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关键词： Mathematics  

ISBN: (数字)9789811250507 ISBN: (纸本)9789811250491

摘要： This volume presents a pedagogical review of the functional distribution of anomalous and nonergodic diffusion and its numerical simulations, starting from the studied stochastic processes to the deterministic partial differential equations governing the probability density function of the functionals. Since the remarkable theory of Brownian motion was proposed by Einstein in 1905, it had a sustained and broad impact on diverse fields, such as physics, chemistry, biology, economics, and mathematics. The functionals of Brownian motion are later widely attractive for their extensive applications. It was Kac, who firstly realized the statistical properties of these functionals can be studied by using Feynman's path *** recent decades, anomalous and nonergodic diffusions which are non-Brownian become topical issues, such as fractional Brownian motion, Lévy process, Lévy walk, among others. This volume examines the statistical properties of the non-Brownian functionals, derives the governing equations of their distributions, and shows some algorithms for solving these equations numerically.

关键词： 高考导数题   零点不可求   求解对策  

摘要： 导函数零点不可求问题常出现在导数压轴题中，这类问题综合性强，方法灵活，是考生的拦路虎.但也不是无法逾越，可以通过猜想验根，虚拟设根等手段巧妙求解，本文结合实例加以说明.

关键词： 三角函数   导数   解题策略  

摘要： 本文通过一道以三角函数为背景的导数题的分析，给出洛必达法则、泰勒展开、领域分析等高观点下的解题策略，帮助学生突破思维的瓶颈，拓宽数学的视野，“既见树木又见森林”,从而提升学生的数学核心素养.

关键词： Herpes simplex encephalitis   herpes human virus 6 encephalitis   Japanese encephalitis   neurosyphilis   autoimmune encephalitis   gliomatosis cerebri   status epilepticus   hippocampal sclerosis   ischemic stroke  

摘要： T2/FLAIR hyperintensity in the mesial temporal lobe is the most common MR finding of herpes simplex encephalitis, but may be observed in other infectious and non-infectious diseases. The former includes herpes human virus 6 encephalitis, Japanese encephalitis, and neurosyphilis, and the latter autoimmune encephalitis, gliomatosis cerebri, bilateral or paradoxical posterior cerebral artery infarction, status epilepticus, and hippocampal sclerosis. Thus, T2/FLAIR hyperintensity in the mesial temporal lobe is not a disease-specific magnetic resonance imaging finding, and these conditions must be differentiated to ensure proper treatment. We review diseases that present with T2/FLAIR hyperintensity in the mesial temporal lobe and provide a helpful flow chart based on clinical and radiologic features.

关键词： Anagliptin   Sitagliptin   Dipeptidyl peptidase-4 inhibitor   Proprotein convertase subtilisin/kexin  

摘要： Aim: Proprotein convertase subtilisin/kexin type 9 (PCSK9) degrades the low-density lipoprotein (LDL) receptor, leading to hypercholesterolemia and cardiovascular risk. Treatment with a statin leads to a compensatory increase in circulating PCSK9 level. Anagliptin, a dipeptidyl peptidase-4 (DPP-4) inhibitor, was shown to decrease LDL cholesterol (LDL-C) levels to a greater extent than that by sitagliptin, another DPP-4 inhibitor, in the Randomized Evaluation of Anagliptin versus Sitagliptin On low-density lipoproteiN cholesterol in diabetes (REASON) trial. We investigated PCSK9 concentration in type 2 diabetes mellitus (T2DM) and the impact of treatment with anagliptin or sitagliptin on PCSK9 level as a sub-analysis of the REASON trial. Methods: PCSK9 concentration was measured at baseline and after 52 weeks of treatment with anagliptin (n=122) or sitagliptin (n=128) in patients with T2DM who were receiving statin therapy. All of the included patients had been treated with a DPP-4 inhibitor prior to randomization. Results: Baseline PCSK9 level was positively, but not significantly, correlated with LDL-C and was independently associated with platelet count and level of triglycerides. Concomitant with reduction of LDL-C, but not hemoglobin A1c (HbA1c), by anagliptin, PCSK9 level was significantly increased by treatment with sitagliptin (218 +/- 98 vs. 242 +/- 115 ng/mL, P=0.01), but not anagliptin (233 +/- 97 vs. 250 +/- 106 ng/mL, P=0.07). Conclusions: PCSK9 level is independently associated with platelet count and level of triglycerides, but not LDL-C, in patients with T2DM. Anagliptin reduces LDL-C level independent of HbA1c control in patients with T2DM who are on statin therapy possibly by suppressing excess statin-mediated PCSK9 induction and subsequent degradation of the LDL receptor.