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  new proof
     A New Proof for the Algebra Criterion of the Equation x(t)+ax(t)+bx(t-τ)=0 with Asymptotic Stability
     方程x(t)+ax(t)+bx(t-τ)=0渐近稳定性代数判据的新证明(Ⅰ)
短句来源
     A New Proof of a Theorem Concerning the Set {N_k~-(x)}_k~n=0
     关于集{N_k~-(x)}_k~n=0的一个定理的新证明(英文)
短句来源
     A New Proof of the Nassrallah-Rahman Integral
     Nassrallah-Rahman积分的一个新证明
短句来源
     In this peper one makes some discussion on the relation between radicals of arbitray ring R and R[x], the polynomial ring on R, and obtained the characteristic property of some radicals, at last, one gives a new proof of the theorems β(R[x])=β(R)[x]=(β(R[x])∩R)[x], where β is Baer lower nil radical.
     本文就任意环R与R上多项式环R[x]的根之间的关系作了讨论,得到了一些根性质的特征性质,并给出定理β(R[x])=β(R)[x]=(β(R[x])∩ R)[x]的新证明,其中β是Baer下诣零根。
短句来源
     A New Proof about the Uniform Dimension Result of Wiener Sheet
     Wiener Sheet一致维数结果的新证明
短句来源
更多       
  a new proof
     A New Proof for the Algebra Criterion of the Equation x(t)+ax(t)+bx(t-τ)=0 with Asymptotic Stability
     方程x(t)+ax(t)+bx(t-τ)=0渐近稳定性代数判据的新证明(Ⅰ)
短句来源
     A New Proof of a Theorem Concerning the Set {N_k~-(x)}_k~n=0
     关于集{N_k~-(x)}_k~n=0的一个定理的新证明(英文)
短句来源
     A New Proof of the Nassrallah-Rahman Integral
     Nassrallah-Rahman积分的一个新证明
短句来源
     In this peper one makes some discussion on the relation between radicals of arbitray ring R and R[x], the polynomial ring on R, and obtained the characteristic property of some radicals, at last, one gives a new proof of the theorems β(R[x])=β(R)[x]=(β(R[x])∩R)[x], where β is Baer lower nil radical.
     本文就任意环R与R上多项式环R[x]的根之间的关系作了讨论,得到了一些根性质的特征性质,并给出定理β(R[x])=β(R)[x]=(β(R[x])∩ R)[x]的新证明,其中β是Baer下诣零根。
短句来源
     A New Proof about the Uniform Dimension Result of Wiener Sheet
     Wiener Sheet一致维数结果的新证明
短句来源
更多       
  new prove
     A New Prove for Existence of Bernoulli Limit, and Bernoulli’s Application in the Finance,Medicine,Microbiology
     Bernoulli极限存在性的新证明与Bernoulli极限在金融学和医学微生物学中的应用
短句来源
     New Prove of Euler's Formula
     Euler公式的新证明
短句来源
     The Unified Definition of Limit of Simple Function and New Prove of Related Propositions
     一元函数极根的统一定义及有关命题的新证明
短句来源
  new method of proving
     A New Method of Proving Rolle Value Theorem
     Rolle中值定理的一个新证明
短句来源
     A New Method of Proving Lagrange Value Theorem
     Lagrange中值定理的一个新证明
短句来源

 

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      new proof
    In the case of 3-dimensional commutative algebras a new proof of a recent theorem of Katsylo and Mikhailov about the 28 bitangents to the associated plane quartic is given.
          
    As an immediate application we obtain a new proof of the main theorem of standard monomial theory for classical groups.
          
    We also use known results about canonical bases forUq2 to get a new proof of recurrent formulas for KL polynomials for maximal parabolic subgroups (geometrically, this case corresponds to Grassmannians), due to Lascoux-Schützenberger and Zelevinsky.
          
    As a corollary, we obtain a new proof for Roberts' well-known counterexample in dimension seven.
          
    A new proof of Cohen-Macaulayness (and thus normality) for Schubert varieties is also obtained.
          
    更多          
      a new proof
    In the case of 3-dimensional commutative algebras a new proof of a recent theorem of Katsylo and Mikhailov about the 28 bitangents to the associated plane quartic is given.
          
    As an immediate application we obtain a new proof of the main theorem of standard monomial theory for classical groups.
          
    We also use known results about canonical bases forUq2 to get a new proof of recurrent formulas for KL polynomials for maximal parabolic subgroups (geometrically, this case corresponds to Grassmannians), due to Lascoux-Schützenberger and Zelevinsky.
          
    As a corollary, we obtain a new proof for Roberts' well-known counterexample in dimension seven.
          
    A new proof of Cohen-Macaulayness (and thus normality) for Schubert varieties is also obtained.
          
    更多          
      new prove
    It also gave a new prove that deciding if a graph has a triangulation with state space beneath a threshold is NP-complete.
          
      new method of proving
    We introduce a new method of proving lower bounds on the depth of algebraicd-degree decision (resp.
          
    We develop a new method of proving that groups acting on various classes of spaces, with nontrivial stabilizers admitted, are automatic or biautomatic.
          
    We suggest a new method of proving the Michael finite-dimensional selection theorem.
          


    In [3], A. Brauer considered a method to compute the maximal eigenvalue of Positive metriees (in the sense that all elements are positive). In this paper we reproved Brauer's theorem by refining his method, so that our way is simpler and quicker. Showing by an example, we showed that at least in certain cases, our method is faster than that of Hall and Porsching deduced in 1968. Our method is further extended to some other types of matrices, such as irreducible non-negative matrices and so-called sub-non-negative...

    In [3], A. Brauer considered a method to compute the maximal eigenvalue of Positive metriees (in the sense that all elements are positive). In this paper we reproved Brauer's theorem by refining his method, so that our way is simpler and quicker. Showing by an example, we showed that at least in certain cases, our method is faster than that of Hall and Porsching deduced in 1968. Our method is further extended to some other types of matrices, such as irreducible non-negative matrices and so-called sub-non-negative matrices defined in this paper.

    在[3]中,A·Brauer研究了一个计算正矩阵(即所有元素都为正数的矩阵)最大特征值的方法,在本文中,我们给出Brauer定理的一个新的证明,从中找到一个更简单且收敛更快的方法,并用实例说明这个方法的确比Hall和Porsching在1968年提出的方法收敛更快,我们还将本文的方法推广到其他一些矩阵类(如既约非负矩阵以及本文定义的准非负矩阵)。

    A series■a_n is said to be (Riemann) summable (R,k)(k≥1 being an integer)to the sum s,if the expression ■ converges in the neighbourhood of h=0 and tends to s as h→0. Let f(t)be a periodic function with period 2π,integrable(L)over(0,2π),and ■ The(R,k)means for ■[f] at x are ■ Lee has recently proved that if f■L(0,2π)has a simple discontinuity at a point x_0,the means R_k~k(f,x_0)does not show Gibb’s phenomenon at x_0. There exists however some mistakes in Lee’s argument.A correction of Lee’s proof is given in...

    A series■a_n is said to be (Riemann) summable (R,k)(k≥1 being an integer)to the sum s,if the expression ■ converges in the neighbourhood of h=0 and tends to s as h→0. Let f(t)be a periodic function with period 2π,integrable(L)over(0,2π),and ■ The(R,k)means for ■[f] at x are ■ Lee has recently proved that if f■L(0,2π)has a simple discontinuity at a point x_0,the means R_k~k(f,x_0)does not show Gibb’s phenomenon at x_0. There exists however some mistakes in Lee’s argument.A correction of Lee’s proof is given in the present note. The second object of the present paper is to extend a theorem in [1] into the following form: If f■L(0,2π) and k≥1,then the Fourier series ■[f,x]is summable(R,k) to sum f(x) almost everywhere.

    本文指出,李经熙在1978年全国数学会上报告的题为“用黎曼求和法(R,k)求和时的吉卜斯现象”的论文中的主要定理的证明是错误的.本文纠正了他的错误,给出了新的证明方法.其次把专著[1]中的关于几乎处处(R,k)求和的定理加以推广.

    The matrices of class M have been investigated in detail by Householder.In this paper,we shall discuss the matrices of class M by using the L-norm,instead of the concept of the convex body.A comparatively short and new proof on the suf- ficient condition for a matrix to be of class M is given.When A is a matrix of class M,we find a concrete form of the matrix L such that‖A‖_L=p(A). Having Discussed the stability problems with the matrices of class M,we give a general sufficient condition on stability.First,the...

    The matrices of class M have been investigated in detail by Householder.In this paper,we shall discuss the matrices of class M by using the L-norm,instead of the concept of the convex body.A comparatively short and new proof on the suf- ficient condition for a matrix to be of class M is given.When A is a matrix of class M,we find a concrete form of the matrix L such that‖A‖_L=p(A). Having Discussed the stability problems with the matrices of class M,we give a general sufficient condition on stability.First,the statement(H)by Kreiss is equivalent to the following:(L)There is a constant C>0 and,for each A ∈,a nonsingular matrix L such that ‖L‖_2·‖L~(-1)‖_2≤C,‖A‖_L≤1.Secondly,let the non- singular matrix V transform A into a Jordan canonical matrix.If‖V‖_2·‖V~(-1)‖_2≤ c~2,where c=const>0,then Von-Neumann condition is also sufficient for stability when A is the matrix of class M.However,if there is a constant r<1,and ρ(A)≤ r<1,then the difference scheme is stable when A is not a matrix of class M.

    Householder 在[1]中详细讨论过 M 类矩阵.本文不用几何上的凸体概念,而用 Young所引入的 L 模来讨论 M 类矩阵,给出一个 M 类矩阵充分条件的较为简单的新证明.同时,若A 是 M 类矩阵,给出了一类具体的非奇异矩阵 L,使得‖A‖L=■(A).但我们未能找到使得‖A‖L=■(A)的通解 L.然后用 M 类矩阵来讨论差分格式稳定性问题,给出了一个比较一般的实用的稳定性充分条件.

     
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