The Creating Subject,the Brouwer–Kripke Schema,and infinite proofs

Kripke’s Schema (better the Brouwer–Kripke Schema) and the Kreisel–Troelstra Theory of the Creating Subject were introduced around the same time for the same purpose, that of analysing Brouwer’s ‘Creating Subject arguments’; other applications have been found since. I first look in detail at a representative choice of Brouwer’s arguments. Then I discuss the original use of the Schema and the Theory, their justification from a Brouwerian perspective, and instances of the Schema that can in fact be found in Brouwer’s own writings. Finally, I defend the Schema and the Theory against a number of objections that have been made.     

Nonlinear fractional magnetic Schrödinger equation: Existence and multiplicity

In this paper we focus our attention on the following nonlinear fractional Schrödinger equation with magnetic field

${\epsilon }^{2s}{(?\mathrm{\Delta })}_{A/\epsilon }^{s}u+V(x)u=f(|u{|}^2)u\text{ in }{\mathbb{R}}^N,$

where $\epsilon >0$ is a parameter, $s\in (0,1)$, $N\ge 3$, ${(?\mathrm{\Delta })}_A^s$ is the fractional magnetic Laplacian, $V:{\mathbb{R}}^N\to \mathbb{R}$ and $A:{\mathbb{R}}^N\to {\mathbb{R}}^N$ are continuous potentials and $f:{\mathbb{R}}^N\to \mathbb{R}$ is a subcritical nonlinearity. By applying variational methods and Ljusternick–Schnirelmann theory, we prove existence and multiplicity of solutions for ε small.     

“四环递进”教学法在农科高等数学教学中的尝试

简要介绍在中学理科教学中广泛使用的一种方法——"四环递进"教学法.结合教学实际,阐述在农科院校高等数学教学中应用该方法的必要性与可行性.通过实例说明如何使用该方法,并通过实际数据说明该方法在高等数学教学中的有效性.     

《概率论与数理统计》课程教学的探索与实践

结合多年的《概率论与数理统计》课程的教学实际,对该课程的优化教学过程,分层次教学和完善课程的考核评价等方面进行了一些探索与实践,以激发学生的学习兴趣与热情,培养学生应用概率统计方法解决问题的能力.     

工科复变函数中的迁移教学

迁移是指一种学习对另一种学习的影响.影响学生学习迁移的主要因素有:学生原有知识的准备状态、概括水平、认知结构变量、学习材料的性质、学习的指导.为了能有效促进学生学习正迁移的发生,同时防止学生学习负迁移的发生,在工科复变函数教学中针对其特点采取以下教学策略:注意加强工科复变函数与高等数学的衔接;突出转化和类比的数学思想方法的教学;加强复变函数学习方法的指导.     

独立学院高等数学课程的几种分层次教学方案探讨

独立学院办学规模的快速扩张导致学生的数学素质参差不齐,给高等数学的教学带来新的挑战.在已有的分层次教学法的基础上,结合独立学院的实际情况,探讨了适合独立学院的按教学对象分层次、教学内容分层次和教学模式分层次的几种分层次教学方案.     

线性规划精品课程建设的实践与思考

精品课程建设对提高高校教学质量具有重大意义.本文结合我校实际,讨论了线性规划精品课程建设的实践与设想,提出了相应的教改措施.     

Using FSBT technique with Rough Set Theory for personal investment portfolio analysis

This study proposes a novel Forward Search and Backward Trace (FSBT) technique based on Rough Set Theory to improve data analysis and extend the scope of observations made from sample data to solve personal investment portfolio problems. Rough Set Theory mathematically classifies data into class sets. The class set with the most objects may generate one decision rule. The rules generated from RST are rough and fragmented, that are very difficult to interpret the information. An empirical case is used to generate more than 85 rules by the RST method in comparison with FSBT method which only generated 14 rules. This result can show our proposed method is better than traditional RST method based on class sets that contain the most objects. Much of human knowledge is described in natural language. It is a very important thing to convert information from computer databases into normal human language. Sample data taken from features with the same backgrounds are used to compile different portfolios that investment companies and investment advisors can employ to satisfy the investor’ needs. The method not only can provide decision-making rules, but also can offer alternative strategies for better data analysis. We believe that the FSBT technique can be fully applied in research on investment marketing.     

Using the Relational Paradigm: effects on pupils’ reasoning in solving additive word problems

Pupils’ difficulties in solving word problems continue to attract attention: while researchers highlight the importance of relational reasoning and modelling, school curricula typically use short word problems to develop pupils’ knowledge of arithmetic operations and calculation strategies. The Relational Paradigm attributes the leading role in mathematics learning to the development of relational thinking. Using this perspective, we implemented a new approach to teaching additive word problem-solving in primary school, encouraging relational thinking and modelling. We compared the overall results of additive word problems solved by Grade 2 elementary pupils in the experimental group (N?=?216) and in the control group (N?=?196). Our data show: (a) on average, the experimental group performed significantly better in problem-solving than the control group; and (b) in the control group, there was a considerable lack of success in solving problems that require relational thinking—there was no such effect in the experimental group.     

Synthesis and reactivity of novel 3-isothiocyanatopropylsilatrane derived from aminopropylsilatrane: X-ray crystal structure and theoretical studies

A novel silatrane containing Si ← N bond (2.160 Å), has been synthesized by the reaction of 3-aminopropylsilatrane (1), dicyclohexylcarbodiimide (2) and CS₂. The structure was established by elemental analysis, spectroscopic methods (IR, ¹H NMR, ¹³C NMR and Mass spectroscopy) and X-ray crystallography. It was correlated with theoretical studies such as semiempirical (AM1, PM3, PM3MM and MNDO), Density Functional Theory (B3LYP) and Hartree-Fock at 3-21+G^∗ and 6-31G^∗(d) levels. The reactivity of compound 3 was studied with some Lewis acids and bases that showed the formation of corresponding adducts (4-7), which were characterized by elemental analysis, IR and NMR (¹H, ¹³C) spectroscopy.