构造法简证一类三角不等式

１９９６年,周永良先生在全国第三届初等数学研究学术交流会论文集中提出如下三角不等式在锐角三角形ＡＢＣ中,有ｃｏｓ（Ｂ－Ｃ）ｃｏｓＡ＋ｃｏｓ（Ｃ－Ａ）ｃｏｓＢ＋ｃｏｓ（Ａ－Ｂ）ｃｏｓＣ≥６（１）ｃｏｓＡｃｏｓ（Ｂ－Ｃ）＋ｃｏｓＢｃｏｓ（Ｃ－Ａ）＋ｃｏｓ...     

A Construction of Cartesian Authentication Codes from Vector Space and Dual Authentication Codes

ＡＣｏｎｓｔｒｕｃｔｉｏｎｏｆＣａｒｔｅｓｉａｎＡｕｔｈｅｎｔｉｃａｔｉｏｎＣｏｄｅｓｆｒｏｍＶｅｃｔｏｒＳｐａｃｅａｎｄＤｕａｌＡｕｔｈｅｎｔｉｃａｔｉｏｎＣｏｄｅｓＦｅｎｇＲｏｎｇｑｕａｎ（冯荣权）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ...     

The Characterizations of Weighted H^p（w）Spaces on the Certain Groups

ＴｈｅＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｓｏｆＷｅｉｇｈｔｅｄ　Ｈ~ｐ（ｗ）ＳｐａｃｅｓｏｎｔｈｅＣｅｒｔａｉｎＧｒｏｕｐｓＺｏｕＪｉｎ（邹进）（Ｌｅｓｈａｎ，ＴｈｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：ＴｈｅｗｅｉｇｈｔｅｄＨＰ（?..     

Some Constructions of Cartesian Authentication Codes from Pseudo－symplectic Geometry

ＳｏｍｅＣｏｎｓｔｒｕｃｔｉｏｎｓｏｆＣａｒｔｅｓｉａｎＡｕｔｈｅｎｔｉｃａｔｉｏｎＣｏｄｅｓｆｒｏｍＰｓｅｕｄｏ－ｓｙｍｐｌｅｃｔｉｃＧｅｏｍｅｔｒｙＧａｏＹｏｕ（高有）（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉｃＳｃｉｅｎｃｅ，ＮｏｒｔｈｅａｓｔＩｎｓｔ...     

Fekete┐SzegoProblemforStronglyBazilevicFunctions

Ｆｅｋｅｔｅ┐ＳｚｅｇｏＰｒｏｂｌｅｍｆｏｒＳｔｒｏｎｇｌｙＢａｚｉｌｅｖｉｃＦｕｎｃｔｉｏｎｓＧａｏＣｈｕｎｙｉ（高纯一）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣｈａｎｇｓｈａＣｏｍｍｕｎｉｃａｔｉｏｎｓＩｎｓｔｉｔｕｔｅ，Ｃｈａｎｇｓ...     

The Cartesian Closedness of the Category CDL and Function Spaces on Topological CDL''''s

ＴｈｅＣａｒｔｅｓｉａｎＣｌｏｓｅｄｎｅｓｓｏｆｔｈｅＣａｔｅｇｏｒｙＣＤＬａｎｄＦｕｎｃｔｉｏｎＳｐａｃｅｓｏｎＴｏｐｏｌｏｇｉｃａｌＣＤＬ＇ｓＹａｎｇＺｈｏｎｇｑｉａｎｇ（杨忠强）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａａｎｘｉＮ...     

ON GENERALIZATION OF SONAR SEQUENCES AND INTERMODULATION－FREE FREQUENCIES ASSIGNMENT SEQUENCES

ＣＨＥＮＷＥＮＤＥ（陈文德）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８０，ＣｈｉｎａａｎｄＳｔａｔｅＫｅｙＬａｂｒａｒｙｏｆＩｎｆｏｒｍａｔｉｏｎＳｅｃｕｒ...     

The Sufficient and Necessary Conditions for the Space X in －Space（X，）to be a Cohomology Sphere

ＴｈｅＳｕｆｆｉｃｉｅｎｔａｎｄＮｅｃｅｓｓａｒｙＣｏｎｄｉｔｉｏｎｓｆｏｒｔｈｅＳｐａｃｅＸｉｎ－Ｓｐａｃｅ（Ｘ，）ｔｏｂｅａＣｏｈｏｍｏｌｏｇｙＳｐｈｅｒｅＺｈａｎｇＺｅｎｇｘｉ（张增喜）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｃａ...     

The Projection onto a Direct Product of Convex Cones

ＴｈｅＰｒｏｊｅｃｔｉｏｎｏｎｔｏａＤｉｒｅｃｔｒｏｄｕｃｔｏｆＣｏｎｖｅｘＣｏｎｅｓＬｉｕＷｅｉ（刘维）ａｎｄＳｈｉＮｉｎｇｚｈｏｎｇ（史宁中）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｅａｓｔＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃ...     

A Necessary and Sufficient Condition for Admissibility of Nonnegative Quadratic Estimator

ＡＮｅｃｅｓｓａｒｙａｎｄＳｕｆｆｉｃｉｅｎｔＣｏｎｄｉｔｉｏｎｆｏｒＡｄｍｉｓｓｉｂｉｌｉｔｙｏｆＮｏｎｎｅｇａｔｉｖｅＱｕａｄｒａｔｉｃＥｓｔｉｍａｔｏｒＬｕＣｈａｎｇｙｕ（鹿长余）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｎｏｒｔｈｅａ...     

出租车司机社会贡献评价方法研究

出租车司机的社会贡献对于促进城市经济发展和社会进步具有重要的作用,评价出租车司机的社会贡献是激励出租车司机多做社会贡献的重要手段。为了评价出租车司机的社会贡献,本文提出了一种基于实际出租车运营数据的评价方法。本文设计了运营特性、重点区域、恶劣天气、大事件四个体现司机社会贡献的指标,以此构建了出租车司机社会贡献评价指标体系,进而选用了主观赋权法G1法和客观赋权法拉开档次法相结合的赋权方式对指标赋权,并选择四种评价信息集结方法建立了出租车司机社会贡献评价模型。最后,通过实际的出租车运营数据验证了本方法的可行性。本文为评价出租车司机社会贡献提供了一种研究思路和方法,并对政府政策的制定和企业策略的实施具有一定的启示。     

培养学生科学思维和创新能力的研究与实践——谈大学数学研究型教学

通过从一个导数值等式的证明谈起,探讨教师在课堂教学中如何根据教学内容创设能激起学生新异感的问题情景,启发和引导学生发散思考,类比、联想、猜想,探索和发现新问题并给出解答.使学生思维不断攀升,丰富教学内容,激发学生兴趣,培养学生科学思维方法和创新能力.     

Effects of imprecise weighting in hierarchical preference programming

Preference programming is a general term for multi-criteria decision analytical approaches allowing incomplete preference information. In the PAIRS method, interval judgments are assigned to weight ratios between attributes to model imprecision in multi-attribute value trees. This paper studies the effects of a hierarchical model structure on the overall imprecision, as the form of the hierarchy also affects the form of imprecision that can be assigned to the model. The aim is to find out good procedural practices for reducing overall imprecision descending inherently from the model structure. The study provides simulation results about the ability of various weighting schemes to identify dominated alternatives, which are discussed with respect to other issues related to the weighting process. According to the results, a hierarchical model is structurally somewhat more unable to identify dominances than a corresponding nonhierarchical model, but its cognitive advantages often cancel out this. The results also suggest paying reasonable attention to the precision of the lower level judgments and to identifying possible correlations between the criteria.     

Hemivariational inequality approach to constrained problems for star-shaped admissible sets

The hemivariational inequality approach is applied to establish the existence of solutions to a large class of nonconvex constrained problems in a reflexive Banach space. The admissible sets are supposed to be star-shaped with respect to a ball. Due to a discontinuity property of the Clarke directional differential related to the corresponding distance functions, the proposed method permits one to attain the solution without passing to zero with the penalization parameter. Some applications to nonconvex constrained variational problems illustrate the theory.     

Transition to turbulence, small disturbances, and sensitivity analysis I: A motivating problem

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new “mostly linear” theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence. In this part, we study a highly sensitive one-dimensional Burgers' equation as a motivating problem. Sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance. Also, sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem. In the second part of this work, this analysis will be extended to the three-dimensional Navier-Stokes equations to show that small disturbances have great potential to trigger transition to turbulence.     

快递企业航空货运网络的构建

快递业竞争激烈,构建高效合理的航空货运网络是快递企业提高竞争力的重要手段。“枢纽—辐射”式航空货运网络是整合航空快递资源、提高航空快递资源利用效率、提高快递企业竞争力的有效模式。本文以降低航空快递网络成本、加快航空快递处理时间为目标,从航空快递网络枢纽的选取、指派关系的确定、枢纽个数的选择三个方面研究了航空快递网络模型建立问题,选用遗传算法求解不同枢纽个数下航空快递网络的运输成本,并据此进行枢纽的选取,运用重力模型法进行指派关系的确定,在此基础上运用超效率DEA模型确定枢纽个数。接着,以包含17个节点的顺丰航空快递网络的规划为例,对本文所提出的模型和算法进行了验证,验证结果证实了模型的合理性。本文的研究为快递企业构建航空货运网络提供了科学实用的方法,该方法的使用可以降低航空货运成本,提高效率,从而提高快递企业的竞争力。     

Factorisation of Littlewood-Richardson coefficients

The hive model is used to show that the saturation of any essential Horn inequality leads to the factorisation of Littlewood-Richardson coefficients. The proof is based on the use of combinatorial objects known as puzzles. These are shown not only to account for the origin of Horn inequalities, but also to determine the constraints on hives that lead to factorisation. Defining a primitive Littlewood-Richardson coefficient to be one for which all essential Horn inequalities are strict, it is shown that every Littlewood-Richardson coefficient can be expressed as a product of primitive coefficients. Precisely the same result is shown to apply to the polynomials defined by stretched Littlewood-Richardson coefficients.     

Strategic commitment to price to stimulate downstream innovation in a supply chain

It is generally in a firm’s interest for its supply chain partners to invest in innovations. To the extent that these innovations either reduce the partners’ variable costs or stimulate demand for the end product, they will tend to lead to higher levels of output for all of the firms in the chain. However, in response to the innovations of its partners, a firm may have an incentive to opportunistically increase its own prices. The possibility of such opportunistic behavior creates a hold-up problem that leads supply chain partners to underinvest in innovation. Clearly, this hold-up problem could be eliminated by a pre-commitment to price. However, by making an advance commitment to price, a firm sacrifices an important means of responding to demand uncertainty. In this paper we examine the trade-off that is faced when a firm’s channel partner has opportunities to invest in either cost reduction or quality improvement, i.e. demand enhancement. Should it commit to a price in order to encourage innovation, or should it remain flexible in order to respond to demand uncertainty. We discuss several simple wholesale pricing mechanisms with respect to this trade-off.     

Integrated Fuzzy AHP–TOPSIS for selecting the best plastic recycling method: A case study

Due to the rapid depletion of natural resources and undesired environmental changes in a global scale, it is necessary to conserve the natural resources and protect the environment. Industries which manufacture plastic based products have the necessity to recycle plastics. There are number of methods to recycle plastics. Since the selection of the best recycling method involves complex decision variables, it is considered to be a multiple criteria decision-making (MCDM) problem. This article develops an evaluation model based on the fuzzy Analytic Hierarchy Process (AHP) and the technique for order performance by similarity to ideal solution (TOPSIS) to enable the industry practitioners to perform performance evaluation in a fuzzy environment. The purpose of the study is to determine the best method for recycling plastics among the various plastic recycling processes. By observing the results, it is identified that mechanical recycling process is found to be the best plastic recycling process using the integrated approach.     

考虑充电设施重入的电动汽车旅行商问题研究

出于减少环境危害和响应相关法规的考虑,物流企业开始逐步将运输车辆转变为电动汽车;而由于电动汽车的续航里程有限,对电动汽车的路径优化也将涉及充电设施。充电设施的“重入”是指电动汽车返回之前已经通过的充电设施进行充能的现象,它的存在需要改变经典旅行商问题模型中的“子回路约束”。本文聚焦于充电设施的“重入”,构建了一个无需预估充电设施重入次数上限的电动汽车旅行商问题模型,并通过引入路径可行性判别方法和增加充电设施选择与重复策略,设计了一种改进蚁群算法对问题进行求解。结果表明:与未考虑重入的模型相比,本文提出的考虑充电设施重入的模型能在电动汽车电池容量较低的情况下求出最优解,同时也能够使充电设施承担多次充电任务,从而在较少充电设施情况下依然能够得到可行的最优路径。