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

This ebook offers with probably 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, errors correcting codes, and probability administration. It additionally exhibits that arithmetic can be utilized to unravel difficulties from nature, e.g., slime mildew algorithms.

One of the original beneficial properties of this e-book is that it indicates readers tips to use natural and utilized arithmetic, specifically these mathematical theory/techniques built within the 20th century, and constructing now, to unravel utilized difficulties in different fields of undefined. every one bankruptcy comprises clues on the right way to use "mathematics" to resolve concrete difficulties confronted in in addition to sensible applications.

The target market isn't restricted to researchers operating in utilized arithmetic and contains these in engineering, fabric sciences, economics, and existence sciences.

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Extra resources for A Mathematical Approach to Research Problems of Science and Technology: Theoretical Basis and Developments in Mathematical Modeling (Mathematics for Industry)

Example text

G. [32]). Compare this with the confluent Heun operator H1Rabi for the Rabi model. Then, taking r = 4g 2 , A = −(E + g 2 ) with a suitable choice of k in this equation gives the latter. ⎧ ⎨ 01 Remark 8 Let K = . Similarly to Lemma 2, one can show that the eigenvalue 10 ˜ = 0, where problem K Q K ϕ = ωϕ is equivalent to the equation Ω ← (R)u R˜ := ⎦ 2 ⎤ (H − ν) (sinh 2κ)(E − F) − (cosh 2κ)H + ν + (εν)2 ∈ U (sl2 ). sinh 2κ 32 M. Wakayama ˜ similarly to that of a (R) yields H Rabi in Then, a confluence procedure for a (R) 2 Remark 7.

Moreover, one should note that only w4 (t) one can give its explicit expression by a sum of two such differential Eisenstein series [16]. Furthermore, to understand the structure, especially the dimension of a space of residual modular forms, it is important to consider the Eichler cohomology groups [5] associated with several (2)-modules made by a set of certain functions on the Poincaré upper half plane, such as the space (field) of rational functions C(τ ), the space of holomorphic/meromorphic functions with some decay condition at the infinity (cusps), etc.

T. Iyama, S. Kiyomoto, K. Fukushima, T. Tanaka, T. Takagi, in IEICE Transaction on Implementation of Pairing Based Cryptosystem on Mobile Phones, vol. J95-A, no. 7 (2012), pp. 579–587 (in Japanese) 15. T. Izu, T. Takagi, in Efficient Computations of the Tate Pairing for the Large MOV Degrees, ICISC 2002. LNCS, vol. 2513 (2002), pp. 283–297 16. N. 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.

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