Download A Mathematical Approach to Research Problems of Science and by Ryuei Nishii, Shin-ichiro Ei, Miyuki Koiso, Hiroyuki Ochiai, PDF
By Ryuei Nishii, Shin-ichiro Ei, Miyuki Koiso, Hiroyuki Ochiai, Kanzo Okada, Shingo Saito, Tomoyuki Shirai
This e-book offers with essentially the most novel advances in mathematical modeling for utilized clinical expertise, together with special effects, public-key encryption, facts visualization, statistical information research, symbolic calculation, encryption, blunders correcting codes, and danger administration. It additionally indicates that arithmetic can be utilized to unravel difficulties from nature, e.g., slime mould algorithms.
One of the original positive aspects of this ebook is that it exhibits readers easy methods to use natural and utilized arithmetic, specifically these mathematical theory/techniques constructed within the 20th century, and constructing now, to resolve utilized difficulties in numerous fields of undefined. each one bankruptcy contains clues on the way to use "mathematics" to resolve concrete difficulties confronted in in addition to useful applications.
The audience isn't really restricted to researchers operating in utilized arithmetic and contains these in engineering, fabric sciences, economics, and lifestyles sciences.
Read or Download A Mathematical Approach to Research Problems of Science and Technology: Theoretical Basis and Developments in Mathematical Modeling PDF
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Additional info for A Mathematical Approach to Research Problems of Science and Technology: Theoretical Basis and Developments in Mathematical Modeling
Example text
There is a third point P3 through line l on elliptic curve. Let h be the line through P3 and the point at infinity ∧. Then h is the vertical line to the x-axis from P3 , and the symmetric point of P3 to the x-axis on elliptic curve becomes the resulting addition P1 + P2 . In ECDBL, let P3 be another point on the elliptic curve that is on the tangent line l on point P1 . The doubling 2P1 is another crossing point of h that passes through P3 and the point at infinity ∧. We usually use elliptic curves of prime order in ECC in order to avoid subgroup attacks.
ECC has equivalent security to that of an RSA cryptosystem, but with a shorter key size. Recently, pairing-based cryptography (PBC) has attracted the attention of researchers and organizations concerned with cryptography. PBC enables many novel cryptographic protocols, such as ID-based encryption [4, 22], which cannot be efficiently constructed using RSA or ECC. In particular, PBC involves a pairing that reduces the discrete logarithm problem on elliptic curves to one over finite fields. In this chapter, we give a short overview of the development of public-key cryptography, starting with the RSA cryptosystem and moving on to ECC and PBC.
14, 539–604, 669–690 (2002) [ibid 15, 955–963 (2003)] 29. A. Parmeggiani, M. Wakayama, Oscillator representations and systems of ordinary differential equations. Proc. Nat. Acad. Sci. USA 98, 26–30 (2001) 30. A. Parmeggiani, On the spectrum of certain non-commutative harmonic oscillators and semiclassical analysis. Commun. Math. Phys. 279, 285–308 (2008) 31. I. Rabi, Space quantization in a gyrating magnetic field. Phys. Rev. 51, 652–654 (1937) 32. Y. Slavyanov, W. Lay, A Unified Theory Based on Singularities, Oxford Mathematical Monographs (Oxford University Press, Oxford, 2000) 33.