* In Japan, according to M. Iwasawa at the National Institute of Population and Social Security Research, less than 3 % of females between 25-29 are currently cohabiting, but more than 1 in 5 have had some experience of an unmarried partnership, including cohabitation.

A more recent Iwasawa study has shown that there has been a recent emergence of non-marital cohabitation.

In the last ten years he has focused on the study of various aspects of non-commutative Iwasawa theory, for instance, the study of the arithmetic of elliptic curves in nonabelian infinite extensions.

Via the theory of zeta integrals initiated by Kenkichi Iwasawa and by John Tate in Tate's thesis it is related to the study of the zeta function of global fields.

Tate's thesis ( 1950 ) on Fourier analysis in number fields has become one of the ingredients for the modern theory of automorphic forms and their L-functions, notably by its use of the adele ring, its self-duality and harmonic analysis on it ; independently and a little earlier, Kenkichi Iwasawa obtained a similar theory.

The latter was explicitly introduced in papers of Kenkichi Iwasawa and John Tate.

Also, starting with any compact real form of a semisimple Lie algebra g its complexification as a real Lie algebra of twice the dimension splits into g and a certain solvable Lie algebra ( the Iwasawa decomposition ), and this provides a canonical bicrossproduct quantum group associated to g. For su ( 2 ) one obtains a quantum group deformation of the Euclidean group E ( 3 ) of motions in 3 dimensions.

In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields.

It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields.

In the early 1970s, Barry Mazur considered generalizations of Iwasawa theory to abelian varieties.

More recently ( early 90s ), Ralph Greenberg has proposed an Iwasawa theory for motives.

Iwasawa worked with so-called-extensions: infinite extensions of a number field with Galois group isomorphic to the additive group of p-adic integers for some prime p. Every closed subgroup of is of the form, so by Galois theory, a-extension is the same thing as a tower of fields such that.

Iwasawa studied classical Galois modules over by asking questions about the structure of modules over.

More generally, Iwasawa theory asks questions about the structure of Galois modules over extensions with Galois group a p-adic Lie group.

In order to get an interesting Galois module here, Iwasawa took the ideal class group of, and let be its p-torsion part.

In fact, is a module over the Iwasawa algebra ( i. e. the completed group ring of over ).

The main conjecture of Iwasawa theory was formulated as an assertion that two methods of defining p-adic L-functions ( by module theory, by interpolation ) should coincide, as far as that was well-defined.

* Greenberg, Ralph, Iwasawa Theory-Past & Present, Advanced Studies in Pure Math.

Combining this with the p-parity theorem by and the announced proof of the main conjecture of Iwasawa theory for GL ( 2 ) by, they conclude that a positive proportion of elliptic curves over Q have analytic rank zero, and hence, by, satisfy the Birch and Swinnerton-Dyer conjecture.

* Borel, A .; Chowla, S .; Herz, C. S .; Iwasawa, K .; Serre, J .- P. Seminar on complex multiplication.

* 1928 – Yoshihiko Amino, Japanese historian ( d. 2004 )

The current Prime Minister is Yoshihiko Noda, who took the post on 2 September 2011.

* January 22 – Yoshihiko Amino, Japanese historians ( d. 2004 )

A particularly interesting example of this, first described in the 1970s by Yoshihiko Futamura, is when prog is an interpreter for a programming language.

* Yoshihiko Futamura, http :// www. brics. dk /~ hosc / local / HOSC-12-4-pp381-391. pdf Partial Evaluation of Computation Process – An Approach to a Compiler-Compiler

Super Mario RPG was directed by Yoshihiko Maekawa and Chihiro Fujioka and produced by Shigeru Miyamoto.

These include the two directors, Yoshihiko Maekawa and Chihiro Fujioka, as well as music composer Yoko Shimomura.

The following prime minister, Yoshihiko Noda " staked his political life " on raising the tax.

In August 2011, Kan resigned, and Yoshihiko Noda became Prime Minister.

Japanese Wadō-ryū stylists Tatsuo Suzuki, Teruo Kono, Masafumi Shiomitsu, H. Takashima, Naoki Ishikawa, Yoshihiko Iwasaki and many others spread the art in Europe.

Under Tsujiyoko's supervision, the game was scored by Saki Haruyama, Yoshihiko Kitamura, and Yoshito Hirano.

Ryoun-kai has about 40 seats in the assembly and is led by Seiji Maehara and Yoshihiko Noda.

At that time, Yoshihiko Noda, most recently finance minister, was elected as the new DPJ leader and, as leader of the largest party in the Diet, becomes prime minister as well.

: A female student who had a run-in with Yoshihiko when he looked for a ball that went through the library's window.

The potential romance was cut short when she transferred back to France, as she was just an exchange student, and Yoshihiko learned the kissing is just European custom, although it turns out Aya has a different view on the romance.

This girl with immature emotional swings did guide Yoshihiko out of his disinterest in the sport, and they become a couple.

Yoshihiko doesn't know that, even mistaking her for a generic girl in a Santa suit distributing flyers.

Yoshihiko became her unwitting " reindeer " for the rest of the day.

Earlier in the series Yoshihiko and his girlfriend Natsue went to one of her concerts.

In 2006, development begun on the L10 series GS under Yoshihiko Kanamori, with the design process finalizing under Akio Toyoda in 2009.

For example, on April 20, 2012 the opposition Liberal Democratic Party ( LDP ), Your Party and New Renaissance Party submitted censure motions against ministers of Prime Minister Yoshihiko Noda's cabinet.