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Singular integral on bounded strictly pseudoconvex domain

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Applied Mathematics(A Journal of Chinese Universities) 2008年第3期23卷 273-278页

作者： gong ding-dong Dept.of Math.,Zhejiang Univ.,Hangzhou 310027,China Dept.of Math.Sci.,Zhejiang Sci-Tech Univ.,Hangzhou 310018,China. Dept. of Math. Zhejiang Univ. Hangzhou China Dept. of Math. Sci. Zhejiang Sci-Tech Univ. Hangzhou China

Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well.

关键词： strictly pseudoconvex domain singulax integral composition formula singular integral equation

广义上半空间的Cauchy-Fantappié型奇异积分

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厦门大学学报（自然科学版） 2012年第5期51卷 813-817页

作者：龚定东浙江理工大学数学科学系浙江杭州310018

Cn(n>1)中的广义上半空间是一特殊的无界域.本文利用广义上半空间上的全纯的Cauchy-Fantappié核研究了Cauchy型积分的边界行为,得到了奇异积分的Cauchy主值的存在性.此处Cauchy型积分的密度函数是一类特殊的Hlder函数.进一步研究了Ca... 详细信息

Cn(n>1)中的广义上半空间是一特殊的无界域.本文利用广义上半空间上的全纯的Cauchy-Fantappié核研究了Cauchy型积分的边界行为,得到了奇异积分的Cauchy主值的存在性.此处Cauchy型积分的密度函数是一类特殊的Hlder函数.进一步研究了Cauchy型积分的边界极限值,得到了Plemelj公式.广义上半空间中Cauchy型积分在无穷远点处的边界行为的处理是无界域情形特有的.

关键词：广义上半空间 Cauchy-Fantappié型核奇异积分 Plemelj公式

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一类Hopf流形上的强可滤丛

厦门大学学报（自然科学版） 2009年第4期48卷 470-473页

作者：甘宁龚定东集美大学理学院福建厦门361021 浙江理工大学数学科学系浙江杭州310018

Hopf流形是一类简单但却很重要的非代数流形,其上的全纯向量丛的性质是复几何研究的一个热点.研究了一类Hopf流形上强可滤丛的性质,得到了其上同调群的计算公式,证明了其第i(i>1)个陈类都为0,最后证明了一类具有交换基本群的Hopf曲面上... 详细信息

Hopf流形是一类简单但却很重要的非代数流形,其上的全纯向量丛的性质是复几何研究的一个热点.研究了一类Hopf流形上强可滤丛的性质,得到了其上同调群的计算公式,证明了其第i(i>1)个陈类都为0,最后证明了一类具有交换基本群的Hopf曲面上的强可滤丛都为单丛.这些结果可应用于Hopf流形上连续向量丛的全纯结构存在性问题的研究.

关键词： Hopf流形全纯向量丛强可滤结构陈类

Direct Solutions of Some Singular Integral Equations on the Building Domain of Complex Biballs

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Chinese Quarterly Journal of Mathematics 2014年第1期29卷 39-44页

作者： gong ding-dong GUO Yu-qin Department of Mathematical Sciences Zhejiang Sci-Tech University Hangzhou 310018 China Library of Zhejiang Sci-Tech University Hangzhou 310018 China

By means of the method of solid angle coefficients and the permutation formula on the building domain of complex biballs,direct solutions of some singular integral equations with variable coefficients are discussed an... 详细信息

关键词： the building domain of complex biballs solid angle coefficients singular integral equations with variable coefficients explicit solutions

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复双球垒域上奇异积分的Cauchy主值

数学的实践与认识 2012年第1期24卷 165-169页

作者：龚定东郭玉琴浙江理工大学数学科学系浙江杭州310018 浙江理工大学图书馆浙江杭州310018

利用一种新的挖法定义复双球垒域上的立体角系数,得到奇异积分的Cauchy主值的存在性.推广了复超球上的奇异积分理论.

关键词：复双球垒域立体角系数奇异积分的Cauchy主值

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Painleve定理的拓广

浙江理工大学学报（自然科学版） 2009年第4期26卷 638-640页

作者：龚定东浙江理工大学理学院杭州310018

R2中的Painleve定理在求解方程的边值问题中有十分重要的作用。此定理对多复变数中的Cauchy型积分的边界行为的研究也起关键作用。将R2中的Painleve定理推广到Cn(n>1)中,得到复的Painleve定理。并简述其在多复变数奇异积分研究中的应用。

关键词： Painleve定理多复变数奇异积分

Correlation analyse between thyroid hormone levels and severity of schizophrenia symptoms

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World Journal of Psychiatry 2025年第1期15卷 63-71页

作者： Qi-Hui Jiang Wei-dong gong Department of Endocrinology and Metabolism Hengyang Central HospitalHengyang 421000Hunan ProvinceChina Breast Tumor Surgical Outpatient Hengyang Central HospitalHengyang 421000Hunan ProvinceChina

BACKGROUND The imbalance of hormone levels in the body is closely related to the occurrence and progression of schizophrenia,especially thyroid *** To study the relationship between triiodothyronine(T3),thyroxine(T4),free T3(FT3),free T4(FT4),thyroid stimulating hormone(TSH)and *** In this study,100 schizophrenia patients were selected from our hospital between April 2022 and April *** clinical data were analyzed *** on the Positive and Negative Syndrome Scale(PANSS)score,patients were divided into mild(1-3 points,n=39),moderate(4 points,n=45),and severe groups(5-7 points,n=16).Additionally,55 healthy individuals served as a control *** blood samples were collected to measure T3,T4,FT3,FT4,TSH,and cortisol concentrations,analyzing their relationship with PANSS *** The serum levels of T3,FT3,FT4,TSH and cortisol in the schizophrenia group were lower than those in the control group(P<0.05).With the increase of the severity of the disease,the concentrations of T3 and T4 decreased,while the con-centrations of TSH and cortisol increased(P<0.05).The concentrations of TSH and cortisol were positively correlated with the PANSS score,while T3 and T4 were negatively correlated with the PANSS score(P<0.05).The receiver ope-rating characteristic curve results showed that T3,T4,TSH,and cortisol had good efficacy in the diagnosis of *** results showed that decreased T3 level,decreased T4 level,decreased TSH level and increased cortisol level may be independent risk factors for *** Thyroid hormone levels are associated with the severity of schizophrenia symptoms,which can provide new solutions for the diagnosis and treatment of schizophrenia.

关键词： Thyroid hormone Schizophrenia Symptom severity Positive and Negative Syndrome Scale score Cortisol

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正则线性凸区域上可微分函数的积分表示

牡丹江师范学院学报（自然科学版） 2008年第4期34卷 5-6页

作者：龚定东杨邦明浙江理工大学理学院

利用一种改进的方法建立线性凸区域上的无穷次可微分函数的积分表达式.

关键词：线性凸区域函数C^∞ 积分表示

Potassium and calcium channels in different nerve cells act as therapeutic targets in neurological disorders

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Neural Regeneration Research 2025年第5期20卷 1258-1276页

作者： Qing Qiu Mengting Yang Danfeng gong Haiying Liang Tingting Chen Department of Pharmacology School of PharmacyNantong UniversityNantongJiangsu ProvinceChina Jiangsu Province Key Laboratory of Inflammation and Molecular Drug Target NantongJiangsu ProvinceChina Department of Pharmacy Longyan First Affiliated Hospital of Fujian Medical UniversityLongyanFujian ProvinceChina

The central nervous system, information integration center of the body, is mainly composed of neurons and glial cells. The neuron is one of the most basic and important structural and functional units of the central nervous system, with sensory stimulation and excitation conduction functions. Astrocytes and microglia belong to the glial cell family, which is the main source of cytokines and represents the main defense system of the central nervous system. Nerve cells undergo neurotransmission or gliotransmission, which regulates neuronal activity via the ion channels, receptors, or transporters expressed on nerve cell membranes. Ion channels, composed of large transmembrane proteins, play crucial roles in maintaining nerve cell homeostasis. These channels are also important for control of the membrane potential and in the secretion of neurotransmitters. A variety of cellular functions and life activities, including functional regulation of the central nervous system, the generation and conduction of nerve excitation, the occurrence of receptor potential, heart pulsation, smooth muscle peristalsis, skeletal muscle contraction, and hormone secretion, are closely related to ion channels associated with passive transmembrane transport. Two types of ion channels in the central nervous system, potassium channels and calcium channels, are closely related to various neurological disorders, including Alzheimer's disease, Parkinson's disease, and epilepsy. Accordingly, various drugs that can affect these ion channels have been explored deeply to provide new directions for the treatment of these neurological disorders. In this review, we focus on the functions of potassium and calcium ion channels in different nerve cells and their involvement in neurological disorders such as Parkinson's disease, Alzheimer's disease, depression, epilepsy, autism, and rare disorders. We also describe several clinical drugs that target potassium or calcium channels in nerve cells and could be u

关键词： astrocytes calcium channels central nervous system extracellular ion concentration microglia neurological disorders neurons potassium channels