Pell方程组x~2-(c~2-1)y~2=y~2-2p_1p_2p_3z~2=1的公解

设p_1,p_2,p_3为不同的奇素数,c1是整数.给出了Pell方程组x~2-(c~2-1)y~2=y~2-2p_1p_2p_3z~2=1的所有非负整数解(x,y,z),从而推广了Keskin (2017)和Cipu(2018)等人的结果.     

On Constacyclic Codes over Z_(p_1p_2…p_t)

Let t ≥ 2 be an integer, and let _(p_1, ···, p_t)be distinct primes. By using algebraic properties, the present paper gives a sufficient and necessary condition for the existence of non-trivial self-orthogonal cyclic codes over the ring Z_(p_1p_2···p_t)and the corresponding explicit enumerating formula. And it proves that there does not exist any self-dual cyclic code over Z_(p_1p_2···p_t).     

关于[m,n,p_1,p_2,…,p_s]指数型群

本文给出了[m,n,p_1,p_2,…,p_s]指数型群的结构,改进了前人的结果.     

数列（p_1／（n＋p_2））~（q_1n＋q_2）单调性

数列（ｐ_１／（ｎ＋ｐ_２））~（ｑ_１ｎ＋ｑ_２）单调性梁长林（华东地质学院）我们可以求出，极限，其中ｐ１，ｐ２，ｑ１，ｑ２为常数，下面讨论ｘｎ的单调性，因为ｘｎ与Ｉｎｘｎ有相同的单调性，所以考虑函数单调性设ｘ充分大，当Ｐ１〔２ｑ２—２ｐ２ｑ１—Ｐ１ｑ?..     

一类(p_1(x),p_2(x))-双调和方程解的存在性及多重性

研究一类(p_1(x),p_2(x))-双调和方程在Navier边界条件下的边值问题:利用山路引理和Fountain定理证明了这类方程解的存在性和多重性.     

方程dy/dx=(q_(00)+q_(10)x+q_(01)y+q_(20)x~2+q_(11)xy+q_(02)y~2)/(p_(00)+p_(10)x+p_(01)y+p_(20)x~2+p_(11)xy+p_(02)y~2)所定义的积分曲线的定性研究(Ⅰ)

<正> §1.引言自从1955年苏联学者和証明实系数方程dy/dx=q_(00)+q_(10)x+q_(01)y+q_(20)x2+q_(11)xy+q_(02)y~2/p_(00)+P_(10)x+P_(01)y+p_(20)x~2+P_(11)xy+p_(02)y~2(1)最多只有三个极限圈以后,关于方程(1)的极限圈的分布問題引起我国数学工作者的极大的注意.首先,秦元勳在[2]中得到了方程(1)以二次曲綫为极限圈的充要条件,并同时研究了滿足这种条件的方程(1)的积分曲綫的全局結构.其后,本文作者之一在[3]中     

关于(p_2/d_1)~(1/2)的简单连分数

设α是正实数,[α_0;α_1,α_2。…]是α的简单连分数;d 是非平方整数,d_1、d_2是适合 d_1d_2=d,1≤d_10,α_i=α_(n-1)(i=1…,α-1).     

Sur l'anneau de cohomologie du schéma de Hilbert de C2

We express the product of the cohomology ring of the Hilbert scheme in terms of the center of the algebra of the symmetric group. We give a conjecture for the case of crepant resolutions of symplectic quotient singularities.     

方程dy/dx=(q_(00)+q_(10)x+q_(01)y+q_(20)x~2+q_(11)xy+q_(02)y~2)/p_(00)+p_(10)x+p_(01)y+p_(20)x~2+p_(11)xy+p_(02)y~2)所定义的积分曲线的定性研究(Ⅱ):极限圈的唯一性

<正> 作为[1]的定理1的特例,我們知道方程dy/dt=x,dx/dt=-y+mxy+ny~2(mn≠0)(1)沒有周期解.此方程有一个指标为+1的初等奇点(0,0)和一个鞍点(0,1/n).(0,0)的稳定性由mn的符号决定,当mn>0时为不稳定,mn<0时为稳定.今后不妨設m<0(否則将x,t改号),n<0(否則将y,t改号),于是由旋轉向量場的理論[2],知道当d<0而絕对值足够小时方程     

向量值Lipschitz鞅空间p_λ~β(X)和p_∧~β(X)

本文研究了Ｂａｎａｃｈ空间值Ｌｉｐｃｈｉｔｚ 鞅空间。与与 之间的相互嵌入关系,以及与小指标Ｈａｒｄｙ 鞅空间,的共轭空间之间的相互嵌入关系,其结果与值空间的凸性和光滑 性有着密切的联系,     

向量值Lipschitz鞅空间p_λ~β(X)和p_∧~β(X)

本文研究了Ｂａｎａｃｈ空间值Ｌｉｐｃｈｉｔｚ 鞅空间。与与 之间的相互嵌入关系,以及与小指标Ｈａｒｄｙ 鞅空间,的共轭空间之间的相互嵌入关系,其结果与值空间的凸性和光滑 性有着密切的联系,     

A propos de la fonction de Artin en dimension N⩾2

In this Note we give a counter-example to a generalization in dimension $N?2$ of a result of Hickel in dimension 1 [Am. J. Math. 115 (1993) 1299–1334] which relates the Artin function of a germ of holomorphic function to the Artin function of its Jacobian ideal. Such links are important in order to prove the linear Artin approximation theorem that has been conjectured fifteen years ago [Spivakovsky, Proceedings of the II SBWAG, Santiago de Compostela 54 (1990) 237–254]. To cite this article: G. Rond, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Distribution asymptotique de l'affinité L2 de densités gaussiennes

After recalling the L² affinity measure between two multidimensionnal Gaussian density functions, we prove its asymptotic normality when parameters of one density are replaced by their maximum likelihood estimators. We extend this result to the vectorial case and we use it to allocate an estimated density to a class of densities as does the discriminant analysis method. As an application, a dating method for archeological data is proposed.     

Un revêtement de l'arbre de GL2 d'un corps local

Let F be a non-archimedean local field with residue class field k. Put G=GL₂(F), =PGL₂(k) and let X denote the Bruhat–Tits tree of G. We construct a one-dimensional simplicial complex , equipped with an action of G × and with a G × -equivariant simplicial projection (for the trivial action of on X). We prove that the cohomology with compact support contains nontrivial representations of G (in particular positive level supercuspidal representations).     

Capacité de la réunion de trois intervalles et fonctions thêta de genre 2

We give a formula for the capacity of an union of three intervals. In the case of two intervals such a formula has been found by N.I. Achieser. The formula proposed here uses genus two theta functions and we recover Achieser's formula when we degenerate an interval or when there is a symmetry.     

方程(dy)/(dx)=(q_(00)+q_(10)x+q(10)y+q_(20)x~2+q_(11)xy+q_(02)y~2)/(p_(00)+p_(10)x+p(10)y+p_(20)x~2+p_(11)xy+p_(02)y~2)所定义的积分曲线的定性研究(Ⅲ):Ⅰ类方程的极限环的个数

<正> 按照文[1]的分类,我们研究其中的I类方程,它是最一般形式可化为dx/dy=-y+dx+lx~2+xy+ny~2=P(x,y),dy/dt=x=Q(x,y).当 d=0时文[1]已证明此方程不存在极限环,这时有限远奇点 O(0,0)为焦点,l+n>0时为稳定,l+n<0时为不稳定,当 n≠0 时还有另一奇点 N(0,1/n),为鞍点.为确定起见,以下均假定 l+n>0(l+n=0 时以原点为中心,由旋转向量场的理论可知加上 dx 项以后不产生极限环故不必讨论,l+n<0 时则将 y,t 改号即可化为 l+n>0的情况).由旋转向量场理论可知 d<0 而|d|甚小时在原点 O 附近产生不稳定极     

Quelques propriétés des solutions de l'équation de Ginzburg-Landau sur un ouvert de ∝2

For a solution u of –u=u(1–|u|²) on the whole plane, |u|<1 holds everywhere unless u=eⁱ for some ; the derivatives of order k have moduli a constant M _kdepending only on k. For a solution u on an open set ², the moduli of u and its derivatives have upper bounds depending only on the distance to ²\ therefore the set of solutions on a given is compact in C() for the topology of uniform convergence on compact subsets of . For a solution u such that |u|<1, 1–|u| satisfies an estimation similar to the classical Harnack inequality for positive harmonic functions.Finally, if is bounded and |u| has a lim supm at each boundary point, the |u|m in if m1, but if m<1 then |u| admits only a majorant S _m with values in ]m, 1[ and sufficient conditions are given for lim S _m =0 or S _m =O(m) as m0.

     

Sur le 2-groupe de classes d'idéaux de ℚ(√d,i)

Let ℕ,i=√−1,k=ℚ(√d,i) andC ₂ the 2-part of the class group ofk. Our goal is to determine alld such thatC ₂⋍ℤ/2ℤ×ℤ/2ℤ. Soientd∈ℕ,i=√−1,k=ℚ(√d,i), etC ₂ la 2-partie du groupe de classes dek. On s'intéresse à déterminer tous lesd tel queC ₂⋍ℤ/2ℤ×ℤ/2ℤ.      

Dynamique des groupes paraboliques d'automorphismes polynomiaux de ℂ2

Résumé  Nous étudions la dynamique de certains groupes abéliens d'automorphismes polynomiaux de ², que nous appelons groupes paraboliques. Nous montrons que ces groupes sont toujours formellement linéarisables, et que la linéarisante peut être strictement formelle ou au contraire convergente. Nous montrons ensuite que sous une hypothèse d'uniformité un groupe parabolique admet un (1,1) courant positif fermé invariant. Enfin nous donnons un exemple de groupe parabolique non uniforme n'admettant aucun (1,1) courant positif fermé invariant.

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We study the dynamics of a class of abelian groups of polynomial automorphisms of ², that we call parabolic groups. We show that these groups are always formally linearizable, and the linearizing map could be strictly formal or convergent. Further we show that under an uniformity hypothesis a parabolic group has a invariant (1, 1) positive closed current. Lastly we give an example of parabolic group that does not admit any invariant (1,1) positive closed current.