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  solutions
     In this paper we proved that the equation gcd(a_1,a_2,…,a_n)+1cm(a_1,a_2,…,a_n)=a_1a_2…a_n,has positive integer solutions (a_1,a_2…a_n) if and only if n=2 and it has only the solution (a_1,a_2)=(2,2).
     证明了:方程 gcd(a_1,a_2,…,a_n)+1cm(a_1,a_2,…,a_n)=a_1a_2…a_n 仅当 n=2时有正整数解(a_1,a_2)=(2,2).
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     Theorem 2:the Diophantine equation s~4-8s~3t+6s~2t~2+8st~3+t~4=1 have only integer solutions (s,t)=(±1,0)and(0,±1)?
     丢番图方程s4-8s3 t+6s2 t2 +8st3 +t4=1仅有整数解 (s ,t) =(± 1,0 )和 ( 0 ,± 1)。
短句来源
     The Solutions of Diophantine Congruence Equation x~(2n) + (x + 1)~(2n)+…+ (x+h)~(2n)≡ (x+h + 1)~(2n) (mod17) (I)
     不定同余方程x~(2n)+(x+1)~(2n)+…+(x+h)~(2n)≡(x+h+1)~(2n)(mod17)的解(Ⅰ)
短句来源
     The Solutions of Diophantine Congruence Equation x~(2n)+(x+1)~(2n)+ + (x+h)~(2n) = (x+h+1)~(2n)(mod 11) (I)
     不定同余方程x~(2n)+(x+1)~(2n)+…+(x+h)~(2n)≡(x+h+1)~(2n)(mod11)的解(Ⅰ)
短句来源
     The Solutions of Diophantine Congruence Equation x~(2n)+(x+1)~(2n)+ +(x+h)~(2n)=(x+h+1)~(2n)(mod 11) (II)
     不定同余方程x~(2n)+(x+1)~(2n)+…+(x+h)~(2n)≡(x+h+1)~(2n)(mod11)的解(Ⅱ)
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  “解(”译为未确定词的双语例句
     and (x,y,p) =(3,2,1),(3,-3,1) with D=2p,p≡2,3,5 (mod 9);
     在D =2p ,p≡ 2 ,3,5 (mod 9)时仅有解 (x ,y ,p) =(2 ,1,3) ,(- 3,1,3) ;
短句来源
     and (p,x,y)= (3,3,1),(3,-4,1),(5,4,1),(5,-5,1),(5,6 859,133),(5,-6 860,133) with D=4p,p=5 or p≡2,3 (mod 9).
     在D =4p ,p=5或p≡ 2 ,3(mod 9)时仅有解 (p ,x ,y) =(3 ,3,1) ,(3,- 4,1) ,(5 ,4,1) ,(5 ,- 5 ,1) ,(5 ,6 85 9,133) ,(5 ,- 6 86 0 ,133)。
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     (x~3-8)=35y~2 has only integer solution(x,y)=(2,0).
     x3-8=35y2仅有整数解(x,y)=(2,0).
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     2π-Periodic Solution of the Equation ü+bu r+g(u(t-τ))=p(t)
     方程ü+bu~r+g(u(t-τ))=p(t)的2π-周期解(英文)
短句来源
     Let a, b be positive integers such that a>b, gcd (a, b) - 1 and 2|ab, then it can be proved that if 2||ab, the equation (a2 - b2)x + (2ab)y = (a2 + b2)z has only the positive integer solution (x, y, z) = (2, 2, 2) with x=y=z=0(mod2).
     设a,b是适合a>b,gcd(a,b)=1,2|ab的正整数,证明了当2||ab时,方程(a2-b2)x+ (2ab)y=(a2+b2)z仅有正整数解(x,y,z)=(2,2,2)可使x,y,z均为偶数。
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  相似匹配句对
     How dowe decide the solution of the equation?
     怎样定?
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     The Solution of Inversion Eqation
     逆序方程的
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     b) The solution of the inequality.
     (2)不等式;
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     STABILITY OF THE SOLUTION OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION
     关于NFDE(D,f)的稳定性
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  solutions
The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type.
      
On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al.
      
A simple parametrization is given for the set of positive measures with finite support on the circle group T that are solutions of the truncated trigonometric moment problem:
      
In this case there could be infinitely many functions that are "weak" but not classical solutions.
      
We study the existence and regularity of compactly supported solutions φ = (φv)v=0/r-1 of vector refinement equations.
      
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1. The conformity of the pattern of Cicindela anchoralis to what has been considered typical of the genus becomes in- telligible if the middle band, which is undoubtedly the most variable of the markings of this species, is assumed to have shifted forward and to have developed extensions both cephaled and caudad along the lateral margin and on the disc of the eIytron.2. The variation of the pattern is of the continuous type and proceeds in one principal direction. As expected, some in- dividuals depart from...

1. The conformity of the pattern of Cicindela anchoralis to what has been considered typical of the genus becomes in- telligible if the middle band, which is undoubtedly the most variable of the markings of this species, is assumed to have shifted forward and to have developed extensions both cephaled and caudad along the lateral margin and on the disc of the eIytron.2. The variation of the pattern is of the continuous type and proceeds in one principal direction. As expected, some in- dividuals depart from this main series, in one way or another and ten such sub-types have been recognized in this study. The range of variation is very considerable.3. The male sex is found to have a greater tendency to lose its pigmentation, and this fact is interpreted as indicating its having a more variable middle band.4. Mating between the different types is entirely at random, the frequency of any given combination is apparently a function of the abundance of the individuals in a given class.5. In describing the elytral pattern of this species, Chevrolat (1845) used these words: "vitta anchorali, cum lienola pone humerum (femina amplioribus); cupreis". He evidently had regarded as typical the pattern showing fullest pigmentation. The present study shows, on the other hand, that such a pat- tern, while most primitive, is not the most representative. The typical pattern is to be sought in Class Ⅳ, the model class. This last remark certainly has wider application and merits the consideration of taxonomists describing highly variable forms.

斑蝥科甲虫翅鞘色型之差異,在一部份種類中,極为顯著。本篇所論,根據中國种錨紋斑蝥,於廿二年夏採於厦門北岸,計雌雄共九百餘個,內有交配者六十二對,所得結論如下: (一)本種色型,甚为異特。若以美人薛福特氏所立之本屬理想模式色型推,則其中間淡色横斑,較为移前,其左右則向上下分枝成H形。 (二)此種色型之變異為連續式仝趨一主要方向,但依其變異之分岐,可别为十種副式色型,詳情已於西文中加以討論。 (三)雄虫翅鞘之中間淡色横斑變異較大,其深色紋斑之傾向於縮小亦因之較雌性为甚。 (四)兩性交配,与色型之差異,全無關係。 (五)大部份個數皆呈現中間色型。其趨向於兩極端者(深色或淡色特别發達者)乃屬少数。因此分類學者於記述变異極大之種類時,應发中間色型者為代表。

The differential equation for relaxation oscillation with external impressed e.m.f. is written as

张弛振动之代表算式为一非直线的二次微分方程式在数学上至今未获完全答颇耳氏(Van der Pol)曾以半算半作图之方法研究强弛振动,但共方法仅能用於无外加控制电压之情形下故控制影响未能说本文叙述用罗勃氏(A.A.Bobb)作图方法析张弛振动之问题,自由振动与控制振动均可应用文中叙明通常之起始条件如何不适宜於作图及如何试设一边界条件而得正确之结果用此方法张弛振动之普通特性与频率减倍之现象,均能说控制波与强弛振动波之相的关系,亦曾加以讨论所设对称的三次抛物线形之振动特性,未能完满释偶谐控制波之控制功效

The evaluation of exchange integrals which occur in the quantum theory of molecules is reduced to the solution of Poisson's equation.

用量子力学释分子构造时产生一种对换积分。此文将求此种积分之问题变为Poisson偏微分方程式之问题。

 
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