By Veblen O., Whitehead J. H.

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This booklet is a translation of an authoritative introductory textual content in response to a lecture sequence brought by means of the popular differential geometer, Professor S S Chern in Beijing collage in 1980. the unique chinese language textual content, authored via Professor Chern and Professor Wei-Huan Chen, used to be a different contribution to the maths literature, combining simplicity and financial system of technique with intensity of contents.

A learn of linear order and continuity to provide a origin for traditional actual or advanced geometry.

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Low temperatures are achieved using a 3 He/4 He dilution refrigerator, while the magnetic ﬁeld is provided either by a superconducting solenoid or a Bitter magnet, or a combination of both. The low-frequency magnetotransport measurements are typically performed with a current excitation of 10−9 A, corresponding to an electric ﬁeld of 10−4 V cm−1 and using the lock-in technique. 1 Shubnikov-de Haas oscillations and the IQHE A large magnetic ﬁeld applied perpendicular to the plane of a 2DES acts like a harmonic oscillator potential and leads to the quantization of the orbital motion.

729 Seminar 2. Twisting a Single DNA Molecule: Experiments and Models by T. -F. Allemand, D. Bensimon, V. Croquette, C. Bouchiat, M. Me´zard and R. 1 Forces at the molecular scale . . . . . . . . . . . . 2 Brownian motion: A sensitive tool for measuring forces . . . . 1 The Freely jointed chain elasticity model . . . . . . . . 2 The overstretching transition . . . . . . . . . . . . 5 torsional buckling instability The buckling instability at T = 0 .

3 Precision of circulation and ﬂux quantization measurements . . . 3 Magnus force 786 Magnus force and two-ﬂuid model . . . . . . . . . . 786 Vortex moving in a neutral superﬂuid . . . . . . . . . 788 Transverse force in superconductors . . . . . . . . . . 1 Introduction . . . . . . . . . . . . 3 Bloch’s theorem and the Laughlin argument . . 4 Chern numbers . . . . . . . . . . . 5 Fractional quantum Hall eﬀect . . . . .