By Ryuei Nishii, Shin-ichiro Ei, Miyuki Koiso, Hiroyuki Ochiai, Kanzo Okada, Shingo Saito, Tomoyuki Shirai

This ebook bargains with probably the most novel advances in mathematical modeling for utilized medical expertise, together with special effects, public-key encryption, info visualization, statistical information research, symbolic calculation, encryption, errors correcting codes, and threat administration. It additionally exhibits that arithmetic can be utilized to unravel difficulties from nature, e.g., slime mildew algorithms.

One of the original positive factors of this publication is that it indicates readers how one can use natural and utilized arithmetic, specially these mathematical theory/techniques built within the 20th century, and constructing now, to unravel utilized difficulties in numerous fields of undefined. every one bankruptcy contains clues on the best way to use "mathematics" to unravel concrete difficulties confronted in in addition to useful applications.

The audience isn't restricted to researchers operating in utilized arithmetic and contains these in engineering, fabric sciences, economics, and existence 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 resources for A Mathematical Approach to Research Problems of Science and Technology: Theoretical Basis and Developments in Mathematical Modeling**

**Example text**

Koblitz, Elliptic curve cryptosystems. Math. Comput. 48, 203–209 (1987) 17. K. W. ), in The Development of the Number Field Sieve, Lecture Notes in Mathematics, vol 1554 (Springer, Berlin, 1993) 18. V. Miller, in Use of Elliptic Curves in Cryptography, CRYPTO 1985. LNCS, vol. 218 (Springer, 1985), pp. 417–426 19. V. Miller, The Weil pairing, and its efficient calculation. J. Cryptol. 17(4), 235–261 (2004) 20. J. Pollard, A Monte Carlo method for factorization. BIT Numer. Math. 15(3), 331–334 (1975) 21.

4 Lie Algebraic Description To draw the picture more precisely we recall the representation theoretic setting. Let H, E and F be the standard generators of sl2 defined by ⎨ 1 0 , 0 −1 ⎧ H= E= ⎧ ⎨ 01 , 00 F= ⎧ ⎨ 00 . 10 They satisfy the commutation relations [H, E] = 2E, [H, F] = −2F, [E, F] = H. For the triplet (κ, ε, ν) ∈ R3>0 , define a second order element R of the universal enveloping algebra U (sl2 ) of sl2 by R := ⎦ 2 ⎤ (sinh 2κ)(E − F) − (cosh 2κ)H + ν (H − ν) + (εν)2 . sinh 2κ Let us consider the representation (Ω ← , C[y]) of sl2 given by Ω ← (H ) = yϕ y + 1/2, Ω ← (E) = y 2 /2, Ω ← (F) = −ϕ y2 /2.

Anal. Appl. 105, 595–609 (2014) 9. F. Hiroshima, I. Sasaki, Multiplicity of the lowest eigenvalue of non-commutative harmonic oscillators. Kyushu J. Math. 67, 355–366 (2013) 10. R. C. Tan, in Non-abelian Harmonic Analysis. Applications of S L(2, R) (Springer, Berlin, 1992) 11. T. Ichinose, M. Wakayama, Zeta functions for the spectrum of the non-commutative harmonic oscillators. Commun. Math. Phys. 258, 697–739 (2005) 12. T. Ichinose, M. Wakayama, Special values of the spectral zeta function of the non-commutative harmonic oscillator and confluent Heun equations.