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9KJ00006190267論文Papeｒdepartmental bulletin pape

今村, みゑ子

2853

イマムラ, ミエコ

IMAMURA, Mieko

2854

A Study of Mushi Mezuru Himegimi

12KJ00006190270論文Papeｒdepartmental bulletin pape

小川, 真人

2861

オガワ, マサト

OGAWA, Masato

2862

Media Arts and Repetition : Towards Analysis of "Loop-images" in Media Arts

13KJ00006190271論文Papeｒdepartmental bulletin pape

西村, 安弘

2863

ニシムラ, ヤスヒロ

NISHIMURA, Yasuhiro

2864

From Budo Novels to Passionate Sport Manga : A Critical Essay on Stoic Images of Miyamoto Musashi and His Descendants


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1KJ00006098799論文Articledepartmental bulletin pape

前原, 和寿

マエハラ, カズヒサ

MAEHARA, Kazuhisa

LANG-BOMBIERI'S CONJECTURES
KAZUHISA MAEHARA*
Contents
1. Introduction 1
2. Review Iitaka-Viehweg conjecture 2
3. Application to Geometric Diophantus problems 4
4. Arithmetic Iitaka-Viehweg conjecture 6
5. Application of Arithmetic Iitaka-Viehweg conjecture 7
References 9
Abstract. In this article we generalize Iitaka-Viehweg conjectures for geometric varieties([Km4])
to those for arithmetic ones. They are applicable to Diophantine problems as well as
geometiric Diophantine problems.
1. Introduction
We shall prove the following conjectures proposed by Lang and Bombieri([SL]):
Conjecture 1. Let K be an arithmetic eld and X a variety dened over K. Assume
that X be a variety of general type. Then it has no dense set of K-rational points in X.
This is well known as Mordell's conjecture in case of curves of genus  2 and is shown
by Faltings([F]).
There is an analogue of the conjecture, which is proposed by Noguchi([No], [Km1],
[Km2]. [Km3]):
Conjecture 2. Let X and S be algebraic varieties over the eld of the complex numbers.
Assume that X=S be a bre space with the geometric generic bre of general type. If X=S
has a dense set of rational sections in X, then var(X=S) = 0.
First applying Kollar-Kawamata's theorem([Kaw], [Ko2], [Ko1], [Mat]), we shall prove
the conjecture 2. Secondary we shall show an arithmetic version the conjecture 1 later.
* Associate professor, General Education and Research Center, Tokyo Polytechnic University,  
 Received Sept.11, 2009 E-mail address: maehara@gen.t-kougei.ac.jp. 
 
1 
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 32 No.1 (2009) 
2. Review Iitaka-Viehweg conjecture
Iitaka proposed the following conjecture in 1970:
Conjecture 3. ([I]) Let X=S be a bre space over the eld of the complex numbers and
X the geometric generic bre of X=S. Then (X)  (X) + (S).
Viehweg raised the following
Conjecture 4. ([V]) Let f : X ! S be a bre space X=S with the geometric generic bre
of Kodaira dimension  0. Then there exists a number m such that
(det f!
mX=S)  var(X=S):
Notation 1. ([SGA], [GG]. [I], [V]. [Ko2], [Dix], [MiyPet]), [Mat])
(1) Let k be a eld. A geometrically irreducible, reduced, smooth scheme X over k is
said to be a non singular variety over k.
(2) Let X be a non singular variety of dimension d and 
1X the dierential sheaf over
X. Let !X denote 

d
X .
(3) A connected proper surjective morphism f : X ! S of non singular varieties X
and S is said to be a bre space X=S.
(4) Let f : X ! S be a bre space X=S. !X=S denotes !X 
 f! 1S .
(5) Let L be an invertible sheaf over X. (L) denotes the maximal dimension of the
image variety of the rational map X ! P( (X;L
m)) dened by  (X;L
m) 

OX ! L
m for m >> 0. We call (L) Iitaka dimension of L.
(6) (!X) is said to be Kodaira dimension of X, which is denoted by (X).
(7) Let X=S be a bre space. We denote by var(X=S) the minimal dimension of T
such that there exists a generically nite morphism S 0 ! S in which X S S 0 is
birationally equivalent to S 0 T X0 for some varieties T , X0 with X0=T a bre
space. This dimension is called Viehweg dimension of a bre space X=S.
X  S 0

//
{{ww
ww
ww
ww
w
X0 T S 0
/
//
//
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//
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//
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X
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;;
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ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 32 No.01 (2009) 2
(8) The category of bands([Gir], [SGA]) of pronite groups([Se], [Shatz], [RBZL],
[Zuo]) is dened in the following. The objects are the pronite groups and the
arrows are the homomorphisms of pronite groups modulo inner automorphisms.
(9) A Q-divisor D is said to be eective if (D)  0.
We have proved the two conjecture 3 and 4. Recall the sketch of the proof.
(1) Let X=S be a bre space with the geometric generic bre of Kodaira dimension
 0([I]). We may assume var(X=S) = dimS by Viehweg's comment. Construct a
generically nite cover Y of X such that
(a) Y is a variety of general type or a variety with the abundant canonical divisor,
(b) maxm>0 (det f!
mX=S) = maxm>0 (det g!

m
Y=S), where maxm>0 (det g!

m
Y=S) 
var(Y=S) is obtained by Kollar and Kawamata independently.
(2)
var(Y=S)  var(X=S):
The following Mochizuki's theorem is available to prove (2) above.
Theorem 1. ([Mch]) Let p be a prime number. Let K be a subeld of a nitely generated
eld extension of Qp. Let L;M be function elds of arbitrary dimension over K. Let
HomSpec(K)(Spec(L); Spec(M)) be the set of K-morphisms from Spec(L) to Spec(M). Let
Homopen K ( L; M) over  K, the set of open continuous homomorphisms of pronite groups
considered up to composition with an inner automorphism arising from Ker( M; K),
where  L and  M are the absolute Galois groups of L and M , respectively. Then the
natural map HomSpec(K)(Spec(L); Spec(M))! Homopen K ( L; M) is bijective.
Let p be a prime number. Let K be a subeld of a nitely generated eld extension of
Qp. Note that there exists an isomorphism  : K = C.
Let X be the geometric generic bre of X=S. Then there exists a variety FK0 and a
nite extension eld K0 of Q such that FK0 K0 K0 = X.
Let BirC(X) = Bir K0(FK0 
K0 K0). There exists a denition eld K of Bir K0(FK0 
K0
K0) such that BirK(FK)
K K = BirCX and that K is a nite extension eld of Q since
Bir(X) is an algebraic group. Fix K once for all.
Let  :  FK !  K denote the structure map associated to FK ! Spec(K), which is a
surjection since K is algebraically closed in the rational function eld of F . Let Z( FK )
denote the centre of  FK . Then  induces  : Z( FK )! Z( K).
Hence consider a crossed module
( 1(Z( K))! Aut K (FK)):
There exists an exact sequence by Breen([Breen1], [Breen2], [BJ])
0! Z( FK )[1]! ( 1(Z( K))! Aut K (FK))! Out K (FK)! 1
LANG-BOMBIERI'S CONJECTURES 3 
and a long exact sequence:
0! H1( SK ; Z( FK )[1])! H1( SK ; ( 1(Z( K))! Aut K (FK)))! H1( SK ;Out K (FK))
We proved the following lemma making use of revised Matsumura's theorem.
Lemma 1. ([Mat]) Let FK be a variety of (FK)  0. Then BirK(FK) has at most
countable connected components and the connected component which contains an identity
element is of nite type over K.
We can take base change K 0=K which is a nite extension so that the image of the
extension element  XK associated to X=S is a trivial map in H
1( SK ;Out K (FK))
=
Hom( SK ;Out K (FK)). Thus  XK is going up to H
1( SK ; Z( FK )[1]), which turns out to
a central extension.
To prove var(Y=S)  var(X=S), we have proved that it is enough to show that
var(Y=S) = 0 implies var(X=S) = 0.
Assume var(Y=S) = 0. Then the extension 1 !  F K !  XK !  SK ! 1 associated
to a bre space X=S=SpecK splits. Hence  XK is a semi-direct product. This extension
is central since the argument above. On the other hand, a central extension which is a
semi-direct product is a trivial product.
By Breen's theory([Breen1], [Breen2], [AM]), we have
H1( SK ; (
 1(Z( K))! Aut K (FK))) = Ext K ( SK ; FK );
whose neutral element is  SK  K  FK . The sketch of the proof nishes.
3. Application to Geometric Diophantus problems
Theorem 2. Let X=S be a bre space with the geometric generic bre of general type.
Assume that there is a dense set of rational sections of X=S in X. Then var(X=S) = 0.
Proof. It suces to prove the assertion for every curve C on S. Namely we will prove for
a bre space XC=C. Change the base curve C by a normal curve C
0 of genus g(C 0)  2.
Let X=C denote such a bre space and an image of a rational section C, which is in fact
a section of X=C.
Since (!X=C)  (!X), there exist a number m and the following commutative square
for dimX = n:
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 32 No.01 (2009) 4


mnX
OX(mKX)
OO


mC
OO
// 

mnC
\\999999999999999999
Restricting the commutative diagram above to a curve C on X, we have


mnX jC
?
??
??
??
??
??
??
??
??
??
?
OX(mKX)jC
OO


mC jC
OO
// 

mnC jC
Thus we have the upper bound of the intersections
(C; KX)  n deg 
1C = n(2g(C)  2):
Since (C) = 1 and (!X)  (!X) + (!C), we obtain (!X) = dimX. Hence !X is
big.
For any ample invertible sheaf L there exists a number ` such that L ,! !`X (Kodaira's
Lemma). We have the estimation of intersections (C; L)  `(C; !X)  n`(2g(C)   2)
for every curve which is not contained in the stable base locus of !X . These curves are
parametrized by Hilbert schemesHilb
p(m)
X , where the Hilbert polynomials p(m) are a nite
number of polynomials since (C; L)  n`(2g(C)   2). Hence one can nd a variety T
which is a component of parametrizing Hilbert schemes and a dominant rational map  
over C such that  : T  C ! X over C. See the following diagram:
T   = fCg  T X //
''OO
OOO
OOO
OOO
OO
oo
vvmmm
mmm
mmm
mmm
X

T  C //
OO
C
Here   is the restriction of the universal family over Hilb
p(m)
X to T . Hence   is birationally
equivalent to T  C. Therefore
0 = var(T  C=C)  var(X=C)
and var(X=S) = 0. 
LANG-BOMBIERI'S CONJECTURES 5 
Theorem 3. Let k be an algebraically closed eld of characteristic 0. Let X be a variety
of general type over k and g a number which is not less than 1. Then the set of non
singular curves fCg of genus g in X which do not contained in a xed hyperplane forms
a bounded set, i.e., given an ample invertible sheaf L over X, (C; L

m) are a nite
number of polynomials in m.
Proof. Let X ! P1 be a bre space obtained by Lefshetz pencil up to birational equiv-
alence. For each curve C in X, we have a bre space X P1 C ! C. Applying the
argument above to these bre spaces, we complete the proof. 
Note that even if g = 0, the assertion holds since it is enough to change the direction
of a homomorphism in the diagram above to !
nmC ! !C .
Next we shall prove the following result which is an analogue of Hermite's theorem.
Theorem 4. Let C be a curve, S a set of points on C and d a number. Given a covering
degree  d of covers over C, there exists only a nite number of nite covers over C which
are etale outside S.
Proof. Let B be such a nite cover over C. There are a nite number of !B=C for all such
covers B. Since B = Proj(m0 !
mB=C), we get the theorem. 
Theorem 5. Let X be a variety and C, D curves. Let f : X ! C  D be a proper
surjective morphism. Assume f is smooth over Co  Do, where Co and Do are open
subsets of C and D, respectively. Then var(f)  1.
To prove an analogue of Lang-Trotter's conjectures it seems to be applicable .
4. Arithmetic Iitaka-Viehweg conjecture
Denition 1. Let K be a nite extension of Q. Let OK denote the integral closure of
Z  K. We call an arithmetic variety if it is an irreducible and reduced scheme which is
at and projective over SpecOK:
f : X ! SpecOK
and if, moreover, the base change f : X ! SpecK is an irreducible and reduced morphism.
We propose an arithmetic Iitaka-Viehweg conjecture:
Conjecture 5. Let f : X ! S be an arithmetic bre space dened over SpecOK and let
the geometric generic bre of the bre space of Kodaira dimension  0.
(1) If dimS  2, maxm>0 (det f!
mX=S)  var(X=S)  1.
(2) If, especially, S = SpecOK, maxm>0 (det f!
mX=S)  var(X=S)  1
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 32 No.01 (2009) 6
Note that the latter conjecture is essential. By taking pull-back through SpecK !
SpecOK , we have an ordinary bre space X=S over SpecK. By Iitaka's lemma, we
obtain (det f!
mX=S)  (det f!
mX=S) + 1. Note that var(X=S)  var(X=S) + 1. If
the geometric generic bre is of general type, we can show maxm>0 (det f!
mX=S) 
maxm>0 (det f!
mX=S) + 1. In general, construct a cover such that the bre is of general
type and that the same value as maxm>0 (det f!
mX=S) and we get maxm>0 (det f!

m
X=S) 
maxm>0 (det f!
mX=S) + 1.
Lemma 2 (Moriwaki([Mo])). Let K be an algebraic eld, X a projective irreducible re-
duced variety over K and L an invertible sheaf over X. Then there exists a couple (X ;L)
such that
(1) X ! Spec(OK) is an arithmetic projective variety and its generic bre is X.
(2) Forgetting the underling metric structure L, it is Q-equivalent to L.
Lemma 3. f!
mX=S is weakly positive for m > 0.
Proof. Let L be an ample invertible sheaf over S. Then H1(X ; !X 
 fL)! H1(X ; !X 

fL
m) is injective for m  2 since Koll'ar-Viehweg results. Hence H1(S; f!X 
L) = 0.
Using the dualizing sheaf, we have
H0(S; !OK 
HomOK (f!X 
 L;OK)) = 0
Hence f!X=S is weakly positive. By Viehweg's method([V], [Fuj], [Ws]), we can complete
the proof. 
Lemma 4. Assume (!X) = dimX and dimS = 1. Then deg det f!
mX=S > 0.
Proof. By weak positivity, deg det f!
mX=S  0. If deg det f!
mX=S = 0, then var(X=S = 0,
which is absurd. 
Proposition 1. (1) Assume (!X) = dimX and dimS = 1. Then maxm>0 (det f!
mX=S) 
var(X=S)  1.
(2) Assume (!X) = dimX. Then max
m>0
(det f!
mX=S)  var(X=S)  1.
Proof. Take a generically nite cover Y such that
(1) max
m>0
(det f!
mY=S) = maxm>0
(det f!
mX=S).
(2) (Y ) = dimY , max
m>0
(det f!
mY=S)  var(Y=S)  1
Making use of var(Y=S)  var(X=S), we obtain the theorem. 
5. Application of Arithmetic Iitaka-Viehweg conjecture
Theorem 6. Let X=S be a bre space with X of general type. Then X has no dense set
of rational points.
LANG-BOMBIERI'S CONJECTURES 7 
In other words, we have the following theorem.
Theorem 7. Let X=S be an arithmetic bre space with the generic bre X of general
type. Then there exists no dense set of rational sections.
Proof. We will apply the following theorem.
Lemma 5 (Northcott([Szp]), [Mo]). For any  > 0 and M the set fx 2 Pn( Qj[Q(x) :
Q]  e; hnv(x) Mg is nite.
By Iitaka's conjecture, (!X=S)  0. Take the base change such that [K : Q] > 1. We
have
0! OK ! !OK ! 
OK=Z ! 0:


mnX
OX(mKX)
OO
!
mS
OO
// 

mnS=Z
\\999999999999999999
Restrict the commutative diagram above to a curve S on X, we have


mnX jS
7
77
77
77
77
77
77
77
77
7
!
mX jS
OO
!
mS jS
OO
// 

mnS=Z
Proposition 2. We have the following results:
(1) Let K` be the kernel such that the following becomes exact sequences : 0! K` !
!
n`OK ! 

n`OK=Z ! 0.
(2) We have an injection OK ! K` and
(3)
H1(S; Hom(!X=ZjS ; K`)) = H0(S; !OK 
 !X=ZjS 
K 1` ) = 0
for ` >> 0.
Let K denote the set of the places of K at innities and r1 the number of the real
places, r2 the number of the complex places  such that  or  belongs to K([Szp]).
Note that deg!OK =  2(OK) =  2 log(2r2D 1=2)([Szp]). Apply the following lemma
to get the proof.
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 32 No.01 (2009) 8
Lemma 6. Let \nSupp(Coker(H0(C; nL) 
 OC ! nL)) = SBs(L). Then there exists a
number N such that for any point x 2 (X n SBs(L))( K), h(C;L)(x)  N .
Lemma 7 (Northcott([Szp])). Let X be a projective variety over SpecK and L an ample
invertible sheaf over X. Let hL : X( K) ! R denote the height function associated to L.
Then for any positive real numbers , M , the set fx 2 X( K)j[K(x) : Q]  ; hL(x) Mg
is a nite set.
This completes the theorem. 
References
[AM] Adem, A. and Milgram, R., Cohomology of nite groups., Grundlehren math. Wiss. 309, p. 317
(1991).
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ISBN 0 521 80309 8 2001
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Jersey pp.201 1995.
[Ko2] Kollar, J., Rational curves on algebraic varieties., Springer, Berlin-Heiderberg-Newyork-Tokyo,
(1995)
[Km1] Maehara, K., Diophantine problems of algebraic varieties and Hodge theory in International Sym-
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LANG-BOMBIERI'S CONJECTURES 9 
[Km3] Maehara, K., Conjectures on birational geometry, A.C.Rep. T.I.P. Vol.24, No.1, pp.1-10(2001).
[Km4] Maehara, K., NON COMMUTATIVE ALGEBRAIC AND BIRATIONAL GEOMETRY ,
A.C.Rep. T.I.P. Vol.31, No.1, pp.27-63(2008).
[Mats] Matsuki, K., Introduction to the Mori Program., Universitext p. 468 Springer 2000
[Mat] Matsumura, H., On algebraic groups of birational transformations.,Rend. Accad. Naz. Lincei, Serie
VIII,34, 151-155 (1963).
[MO] Matsumura, H.and Oort, F., Representability of group functors, and automorphisms of algebraic
schemes, Inventiones Mathematicae, 1967 - Springer.
[Mo] Moriwaki, A., Arithmetic height functions over nitely generated elds, Invent. Math. 140 (2000),
101-142.
[MiyPet] Miyaoka, Y., Peternel T., Geometry of Higher Dimensional Algebraic Varieties., DMV Seminar
Band 26 Birkhaiser p. 213 1997
[Mch] Mochizuki, S., The local Pro-p Anabelian Geometry of Curves., Research Institute for Mathemat-
ical Sciences, Kyoto University RIMS-1097(1996).
[No] Noguchi, J., A higher dimensional analogue of M's conjecture over function elds, Math.Ann.
258(1981), 207-212.
[RBZL] Ribes, L., Zalesskii, P., Pronite Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete
3.Folge Vol.40 Springer(1991).
[Ws] Schmid, W., Variation of Hodge structure: the singularities of the period mapping., Inventiones
math., 22., pp. 211-319(1973).
[Se] J-P. Serre. Cohomologie Galoisienne, Lecture Notes in Mathematics. , 5 4th Ed. 1973.
[Szp] Szpiro, L. Seminaire sur les pinceaux arithmetiques: La conjecture de Mordell, Societe
Mathematique de Frace. 127 p. 287(1985).
[SL] Lang, S., Fundamentals of Diophantine Geometry. Springer-Verlag New York Berlin Heiderberg
Tokyo, p. 361(1983).
[Shatz] Shatz, S., Pronite groups, arithmetic, and geometry., Annals of Math. studies, N. 67, Princeton
Uni. Press, p. 252,(1972).
[V] Viehweg, E. Quasi-projective Moduli for Polarized Manifolds., Ergebnisse der Mathematik und ihrer
Grenzgebiete, 3.Folge.Band 30, p. 320 (1991).
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1708, Springer, ISBN 3-540-66312-6.
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 32 No.01 (2009) 10


LANG-BOMBIERI'S CONJECTURES

表紙

7KJ00006190265論文Papeｒdepartmental bulletin pape

白倉, 克文

2849

シラクラ, カツフミ

SHIRAKURA, Katsufumi

2850

On Lermontov's Lyric Poetry

作品(中扉)

4KJ00006098859論文Articledepartmental bulletin pape

木下, 照弘

1251

キノシタ, テルヒロ

小西, 良弘

1252

コニシ, ヨシヒロ

Kinoshita, Teruhiro

1253

Konishi, Yoshihiro

1254

シミュレーションデータに基づいたマイクロ波回路設計パラメータの
決定方法と設計ソフトウェアの開発
木下 照弘 ¤1 小西 良弘 ¤2
Method of interpolation from simulation data for microwave circuit
design and it's software tool
Teruhiro Kinoshita ¤1 Yoshihiro Konishi ¤2
Abstract The method to determine the design parameters based on the simulation date has
been discussed in microwave circuit design. Using interpolation of the discrete data, and de¯ning
quadratic error criterion for the design parameters in error space, the method of Gauss-Newton
algorithm is applied to determine the parameters. Software tool has been also developed using this
method. Numerical result of the calculation shows that our method is e®ective for determining the
parameters for the microwave circuit.
1 はじめに
コンピュータの高性能化に伴い，マイクロ波回
路の設計においてもシミュレータが盛んに活用さ
れている [1]．一般に，マイクロ波シミュレータ
は，誘電率や線路形状・寸法などの設定値 (パラ
メータ)から，インピーダンスなどの特性を数値
的に推定する解析ツールである．これに対し，設
計では所望の特性を得るための設定値を決定する
必要がある．このように，解析と設計は逆の関係
にあることから，シミュレーション結果を設計に
活用するには工夫が必要となる．実用的な面から
はシミュレータにより得られた結果をデータとし
て読み取り，特性値を入力するとパラメータ値を
算出して表示するツールが望まれる．
ここでは，シミュレータによる解析データの設
計への活用方法として，設計パラメータを離散的
に変化させて得られる解析値の数表をもとに，補
間により特性値からパラメータを決定する方法に
ついて報告する．特性値が 1つで，かつ，設計パ
ラメータが 1つの場合は，パラメータを変化させ
て得られる特性値のグラフから所望の特性値を与
えるパラメータを決定することは容易であるが，
特性値，および，設計パラメータが複数の場合は，
計算機の利用を考えることになる．ここでは，パ
ラメータが複数の場合について，離散的なシミュ
レーションデータの数表から補間関数を定義し，
逐次近似により所望の特性を得るための設計パラ
メータの決定方法について述べる [2]．具体的に，
設計パラメータが 2つの場合について．それらを
決定するプログラムを作成したので，併せて報告
する．
2 原理
任意の個数の設計パラメータに対して適用可能
であるが，以下では，設計パラメータが２つの場
合について述べる．
＊1 東京工芸大学工学部コンピュータ応用学科教授 
＊2 ケイラボラトリー 
 2009 年 9 月28 日 受理 
26
東京工芸大学工学部紀要 Vol. 32 No.1（2009） 
2.1 補間関数
2.1.1 線形補間
2次元の離散的なデータを区分的な関数を用い
て補間する場合には，幾つかの関数が考えられる
が，ここでは，等間隔でデータが与えられている
ものとして，式 (1)に示す区分的な関数を補間に
用いる．
-1.5
-1
-0.5
 0
 0.5
 1
 1.5x -1.5
-1
-0.5
 0
 0.5
 1
 1.5
y
 0
 0.2
 0.4
 0.6
 0.8
 1
 1.2
図 1: 区分的関数 Á(x; y)
Á(x; y)
=
8>>>><>>>>:
(1¡ jxj)(1¡ jyj);
jxj · 1; かつ jyj · 1
0;
その他
(1)
を用いて，x; y 方向に等間隔な格子上の離散点
(xi; yj) で与えられたデータ値
ai;j ; (i = 1; 2; 3; ¢ ¢ ¢ ; N; j = 1; 2; 3; ¢ ¢ ¢ ;M)
に対して，補間関数を次のように定義する：
f(x; y) =
NX
i=1
MX
j=1
ai;j Á
µ
x¡ xi
¢x
;
y ¡ yj
¢y
¶
(2)
ここで，
¢x = xi+1 ¡ xi
¢y = yj+1 ¡ yj
である．
2.1.2 3次近似
式 (2) は離散データの折れ線近似 (線形近似)
である．高次の曲線を用いれば滑らかな補間を行
なうことができる．そこで，線形近似に加えて，
3 次曲線による近似を検討する．データの間隔
を ¢x;¢y とし，(i¢x; j¢y)での値が ai;j ; (i =
1; 2; 3; ¢ ¢ ¢ ; N; j = 1; 2; 3; ¢ ¢ ¢ ;M)であるデータ列
に対して，
n¢x · x < (n+ 1)¢x;
m¢y · y < (m+ 1)¢y
での値を x = i¢x; y = j¢y において ai;j ; (i =
n¡1; n; n+1; n+2; j = m¡1;m;m+1;m+2)
を通る x; y それぞれについて 3次式の曲面で近
似する．
f(x; y) =
n+2X
i=n¡1
m+2X
j=m¡1
ai;j
£gi¡n+1
µ
x¡ n¢x
¢x
¶
£gj¡m+1
µ
y ¡m¢y
¢y
¶
(3)
ただし，
g0(x) = ¡16x(x¡ 1)(x¡ 2) (4)
g1(x) =
1
4
(x+ 1)(x¡ 1)(x¡ 2) (5)
g2(x) = ¡12(x+ 1)x(x¡ 2) (6)
g3(x) =
1
6
(x+ 1)x(x¡ 1) (7)
である．
2.2 逐次近似
2つの設計パラメータ (x; y)に対して特性値 1
および，特性値 2の離散値がシミュレーションな
どにより得られたとき，式 (2)あるいは，式 (3)よ
り特性値を補間する連続関数 f1(x; y)と f2(x; y)
が求まる．
シミュレーションデータに基づいたマイクロ波回路設計パラメータの決定方法と設計ソフトウェアの開発 27 
f1; f2 に対する所望の値を h1; h2 として，こ
の特性値を得るための設計パラメータ x; y は，
連立非線型方程式
f1(r) = h1 (8)
f2(r) = h2 (9)
の解である．これらに対して誤差関数
I(r) = ff1(r)¡ h1g2 + ff2(r)¡ h2g2
(10)
を定義し，
I(r) = 0 (11)
を満足する r = (x; y)の逐次近似解 (数値解)を
求める．I(r) ¸ 0であるから，求める解は I(r)
の最小値でもある．そこで，ガウス・ニュートン
法により連立方程式 (8), (9)の数値解を求めるこ
とができる．1次導関数による線形近似により得
られる0BB@
@f
(k)
1
@x
@f
(k)
1
@y
@f
(k)
2
@x
@f
(k)
2
@y
1CCA
Ã
¢x
¢y
!
=
Ã
f
(k)
1 ¡ h1
f
(k)
2 ¡ h2
!
¢x = x(k) ¡ x(k+1)
¢y = y(k) ¡ y(k+1)
を
Ã
¢x
¢y
!
について解たものを整理すれば，設
計パラメータ (x; y)を決定する逐次近似式Ã
x(k+1)
y(k+1)
!
=
Ã
x(k)
y(k)
!
¡
0BB@
@f
(k)
1
@x
@f
(k)
1
@y
@f
(k)
2
@x
@f
(k)
2
@y
1CCA
¡1Ã
f
(k)
1 ¡ h1
f
(k)
2 ¡ h2
!
(12)
(k = 1; 2; 3; ¢ ¢ ¢) が得れる．適当な初期値Ã
x(o)
y(0)
!
から始めて，逐次式 (12)により数値
解を求めることができる．
3 設計パラメータの決定
図 2および，図 3に示す誘電体基板中に電極を
埋め込んだ縦型平面回路 [3]について，離散的に
得られた電気特性より電極の幅および間隔を決定
する．
この回路は z軸を伝搬方向とする密結合マイク
ロ波線路であり，接地基板上の比誘電率が "r で
ある誘電体層に幅 aの電極 2枚を間隔 dで埋め
込んで構成される．誘電体層の厚み hで規格化
した a=h; d=hが設計パラメータとなる．
x
y
a
d
h
 
r
o接地
図 2: 縦型平面回路の断面図
d
h
a
 
r接地 x
y
z o
図 3: 基板中の縦型平面回路
東京工芸大学工学部紀要  Vol32  No.1（2009） 28
表 1: 縦型平面回路のインピーダンス
Zeven ("r = 1)
d=h
Zeven(­) 0.4 0.5 0.6 0.7
0.5 271.905765 262.032957 253.805461 246.609931
a=h 0.6 262.483866 253.389693 245.618486 237.875800
0.7 254.665063 246.115961 238.657957 231.928856
0.8 247.699046 239.693261 232.605351 225.967855
Zodd ("r = 1)
d=h
Zodd(­) 0.4 0.5 0.6 0.7
0.5 74.4964226 84.5749727 93.1892911 100.601410
a=h 0.6 66.7320763 76.2056696 84.4794496 92.3072956
0.7 60.4322505 69.5648469 77.3929649 84.2090386
0.8 55.3093776 63.9451625 71.4722593 78.1319798
2つの電極を同相で励振した場合 (偶励振時)の
接地とのインピーダンス Zeven と逆相で励振し
た場合 (奇数励振時)のインピーダンス Zodd を
特性値とし，設計パラメータ a=h; d=hを決定す
る．図 4にそれぞれの励振時での線路の等価回路
(断面図)を示す．表 1に偶励振，および，奇励振
a
d/2
a
d/2
(b) Zodd（奇励振）
(a) Zeven（偶励振）
m
a
gn
et
ic 
wa
ll
 
r
 
rh
h
図 4: 偶励振と奇励振に対する等価線路
でのインピーダンス Zeven; Zodd の有限要素法
によるシミュレーション結果の一部を示す．比誘
電率 "r = 1の場合に，d=hを 0.1 間隔で 0:4～
0:7まで変化させ，a=hも 0.1 間隔で 0:5～0:8と
変化させている．
図 4 に示す偶励振と奇励振時での等価回路か
らもわかるように，偶励振では奇励振と比較して
電極と接地間の静電容量が小さく，インピーダン
スは大きくなる．また，電極幅 aの増加に伴い,
静電容量が増加し,インピーダンスは小さくなる.
電極間隔 dが小さくなると奇励振では電極間隔が
狭くなりインピーダンスは減少するのに対して,
偶励振では実効的な電極の面積が小さくなりイン
ピーダンスは増加している.
インピーダンスの変化はなだらかであることか
ら，比較的容易に所望の Zeven; Zodd を得るた
めのパラメータ a=h; d=hを決定できると予測さ
れる．
例として Zeven = 250[­]; Zodd = 80[­]に対
応する a=h; d=hを求める．表 1の値をもとに描
いた d=h{a=h平面上での誤差
I = (Zeven ¡ 250)2 + (Zodd ¡ 80)2
の平方根
p
I を図 5a, 5bに示す．図 5bは図 5a
中の誤差が小さくなる部分を拡大して描いたもの
シミュレーションデータに基づいたマイクロ波回路設計パラメータの決定方法と設計ソフトウェアの開発 29 
である．
p
I(a=h; d=h)の等高線は，I = 0を中
心とした単調な同心円に近い曲線を描いており，
I = 0となる (a=h; d=h)の値が容易に求まる．図
中に a=h = 0:5; d=h = 0:6を初期値として，逐次
近似により I = 0の数値解を求めたときの逐次
近似値を○印で示す．
10
40
4060
80
100
120
140150
0.2 0.4 0.6 0.8 1.0
0.2
0.4
0.6
0.8
1.0
dh
ah
図 5a: 誤差 I の等高線図および逐次近似 (全体)
2
4
6
6
8
10
12
12
12
14
16
0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64
0.50
0.52
0.54
0.56
0.58
0.60
0.62
0.64
dh
ah
図 5b: 誤差 I の等高線図および逐次近似 (部分拡
大図)
さらに，図 6に逐次近似により誤差が零に収束
する様子を示す．横軸はくり返しの回数k，縦軸は
誤差 I(k)である．3回のくり返しで誤差は 10¡12
以下になり，収束が非常に速いことがわかる．
1 2
1
10−4
10−8
(k)
I(k)
e
rr
o
r
図 6: 誤差 I の収束
Zeven = 250[­]; Zodd = 80[­]に対して得ら
れた d=h; a=hの値は
a
h
= 0:598939
d
h
= 0:5447707
であった．
表 2: 縦型平面回路のインピーダンス
Zeven ("r = 1)
d=h
Zeven[­] 0.3 0.5 0.7
0.3 310.974873 286.219758 269.139672
a=h 0.5 283.232551 262.032957 746.609931
0.7 264.128994 246.115961 231.928856
Zodd ("r = 1)
d=h
Zodd[­] 0.3 0.5 0.7
0.3 84.3173261 109.578704 127.050325
a=h 0.5 62.3430954 84.5249727 100.601410
0.7 50.3590631 69.5648469 84.2090386
次に，電極幅 a=hおよび電極間隔 d=hのサン
プリング間隔 (パラメータの間隔)に対する解の
依存性を検討する目的で，表 2に示すように間隔
¢(a=h);¢(d=h)を大きくしたデータから補間関
数を構成した場合について同様の計算を行う．こ
のときの計算結果および，1次補間と 3次補間の
違いによる結果を表 3に示す．
東京工芸大学工学部紀要  Vol32  No.1（2009） 30
表 3: 補間の次数およびパラメータの間隔の違い
に対する比較
(Zeven = 250[­]; Zodd = 80[­])
1次補間
a=h d=h
¢(a=h) = ¢(d=h) = 0:1 0.5989392 0.5447706
¢(a=h) = ¢(d=h) = 0:2 0.6080750 0.5465167
絶対誤差 0.0091358 0.0017461
誤差/データ間隔 約 9% 約 2%
3次補間
a=h d=h
¢(a=h) = ¢(d=h) = 0:1 0.59888893 0.54359990
¢(a=h) = ¢(d=h) = 0:2 0.59739095 0.54293036
絶対誤差 0.00149834 0.00066944
誤差/データ間隔 約 1% 約 1%
表 3のパラメータの間隔を変えた場合の結果よ
り，1次補間においてもパラメータの間隔に対し
て 10%以内の精度で解が得られており，3次補間
では 2%未満であることがわかる．
4 設計ツールの作成
設計現場で活用することを考慮すると，キー
ボード操作を極力省略した GUIを備えたプログ
ラムとすることが望ましい．また，
unix os など様々な環境下で動作する必要もある．
そこで，ここでは，OSへの依存が比較的少ない
Java Applet として動作するプログラムを作成
した．また，既存のシミュレータでは解析結果を
MS Excel などの表計算データとして結果を出力
するものが多く見掛けられるので，テキスト形
式，および，csv 形式のファイルからデータを読
み込むこととした．
作成したクラスと機能の概要は以下である：
² Interpolationクラス
main メソッドを含むクラスであり，java
swing を拡張した，ボタンなどの GUI機能
を持つ．シミュレーションデータファイルの
オープン，目標値の入力，逐次近似の実行，
結果の表示などを行う．
² Functionクラス
データファイルへのポインタを受け取り，字
句解析クラスと して，データファイルに
含まれるデータ間隔などのパラメータ値の
解読，離散データの読み取り，補間関数，お
よび，その導関数のメソッドを持つ．
作成した Java Applet上でシミュレーションデー
タ (CSVファイル)から設計値を求めたときの様
子を図 7に示す．
図 7: 実行ウィンドウ (Java Applet)
5 まとめ
マイクロ波シミュレータから得られるような離
散的パラメータに対する特性値の数表を補間し
て，特性値からパラメータ値を逆に決定する方法
について検討した．誘電体基板中の縦型平面回路
についてのシミュレーションデータを補間して，
偶励振，および，奇励振時のインピーダンスを指
定することで，設計パラメータである電極幅と間
隔を決定する場合について述べた．この方法はパ
ラメータが 3つ，4つと増えた場合にも拡張可能
である．
謝辞
今回の報告にあたり，貴重なデータをご提供
下さった大阪大学の塩見英久先生，EMテクノロ
ジーの薮内広一氏，および，アンソフト・ジャパ
ンの鈴木誠氏に感謝申し上げます．
MS Windows,
協調
シミュレーションデータに基づいたマイクロ波回路設計パラメータの決定方法と設計ソフトウェアの開発 31 
参考文献
[1] 小暮裕明, \電磁界シミュレータで学ぶ高周波
の世界," CQ出版, 1999.
[2] 木下照弘，小西良弘，\マイクロ波回路設計に
おける，シミュレーションデータを元にしたパ
ラメータの補間," 輻射科学研究会資料, RS09-
08, 2009.
[3] 小西良弘, \マイクロ波フィルタ回路の構成と
設計," MWE2008 Micorwave Workshop Di-
gest, pp. 483{492, 2008.
東京工芸大学工学部紀要  Vol32  No.1（2009） 32


Method of interpolation from simulation data for microwave circuit design and it's software tool

4KJ00006101159論文Articledepartmental bulletin pape

田邉, 寛

3200

タナベ, ヒロシ

TANABE, Hiroshi

1818

* Associate Professor. General Education and Research Center, Tokyo Polytechnic University 
 Received sept 8, 2009 
 
 
Speech Training Introduced in Required English Classes 
Hiroshi TANABE* 
 
Abstract  
    The effects of the introduction of a speech training method on the motivational change of university 
students and their apprehension of the effects of the course were examined. The results show the use of 
materials in a special field of study is accepted by the students and the speech training that is based upon 
the contents is accepted as effective though the habituation of the method requires some more thoughtful 
devisal of the whole procedure of the introduction. 
 
Introduction 
     Nation and Newton (2009) showed five causes and solutions for learners who were not willing to 
speak. Causes described are: 1) inadequate vocabulary, 2) inadequate control of grammar, 3) lack of 
fluency, 4) shyness, and 5) lack of encouragement. The first three of these causes are personal and each 
student has his or her level of problems. For the causes, 4 and 5, they suggest the use of small groups 
where their mental tension is lower and they are easily encouraged among group members. For the first 3 
sets of problems some kind of individualized approach will be necessary. The speech training method 
introduced in this paper, which is also introduced in the previous research (Tanabe, 2005), is not only for 
the classroom activity but mainly for the individual learning situation. This paper discusses the effects of 
the introduction of the speech training method on the motivational change of university students and their 
apprehension of the effects of the course based on the idea of content based approach that would provide 
the contents or topics of speech for the students.  
 
Research Method 
Method 
    A questionnaire with 16 items was given to the subjects after the course of three months of regular 
English classes of two different universities.  
 
Subjects 
There were three groups of subjects in this study. Two groups of students were in the first year of Keio 
University majoring in literature and another was in the second year of Tokyo Polytechnic University who 
was majoring the imaging art (TPU). There were 10 students in the first group (Keio 1), 18 in the second 
group (Keio 2) and 22 in TPU at the time of this research. The members of the two groups of Keio 
University were in the third level, the first having the highest scores and the fourth the lowest. The levels 
would be estimated as that of the second grade or pre-first grade of The Step Examination (Eiken) or 600 to 
700 points in the TOEIC examination. The level of the students of TPU was lower as the third grade of 
STEP examination or 450 to 500 in the TOEIC examination. The contents dealt with in each class were 
those of applied linguistics for Keio 1, human behavior for Keio 2 and TPU.  
 
Philosophy of Teaching 
    The content-based approach was taken. The philosophy presented here was the same as the one 
35 
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 32 No.2 (2009) 
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 32 No.2 (2009) 
 
presented in 2008. The purposes of the use of that approach were: 
(1) to motivate the students by introducing the specialized field in the level of higher education, 
(2) to provide students with the opportunity of the practical use of English, 
(3) to provide students with the opportunity of immersing in the situation with a lot of comprehensible 
input (Krashen, 1972 in Tanabe, 2008) . 
 
Syllabus of the course 
     The syllabus and the contents of the classes were almost the same as the one presented by Tanabe, 
2008. The only difference was audio-visual materials were frequently used for Keio 2 and TPU. The AV 
materials were used almost two times in a month. This was to complement the lacking information that was 
caused by the lecture sometimes given in English and the abstract idea of the complicated brain structures 
and functions, etc.  
For Keio 1  
Textbooks 
The Natural Approach by Krashen (1972)*1, The Language Learning Strategies by Oxford (1985)*2, and 
Understanding Second Language Acquisition (1985) *3 were mainly read. 
Topics were: 
1) Introduction (1 hour) 
2) Language Learning Strategies (4 hours) 
3) Interlanguage (3 hours) 
4) Language Acquisition Theories (5 hours) 
 
For Keio 2 and TPU 
Textbooks 
Emotional Intelligence by Goldman (1994)*4, People Watching by Morris (1977)*5, and Human 
Motivation by Franken (1982) *6 were mainly read.  
Topics were: 
1) Introduction (1 hour) 
2) Past and Current Issues in Motivation (4 hours) 
3) Emotion and Human Behavior (4 hours) 
4) Components of Human Motivation (4 hours) 
 
     Followings are the instruction about the self-training method of presentation that were explained by 
the instructor for both groups of the students: 
 
Monologue Method of Speech Training 
  
     Prepare topics in a specific field. Speak to a microphone. When you find words you don’t know,      
     look them up in the dictionary. You don’t have to stop the recording during the whole process. You  
     can go back and start from the beginning. You can stop and think as long as you want. After school,  
     you can summarize the points of lectures and explain them in English. You can also summarize the  
     sections of a book as you proceed to the next section. In that case, you can use vocabulary in the  
     book and it makes the training more efficient. You can do it without recording equipment, but it may  
36
Speech Training Introduced in Required English Classes 
 
     make your training more meaningful and you can recognize your development after a few months.  
     Try in three minutes fast and then increase the length of the speech. Just try it and report your trial.     
                                                                         (Tanabe, 2005) 
 
     The major difference of the class schedule among the classes was that in Keio 1, each student had the 
chance of presenting their summary of each class about three to five minutes at the end of the class every 
week. The other two classes did not have the opportunity to present in public. 
 
Results and Discussion 
The following are the questionnaire items: 
Evaluated on five-point scales having 10 “very positive” to 1 “very negative.”  
The reasons are given for each evaluation. 
Table 1. Average for each questionnaire item 
Average 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 
KEIO 1 1.7  8.8 1.0 2.5 8.0 4.6 8.3 8.7 7.3 8.3 8.6 8.4 N/A N/A N/A 9.0 
KEIO 2 3.5  8.3 1.0 1.5 7.8 5.7 6.6 9.0 8.7 9.5 9.3 9.8 9.6 8.8 8.2 9.1 
TPU 2.7  6.1 1.4 4.2 6.9 5.5 6.7 8.5 6.3 8.1 8.1 8.4 8.4 9.1 6.8 7.4 
N (total)  35 35 38 40 31 31 42 36 28 28 28 28 24 29 23 31 
 
     In the question from 9 to 16, the procedure of the classes was evaluated. These questions were given 
in order to eliminate the other factors that would affect the questions that asked the major interest of this 
paper the introduction of speech training in required English classes: Q9) Were the materials in the first 
semester presented in the appropriate level for you?, Q10) Did the class move forward too fast or too slow?, 
Q11) Was the quantity of the contents presented appropriate for the class purpose?, Q12) Was the quality of 
the presentation by the lecturer good enough?, Q13) Was the frequency of the use of audio-visual materials 
appropriate for the class purpose?, Q14) Were the contents of the audio-visual materials appropriate for the 
class purpose?, Q15) Was the use of subtitles appropriate for understanding the videos?, Q16) Was the style 
of the class appropriate for the class objectives?  
     The answers from the three groups to the question above show their satisfaction with the class 
procedure and this might not affect the evaluation of the speech training method in question at least 
negatively. 
 
The Questionnaire items and the replies from the students 
    The ratio of each answer was shown in the square brackets: 
1. Did you do the speech training taught in the beginning of the lecture at home? 
Positive (Evaluated as from 7 to10 point) [0, 0%] 
Neutral (4-6) [9, 25.7%] 
Negative (1-3) [25, 71.4%] 
     As are shown above, there is no student who evaluated he or she regularly did the speech training as 
taught in the class. In Keio1, where the subjects regularly had the opportunity of presenting among their 
classmates they evaluated as 1.7 on an average, which is lower than those of the other two classes of 3.5 of 
Keio 2 and 2.7 of TPU. This is contradictory to the general assumption.   
37 
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 32 No.2 (2009) 
 
2. Was the speech training effective for the reading class? 
Positive (7 -10) [22, 62.9%] 
Neutral (4-6)[10, 28.6%] 
Negative (1-3)[3, 8.6%] 
     In Keio 1, where the subjects had the regular opportunity of the presentation, all of them answered 
positively about this question. In the other classes, where they rarely had the opportunity gave fairly high 
points to this question. The negative reasons induced from their comments are they had less general 
motivation for the class or for the learning if English because no one who evaluated this item below three 
gave any comment. 
 
3. Have you ever experienced the speech training method that recommended you to summarize the 
learning contents at the last part of the class? 
     Small number of the students had the experience of that kind of speech training. One student in 
Keio1 answered he or she had a conversation class but was not taught that way of speech training. 
 
4. Do you do something for your speech training? 
     More number of students in TPU answered they did speech training of some kind. Several students 
listened to and sang English songs. One student went to a conversation school and asked questions when he 
or she could not understand the lecturer. Another student watched movies in English. The other student 
talked with an Indian friend.  
 
5. Was the speech training asked in the question 3 effective for you? 
     The average points to this question were high. TPU showed a little lower point, though. The 
examples of the comments from Keio 1 and 2 were: “Good for reviewing contents,”“I can speak because I 
did this training,” “I found what to learn to become able to speak in English,” “I became able to speak 
English after these three months,”“Sometimes I couldn’t use basic words but I could remember those 
words by checking them in the dictionary,”“This training motivated me. This is good for reviewing 
contents and vocabulary.” The comments of the TPU students were: “I think it is effective, but I sometimes 
can’t understand the lecture given in English.”, Summarizing the contents at the end of the class is very 
good for learning,” “I don’t need grammar tests any more, so speech training is a good idea,”“This is very 
effective, but I often have problem of vocabulary.” 
    From these comments, many of the students understood the superiority of the speech training method, 
but some students of TPU thought they needed some more vocabulary to take this method.  
 
6. Did the speech training asked in the question 3 motivate you for the English learning? 
     The average points of the three groups showed the speech training method did not affect the other 
area of motivation for the English learning. The comments from the students of Keio 1 and 2 were: “I was 
too nervous speaking in public,” “I was motivated at the spot but I could not continue to be 
motivated,”“The method needed a lot of mental and physical endeavor,”“I would like to try the method and 
see what happens,” “I became able to read faster and felt enjoyment in learning,”“I basically have an 
inferiority complex in speaking in English,”“I don’t like speaking in public,”“I was motivated to train 
speaking in English for myself.” They evaluated lower in points but they appreciated the method in their 
comments. They tended to be strict about evaluating their progress and that attitude seemed to be reflected 
38
Speech Training Introduced in Required English Classes 
 
in the score of the average points. The comments of TPU had the same tendency: “I made a progress in this 
class, but I need much more effort.” 
 
7. Do you agree to the idea of learning reading taught in English in a reading class? 
     Teaching reading in English is to provide readiness of grammar and vocabulary to ease the speech 
training. The expressions and vocabulary used in the lecture also are the target items of the class. The 
problem in the use of English is that students should agree to the idea and tolerate the ambiguity of certain 
contents explained in English. The lower evaluation by the students showed that teaching reading in 
English requires certain conditions to meet. The comments by the students would suggest this. Followings 
are the comments of the Keio group: “I know it effective but learning in English causes uneasiness,” “I 
don’t have good opportunity to study contents in English, so I think it’s effective,” “I need listening 
ability,” “I need some Japanese,”“I want to be able to read than speak,”“It seems to hard for me,”“I think it 
will be effective but I am not sure I can keep up with the lecture,” “I process English language according to 
the grammar and I cannot follow the contents given in spoken English.” Followings are those of TPU: “I 
need both English and Japanese explanation in the lecture,” “I cannot understand the contents clearly in 
English,” “I don’t understand the lecture contents fully,” “I don’t understand English,” “Using AV materials 
help me to understand the contents,”,“I don’t have enough vocabulary.” While TPU students scored lower, 
many of the other comments not here were positive about learning reading in English.  
 
8. Do you agree to the idea of learning reading English in a special field of study? 
     This topic is thought to be closely related to the basic motivation for the learning in the class. The 
students of Keio 1 and 2 chose the theme or the content of the class according to the syllabi. In the case of 
the students of TPU, they had no choice than to take the class. The point of discussion here would be the 
evaluation of this questionnaire item by TPU and the result was that there was no big difference among the 
groups. The typical examples of the comments of Keio are: “I fully agree because I want to learn in the 
special field,” “I cannot choose good reading materials by myself,” “I want to study in a special field as a 
university student,” “A little difficult, but it provides us a good opportunity to think about the subject,” “It 
is just interesting,”“I can learn both English and contents,” “I cannot study in the special field by myself, 
but in the class I can study effectively,” “This is a good preparation to study in a specific field.” Almost the 
same sorts of reactions were elicited by TPU: “The materials were very interesting,” “Technical terms are 
hard to memorize,” “It is a lot better than learning stupid samples of conversation,” “I can learn both 
English and contents,” “It depends on the contents,” “It is motivating,” “Setting a theme is a good way to 
learn about,” “Studying English in a special field is effective in learning English,” “The level of English 
was too high, but I was passionately interested in the contents.” These comments eradicated the uneasiness 
for the teachers of English in dealing with a theme in a specific field of study for a required English class 
where general topics have been chosen for English teaching. 
 
16. Was the style of the class appropriate for the class objectives? 
     The basic style of the class of reading comprehension, discussion, lecture in English and AV 
materials for Keio 2, and TPU was generally accepted by the students. The questionnaire item 16 had 
choices for the improvement of the class. 
1) More opportunity of discussion is necessary. 
2) More lecturer’s comments are welcome. 
39 
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 32 No.2 (2009) 
 
3) More use of AV materials is welcome. 
4) Lecturer’s explanation of English structure and contents is necessary. 
5) Quizzes should be given. 
6) More writing assignments are necessary.  
7) More time for listening practice is necessary. 
8) More opportunity of discussion in English is necessary. 
9) Basic grammar of English, etc. 
 
Table 2. Idea about improvement of the class 
 1 2 3 4 5 6 7 8 9 
Keio 1 1 0 2 0 0 0 0 2 0 
Keio 2 3 0 2 1 0 1 1 0 0 
TPU 2 1 12 6 0 1 1 1 2 
 
     The results showed the use of AV materials and discussion is welcomed by the students. The students 
of TPU majored in the imaging art and this might have affected the basic favor of the use of AV materials. 
That small number of the requests from the students means the class management in general is accepted by 
the students. 
 
Conclusion 
     The effects of the introduction of a speech training method on the motivational change of university 
students and their apprehension of the effects of the course are examined. The results showed the use of 
materials in a special field of study iss accepted by the students and the speech training that is based upon 
the contents are accepted as effective though the habituation of the method required some more thoughtful 
devisal of the whole procedure of the introduction. 
 
References  
[1]  Brinton, Donna, M., Snow, Marguerite, Ann, and Wesche, Marjorie ( 2003) Content-Based Second 
Language Instruction. The University of Michigan Press.  
 
[2]  Nation I.S.P and Newton, Jonathan. (2009) Teaching ESL/EFL Listening and Speaking. Routledge. 
 
[3]  Richards,C.,Jack, and Rodgers, S., Theodore (1986) Approaches and Methods in Language Teaching: 
a description and analysis. Cambridge University Press. 
 
[4]  Tanabe, Hiroshi. (2004) “Student Understanding of the Philosophy of Content Based Approach in a 
General English Course”. The Academic Reports of Engineering Tokyo Polytechnic University 
Vol.27.No.2 pp. 1-17 
 
[5]  Tanabe, Hiroshi (2005) “Effects of Teaching Styles on Motivation for Self-Training by Students in 
    Teaching of Presentation in L2”. The Academic Reports of Engineering Tokyo Polytechnic University 
Vol.28.No.2 pp. 1-7 
40
Speech Training Introduced in Required English Classes 
 
[6]  Tanabe, Hiroshi (2008) “Reactions of Students to the Use of Content-Based Approach in a Regular 
Course of English as a General Education Subject”. The Academic Reports of Engineering Tokyo 
Polytechnic University Vol.31.No.2 pp. 9-19 
 
Notes 
*1 Stephen. Krashen., and T. Terrell. (1983) The Natural Approach. Prentice Hall. 
*2 Rebecca. L. Oxford. (1990) The Language Learning Strategies: what every teacher should know. 
Longman. 
*3 Rod.Ellis. (1985) Understanding Second Language Acquisition. Oxford University Press. 
*4 Daniel. Goldman. (1994) Emotional Intelligence. Bantam. 
*5 Desmond. Morris. (1977) People Watching. Random House. 
*6 Robert. E. Franken. (1982) Human Motivation. Brooks/Cole Publishing Company. This book is written 
according to the idea of componential approach to human motivation. The theory explains human activity 
is explicable in terms of three aspects such as "biological", "cognitive", and "learned" factors. This book 
mediates fields such as psychology, neurology, behaviorism, etc., which separately deals with the human 
motivation. (Tanabe, 2004) 
 
41 


Speech Training Introduced in Required English Classes

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