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THREE NEW F ACTORS OF FERMAT NUMBERS

R.P.BRENT,R.E.CRANDALL,K.DILCHER,AND C.VAN HALEWYN

Abstract

We report the discovery of a new factor for each of the Fermat numbers F13,F15,F16.These new factors have27,33and27decimal digits respectively.Each factor was found by the elliptic curve method.After division by the new factors and previously known factors,the remaining cofactors are seen to be composite numbers with2391,9808and19694decimal digits respectively.

Comments

Only the Abstract is given here.The full paper appeared as[2].A preliminary version(with two factors and three authors)appeared as[1].

References

[1]R.P.Brent,R.E.Crandall and K.Dilcher,em Two new factors of Fermat numbers,Technical Report

TR-CS-97-11,CSL,ANU,May1997,7pp.rpb175tr

[2]R.P.Brent,R.E.Crandall,K.Dilcher and C.Van Halewyn,“Three new factors of Fermat numbers”,

Mathematics of Computation S0025-5718(00)01207-2(published electronically1March2000).rpb175.

Oxford University Computing Lab,Wolfson Building,Parks Road,Oxford OX13QD,UK E-mail address:Richard.Brent@https://www.sodocs.net/doc/0f4962217.html,

Center for Advanced Computation,Reed College,Portland,OR97202,USA

E-mail address:crandall@https://www.sodocs.net/doc/0f4962217.html,

Department of Mathematics and Statistics,Dalhousie University,Halifax, Nova Scotia B3H3J5,Canada

E-mail address:dilcher@cs.dal.ca

Department of Computer Science and Engineering,Oregon Graduate Institute

Current address:Deutsche Bank AG,London,England

E-mail address:Christopher.van-halewyn@https://www.sodocs.net/doc/0f4962217.html,

1991Mathematics Subject Classi?cation.11Y05,11B83,11Y55;Secondary11-04,11A51,11Y11,11Y16, 14H52,65Y10,68Q25.

Key words and phrases.discrete weighted transform,DWT,ECM,elliptic curve method,factorization,Fermat number,F13,F15,F16,F18,integer factorization.

Comments c 1997,the authors.

Copyright c 2000,American Mathematical Society.

rpb175a typeset using A M S-L A T E X.

References引用格式范文赏析

References引用格式范文赏析 Assignment的引用格式 国外每所大学在论文或者作业中对reference参照系统要求不一样,比如有的学校要求用哈佛文献标注格式,有的学校要求用CMS芝加哥文献标注格式,当然还有其他类型的格式,这就要求同学们向老师咨询清楚该次作业要求使用哪种文献标注格式,不要到时候白忙活。下面为大家整理了一篇references写作的范文,大家可以学习一下这篇reference里面的写作方法。 References Alpert, F, Heaney, J & Kuhn, KL 2009, ‘Internships in marketing: Goals, structures and assessment –Student, company and academic perspectives’, Australasian Marketing Journal, vol. 17, no. 1, May, pp. 36–45. Boud, D 2001, ‘Using journal writing to enhance reflective practice’, New Directions for Adult and Continuing Education, no. 90, Summer, pp. 9–17. Boyatzis, RE 2007, ‘Developing emotional intelligence competencies’, in J Ciarochi & JD Mayer (eds), Applying Emotional Intelligence, Psychology Press, New York, pp. 28–52. Ca rson, L & Fisher, K 2006, ‘Raising the bar on criticality: Students’ critical reflection in an internship’, Journal of Management Education, vol. 30, no. 5, October. Fisher, K n.d., ‘Critical self-reflection: what is it and how do you do it?’, Southern Cross University Teaching and Learning Seminar Notes. Richert, AE 1990, ‘Teaching teachers to reflect: A consideration of programme structure’, Journal of Curriculum Studies, no. 22, pp. 509–527. Sch?n, DA 1998, The reflective practitioner: How professionals think in action,Ashgate Arena, London. Weighart, S 2009, Learning from experience: A resource book by and for co-op/internship professionals, Mosaic Eye Publishing, USA.

虚拟现实 触觉 With References

虚拟现实:触觉 在触觉虚拟现实设备中,首先介绍了触觉虚拟现实设备了理论基础和物理原理。然后我们介绍了触觉虚拟现实设备目前的理论发展情况。接着,我们介绍了一些桌面式虚拟现实反馈设备,如PHANTOM、MIRAISENS,以及一些穿戴式虚拟现实反馈设备,如CyberGrasp、中视典数据手套。最后,我们展望了触觉虚拟现实理论基础在今后能够有哪些改良和发展,以及触觉设备在今后能够有那些方面的提升和创新。 一、背景 虚拟现实技术是一种有效的模拟人在自然环境中视、听、动等行为的高级人机交互技术。在实现了视觉体验与听觉体验的高度结合之后,虚拟现实技术开始朝人类的触觉感官进发。触觉源自于希腊语“Haptesthai”,意思是解除物体的感觉,触觉指的是人通过皮肤对热、压力、振动、滑动以及物体表面纹理、粗糙度等特性的感知。触觉反馈是指在人机交互过程中,计算机对操作者的输入做出响应,并通过触觉反馈设备作用于操作者的过程。 二、工作原理 触觉反馈的虚拟现实系统由操作者、触觉反馈设备和虚拟环境组成。触觉反馈设备的主要功能是利用传感器测量操作者的运动和位置,将数据实时、准确地输入计算机,并且将虚拟环境中生成的力感和触感反馈给操作者,让操作者又身临其境的沉浸感。虚拟环境接受由传感器传入的数据,根据一些特定的算法生成三维图像和控制信号,分别传给显示设备和触觉反馈设备。 三、理论研究

力觉和触觉的生成研究最早可追溯到1954年。在远程控制的核环境集成机器人系统中,德国科学家开展了力觉生成的研究。经过几十年的缓慢发展,人们逐渐意识到触觉的生成和反馈具有广泛的应用前景。近年来,触觉再现技术的重要性已被广泛认识并开始得到重点研究。美国的斯坦福大学、哈佛大学、西北大学、华盛顿大学、麻省理工学院等先后开展了触觉建模和触觉再现的研究。 目前,最常见的力觉和触觉生成算法是利用PHANTOM设备,根据虚拟物体的刺穿深度运用虎克定律计算接触力。当用户手指操作PHANTOM设备与虚拟环境交互,作为手指化身的“Avatar”接触到虚拟物体时,Massie和Salisbury提出用弹簧线性力学模型来模拟它们之间的力学关系,运用虎克定律计算作用力,并且反馈到用户的真实手指上。依据虚拟物体刺穿深度的不同求解方法,该方法又可分为基于点的接触力生成算法和基于射线的接触力生成算法。 国内对触觉生成也展开了相关研究。浙江大学CAD&CG国家重点实验室的杨文珍等通过试验得到指尖接触力与接触面积之间关系的数据样本,利用回归方程建立两者之间关系的经验公式,然后以虚拟指尖接触面积为变量计算出指尖接触力。采用软手指接触模型。依据虚拟手最小平衡力抓持假设,用近似摩擦锥等作为优化目标函数来求解抓持力,并最终在虚拟环境中进行了实现。 东南大学的吴涓和宋爱国等提出了一种基于物理意义的快速力反馈形变模型和实时力觉相应算法。该方法不仅计算速度快,可以满足力反馈的实时性要求,而且能够同时保证接触力和形变的计算具有较高的精度。 四、产品开发 1.桌面式反馈设备 桌面式反馈设备通常是固定在桌面或者是地面上的,更像是一个小型的机器人。操作者控制这些桌面式反馈设备的末端进行操作。反馈设备通过检测末端点的位置来计算力的大小,通过驱动装置来给操作者提供触觉反馈的感觉。 (1)Phantom 由美国Sensable公司生产的“Phantom”是一个典型的桌面式反馈设备,在世界范围内都用得很广泛。在Phantom发明之前,电脑使用者仅能凭借看或是听和电脑或设备互动,而在很多任务或工作中都扮演着最重要角色的触觉,很显然的被忽略了。Phantom的出现改变了这样的情况。就像使用者通过屏幕看见影像,通过音响装置听见合成声音一般,Phantom可以让使用者触摸并且可操作虚拟的物体。

Solidwork外部参考引用(External References)培训教程

Solidwork外部参考引用(External References)培训教程外部参考引用(External References) 外部参考引用是在一个文档依赖于另一个文档求解时生成的。如果参考文件改变,则依赖于它的文件也改变。 在装配体中,您可以在零部件中生成一个参考其它零部件几何特征的关联特征。则此关联特征对其它零部件进行了外部参考。如果您改变了参考零部件的几何特征,则相关的关联特征也会相应改变。 如果更新路径可用,关联特征会自动更新。更新路径包含在您建立参考关系的装配体中。如果更新路径不可用(例如,如果装配体文档已关闭),则在下次您打开包含更新路径的装配体时进行更新。 关联特征的更新路径显示在装配体的 FeatureManager 设计树中。您可通过用右键单击顶层装配体图标并选择隐藏更新夹或显示更新夹来隐藏或显示所有这些关联图标。 当在关联装配体中设计时,您可以选择不生成生成外部参考引用。 FeatureManager 设计树规则 在 FeatureManager 设计树中,任何具有外部参考的项目都有一个指示参考状态的后缀: ?后缀 -> 表明参考是关联的。它是解出的和最新的。 ?后缀 ->? 表明参考是非关联的。特征是未解出的或不是最新的。如要解出和更新特征,请打开包含更新路径的装配体。 ?后缀 ->* 意味着该参考引用被锁定。 ?后缀 ->x 意味着该参考引用被中断。 若要列举零件或特征上的外部参考引用,用右键单击零件或特征或右键单击更新夹,然后选取列举外部参考引用。 相关主题 列出外部参考引用 锁定和中断外部参考引用 控制生成外部参考引用 外部参考引用规则 外部参考引用 - 选项

参考文献标准

3. References All sources included in the References section must be cited in the body of the paper (and all sources cited in the paper must be included in the References section). A. Pagination: The References section begins on a new page. B. Heading: References (centered on the first line below the manuscript page header). C. Format: The references (with hanging indent) begin on the line following the References heading. Entries are organized alphabetically by surnames of first authors. D. Authors: Authors are listed in the same order as specified in the source, using surnames and initials. Commas separate all authors. When there are two to six authors, use the ampersand & after a comma and before the last author. When there are seven or more authors, lis t the first six and then use “et al.” for remaining authors. If no author is identified, the title of the document begins the reference. For example, Wolchik, S. A., West, S. G., Sandler, I. N., Tein, J., Coatsworth, D., Lengua, L., et al. (2000). An experimental evaluation . . . . One-author entries precede multiple-author entries beginning with the same surname. For example, Alleyne, R. L. (2001). …. Alleyne, R. L., & Evans, A. J. (1999). …. References with exactly the same author (or authors in the same order) are arranged by year of publication, the earliest first. For example, Hewlett, L. S. (1996). …. Lewlett, L. S. (1999). …. Cabading, J. R., & Wright, K. (2000). …. Cabading, J. R., & Wright, K. (2001). …. References by the same author (or by the same two or more authors in the same order) with the same publication date are arranged alphabetically by the title (excluding A,An or The) that follows the date. However, if the references with the same authors published in the same year are identified as articles in a series (e.g., Part 1 and Part 2), order the references in the series order, not alphabetically by title. Lowercase letters – a, b, c, and so on – are placed immediately after the year, within the parentheses. For example, Baheti, J. R. (2001a). Control . . . . Baheti, J. R. (2001b). Roles of . . . . E. Publication date: Publication date is put in parentheses following authors, with a period following the closing parenthesis. If no publication date is identified, use

英文简历十大元素之(10)证明人References

英文简历十大元素之(10)证明人References 在英语简历的最后写出证明人,可以让雇主感觉到你的简历是真实可靠经得起查询的。如果你的证明人有名望,会对雇主产生一定的影响。 以下几种人可作为证明人的人选: a.校长、系主任、任课老师,这些人可以证明你的学业情况及性格。 b.单位的领导,以便证明你的工作能力、业务成就和个性。 c.同事或同学,通常证明你的个性与爱好。 写证明人应包括姓名、职位、单位、电话及地点。例如: References Gaoxu Dai, Chairman Prof. Dahai Li Dept. of Computers Dept. of Computers Guangdong Institute of guangdong Institute Commerce of Commerce Guangzhou Guangzhou Tel: 4561790 Tel: 4561791 证明人 广州广东商学院广州广东商学院 计算机系计算机系 戴高旭主任李大海教授 电话:4561790电话:4561791 以上这个例子,适应于大学应届毕业生,证明人一位是系主任,一位是任课教师。 References Mr. Yingming Ma Prof. Fucheng Liu Manager Export Dept. Dept. of Interna- Jiangsu Arts and Crafts Corp. tional Trade Nanjing Nanjing University Tel: 6539402 Tel: 3695718 证明人 南京江苏工艺品进出口公司南京大学 出口部经理国际贸易系 马英明先生刘府城教授 电话:6539402电话:3695718 以上这个例子,适应于大学毕业后才工作一两年的应聘者,证明人一个是工作单位的领导,一个是毕业学校的任课老师。 References Mr. *** Ms. ***** Manager, Import Dept. Manager, Export Dept. ************** and Export Corp. Co., Ltd Beijing Nanhai Tel: 证明人 ***************有限公司 进口部经理出口部经理

References(原始)

References 1.L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge University, 2004). 2.V. K. Valev, J. J. Baumberg, C. Sibilia, and T. Verbiest, “Chirality and chiroptical effects in plasmonic nanostructures: Fundamentals, recent progress, and outlook,” Adv. Mater. 25, 2517–2534 (2013). 3.Lei Kang, Shoufeng Lan, Yonghao Cui, Sean P. Rodrigues , Yongmin Liu, Douglas H. Werner, and Wenshan Cai, “An Active Metamaterial Platform for Chiral Responsive Optoelectronics,” Adv. Mater. 27(29), 4377–4383, (2015). 4.W. M. Zhu , Q. H. Song , L. B. Yan , W. Zhang , P. C. Wu , L. K. Chin , H. Cai , D. P. Tsai , Z. X. Shen , T. W. Deng , S. K. Ting , Y. D. Gu , G. Q. Lo , D. L. Kwong , Z. C. Yang ,R. Huang , A. Q. Liu, and N. I. Zheludev, “A Flat Lens with Tunab le Phase Gradient by Using Random Access Reconfigurable Metamaterial,” Adv. Mater. 27(32), 4739–4743, (2015). 5.J. Zhou, J. Dong, B. Wang, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79(12), 121104 (2009). 6. E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79(3), 035407 (2009). 7.Z. Li, R. Zhao, T. Koschny, M. Kafesaki, K. B. Alici, E. Colak, H. Caglayan, E. Ozbay, and C. M. Soukoulis, “Chiral metamaterials with negative refractive index based on four …U? split ring resonators,” Appl. Phys. Lett. 97(8), 081901 (2010). 8.R. Zhao, L. Zhang, J. Zhou, T. Koschny, and C. M. Soukoulis, “Conjugated gammadion chiral metamaterial with uniaxial optical activity and negative refractive index,” Phys. Rev. B 83(3), 035105 (2011). 9.Z. Li, K. B. Alici, H. Caglayan, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, “Composite chiral metamaterials with negative refractive i ndex and high values of the figure of merit,” Opt. Express 20(6), 6146–6156 (2012). 10.V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure,” Phys. Rev. Lett. 97(17), 177401 (2006). 11.K. Song, X. Zhao, Q. Fu, Y. Liu, and W. Zhu, “Wide-angle 90°-polarization rotator using chiral metamaterial with negative refractive index,” J. Electromagn. Waves Appl. 26(14–15), 1967–1976 (2012). 12.M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007). 13.D. H. Kwon, P. L. Werner, and D. H. Werner, “Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation,” Opt. Express 16(16), 11802–11807 (2008). 14.M. Saba, M. Thiel, M. D. Turner, S. T. Hyde, M. Gu, K. Grosse-Brauckmann, D. N. Neshev, K. Mecke, and G. E. Schr?der-Turk, “Circular dichroism in biological photonic crystals and cubic chiral nets,” Phys. Rev. Le tt. 106(10), 103902 (2011). 15.Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870–876 (2012).

土动力学References

Bibliography References Cited Association of American Railroads, (2004) Railroad Facts, 2004 edition, L. C. Card No. A66-7305. Andreasson, B., (1998) High Speed Lines on Soft Ground: Numerical Analysis by the FLAC and FLAC3D Programmes. internal report, Jacobson and Widmark AB, Goteborg, Sweden. AREA, (1975) Manual Recommendation, Special Committee on Concrete Ties, Part 10 Concrete Ties (and Fastenings). Bulletin 655, American Railroad Engineering Association. Armstrong, J. H., (1998) The Railroad: What it is, What it does. 4th Edition, Simmons-Boardman. ASTM, (2003) D4015-92: Standard Test Methods for Modulus and Damping of Soils by the Resonant-Column Method. Annual Book of ASTM Standards, Vol. 4.08, American Society for Testing and Materials, pp. 473-494. Balendra, T., K. Chua, H., Lo, K. W. and Lee, S. L., (1989) Steady-state vibration of sub way-soil-building system. Journal of Engineering Mechanics, ASCE, Volume 115(1), pp. 145-162. Bathe, K. J., and Wilson, E. L., (1976)Numerical Methods in Finite Element Analysis. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.

常用参考文献样本Reference的写法

References写法标准 (https://www.sodocs.net/doc/0f4962217.html,留文代写References标准) Rosenzweig, E. D. & Roth, A.V. (2007) ‘B2B seller competence: Construct development and measurement using a supply chain strategy lens’, Journal of Operations Management, 25(6), pp.1311-1331 杂志的写法该文献在文中的表示方法为:(Rosenzweig & Roth,2007) Cairncross, F. (2001) The death of distance: how the communication revolution will change our lives. 2nd edn. Boston: Harvard Business School Press. 书的文献该文献在文中的表示方法为:(Cairncross,2001) Leiner, B. M et al. (2005) ‘A brief history of the Internet’.Internet Society [Online] A vailable at:https://www.sodocs.net/doc/0f4962217.html,/internet/history/brief.shtml (Accessed: 30 March 2010) 网络期刊同时作者人数等于或超过4人,该文献在文中的表示方法为:(Leiner et al.,2005) Qing, M. (2006) Available at: https://www.sodocs.net/doc/0f4962217.html,/article/2006/0505/A20060505528312.shtml (Accessed: 30 March 2010). 找到作者但是没有找到文章明的网络资源该文献在文中的表示方法为:(Qing,2006) Kortewag, A. (2004) Financial leverage and expected stock returns: Evidence from pure exchange offers, Available at SSRN: https://www.sodocs.net/doc/0f4962217.html,/abstract=597922, (Accessed: April 30, 2010)

references for sentence rewriting

例1 汉语原句这种新方法具有效率高、容易调整的优点。 英语错句This kind of new method have the advantage of high efficiency, easy adjustment. 改正后的句子This new method has the advantages of high efficiency and easy adjustment. 例2 汉语原句本文首先讨论了这种信号的特点,然后讨论了它的产生。 需改进:This paper first discusses the features of this signal, and then its generation is described. (主动被动混用,两句主语不一致) 改进:This paper first discusses the features of this signal, and then describes its generation. 不过本句最好 进一步改进:This paper begins with the discussion on the features of this signal, followed by the description of its generation. 例4 汉语原句我们的方法与以前讨论同一问题的文章中所述的不同。 英语错句Our method is different from previous articles discussed the same problem. 问题诊断:方法不是与文章比,文章与讨论之间的逻辑关系的问题) 改正:Our method is different from those presented(described)in the papers available(published before)on (discussing)the same problem. 例5 汉语原句只有通过对该系统性能的研究,我们才能了解它的优点。 英语错句Only through studied the performance of the system, its advantages can be understood. 改正后的句子Only through the study of the performance of the system can one(we)understand(appreciate)its advantages. 例6 汉语原句本文对提高打印速度和印字质量提供了一种计算机辅助设计手段。 英语错句This paper provided a kind of means of computer aid design for progressing the printing speed and the printing quality. 问题诊断: 1. 模糊语言kind of , 2. progress不及物动词,其后不能接宾语 改正: This paper presents a CAD method for increasing the printing speed and improving the printing quality. 例9 汉语原句这个方法需要精确的定位,这就使得它的实现具有一定的难度。 英语错句This method requires accurate location and this makes its realization have a little difficulty. 问题诊断:make sb. Do; ake sth. Done; make sb./sth. adj. 改正后的句子This method requires accurate location, thus making(或which makes)its realization somewhat difficult. 例11 汉语原句最后提出了实现这种方法应注意的一些问题和解决方法。 英语错句At last, we provided some problems that could be noted in implementing this method and solving ways. 问题诊断:problem 与provide 搭配不当,could 语气含糊 改正后的句子Finally, some problems that deserve to be noted in implementing this method and their solution are presented. 例12 汉语原句由于缺陷的存在,构件的疲劳寿命将大大降低。

references 申请国外postdoc实用推荐信模板

references 申请国外postdoc实用推荐信模板To Whom it May Concern: It is my honor to recommend John Doe for matriculation into the Graduate program at Rochester Institute. I have had the pleasure to know and work with John for the last six years. He he first worked with me as an intern in the software development organization at XYZ in Syracuse, NY. Following his graduation from Rochester Institute, I was fortunate enough to keep track of his career so that when the opportunity arose, I was able to recruit him to his current position at ABCD. The characteristics of John that attracted my attention then, and led me to hire him out of Company B last year, make it easy for me to give him an unqualified endorsement for graduate study. John brings to all of his activities energy, enthusiasm, and commitment. This is to be expected in any successful member of an entrepreneurial organization, and in this regard John fits in well. Be it in the parsing of intricate algorithms in a billing system, the crafting of an object hierarchy, or the establishment of best practices with an emerging technology, John consistently delivers high-quality software for our organization. This speaks to his overall intellect and ability to learn, attributes that will serve him well in graduate study. While John is a relatively junior member of our organization as measured by tenure, he quickly established himself as a go-to person in the product domains in which he has worked. He has been ever-willing to

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