On the Change Rule of 3x + 1 Problem

This article introduces a change rule of 3x + 1 problem (Collatz conjecture), it’s named LiKe’s Rule. It’s a map of 3x + 1 problem, and details the path of each step of the change: For any positive integer, change by the Collatz conjecture. 1) This positive integer will change to an odd number;2) The odd number must change to a number of LiKe’s second sequence {3n – 1| n ∈ Z+};3) Then this 3n - 1 will change to a smaller 3n – 1 and gradually decrease to 8 (that is 32 - 1) then back to 1 in the end. If we can determine each step, the Collatz conjecture will be true. This is certainly more valuable than 2n (it might even explain 2n). And to illustrate the importance of this rule, introduced some important funny corollaries related to it.

Design of New Thiadiazole Derivatives with Improved Antidiabetic Activity

Diabetes is a serious, long-term (or chronic) disease that occurs when a person’s blood sugar levels are high because their body cannot produce enough insulin, or does not produce enough insulin or that it cannot effectively use the insulin it produces. According to the literature, this disease has several causes, but certain types of diabetes such as type 2 diabetes are most closely linked to a metabolic disorder due to abdominal obesity. Thus, the number of individuals with type 2 diabetes is increasing. It is with this in mind that we work to improve human health. The aim of this study is to design new derivatives of 1,3,4-thiadiazole with improved antidiabetic activity by the mathematical model of multiple linear regression (MLR) established previously. The analysis of the effect on the substituents influencing the antidiabetic activity, fourteen (14) new molecules coded CDTH were generated and presenting values of the potential of inhibitory concentration higher than that of the base compound (pIC50 = 2.526). But thirteen (13) of these new compounds belong to the domain of applicability of the MLR model established previously. In addition, the thermodynamic quantities of formation formed at 298K have been calculated. Lipinski’s rule and pharmacokinetic properties proved that five (5) (TH4, TH9, TH10, TH13 and TH14) new molecules can be used as diabetes medicine.

High Accuracy Arithmetic Average Discretization for Non-Linear Two Point Boundary Value Problems with a Source Function in Integral Form

In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.

药物经济学评价中Markov模型的周期内校正方法探讨

目的:为减少药物经济学研究中Markov模型的误差提供参考。方法:参考国外相关文献,解释Markov模型误差产生的原理,并介绍常用的半周期法、梯形法、Simpson’s 1/3法、Simpson’s 3/8法、生命表法及其在Excel、TreeAge软件中的实现方法。结果与结论:Markov模型因离散化过程而产生误差,使用周期内校正方法可校正这一误差。半周期法是最常用的校正方法,是通过增加第1周期一半的结果并减去最后1周期一半的结果进行校正;梯形法的校正是以区间首尾端点值的均值代表该区间,以直角梯形的面积作为累计的结果;Simpson’s 1/3法和Simpson’s 3/8法则在梯形法的基础上在区间中插值并以插值点所在的连续曲线代表整个曲线;寿命表法的校正中,生存人年数为该年龄组的组距与该年龄组和下一年龄组尚存人数的均值的乘积,生存人年数则为各年龄组生存总人年数的总和。在Excel中,可根据方法原理设置函数来实现校正;而在TreeAge软件中,可通过设置Init Rwd、Incr Rwd、Final Rwd的函数表达式来实现校正。在使用Markov模型进行药物经济学评价时,对于周期校正方法的选择,若从建模的易用性、适用情形的广泛性等角度出发,建议使用梯形法;从结果的精确性角度出发,则建议使用Simpson’s 1/3法,以提高Markov模型的准确度。