1,722,787 research outputs found
Xiu xiang di yi cai zi shu : [50 juan, 120 hui] /
No full textJing du liu li chang Bao jing tang chong kan xin ban.At head of title: Sheng tan wai shu.Mode of access: Internet
Guangdong yu di quan tu. v.1
No full text張人駿編.綫裝, 1函.框26.8x27.2公分, 白口, 四周單邊, 版心中鐫卷次.石經堂印.Zhang Renjun bian.Xian zhuang, 1 han.Kuang 26.8x27.2 gong fen, bai kou, si zhou dan bian, ban xin zhong juan juan ci.Shi jing tang yin
Energy flow theory of nonlinear dynamical systems with applications
Full text linkThis monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously return to some examples in each chapter to illustrate the applications of the discussed theory and approaches. It can be used as an undergraduate or graduate textbook or a comprehensive source for scientists, researchers and engineers, providing the statement of the art on energy flow or power flow theory and methods
Yan Huagu shi ji
No full text嚴粲述.綫裝.附《蒙齋袁先生手帖》, 《詩緝清濁音圖》, 《十五國風地理圖》.《詩緝清濁音圖》後鐫"趙府栞于居敬堂"刊記.框20.2 x 14.3公分, 9行18字, 小字雙行同, 白口, 四周雙邊, 單綫魚尾. 版心上鐫"味經堂", 中鐫書名及卷次.鈐: "沙羡邾", "藏之名山傳之其人", "明上谷鶴林梁氏藏書記", "臣樟私印", "秋崖子朱克生".Xian zhuang.Fu "Meng zhai Yuan xian sheng shou tie", "Shi ji qing zhuo yin tu", "Shi wu guo feng di li tu"."Shi ji qing zhuo yin tu" hou juan "Zhao fu kan yu ju jing tang" kan ji.Kuang 20.2 x 14.3 gong fen, 9 hang 18 zi, xiao zi shuang hang tong, bai kou, si zhou shuang bian, dan xian yu wei. Ban xin shang juan "Wei jing tang", zhong juan shu ming ji juan ci.Qian: "Sha yi zhu", "Cang zhi ming shan zhuan zhi qi ren", "Ming shang gu he lin liang shi zang shu ji", "Chen zi si yin", "Qiu ya zi mi ke sheng".Yan Can shu
Jiu yao shi kao
No full text[翁方綱錄].綫裝, 1函.內封背頁印"光緖歲在辛卯[1891]秌七月廣州石經堂書局影印"見《香港中文大學圖書館中國古藉目錄》(2004, p. 210)附: 九曜石考 : 上, 下卷.Xian zhuang, 1 han.Nei feng bei ye yin "Guangxu sui zai xin mao [1891] qiu qi yue Guangzhou Shi jing tang shu ju ying yin"Jian "Xianggang Zhong wen da xue tu shu guan Zhongguo gu ji mu lu" (2004, p. 210)[Weng Fanggang lu].Fu: Jiu yao shi kao : shang, xia juan
An investigation into natural vibrations of fluid-structure interaction systems subject to Sommerfeld’s radiation condition
No full textA fluid-structure interaction system subject to Sommerfeld’s condition is defined as a Sommerfeld system which is divided into three categories: Fluid Sommerfeld (FS) System, Solid Sommerfeld (SS) System and Fluid Solid Sommerfeld (FSS) System of which Sommerfeld conditions are imposed on a fluid boundary only, a solid boundary only and both fluid and solid boundaries, respectively. This paper follows the previous initial results claimed by simple examples to further mathematically investigate the natural vibrations of generalized Sommerfeld systems. A new parameter representing the speed of radiation wave for generalized 3-D problems with more complicated boundary conditions is introduced into the Sommerfeld condition which allows investigation of the natural vibrations of a Sommerfeld system involving both free surface and compressible waves. The mathematical demonstrations and selected examples confirm and reveal the natural behaviour of generalized Sommerfeld systems defined above. These generalized conclusions can be used in theoretical or engineering analysis of the vibrations of various Sommerfeld systems in engineering
Natural vibration of two-dimensional slender structure-water interaction systems subject to Sommerfeld radiation condition
No full textThe dynamic behaviour of 2-dimensional flexible slender structure-water interaction systems subject to a Sommerfeld radiation condition at the infinity boundary of the water domain is investigated. A new parameter, the speed of radiation wave, is introduced into the Sommerfeld radiation condition to consider the influences of both of the pressure wave and the free surface wave of the water, which is an extension of the original Sommerfeld condition. The governing equations describing the dynamic behaviour of the system are analysed and solved using a separation of variables method. It is demonstrated that the natural vibration of the 2-dimensional slender structure-water interaction system subject to a Sommerfeld radiation condition is governed by a complex eigenvalue equation which has only pairs of complex conjugate eigenvalues. The number of the pairs of complex conjugate natural frequencies equals the number of the natural modes of the corresponding dry structure and is independent of the continuous fluid domain which has infinite degrees of freedom. The examples, including four cases of shallow water, deep water, no free surface wave and incompressible water, demonstrate and illustrate the developed theoretical and numerical method
A proof of the four-colour theorem
No full textThe four-colour problem remained unsolved for more than a hundred years has played a role of the utmost importance in the development of graph theory. The four-colour theorem was confirmed in 1976, which is not completely satisfied due to: i) part of the proof using computers cannot be verified by hand; ii) even the part, supposedly hand-checkable, is extraordinarily complicated and tedious, and as far as we know, no one has entirely verified it. Seeking a hand-checkable proof of the four-colour theorem is one of world-interested problems, which is addressed in this paper. A necessary and sufficient condition for n-colour theorem in a space is: there exists a largest n-complete graph base in the same space. Examples are given to illustrate applications
Chaotic motions in Newton's gravity field revealed from energy flow investigations
No full textMathematicians have searched the evidence for motion stabilities in Solar System. A predication indicated “Earth’s orbit can become chaotic”. Until now, It have not been found any theoretical / numerical results on chaotic motion orbits in Newton’s gravity field. Newton’s gravity field is one of central-force fields like electromagnetic / quantum ones, so its motion characteristics revealed can be applied to research of quantum systems. This paper intends to tackle this historic problem based on the energy flow numerical investigations. we have shown some chaotic motions in Newton’s gravity field. Depending on initial conditions, mechanical-energy H and angular-momentum, particle motion-paths are hyperbolas (H > 0) or parabolas (H = 0) as infinite motions. Negative energies (H < 0) show ellipse orbits of periodical motions with constant time-averaged potential / kinetic energies and zero-time averaged energy flows. Chaotic motion, appearing when H < 0 due to small disturbances / initial conditions, behaves periodical one of infinite period: a repeating motion between the two zero-radial-speed circles, and its starting and ending points never coinciding, and the characteristics of time averaged energy-flow variables are same as the periodical ones when the average time tends infinite. Therefore, the revealed chaotic motion is a stable infinite long period periodical motion restricted in a finite space. This result can address the predication of chaotic Earth’ orbit. New findings will benefit to tackle particle motions in central-force fields of modern physics. The energy-flow theory provides a generalised means to reveal hidden nonlinear phenomena of nature
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