移动社交网络中基于友好关系下的异或转发机制

任丽丽1,张2*

(1. 蚌埠医学院公共基础学院,安徽蚌埠2330302. 安庆师范大学数学与计算科学学院,安徽安庆246133)

摘要:移动社交网络是DTNs网络的典型应用,该网络的特点是缺乏端到端的持续连接。为克服这一障碍,提高数据的传递率,文章分析了移动社交网络中节点与社区、节点与节点之间的联系,把友好节点作为待选节点,通过交集的形式提出了一种基于友好关系下的异或转发策略(FRXO)。通过计算机仿真实验与DTNs网络中经典算法相比后发现,FRXO算法的传递率高于Label算法且能明显降低网络中数据包的拷贝数目,有效地减少了资源消耗。

关键词:移动社交网络;社区;异或运算;转发机制;友好关系

Forwarding Mechanism in Social Networks Based on XOR Operation Under the Friendly Relations

REN Lili1ZHANG Xu2*

1.School of Public Foundation, Bengbu Medical College, Bengbu 233030, China; 2. School of Mathematics and Computation Science, Anqing Normal University, Anqing 246133, China)

Abstract:Social network is the typical application of DTNs network. The characteristic of the DTNs network is the lack of end-to-end link. In order to overcome the obstacle and improve the delivery rate, the paper analyzed the relation between the nodes and community in the social network. Under the background of friendly node as to stay the selected node, through the form of intersection was proposed based on an exclusive or forwarding strategy under the friendly relations, an efficient forwarding strategy based on XOR operation was proposed. Finally, the experimental results showed that compared with the existing well-known algorithm, the FRXO algorithm can obviously reduce the overhead of network resources and the delivery rate is better than that of the Label, thus can effectively reduce the resource consumption.

Key words: mobile social network; community; XOR operation; forwarding mechanism; friendly relationship

车联网环境下考虑续航时间约束的公交车辆行车计划编制

史桂红

(苏州健雄职业技术学院软件与服务外包学院,江苏太仓 215411

摘要公交车辆的行车计划智能化编制是互联网+交通和公交优先战略的重要体现,也是提高公交吸引力和缓解城市交通拥堵的有效途径。在对现有行车计划编制模型进行研究的基础上,提出了燃料续航时间约束条件下的多场站行车计划编制模型,并依托车联网环境的信息交互,探讨了续航时间约束下的车辆调度问题与背包问题的对应关系,提出了一种应用贪婪算法求解该问题的方法。最后,通过算例验证了模型的有效性,并对比了参与调度车辆数目与续航时间约束对结果的影响。分析结果表明:在续航时间约束不变的情况下,增加调度车辆的数目,可以降低空驶时间和执行里程,但车辆执行时间的波动性增大,车辆间运行公平性降低;增加续航里程可以增加车辆的使用频率,提高车辆的使用效率。公交车辆的行车计划编制不仅要考虑费用,还需考虑车辆接受班次任务的均衡性,宜根据不同的续航时间约束条件来管理调度车辆。

关键词:公交车辆;车联网;行车计划编制;燃料续航时间

Study of Bus Scheduling with Route and Fueling Time Constraints Under the Connected Vehicle Environment

SHI Guihong

School of Software and Services OutsourcingSuzhou Chien-Shiung Institute of Technology, Taicang 215411, China

Abstract:Intelligent transit vehicle scheduling is an important aspect of both “Internet + Traffic” and the national strategy of bus priority, which is also the effective way to improve the public transit attractiveness and relieve the urban traffic congestion. This study reviewed the existing research on public transit vehicle scheduling problem and proposed a model of multiple depot vehicle scheduling problem with route and fueling time constraints (MDVSPRTC). Based on the information transmission via the connected vehicle environment, the paper analysed MDVSPRTC and combined with models of solving the existing regional bus vehicles scheduling problem. By discussing the correspondence between MDVSPRTC and the knapsack problem, and a solving method was proposed by using the greedy algorithm. At last, the model was testified by calculation examples, and the impacts of least vehicles and route and fueling time were also analyzed. The results showed that in the case of constant fueling time, the increasing of the number of vehicles involved in the scheduling decreases the running time and mileage. However, the fluctuation of vehicle execution time increased and the fairness of vehicle operation reduced with the increasing of the number of vehicles. An increasing of fueling time resulted in an increase of the vehicle use frequency and vehicle efficiency enhancement. It is not only necessary to consider the cost, but also need to consider the balance of the vehicle to be assigned to the task, so it is necessary to manage the vehicle according to the different fueling time constraints.

Key wordsbus priority; connected vehicles; vehicle scheduling problem; fueling time

基于物联网的大型带式输送机智能监控系统

1,2,张1,解泽洋1,杨1

(1. 南通大学交通学院,江苏南通2260192. 南通先进通信技术研究院,江苏南通226019)

摘要为提升散货码头大型带式输送机智能化监控水平,设计了基于物联网的大型带式输送机智能监控系统。在散料输送过程中,该系统可全程对带式输送机物料输送状态进行实时监控,实现了运行过程中物料瞬时流量、带速、功率等状态参数的实时监测,还可根据带式输送机物料瞬时流量远程调节带速,从而实现大型带式输送机系统最佳节能效果。实验结果表明,该系统具有智能化程度高、扩展灵活、性能稳定等优点,说明了系统设计的合理性、稳定性与实用性,可为港口大型带式输送机调速协调控制策略制定提供决策支持。

关键词:大型带式输送机;物联网;智能监控;无线通信

Intelligent Surveillance System of Large Belt Conveyor Based on Internet of Things Technology

ZENG Fei1,2, ZHANG Qi1, XIE Zheyang1,YANG Fan1

1. School of Transportation, Nantong University, Nantong 226019China2. Nantong Research Institute for Advanced Communication Technologies, Nantong 226019, China)

AbstractIn order to enhance the intelligent surveillance level of large belt conveyor in bulk terminal, an intelligent surveillance system of large belt conveyor based on internet of things technology was proposed. In the process of bulk material conveying on the belt, the states of bulk material conveying on the belt conveyor can be monitored in real-time, state parameters such as the instantaneous flow rate, belt speed, and power. It could also realize the best energy saving effect of large belt conveyor system by adjusting the belt speed according to material flow of belt conveyor. Experiments showed that the system has the advantages of low power consumption, low cost, flexible extension and stable performance. It could illustrate the rationality, stability and practicability of the system. It could provide the decision-making support for developing the control strategy of the large belt conveyor in bulk material.

Key wordslarge belt conveyors; internet of things; intelligent surveillance; wireless communication

一种中功率LED路灯模组设计

蔡彬彬,胡为民

(江苏工程职业技术学院建筑工程学院,江苏南通 226007

摘要:设计了一种中功率LED路灯模组,该模组由 PCB铝基板、灯珠组、塑料透镜、散热器,以及设于塑料透镜与PCB铝基板间的防水胶圈构成。灯珠组由4颗中功率3030双晶灯珠组成,呈正方形分布。塑料透镜采用防UVPC材料,为一凸曲面罩,呈中空半球面形。利用DIALUX软件,针对道路照明要求的照度均值、照度均匀性、环境比、亮度均值、亮度均匀性等指标,对该模组进行了仿真实验,并通过实例进行了验证。从DIALUX仿真和实测结果来看,该模组能满足城市主干道路路灯的技术要求,具有较好的市场应用前景。

关键词LED;中功率;路灯模组

Design of a Middle Power LED Street Lamp Module

CAI Binbin, HU Weimin

School of Civil Engineering and Architecture, Jiangsu College of Engineering and TechnologyNantong 226007, China

AbstractThis paper introduced a middle power LED streetlight module, the module consists of aluminum PCB substrate, beads, plastic lens, radiator and is arranged on the plastic lens and PCB aluminum substrate waterproof apron.The four group consists of a lamp power in 3030 crystal beads, square distribution. The plastic lens adopts the anti PC UV material, and is a convex curved face mask, which is in a hollow hemispherical shape using The Dialux software and adopting the module. According to the requirements of road lighting illumination mean, uniform illumination environment, ratio, mean luminance, luminance uniformity of simulation experiment, the indicators from the Dialux simulation, module index can fully meet the technical requirements of urban trunk road lamp, and has a promising prospect in the market.

Key wordsLEDmedium powerstreet lamp module

潜艇大型集体逃生舱上浮数值模拟研究

孙济政,黄祥兵*

(海军工程大学舰船工程系,湖北武汉 430033

摘要为探讨如何提高大型集体逃生舱的上浮安全性和优化大型集体逃生舱设计方案,通过对3种典型顶部设计(胶囊体、圆柱体、菱形体)的逃生舱模型,运用Fluent软件分别对其上浮状态进行仿真模拟,计算得出各方案逃生舱上浮过程中的最大速度,比较了不同顶部设计方案的优缺点。结果表明,针对大型集体逃生舱,3种典型顶部设计不能达到安全上浮标准,还需结合其他减速手段。

关键词:潜艇;逃生舱;上浮;速度

Numerical Simulation of the Large Submarine Escape Capsules

SUN JizhengHUANG Xiangbing*

Department of Naval Architecture Engineering, Naval University of EngineeringWuhan 430033China

Abstract In order to discuss how to improve the safety of large-sign escape capsule and optimize the design scheme of large-sign escape capsule, the escape capsules model with different top design was proposed in this paper, and the FLUENT software was used to simulate the floating state of each design, and the maximum floating velocity of escape capsule with different top design of the submarine was calculated, the advantages and disadvantages of different top design schemes were analyzed and compared. The results showed that the designs proposed can not reach the standard of safe ascent, and it should be combined with other methods.

Key wordssubmarineescape capsuleascent; velocity

汽车空调电磁离合器皮带轮减重槽ANSYS电磁优化

肖龙雪1, 2

1. 南通大学杏林学院,江苏南通 226007 2. 南通大学工程训练中心,江苏南通 226019

摘要:为探究汽车空调用电磁离合器皮带轮上减重槽的加工位置、切槽深度和宽度分别对其产生电磁吸力大小的影响,建立了该离合器的有限元优化计算模型,在忽略了影响计算精度的部分不规则结构后,根据单一变量原则,借助有限元软件ANSYS电磁分析模块,计算得到了该电磁离合器在各单一因素影响下的电磁吸力变化规律,给出了皮带轮减重槽的加工位置和尺寸的优先选取值。结果表明:为了在实际加工时能较多地切除材料并保证精度,在仅考量电磁吸力而不考虑结构刚度等因素的情况下,该电磁离合器皮带轮的减重槽可以偏向皮带轮内测加工,减重槽切槽宽度可以选择为6 mm,切槽深度可以选择为7 mm

关键词:汽车空调;电磁离合器;皮带轮;减重槽;有限元;电磁分析

ANSYS Electromagnetic Optimization for Pulley Multi-pocket of Electromagnetic Clutch of Automotive Air-Conditioning

XIAO Longxue1, 2

(1. Nantong University Xinglin College, Nantong 226007, China;2. Engineering Training Center, Nantong University, Nantong 226019, China)

Abstract:To explore the electromagnetic suction variation regularities respectively caused by the change of processing position, cutting depth and width of the pulley multi-pocket of a kind of automotive air-conditioning electromagnetic clutch, based on the preliminary calculation and analysis, the finite element optimization calculation model was established after ignoring the irregular structure which influenced the grid division and influenced the calculation precision. According to the principle of single variable, after the finite element electromagnetic analysis for the model with the help of the software ANSYS, these variation regularities had been gotten, and the priority selection values of the processing position and structure size of the electromagnetic clutch pulley multi-pocket were recommended. Results showed that the only consideration factors such as electromagnetic suction without considering the structural stiffness, and in the actual process could more removal of material and to ensure accuracy, the position of multi-pocket of electromagnetic clutch pulley could be close to the inner, the cutting width could be accepted as 6 mm, the cutting depth could be accepted as 7 mm.

Key words:automotive air-conditioning; electromagnetic clutch; pulley; multi-pocket; ANSYS;electromagnetic analysis

超声表面冲击及喷丸强化后TC4钛合金的生物相容性

赵雅君1,曹小建2,金2,丁华建2 *

1. 内蒙古大学生命科学学院,内蒙古呼和浩特 0100212. 南通大学建筑工程学院,江苏南通 226019

摘要:分别在静荷载25 N、振幅30 μm、冲击数36 000/mm2的条件下对TC4钛合金进行超声表面冲击强化(UNSM)处理、采用传统喷丸技术(硬度45~50HRC且直径1 mm钢丸,阿尔门强度0.10~0.15 mmA,覆盖率100%)TC4进行喷丸处理,然后对比研究两种工艺对TC4生物相容性的影响,包括体液腐蚀行为、表面钙磷的矿化沉积及纤维软骨细胞早期黏附行为,并对处理后TC4钛合金的表面形貌、极化曲线、腐蚀形貌、细胞黏附等进行分析。结果表明:超声冲击可让TC4维持较好的平整度,而喷丸使材料表面粗糙度明显增加;UNSM处理和喷丸处理均在TC4表面产生点腐蚀坑,UNSM处理后的表面点腐蚀坑最多,而喷丸处理后TC4的耐体液腐蚀性能最差;两种表面处理均可增强TC4表面钙磷元素的沉积,且两种表面处理均可增进纤维软骨细胞的早期黏附,UNSM作用更佳

关键词超声冲击;喷丸;TC4钛合金;生物相容性;钙磷沉积;纤维软骨细胞

Biocompatibility of TC4 Subjected to Ultrasonic Surface Impact and Shot Peening

ZHAO Yajun1, CAO Xiaojian2, JIN Jiang2, DING Huajian2*

(1. School of Life Sciences, Inner Mongolia University, Huhehaote 010021, China; 2. School of Civil Engineering and Architecture, Nantong University, Nantong 226019, China)

Abstract: The effect of ultrasonic nanocrystal surface modification (UNSM) and shot peening (SP) on the biocompatibility of TC4 was investigated, including the corrosion behavior in simulated body fluid (SBF), the deposition of calcium and phosphorus, and the earlier adhension of fibrochondrocyte. UNSM was carried out with the condition of a static load of 25 N, vibration amplitude of 30 μm and 36 000 strikes per unit. TC4 specimens were treated using conventional shot peening (steel balls of 1.0 mm in diameter, hardness of 45~50 HRC) leading to an Almen intensity (French standard AFNOR NFL 06832) of 0.10 ~ 0.15 mmA. The overlapping rate was 100%. The surface topography, polarisation curve, corrosion feature, and the adhension of fibrochondrocyte were studied. Findings showed that: UNSM maintains the good surface, while shot peening increases the surface roughness; Etch pits are exist on both the UNSMed and SPed surface, UNSM makes the most etch pits, but the corrosion property of shot peening is the worst; The deposition of calcium and phosphorus is enhanced after both the two treatments; They also improve the earlier adhension of fibrochondrocyte, UNSM can achieve a better result.

Key words: UNSM; shot peening;TC4; biocompatibility; calcium and phosphorus deposition; fibrochondrocyte

掺碳TiO2纳米纤维负载PdRu催化剂的制备及对甲醇的电催化性能

蒋建婷,张文静,王蔚,徐娴,鞠剑峰*

(南通大学化学化工学院,江苏南通 226019

摘要:以掺CTiO2纳米纤维为载体,通过化学还原法制备了一种新型直接甲醇燃料电池阳极催化剂PdRu/TiO2-C。采用SEMXRD和电化学分析等对其形貌、结构和电化学性能进行了表征。结果表明,PdRu/TiO2-C纳米纤维催化剂对甲醇具有良好的催化活性,PdRu物质的量比为11时催化剂对甲醇的电催化氧化活性最高。

关键词:直接甲醇燃料电池;阳极催化剂;二氧化钛;纳米纤维

Preparation of Carbon Doped TiO2 Nanofibers Loading PdRu and Its Electrocatalytic Activity for Methanol

JIANG JiantingZHANG WenjingWANG WeiXU XianJU Jianfeng*

(School of Chemistry and Chemical Engineering, Nantong University, Nantong 226019, China)

Abstract: A novel PdRu/TiO2-C nanofiber electrocatalyst was synthesized by the chemical reduction method using carbon doped TiO2 nanofiber as support. The pattern, structure and electrochemical performances of the PdRu/TiO2-C nanofiber catalyst were characterized by SEM, XRD and electrochemical analysis. The PdRu/TiO2-C nanofiber electrocatalyst has shown promising catalytic activity for methanol electro-oxidation. The electrocatalytic oxidation activity of methanol reached the highest when the mass ratio of Pd and Ru was 11.

Key words: direct methanol fuel cell; anode catalyst; TiO2 ; nanofibe

湿法成网液体过滤材料的开发与性能研究

王露莹,张旭,李素英*,马丹丹,周美玲

(南通大学纺织服装学院,江苏南通226019

摘要以涤纶纤维、ES纤维及涤纶浆粕为原料,采用湿法成网、热轧加固工艺制备液体过滤材料,研究了纤维长度、热轧温度、热轧时间3个单因素对材料的均匀性、透气性、断裂强力、透水性及过滤性能的影响。实验结果表明:随着涤纶纤维长度的增加,湿法液体过滤材料的均匀性降低;热轧温度越高,纤维粘结效果越好,试样强力越高;采用12 mm的涤纶纤维,热轧温度为150 ,热轧时间为2 min,其过滤精度与有效孔径O95最小,均为2 μm,过滤效率最高达83.5%;所有试样都能达到对粒径≥5 μm粒子的过滤精度,适合作为常温、中性液体过滤材料。

关键词:湿法成网;液体过滤;非织造材料

Study on the Development and Performance of Liquid Filtration Material

WANG LuyingZHANG Xu LI Suying*MA DandanZHOU Meiling

School of Textile and Clothing, Nantong University, Nantong 226019, China)

Abstract: In this paper, the materials consisted of polyester fiber, ES fiber and polyester pulp, prepared by wet process and hot rolling, and the effects of fiber length, hot rolling temperature and hot time on the uniformity, permeability, tensile strength, impact resistance and filtration performance of materials were studied. Results showed that with the increase of polyester fiber length, the uniformity of wet liquid filtration material was getting worse; the hot rolling temperature was higher, the bonding effect of fibers was better, so the strength of samples was higher. When the length of polyester fiber was 12 mm, hot rolling temperature was 150 degrees centigrade, hot rolling time was 2 min, the filtering accuracy and the effective aperture of O95 got the minimum which both were 2 μm, and the best filtration efficiency was 83.5%; Otherwise, the filtering precision of particle size of all the samples were greater than 5 μm. The materials are suitable for normal temperature, neutral liquid filtration material.

Key words: wet process; liquid filtration; nonwovens

非对称n阶网络的等效电阻及复阻抗研究

王一骁,余清怡,谭志中*

南通大学理学院,江苏南通226019

摘要:研究了一类非对称的n阶网络任意两个节点间的等效电阻及LC复阻抗网络问题.首先给出了n阶网络的两个等效电阻公式,然后采用网络分析构建差分方程模型,以及边界条件方程和电流在输入与输出点的约束方程,证明了所给出的两个等效电阻公式的正确性。同时给出了无穷网络的等效电阻公式,并且将特殊情形下的结论与其他结论进行了对比讨论.文章所提出的方法和得到的结论应用于复阻抗网络的研究,分析了一类LC网络的等效复阻抗问题,绘制出相应的复阻抗随频率变化的图形,发现了LC网络在特定条件下的振荡特性和共鸣特性。

关键词:电路网络;差分方程;等效电阻;基尔霍夫定律;共鸣

Study on the Equivalent Resistance and Impedance of an Asymmetric n-step Network

WANG YixiaoYU Qingyi TAN Zhizhong*

(School of Sciences, Nantong University, Nantong 226019, China)

Abstract: The problem of the equivalent resistance between any two nodes of an asymmetric n-step resistor network and its LC network was investigated. First of all, two general formulae of equivalent resistance between any two nodes of an n-step resistor network were proposed; Second the differential equation by the method of network analysis was modeled, and the constraint equation by the currents of input and output was also modeled, thus the formula of equivalent resistance was proved by using the above equations; In the meantime, the formula of equivalent resistance in the infinite network is given, and the conclusions in special cases were compared and discussed with other conclusions, and validate the correctness of the conclusions obtained in this paper. As applications, the proposed method and results were suitable for the research of complex impedance network as well, an n-step LC impedance network was further explored in detail, and the corresponding graphics of the complex impedance changes with the change of parameters was drawn, and the characteristics of oscillation and resonance in the LC network under certain conditions was found.

Key words: circuit network; difference equation; equivalent resistance; Kirchhoff's law; resonance

循环的或1-旋转的791113-太阳系的存在性

臧碧莲,王金华*

(南通大学理学院,江苏南通226019

摘要:设整数k2k-太阳图SCk)是一个由k-圈图的每个顶点向外伸出一条悬挂边得到的图。Vk-太阳系是完全图Kvk-太阳系的一个分解。如果子vk-太阳系存在一个v阶自同构,则称该k-太阳系是循不的;如果vk-太阳系存在一个包含一个不动点和一个长为v-1轮换的自同构,则称该k-太阳系是1-旋转的。应用差的方法直接证明了当v≡1mod 4k)时,存在v阶循环的k-太阳系;v≡0mod 4k)时,存在v1-旋转的k-太阳系,其中k=791113

关键词:分解;太阳图;太阳系;循环的k-太阳系;1-旋转的k-太阳系

Existence of Cyclic or 1-Rotational k-Sun Systems for k=7,9,11,13

ZANG Bilian, Wang Jinhua*

(School of Sciences, Nantong University, Nantong 226019, China)

Abstract: Let k be a positive integer and k2. A k-sun graph S(Ck) is a graph obtained from a k-cycle by adding a pendent edge to each vertex of the k-cycle. A k-sun system of order v is a decomposition of complete graph Kv, into k-sun graphs. A k-sun system of order v is cyclic if it admits an automorphism of order v and 1-rotational if it admits an automorphism containing one fixed point and a cycle of length v-1. By applying differenec method, it was found that there exist a cyclic k-sun system of order v for v≡1mod 4k and a 1-rotationl k-sun system of order v for v≡0mod 4k,where k=7,9,11,13.

Key words: decomposition; sun graph; sun system; cyclic k-sun system; 1-rotational k-sun system

同阶子群个数的集合为{1m}的幂零群

雪,张庆亮*

(南通大学理学院,江苏南通226019

摘要:把同阶的子群看作一类,并用n(G)表示G的同阶子群个数的集合.通过数量分析对n(G)={1m}的幂零群进行了分类,完善了相关工作,得到了相关结果:如果G为有限幂零群且n(G)={1m},那么G=H×P,这里HG的循环正规Hall子群,PGSylow p-子群。另外,下面结论之一成立:1m=1+pP同构于×CpQ8M(n1,1)(D8)中的某一个,这里M(n1,1)=a,b|=bp=1,ab=;2) m=1+p+p2, P同构于Cp×Cp×CpM21*中的某一个,这里“*”表示中心积,M21=a,b|=bp=1,ab=a1+p

关键词:同阶子群;幂零群;有限群

Nilpotent Groups with Set of the Number of Same Order Subgroups {1m}

DAI Xue, ZHANG Qingliang*

(School of Sciences, Nantong University, Nantong 226019, China)

Abstract: Subgroups with the same order are seen as one class. Let n(G) be the set of the number of subgroups with the same order. This paper classify the nilpotent groups with n(G) ={1m} by the analysis of quantity, and this work perfects the existing result. The main result is as following: if G is a finite nilpotent group and n(G) ={1m}, then G=H×P, where H is the cyclic normal Hall-subgroup of G and P is the Sylow p-subgroup of G. Moreover, one of the following statements holds: 1) m=1+pP is one of the following groups:×CpQ8, M(n1,1) except D8, where M(n1,1)=a, b| =bp=1,ab=;2) m=1+p+p2, P is one of the following groups: Cp×Cp×Cp, M21*where “*” denotes the central product and M21=a,b|=bp=1,ab=a1+p.

Key words: subgroups with the same order; nilpotent group; classification

广义C-映象不动点的存在性

媛,丛培根,张树义*

(渤海大学数理学院,辽宁锦州 121013

摘要:在完备的度量空间, 研究了满足的广义映象不动点的存在性问题, 其中, 是一对称函数, , 常数, 证明了这类带有对称函数的广义映象的新型不动点定理, 从而改进和推广了现有文献中的相应结果

关键词:完备度量空间;广义映象;不动点;存在性

The Existence of Fixed Point for Generalized mappings

LIN YuanCONG PeigenZHANG Shuyi*

(College of Mathematics and PhysicsBohai UniversityJinzhou 121013China )

Abstract: In the paper, the existence problem of fixed point for generalized mappings satisfyingorwere studied in complete metric spaces, where, is a symmetric function satisfying , where and are three constants with and . Some new fixed point theorems for this class of generalized mappings with symmetric function were confirmed, which improves and extends the corresponding results of current research.

Key words: complete metric space; generalizedmappingsfixed point; existence

α-斜线性McCoy

刘亮亮,陈国龙*

(淮北师范大学数学科学学院,安徽淮北235000

摘要:作为线性McCoy模和α-McCoy环的推广,引入了α-斜线性McCoy模的概念,研究了α-斜线性McCoy模的若干性,讨论了α-斜线性McCoy模与其他模之间的关系,证明了:Mα-斜线性McCoy的当且仅当TM)是α-斜线性McCoy的;Rα-斜线性McCoy的当且仅当每个平坦右R-模是α-斜线性McCoy的等主要结果。最后给出了α-斜线性McCoy模的矩阵扩张。

关键词McCoy模;α-McCoy环;α-斜线性McCoy模;线性McCoy

α-Skew Linearly McCoy Modules

LIU Liangliang, CHEN Guolong*

(College of Mathematics Science, Huaibei Normal University, Huaibei 235000, China)

Abstract: The α-skew linearly McCoy modules were introduced, which were a common generalization of linearly McCoy modules and α-skew McCoy rings, the α-skew linearly McCoy modules in introduced. Some basic propertied such modules were explored, the relationships between quasi-α-skew linearly McCoy modules and the other modules were discussed, proving that M is α-McCoy if and only if its torsion submodule T(M) is α-skew McCoy; R is α-skew McCoy if and only if every flat R-module is α-skew McCoy. And the matrix extensions of α-skew linearly McCoy modules were presented.

Key words: McCoy modules; α-skew McCoy rings; α-skew linearly McCoy modules; linearly McCoy modules

关于Legendre猜想的一个判定准则

(南京大学数学系,江苏南京210093)

摘要 Legendre猜想是数论中一个与素数间隙有关的猜想,它断言对于每个正整数,在之间都有一个素数。为此,文章首先研究了夹在之间的奇数,刻画了小于一个给定平方数的奇素数的特点。然后证明了如下的判定准则:若,则Legendre猜想成立,反之若,则Legendre 猜想不成立。

关键词 Legendre猜想;素数间隙;平方数;判定准则

A Criterion for the Legendre's Conjecture

XIAO Huan

(Department of Mathematics, Nanjing University, Nanjing 210093, China)

Abstract:Legendre's conjecture is a conjecture on prime gap in number theory. It states there is a prime between and for every positive integer . In this paper a criterion for the conjecture was presented, to this end the odd primes less than a square was considered and a characterization of these odd primes was given and then a criterion for the Legendre's conjecture was also put forward: if then the Legendre's conjecture holds, otherwise if then the Legendre's conjecture fails.

Key words: Legendre's conjecture; prime gap; square number; criterion

完备非紧流形上Schrdinger算子的加权热容度

张泽宇,周俞洁,王林峰*

(南通大学理学院,江苏南通226019

摘要:在几何分析中, 加权Hodge-Laplacian算子非常重要, 在酉等价的意义下, 它表现为初始度量的Schr?dinger算子。另外,完备非紧流形上热容度问题是几何分析中的一个有趣的问题, 在这个方面亦有不少研究结果. 文章首先给出了相应于初值的Schr?dinger算子的加权热容度的定义;进一步, 在权函数满足一定条件下, 利用热核的性质以及H?lder不等式, 得到加权热容度的上界估计

关键词Schr?dinger算子;热核;加权热容度;完备非紧流形

Weighted Heat Content of a Schr?dinger Operator on Complete Noncompact Manifolds

ZHANG ZeyuZHOU YujieWANG Linfeng*

(School of Sciences, Nantong University, Nantong 226019,China)

Abstract: In geometric analysis, the weighted Hodge-Laplacian operator is important and expresses as a Schr?dinger operator of the initial metric in the unitarily equivalent sense. On the other hand, the heat content question on a complete noncompact manifold is an interesting question in geometric analysis, there are many results in this direction. This paper firstly attempted to define the weighted heat content of the Schr?dinger operator associated with a given initial value. Furthermore, by using the properties of the heat kernel and the H?lder inequality, an upper bound estimate of the heat content under suitable conditions of the weighted function was established.

Key words: Schr?dinger operator; heat kernel; weighed heat content; completenoncompact manifold

一类射影平坦球对称芬斯勒度量

超,李璐璐,宋卫东*

(安徽师范大学数学计算机科学学院,安徽芜湖241000

摘要:讨论了球对称芬斯勒度量,其中xBn(r)RnyTxBn(r)\{0}φ:[0,r)×RR,通过构造其射影平坦偏微分方程,得到了一个可以展成形如的解。

关键词:芬斯勒度量;球对称;射影平坦

Study on Projectively Flat Spherically Symmetric Finsler Metrics

HE Chao, LI Lulu, SONG Weidong*

(College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China)

Abstract: In this paper, spherically symmetric Finsler metrics was studied where xBn(r)RnyTxBn(r)\{0} andφ:[0,r×RR. By investigating a PDE equivalent to these metrics being locally projectively flat, a solution of the PDE just likewas obtained.

Key words: Finsler metric; spherically symmetric; projectively flat

一类三阶边值问题正解的存在性和唯一性

(江苏联合职业技术学院南京分院,江苏南京 210019

摘要:利用Banach空间中的压缩映象原理,讨论了一类三阶边值问题正解的存在性和唯一性,得到了该边值问题正解存在唯一性的充分条件。

关键词:压缩映象原理;边值问题;正解;存在性;唯一性

Existence and Uniqueness of Positive Solution for a Third-Order Boundary Value Problems

WU Chen

(Branch of Nanjing Jiangsu Union Technical Institute, Nanjing 210019, China)

Abstract: The existence and uniqueness of positive solution for a third-order boundary value problem were considered with the help of the Banach contraction mapping principle, and enough conditions for the existence and uniqueness of positive solutions were obtained.

Key words: contraction mapping principle; boundary value problems; positive solution; existence; uniqueness

粗糙集导出空间中的连通类

钟满田

(罗定职业技术学院教育系,广东罗定 527200

摘要:基于等价关系R导出的拓扑空间可作为Pawlak粗糙集模型的推广,引入了Pawlak粗糙集导出的近似拓扑空间概念,研究了Pawlak粗糙集导出的近似拓扑空间有范畴为ACTop的性质、连通类及连续封闭性,说明了一族近似拓扑空间连通类的交集是连通类。结果表明采用拓扑学中的连通类理论与方法研究粗糙集是可行的。

关键词:粗糙集模型;拓扑空间;连通类

Connected Classes in Rough Set Derived Space

ZHONG Mantian

Department of Education, Luoding Polytechnic, Luoding 527200, China

AbstractThe topological space derived from the equivalence relation R was introduced as a Pawlak rough set model, and the concept of approximate topological space derived from Pawlak rough sets was introduced, and the approximate topological space was explored which derived from the Pawlak rough set has the property of ACTop, the connected class and its continuous closure, the family intersection of approximate topological spatial connectivity was connected, to obtain that it is feasible to study the rough set with the theory and method of connectivity in topology conclusion.

Key words: rough set model; topological space; connected classes