Analysis of Progressively Type-Ⅱ Inverted Generalized Gamma Censored Data and Its Engineering Application

A novel inverted generalized gamma(IGG)distribution,proposed for data modelling with an upside-down bathtub hazard rate,is considered.In many real-world practical situations,when a researcher wants to conduct a comparative study of the life testing of items based on cost and duration of testing,censoring strategies are frequently used.From this point of view,in the presence of censored data compiled from the most well-known progressively Type-Ⅱ censoring technique,this study examines different parameters of the IGG distribution.From a classical point of view,the likelihood and product of spacing estimation methods are considered.Observed Fisher information and the deltamethod are used to obtain the approximate confidence intervals for any unknown parametric function of the suggestedmodel.In the Bayesian paradigm,the same traditional inferential approaches are used to estimate all unknown subjects.Markov-Chain with Monte-Carlo steps are considered to approximate all Bayes’findings.Extensive numerical comparisons are presented to examine the performance of the proposed methodologies using various criteria of accuracy.Further,using several optimality criteria,the optimumprogressive censoring design is suggested.To highlight how the proposed estimators can be used in practice and to verify the flexibility of the proposed model,we analyze the failure times of twenty mechanical components of a diesel engine.

Probability Laws Derived from the Gamma Function

Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. Namely the gamma, beta, and Student law, through the chi-square law and the normal law are all distributions resulting from applications of Euleur functions.

Clinical efficacy of Gamma Knife® combined with transarterial chemoembolization and immunotherapy in the treatment of primary liver cancer

BACKGROUND This study was designed to investigate the clinical efficacy and safety of Gamma Knife®combined with transarterial chemoembolization(TACE)and immunotherapy in the treatment of primary liver cancer.AIM To investigate the clinical efficacy and safety of Gamma Knife®combined with TACE and immune-targeted therapy in the treatment of primary liver cancer.METHODS Clinical data from 51 patients with primary liver cancer admitted to our hospital between May 2018 and October 2022 were retrospectively collected.All patients underwent Gamma Knife®treatment combined with TACE and immunotherapy.The clinical efficacy,changes in liver function,overall survival(OS),and progression-free survival(PFS)of patients with different treatment responses were evaluated,and adverse reactions were recorded.RESULTS The last follow-up for this study was conducted on October 31,2023.Clinical evaluation of the 51 patients with primary liver cancer revealed a partial response(PR)in 27 patients,accounting for 52.94%(27/51);stable disease(SD)in 16 patients,accounting for 31.37%(16/51);and progressive disease(PD)in 8 patients,accounting for 15.69%(8/51).The objective response rate was 52.94%,and the disease control rate was 84.31%.Alanine aminotransferase,aspartate aminotransferase,lactate dehydrogenase,and alpha-fetoprotein isoform levels decreased after treatment compared with pretreatment(all P=0.000).The median OS was 26 months[95%confidence interval(95%CI):19.946-32.054]in the PR group and 19 months(95%CI:14.156-23.125)in the SD+PD group,with a statistically significant difference(P=0.015).The median PFS was 20 months(95%CI:18.441-34.559)in the PR group and 12 months(95%CI:8.745-13.425)in the SD+PD group,with a statistically significant difference(P=0.002).Common adverse reactions during treatment included nausea and vomiting(39.22%),thrombocytopenia(27.45%),and leukopenia(25.49%),with no treatment-related deaths reported.CONCLUSION Gamma Knife®combined with TACE and immune-targeted therapy is safe and effective in the treatment of primary liver cancer and has a good effect on improving the clinical benefit rate and liver function of patients.

Cortico-striatal gamma oscillations are modulated by dopamine D3 receptors in dyskinetic rats

Long-term levodopa administration can lead to the development of levodopa-induced dyskinesia.Gamma oscillations are a widely recognized hallmark of abnormal neural electrical activity in levodopa-induced dyskinesia.Currently,studies have reported increased oscillation power in cases of levodopa-induced dyskinesia.However,little is known about how the other electrophysiological parameters of gamma oscillations are altered in levodopa-induced dyskinesia.Furthermore,the role of the dopamine D3 receptor,which is implicated in levodopa-induced dyskinesia,in movement disorder-related changes in neural oscillations is unclear.We found that the cortico-striatal functional connectivity of beta oscillations was enhanced in a model of Parkinson’s disease.Furthermore,levodopa application enhanced cortical gamma oscillations in cortico-striatal projections and cortical gamma aperiodic components,as well as bidirectional primary motor cortex(M1)↔dorsolateral striatum gamma flow.Administration of PD128907(a selective dopamine D3 receptor agonist)induced dyskinesia and excessive gamma oscillations with a bidirectional M1↔dorsolateral striatum flow.However,administration of PG01037(a selective dopamine D3 receptor antagonist)attenuated dyskinesia,suppressed gamma oscillations and cortical gamma aperiodic components,and decreased gamma causality in the M1→dorsolateral striatum direction.These findings suggest that the dopamine D3 receptor plays a role in dyskinesia-related oscillatory activity,and that it has potential as a therapeutic target for levodopa-induced dyskinesia.

SOME COMPLETELY MONOTONIC FUNCTIONS ASSOCIATED WITH THE q-GAMMA AND THE q-POLYGAMMA FUNCTIONS

In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q 〉 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].

Point spread functions for a small gamma camera with pinhole collimator

A set of point spread functions (PSF) has been obtained by means of Monte-Carlo simulation for asmall gamma camera with a pinhole collimator of various hole diameters. The FOV (field of view) of the camera isexpended from 45 mm to 70 mm in diameter. The position dependence of the variances of PSF is presented, and theacceptance for the 140 kev gamma rays is explored. A phantom of 70 mm in diameter was experimentally imaged inthe camera with effective FOV of only 45 mm in diameter.

Analytical solution of modified point kinetics equations for linear reactivity variation in subcritical nuclear reactors adopting an incomplete gamma function approximation

The present work aims to achieve a fast and accurate analytical solution of the point kinetics equations applied to subcritical reactors such as ADS (Accelerator-Driven System), assuming a linear reactivity and external source variation. It was used a new set of point kinetics equations for subcritical systems based on the model proposed by Gandini & Salvatores. In this work it was employed the integrating factor method. The analytical solution for the case of interest was obtained by using only an approximation which consists of disregarding the term of the second derivative for neutron density in relation to time when compared with the other terms of the equation. And also, it is proposed an approximation for the upper incomplete gamma function found in the solution in order to make the computational processing faster. In addition, for purposes of validation and comparison a numerical solution was obtained by the finite differences method. Finally, it can be concluded that the obtained solution is accurate and has fast numerical processing time, especially when compared with the results of numerical solution by finite difference. One can also observe that the gamma approximation used achieve a high accuracy for the usual parameters. Thus we got satisfactory results when the solution is applied to practical situations, such as a reactor startup.

COMPLETE MONOTONICITY FOR A NEW RATIO OF FINITELY MANY GAMMA FUNCTIONS

In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithmic derivative of the ratio,and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.

Gamma Functions and Siegel Integrals on Nonselfdual Cones

In this paper,we will define Gamma functions and Siegel integrals on nonselfdual cones and give some applications.

Analytical Evaluation of Non-Elementary Integrals Involving Some Exponential, Hyperbolic and Trigonometric Elementary Functions and Derivation of New Probability Measures Generalizing the Gamma-Type and Gaussian-Type Distributions

The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, and where α,η and β are real or complex constants are evaluated in terms of the confluent hypergeometric function 1F1 and the hypergeometric function 1F2. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions 1F1 and 1F2. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (x2) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.

The Infinite Polynomial Products of the Gamma and Zeta Functions

Starting with the binomial coefficient and using its infinite product representation, the infinite product representation of the gamma function and of the zeta function are composed of an exponential and of a trigonometric component and proved. It is proved, that all these components define imaginary roots on the critical line, if written in the form as they are in the functional equation of the zeta function.

一般Gamma型算子在Orlicz空间内的逼近

讨论一般Gamma型算子在Orlicz空间内的逼近问题,由于Orlicz空间比连续函数空间和Lp空间“大”,范数结构也比Lp空间复杂,所以在Orlicz空间内研究Gamma算子的逼近问题具有一定的拓展性。借助Cauchy⁃Schwarz不等式、Jensen不等式、光滑模和N函数的凸性等,证明一般Gamma型算子在Orlicz空间内的有界性,给出该算子在Orlicz空间内的逼近正定理。

联系着广义gamma函数的Raabe型积分

通过渐近公式与分析方法计算了若干联系着广义gamma函数的Raabe型积分.

虚拟现实技术对不完全脊髓损伤患者下肢功能的影响

目的探讨虚拟现实技术(VR)对不完全脊髓损伤患者下肢运动功能、平衡能力、躯干控制能力及步行能力的影响。方法选自郑州大学第一附属医院康复医学科2022年1月至2023年12月治疗的46例不完全脊髓损伤患者,采用随机数字法分成治疗组、对照组,各23例。两组接受相同的康复治疗,治疗组在此基础上增加VR 30 min,对照组在常规康复治疗的基础上继续康复训练30 min,每周5 d,疗程8周。治疗前及治疗8周后,分别采用脊髓损伤下肢功能量表(ASIA)、Berg平衡量表(BBS)、躯干控制测试量表(TCT)、Holden功能性步行量表(FAC)对患者下肢运动能力、平衡能力、躯干控制能力及步行能力进行评定。结果两组治疗前ASIA、BBS、TCT、FAC评分比较,差异无统计学意义(P>0.05);两组治疗后ASIA、BBS、TCT、FAC评分比治疗前提高,且治疗组高于对照组(P<0.05)。结论基于VR的康复治疗能改善不完全脊髓损伤患者的下肢功能,提高其平衡能力、躯干控制能力和步行能力。

LEGAN:一种新的暗弱光照图像增强算法

针对暗弱光照图像所存在的亮度、对比度、信噪比低,以及噪声污染大等问题,提出了一种新的暗弱光照图像增强算法LEGAN。该算法将图像输入至所提伽马曲线估计网络求得包含伽马参数的特征图,再经过LEB模块增强亮度,并通过级联LEB的方式迭代增强结果。采用基于PatchGAN的全局-局部判别器结构来提高图像分辨率和恢复图像细节。通过引入感知损失来限制真实标签和输出结果之间的差距,利用照明平滑度损失保持相邻像素之间的单调性关系,同时结合空间一致性损失来增强图像的空间相关性。实验结果表明,相比于现今大多数主流增强算法,该算法的细节还原度相对较高,且能有效避免增强后的图像出现局部亮度不佳等问题。

股骨近端防旋髓内钉与Gamma钉内固定治疗股骨粗隆间骨折的疗效比较

目的:探究股骨近端防旋髓内钉(PFNA)与Gamma钉内固定治疗股骨粗隆间骨折的疗效比较。方法:选取2021年5月—2023年5月于广州市南沙区第二人民医院收治的股骨粗隆间骨折患者60例为研究对象,随机分为PFNA组与Gamma组,各30例。Gamma组患者应用Gamma钉内固定,PFNA组患者应用PFNA内固定。比较两组围术期指标(手术时间、术中出血量、下地负重时间、骨折愈合时间)、疗效优良率、髋关节功能Harris评分及术后并发症情况。结果:PFNA组手术时间、骨折愈合时间均短于Gamma组,术中出血量少于Gamma组,下地负重时间长于Gamma组,差异有统计学意义(P<0.001);PFNA组疗效优良率高于Gamma组,差异有统计学意义(P=0.044);治疗后,两组Harris评分均升高,PFNA组高于Gamma组,差异有统计学意义(P<0.001);PFNA组术后并发症发生率低于Gamma组,差异有统计学意义(P=0.023)。结论:股骨粗隆间骨折通过PFNA内固定治疗的疗效优于Gamma钉内固定,且术后并发症轻微,髋关节功能恢复佳,利于缩短骨折愈合时间,值得推广及深入探究。

余元公式的一种直接证法

余元公式是数学分析中的一个重要公式,在积分学中有许多应用,但其证明往往繁琐复杂.本文通过直接计算有理函数积分证明了余元公式,适宜于数学分析课程中讲解,以供广大师生们参考.

考虑个体差异的车轮二元相关退化可靠性分析

由于动车组车轮受加工装配及工况载荷等不确定因素的影响,车轮退化过程复杂,存在显著的个体差异及多个性能退化特征量,且多个退化特征量间相互耦合,仅考虑单个性能特征量难以全面反映其退化过程。因此,以轮缘和轮径作为车轮退化特征量,通过随机化尺度参数表征车轮个体差异,采用Gamma过程和Copula函数建立二元相关退化模型,并根据赤池信息准则(Akaike Information Criterion, AIC)筛选Copula函数,得到可靠度解析式。基于某型动车组车轮实测磨耗数据,对车轮进行可靠性分析,同时通过车辆动力学模型进行仿真验证。结果显示:考虑二元相关时的可靠性结果比仅考虑一元退化更贴近车辆实际运行情况;根据动力学仿真结果体现了考虑个体差异的必要性,表明所提模型能够更准确地表征车轮退化过程,可为可靠性分析以及维修决策优化提供理论支撑。

针灸结合三氧直肠灌注对不完全性脊髓损伤小便障碍的疗效研究

目的:观察针灸结合三氧直肠灌注对不完全性脊髓损伤小便障碍患者逼尿肌损伤修复及膀胱功能、应激状态和尿动力学的影响。方法:选择2022年7月—2023年7月于广西壮族自治区江滨医院治疗的86例不完全性脊髓损伤小便障碍患者,按照随机数字表法分为两组,三氧直肠灌注组43例,基础治疗的同时给予患者三氧直肠灌注治疗;针灸联合组43例,三氧直肠灌注组治疗基础上给予患者针灸治疗。比较两组临床疗效,治疗前、后评价中医证候,记录两组患者每次排尿量、膀胱安全容量,给予患者国际下尿路功能症状(LUTS)、尿失禁生活质量问卷(I-QOL)评价,测定膀胱顺应性、充盈期膀胱压力、最大尿流速时逼尿肌压力,检测热休克蛋白70(HSP70)、活性氧(ROS)、超氧化物歧化酶(SOD)水平。结果:针灸联合组总有效率较三氧直肠灌注组高(P<0.05);中医证候评分较三氧直肠灌注组降低(P<0.01);膀胱安全容量、每次排尿量大于三氧直肠灌注组(P<0.01),I-QOL评分高于三氧直肠灌注组(P<0.01),LUTS评分少于三氧直肠灌注组(P<0.01);最大尿流速时逼尿肌压力、充盈期膀胱压力低于三氧直肠灌注组(P<0.05),膀胱顺应性高于三氧直肠灌注组(P<0.01);HSP70、ROS水平低于三氧直肠灌注组(P<0.05),SOD水平高于三氧直肠灌注组(P<0.01)。结论:针灸结合三氧直肠灌注治疗不完全性脊髓损伤小便障碍患者,可抑制氧化应激,促进修复受损逼尿肌,改善尿动力学,提升膀胱功能、排尿功能、临床疗效及生活质量。

钢梁腐蚀相关性对钢-混组合梁桥体系可靠度的影响

服役环境中钢主梁的腐蚀本质上是一个随机过程,腐蚀深度随机变量既有时变性亦有空间性。现有测量方法只能获得单根钢梁腐蚀深度数据,尚不能明确结构体系腐蚀深度变量的联合分布模式,可能导致腐蚀结构体系可靠度计算模型失真。以某钢-混凝土组合梁桥为研究对象,首先建立了钢主梁腐蚀深度增长Gamma随机过程模型,并利用钢梁腐蚀深度实测数据对模型进行了验证;然后采用Kendall秩相关系数量化表征主梁腐蚀深度相关性,推导了腐蚀钢梁的时变抗力计算公式;最后基于Copula函数提出了考虑主梁腐蚀相关性的梁桥体系失效概率计算方法,对比研究了钢梁腐蚀相关性对钢-混组合简支梁桥体系可靠度的影响。研究结果表明:桥梁运营前期腐蚀相关性对梁桥受力性能影响较小,在运营中后期,中高程度的腐蚀相关性将会对梁桥体系的可靠度影响较大。研究提出了钢梁腐蚀空间相关性量化方法,获得了更精确的钢-混组合梁桥体系可靠度计算方法,可为组合梁桥体系的时变可靠度评定提供参考。