Polysurfacic tori or kideas are three-dimensional objects formed by rotating a regular polygon around a central axis. These toric shapes are referred to as “polysurfacic” because their characteristics, such as the n...Polysurfacic tori or kideas are three-dimensional objects formed by rotating a regular polygon around a central axis. These toric shapes are referred to as “polysurfacic” because their characteristics, such as the number of sides or surfaces separated by edges, can vary in a non-trivial manner depending on the degree of twisting during the revolution. We use the term “Kideas” to specifically denote these polysurfacic tori, and we represent the number of sides (referred to as “facets”) of the original polygon followed by a point, while the number of facets from which the torus is twisted during its revolution is indicated. We then explore the use of concave regular polygons to generate Kideas. We finally give acceleration for the algorithm for calculating the set of prime numbers.展开更多
设 M 是连通的、可定向的、完备的3维 C~∞黎曼流形,C:M→S^4(1)是从 M 列4维单位球面 S^4(1)中的等距浸入.主曲率 h_1,h_2,h_3满足 h_1=h_2=R(常数).本文证明了:浸入或者是全脐的,或者是无脐点的;若浸入是全脐的.或无脐点且 h_3为常数,...设 M 是连通的、可定向的、完备的3维 C~∞黎曼流形,C:M→S^4(1)是从 M 列4维单位球面 S^4(1)中的等距浸入.主曲率 h_1,h_2,h_3满足 h_1=h_2=R(常数).本文证明了:浸入或者是全脐的,或者是无脐点的;若浸入是全脐的.或无脐点且 h_3为常数,则 M 可完全确定:若 h_3不是常数,则 M 微分同胚于 E^4中环准超环面.展开更多
MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2] and references cit...MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2] and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:展开更多
In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying Rssmann's non-degeneracy condition when symplectic integrators are applied to them. Meanwhile, we give an esti...In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying Rssmann's non-degeneracy condition when symplectic integrators are applied to them. Meanwhile, we give an estimate of the measure of the set occupied by the invariant tori in the phase space. On an invariant torus,numerical solutions are quasi-periodic with a diophantine frequency vector of time step size dependence. These results generalize Shang's previous ones(1999, 2000), where the non-degeneracy condition is assumed in the sense of Kolmogorov.展开更多
目的 探讨奥曲肽联合硫酸奈替米星对化脓性阑尾炎术后感染的预防作用及对患者辅助性T细胞17（helper T cell17,Th17）/调节性T细胞（regulatory T cells,Treg）失衡的影响。方法 选取2014年8月~2016年5月浙江象山中医医院收治的急性化...目的 探讨奥曲肽联合硫酸奈替米星对化脓性阑尾炎术后感染的预防作用及对患者辅助性T细胞17（helper T cell17,Th17）/调节性T细胞（regulatory T cells,Treg）失衡的影响。方法 选取2014年8月~2016年5月浙江象山中医医院收治的急性化脓性阑尾炎患者148例,随机分为观察组（n=74）和对照组（n=74）。2组均行腹腔镜阑尾炎切除术,术后对照组采用硫酸奈替米星联合奥硝唑抗感染,观察组同时加用醋酸奥曲肽皮下注射。检测治疗前后血清白细胞介素4（interleukin 4,IL-4）、IL-6、IL-10、IL-17、IL-23、转化生长因子β（transforming growth factorβ,TGF-β）及干扰素γ（interferonγ,IFN-γ）水平;检测Th17、Treg细胞比例及相关转录因子表达水平,分析Th17/Treg变化。结果 治疗后2组患者IL-4、IL-6、IL-10、IL-17、TGF-β均降低,IFN-γ升高（P〈0.05）,观察组各项指标改善情况优于对照组（P〈0.05）;治疗后2组患者Th17、Treg细胞比例及相关转录因子孤独核儿受体γt（orphan nuclear receptorγt,RORγt）、叉头/翼状螺旋转录因子（Forkhead box protein P3,Fox P3）表达水平降低,Th17/Treg降低（P〈0.01）,观察组各项指标低于对照组;2组患者术后切口感染、腹腔感染等不良反应发生率比较差异无统计学意义。结论 奥曲肽联合硫酸奈替米星可预防化脓性阑尾炎患者术后感染,调节Th17/Treg失衡,恢复免疫功能,且无明显不良反应。展开更多
文摘Polysurfacic tori or kideas are three-dimensional objects formed by rotating a regular polygon around a central axis. These toric shapes are referred to as “polysurfacic” because their characteristics, such as the number of sides or surfaces separated by edges, can vary in a non-trivial manner depending on the degree of twisting during the revolution. We use the term “Kideas” to specifically denote these polysurfacic tori, and we represent the number of sides (referred to as “facets”) of the original polygon followed by a point, while the number of facets from which the torus is twisted during its revolution is indicated. We then explore the use of concave regular polygons to generate Kideas. We finally give acceleration for the algorithm for calculating the set of prime numbers.
文摘设 M 是连通的、可定向的、完备的3维 C~∞黎曼流形,C:M→S^4(1)是从 M 列4维单位球面 S^4(1)中的等距浸入.主曲率 h_1,h_2,h_3满足 h_1=h_2=R(常数).本文证明了:浸入或者是全脐的,或者是无脐点的;若浸入是全脐的.或无脐点且 h_3为常数,则 M 可完全确定:若 h_3不是常数,则 M 微分同胚于 E^4中环准超环面.
文摘MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2] and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:
基金supported by National Natural Science Foundation of China(Grant No.11671392)
文摘In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying Rssmann's non-degeneracy condition when symplectic integrators are applied to them. Meanwhile, we give an estimate of the measure of the set occupied by the invariant tori in the phase space. On an invariant torus,numerical solutions are quasi-periodic with a diophantine frequency vector of time step size dependence. These results generalize Shang's previous ones(1999, 2000), where the non-degeneracy condition is assumed in the sense of Kolmogorov.
