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.

Convergence analysis for the Secant method based on new recurrence relations

A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.

On the Extension of the Three-Term Recurrence Relation to Probabilities Distributions without Moments

In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.

Temporal pattern of resolution/recurrence of choroidal neovascularization during bevacizumab therapy for wet age-related macular degeneration

AIMTo characterize temporal pattern of resolution and recurrence of naive choroidal neovascularization (CNV) secondary to wet age-related macular degeneration (AMD) treated with intravitreal bevacizumab on as needed regimen, and to analyze baseline risk factors for CNV resolution or recurrence.

Friendly Neighbor, Strategic Partner——Commemorating the 50th Anniversary of the Establishing of Sino-Russian Relations

I On the occasion of the 5 0th anniversary of the founding of the People’S Re-public of China and of the establishment of diplomatic ties between the PRC andRussia,both countries have pledged to take this opportunity to further strengthenand develop bilateral relations in the coming 21st century. Looking back at the 50-year relationship between China and Russia,it is notdifficult to see that it underwent not only close cooperation,but also severe con-

Estimating the Recurrence Periods of Earthquake Data in Turkey

In this paper, the 231 earthquake data of magnitude 5 and higher, between north (39.00o-42.00o) and east (26.00o-45.00o) coordinates in Turkey from July 12, 1900 to October 23, 2011 are statistically analyzed. The probability density function and cumulative function of the magnitude are derived. It is shown that magnitude random variable is distrib-uted as the exponential distribution. The recurrence periods is also calculated. Recurrence period is estimatedapproxi-matelytwo times a year for an earthquake having magnitude 5.2. Using the Gutenberg-Richter function, the relation between magnitude and frequency is represented.

On Relations for Moments of Generalized Order Statistics for Lindley–Weibull Distribution

Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.

China-Singapore Intergovernmental Cooperation and Economic and Trade Relations

Since the establishment of diplomatic relations between China and Singapore in 1990, both the economic and political ties between the two countries have experienced a substantial growth. China-Singapore Suzhou Industrial Park, China-Singapore （Chongqing） Demonstrative Initiative on Strategic Connectivity, and the compatibility between Singapore ~ development strategy and China＇ s Belt and Road initiative are testimony to the ever-growing bilateral economic and trade links. The deepening and expanding economic and trade relations between China and Singapore enhance political mutual trust, propelling China＇s economic and industrial upgrading. At the same time, they exert a positive influence on the development of China-ASEAN relations and an effective implementation of the Belt and Road initiative in Southeast Asia.

Close Neighbors Plus Relatives──An unforgettable Trip to the Philippines

At the invitation of the.Asian Center of the Philip-pine University,a five-mem-berCAFIU delegation visited the Philippines.The host high-ly regarded our visit,gave us a W arm and courteous recep-tion.Mr.Estrada.

Management of recurrent rectal cancer:A population based study in greater Amsterdam

AIM： To analyze, retrospectively in a populationbased study, the management and survival of patients with recurrent rectal cancer initially treated with a macroscopically radical resection obtained with total mesorectal excision （TME）. METHODS： All rectal carcinomas diagnosed during 1998 to 2000 and initially treated with a macroscopically radical resection （632 patients） were selected from the Amsterdam Cancer Registry. For patients with recurrent disease, information on treatment of the recurrence was collected from the medical records. RESULTS： Local recurrence with or without clinically apparent distant dissemination occurred in 62 patients （10%）. Thirty-two patients had an isolated local recurrence. Ten of these 32 patients （31%） underwent radical re-resection and experienced the highest survival （three quarters survived for at least 3 years）. Eight patients （25%） underwent non-radical surgery （median survival 24 rno）, seven patients （22%） were treated with radio- and/or chemotherapy without surgery （median survival 15 mo） and seven patients （22%） only received best supportive care （median survival 5 too）. Distant dissemination occurred in 124 patients （20%） of whom 30 patients also had a local recurrence. The majority （54%） of these patients were treated with radio- and/or chemotherapy without surgery （median survival 15 mo）. Twenty-seven percent of these patients only received best supportive care （median survival 6 mo）, while 16% underwent surgery for their recurrence. Survival was best in the latter group （median survival 32 mo）. CONCLUSION： Although treatment options and survival are limited in case of recurrent rectal cancer after radical local resection obtained with TME, patients can benefit from additional treatment, especially if a radical resection is feasible.

Clinical and echocardiographic analysis of patients suffering from recurrent takotsubo cardiomyopathy

Background Recurrence of takotsubo cardiomyopathy （TTC） is a well-known complication. However, current literature lists only a few isolated cases. We aimed to determine the incidence and clinical significance of recurrent TTC. Methods ＆ Results Our institutional database constituted a collective of 114 patients diagnosed with TTC since 2003. Close follow-up of these patients revealed a recurrence of TTC in seven of these （6.1%）. The time interval between the index event and its recurrence varied between six months and six years. Arterial hypertension was more revealed in the recurrence group of TTC compared to non-recurrence group, （P = 0.02）. Chronic obstructive pulmo- nary disease and/or asthma was more diagnosed in the recurrence group, （P = 0.04）. Clinical events like fight ventficular involvement, TTC related complications such as life-threatening arrhythmias, pulmonary congestion and in hospital death were observed more frequently in the recurrent episode. Over a mean follow-up of one year the mortality rate was similar in both groups. Conclusions Recurrence of TTC within six years after index event is not an uncommon phenomenon. In the event of right ventricular involvement in the relapse phase, it might be associated with a higher complication rate. TTC recurrence should be the first differential diagnosis in patients with a past history of TTC.

A new class of three-variable orthogonal polynomials and their recurrences relations

A new class of three-variable orthogonal polynomials, defined as eigenfunctions of a second order PDE operator, is studied. These polynomials are orthogonal over a curved tetrahedron region, which can be seen as a mapping from a traditional tetrahedron, and can be taken as an extension of the 2-D Steiner domain. The polynomials can be viewed as Jacobi polynomials on such a domain. Three-term relations are derived explicitly. The number of the individual terms, involved in the recurrences relations, are shown to be independent on the total degree of the polynomials. The numbers now are determined to be five and seven, with respect to two conjugate variables z, $ \bar z $ and a real variable r, respectively. Three examples are discussed in details, which can be regarded as the analogues of the Chebyshev polynomials of the first and the second kinds, and Legendre polynomials.

A General Solution for a Class of Non-Homogeneous Recurrence Relations with Two Indices

In this paper,we present the formula of a solution for a class of recurrence relations with two indices by applying iteration and induction according to the principle of solving algebraic equa-tions. It provides a concrete model to solve the concerned prob-lems with modern computing tools.

Explicit Relations of Physical Potentials Through Generalized Hypervirial and Kramers' Recurrence Relations

Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike （non-diagonal case） and Kramers＇ （diagonal case） recurrence relations for arbitrary x^k which is independent of the central potential V（x）. Some significant results in diagonal case are obtained for special k in xk （k ≥2）. In particular, we find the orthogonal relation 〈n1｜n2〉 = δh1,n2 （k = 0）, 〈n1[V＇（x）｜n2〉 = （En1-En2）^2〈n1｜x｜n2〉 （k = 1）, En = （n｜V＇（x）x/2｜n〉 ＋ （n｜V（x）｜n〉 （k = 2） and -4En（n｜x｜n） ~ 〈n｜V＇（x）x^2｜n〉 ＋ 4〈n｜V（x）x｜n〉 =0 （k=3）. The latter two formulas can be used directly to calculate the energy levels. We present useYul explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.

Associated Hermite Polynomials Related to Parabolic Cylinder Functions

In analogy to the role of Lommel polynomials ?in relation to Bessel functions Jv(z) the theory of Associated Hermite polynomials in the scaled form ?with parmeter v to Parabolic Cylinder functions Dv(z) is developed. The group-theoretical background with the 3-parameter group of motions M(2) in the plane for Bessel functions and of the Heisenberg-Weyl group W(2) for Parabolic Cylinder functions is discussed and compared with formulae, in particular, for the lowering and raising operators and the eigenvalue equations. Recurrence relations for the Associated Hermite polynomials and for their derivative and the differential equation for them are derived in detail. Explicit expressions for the Associated Hermite polynomials with involved Jacobi polynomials at argument zero are given and by means of them the Parabolic Cylinder functions are represented by two such basic functions.

A clinicopathological study on IgG4-related ophthalmic disease

AIM： To investigate clinicopathological features of immunoglobulin G4-related ophthalmic disease（IgG4-ROD）, and analyze the recurrence rates following systemic corticosteroid administration.METHODS： We retrospectively searched clinical features, laboratory and histological findings based on the medical records of 21 patients with IgG4-ROD. All the patients examined in this study underwent surgical resection in the ocular adnexal lesions and underwent histological evaluation. This study further investigated clinical and histopathological features of 15 patients who received systemic corticosteroid after the resection.RESULTS： The mean age of the patients consisting of 7 males（33%） and 14 females（67%） was 61y. Fourteen patients were diagnosed as definitive, and 2 and 5 patients were probable and possible IgG4-ROD, respectively. Eyelid swelling was an initial symptom in 11 patients（52%） who did not show systemic involvements at a diagnosis. Fifteen patients received systemic corticosteroid administration, and all showed remission of inflammation. Among them, 10 patients did not recur, whereas 5 patients（33%） recurred during tapering. There were no significant difference between patients with or without recurrence in clinicopathological features.CONCLUSION： In this study, female patients are more predominant in IgG4-ROD. While inflammation recurs in one-third of patients, this study do not identify factors associated with recurrence after systemic corticosteroid administration.

Complement-mediated renal diseases after kidney transplantation-current diagnostic and therapeutic options in de novo and recurrent diseases

For decades, kidney diseases related to inappropriate complement activity, such as atypical hemolytic uremic syndrome and C3 glomerulopathy(a subtype of membranoproliferative glomerulonephritis), have mostly been complicated by worsened prognoses and rapid progression to end-stage renal failure. Alternative complement pathway dysregulation, whether congenital or acquired, is well-recognized as the main driver of the disease process in these patients. The list of triggers include: surgery, infection, immunologic factors, pregnancy and medications. The advent of complement activation blockade, however, revolutionized the clinical course and outcome of these diseases, rendering transplantation a viable option for patients who were previously considered as non-transplantable cases.Several less-costly therapeutic lines and likely better efficacy and safety profiles are currently underway. In view of the challenging nature of diagnosing these diseases and the long-term cost implications, a multidisciplinary approach including the nephrologist, renal pathologist and the genetic laboratory is required to help improve overall care of these patients and draw the optimum therapeutic plan.

引入激活扩散的类分布关系近邻分类器

针对同质性关系分类器基于一阶Markov假设简化处理的局限性,在类分布关系近邻分类器构建类向量和参考向量时,引入局部图排序激活扩散方法,并结合松弛标注的协作推理方法,通过适当扩大分类时邻居节点的范围增加网络数据中待分类节点的同质性,从而降低分类错误率.对比实验结果表明,该方法扩大了待分类节点的邻域,在网络数据上分类精度较好.

奥法妥木单抗治疗视神经脊髓炎谱系疾病疗效分析

目的探讨奥法妥木单抗治疗视神经脊髓炎谱系疾病(NMOSDs)的疗效及安全性。方法纳入2022年4月至2023年3月郑州大学第一附属医院采用奥法妥木单抗治疗方案的25例NMOSDs患者,分为定期给药组(A组,12例)及按CD19+B细胞百分比给药组(B组,13例),计算用药前和用药1年时年化复发率(ARR)、复发例数、复发次数和时间、复发症状,采用扩展残疾状态量表(EDSS)评估神经功能,记录用药期间药物不良反应。结果奥法妥木单抗治疗1年时3例(12%)复发,A组1例患者复发2次,分别为用药后1和5个月;B组2例患者复发,1例复发2次,为用药后2和6个月,1例复发1次,为用药后2个月。两组用药1年时与用药前仅ARR变化幅度差异具有统计学意义(F=29.061,P=0.000),A组用药1年时ARR较用药前下降(t=13.215,P=0.001),B组用药1年时ARR亦较用药前下降(t=19.259,P=0.000)。有8例出现注射部位疼痛、3例注射后发热、1例注射后头痛,其中1例诊断为细菌性脑膜炎;14例感染新型冠状病毒,其中1例因新型冠状病毒感染致肺炎入住重症监护病房;均无残疾、死亡等严重不良反应,EDSS评分均未增加。结论奥法妥木单抗定期给药或依据CD19+B细胞百分比给药均可减少患者复发风险,改善EDSS评分;早期与糖皮质激素联用需警惕感染风险。

基于GRA-GRU的淮河流域水质预测研究

水质指标具有多元相关性、时序性和非线性的特点,为有效预测河流水质变化,针对水质数据存在缺失和异常的问题,提出基于灰色关联分析-门控循环单元(Grey Relational Analysis-Gated Recurrent Unit, GRA-GRU)的水质预测模型。以淮河流域水质数据为样本,使用线性插值修补缺失数据和剔除的异常数据。使用灰色关联分析计算不同水质指标间的相关性,选择高相关性的水质指标以确定输入变量,并使用门控循环单元(Gated Recurrent Unit, GRU)预测不同的水质指标。将GRA-GRU的预测结果与反向传播神经网络(Back Propagation Neural Network, BPNN)、循环神经网络(Recurrent Neural Network, RNN)、长短期记忆神经网络(Long Short Term Memory, LSTM)、GRU及灰色关联分析-长短期记忆神经网络(Grey Relational Analysis-Long Short Term Memory, GRA-LSTM)进行对比分析,结果显示GRA-GRU在不同水质指标预测上具有较好的适应性,可以有效降低预测误差。其中,与其他模型相比,GRA-GRU预测的化学需氧量在均方根误差上分别降低了3.617%、0.681%、0.478%、1.505%和0.471%。