Dynamically adaptive tree grid modeling for simulation and visualization of rainwater overland flow

Modeling and visualization of a rainwater overland flow is an important tool for a risk assessment, preparation, evacuation planning, and real‐time forecasting of flood warning. The objective of this research is to develop a numerical software to visualize the rainwater overland flow based on a finite volume method for shallow water equations and in combination with the dynamically adaptive tree grid technique and the dynamic domain‐defining method. The obtained simulations for several experiments were tested and compared with results in literature, both theoretical and experimental results. The comparisons with non‐adaptive grids show that the developed algorithm for simulation is very efficient and has a potential for practical usages, in terms of computational times and accuracy. Copyright © 2015 John Wiley & Sons, Ltd.     

关于避免多个不可实施因子水平组合的正交表构造

在正交表的实际应用中，有时会发生某些因子的水平组合无法进行试验的情形，使得现有的正交表不适用。Ｃｈｅｎｇ和Ｌｉ讨论了这种情况下的正交表的构造问题，并给出了关于避免两个不可实施的因子水平组合的正交表的构造方法。     

Responsibility for proving and defining in abstract algebra class

There is considerable variety in inquiry-oriented instruction, but what is common is that students assume roles in mathematical activity that in a traditional, lecture-based class are either assumed by the teacher (or text) or are not visible at all in traditional math classrooms. This paper is a case study of the teaching of an inquiry-based undergraduate abstract algebra course. In particular, gives a theoretical account of the defining and proving processes. The study examines the intellectual responsibility for the processes of defining and proving that the professor devolved to the students. While the professor wanted the students to engage in all aspects of defining and proving, he was only successful at devolving responsibility for certain aspects and much more successful at devolving responsibility for proving than conjecturing or defining. This study suggests that even a well-intentioned instructor may not be able to devolve responsibility to students for some aspects of mathematical practice without using a research-based curriculum or further professional development.     

不充当自同构群的有限群

设ｐ为奇素数，本文将用一些新的技巧来证明，当Ｐ是阶小于Ｐ＾１１的交换Ｐ－群时，自同构群方程Ａｕｔ（Ｘ）＝Ｐ无解。这个结果使ＭａｃｈＨａｌｅ在１９８３年的工作得到了突破，并且我们所给的方法具有广泛性。     

Defining systems and Newton-like methods for finding singular solutions to nonlinear boundary value problems

A technique proposed earlier for constructing defining systems, which are a means for finding singular solutions to nonlinear equations, and the Newton-like methods based on this technique are now analyzed from the point of view of their stability with respect to perturbations in the operator of the equation. The results obtained make it possible to extend this approach to nonlinear boundary value problems for ordinary differential equations.     

Curran两个猜想的证明

本文证明：（１）Ｃｕｒｒａ的两个猜想；（２）ｐ^７阶非循环群是ＬＡ群．     

Elementary Regular Rings. II

We extend the well-known result by Burris and Werner on existence of defining sequences for elementary products of models to arbitrary enrichments of Boolean algebras (we obtain a complete analog of the Feferman–Vaught theorem). This enables us to establish decidability of the elementary theory of a classical object of number theory, the ring of adeles.     

Curran第三猜想的一个反例

本文证明了：当ｐ＞２，ｎ≥６时，存在ｐ￣ｎ阶群Ｇ使得｜ＡｕｔＧ｜＝ｐ￣（ｎ＋１）．由此得到３－群作为有限群的自同构群的最小阶为３￣７．从而给出了Ｇｕｒｒａｎ在１９８９年提出的猜想的一个反例。     

Self‐defining tree‐like classifiers for interpretation of Raman spectroscopic experiments

In this contribution, a technique is proposed to create a data‐driven interpretation of a given chemometric analysis of a Raman dataset. In real‐world applications, the chemometric analysis is fixed by some external measurement, for example, a legal standard, or a set of fixed goals. Thus, the exact chemometric work flow is fixed because of those goals. However, a further optimization, for example, of the measurement itself relies on an interpretation of the resulting chemometric analysis. For this purpose, a data‐driven analysis of the chemometric analysis itself has to be carried out. This contribution tries to achieve that goal by combining two methods. The first proposed technique is the calculation of the so‐called importance map, which allows the computation of the importance of every channel for a given model and a given dataset. This importance map is constructed after the complete result of an out‐of‐bag (OOB) validation and the decrease of accuracy by randomized channels. The second technique is the growing of the optimal decision tree based on the action of the model used for chemometric analysis. By this way, a clustering is achieved on which by binary classifiers, the optimal decision tree is grown. This tree can be interpreted as dividing the whole dataset into meta clusters. Combining these techniques, a new way of interpreting datasets based on the chosen model is proposed. This combination closes the gap between chemometric analysis and the need for interpretation. Copyright © 2016 John Wiley & Sons, Ltd.     

Involutive Distributions,Invariant Manifolds,and Defining Equations

We introduce the notion of an invariant solution relative to an involutive distribution. We give sufficient conditions for existence of such a solution to a system of differential equations. In the case of an evolution system of partial differential equations we describe how to construct auxiliary equations for functions determining differential constraints compatible with the original system. Using this theorem, we introduce linear and quasilinear defining equations which enable us to find some classes of involutive distributions, nonclassical symmetries, and differential constraints. We present examples of reductions and exact solutions to some partial differential equations stemming from applications.