Small solutions of the congruencea1x12 +a2x22 +a3x32 +a4x42 ≡c(modp)

For any integersa ₁,a ₂,a ₃,a ₄ andc witha ₁ a ₂ a ₃ a ₄≢0(modp), this paper shows that there exists a solutionX=(x ₁,x ₂,x ₃,x ₄) ∈Z ⁴ of the congruencea ₁ x ₁ ² +a ₂ x ₂ ² +a ₃ x ₃ ² +a ₄ x ₄ ² ≡c(modp) such that

Ueber das volle Formensystem der tern?ren biquadratischen Formf=x13x2+x23x3+x33x1

Ohne ZusammenfassungHieizu cme Tale     

环F2+uF2+vF2上自对偶码的两种构造方法

本文研究环R=F2+uF2+vF2上的自对偶码问题.利用Rn到F3n2的Gray映射及R上的自对偶码C的Gray像为F2上自对偶码,获得了R上任何偶长度的自对偶码存在性的结论.最后,给出了R上两种构造自对偶码的方法.     

关于m-HPK(n1,n2,n3,n4)-残差图

本文研究了3-维超平面完备残差图以及m 重3-维超平面完备残差图. 利用容斥原理以及集合的运算性质等方法, 分别获得了3-维超平面完备残差图和m 重3-维超平面完备残差图的最下阶以及二者的唯一极图, 将文献[1] 中定义的残差图从平面推广到超平面上.     

2(n1+n2)-(k1+k2)42混合水平裂区设计包含纯净效应的条件

混水平部分因析裂区设计在各类试验中有广泛应用. 在三因子及更高阶交互作用可以忽略这一很弱的假设下, 试验者可以得到纯净主效应或者纯净两因子交互作用成分的无偏估计. 本文给出了含有两个四水平因子和若干二水平因子的混水平裂区设计包含各类纯净主效应或者纯净两因子交互作用成分的条件以及构造相应设计的方法.     

NH3+自由基离子的电子自旋共振

本文研究了俘获于掺杂VO⁺⁺离子的(NH₄)₂Zn(SO₄)₂·6H₂O单晶中NH₃⁺自由基离子的ESR.从实验上分别测出π电子自由基NH₃⁺的¹⁴N和¹⁵N核超精细分裂.结果表明,氮核超精细偶合张量具有近似于圆柱形对称。对于¹⁵N来说,A₁₁=44.8,A₂₂=19.3,A₃₃=17.8高斯.对于¹⁴N来说,A₁₁=31.1,A₂₂=12.5,A₃₃=11.8高斯.在室温下,NH₃⁺自由基绕A₁₁方向作圆锥体运动.文中最后讨论了NH₃⁺自由基离子的可能生成机理。     

Embedding into l ∞2 Is Easy, Embedding into l ∞3 Is?NP-Complete

We give a new algorithm for enumerating all possible embeddings of a metric space (i.e., the distances between every pair within a set of n points) into ℝ² Cartesian space preserving their l _∞ (or l ₁) metric distances. Its expected time is (i.e., within a poly-log of the size of the input) beating the previous algorithm. In contrast, we prove that detecting l _∞³ embeddings is NP-complete. The problem is also NP-complete within l ₁² or l _∞² with the added constraint that the locations of two of the points are given or alternatively that the two dimensions are curved into a three-dimensional sphere. We also refute a compaction theorem by giving a metric space that cannot be embedded in l _∞³; however, it can be embedded if any single point is removed. This research is partially supported by NSERC grants. I would like to thank Steven Watson for his extensive help on this paper.     

矩阵方程A1Z+ZB1=C1的广义自反最佳逼近解的迭代算法

本文研究了Sylvester复矩阵方程A_1Z+ZB_1=c_1的广义自反最佳逼近解.利用复合最速下降法,提出了一种的迭代算法.不论矩阵方程A_1Z+ZB_1=C_1是否相容,对于任给初始广义自反矩阵Z_0,该算法都可以计算出其广义自反的最佳逼近解.最后,通过两个数值例子,验证了该算法的可行性.     

d8(C3v*)EPR理论与CsMgCl3:Ni2+的光、磁性质研究

本文给出了O_h点群表象中的d^2,8(C_3v^*)完全强场矩阵,并借助于这种矩阵的特征值和特征矢量,建立了CsMgX₃:Ni²⁺(X=Cl,B,I)类晶体的全组态混合EPR理论。应用这一理论,对CsMgCl₃晶体中的Ni²⁺杂质离子的光学吸收谱、基态零场分裂参量D、顺磁g因数、基态Zeeman分裂以及EPR条件(B,hv₀)进行了统一的计算。结果与观测非常一致,从而首次对CsMgCl₃:Ni²⁺的光、磁性质作出了统一的理论解释。     

关于L2(En+1+,(dxdy)/(yn+1)中的柱面函数空间的正交直和分解

本文利用小波变换给出了L²(E_n+1⁺,(dxdy)/(yⁿ⁺¹)中的柱面函数空间的一种正交直和分解.在这种分解下定义了Toeplitz-Hankel型算子,得到了类似的Schatten-Von Neumann性质.     

探究x0x+y0y=r2与x0x+y0y=x02+y02的几何意义

问题背景苏教版教材必修二P105有这样一道习题:已知圆C的方程是x2+y2=r2,求经过圆C上一点M(x0,y0)的切线的方程.同学们在处理该问题时给出以下的解答过程:如图1,设切线的斜率为k,半径OM的斜率为k1,因为圆的切线垂直于过切点的半径,于是k=     

Nonexistence of [n, 5, d]q Codes Attaining the Griesmer Bound for q4 ?2q2 ?2q+1 ≤ d≤ q4?2q2 ?q

We prove that there does not exist a [q⁴+q³−q²−3q−1, 5, q⁴−2q²−2q+1]_q code over the finite field for q≥ 5. Using this, we prove that there does not exist a [g_q(5, d), 5, d]_q code with q⁴ −2q² −2q +1 ≤ d ≤ q⁴ −2q² −q for q≥ 5, where g_q(k,d) denotes the Griesmer bound.MSC 2000: 94B65, 94B05, 51E20, 05B25     

与4/p = 1/(n1) + 1/(n2) + 1/(n3) 相关的素变量均值估计

如果n是正整数,我们用f（n）表示丢番图方程4/p=1/n_1＋1/n_2＋1/n_3的正整数解（n1,n2,n3）的个数.对于素数p,f（p）可以分解为f1（p）＋f2（p）,这里fi（p）（i=1,2）为分母n1,n2,n3中恰有i个能被p整除的解的个数.本文我们将研究关于均值∑p〈xfi（p）,i=1,2,的估计,其中p表示素数.     

Quasirecognition by prime graph of F4(q) where q?=?2n?>?2

The prime graph of a finite group G is denoted by Γ(G). In this paper as the main result, we show that if G is a finite group such that Γ(G) = Γ(F ₄(q)), where q = 2 ⁿ  > 2, then G has a unique nonabelian composition factor isomorphic to F ₄(q). We also show that if G is a finite group satisfying |G| = |F ₄(q)| and Γ(G) = Γ(F ₄(q)), where q = 2 ⁿ  > 2, then G @ F₄(q){G \cong F_4(q)}. As a consequence of our result we give a new proof for a conjecture of Shi and Bi for F ₄(q) where q = 2 ⁿ  > 2.     

具有常余维数2k+4不动点集的(Z2)k作用

本文通过构造上协边环MO_*的一组生成元决定了J_*,k^2k+4.     

Massless excitations of long strings in AdS4 × ?P3

We consider the AdS₄ × ℂℙ³ IIA superstring sigma model in the background of a “spinning string” classical solution with two charges. In the limit when one of the spins is infinite, there are massless excitations which govern the long-range worldsheet properties of the model. We obtain a sigma model of ℂℙ³ with fermions which describes the dynamics of these massless modes.     

KO?i groups of G3(?n), n odd

We use the work of Karoubi and Mudrinski on the real Grothendieck's groups of certain complex projective bundles to show that the torsion of the KO ^–i groups of G ₃( ⁿ ), n odd, are related to the known torsion of the KO ^–i groups of G₂( ⁿ ).     

R13中混合型曲面保主曲率等距变形

本文研究了Minkowski空间R₁³曲面的等距变形问题.建立了R₁³中曲面的共形、等距等概念.推广了O.Bonnet和S.S.Chern关于欧氏空间的结论.对R₁³出现的新情况——曲面的中曲率梯度类光作了一定探讨,得出的主要结果为:非平坦的、允许保主曲率等距变形的曲面一定不是W-曲面.