Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits...Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.展开更多
Prostate cancer is the most commonly diagnosed cancer and the second leading cause of cancer mortality in men in the Western World. In the initial stages, prostate cancer is dependent on androgens for growth which is ...Prostate cancer is the most commonly diagnosed cancer and the second leading cause of cancer mortality in men in the Western World. In the initial stages, prostate cancer is dependent on androgens for growth which is the basis for androgen ablation therapy. The effects of androgens are mediated by the Androgen Receptor (AR). Therefore, studies focus on the identification of AR-regulated genes that are also highly expressed in the prostate. STAMP family genes STAMP1/STEAP2 and STAMP2/STEAP4 have only expressed in androgen receptor-positive cells, the role of AR in STAMP family gene expression is an important question. STEAP (Six Transmembrane Epithelial Antigen of Prostate) is the first characterized prostate of enriched six transmembrane gene, expressed in metastatic prostate cancer samples, it is tempting to speculate that STAMP/STEAP family genes may be involved in similar functions with a role for both the normal biology and pathophysiology of the prostate. Using siRNA technology in LNCaP cells expressing STAMP genes per se, an apoptosis panel including pro-apoptotic and/or apoptotic molecules was assayed by RT-PCR, By this research project, prostate-specific STAMP gene family and its regulatory effects on the p53- and caspase-related pathways were characterized.展开更多
肝细胞癌(hepatocellular carcinoma,HCC)是最常见的一种原发性肝癌,可由多种病因引起,当前在我国乙型肝炎病毒(hepatitis B virus,HBV)感染是最重要的原因。HCC的发生、发展过程受到多种细胞因子以及细胞内多种信号通路网络的调控。近...肝细胞癌(hepatocellular carcinoma,HCC)是最常见的一种原发性肝癌,可由多种病因引起,当前在我国乙型肝炎病毒(hepatitis B virus,HBV)感染是最重要的原因。HCC的发生、发展过程受到多种细胞因子以及细胞内多种信号通路网络的调控。近年来,临床与基础研究均表明铁死亡(ferroptosis)在HCC的发生、发展中扮演着重要的角色。铁死亡可以通过调节细胞内铁离子水平以及脂质过氧化程度等,影响肝脏疾病的发展进程。许多学者认为,铁死亡可以作为HCC疾病诊断、预防和治疗靶标。该文综述了铁死亡在防治HCC中的作用以及相关研究进展。展开更多
文摘Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.
文摘Prostate cancer is the most commonly diagnosed cancer and the second leading cause of cancer mortality in men in the Western World. In the initial stages, prostate cancer is dependent on androgens for growth which is the basis for androgen ablation therapy. The effects of androgens are mediated by the Androgen Receptor (AR). Therefore, studies focus on the identification of AR-regulated genes that are also highly expressed in the prostate. STAMP family genes STAMP1/STEAP2 and STAMP2/STEAP4 have only expressed in androgen receptor-positive cells, the role of AR in STAMP family gene expression is an important question. STEAP (Six Transmembrane Epithelial Antigen of Prostate) is the first characterized prostate of enriched six transmembrane gene, expressed in metastatic prostate cancer samples, it is tempting to speculate that STAMP/STEAP family genes may be involved in similar functions with a role for both the normal biology and pathophysiology of the prostate. Using siRNA technology in LNCaP cells expressing STAMP genes per se, an apoptosis panel including pro-apoptotic and/or apoptotic molecules was assayed by RT-PCR, By this research project, prostate-specific STAMP gene family and its regulatory effects on the p53- and caspase-related pathways were characterized.
文摘肝细胞癌(hepatocellular carcinoma,HCC)是最常见的一种原发性肝癌,可由多种病因引起,当前在我国乙型肝炎病毒(hepatitis B virus,HBV)感染是最重要的原因。HCC的发生、发展过程受到多种细胞因子以及细胞内多种信号通路网络的调控。近年来,临床与基础研究均表明铁死亡(ferroptosis)在HCC的发生、发展中扮演着重要的角色。铁死亡可以通过调节细胞内铁离子水平以及脂质过氧化程度等,影响肝脏疾病的发展进程。许多学者认为,铁死亡可以作为HCC疾病诊断、预防和治疗靶标。该文综述了铁死亡在防治HCC中的作用以及相关研究进展。
