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Seminar on Complex Multiplication ab 26.49 € als Taschenbuch: Seminar Held at the Institute for Advanced Study Princeton N. Y. 1957-58. Auflage 1966. Aus dem Bereich: Bücher, Wissenschaft, Mathematik,

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Seminar on Complex Multiplication ab 26.49 EURO Seminar Held at the Institute for Advanced Study Princeton N. Y. 1957-58. Auflage 1966

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Seminar paper from the year 1997 in the subject Technology, grade: 1 (A), Loughborough University (Department of Aeronautical and Automotive Engineering), 4 entries in the bibliography, language: English, abstract: Conventionally a signal is a physical variable that changes with time and contains information. The signal may be represented in analogue (continuos) or discrete (digital) form. The majority of the physical variables of interest for the engineer are of analogue form. However digital data acquisition equipment favour a digital representation of the analogue signal. The digital representation of a analogue signal will effect the characteristic of the signal. Thus an understanding of the underlying principles involved in signal processing is essential in order to retain the basic information of the original signal. The primary goal to use the Discrete Fourier Transform (DFT) is to approximate the Fourier Transform of a continuous time signal. The DFT is discrete in time and frequency domain and has two important properties: - the DFT is periodic with the sampling frequency - the DFT is symmetric about the Nyquist frequency Due to the limitations of the DFT there are three possible phenomena that could result in errors between computed and desired transform. - Aliasing - Picket Fence Effect - Leakage The DFT of a signal uses only a finite record length of the signal. Thus the input signal for the DFT can be considered as the result of multiplying the signal with a window function. Multiplication in the time domain results in convolution in the frequency domain, which will influence the spectral characteristic of the sampled signal. In the table below rectangular and Hanning window are compared: [...] Table The Fast Fourier Transform (FFT) is a computationally efficient algorithm for evaluating the DFT of a signal. It is imported to appreciate the properties of the FFT if it is to be used effectively for the analysis of signals. In order to avoid aliasing and resulting misinterpretation of measurement data the following steps should be followed: [...]

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Statement of results.- Modular forms.- Class invariants I.- Class invariants II.- Class fields.- Remarks on class-invariants and related topics.- Construction of class fields.- Computation of singular j-invariants.

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This book is based on the lectures given at the Oberwolfach Seminar on Tropical Algebraic Geometry in October 2004. Tropical Geometry ?rst appeared as a subject of its own in 2002, while its roots can be traced back at least to Bergman&#8217;s work [1] on logarithmic limit sets. Tropical Geometry is now a rapidly developing area of mathematics. It is int- twined with algebraic and symplectic geometry, geometric combinatorics, in- grablesystems, and statistical physics. Tropical Geometry can be viewed as a sort of algebraic geometry with the underlying algebra based on the so-called tropical numbers. The tropicalnumbers (the term &#8220;tropical&#8221; comesfrom computer science and commemorates Brazil, in particular a contribution of the Brazilian school to the language recognition problem) are the real numbers enhanced with negative in?nity and equipped with two arithmetic operations called tropical addition and tropical multiplication. The tropical addition is the operation of taking the m- imum. The tropical multiplication is the conventional addition. These operations are commutative, associative and satisfy the distribution law. It turns out that such tropical algebra describes some meaningful geometric objects, namely, the Tropical Varieties. From the topological point of view the tropical varieties are piecewise-linearpolyhedral complexes equipped with a particular geometric str- ture coming from tropical algebra. From the point of view of complex geometry this geometric structure is the worst possible degeneration of complex structure on a manifold.

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