Generalized syntheses of large-poremesoporous metal oxides with semicrystalline frameworks

非水体系合成蜂窝状金属氧化物介孔材料Ξ胡　立,俞　秋,邓　斌,余瑞金,宋瑞琦,徐安武(中山大学化学与化学工程学院,广东广州510275)摘　要:以无水金属氯化物为前驱体,CH 2CHCH 2O (C 2H 4O )12H 为模板剂,在无水乙醇体系中合成出三维蜂窝状金属氧化物介孔材料。

利用XRD 、BET 、TE M 等手段对其进行了表征。

经过400℃焙烧除去表面活性剂后,得到高质量的蜂窝状金属氧化物介孔分子筛。

热稳定性好、比表面积高、孔壁晶化较好的蜂窝状金属氧化物介孔材料在催化、吸附与分离、传感器等领域有着潜在的应用价值。

关键词:蜂窝状介孔材料;金属氧化物;表面活性剂;自组装;非水体系中图分类号:O613172;O74313 文献标识码:A 文章编号:052926579(2004)0620128203 自从1992年美孚(M obil )公司首次报道M41S 系列介孔氧化硅分子筛以来,介孔材料就成为国际上跨学科的研究热点[1,2]。

其中人们对介孔氧化硅作了大量研究,并发展了多条路径成功合成出不同孔径、结构、比表面积的介孔氧化硅材料[3-5]。

与氧化硅相比,非硅组成介孔分子筛特别是金属氧化物在光、电、磁、传感器、催化等众多领域有着潜在的应用价值[6]。

Y ang 等[7]首先报道了在非水体系合成出系列金属氧化物有序介孔材料。

由于一维有序介孔材料不利于分子的扩散和传输,其应用受到限制。

而三维蜂窝状金属氧化物介孔材料更有利于分子的扩散和传输[8]。

Pinnavaia 等[4]首先利用非离子表面活性剂(如C n E O m )在水溶液及中性条件下合成出蜂窝状氧化硅介孔分子筛(MS U-1)。

有关蜂窝状金属氧化物介孔分子筛的研究报道不多。

本文以无水金属氯化物为前驱体,非离子表面活性剂CH 2CHCH 2O (C 2H 4O )12H 为模板剂,在无水乙醇溶液中合成出三维蜂窝状金属氧化物介孔分子筛。

1　实验部分111　样品合成1g CH 2CHCH 2O (C 2H 4O )12H 溶于10g 无水乙醇中,称取0101m ol 无水氯化物,在剧烈搅拌下缓慢滴加到上述溶液中,搅拌015h 后,倒入直径为10cm 的表面皿中,在40℃反应4～7d 。

A Generic Concept for Large-Scale MulticastMarkus HofmannInstitute of Telematics, University of Karlsruhe,Zirkel 2, 76128 Karlsruhe, GermanyPhone: +49 721 608 3982, Fax: +49 721 388097E-mail: hofmann@rmatik.uni-karlsruhe.deURL: rmatik.uni-karlsruhe.de/~hofmann* Abstract. Upcoming broadband networks offer a bearer service suitable formodern distributed applications. High bandwidth capacity and low transferdelay are two characteristics of such communication services. Beside these per-formance-oriented parameters, many applications have additional requirementsin respect to quality of the used communication service. Computer SupportedCooperative Work, distributed parallel processing and virtual shared memory,for example, depend on error-free data exchange among multiple computer sys-tems. Additional problems occur for the provision of a reliable multipoint ser-vice, where errors are more likely and the sender has to deal with numerousreceivers. In order to meet the required reliability, powerful and scalable errorcontrol mechanisms are essential. Therefore, this paper presents a novel concept,named Local Group Concept (LGC), for large-scale reliable multicast.Keywords. Reliable Multicast, Large-Scale Networks, Local Groups, ImplosionControl, Retransmissions, Dynamic Groups1MotivationIn the near future, global information exchange will become an essential resource in worldwide economies. Forthcoming computer applications will require reliable data transfer within large groups, whose members may be spread worldwide. To support reliable information exchange in such a scenario, protocols have to be changed to pro-vide efficient and scalable multicast error control and traffic control.One problem new protocols have to deal with is known as the implosion problem. As the number of communication participants becomes very large, a sender is swamped with return messages from its receivers. These messages may be generated as a result of status requests or as a result of data loss in conjunction with retransmission-based error control. The effect of implosion is twofold. Firstly, the large number of return messages results in processing overhead at the sender and, therefore, delays data com-munication. Secondly, a tremendous amount of control units may cause an excess of both, bandwidth and bufferspace, which in turn causes additional message losses. An optimal control scheme for multicast communication would reduce the number of sta-tus reports received by the sender down to one.A second issue of great importance is the development of efficient error correction schemes for multicast communication. Common protocols use Go-Back-N or selective* In Proceedings of International Zurich Seminar on Digital Communications(IZS’96), Zurich, Switzerland, Springer Verlag, February 1996.repeat to retransmit lost and corrupted data. Receivers do request missed data directly from the multicast sender without any consideration of network topology and actual network load. In case of group communication, it is also possible to exchange data with other receivers. It is preferable to request lost and corrupted data from a commu-nication participant placed next to the end-system missing some information. An opti-mal error correction scheme would stimulate the retransmission of missed data units by the receiver located closest to the failing system. This would minimize transfer delay and network load. However, it seems to be very hard to develop an optimal con-trol and error correction scheme. There will be always some kind of trade-off between complexity of protocol mechanisms and benefits to be achieved by an optimal solu-tion.Many protocols have been developed to support data exchange among various com-munication participants. Some of these protocols, such as MTP (Multicast Transport Protocol) [1] and RMP (Reliable Multicast Protocol) [2], implement a centralized con-trol and error correction scheme to provide a totally ordered multicast delivery. The central instance controlling data transfer may become a bottleneck when dealing with numerous receivers. Therefore, these protocols will not scale well in respect of the group size. An approach based on the establishment of so called multicast servers within the network is given in [3]. Other protocols with centralized, sender-based con-trol integrate special mechanisms to avoid acknowledgment implosion. A recent ver-sion of XTP (Xpress Transfer Protocol) [4], for example, defines damping and slotting algorithms to reduce implosion. Instead of returning control units exclusively to the multicast sender, receivers transmit them after a random delay to the whole group. Consequently, every group member receives this message and skips its status report if the incoming control unit corresponds to its personal state. This mechanism might reduce the number of acknowledgments to be processed by the sender. But in large-scale global networks, the usefulness of multicasting control units is very questionable [5]. A large number of participants together with the mechanism described above may cause a flood of control units all over the global network. SRM (Scalable Reliable Multicast) [6], which integrates a similar mechanism to implement a receiver-based error control, uses timers carefully set to avoid a flood of retransmission requests. However, the correct setting of timers will be very difficult for high dynamic networks with quickly changing load and frequently changing network structure.This paper presents a novel error control mechanism suitable for global heterogeneous networks. It combines the advantages of both, sender-based and receiver-based control schemes. The concept aims at reducing transfer delay, network load and the acknowl-edgment processing overhead at the sending side. Section 2 and Section 3 present the proposed framework based on the Local Group Concept (LGC). Section 4 gives results of a performance analysis in respect to a simple example scenario. Finally, Section 5 draws concluding remarks.2The Local Group Concept (LGC)The Local Group Concept (LGC) presented in this paper is based on a best-effort delivery model with multicast support. While these requirements are perfectly in con-formity with IP and the current MBone, the Local Group Concept is not restricted to the Internet protocol family. Although this paper focuses on the use of the traditional IP multicast distribution model, the generic concept can also be integrated in anextended ATM Adaption Layer or in other protocol architectures with multicast sup-port. Additionally, LGC avoids changes within internal network equipment, such as ATM switches or IP routers. The integration of implosion control into these systems requires protocol processing capabilities inside themselves. This implies more com-plex and less flexible intermediate systems. In addition, a router doing implosion con-trol for hundreds of multicast connections will soon become a bottleneck. Therefore, the LGC approach focuses on implosion control on end-to-end basis.2.1Basic Principles of LGCThe problem with implosion is that a single system has to control a very large number of receivers. The basic principle of the Local Group Concept is to split the burden of acknowledgment handling and to distribute error correction as well as traffic control among all the members of the multicast group. To achieve better scalability of point-to-multipoint services in respect of group sizes, distances, and data rates, LGC divides global multicast groups into separate subgroups. These subgroups will combine com-munication participants within a local region, forming so called Local Groups (LG). Each of them is represented by a specific communication node, named local Group Controller (GC). These nodes support the provision of the following enhanced serv-ices:•Local Retransmissions:Controllers of Local Groups are able to perform and to coordinate retransmissions of lost and corrupted data within their subgroup. This reduces delay caused by retransmissions and decreases the load for sender and net-work.•Local Acknowledgment Processing: The integration of acknowledgment process-ing capabilities into local Group Controllers reduces the acknowledgment implo-sion problem of reliable multicast for large groups. Local Group Controllers evaluate received control units and inform the multicast sender about the status of the Local Group. This includes error reports as well as parameters to control data flow. Parallel processing of status reports and their combination to a single mes-sage per Local Group relieves the multicast sender as it reduces the number of con-trol units to evaluate at the sending side.In each local region, one of the receivers is determined to function as local Group Controller. The sender itself is defined always as a local Group Controller. The dedi-cated system has to collect status messages from all members of its subgroup and has to forward them to the multicast sender in a single composite control unit. Controllers of subgroups are also responsible for organizing local retransmissions. After evaluat-ing received status messages a local Group Controller tries to transfer lost data units to all receivers that have observed errors or losses. To retransmit data units a local Group Controller can use either unicast or restricted multicast transmission. This decision may be static or dynamically based on the number of failed receivers. If a controller itself misses some data units, it will try to get them from another member of its Local Group. Therefore, a multicast sender has only to retransmit messages missed by all members of a subgroup. Local retransmissions lead to shorter delays and decrease the number of data units flowing through the global network.An example scenario illustrating the basic idea and the advantage of the Local Group Concept is given in Figure 1. A multicast sender communicates over a satellite link with four receivers, which are connected to a common router. The satellite link is char-acterized by high transfer delay and high carrier fees. Therefore, it is desirable to reduce data traffic over this link. In this type of scenario it is useful to combine all four receivers into a single subgroup. One of the receiving end-systems has to function as the controller of the subgroup. In this case, local retransmissions do not traverse the satellite link. This reduces transfer delay and network load within the satellite link.Fig. 1. Combining End-Systems to one Local GroupIn this example, the decision to combine all four receivers into one single subgroup was based on the intention of minimizing transfer delay. The next Section deals with aspects that influence the creation and structure of Local Groups.2.2Metrics for Building Local GroupsThe Local Group Concept is based on the combination of receivers within a ‘local region’. Thus, the term ‘local region’ has to be clarified. Some kind of metric is neces-sary to determine the distance between two communication nodes. The suitability of different metrics, such as delay, bandwidth, throughput, error probability, reliability, carrier fees, or number of hops between two nodes, depends mainly on the application using a communication service. While an interactive application may wish to mini-mize transfer delay, a user transferring data files is interested in reducing financial costs of the transfer. However, there is a trade-off between complexity due to general distance metrics and efficiency when using simple metrics such as hop counts. A dis-cussion about the usefulness of metrics such as transfer delay or hop counts can be found in [7] and [8]. The decision which kind of metric can be used also depends on the underlying network protocol. In some cases it is necessary that the routing protocol supports the chosen unit of measurement. IP, for example, considers metrics like delay, throughput, and reliability, while the ISO protocol IS-IS supports bandwidth, error probability, delay and financial costs [9]. Combinations of these mentioned met-rics can also be taken into consideration. If the underlying network service supports no metric at all, the measured round trip time may be defined as the distance between two stations.A simple solution for a similar problem has been proposed in [10]. The generation of local multicast regions as defined in the Designated Status Protocol (DSP) and the Combined Protocol (CP) is mainly based on addresses and the geographical location of end-systems (for example, end-systems connected to a common switch). Such a static mechanism leads to problems supporting huge MANs (e.g., DQDB or FDDI) and mobile environments. The definition of local regions based on the geographic location of end-systems does not work very well in general, as mentioned in [7], because geographic information often does not correlate to network structure. There-fore, the Local Group Concept aims at flexible, dynamic and application-depending generation of Local Groups.2.3Selection and Placement of Group ControllersAn important detail in the design of a concept like LGC is the decision where to place the functionality of local Group Controllers. The question arises which type of com-munication system is suitable to be responsible for controlling a Local Group. Possible answers are, for example, end-systems, routers, or switches. If there are several suita-ble systems, which selection will fit best?The CP protocol mentioned in [10] uses local exchanges (e.g., routers or ATM switches) to combine status messages of receivers within a local region. This solution implies modifications of local exchanges and restricts the Local Group Concept to operate in the network layer. By placing local Group Controllers into end-systems, the concept becomes ‘layer-independent’. In addition, the end-system-based approach avoids the necessity of any changes in switches and routers. In this case, the protocol mechanism can be used in networks based on different protocol architectures. The placement of local Group Controllers in end-systems scales better for a large number of multicast connections. A local exchange doing retransmissions and acknowledg-ment processing for different multicast connections may soon become a bottleneck. It is advantageous to parallelize the job of handling different Local Groups and to dis-tribute it to several communication nodes. Each multicast connection should have its own, separate local Group Controller. The end-system based solution allows for choosing different communication participants within the same local region for differ-ent multicast connections.The Local Group Concept presented in this paper integrates the functionality of local Group Controllers into normal end-systems. In principle, every communication partic-ipant is able to perform the tasks necessary for controlling a subgroup. This strategy is similar to the selection of a monitor station within a Token Ring network [11]. One member per Local Group is designated as the active controller. The selected station represents the Local Group and performs local acknowledgment processing and local retransmissions.Another important issue is the dynamic change of communication groups and network traffic. The structure of Local Groups and the placement of their controllers should always be adapted to the actual state of the network and the communication group. Therefore, it must be possible to move functionality of local Group Controllers during the lifetime of a connection.The DSP protocol described in [10], for example, combines status messages in end-systems, which are selected at connection setup time. For that reason, no chance to reassign the role of a Group Controller is given. Careful selection and placement oflocal Group Controllers assist in optimizing network load and transfer delay. Charac-teristics such as processing capacity, memory size, and location within the network, determine the suitability of an end-system for the role as a local Group Controller. Other important issues concern network topology, group size, and group structure. Due to this wide range of parameters, there is no simple algorithm to find the optimal local Group Controller. Instead, near-optimal algorithms or other heuristics could be applied. A simple solution is to define the member next to the multicast sender as local Group Controller.LGC defines local Group Controllers in the following manner. The initiator of a new Local Group always becomes the first controller of this subgroup. After a certain period of time or after joining of a new member, the local Group Controller initiates a reconfiguration process. During this process, every member of the Local Group reports its parameters relevant for the decision to the local Group Controller. Like the metric used to determine the distance between two systems, these values may depend on the application using the communication service. Possible parameters are distance to the multicast sender, performance, and buffer space of each end-system or the loca-tion of a receiver in relation to other members of the Local Group. Based on informa-tion obtained from its members, the local Group Controller determines the most suitable end-system to take over the role as local Group Controller in the future. If a change is advantageous, all necessary information migrates from the old to the new controller and all members of the Local Group are informed about this change. During this reconfiguration process, every join or leave request is queued and performed later.2.4Hierarchy of Local Group ControllersTo improve the benefits of LGC, Local Groups can be organized in a hierarchical structure. A hierarchy of Local Groups exists, if a local Group Controller LG2 does not report directly to the multicast sender. Instead, it sends retransmission requests and status reports representing the whole Local Group to a local Group Controller LG1 next to itself. This one treats LG2 like a normal receiver. Therefore, all retransmission requests of LG2 are redirected to and satisfied by LG1. In this case, LG1 is named the parent of LG2, while LG2 is the child of LG1. It is obvious that this hierarchy will decrease transfer delay, network load, and implosion additionally.Two changes have to be made to support a hierarchical structure. Firstly, every local Group Controller (except the multicast sender) has to subscribe to the nearest Local Group as a normal receiver. Secondly, every local Group Controller has to redirect its control messages to the next local Group Controller at an upper level (to its parent). Additionally, it may be necessary to increase timeout values of parents, because child-ren have to collect all status reports of their members before answering to their parent. This timeout adaption could be done dynamically during a synchronizing handshake. The remainder of this paper does not consider the hierarchy in more detail. Neverthe-less, all the algorithms described in the following Sections may be easily modified to support hierarchical Local Groups.3Protocol Mechanisms realizing LGCThe following Subsections give a more detailed description of the Local Group Con-cept. A complete specification including pseudo code for integrating the concept into existing multicast protocols can be found in [12].3.1Joining Group CommunicationBefore receiving any data, new communication participants have to subscribe to a nearby Local Group in respect to the chosen metric. A simple possibility to find an appropriate local Group Controller is to use a service similar to the Host Anycasting Service described in [13]. The search may be based on routing information, too, obtained directly from routing tables. If there is no support by the network layer at all, an expanding ring mechanism [7] based on round trip times can be used. The overhead produced by this search strongly depends on the mechanism applied to find an appro-priate Local Group. An end-system using the Host Anycasting service just sends one anycast request and gets back a single answer within a period of time corresponding to the round trip time between itself and the answering Group Controller. In contrast, an expanding ring search will cause much more overhead. Depending on the result of the search, different actions have to be performed:•If no Local Group is found within a defined distance according to the chosen met-ric, the joining end-system establishes a new subgroup, appoints itself as Group Controller and informs the multicast sender about this event. Hence, the multicast sender has knowledge of all Local Groups and their representative controllers.•If an appropriate Local Group exists within a certain distance, the joining end-sys-tem registers itself at the corresponding Group Controller. Therefore, a local Group Controller always knows the identity of all its members. This is a prerequisite for providing a reliable multicast service.After subscription to a Local Group, the end-system is allowed to participate in the group communication. The division of dynamic communication groups into local sub-groups has to be updated after a certain time. Due to dynamic changes in group mem-bership, it is necessary to modify the group structure. For example, it may be preferable to place the local Group Controller in a newly joined participant that is located in the center of the subgroup. Such a reconfiguration process could be imple-mented according to the mechanism mentioned in Subsection 2.3. A reconfiguration is also necessary, if the division into Local Groups is based on routing information, which can be incorrect for limited periods of time and which is not globally consistent. Periodic updates of the group structure correct errors caused by temporary inconsistent metric information.Due to the knowledge of group membership, a multicast sender is able to guarantee the correct data transfer to all of its children. Local Group Controllers are responsible for correct transmission of user data to all members of their subgroup. This allows to pro-vide a reliable multicast service that scales well for either long distances and a large number of receivers.3.2Transfer of Multicast DataThe sender multicasts data units (e.g., using IP-multicast) to all destinations. After a certain period of time, the sending station requests the status of all receivers. Instead of returning control units directly to the sender, receivers transmit them to the controller of their Local Group. The controller collects incoming status messages, processes them, and calculates the status of the whole subgroup. Applying the knowledge of received control units, a local Group Controller requests data units missed by itself from other members of the subgroup and performs all relevant local retransmissions. In addition, the controller combines received status messages into a single acknowl-edgment and transmits it to the multicast sender. The acknowledgment includes the request for all data units missed by all members of the Local Group. This mechanism ensures that every data unit received successfully by at least one group member is not requested at the multicast sender anymore, even if the Group Controller itself misses this data unit.After the reception of user data, receivers deliver the information to the service user. However, they are not allowed to release the corresponding buffer space. This is because the local Group Controller may miss these data and request it at a later stage. Therefore, receivers have to wait either for a sufficient amount of time, or for an explicit permission by the local Group Controller before releasing the receive buffer. The period of time data must be kept by receivers depends among other issues on the radius of the Local Group and the frequency of status requests.3.3Leaving Group CommunicationIf a normal receiver wants to leave group communication, it unsubscribes itself at the corresponding local Group Controller. After performing necessary retransmissions, the Group Controller confirms unsubscription and the receiver is allowed to leave.If an end-system functioning as a local Group Controller wants to leave communica-tion, first of all an appropriate successor has to be determined. The new controller obtains all relevant group management information, like status and member informa-tion, from its predecessor. Afterwards, all members of the Local Group are informed about the identity of their new controller. Henceforth, it is the new local Group Con-troller that deals with new data sent by the multicast sender and that receives status reports from group members. However, the leaving Group Controller has to ensure immediately that all outstanding retransmissions to its former members have been dealt with, before being allowed to leave.If the leaving end-system is the only one within its Local Group, it just unregisters itself directly at the multicast sender or at its parent.3.4Fault ToleranceWith respect to fault tolerance it is interesting in which way the Local Group Concept handles failures of a local Group Controller. The question arises, how sending and receiving end-systems discover such a failure and what will be done in this case.As mentioned above, local Group Controllers must periodically send messages to initi-ate a buffer release at receiving sides. If a local Group Controller fails, receivers will not get such messages any more. In this case, they infer a failure of their local Group Controller. The multicast sender or other controllers within a Local Group hierarchy detect a failing child from the missing answer in response to a status request. Every end-system reports such a failure to its parent.The reaction to the failure of a local Group Controller depends strongly on the applica-tion given group semantic. If the application requires an all reliable communication service and at least one of the local Group Controllers fails, the connection will be aborted and an error will be indicated to the service user. If the failure of a receiver is acceptable and an active controller fails, another group member has to take its role. For example, this could be a replicated local Group Controller (similar to the solution presented in[14]) or a dynamically determined successor within the Local Group. It isalso possible that all members of the failed Local Group search for a new Local Group according to the mechanism described in Section 3.1.3.5Integration of Local Groups in XTPAs an example of integrating the novel concept into existing transport protocols, the mechanisms described above have been adopted to XTP, version 3.6 [4]. Work is ongoing to integrate the Local Group Concept into an implementation of XTP 4.0 [15]. An additional packet type for migration of management information must be added. To implement a k-reliable multicast service, sender and Group Controllers must be able to distinguish between different receivers. Therefore, an additional field identify-ing individual source addresses has to be integrated into CNTL packets of XTP.4Performance EvaluationAnalytical methods were applied and simulations were performed in order to evaluate the benefits of the Local Group Concept. The simulations were based on BONeS/ Designer, an event-driven network simulation tool by Comdisco. During evaluation, two important measures were focused:•Transfer Delay, which is the primary concern from the application’s point of view.•Network Load, the most interesting measure from the networker’s perspective. The simulation scenario consists of a sender and various receivers that are connected to a local area network. The sender is linked to the LAN over a wide area network. If the satellite link in Figure 1 is replaced by a wide area network, these two scenarios will be identical.The evaluation examined the impact of group size on average transfer delay and net-work load. The values obtained for the Local Group Concept were compared to the corresponding results for two common sender-based techniques using multicast and unicast retransmission. Transfer delay was assumed to 20 ms for the wide area link, which is approximately the delay for transferring data between the East and West coast of the USA. Transfer delay within the local area network was fixed at 2 ms. Error probability was assumed to be 10-1 for message loss caused by buffer overflow or bit errors, which is not uncommon for highly loaded internetworks. This value was derived from many measurings to randomly selected internet hosts using ping com-mand. Other simulation parameters included data rate, processing delay within com-munication systems, status request rate, and burst length.The impact of group size on average transfer delay is given in Figure 2. The graph shows for all techniques an increase in the average transfer delay with increasing num-bers of receivers. The sharp increase for the common, sender-based approach can be explained with the large number of acknowledgments that have to be processed solely by the multicast sender. The relative high values for average transfer delay are mainly caused by retransmissions over the wide area link. Local retransmissions, as proposed by the Local Group Concept, effect a less strong increase in transfer delay. The benefit for the Local Group Concept is extremely high for large communication groups, but transfer delay still increases with the number of receivers. The establishment of several Local Groups with a restricted number of receivers leads to a distribution of acknowl-edgment processing to different local Group Controllers. In the third simulation, the。

小学下册英语第1单元期中试卷英语试题一、综合题(本题有50小题，每小题1分，共100分.每小题不选、错误，均不给分)1 There are many _____ in the fridge. (fruits/colors/books)2 The __________ can reveal the history of the Earth's geological formations.3 What is the term for animals that are active at night?A. DiurnalB. NocturnalC. CrepuscularD. Seasonal答案:B4 The __________ (文化教育) enriches lives.5 The plant grows better with _______ (植物在_______下生长得更好).6 She is _____ (singing) a lullaby.7 The __________ is the amount of space occupied by a substance.8 An endothermic process absorbs ______.9 Ants can carry items many times their ______ (重量).10 What is 100 divided by 4?A. 20B. 25C. 30D. 40答案:B11 什么是美国著名作家，因其小说《了不起的盖茨比》而闻名？A. F. Scott FitzgeraldB. Ernest HemingwayC. Mark TwainD. John Steinbeck答案: A12 The __________ is the main source of food for many animals.13 The __________ is shining brightly.14 What do we call the process of removing waste from the body?A. DigestionB. ExcretionC. RespirationD. Circulation答案:B15 In math class, I learned how to ______ (计算) and solve problems. It’s like a puzzle that I enjoy!16 What do you call the person who sings?A. DancerB. PainterC. SingerD. Writer17 The __________ (历史的再现) reflects our journey.18 The ______ (植物的价值) extends beyond aesthetics.19 The ____ has big wings and can glide through the air.20 A _______ is a chemical reaction that produces heat and light.21 What do you call animals that can fly?A. MammalsB. BirdsC. ReptilesD. Amphibians答案:B22 Many plants have unique ______ (特征) that help them thrive.23 What is the opposite of "hot"?A. ColdB. WarmC. BoilingD. Spicy答案:A24 What is the name of the famous mountain located in Africa?A. KilimanjaroB. DenaliC. EverestD. Elbrus25 The ________ was a defining moment in the struggle for rights.26 The country known for its ancient ruins is ________ (意大利).27 We should _______ nice to everyone.28 What is the largest planet in our solar system?A. EarthC. JupiterD. Mars答案:C29 The chemical symbol for rhodium is ______.30 中国的________ (history) 充满了战争与和平的故事。

高三英语学术文章单选题50题1. In the scientific research paper, the term "hypothesis" is closest in meaning to _.A. theoryB. experimentC. conclusionD. assumption答案：D。

解析：“hypothesis”的意思是假设，假定。

“assumption”也表示假定，假设，在学术语境中，当提出一个假设来进行研究时，这两个词意思相近。

“theory”指理论，是经过大量研究和论证后的成果；“experiment”是实验，是验证假设或理论的手段；“conclusion”是结论，是研究之后得出的结果，所以选D。

2. The historical article mentioned "feudal system", which refers to _.A. democratic systemB. hierarchical social systemC. capitalist systemD. modern political system答案：B。

解析：“feudal system”是封建制度，它是一种等级森严的社会制度。

“democratic system”是民主制度；“capitalist system”是资本主义制度；“modern political system”是现代政治制度，与封建制度完全不同概念，所以选B。

3. In a literary review, "metaphor" is a figure of speech that _.A. gives human qualities to non - human thingsB. compares two different things without using "like" or "as"C. uses exaggeration to emphasize a pointD. repeats the same sound at the beginning of words答案：B。

Presenting a speech （做演讲）Of all human creations, language may be the most remarkable. Through language we share experience, formulate values, exchange ideas, transmit knowledge, and sustain culture. Indeed, language is vital to think itself. Contrary to popular belief, language does not simply mirror reality but also helps to create our sense of reality by giving meaning to events.在人类所有的创造中，语言也许是影响最为深远的。

我们用语言来分享经验，表达(传递？)价值观，交换想法，传播知识，传承文化。

事实上，对语言本身的思考也是至关重要的。

和通常所认为的不同的是，语言并不只是简单地反映现实，语言在具体描述事件的时候也在帮助我们建立对现实的感知。

——语序的调整。

Good speakers have respect for language and know how it works. Words are the tools of a speaker’s craft. They have special uses, just like the tools of any other profession. As a speaker, you should be aware of the meaning of words and know how to use language accurately, clearly,vividly,and appropriately.好的演讲者对语言很重视，也知道如何让它发挥更好的效果。

2022年考研考博-考博英语-南开大学考试全真模拟易错、难点剖析AB卷（带答案）一.综合题(共15题)1.单选题The discussion was so prolonged and exhausting that （） we had to stop for refreshments. 问题1选项A.at largeB.at easeC.at randomD.at intervals【答案】D【解析】固定搭配词组辨析。

at large“详尽的”;at ease“安逸, 舒适”;at random“随便地, 任意地”;at intervals“不时地, 间断地”。

句意:讨论时间太长, 使人精疲力竭, 我们不得不不时地停下来吃点点心。

选项D符合句意。

2.单选题The consolidation of the crumbling walls and towers has been carried out in （） with a program agreed with by the Department of the Environment.问题1选项A.caseB.accordanceC.placeD.charge 【答案】B【解析】固定搭配。

in accordance with为固定搭配，表示“依照，与...一致”。

3.单选题In the last 12 years total employment in the United States grew faster than at any time in the peacetime history of any country—from 82 to 110 million between 1973 and 1985—that is, by a full one third. The entire growth, however, was in manufacturing, and especially in non-blue-collar jobs.This trend is the same in all developed countries, and is, indeed, even more pronounced in Japan. It is therefore highly probable that in 25 years developed countries such as the United States and Japan will employ no larger a proportion of the labor force in manufacturing than developed countries now employ in farming—at most, 10 percent. Today the United States employs around 18 million people in blue-collar jobs in manufacturing industries. By 2010, the number is likely to be no more than 12 million. In some major industries the drop will be even sharper. It is quite unrealistic, for instance, to expect that the American automobile industry will employ more than one-third of its present blue-collar force 25 years hence, even though production might be 50 percent higher.If a company, an industry or a country does not in the next quarter century sharply increase manufacturing production and at the same time sharply reduce the blue-collar work force, it cannot hope to remain competitive—or even to remain “developed.” The attempt to preserve such blue-collar jobs is actually a prescription for unemployment.This is not a conclusion that American politicians, labor leaders or indeed the general public can easily understand or accept. What confuses the issue even more is that the United Stales is experiencing several separate and different shifts in the manufacturing economy. One is the acceleration of the substitution of knowledge and capital for manual labor. Where we spoke of mechanization a few decades ago, we now speak of “robotization” or “automation”. This is actually m ore a change in terminology than a change in reality. When Henry Ford introduced the assembly line in 1909, he cut the number of man— hours required to produce a motor car by some 80 percent in two or three years—far more than anyone expects to result from even the most complete robotization. But there is no doubt that we are facing a new sharp acceleration in the replacement of manual workers by machines—that is, by the products of knowledge.1.According to the author, the shrinkage in the manufacturing labor force demonstrates（） .2.American politicians and labor lenders tend to dislike（） .3.According to the author, in the coming 25 years, a developed country or industry, in orderto remain competitive, ought to（） .4.This passage may have been excerpted from（） .问题1选项A.the degree to which a country's production is robotizedB.a reduction in a country’s manufacturing industriesC.a worsening relationship between labor and managementD.the difference between a developed country and a developing country问题2选项A.confusion in manufacturing economyB.an increase in blue-collar work forceC.internal competition in manufacturing productionD.a drop in the blue-collar job opportunities问题3选项A.reduce the percentage of the blue-collar work forceB.preserve blue-collar jobs for international competitionC.accelerate motor-can manufacturing in Henry Ford's styleD.solve the problem of unemployment问题4选项A.a magazine about capital investmentB.an article on automationC.a motor-car magazineD.an article on global economy【答案】第1题:A第2题:D第3题:A第4题:D【解析】1.信息推理题。

介孔硅铝酸盐材料的合成、表征及催化应用徐玲;包呼和牧区乐;王晓磊;美春;马媛媛;刘宗瑞【摘要】采用NaOH调节体系的pH值,通过改变造孔剂柠檬酸的加入量,制备了一系列新型介孔硅铝酸盐材料,并利用X射线衍射(XRD)、透射电镜(TEM)和N2吸附-脱附等进行表征,同时分析了不同柠檬酸加入量对材料孔结构的影响.结果表明:合成材料具有蠕虫状内交联的介孔结构,具有较强的酸性；柠檬酸与铝物质的量比为13的样品在苯酚与叔丁醇烷基化反应中具有较高的催化活性和对2,4-二叔丁基苯酚(2,4-DTBP)的选择性；较高的苯酚转化率和对2,4-DTBP的选择性主要归因于催化剂较强的酸性和较大的介孔孔径.%A series of mesoporous aluminosilicate catalysts was synthesized from the synthesizing system with different amounts of citric acid (CA) as pore-forming agent and NaOH as pH adjusting agent. XRD, TEM and N2 adsorption characterization results confirm the presence of interconnected worm-like mesoporous structure in the mesoporous aluminosilicate catalysts. The effect of different amount CA on the porous structures of the mesoporous aluminosilicate materials was investigated. NH3-TPD characterization suggests that most of Al was introduced into mesoporous framework and imparted acid sites. Catalytic test shows that the mesoporous aluminosilicate catalyst with n(CA): n(Al) = 13 exhibits higher catalytic activity than the other catalyst for the alkylation of phenol with tert-butanol. The excellent catalytic activity and high 2,4-di-TBP selectivity are mainly assigned to the acidity together with the large pore size of the mesoporous aluminosilicate catalyst.【期刊名称】《吉林大学学报（理学版）》【年(卷),期】2012(050)006【总页数】5页(P1252-1256)【关键词】介孔硅铝酸盐;柠檬酸;烷基化反应;苯酚叔丁基化【作者】徐玲;包呼和牧区乐;王晓磊;美春;马媛媛;刘宗瑞【作者单位】内蒙古民族大学化学化工学院,内蒙古通辽 028043;内蒙古民族大学化学化工学院,内蒙古通辽 028043;内蒙古民族大学化学化工学院,内蒙古通辽028043;内蒙古民族大学化学化工学院,内蒙古通辽 028043;吉林大学化学学院,长春 130021;内蒙古民族大学化学化工学院,内蒙古通辽 028043【正文语种】中文【中图分类】O611有序介孔材料M41S的发现[1-4]促进了多孔材料的发展, 这些介孔材料广泛应用于催化、生物分离技术及分子工程等领域. 目前对介孔材料的合成研究较多, 如：赵东元等[5-6]合成了具有均匀的二维六方孔道结构的介孔材料(命名为SBA-15). 此外, 离子型和中性表面活性剂可作为模板剂, 粒子间通过静电和氢键的作用而形成介孔孔道.文献[7]利用小分子有机添加剂作为分子模板剂合成介孔材料; 文献[8-9]使用羟基羧酸化合物作为成孔剂, 通过溶胶-凝胶过程合成了具有大的比表面积和高孔隙率的介孔二氧化硅材料. 柠檬酸作为一种有机添加剂, 在溶胶-凝胶过程中可以生成介孔二氧化硅材料. 在pH<10的情况下, 柠檬酸可以与铝物种配位形成稳定的铝-柠檬酸复合物[10]. 文献[11]以柠檬酸为成孔剂制备了一种新型的介孔硅铝酸盐催化剂, 在制备过程中利用三丙基氢氧化铵(TPAOH)调整合成体系的pH值; 文献[12]采用NaOH代替TPAOH调整合成体系的pH值, 得到了介孔材料. 本文在文献[12]的基础上, 考察造孔剂柠檬酸的加入量对介孔硅铝酸盐催化剂孔结构及催化性能的影响.1 实验1.1 样品制备将5份0.05 g NaOH分别溶于10 mL水中, 向每份NaOH溶液中加入0.284 0 g 十八水硫酸铝搅拌至澄清, 再分别向合成体系中缓慢滴加5 mL正硅酸乙酯, 待其充分水解后, 加入不同量的柠檬酸(CA), 搅拌均匀后装釜, 在373 K条件下放置24 h, 产物经过滤、洗涤干燥后在823 K空气气氛中焙烧6 h, 得到不同n(CA)∶n(Al)的产物, 其n(CA)∶n(Al)=13,21,32,53,64. 将焙烧样品用2 mol/L的NH4NO3溶液在85 ℃交换2次, 每次4 h. 交换样品在500 ℃焙烧8 h, 最后得到氢型样品. 1.2 样品表征样品的X射线衍射(XRD)分析采用日本岛津X射线衍射仪(Shimadzu XRD-6000型), Cu Kα靶, 管电压为30 kV, 管电流为40 mA. 样品的孔结构在透射电镜(TEM, Hitachi H-8100型, 日本日立公司)上观测, 操作电压为200 kV. 样品的比表面积和孔体积在吸附仪(Micromeritics, ASAP2010型, 美国Mike公司)上测定, 测定前样品需预处理：在573 K下脱气3 h, 液氮温度下进行吸附, N2为吸附质. Al元素含量采用美国Perkin-Elmer公司生产的Optima3300 DV仪器通过ICP法测定; Si 元素含量采用重量分析方法测量. 催化剂表面酸性测试在自制氨气程序升温脱附(NH3-TPD)装置上进行, TCD作为检测器, He为载气. 操作过程为：将50mg(40～60目)催化剂在N2流中773 K活化1 h后, 降温至373 K, 吸附气袋中的氨气0.5 h, 物理吸附的氨气在373 K下吹扫1 h, 在N2流中以10 K/min 升温速率脱附, 色谱工作站记录NH3脱附曲线.1.3 催化性能测试苯酚叔丁基化反应采用连续流动石英管固定床反应器(石英管内径6 mm), N2为载气. 催化剂装填量为0.5 g, 硅铝酸盐催化剂在773 K的N2氛围中活化1 h后, 降至418 K. 从反应器顶部用微量加样器加注反应物. 反应2 h后取样分析. 分析仪器为日本岛津公司GC-8A型气相色谱, 进样口温度为573 K, 柱温为438 K, XE60型毛细管柱(20 m×0.23 mm), 氢火焰检测. 苯酚转化率和产物选择性以酚类的归一化方法进行计算.2 结果与讨论2.1 XRD分析图1为加入不同量柠檬酸合成材料的XRD谱. 由图1可见, 不同n(CA)∶n(Al)合成样品在2θ=15°～30°均存在一个较宽的衍射峰, 表明合成材料为无定型结构, 且柠檬酸在合成过程中未形成晶体. 此外, 焙烧后的样品也为无定形结构. XRD结果表明, 合成材料的孔壁均未形成特征的晶体结构. 样品的小角XRD谱不存在衍射峰, 表明样品没有长程有序结构.n(CA)∶n(Al): a. 13； b. 21； c. 32； d. 53； e. 64.图1 未经焙烧的不同n(CA)∶n(Al)合成样品XRD谱Fig.1 XRD patterns of non-calcined samples with different n(CA)∶n(Al)2.2 TEM分析焙烧后样品的TEM照片如图2所示. 由图2可见, 样品具有蠕虫状内交联的介孔结构, 随着n(CA)∶n(Al)的增加, 介孔的孔径逐渐增大. 图2中未观察到长程有序的孔结构, 该结果与XRD表征分析一致.2.3 孔结构分析图3为不同n(CA)∶n(Al)合成样品的N2吸附-脱附等温线和相应的孔径分布. 由图3(A)可见, 样品的等温线为典型的Ⅳ型等温线(根据IUPAC定义), 表明合成材料为介孔材料. 由等温曲线中滞后环的形状可见, 样品中存在“墨水瓶”状介孔. 新型介孔硅铝酸盐催化剂中介孔的形成是由于焙烧后除去柠檬酸时留下的孔隙[7]所致. 由图3(B)可见, 随着样品n(CA)∶n(Al)的增加, 样品的孔径分布峰值逐渐增大, 表明介孔的孔径逐渐增大, 孔径参数列于表1. 由表1可见, 随着柠檬酸量的增加, 样品的比表面积逐渐减小, 孔径逐渐增大, 产物中骨架铝含量以n(CA)∶n(Al)=13的样品最多, n(CA)∶n(Al)=64的样品最少. 其原因可能是：在合成过程中柠檬酸与铝物种配位形成稳定的铝-柠檬酸复合物, 柠檬酸的量增多, 导致骨架铝含量减小, 因此终产物中骨架铝含量呈减小的趋势.n(CA)∶n(Al): (A) 13； (B) 32； (C) 64.图2 不同n(CA)∶n(Al)合成样品的TEM 照片Fig.2 TEM images of samples with different n(CA)∶n(Al)图3 样品的N2吸附-脱附等温曲线(A)及孔尺寸分布(B)Fig.3 Isotherms of N2 adsorption-desorption (A) and pore size distributions of samples (B)表1 催化剂的孔参数Table 1 Textural properties of mesoporous aluminosilicate catalystsn(CA)∶n(Al)初始凝胶n(Si)∶n(Al)n(CA)∶n(Al)产物w(Al)/%n(Si)∶n(Al)BET比表面积/(m2·g-1)孔容/(cm3·g-1)孔径/nm1325130.320124.328430.773.52125210.289141.158030.924.23225320.3 03133.587621.065.05325530.264157.026411.146.16425250.260155.975991. 187.22.4 催化剂酸性分析n(CA)∶n(Al): a. 13； b. 21； c. 32； d. 53； e. 64.图4 不同n(CA)∶n(Al)合成样品的NH3-TPD曲线Fig.4 NH3-TPD profiles of samples with different n(CA)∶n(Al)不同n(CA)∶n(Al)合成样品的NH3-TPD曲线如图4所示. 由图4可见, 新型介孔硅铝酸盐催化剂在400～450 K和500～650 K存在2个脱附峰. 低温区脱附峰对应弱酸中心, 高温区脱附峰对应强酸中心, 表明存在中等强度酸性位[13]. NH3-TPD结果表明, 合成材料均具有较强的酸性, 这是由于柠檬酸与铝物种间的相互作用所致. 即柠檬酸和铝物种间的相互作用对于改进框架铝含量和新型催化剂的酸度非常重要.2.5 催化性能表征苯酚叔丁基化反应是典型的Friedel-Crafts烷基化反应, 其主要产物有2-叔丁基苯酚(2-TBP)、 4-叔丁基苯酚(4-TBP)和2,4-二叔丁基苯酚(2,4-DTBP), 并生成少量的2,4,6-三叔丁基苯酚(2,4,6-TTBP). 反应活性主要与催化剂的酸性、孔道结构和表面积有关. 在优化实验条件下, 新型介孔硅铝酸盐催化剂苯酚叔丁基化反应结果列于表2.表2 苯酚与叔丁醇烷基化反应结果*Table 2 Results of alkylation of phenol with tert-butanoln(CA)∶n(Al)苯酚转化率/%产物的选择性/%2-TBP4-TBP2,4-DTBP2,4,6-TTBP1380.44.344.547.53.52171.56.393.60.23270.310.743.144.12.05371.26.8 93.10.16452.017.445.037.5*反应温度=418 K; n(苯酚)∶n(TBA)=1∶1.25; 流速=2.20 L/h.由表2可见, n(CA)∶n(Al)=13样品的苯酚转化率最高, 为80.4%, 4-TBP和2,4-DTBP的选择性分别为44.5%,47.5%, 并生成少量的2,4,6-TTBP. 这是由于n(CA)∶n(Al)=13样品的骨架铝含量最高、酸性最强和比表面积最大所致.n(CA)∶n(Al)=64样品的催化活性最低, 苯酚的转化率为52.0%. 这是由于其骨架铝的含量最低、酸性最弱和比表面积最小所致. n(CA)∶n(Al)=21,53的样品骨架铝含量相近, 属于中等强度的酸性催化剂, 因此催化活性相近, 对4-TBP的选择性均较高, 达到90%以上. 而n(CA)∶n(Al)=32的样品与n(CA)∶n(Al)=21的样品相比, 其骨架铝含量较高, 因此其酸性较强, 对2,4-DTBP的选择性较高, 但由于其比表面积较小, 因此苯酚的转化率相对较低. 此外, 随着反应时间的延长, 催化剂并未明显失活, 主产物的选择性也未明显变化, 这是由于样品的孔径较大, 反应物和产物能够较好的扩散所致.综上所述, 本文以柠檬酸为造孔剂合成了具有较高比表面积的新型介孔材料, 在水热条件下形成了内交联的蠕虫状介孔. 表征结果表明, 该方法可将铝物种引入介孔二氧化硅骨架, 其中n(CA)∶n(Al)=13 样品的骨架铝含量最高, 酸性最强, 将其合成材料应用于苯酚叔丁基化反应中, 其苯酚转化率和2,4-DTBP的选择性均较高.参考文献【相关文献】[1] Kresge C T, Leonowicz M E, Roth W J, et al. 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a rX iv:mat h /67441v1[mat h.DG ]18J ul26A generalization of Reifenberg’s theorem in R 3G.David,T.De Pauw T.Toro ∗Abstract In 1960Reifenberg proved the topological disc property.He showed that a subset of R n which is well approximated by m -dimensional affine spaces at each point and at each (small)scale is locally a bi-H¨o lder image of the unit ball in R m .In this paper we prove that a subset of R 3which is well approximated by a minimal cone at each point and at each (small)scale is locally a bi-H¨o lder deformation of a minimal cone.We also prove an analogous result for more general cones in R n .1Introduction In 1960,thanks to the development of algebraic topology,Reifenberg was able to formulate the Plateau problem for m -dimensional surfaces of varying topological type in R k (see [R1]).He proved that given a set Γ⊂R k homeomorphic to S m −1there exists a set Σ0with ∂Σ0=Γwhich minimizes the H m Hausdorffmeasure among all competitors in the appropriate class.Furthermore he showed that for almost every x ∈Σ0there exists a neighborhood of x which is a topological disk of dimension m .A remarkable result in [R1]is the Topological Disk Theorem.In general terms it says that if a set is close to an m -plane in the Hausdorffdistance sense at all points and at all (small enough)scales,then it is locally biH¨o lder equivalent to a ball of R m .Using a monotonicity formula for the density,Reifenberg proved that some open subset of full measure of Σ0satisfies this condition.In 1964he proved an Epiperimetric inequality for solutions to the Plateau problem described above.This allowed him to show that the minimizer Σ0is locally real analytic (see [R2],and [R3]).Although the Topological Disk Theorem has never again been used as a tool to study the regularity of minimal surfaces it has played a role in understanding their singularities as well as the singular set of energy minimizing harmonic maps (see [HL]).Reifenberg’s proof has been adapted to producebiLipschitz,quasi-symmetric and biH¨o lder parameterizations both for subsets of Euclidean space and general metric spaces (under the appropriate flatness assumptions).See [To],[DT],and [CC].In 1976J.Taylor [Ta]classified the tangent cones for Almgren almost-minimal sets in R 3.She showed that there are three types of nonempty minimal cones of dimension 2in R 3:the planes,sets that are obtained by taking the product of a Y in a plane with a linein the orthogonal direction,and sets composed of six angular sectors bounded by four half lines that start from the same point and make(maximal)equal angles.See the more precise Definitions2.2and2.3.By lack of better names,we shall call these minimal cones sets of type1,2,and3respectively.In this paper we generalize Reifenberg’s Topological Disk Theorem to the case when the set is close in the Hausdorffdistance sense to a set of type1,2or3at every point and every(small enough)ly,if E is a closed set in R3which is sufficiently close to a two-dimensional minimal cone at all scales and locations,then there is,at least locally,a bi-H¨o lder parameterization of E by a minimal cone.Reifenberg’s theorem corresponds to the case of approximation by planes.Let usfirst state the main result and comment later. Theorem1.1For eachε∈(0,10−15),we canfindα∈(0,1)such the following holds.Let E⊂R3be a compact set that contains the origin,and assume that for each x∈E∩B(0,2) and each radius r>0such that B(x,r)⊂B(0,2),there is a minimal cone Z(x,r)that contains x,such that(1.1)D x,r(E,Z(x,r))≤ε,where we use the more convenient variant of Hausdorffdistance D x,r defined by1D x,r(E,F)=Notice that by(1.4)and(1.5)the restriction of f to Z∩B(0,3/2)provides a biH¨o lderparameterization a piece of E that contains E∩B(0,1).This may be enough information, but in some cases it may also be good to know that this parameterization comes from abiH¨o lder local homeomorphism of R3,as in the statement,because this yields informationon the position of E in space.For instance,we can use Theorem1.1to construct local retractions of space near E onto E.Remark1.1We shall see that when Z(0,2)is a plane,we can take Z to be a plane;whenZ(0,2)is a set of type2centered at the origin,we can take Z to be a set of type2centered at the origin;when Z(0,2)is a set of type3centered at the origin,we can take Z to be aset of type3centered at the origin.In addition,our proof will yield that(1.7)B(0,17/10)⊂f(B(0,18/10))⊂B(0,2),(1.8)E∩B(0,18/10)⊂f(Z∩B(0,19/10))⊂E∩B(0,2),and that(1.5)and(1.6)holds for x,y∈B(0,18/10).In fact,we shall omit the case of the plane(too easy and well known),and concentrateon the two other special cases.The general case will essentially follow.Remark1.2It would be a little too optimistic to think that f is quasisymmetric.This is already false when Z(0,2)is a plane,because E could be the product of R with a snowflakein R2.Remark1.3Theorem1.1can probably be generalized to a number of situations,where approximation by minimal sets of types1,2,and3is replaced with approximation by varioustypes of sets with a hierarchical simplex structure.We did notfind the optimal way to statethis,and probably this would make the proof a little heavier.What we shall do instead is state a slightly more general result in Theorem2.2,prove Theorem1.1essentially as itis,and add a few comments from place to place to explain how to generalize the proof forTheorem2.2.A more general statement,if ever needed,is left out for future investigation.Our proof will use the hierarchical structure of E.We shall see that E∩B(0,2)splitsnaturally into three disjoint subsets E1,E2,and E3,where E j is the set of points where Elooks like a set of type j in small balls centered at x(more precise definitions will be given in Section4).If Z=Z(0,2)is a plane,we do not need sets of type2or3in smaller balls,and we are in the situation of Reifenberg’s theorem.Two other main cases will remain,as in Remark1.2.The case when Z is set of type2,with its spine passing through the origin(see Definition2.2below),and the case when Z is set of type3centered at the origin.In thefirst case,we shall see that E3∩B(0,199/100)is empty and E2is locally a Reifenberg-flat one-dimensional set;in the second case,E3∩B(0,3/2)is just composed of one point near the origin,and away from this point E2is locally a Reifenberg-flat.See the end of Section4for details3The sets E1and E2will play a special role in the proof.Even though we shall in fact construct f directly as an infinite composition of homeomorphisms in space(that move points at smaller and smaller dyadic scales),we shall pay much more attention to the definition of f on E2,and then E,just as if we were defining ffirst from the spine of Z to E2,then from Z to E,then on the rest of B(0,3/2).The construction yields that the restriction of f to Z to each of the three or six faces of Z is of class C1if the approximation at small scales is sufficiently good(for instance if we can takeε=Crβon balls of radius r),see Section10.Theorem1.1will be used in[D1]and[D2]to give a slightly different proof of J.Taylor’s regularity result for minimal sets from[Ta].The plan for the rest of this paper is as follows.In Section2we define sets of type2 and3and state a uniform version of our main theorem.We also discuss the moreflexible version of Theorem1.1mentioned in Remark1.3.In Section3we record some of the simple geometrical facts about minimal sets of types1,2,3,and in particular lower bounds on their relative Hausdorffdistances,that will be used in the proof.In Section4we show that E∩B(0,2)is the disjoint union of E1,E2and E3,that E1is locally Reifenberg-flat,and that E3is discrete.In Section5we define the partitions of unity which we use in the construction of the biH¨o lder parameterization.In Section6we construct a parameterization of E2when E3is empty.In Section7we extend this to a parameterization of E.In Section8we explain how to modify the construction when there is a tetrahedral point in E3.In Section9we extend the parameterization to the whole ball.Finally,in Section10,we prove that our parameterization of E is C1on each face of Z when the numbers D x,r(E,Z(x,r))tend to0 sufficiently fast,uniformly in x,as r tends to0.Acknowledgments:Part of this work was completed in Autumn,2005.T.Toro was vis-iting the Newton Institute of Mathematical Sciences in Cambridge,U.K.and the University College London in London.She would like to thank these institutions for their hospitality. 2Two other statementsWe start with a uniform version of Theorem1.1.Definition2.1A set E⊂R3isε-Reifenbergflat(of dimension2)if for each compact set K⊂R3there exists r K>0such that for x∈E∩K and r<r K,D x,r(E,L)≤ε,(2.1)infL∋xwhere the infimimum is taken over all planes L containing x.Note that this definition is only meaningful forεsmall.Reifenberg’s Topological Disk Theorem gives local parameterizations ofε-Reifenbergflat sets.We want to extend this to4theε-minimal sets defined below,butfirst we give a full description of sets of type2and3. Recall that sets of type1are just planes.Definition2.2Define Prop⊂R2byProp={(x1,x2):x1≥0,x2=0}(x1,x2):x1≤0,x2=−√3x1 .Define Y0⊂R3by Y0=Prop×R.The spine of Y0is the line L0={x1=x2=0}.A set of type2is a set Y=R(Y0),where R is the composition of a translation and a rotation.The spine of Y is the line R(L0).Definition2.3Set A1=(1,0,0),A2= −123,−√3,√3 ,and A4= −126))⊂B(x,2r),23r(2.6)E∩B(x,r)⊂f(Z∩B(0,Thus f is a local homeomorphism of the ambient space which sends a minimal cone into theǫ-minimal set.Theorem2.1is an immediate consequence of Theorem1.1.Also,if we can takeεto tend to0in(2.3)(uniformly in x∈E∩K)when r tends to0,then(2.4)holds with constants that tend to0when r tends to0.Let us now try to generalize Theorem1.1.We want to extend the notion of sets of type 1,2,or3.Let usfix integers d≥2(the dimension of our sets)and n≥d+1(the ambient dimension).Sets of type G1are just d-planes in R n.A generalized propeller in R2will be any union P of three co-planar half lines with the same origin,and that meet with angles larger thanπ/2at this point.Incidentally,π/2was chosen a little at random here,and we shall not try to see whether it can be replaced by smaller angles.A set of type G2is a set Y=R(P×R d−1),where P is a generalized propeller in R2 and R is an isometry of R n.When n>d+1,we abused notation slightly,we should have written Y=R(P×R d−1×{0})to account for the last n−d−1coordinates.The spine of R(P×R d−1×{0})is R({0}×R d−1×{0}).A two-dimensional set of type G3in R m is a set T that we can construct as follows.We pick distinct points A j,1≤j≤k,in the unit sphere of R m.Then we choose a graph,as follows.We pick G⊂{1,···,k}2which is symmetric(i.e.,(i,j)∈G when(j,i)∈G),does not meet the diagonal,and is such that for each i∈{1,···,k},there are exactly three j=i such that(i,j)∈G.We callΓthe union of the segments[A i,A j],(i,j)∈G,and then set T={tγ;t≥0andγ∈Γ}(T is the cone overΓ).Equivalently,for each(i,j)∈G,we set F i,j={tz;t≥0and z∈[A i,A j]},and T is the union of the3k/2faces F i,j.In particular, k is even.We add a few regularity constraints.First,the interior of a face F i,j never meets another face,so the faces only meet by sets of three along half lines L j=[0,A j).For each j, exactly three faces F i,j meet L j,and we require that they make angles larger thanπ/2along L j.Thus the union of three half planes that contains these three faces is a two-dimensional set of type G2.We also require that(2.7)|A i−A j|≥τ0for i=jand(2.8)dist(F i,j∩∂B(0,1),F i′,j′∩∂B(0,1))≥τ0when F i,j∩F i′,j′=∅,for some small positive constantτ0that we pick in advance.Another way to state the constraints is to considerΓ′=T∩∂B(0,1):we wantΓ′to be composed of not too small arcs of circles that only meet at their ends,by sets of three,and with angles greater thanπ/2.In addition,we only allow two arcs to be very close when they share at least an end.Let us also allow the case when more than one arc may connect a given pair of points A j(this would imply changing our notation a tiny bit,and taking a graph G that is not6necessarily contained in{1,···,k}2),but demand that k≥4(to avoid the case of a set of type G2).A set of type G3(of dimension d in R n)is a set Z=R(T×R d−2),where R is an isometry of R n and T is a two-dimensional set of type G3in R n−d+2.The spine of Z is the union L of the half lines L i when Z=T is two-dimensional,and R(L×R d−2)when Z=R(T×R d−2).Denote by T Gi the collection of sets of of type Gi(of dimension d in R n),and by T G the union of the three classes T Gi.We claim that in Theorem1.1,we can replace the classof minimal sets with the class T G,as follows.Theorem2.2Let n and d be as above.Let E⊂R n be a compact set that contains the origin,and suppose that for each x∈E∩B(0,2)and r>0such that B(x,r)⊂B(0,2), we canfind Z(x,r)∈T G that contains x,such that D x,r(E,Z(x,r))≤ε.Ifε>0is smallenough,depending only on n,d,andτ0,there is a set Z∈T G such that(1.3)–(1.6)hold. Here againαdepends only onε,n,d,andτ0,and we can takeα=C(n,d,τ0)εforεsmall.The reader may be surprised that we do not require any coherence between the various sets Z(x,r),but this coherence will follow automatically from the fact that D x,r(E,Z(x,r))≤εfor many x and r.For instance,if d=2and Z(0,2)is of type G3,with a center at the origin,our proof will show that for r small,there is a point x r∈E,close to0,such that Z(x r,r)is of type G3,and the number k of half-lines in the spine of Z(x r,r)is the same asfor Z(0,2).The point is that angles between the faces may vary little by little when x and r vary,but things like the type of Z(x,r)and the number k cannot jump randomly.There is an analogue of Theorem2.1in the context of Theorem2.2,which the readermay easily state.The proof of Theorem2.2will almost be the same as for Theorem1.1;what we shall do is proceed with the proof of Theorem1.1,and indicate from time to time which modifications are required for Theorem2.2.3Simple geometrical factsWe shall record in this section a few geometrical properties of the minimal cones that will be used in the construction.The statements will come with various numbers,like1/3or 1/4in the next lemma;these numbers are hopefully correct,but their precise values do not matter,in the sense that it is easy to adapt the value of later constants to make the proof work anyway.In particular,this is what would happen with the proof of Theorem2.2.This means that the reader may skip the proofs if she believes that the results of this section are true with different constants.The geometrical facts below will be used extensively in Section 4,to establish the hierarchical structure of E.Ourfirst lemma says that the Hausdorffdistances between sets of type1,2,and3,are not too small.7Lemma3.1Let Z be a minimal cone of type3centered at x.Then(3.1)D x,r(Z,Y)≥1/3for r>0whenever Y is a set of type1or2.Similarly,(3.2)D x,r(Y,P)>1/3for r>0when Y is a set of type2centered at x and P is a plane,and(3.3)D x,r(Y,P)>1/4for r>0when Y is a set of type2or3whose spine contains x and P is a plane.Proof.We start with the proof of(3.1).By translation,dilation,and rotation invariance,we may assume that x=0,r=1,and Z is the set T0of Definition2.3.It will be good to know that if P is any plane through the origin andπdenotes the orthogonal projection ontoP,then(3.4)B(0,1/3)∩P⊂π(T0∩B(0,1)).Let Q denote the solid tetrahedron with vertices A j,1≤j≤4,(i.e.,the convex hull of the A j),where the A j are as in Definition2.3.It is clear that B(0,1/3)lies on the right ofthe left face of Q(where thefirst coordinate is−1/3).By symmetry,B(0,1/3)lies in Q, because it lies on the right side of each face.Also observe that T0∩Q separates the(open) faces of Q from each other inside Q.For instance,the component in Q\T0of the lower faceis a pyramidal domain bounded by three faces of T0.Let z∈B(0,1/3)∩P be given,and letℓdenote the line through z perpendicular to P.Thenℓmeets Q because B(0,1/3)⊂Q.First suppose that it does not touch any edge of Q.Then it enters Q through one(open)face and leaves it through another one,so it meets T0∩Q.Ifℓtouches a edge of Q,it meets T0∩Q trivially(because the edges are contained in T0).Thusℓmeets T0∩B(0,1)(except perhaps ifℓcontains one of the A j),and hence z∈π(T0∩B(0,1)).The remaining case whenℓcontains some A j is easily obtained by density(and anyway we don’t need it);(3.4)follows.Return to(3.1).If Y is of type2,choose P orthogonal to the spine of Y;thenπ(Y) is a propeller(a set like Prop in(2.2)),and we canfind z∈∂B(0,1/3)∩P such that dist(z,π(Y))≥1/3.Set z n=(1−2−n)z for n>1.By(3.4)we canfind y n∈T0∩B(0,1) such thatπ(y n)=z n.Then dist(y n,Y)=dist(z n,π(Y))≥1/3−2−n,and(3.1)follows from the definition(1.2)The case when Y is a plane is even easier;we choose P perpendicular to Y,so thatπ(Y)is a line.So(3.1)holds in all cases.Let us now prove(3.2).We may assume that x=0and Y is the set Y0=Prop×R in(2.2).Let P be a plane,suppose that D x,r(Y,P)≤1/3,and let usfind a contradiction. First we want to show that P is almost horizontal.Call P0the horizontal plane R2×{0}, and denote by b1,b2,and b3the three points of∂B(0,9)∩ Prop×{0} .108Each b j lies in Y∩B(0,1),so we canfind b′j in P∩B(b j,1/3).Call d the smallest possible distance from a p j to the line through the other two p l.Then d corresponds to the case when,for instance,p j lies at the extreme right of the left-most disk D j and the two other p l lie at the extreme left of the D l.We get that d=92−2·160.Recall that P goes through the b′j.The fact that d>0(or that the p j are not aligned) already implies that P is a graph over P0.We want to show that it is a1-Lipschitz graph, or equivalently that(3.5)|v3|≤|π(v)|when v is a unit vector in the(direction of)the plane P,and v3denotes its last coordinate. Since the triangle with vertices b′j is nondegenerate,we can write v=α(b′j−c j),where α∈R\{0},1≤j≤3,and c j lies in the opposite side[b′k,b′l].Since c j is a convex combination of b′k and b′l,the size of its last coordinate is at most13.On the other hand,|π(b′j−c j)|≥d=413<4110)and b5=(0,0,95−215, while|π(v)|≤21034=173·2054|π(v)|instead of(3.5).Now we take b4=0and b5=(0,0,99100−1100,and |π(v)|≤1100|π(v)|>40Notice that even for sets of type T Gi,Lemma3.1is very easy to prove by compactness, when we allow very small constants instead of1/3and1/4.The next lemmas will make it easier to apply Lemma3.1.Lemma3.2Let T be a minimal cone of type3,and let B be a ball such that54times the radius)does not contain the center of T.Then thereis a minimal cone Y of type1or2such that Y∩B=T∩B.Proof.Again this would be very easy,even for sets of type T Gi,if we allowed a verylarge constant instead of54replaced with the betterconstantα−1,whereα=(2/3)1/2(observe that5Let P denote the plane through0,A2,and A3,and set x t=(−t,0,0)for t>0;we claim√3z=0(just check that0,that dist(x t,P)=αt.Indeed,an equation of P is2√12=αt,as announced. A2,and A3satisfy the equation).Then dist(x t,P)=(2Let x=0be given,and set B x=B(x,α|x|).We just checked that when x=x t,B x does not meet the three faces on the left of T0.For a general x,B x cannot meet the three faces at the same time,because the optimal position for this to happen would precisely be when x lies on the negativefirst axis.By symmetry,B x never meets the three faces of T that bound a given connected component of R3\T.So the worse that it can do is meet the three faces of T that share a single edge[0,A j)(if B x meets two opposite faces,it also meets the three faces that bound some connected component).Supposefirst that B x meets three such faces,and let Y denote the set of type2that contains these faces.We claim that(3.6)T∩B x=Y∩B x.The direct inclusion is clear,because B x only meets the three faces of T that are contained in Y.For the converse inclusion,we just need to check that F∩B x⊂F′∩B x when F is a face of Y and F′is the face of T that is contained in F.Let y∈F∩B x be given.By assumption,B x meets F′,so we can pick z∈F′∩B x.Since B x is open,we can even pick z in the interior of F′.Notice that the segment[y,z]lies in F∩B x by convexity.In addition, (y,z)does not meet the spine of Y(because z lies in the interior of F).Now B x does not meet the other edges of T(those that are not contained in the spine of Y),because if it meets an edge e,it also meets the three faces of T that touch e.So(y,z)does not meet the boundary of F′,and y∈F′.Our claim follows.Next suppose that B x only meets two faces of T.Still denote by Y the set of type2 that contains them.As before,T∩B x⊂Y∩B x trivially.To prove the converse inclusion, consider a face F of Y,andfirst assume that the face F′of T that it contains meets B x. Pick z∈F′∩B x.For each y∈F∩B x,the segment[x,y]is contained in B x,hence it does not meet the boundary of F′(because if B x meets any edge of T,it meets at least three faces),so it is contained in F′,and y∈F′.We just proved that F∩B x⊂F′∩B x.Call F1,F2,and F3the three face of Y,and denote by F′j the face of T which is contained in F j.Exactly two of the F′j meet B x,and the third one does not;let us assume that this last one is F′3.We just need to check that F3does not meet B x either.Suppose it does.Let y j be a point of F j∩B x,j∈{1,2,3}.Call y′j the orthogonal projection of y j onto the plane P through the center of B x and perpendicular to the spine L of Y;then y′j∈F j∩B x as well. Call p the point of L∩P;by convexity of B x and because p is a convex combination of the three y′j,B x contains p.We reached the desired contradiction,because p lies on an edge of P and B x does not meet edges in the present case.So we proved(3.6)in this second case.Finally assume that B x only meets one face F′of T.Then it does not meet any edge of T,so if Y denotes the plane that contains F′,T∩B x contains Y∩B x(as before,B x does not meet the boundary of F′in Y).In this case also we have(3.6).We just proved that for x=0,we canfind a set Y of type1or2such that(3.6)holds. Now let B be as in the statement,and call x its center and r its radius.We know that10B(x,5rLemma3.3Let Z be a minimal cone of type3centered at z,and let T be a minimal cone.If D x,r(T,Z)<1/3,then T is of type3and its center lies in B(z,5r/3).Proof.Let Z and T be as in the statement.If T is of type1or2,we can apply Lemma3.1 directly to get a contradiction.So T is of type3,and let t denote its center.By Lemma3.2, we canfind a set Y of type1or2that coincides with T in B=B(z,4r),Y coincides with T in B(z,43Lemma3.4Let Z be a set of type2or3.Suppose that the ball B(x,r)meets at least two faces of Z,or that Z does not coincide with any plane in B(x,r).Then the distance from x to the spine of Z is at most6r/5.Proof.For sets of type G2or G3(and with6/5replaced with a large constant),this is a simple consequence of(2.8).We now return to the standard case.Let L denote the spine of Z.We can assume that B=B(x,r)does not meet L.If Z does not coincide with any plane in B,it meets at least one face F;call P the plane that contains F.Since B does not meet L,it does not meet the boundary of F in P,so P∩B⊂Z.Then B meets some otherface of F′of Z.Call P′the plane that contains F′,and set D=P∩P′and d=dist(x,D).√Then r≥d cos(30◦)=d3/2≥5/6.So we can assume that Z is of type3.If B(x,d)meets L,then dist(x,L)≤d≤6r/5as needed. Otherwise,P∩B(x,d)⊂F,because B(x,d)meets F and does not meet the boundary of F in P.But P∩B(x,d)goes all the way to the point of D that minimizes the distance to x,so this point lies in L and dist(x,L)≤d.Lemma3.4follows.and(4.3)c(x,r)=inf D x,r(E,T);T is a set of type3centered at x .It is not always true that either a(x,r),b(x,r),or c(x,r)is small(when x∈E and B(x,r)⊂B(0,2)),because,for instance Z(x,r)may be a minimal cone of type3centered anywhere in B(x,r).The pairs where either a(x,r),b(x,r),or c(x,r)is small are interesting to study. Definition4.1Let x∈E∩B(0,2)be given.We say that:•x is of type1when b(x,r)≤1500εfor all r small,•x is of type32as it is,and the value of a8=7follows from the geometry.Then a9=10−3just needsto be small,depending on a5and a6.Also,a10=11just needs to be a little larger than a7. The constant a11=15in Corollary4.1just needs to be larger than2a8.The constants a12=10−3,a13=10−3,and a14=132in Lemma4.3are just geometric constants that come from Lemma3.3.Ourfirst constraint on a3comes from Lemma4.3and is that a3≥a14.No constraint comes from Lemma4.4;the constant in(4.12)is just the same as a11in Corollary4.1.In Lemma4.5,we just need a15=25needs to be large enough(it needs to be larger than 10in our proof,because we want the pair(z1,r/10)to satisfy the assumptions in the lemma, a little above(4.19));other constraints will come later.The value of a16=600follows by geometric computations,and so does a17=150in(4.15).We need to pick a3≥a17in Definition4.1.Thefirst constraint on a2in Definition4.1is that a2be larger than the constant in(4.20).12The constant a18=17in Lemma4.6is just a geometric constant.In(4.24)and the few lines above,10−3needs to be replaced with a9from Lemma4.2.A few lines later,we only get that b(x,r)≤a19ε,instead of500ε;this gives a new constraint on a2,namely that a2≥a19(so that we can deduce that x∈E2).The rest of the proof of(4.23)goes smoothly.In Lemma4.7,a20=24can be replaced with2|z−e|≤εr.Obviously,e∈B(x,r),so we canfind p∈P0such that|p−e|≤10−3r;then |p−z|≤εr+10−3r<ρ/3.Similarly,if p∈P0∩B(y,ρ)we canfind e∈E such that |p−e|≤10−3r.Then e∈B(x,r),so we canfind z∈Z such that|z−e|≤εr;altogether |p−z|≤εr+10−3r<ρ/3,and D y,ρ(Z,P0)<1/3.This is impossible,by Lemma3.1.Next suppose that Z is a set of type3,whose center z∈B(x,99r/100),but whose spine meets B(x,98r/100)at some point y.As before,D y,ρ(Z,P0)<1/3forρ=r/200.Since |z−y|≥r/100,Lemma3.2says that Z coincides with a set Y of type2in B(y,4r/500)= B(y,8ρ/5).Then D y,ρ(Y,P0)<1/3too.But the spine of Y goes through y,so Lemma3.1 says that this is impossible.The same argument excludes the case when Z is a set of type 2whose spine meets B(x,98r/100).We are left with the case when Z is of type1,or else its spine does not meet B(x,98r/100). Let F denote the face of Z that contains x,and P the plane that contains F.The boundary of F is contained in the spine of Z,so it does not meet B(x,98r/100);hence(4.6)F∩B(x,98r/100)=P∩B(x,98r/100).Every point of P∩B(x,98r/100)lies in Z by(4.6),so it isεr-close to E,and then(ε+10−3)r-close to P0.This forces every point of P0∩B(x,r)to be2·10−3r-close to P.This stays true (with a constant larger than2)when we deal with sets of type Gi and approximations with d-planes in R n.If(4.5)fails,(4.6)says that there is another face F1of Z that meets B(x,97r/100)at some point y.We know that y isεr-close to E,hence(ε+10−3)r-close to P0.Hence, dist(y,P)≤(ε+3·10−3)r.[In all these estimates,we use the fact that y∈B(x,99r/100), so the successive points that we implicitly use never lie out of B(x,r).]On the other hand,y lies in some other face of Z,and the angles between faces of Z are not too small,so the distance from y to the spine of Z is less than10−2r.For sets of type Gi,we deduce this from(2.8).This is impossible,because the spine of Z does not meet B(x,98r/100).So(4.5)holds.We now return to the lemma,and let y∈B(x,2r/3)be as in the statement.Let us first estimate a(y,t)for t∈(r/10,4r/10).First observe that B(y,t)⊂B(x,967r/1000). By(1.1)and(4.5),we canfind q y∈P such that|y−q y|≤εr.Set P′=P+(y−q y). We can use P′to compute a(y,t),because it goes through y,so a(y,t)≤D y,t(E,P′).If e∈E∩B(y,t),dist(e,P′)≤dist(e,P)+|y−q y|≤dist(e,P)+εr≤2εr,by(1.1) and(4.5).If p′∈P′∩B(y,t),p=p′−(y−q y)lies in Z∩B(x,97r/100)by(4.5),and dist(p′,E)≤dist(p,E)+εr≤2εr by(1.1).So a(y,t)≤D y,t(E,P′)≤2εr/t≤20ε.The pair(y,t)satisfies the hypothesis of the lemma,namely,a(y,t)≤10−3,so we can iterate the previous argument(this time,keeping y at the center).This yields that a(y,s)≤20εfor r/100≤s≤4r/10,and(after many iterations of the argument)for every s<4r/10.Finally,for each s<4r/10there is a set Z(y,s)as in(1.1),and since a(y,s)≤20εthe proof of(4.5)shows that Z(y,s)coincides with a plane P on B(y,97s/100).We can use P in the definition of a(y,96s/100),and we get that a(y,96s/100)≤100ε/96≤2ε.Since this holds for s<4r/10,Lemma4.1follows.。

小学上册英语第2单元测验卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.My ________ (玩具名称) helps me learn about friendship.2.My grandma loves to __________ (照顾) her pets.3.What sweet treat is made from cocoa?A. CakeB. CandyC. Ice creamD. Chocolate4.Which vegetable is orange and long?A. PotatoB. CarrotC. LettuceD. TomatoB5.What is the name of the famous mouse character?A. Donald DuckB. Mickey MouseC. GoofyD. PlutoB6.Planting _____ (果树) provides food for many creatures.7.The country famous for its chocolates is ________ (瑞士).8. A __________ is a large area of rocky terrain.9.What is the capital of Switzerland?A. GenevaB. ZurichC. BernD. BaselC Bern10.I bought a _______ (new) dress.11.My brother has a _____ (机器人) that can walk and talk. 我的哥哥有一个可以走和说话的机器人。

12. A butterfly undergoes metamorphosis from ______ (幼虫) to adult.13.globe) shows a model of the Earth. The ____14.The __________ was a key moment in the fight for civil rights. (马丁·路德·金的演讲)15.We have a picnic on the _____ (草地).16.What is the name of the largest desert in the world?A. SaharaB. GobiC. ArcticD. Antarctic17. A _____ (蚂蚁) works hard to gather food for winter.18.What do we call a young dolphin?A. CalfB. PupC. KitD. FawnA Calf19.He is flying a ___. (kite)20.What do you call a group of stars?A. GalaxyB. Solar SystemC. ConstellationD. Nebulabustion is the process of burning a _____.22.I enjoy ______ in my free time. It allows me to express my feelings and creativity. Sometimes, I like to ______ with different colors and styles. My favorite materials to use are ______ and ______.23.The _____ (自然灾害) can affect plant growth dramatically.24. (36) Sea is known for its saltiness. The ____25.The _____ is a group of stars that form a picture in the sky.26.My best friend is very __________. (体贴)27.I enjoy ______ (看) funny videos.28.What is the term for a written work that tells a fictional story?A. PoemB. NovelC. ArticleD. EssayB29.What is the name of the famous river in China?A. YangtzeB. MekongC. GangesD. IndusA30.I like eating ________ (chocolate) cake.31.What do you call the main character in a story?A. ProtagonistB. AntagonistC. HeroD. VillainA32.What is the name of the famous wizarding school in Harry Potter?A. HogwartsB. NarniaC. OzD. Neverland答案:A33.The city of Suva is the capital of _______.34.The chemical symbol for manganese is _______.35.We will have a ________ picnic.munity project) addresses local needs. The ____37.My family enjoys going to the ____.38. A chemical reaction that requires heat to proceed is called an ________ reaction.39.ts are ______ (甜) while others are sour. Some fru40.I have a ________ that glows in the dark.41.What is 5 - 1?A. 3B. 4C. 5D. 642.The burning of fossil fuels contributes to ________ change.43. A turtle can retract its head into its ________________ (壳) for protection.44.The chemical formula for phosphoric acid is __________.45.The ______ contributes to the ecosystem.46.The __________ (历史的智慧) guides decision-making.47.The process of making lemonade is an example of creating a _____.48. A ________ (岛) is surrounded by water.49.My friend is a ______. He loves to explore new ideas.50.The _______ of a liquid can change based on temperature.51.My favorite movie star is _______ (名字). 她的表演很 _______ (形容词).52.Heat can speed up ________ reactions.53.The __________ (历史的印记) leaves a legacy.54.What do we call the smallest unit of life?A. OrganB. TissueC. CellD. OrganismC55.I want to _______ a great leader.56.What is the capital of the United Arab Emirates?A. DubaiB. Abu DhabiC. SharjahD. AjmanB57.The sun is _____ after the rain. (shining)58.What do you call the upper part of a tree?A. TrunkB. BranchC. CanopyD. RootsC59.We are going to the ___. (beach) this summer.60.The first person to fly solo nonstop across the Atlantic was _______ Lindbergh.61.What do you call a person who flies an airplane?A. PilotB. EngineerC. MechanicD. Stewardess62.What do you call a group of bees?A. SwarmB. FlockC. SchoolD. Pack63. A metal that is highly malleable is ______.64. A solution that can conduct electricity is called a _______.65.I enjoy watching the __________ fall during winter. (雪)66.I like to play ______ in the garden.67.What is the opposite of "light"?A. DarkB. HeavyC. BrightD. Dim68.My favorite animal is a ______ (兔子) that hops joyfully.69.What is a common pet that purrs?A. DogB. CatC. RabbitD. ParrotB70.The _________ (玩具) shop is full of _________ (颜色鲜艳的) toys.71.The ________ (engineer) designs buildings.72.What is the capital of the Cook Islands?A. AvaruaB. RarotongaC. MangaiaD. AitutakiA73.The ________ (initiative) drives progress.74.What is the freezing point of water?A. 0 degrees CelsiusB. 100 degrees CelsiusC. 50 degrees CelsiusD. 10 degrees CelsiusA75.What do we call the outer layer of the Earth?A. CrustB. MantleC. CoreD. Lithosphere76. A ____(local economy) supports small businesses.77.The ______ (植物分类法) organizes different species.78.Which planet is known for its tilted axis?A. VenusB. NeptuneC. UranusD. Mars79.What do you call a group of wolves?A. PackB. PrideC. FlockD. School80. A base is a substance that can accept _______ ions.81.The _____ (土壤改良) can enhance plant growth.82.I can ___ (knead) dough for bread.83.The chemical formula for copper(I) chloride is _____.84.The ________ has a soft voice.85.The bee gathers nectar from _______.86.What is the opposite of hot?A. WarmB. ColdC. CoolD. ChillyB87.I like to draw pictures of different ______ (天气).88._____ (园艺) can be a relaxing hobby.89.What is 1 + 1?A. 1B. 2C. 3D. 4B90.I enjoy sharing my toy ________ (玩具名称) stories with friends.91.What is the main ingredient in tacos?A. BreadB. TortillaC. RiceD. NoodlesB92.The teacher is in the ___. (classroom)93.Which of these is a primary color?A. PurpleB. OrangeC. GreenD. RedD94.What is the process of making bread called?A. BakingB. FryingC. BoilingD. Grilling95.What is 12 - 5?A. 7B. 8C. 6D. 996.What is the name of the holiday celebrated on February 14?A. New YearB. Valentine's DayC. ThanksgivingD. Christmas97. A chemical reaction that releases heat is called an _______ reaction.98.What is the name of the largest land animal?A. HippopotamusB. ElephantC. GiraffeD. RhinoB99.The __________ is a region known for its mountains.100. A __________ can occur when water mixes with soil and causes it to flow.。