首先,分析了"导讲评研"的教学模式和"微课"的特点,提出了基于"微课"的"导讲评研"的教学模式;其次,将基于"微课"的"导讲评研"教学模式应用于《高等代数》课程教学中,给出了具体实践过程;最后,分析了该教学模式在《高等代数》课程教学中的优点.

以内江师范学院数字仿真与数学实验示范中心的实践教学改革为背景,针对数学类应用型人才培养在实践教学方面的要求,文章提出了以项目和学科竞赛为抓手的应用型人才培养模式,构建以能力为导向、以项目以及学科竞赛为驱动满足应用型创新人才能力提升需要的实践教学体系,充分调动学生的学习兴趣,提高学生的自主学习能力、实践能力和创新能力,以适应国家经济建设与社会发展的需要.

针对普通高等院校数学专业英语教学存在的问题,分析了数学专业英语课程的特点以及教学过程中存在的问题,并对相应问题的解决提出思路.为了提高教学质量应以人为本,正确引导,充分调动学生的学习兴趣,提升学生的积极性;改革教学方法,创造良好的学习氛围;鼓励学生参加实践活动;完善考核评价体系等方面进行改造.

1 引言 1993年,Vague集[1]的概念被首次提出,它是模糊集的一种拓展,被广泛应用于评价和模糊推理等领域.Vague集是描述和处理现实世界中模糊和不确定现象的有力工具之一,它同时考虑隶属与非隶属两方面证据,用一个三元组来描述其隶属度下界,这个三元组同时反应了决策者对某一事物的支持、反对和弃权三方面的信息,使得它们在处理不确定信息时比传统的模糊集有更强的表示能力.

多属性决策问题是现代决策科学的一个重要研究内容,已引起人们极大的关注.然而,多属性决策无论在理论研究还是方法应用,目前尚不成熟,任面临着巨大挑战[1].区间数理论在决策分析等领域有非常强的应用背景,也是决定不确定性问题的主要手段.多属性决策是现代决策科学的一个重要部分,区间数是决策者对决策问题给出的决策信息量,是多属性决策理论中的主要内容之一.所以国内外学者对区间数多属性决策进行了一些研究.国内的主要研究成果有:樊玉英等学者利用TOPSIS方法处理区间数多指标决策,在构造各方案的理想方案基础上,以各方案与理想方案的距离大小来比较,并建立数学优化模型[2];张吉军等学者处理量指标权重为区间数的多指标决策问题,把区间数看成是均匀分布的函数,建立总离差最小的优化模型[3];国外的主要研究有:早在1931年Young就开始了区间数的研究,特别是Chanas S,Kuchta D考虑时间权重为区间数的时序多指标决策问题,利用TOPSIS方法作为计算工具进行了动态排序研究[4];HladíkM提出了一种基于区间数相离度的标准差和平均差极大化方法来计算不确定性多属性决策权重[5]等等.

本文建立基于Vague集的大学体育教练评价模型,确定评价对象为某一类球类运动的大学教练.确定教练的教龄、胜率以及负率为主要的评价指标.然后,根据选取的指标和Vague集的特点,将选出的指标中的教龄作归一化处理.再将教龄和胜率作为影响教练执教能力的正因素,负率作为影响教练指教能力的负因素,将指标值转化为Vague集值.应用Vague集中评分函数的计算公式,建立基于Vague集的大学教练评价模型.最后利用Matlab对随机选出的美国10名篮球教练进行排名.

Program verification is the key technology to ensure the correctness of the program.However,due to essen-tial differences of the classical and quantum world,classical program verification techniques and tools cannot be applied di-rectly to the quantum system.Since quantum programming language is a new formal model of quantum system,the verifica-tion problem of quantum program is more urgent and necessary.We investigate the program verification for the reachable set and the terminating set of specific nondeterministic quantum program described respectively by bit flip channel,phase flip channel,depolarizing channel,amplitude damping channel and phase damping channel starting from computational basic states in quantum communication systems.Then,we combine pairwise the above five quantum programs into nondeterminis-tic quantum programs,and merge these nondeterministic quantum programs into three nondeterministic quantum programs in terms of the similarities of the reachable set of five quantum programs,and discuss the problem for termination and diver-gence of these three nondeterministic quantum programs starting from computational basic states.The results shows that these three nondeterministic quantum programs starting from computational basic state 0 are terminated,while starting from com-putational basic state 1 ,the termination and the divergence of nondeterministic quantum program consisted by bit flip channel and depolarizing channel relates to the two parameters describing two quantum channels,the termination and the divergence of nondeterministic quantum program consisted by bit flip channel and phase flip channel relates to one parameter describing bit flip channel,and nondeterministic quantum program consisted by amplitude damping channel and phase damping channel is divergence without the two parameters describing quantum channel.And the results provide theoretical and technical sup-port for verification of quantum communication protocol in quantum information security.

The local normal colleges and universities are in the process of transition, and the training target of various professional is also changing. In order to adapt to the needs of the development of transformation and to re-alize the training objectives, this paper discusses the optimization of higher algebra teaching content mainly from the aspect of the principles of integration and optimization of the teaching content of higher algebra.

Limitations of the existing literature about the vector space lie mostly in the research of the nature of complemented subspaces.In order to solve this problem,the nature and some features of vector space are put under examination and the concept of 2-maximal subspaces of a vector space is introduced.The properties of 2-maximal subspaces are investigated from the perspectives of complemented subspaces,dimension and isomorphic mapping,which brings forth three major conclusions:(1)Let V be a n-dimensional vector space in domain F,given that M2≤·M1≤·V,then M2=n-2 will be true.(2)Let V be a vector space in domain F,if M2≤·M1≤·V,When,and only when M2 is a complemented subspaces of 2 dimension subspace.(3)Given that f is an isomorphic mapping of a vector space W→V,then one of the 2-maximal subspaces of W,suppose W2,must also be a 2-maximal subspace of V through the isomorphic mapping f.

The idea of quasi-coincidence was applied on interval valued fuzzy sets,a new kind of fuzzy lattice implication subalgebras was proposed,called interval valued(α,β)-fuzzy lattice implication subalgebras.Some properties of this new fuzzy lattice implication algebra were investigated.The relations between(α,β)-fuzzy lattice implication subalgebra and lattice implication subalgebras were studied.Some equivalent characterization theorems of interval valued(α,β)-fuzzy lattice implication subalgebras were established.

Based on the properties of adjoint matrix and full-transposed matrix, some properties of normal matrices are investigated, and many equivalent characterizations of normal matrices are obtained. In particular, the sufficient and necessary conditions of high-order mixed adjoint matrix to be a normal matrix are made clear.

By aid of the order filters in lattice implication algebras,filters determined by the order filters of it are obtained.Firstly,the properties of such filters are studied;Secondly,the necessary and sufficient condition under which the order filters of lattice implication algebras qualify as filters is obtained;Finally,the structure of such filter is determined.

With the introduction of a concept of error parameters,a new extended variable precision covering rough set model is proposed in this paper. The new model is based on the variable precision covering rough set and the extended covering rough set. In addition,the paper discusses some properties of the covering upper approximation and the covering lower approximation operators.

By using the weakly c-normality of maximal subgroups of some Sylow subgroups of Fitting subgroups(generalized Fitting subgroups),some sufficient conditions for a finite group to be supersolvable are proved and the results are generalized to formations.Moreover,some sufficient conditions for a saturated formation containing the class of all finite supersolvable groups to be closed are also obtained.

Let G be a finite group.A subgroup H of a group G is said to be S-quasinormal in G if H permutes with every Sylow subgroup of G.In this paper,in terms of S-quasinormal subgroups,some sufficient conditions for a finite group to be supersolvable or nilpotent are obtained.Under the condition that 2-maximal subgroup of G is S-quasinormal in G,a complete classification of G is obtained.

A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G,there exists an element x∈G such that HTx=TxH.In this paper,we investigate further the influence of s-conditionally permutability of some 2-maximal subgroups of the Sylow subgroup of G,on the structure of finite groups.New criteria for a group G being p-nilpotent are obtained.

Let G be a finite group.A subgroup H of G is said to be π-quasinormally embedded in G,if for each prime divisor p of the order of H,a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroup of G.In terms of the properties of π-quasinormally embedded of maximal or minimal subgroups,some sufficient conditions of a saturated formation containing the class of all finite supersolvable groups or nilpotent groups are obtained,1)Let be a satuated formation containing supersolvable formation and N be a nomal subgroup of a finite group G such that GN ∈.If each maximal subgroup of any sylow subgroup of Q of F(G)of odd order is π-quasinormally embedded in NG(Q)and each maximal subgroup of a sylow 2-π subgroup of F(N)is π-quasinormally embedded in G,then G∈F.2)Let be a satuated formation containing nilpotent formation and H be a nomal subgroup of a finite group G such that GH ∈F.If each minmal subgroup or cyclic subgroup of order 4 of H is π-quasinormally embedded in G,then G∈F.And some known results are generalized and improved.

By aid of the π-quasinormality of some maximal subgroups,a sufficient condition for the satuated formations containing a class of supersolvable groups is obtained.Let F be a satuated formation containing supersolvable formation U and N be a normal subgroup of a finite group G such that GN∈F;suppose that all the maximal subgroups of any odd-order Sylow subgroup Q of F*(N) are π-quasinormally embedded in NG(Q) and each maximal subgroup of a sylow 2-subgroup of F*(N) is π-quasinormally embedded in G,then G∈F.

Using the weakly c-normality of minimal subgroup of to characterize the structure of a finite group,some sufficient conditions of finite supersolvable group are obtained.According to the theory of formations,some sufficient conditions of saturated formation containing the class of all finite supersolvable groups are got,and some known theorems are generalized.

Using the weakly c-normality of subgroups,we obtain some conditions of a finite solvable group. Firstly,a sufficient and necessary condition of a finite solvable group is obtained:G is solvable if and only if A is weakly c-normal in B for any two neighbor subgroups A,B of G.Finally,some sufficient conditions of a finite solvable group are proved:Let G be a finite group,if G satisfies with one of the following conditions,then G is solvable:let M be an arbitrary maximal subgroup,all Sylow subgroups of M are weakly c-normal in G;let M be a arbitrary maximal subgroup,all maximal subgroup of M are weakly c-normal in G;let H be a Hallπ-subgroup of g and 2∈π,if N_G(H) is solvable and it is weakly c-normal in G.