Natural logarithms

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  • Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: A natural series for the natural logarithm...

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  • Lecture Mathematics 53 - Lecture 5.2 provides knowledge of the integrals yielding logarithmic and exponential functions. This chapter presents the following content: Integrals of f(x) = 1/x and of the other circular functions, integrals of exponential functions, the natural logarithmic function: A rigorous approach.

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  • (BQ) Part 1 book "3,000 solved problems in calculus" has contents: Inequalities, absolute value, functions and their graphs, continuity, trigonometric functions and their derivatives, maxima and minima, related rates, rectilinear motion, the natural logarithm,... and other contents.

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  • We verify an old conjecture of G. P´lya and G. Szeg˝ saying that the o o regular n-gon minimizes the logarithmic capacity among all n-gons with a fixed area. 1. Introduction The logarithmic capacity cap E of a compact set E in R2 , which we identify with the complex plane C, is defined by (1.1) − log cap E = lim (g(z, ∞) − log |z|), z→∞ where g(z, ∞) denotes the Green function of a connected component Ω(E) ∞ of C \ E having singularity at z = ∞; see [4, Ch. 7], [7, §11.1]. By an n-gon with...

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  • THE recent development of various methods of modulation such as PCM and PPM which exchange bandwidth for signal-to-noise ratio has intensified the interest in a general theory of communication. A basis for such a theory is contained in the important papers of Nyquist1 and Hartley2 on this subject. In the present paper we will extend the theory to include a number of new factors, in particular the effect of noise in the channel, and the savings possible due to the statistical structure of the original message and due to the nature of the final destination of the information....

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  • Natural Logarithms and Antilogarithms

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  • 14 Exponential functions, continuous growth and differential equations Use the exponential function and natural logarithms to derive the final sum, initial sum and growth rate when continuous growth takes place. Compare and contrast continuous and discrete growth rates.

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  • Topological Hochschild homology and localization 2. The homotopy groups of T (A|K) 3. The de Rham-Witt complex and TR· (A|K; p) ∗ 4. Tate cohomology and the Tate spectrum 5. The Tate spectral sequence for T (A|K) 6. The pro-system TR· (A|K; p, Z/pv ) ∗ Appendix A. Truncated polynomial algebras References Introduction In this paper we establish a connection between the Quillen K-theory of certain local fields and the de Rham-Witt complex of their rings of integers with logarithmic poles at the maximal ideal.

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  • We prove that the existence of an automorphism of finite order on a Q-variety X implies the existence of algebraic linear relations between the logarithm of certain periods of X and the logarithm of special values of the Γ-function. This implies that a slight variation of results by Anderson, Colmez and Gross on the periods of CM abelian varieties is valid for a larger class of CM motives. In particular, we prove a weak form of the period conjecture of Gross-Deligne [11, p. 205]1 .

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  • This paper is a continuation of Fefferman’s program [7] for studying the geometry and analysis of strictly pseudoconvex domains. The key idea of the program is to consider the Bergman and Szeg¨ kernels of the domains as o analogs of the heat kernel of Riemannian manifolds. In Riemannian (or conformal) geometry, the coefficients of the asymptotic expansion of the heat kernel can be expressed in terms of the curvature of the metric; by integrating the coefficients one obtains index theorems in various settings. ...

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  • Annals of Mathematics This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat’s Last Theorem. In this paper we give new improved bounds for linear forms in three logarithms. We also apply a combination of classical techniques with the modular approach to show that the only perfect powers in the Fibonacci sequence are 0, 1, 8 and 144 and the only perfect powers in the Lucas sequence are 1...

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  • Obviously, (1.2) implies the same estimate for M(Z(QN, P)). It was suggested in [2] that in this case the (1+logN) term could be omitted at the cost of multiplying by a constant. The above suggestion means that in the passage from the sum of moduli to the modulus of the sum in (1.1) essential cancellation should take place. As a contribution towards this end the authors showed that any straight line L intersects Z(QN, P) in a set FP of linear measure less than 2eP−1N. Further information about the complement of FP under certain conditions on {zk} is obtained in [1].

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  • Mathematical theories and methods and effective computational algorithms are crucial in coping with the challenges arising in the sciences and in many areas of their application. New concepts and approaches are necessary in order to overcome the complexity barriers particularly created by nonlinearity, high-dimensionality, multiple scales and uncertainty. Combining advanced mathematical and computational methods and computer technology is an essential key to achieving progress, often even in purely theoretical research.

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  • Virtually every branch of the sciences, engineering, economics, and related fields now discusses or refers to chaos. James Gleick's 1987 book, Chaos: making a new science and a 1988 one-hour television program on chaos aroused many people's curiosity and interest. There are now quite a few books on the subject. Anyone writing yet another book, on any topic, inevitably goes through the routine of justifying it. My justification consists of two reasons

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  • This paper presents an approach related to authenticate mutually a RFID (Radio Frequency Identification) tag from a RFID reader by using the cryptography based on Elliptic curve. Our proposal mutual authentication lies on the Elliptic curve discrete logarithm problem, which is considered the core in order to fight against all of attacks like replay attack, forgery attack and man-in-the-middle attack. Scientifically, we prove not only the accuracy and the security of our approach, but also its performance in the mutual authentication between a RFID tag and a reader. ...

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  • Speech signals have a very wide dynamic range: Harsh “oh” and “b” type sounds have a large amplitude, whereas softer sounds such as “sh” have small amplitudes. If a uniform quantization scheme were used then although the loud sounds would be represented adequately the quieter sounds may fall below the threshold of the LSB and therefore be quantized to zero and the information lost. Therefore non-linear quantizers are used such that the quantization level at low input levels is much smaller than for higher level signals.

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