血状态,促进抗心磷脂抗体转阴,且安全性更好。

关于冰雹猜想(Ⅱ)

《关于冰雹猜想(Ⅱ)》是《关于冰雹猜想(Ⅰ)》的继续.首先用排序法求出跌落数的均值.有了均值这个工具,就可以证明定理2.2,进而又证明了定理2.3.定理2.3是说:由1开始的枝状图中,包含了所有大于1的奇数.这是一个与冰雹猜想等价的命题,在此成为一个定理.定理2.5给出了迭代次数m的一个上界,这个上界仅与x1有关.所以,任给一个大于1的奇数x1,则经过有限步即m步就可以迭代到1.

益肾调气法治疗肾虚肝郁型抑郁障碍远期复发率的多中心前瞻性队列研究

目的:评价益肾调气法对肾虚肝郁型抑郁障碍2年复发率的影响。方法:选取2017年1月至2018年4月在全国13个分中心招募肾虚肝郁型抑郁障碍患者,按照接受的治疗方案自然形成中医组、中西医组和西医组,比较3组的复发率。并根据干预的时间,将中医组和中西医组分为低、中、高3个暴露水平,比较不同水平的复发率,评价益肾调气法降低肾虚肝郁型抑郁障碍的远期复发率的效果。结果:共纳入肾虚肝郁型抑郁障碍1314例,其中中医组385例,西医组453例,中西医组476例。中医组、西医组、中西医组的两年复发率分别是23.61%,34.97%、18.14%。中医组比西医组使复发风险降低29.2%(P<0.05),中西医组比西医组使复发风险降低45.5%(P<0.001)。中医组以低中药水平暴露时间(TCM-ET)为参照,高TCM-ET较于低TCM-ET复发风险降低81.4%(P<0.01);中西医组以低TCM-ET为参照,中TCM-ET比低TCM-ET复发风险降低46.9%(P<0.05),高TCM-ET比低TCM-ET复发风险降低65.3%(P<0.01)。结论:益肾调气法治疗肾虚肝郁型抑郁障碍能够降低远期复发率,且中医药干预的暴露水平与复发率之间具有密切的关系,较长的暴露水平显著降低了患者的复发率。

雷火灸结合益肾通淋方对社区老年女性复发性尿路感染的效果

目的:观察雷火灸结合益肾通淋治疗社区老年女性复发性尿路感染患者的效果。方法:选取2021年8月至2023年3月就诊的老年女性复发性尿路感染患者120例,随机分为两组,最终获得有效干预组57例,对照组59例数据信息。两组均根据中段尿培养结果给予足量敏感抗生素治疗并缓解后,进行分组治疗和观察。对照组给予低剂量抑菌疗法,每日单剂量抗菌素1次,根据具体情况调整药物剂量。治疗组在对照组基础上每日服用益肾通淋方,同时加用雷火灸艾灸治疗,3次/周,共治疗12周。分析患者治疗前后中医证候积分评分疗效、尿常规(尿白细胞、尿红细胞水平)、焦虑(SAS)、抑郁(SDS)评分等各项指标的变化。结果:治疗组在改善中医证候方面疗效优于对照组(P<0.05)。治疗前,两组尿白细胞、尿红细胞比较,差异无统计学意义(P>0.05)。治疗后,干预组尿白细胞数明显低于对照组(P<0.001);但两组尿红细胞数比较差异无统计学意义(P>0.05)。治疗后,干预组SAS和SDS评分均低于对照组(P<0.05)。治疗3个月后,治疗组复发率低于对照组,差异具有统计学意义(P<0.05)。结论:雷火灸结合益肾通淋方的治疗方式在社区老年女性复发性尿路感染患者改善临床症状、心理健康及本病的复发率方面有积极作用。

和胃降逆止嗽方治疗胃食管反流性咳嗽(胃气上逆证)临床研究

目的观察和胃降逆止嗽方治疗胃食管反流性咳嗽(胃气上逆证)临床效果。方法96例胃食管反流性咳嗽(胃气上逆证)患者按照随机数字表法分为对照组和观察组各48例。对照组采用调整生活方式联合常规西药治疗,观察组采用调整生活方式联合和胃降逆止嗽方治疗。治疗12周后,评价两组中医证候积分(阵发性咳嗽、咳嗽时泛酸水、嘈杂、上腹不适)、莱塞斯特咳嗽生命质量问卷(lesser cough quality of life questionnaire,LCQ)评分、反流性疾病问卷(reflux disease questionnaire,RDQ)评分、食管运动功能(食管收缩波幅、食管蠕动波传导速度、平均收缩持续时间)、临床治疗效果、疾病复发概率以及治疗安全性。结果比较发现观察组治疗有效率明显高于对照组,对比有统计学差异;对比两组患者治疗后出现阵发性咳嗽等临床症状的概率,发现患者RDQ评分均有下降,但是观察组评分下降较为明显(P<0.05)。两组治疗后LCQ评分均升高(P<0.05),且观察组LCQ评分高于对照组(P<0.05)。治疗后,发现两组患者食管收缩波幅、食管蠕动波传导速度都出现了升高的情况(P<0.05),持续收缩时间明显缩短(P<0.05),且观察组食管运动功能指标改善情况都高于对照组,两组患者对比有统计学差异P<0.05,观察组3个月复发率和治疗后6个月复发率都较低,分别低于对照组3个月复发率(16.67%)和治疗后6个月的复发率(39.58%)(P<0.05)。治疗期间两组患者不良反应发生率相比无统计学意义。结论和胃降逆止嗽方可以有效缓解患者临床症状,同时,还能够促进患者食管运动,减少临床复发,改善生活质量,且治疗安全性高。