論文英語のマニュアル

数理工学者杉原厚吉によれば英作文に強くなるためには 文章と文章をつなぐ道標を上手に配置することが大切であるという。 彼は、コンピュータに文章を理解させる仕事をしている。

杉原厚吉著 理科系のための英文作法文章をなめらかにつなぐ４つの法則 中公新書 1216

（１）帰結をあらわす道標

[接続詞] and,so that

[副詞・副詞句] hence,therefore,thereby,thus,consequently,accordingly,naturally,necessarily in consequence,in consequence of this,for this reason,as a matter of course as a {natural,direct,-}{result,consequence}{of this,-}

[節] This {direcly,naturally,implicitly,-}{demands,implies,indicates,leads us to conclusion} that [A]. From this,we {-,can}{conclude,see} that [A]. From this, it follows that [A]. It follows from this that [A]. This is the reason why [A]. This assures us that [A]. The result of this is that [A].

[文] This implies the following. From this, we {-,can} {get,obtain} the following conclusion. From this, we {-,can} {conclude} {as follows,in the following way}.

(2)理由を表わす道標

[接続詞] for,because,since,as,now that
ex.Now that we know this property, we can explain the next phenomenon.

[副詞・副詞句] indeed,in fact,for the reason that,seeing that,on the ground that, considering that

[節] This {-,mainly,partly} because [A]. On reason for this is [A].

[文] The reason is {the following,as follows}. This can be understood in the following {way,manner,fashion} This can be understood {because of,from} the {followin,next} reason.

(3)逆接または対照を表わす道標

[接続詞] but,through,although,while,whereas

[副詞・副詞句] however,nevertheless,yet,notwithstanding,inspite of this,despite this in despite of this,conversely,on the contrary,contrary to this, in contrast to this,to the contrary,on the other hand,unlike this, at a cost of this

(4)焦点を絞ることを表わす道標

[副詞・副詞句] in particular,particularly,especially,in fact,as a matter of fact

[節] As far as ....is concerned,..... {Note,Keep in mind,Bear in mind} that [A]. It should be {noted,empahsized,kept in mind} that [A]. Here we are interested in [A]. {What is important,An important point,Acrucial point,What we should note, What we want to empahasize,One nice thing} is that [A]. All we {have,need} to do is that [A]. [文] In the above {discussion,observation,consideration}, there is one {important point,point we should note,point we should empahasize}.

(5)情報の追加を表わす道標

[副詞・副詞句] also,moreover,further,furthermore,in addition,besides,besides this,too, in adition to this,at the same time,simultaneously,as well,as well as this together with this

[節] Before concluding this section, wwe should note that [A].

(6)仮定・条件を表わす道標

[接続詞] if,provided that,in case,,in case that,unless,so long as,as far as

[副詞・副詞句] supposing that,on the condition that,oherwise

[節] {Assume,Suppose} that [A]. {Let us,We will} {assume,suppose} that [A].

(7)動機を表わす道標

[副詞・副詞句] To this {end,goal}, [A]. For this purpose, [A]. To solve this problem, [A]. {In order,-} to {accomplish,attain} our purpose, [A].

(8)類似を表わす道標

[副詞・副詞句] similarly,likewise,also,in a similar {way,manner,fashion}, in the same {way,manner,fashion} {as this,-}

(9)例を表わす道標

[副詞・副詞句] for example,for instance,to name a few,say ex.Let us start with a few poin, say three points.

[節] One typical example of this is that [A].

[文] Let us consider {an example,some examples} {of this,-}.

(10)言い換え・要約を表わす道標

[副詞・副詞句] in other words,that is,that is to say,say,thus,in summary,in conclusion, to sum up,namely,in this {way,manner,fashion} ex.Suppose that there is as vertex, say v, on this plane.

[節] This can be restated that [A]. The conclusion of this is that [A]. We{can,-} {conclude,empahasize,restate} that [A].

[文] We can summarize our observation {in the following way,as follows}. From this, we can obtain the following {conclusion,-}.

(11)話題の転換を表わす道標

[副詞・副詞句] by the way,now,next,on the other hand,in any event,any way,in this connection in this relation

[文] Let us return to our original problem. Now we are ready to consider our main problem. {Keeping this in mind, With this in mind,On the basis of these observation}, we will next consider.....

(12)古い情報の確認を表わす道標

[副詞・副詞句] hitherto,up to this time,until now

[節] {Recall,Remember,Let us recall} that [A]. As we {saw,have seen,showed,have shown,{-,have}{observed,pointed out}},[A].

(13)先を指すための道標

[副詞・副詞句] in what follows,hereafter,thereafter,in the sequel,from now on,henceforce, in the following,in this and all subsequent sections,in the {next,following} {way,manner,fashion}

[節] [A], {as follows,as will be shown latter}.

(14)共通の座標軸に対する位置を表わす道標

[副詞・副詞句] fortunately,unfortunately,usually,in general,obviously,of course,certainly trivially,evidently,from this point of view,without loss of generality, without losing generality

[節] {As is well known,As we all know}, [A].

(15)列挙を表わす道標

one....the other..... one.... another..... still another first.....next......next.......finally first......second.....third.......last....... firstly.....secondly.........thirdly.....{finally,lastly}....

数学者の野水克己氏による英語の書き方も参考になる

数学のための英語案内,サイエンス社

(keys words) phrases; sentences

(because of) on account of;due to;in view of

(by Lemma 2) from Lemma 2;by virtue of Lemma 2;by means of (2); with the aid of Lemma 2

(Cauchy's inequality) the Cauchy inequality;Einstein's field equations the Yamabe conjecture

(clearly) obviously;evidently;naturally;easily

(definition) A basis of a vector space is a linearly independent subset which spans the space.

(definition) The rank of a matrix is defined as the dimension of the columnspace.

(definition) This group is known as the symplectic group.

(definition) The vector space V is said to be the direct sum of its subspaces W1,...,Wk if...

(definition) A graph, as we define it, is a 1-dimensional CW complex.

(definition) By the rotation group is meant the group of all orthogonal matrices of determinant 1.

(definition) We call G the Galois group of the extension K of k.

(definition) For a and b,define the continuous function H(a,b) by H(a,b)(x)=(ab)x.

(definition) We define the group G to be the Galois group of the extension K of k.

(definition) A mapping g is called a homeomorphism if it is continuous together with its inverse.

(definition) We say that a Lie group is solvable if its Lie algebra is solvable.

(ending the proof) We have thus proved the theorem(Theorem 1).

(ending the proof) We have completed the proof of Theorem 1.

(ending the proof) This cpompletes the proof of Theorem 1.

(ending the proof) ..., thereby completing the Theorem 1.

(get) obtain;have;conclude;deduce;arrive at; we are led to

(immediately) It follows immediately that ...;immediately from

(in addition) further;furthermore;moreover;besides

(in the same way) in the same fashion;in exactly the same way

(list) enumerate;record;classify

(mapping defined) the mapping defined above; the classification listed below; the space so obtained

(prove) show;establish;verify;demonstrate;check

(show) illustrate;exhibit;demonstrate;explain

(similarly) in a similar fashion;likewise;in like manner analogously

(since) because;for

(starting a proof) Let us prove Theorem 1.

(starting a proof) We use induction on n.The claim is trivial for n=1;assume it is true for n=k-1.

(starting a proof) The proof is by contradiction.Assume the assertion were false. Then we could have ...

(state) assert;claim;indicate;remark;outline;summarize sum up;review;analyse;explain;describe;discuss

(thanks) For his friendly encouragement,I am sincerely grateful to him.

(thanks) The manuscript was typed by Mrs.A and Miss B,to both of whom I express my thanks.

(thanks) I also thank the Nihon Foundation for supporting my research activities.

(thanks) I should like to express my gratitude to Professor Yosida for his useful advice.

(the fact that) the property that;the condition that

(therefore) so;then;thus;thereby;accordingly(in conformity)

(using) Using Lemma 5 we now prove Theorem 4.Theorem 5 can proved by using Lemma 4. a direct product Consider a direct product V × T,where V is a compact group and T a vector group. a direct sum Any representation of V as a diect sum of invariant subspaces is obtained as follows. a first step As a first step, we consider the following situation. a fortiori All identities which hold in F hold a fortiori in any subset of F, provided it is closed under those operations. a sum of The endomorphism A is a sum of endomorphisms of the form B**p+C**q,where p+q=n. a word of A word of explanation(caution) about the various isomorphisms seems to be in order.