并得到了上述方程可積極小正解的存在性、逼近性、穩定性.用英語怎么說？

并得到了上述方程可積極小正解的存在性、逼近性、穩定性.

Existence, approximation and stability of integrable minimum positive solutions for the above equation are gained.

existence

n. 存在，實在，生活，生活方式，實體，存在物；

例句
...this theological conundrum of the existence of evil and suffering in a world created by a good God.
在善良的上帝創造的世界里存在著邪惡和苦難這一神學之謎

approximation

n. 接近，<數>近似值，近似額，粗略估計；

例句
That is a fair approximation of the way in which the next boss is being chosen.
那和下一任老板的選任方式相當類似。

and

conj. 和，與，而且，于是，然后，因此；

例句
I spend a lot on expensive jewelry and clothing...
我花很多錢購買昂貴的首飾和衣服。

stability

n. 穩定（性），穩固，堅定，恒心；

例句
NATO had charted a new course for stability and cooperation in Europe...
北約制訂了保持歐洲穩定與合作的新計劃。

of

prep. 關于，屬于…的，由…制成；aux. 助動詞 [非標準用語、方言] =have [主用于虛擬語氣]；

例句
He did have a real knowledge of the country...
他對該國的確知之甚多。

integrable

adj. 可積（分）的；

例句
This paper investigates the integrable inhomogeneous generalized Heisenberg ferromagnet model by using the prolongation structure theory.
摘要利用延拓結構研究了可積的非均勻推廣的海森堡鐵磁鏈方程.

minimum

n. 最低限度，最小量，最低消費，[數]極小

例句
About 12 inches wide is the absolute minimum you should consider...
12英寸左右的寬度絕對是你應考慮的最低值。

positive

adj. 積極的，確實的，肯定的，[數]正的，[醫]陽性的；n. 正面，正片，[語]原級形容詞，[數]正量；

例句
Pupils should be helped to adopt a positive approach to the environment.
應幫助學生對環境采取積極的態度。

solutions

n. (solution的復數形式)解答，解決（辦法），解釋，[數]解法，解式，解決( solution的名詞復數 )，溶解，溶液，答案；

例句
Published in association with the Council for the Protection of Rural England, the book provides refreshing solutions to the long-term problem of water conservation.
這本書與英格蘭鄉村保護委員會合作出版，就節約水資源這個長期問題提供了全新的解決方法。

for

prep. 為，為了，傾向于，關于，當作；conj. 因為，由于；

例句
I've come looking for a bit of advice.
我特來討教。

the

art. 指已提到的人（物），指說話人與聽者已知的人（物），用于獨一無二的事物前，與形容詞最高級和序數詞連用；

例句
He did have a real knowledge of the country...
他對該國的確知之甚多。

above

prep. 在…上面，超過，大于，不至于；adv. 在上面，超過，更大，上文；adj. 上述的；

例句
He lifted his hands above his head...
他將雙手舉過頭頂。

equation

n. 方程式，等式，相等，[化學] 反應式；

例句
The equation is simple: research breeds new products...
情況很簡單：研究產生新產品。

are

vi. （用于第二人稱單復數現在時，第一、三人稱復數現在時）是；n. 公畝（等于100平方米）；

例句
We are scared to abandon ourselves to our feelings in case we seem weak or out of control.
我們不敢放縱自己的情感，以免顯得太過軟弱或缺乏自制。

gained

v. 獲得( gain的過去式和過去分詞 )，贏得，增加，（鐘、表）走快；

例句
Fans gained more enjoyment barracking him than cheering on the team...
球迷一個勁兒地噓他，興頭遠勝于為球隊加油。

...the spiralling vortex airflow that slows the plane.
使飛機減速的螺旋形氣流渦旋

You just go on ahead. I'll come by later...
你只管先往前走。我隨后就來。

He who spares his rod hates his son, But he who loves him chastens him early.
24不忍用杖打兒子的,是恨惡他;疼愛兒子的, 趁早管教.

For further information, please contact 414 3925, extension 2253.
詳情請致電414 3925,轉分機2253。

He sat there while I made the case for his dismissal...
他坐在那兒，聽我陳述解雇他的理由。

Baroness Thatcher's claims seem credible to many.
撒切爾女男爵的主張在很多人看來是可信的。

Nothing to be got without pains but poverty.
一份耕耘，一份收獲。

This decree obliges unions to delay strikes.
該法令迫使工會推遲罷工。

The right to demand payment from the endorser of a commercial paper when the first party liable fails to pay.
追索權當有支付義務的第一方不能支付時，可以向商業票據的背書人要求支付的權力。

A scab formed on his leg.
他腿上結了個痂.

The introduction attempts to yoke the pieces together.
導言部分試圖將各部分硬拼湊在一起。

...squirrels who bury nuts and seeds.
掩埋堅果和種子的松鼠

...the Cadet Corps.
學員軍訓隊

to suffer from claustrophobia
患幽閉恐怖癥

All Corfield got for his pains was a bullet in the head...
科菲爾德千辛萬苦，到頭來卻被一槍爆頭。

The table is simply a chipboard circle on a base.
這張桌子只不過是在底座上安了一塊圓形刨花板。

Eye for eye and tooth for tooth.
以眼還眼,以牙還牙。

...a series of political scandals that has tainted the political stars of a generation.
令一整代政治明星聲名染上污點的一系列政治丑聞

并得到了上述方程可積極小正解的存在性 、 逼近性、穩定性.用英語怎么說？

并得到了上述方程可積極小正解的存在性、逼近性、穩定性.用英語怎么說？