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Disclosure: Works of Hiroshi Nakazawa
May 10, 2010
Notices (i) The symbol ∗ denotes a work with co-authors.
(ii) The symbol † denotes a work in Japanese.
1)∗ Time dependent problems of scattering in linear lattice system. Progress of
Theoretical Physics 34 (1965), pp. 313-314 (Coauthors: Hideki Sabata and Ei Teramoto).
2) A statistical mechanical model of Brownian motion. Progress of Theoretical Physics
Suppl. No. 36 (1966), 172-192.
3) Energy flow in harmonic linear chain. Progress of Theoretical Physics 39 (1968),
236-237.
4) On the lattice thermal conduction. Progress of Theoretical Physics Suppl. No. 45
(1970), 231-262.
5)† 確率場のウィ−ナ−展開 (乱流理論への応用) (Wiener expansion of stochastic fields
(Applications to the theory of turbulence). 日本物理学会誌 28 (1973), 571-584.
4) Nonlinear stochastic differential equations in statistical physics and integral
representation. Progress of Theoretical Physics 56 (1976) 1411-1433.
7)† Forced Burgers turbulene–解の存在と一意性, 解の構成 (Forced Burgers turbulence –
Existence, uniqueness, and construction of solutions –). 京都大学数理解析研究所講究録
405 (1980), 258-271 (確率過程と開放系の統計力学研究集会 II, 1980 年 3 月).
8) Probabilistic aspects of equation of motion of forced Burgers and Navier-Stokes
turbulence. Progress of Theoretical Physics 64 (1980), 1551-1564.
9) Sample structures of forced Burgers turbulence. Progress of Theoretical Physics 65
(1981), 1565-1583.
10) Stochastic Burgers equation in the inviscid limit. Advances in Applied Mathematics
3 (1982), 18-42.
11) Inviscid disturbance equations in linear stability theory in fluid dynamics and
geophysics. Progress of Theoretical Physics 71 (1984), 913-921.
12) Optical potentials for the enhanced and absorptive scattering of Rossby waves by
shear layers. Progress of Theoretical Physics 72 (1984), 913-921.
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13) Wiener-Ito decomposition of polynomial operators formed with Boson quasi-free
fields. Journal of Mathematical Analysis and Applications 111 (1985), 353-373.
14) Quantization of Brownian motion processes in potential fields. Lecture Notes in
Mathematics No. 1136 (1985), 375-387.(Proceedings of the Workshop on Quantum
Probabilty and Applications II, October 1984, Heidelberg).
15) Stochastic differential equations in quantum statistical mechanics: Observables and
multiple Wiener integrals. Journal of Statistical Physics 45 (1986), 1049-1069.
16) Self-organized structures in the forced Burgers’ turbulence. Lecture Notes in Physics
No. 278 (1987), 82-86 (Proceedings of the First International Conference on the Physics
of Phase Space, April 1986, Maryland).
17) Quasi-stationary structures on a class of forced Burgers turbulence between walls.
Physical Review A35 (1987), 5137-5148.
18) Quantum Brownian motion, irreversibility and nonequilibrium stationary states.
Nuclear Physics B-5A (1988), 255-260 (Proceedings of the Third University of California
Conference on Statistical Mechanics, March 1988, Davis).
19) Generalized Langevin equations of Mori and quantum stochastic processes. Physical
Review A39 (1989), 5391-5398.
20)† 乱流拡散の modeling について – 数値 simulation の基本的ないくつかの問題 (On the
modeling of turbulent diffusion – Some basic problems in numerical simulations). (京都大
学数理解析研究所講究録 719 (1990), 257-268 (流れの不安定性と乱流の構造研究会, 1989
年 1 月).
21) Numerical procedures for sample structures on stochastic differential equations.
Journal of Mathematical Physics 31 (1990), 1978-1989.
22)† 応用と一般教育の中点から見た高専数学教程と専攻科設置計画 (Mathematical
curriculums in Colleges of Technology and programs to set non-degree graduate courses; a
viewpoint between general and applicational education). 高専教育 第 15 号 (1992), 68-72.
23) Some numerical procedures for the covariance function on stochastic differential
equations. Bulletin of Takuma National College of Technology Vol. 20 (1992), 19-30.
24)† 試みとしての高専数学教程と可能性 (A trial on mathematical curriculum in College
of Technology and possibilities). 日本数学教育学会第 74 回全国大会高専大学部会 (1992 年
8 月) 講演論文集 (1992), 32-33.
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25)† 確率微分方程式での数値積分の精度問題 (Precision problems for the numerical
integration of stochastic differential equations). 京都大学数理解析研究所講究録 850
(1993), 42-49 (短期共同研究確率数値解析に於ける諸問題研究集会, 1993 年 6 月).
26)† 応用数学への群論的教科の試み (Group theoretical curriculums as applied
mathematics for students of College of Technology). 高専教育第 17 号 (1994), 82-88.
27)† 代数系と乱数理論–応用数学教育の視点 – (Algebras and random number theory – A
viewpoint as the curriculum on applied mathematics – ). 高専教育第 18 号 (1995), 96-103.
28)† 汎用計算機, ワ−クステ−ションそして VP 上でのデデキント和 (Dedekind sums as a
speed test of computing center machines, workstations and a parallel machine VP). 名古
屋大学大型計算機センタ−ニュ−ス Vol.25 (1994), 363-372.
29)† フルヴィッツの安定性判定定理 (The stability criterion of Hurwitz). 日本数学教育学
会高専部会研究論文誌 Vol. 2 (1995), 1-8.
†
30)∗ 乱数生成の構造 I–巡回群と乗算合同法 (Structures for random number generation I
– Cyclic groups and multiplicative congruential generators). Bulletin of Takuma National
College of Technology Vol. 23 (1996), 25-36 (Coauthor: Naoya Nakazawa).
31)† 乱数生成の構造 II – 有限体と M 系列 (Structures for random number generation II –
Finite fields and M sequences). Bulletin of Takuma National College of Technology Vol.
23 (1996), 37-50.
32)† 乱数生成の構造 III – 法 pn の加算生成法と Marsaglia-Tsai の行列表現 (Structures for
random number generation III – Additive generators with mod pn and the matrix
representation of Marsaglia and Tsai). Bulletin of Takuma National College of
Technology Vol. 24 (1997), 17-24.
33)† 乱数生成の構造 付録. 加算法の Brent の算術演算的解析の概観と補遺 (Appendix to
structures for random number generation: An overview and a supplement of arithmetical
analysis of Brent on additive generators). Bulletin of Takuma National College of
Technology Vol. 24 (1997), 25-30.
34)† 連結 M 系列乱数の「2 次均等分布」次元について (On the 2-distribution of
concatenated M sequence random numbers). Bulletin of Takuma National College of
Technology Vol. 24 (1997), 31-36.
35)† (1998-1999) 「熱 · 統計力学の世界」 The world of thermo-sttistical mechanids/
Printed lecture note for ”Topics of Natural Sciences” at Takuma National College of
Technology (1998-1999).
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36)† (1999) 「一様乱数の数理」 The mathematics of uniform random numbers/ 開成出版
(1999)/ A textbook for applied mathematics at Takuma National College of Technology,
uploaded in ”http://www10.plala.or.jp/h-nkzw/” as ”rans1203.pdf” for the filename.
37)† (2000) 「理想気体ボース-アインシュタイン凝縮体との熱力学的平衡」 Some
thermodynamic equilibria with ideal gas Gose-Einstein condensate/ Bulletin of Takuma
National College of Technology Vol. 28 (2000), 29-34/ Uploaded in
”http://www10.plala.or.jp/h-nkzw/” as ”00kiyou.pdf” for the filename.
38)† (2001) 「Tausworthe 型及び Lewis-Payne 型 M 系列乱数の均等分布性について」
n-distribution properties of M sequence random numbers of the type of Tausworth or
Lewis-Payne/ Bulletin of Takuma National College of Technology Vol. 29 (2001), 19-22/
Uploaded in ”http://www10.plala.or.jp/h-nkzw/” as ”01kiyou.pdf” for the filename.
39)† (August 27, 2001) 「高専教育の数学, 物理学, · · · –思考を可能世界へ解き放って–」
Mathematics, Physics, · · · in the Education at College of Tehnology – Freeing our thoughts
to the world of possibilities –/ 2001 年度国専協教員研究集会 (2001.8.27. 豊橋技科大) 論文
集/ Uploaded in ”http://www10.plala.or.jp/h-nkzw/” as ”01toyohs.pdf” for the filename.
This report expresses personal thought and resolution of H. Nakazawa by 9.11 attacks in
2001.
40)† (2000-2001) 「解析関数の世界」 The world of anylytic functions/ Printed lecture
note for ”Topics of Natural Sciences” at Takuma National College of Technology.
41)† (2001-2002) 「複素解析」 Complex analysis/ Printed lecture note for mathematics
at Takuma National College of Technology.
42)† (2002) 「周期列と数の算法 I. 周期と合同算法」 Periodic sequences and the
arithmetic of numbers I. Periods and congruential arithmetic/ Bulletin of Takuma
National College of Technology Vol.30 (2002), 31-38/ Uploaded in
”http://www10.plala.or.jp/h-nkzw/” with an appendix, as ”02ky1rev.pdf” for the
filename.
43)† (2002)「周期列と数の算法 II. 循環小数と既約剰余群」Periodic sequences and the
arithmetic of numbers II. Periodic decimals and reduced residue class groups/ Bulletin of
Takuma National College of Technology Vol.30 (2002), 39-46/// Uploaded in
”http://www10.plala.or.jp/h-nkzw/” as ”02kiyou2.pdf” for the filename.
44)† (2002) 「周期列と数の算法 III. 周期列の数の一様独立な分布」 Periodic sequences
and the arithmetic of numbers III. Uniform and independent distribution of numbers in
periodic sequences/ Bulletin of Takuma National College of Technology Vol.30 (2002),
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47-52/ Uploaded in ”http://www10.plala.or.jp/h-nkzw/” as ”02kiyou3.pdf” for the
filename.
45)† (2003) 「部分分数分解について」 On partial fraction decomposition/ Bulletin of
Takuma National College of Technology Vol. 31 (2003), 29-36/ Uploaded in
”http://www10.plala.or.jp/h-nkzw/” as ”03kiyou.pdf” for the filename. This is intended
for the convenience of students of Colleges of Technology in Japan.
46)† (July 31, 2004)「一様独立乱数列の剰余類表現 I. 周期列に伴われる剰余類」 Coset
representation of uniform and independent random number sequences I. Cosets associated
with periodic sequences/ Uploaded in ”http://www10.plala.or.jp/h-nkzw/” as
”04persq1.pdf” for the filename.
47) (August 12, 2004) Coset representation of uniform and independent random
number sequences I. Cosets associated with periodic sequences. / Uploaded ”in
http://www10.plala.or.jp/h-nkzw/” as ”04eprsq1.pdf” for the filename.
48)† (July 31-September 8, 2004) 「一様独立乱数列の剰余類表現 II. 剰余類の幾何と
ベルヌーイ試行列」 Coset representation of uniform and independent random number
sequences II. Geometry of cosets and Bernoulli sequences/ Uploaded in
”http://www10.plala.or.jp/h-nkzw/” as ”04persq2.pdf” for the filename.
49) (September 9-September 18, 2004) Coset representation of uniform and
independent random number sequences II. Geometry of cosets and Bernoulli sequences/
Uploaded in ”http://www10.plala.or.jp/h-nkzw/” as ”04eprsq2.pdf” for the filename.
50)∗† (July 5, 2005)「基礎数学」Mathematics I (A textbook for the first grade of
College of Technology)/ Coauthor: Naoya Nakazawa/ Uploaded in
”http://www10.plala.or.jp/h-nkzw/” as ”math1.pdf” for the filename. This aims to serve
as a basic mathematics textbook or a reference for the first grade students of Colleges of
Technology in Japan.
51)† (September 5-November 4, 2005)「皮膚白癬に対する生態学的な戦術について」
On ecological tactics against dermatophyte infections/ Uploaded in
”http://www10.plala.or.jp/h-nkzw/” as ”dermator.pdf” for the filename.
52)∗† (March 9, 2008)「長周期で高精度の一様独立乱数の設計: 数の連が作る点列幾何
の直積群構造及び格子構造に基づく制御」Designs of uniform and independent random
numbers with long period and high precision – Control of the sequential geometry through
product group structures and lattice configurations –/ Coauthor: Naoya Nakazawa/
Uploaded in ”http://www10.plala.or.jp/h-nkzw/” as ”0309.pdf” for the filename. A
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corrected and revised form was uploaded in the same URL as ”309704j.pdf” for the
filename; the correction is in the point that Chinese remainder theorem refers to a
nonlinear shuffling, in the sense of random number applications.
53)∗ (March 9-April 12, 2008) Designs of uniform and independent random numbers
with long period and high precision – Control of the sequential geometry through product
group structures and lattice configurations –/ Coauthor: Naoya Nakazawa/ Uploaded in
”http://www10.plala.or.jp/h-nkzw/” as ”03090403.pdf” for the filename. Its corrected
and revised form (March9-July 8, 2008) was uploaded as ”3978erv.pdf” in the same URL;
the correction is in the conceptual point that Chinese remainder theorem refers to a
nonlinear shuffling, in the sense of random number applications.
54)∗† (August 2, 2009)「一様独立乱数生成方法」Method of Generating Uniform and
Independent Random Numbers/ Coauthor: Naoya Nakazawa/ Submitted to Japan Patent
Office (JPO)/ To be made public as ”2010-040021” in Patent and Utility Model Gazette
Database of the JPO.
55)∗ (March 5, 2009) Method of Generating Random Numbers/ Coauthor: Naoya
Nakazawa/ Submitted to U. S. Patent Office/ Uploaded with the filename ”usprpb3.pdf”
in ”http://www10.plala.or.jp/h-nkzw/.”
56)∗ (May 7, 2009) Representation of Integer Sequences by Cosets and Precision
Problems in Random Number Generation/ Coauthor: Naoya Nakazawa/ Uploaded in
”http://www10.plala.or.jp/h-nkzw/” as ”note507b.pdf” for the filename; its revised form
with small corrections (May 7-August 19, 2009) was uploaded as ”note507z.pdf” in the
same URL.

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