化学变化中质量不守恒

根据相对论中的质能关系E=mc2,如果一个物体以辐射形式放出能量,那么它的质量就要减少,由于在化学变化中将伴随着能量的释放和吸收,经典化学中的质量守恒定律和相对论中的质能关系是相矛盾的;质能关系的存在表明在化学变化中质量不是守恒的,实际上是质能的守恒.

一维河网物质输移模型质量不守恒问题及其修正

质量守恒是数学模型的基本要求。然而,国内一些较为广泛应用的一维河网物质输移模型却存在明显的质量不守恒问题。本文在分析该问题产生原因的基础上,对原模型提出了修正,进而建立满足质量守恒的一维河网物质输移模型,并对修正后的模型进行质量守恒检验。研究结果表明,原模型产生质量不守恒问题的根本原因在于模型的求解变量(物质浓度)定义于河段断面上,而非河段控制体中心,这一不当的设置导致模型在水流转向或者顺逆流的情况下出现质量不守恒的现象;质量等恒测试结果显示,修正后的模型成功解决了原模型质量不守恒的问题,其在计算过程中能够保证质量守恒。

A numerical simulation of seepage structure surface and its feasibility

According to Cubic law and incompressible fluid law of mass conservation, the seepage character of the fracture surface was simulated with the simulation method of fractal theory and random Brown function. Furthermore, the permeability coefficient of the single fracture was obtained. In order to test the stability of the method, 500 simulations were conducted on each different fractal dimension. The simulated permeability coefficient was analyzed in probability density distribution and probability cumulative distribution statistics. Statistics showed that the discrete degree of the permeability coefficient increases with the increase of the fractal dimension. And the calculation result has better stability when the fractal dimension value is relatively small. According to the Bayes theory, the characteristic index of the permeability coefficient on fractal dimension P（Dfi｜ Ri） is established. The index, P（Dfi｜ Ri）, shows that when the simulated permeability coefficient is relatively large, it can clearly represent the fractal dimension of the structure surface, the probability is 82%. The calculated results of the characteristic index verify the feasibility of the method.

Non-Noether Conserved Quantity for Relativistic Nonholonomic System with Variable Mass

Using form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differential equations of motion of the system are established. The definition and criterion of the form invariance of the system under infinitesimal transformations are studied. The necessary and sufficient. condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a non-Noether. conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

Form Invariance and Conserved Quantity for Non-holonomic Systems with Variable Mass and Unilateral Constraints

The paper studies the form invariance and a type of non-Noether conserved quantity called Mei conserved quantity for non-holonomic systems with variable mass and unilateral constraints. Acoording to the invariance of the form of differential equations of motion under infinitesimal transformations, this paper gives the definition and criterion of the form invariance for non-holonomic systems with variable mass and unilateral constraints. The condition under which a form invariance can lead to Mei conservation quantity and the form of the conservation quantity are deduced. An example is given to illustrate the application of the results.

宫颈癌放疗分次间剂量分布映射方法的现状与难点

目的总结宫颈癌联合治疗中远距离外照射放疗(EBRT)与近距离放疗(BT)联合放疗分次间剂量分布映射方法的现状与难点,特别侧重于基于图像配准的方法、剂量与图像配准的区别及关注点。方法检索PubMed、中国知网及万方期刊全文数据库建库至2023-09-20收录的相关文献,中文关键词为“宫颈癌、剂量分布映射、剂量叠加、图像配准”,英文关键词为“cervical cancer、dose distribution mapping、dose accumulation、image registration”。纳入标准:(1)宫颈癌剂量叠加;(2)宫颈癌分次间剂量分布映射;(3)基于图像配准的宫颈癌剂量叠加。排除标准:(1)低质量文献;(2)内容相似或重复。最终共纳入文献51篇。结果在宫颈癌治疗中,EBRT与BT联合的分次间剂量分布映射存在挑战。治疗过程中由于多器官的复杂厘米级位移和形变,可能导致分次间剂量递送误差。将不同放疗阶段的剂量分布映射传递至参考阶段可能引起误差放大效应,增加了精准放疗的难度。结论准确剂量分布映射方法是精确评估累积生物等效剂量的前提条件,直接利用图像配准将组织/肿瘤剂量分布图映射至参考阶段存在局限性,建议深入研究联合放疗分次间剂量分布映射方法。