A Diophantine equation with the harmonic mean
作者：
Zhang, Yong* ;Chen, Deyi
期刊：
Periodica Mathematica Hungarica ,2020年80(1):138-144 ISSN：0031-5303
通讯作者：
Zhang, Yong
作者机构：
[Zhang, Yong] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Hunan, Peoples R China.;[Zhang, Yong] Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.;[Chen, Deyi] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China.
通讯机构：
[Zhang, Yong] C;[Zhang, Yong] H;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Hunan, Peoples R China.;Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.
关键词：
Diophantine equation;Pell’s equation;Integer solutions;Rational parametric solutions
摘要：
Let f∈ Q[x] be a polynomial without multiple roots and deg f≥ 2. We give conditions for f= x2+ bx+ c under which the Diophantine equation 2 f(x) f(y) = f(z) (f(x) + f(y)) has infinitely many nontrivial integer solutions and prove that this equation has infinitely many rational parametric solutions for f= x2+ bx with nonzero integer b. Moreover, we show that it has a rational parametric solution for infinitely many cubic polynomials. © 2019, Akadémiai Kiadó, Budapest, Hungary.
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英文
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On the Diophantine equations z2= f(x) 2± f(y) 2 involving quartic polynomials
作者：
Zhang, Yong* ;Zargar, Arman Shamsi
期刊：
Periodica Mathematica Hungarica ,2019年79(1):25-31 ISSN：0031-5303
通讯作者：
Zhang, Yong
作者机构：
[Zhang, Yong] Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.
通讯机构：
[Zhang, Yong] C;Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.
关键词：
Diophantine equation;Quartic polynomial;Rational solution;Elliptic curve
摘要：
By the theory of elliptic curves, we prove that the Diophantine equations z2= f(x) 2± f(y) 2 have infinitely many rational solutions for some quartic polynomials, which gives a positive answer to Question 4.3 of Ulas and Togbé (Publ Math Debrecen 76(1–2):183–201,2010) for quartic polynomials. © 2018, Akadémiai Kiadó, Budapest, Hungary.
语种：
英文
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Some remarks on Jacobi and Gauss–Seidel-type iteration methods for the matrix equation AXB=C
作者：
Liu, Zhongyun* ;Zhou, Yang;Zhang, Yuelan;Lin, Lu;Xie, Dongxiu
期刊：
Applied Mathematics and Computation ,2019年354:305-307 ISSN：0096-3003
通讯作者：
Liu, Zhongyun
作者机构：
[Liu, Zhongyun; Zhou, Yang; Zhang, Yuelan] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410076, Hunan, Peoples R China.;[Lin, Lu] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.;[Xie, Dongxiu] Beijing Informat Sci & Technol Univ, Sch Sci, Beijing 100192, Peoples R China.
通讯机构：
[Liu, Zhongyun] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410076, Hunan, Peoples R China.
关键词：
Matrix equation;Classical splitting;Convergence;Norm
摘要：
Tian, et al. proposed in [5] several Jacobi and Gauss-Seidel-type iterative methods for solving matrix equation AXB = C. Those methods were demonstrated to be effective by the given numerical experiments. However, we find that there is a technical error in the proof of the main theorem (Theorem 3.3). In this note we first show this erratum by an example. Then we establish a new convergence theorem which contains the Theorem 3.3 in [5] as a special case. (C) 2019 Elsevier Inc. All rights reserved.
语种：
英文
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HERON TRIANGLES WITH FIGURATE NUMBER SIDES (vol 157, pg 478, 2019)
作者：
Peng, J.;Zhang, Y.*
期刊：
Acta Mathematica Hungarica ,2019年159(2):689-689 ISSN：0236-5294
通讯作者：
Zhang, Y.
作者机构：
[Peng, J.; Zhang, Y.] Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.
通讯机构：
[Zhang, Y.] C;Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.
摘要：
It was discovered that the original online version of the paper contained a mistake, on page 481, lines -4 to -1. It should be changed into the following: (Formula presented.). © 2019, Akadémiai Kiadó, Budapest, Hungary.
语种：
英文
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HERON TRIANGLES WITH FIGURATE NUMBER SIDES
作者：
Peng, J.;Zhang, Y.*
期刊：
Acta Mathematica Hungarica ,2019年157(2):478-488 ISSN：0236-5294
通讯作者：
Zhang, Y.
作者机构：
[Peng, J.; Zhang, Y.] Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.
通讯机构：
[Zhang, Y.] C;Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.
关键词：
Heron triangle;figurate number;polygonal number;binomial coefficient;Pellian equation
摘要：
By the theory of Pellian equation and the method of undetermined coefficients, we show that there exist infinitely many isosceles Heron triangles whose sides are polygonal numbers and binomial coefficients.
语种：
英文
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ON THE DIOPHANTINE EQUATION f(x) f(y) = f(z)(n )INVOLVING LAURENT POLYNOMIALS, II
作者：
Zhang, Yong;Zargar, Arman Shamsi*
期刊：
COLLOQUIUM MATHEMATICUM ,2019年158(1):119-126 ISSN：0010-1354
通讯作者：
Zargar, Arman Shamsi
作者机构：
[Zhang, Yong] Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.;[Zargar, Arman Shamsi] Univ Mohaghegh Ardabili, Dept Math & Applicat, Fac Sci, Ardebil 5619911367, Iran.
通讯机构：
[Zargar, Arman Shamsi] U;Univ Mohaghegh Ardabili, Dept Math & Applicat, Fac Sci, Ardebil 5619911367, Iran.
关键词：
Diophantine equation;Laurent polynomial;Rational parametric solution
摘要：
We investigate the non-trivial rational parametric solutions of the Diophantine equation f(x)f(y) - f(z)n, where f = xk +axk-1 + b/x, k ≥ 2, x2 +a/x+b/x2 for n = 1, and f = x2 +ax+b+a3/(27x), x2 +ax+b+a3/(16x)+a4/(256x2) for n = 2. © Instytut Matematyczny PAN, 2019.
语种：
英文
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The general inner-outer iteration method based on regular splittings for the PageRank problem
作者：
Tian, Zhaolu* ;Liu, Yong;Zhang, Yan;Liu, Zhongyun;Tian, Maoyi*
期刊：
Applied Mathematics and Computation ,2019年356:479-501 ISSN：0096-3003
通讯作者：
Tian, Zhaolu;Tian, Maoyi
作者机构：
[Tian, Zhaolu] Shanxi Univ Finance & Econ, Coll Appl Math, Taiyuan 030006, Shanxi, Peoples R China.;[Liu, Yong] Shanxi Univ, Inst Loess Plateau, Taiyuan 030006, Shanxi, Peoples R China.;[Tian, Maoyi; Zhang, Yan] Shandong Univ Sci & Technol, Geomat Coll, Qingdao 266590, Shandong, Peoples R China.;[Liu, Zhongyun] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.
通讯机构：
[Tian, Zhaolu; Tian, Maoyi] S;Shanxi Univ Finance & Econ, Coll Appl Math, Taiyuan 030006, Shanxi, Peoples R China.;Shandong Univ Sci & Technol, Geomat Coll, Qingdao 266590, Shandong, Peoples R China.
关键词：
PageRank;Inner-outer iteration;Regular splitting;Preconditioner;Convergence
摘要：
In this paper, combined the regular splittings of the coefficient matrix I - alpha P with the inner-outer iteration framework [9], a general inner-outer (GIO) iteration method is presented for solving the PageRank problem. Firstly, the AOR and modified AOR (MAOR) methods for solving the PageRank problem are constructed, and several comparison results are also given. Next, the GIO iteration scheme is developed, and its overall convergence is analyzed in detail. Furthermore, the preconditioner derived from the GIO iteration can be used to accelerate the Krylov subspace methods, such as GMRES method. Finally, some numerical experiments on several PageRank problems are provided to illustrate the efficiency of the proposed algorithm. (C) 2019 Elsevier Inc. All rights reserved.
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英文
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Trigonometric transform splitting methods for real symmetric Toeplitz systems
作者：
Liu, Zhongyun* ;Wu, Nianci;Qin, Xiaorong;Zhang, Yulin
期刊：
Computers & Mathematics with Applications ,2018年75(8):2782-2794 ISSN：0898-1221
通讯作者：
Liu, Zhongyun
作者机构：
[Liu, Zhongyun; Wu, Nianci; Qin, Xiaorong] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410076, Hunan, Peoples R China.;[Zhang, Yulin] Univ Minho, Ctr Matemat, P-4710057 Braga, Portugal.
通讯机构：
[Liu, Zhongyun] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410076, Hunan, Peoples R China.
关键词：
Sine transform;Cosine transform;Matrix splitting;Iterative methods;Real Toeplitz matrices
摘要：
In this paper we study efficient iterative methods for real symmetric Toeplitz systems based on the trigonometric transformation splitting (TTS) of the real symmetric Toeplitz matrix A. Theoretical analyses show that if the generating function f of the n×n Toeplitz matrix A is a real positive even function, then the TTS iterative methods converge to the unique solution of the linear system of equations for sufficient large n. Moreover, we derive an upper bound of the contraction factor of the TTS iteration which is dependent solely on the spectra of the two TTS matrices involved. Different from the CSCS iterative method in Ng (2003) in which all operations counts concern complex operations when the DFTs are employed, even if the Toeplitz matrix A is real and symmetric, our method only involves real arithmetics when the DCTs and DSTs are used. The numerical experiments show that our method works better than CSCS iterative method and much better than the positive definite and skew-symmetric splitting (PSS) iterative method in Bai et al. (2005) and the symmetric Gauss–Seidel (SGS) iterative method. © 2018 Elsevier Ltd
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英文
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On products of consecutive arithmetic progressions. II
作者：
Zhang, Y.*
期刊：
Acta Mathematica Hungarica ,2018年156(1):240-254 ISSN：0236-5294
通讯作者：
Zhang, Y.
作者机构：
[Zhang, Y.] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.;[Zhang, Y.] Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.
通讯机构：
[Zhang, Y.] C;[Zhang, Y.] H;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.;Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.
关键词：
Diophantine equation;consecutive arithmetic progression;Pellian equation
摘要：
Let
$${f(x, k, d) = x(x + d)\cdots(x + (k - 1)d)}$$
be a polynomial with
$${k \geq 2}$$
,
$${d \geq 1}$$
. We consider the Diophantine equation
$${\prod_{i = 1}^{r} f(x_i, k_i, d) = y^2}$$
, which is inspired by a question of Erdős and Graham [4, p. 67]. Using the theory of Pellian equation, we give infinitely many (nontrivial) positive integer solutions of the above Diophantine equation for some cases.
语种：
英文
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Some New Congruences Concerning Binomial Coefficients
作者：
贾丽蕊;张勇;蔡天新
期刊：
数学进展 ,2018年47(4):525-542 ISSN：1000-0917
作者机构：
School of Mathematical Sciences,Zhejiang University, Zhejiang, Hangzhou, 310027;College of Mathematics and Computing Science,Changsha University of Science and Technology, Hunan, Changsha, 410114;[贾丽蕊; 蔡天新] School of Mathematical Sciences,Zhejiang University, Zhejiang, Hangzhou, 310027;[张勇] School of Mathematical Sciences,Zhejiang University, Zhejiang, Hangzhou, 310027 College of Mathematics and Computing Science,Changsha University of Science and Technology, Hunan, Changsha, 410114
关键词：
同余;二项式系数;Wolstenholme定理;Morley同余式
摘要：
令$k$为正整数,$p$为素数.设$1 \le a \le p - 1$,$1 \le b \le \frac{{p - 1}}{2}$,本文研究了二项式系数$\left( {\begin{array}{*{20}{c}}{\left( {k + 1} \right)p - a}\\{p - a}\end{array}} \right)$,$\left( {\begin{array}{*{20}{c}}{kp - 1}\\{p - a}\end{array}} \right)$和$\left( {\begin{array}{*{20}{c}}{kp + \frac{{p - 1}}{2} \pm b}\\{\frac{{p - 1}}{2} \pm b}\end{array}} \right)$,$\left( {\begin{array}{*{20}{c}}{kp - 1}\\{\frac{{p - 1}}{2} \pm b}\end{array}} \right)$的同余性质.并得到了一个Morley同余式的推广,以及$\left( {\begin{array}{*{20}{c}}{\left( {k + 1} \right)p - a}\\{p - a}\end{array}} \right)$关于$a$求和的一些同余式.
语种：
中文
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ON THE DIOPHANTINE EQUATION f(x)f(y) = f(z)(n) INVOLVING LAURENT POLYNOMIALS
作者：
Zhang, Yong*
期刊：
COLLOQUIUM MATHEMATICUM ,2018年151(1):111-122 ISSN：0010-1354
通讯作者：
Zhang, Yong
作者机构：
[Zhang, Yong] Changsha Univ Sci & Technol, Coll Math & Comp Sci, Changsha 410114, Hunan, Peoples R China.;[Zhang, Yong] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China.
通讯机构：
[Zhang, Yong] C;[Zhang, Yong] Z;Changsha Univ Sci & Technol, Coll Math & Comp Sci, Changsha 410114, Hunan, Peoples R China.;Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China.
关键词：
Diophantine equations;Laurent polynomials;Rational parametric solutions
摘要：
Using the theory of elliptic curves, we investigate nontrivial rational parametric solutions of the Diophantine equation f(x)f(y) = f(z)n, where n = 1, 2 and f(X) are some simple Laurent polynomials. © Instytut Matematyczny PAN, 2018.
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英文
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Robust parameter identification using parallel global optimization for a batch nonlinear enzyme-catalytic time-delayed process presenting metabolic discontinuities
作者：
Yuan, Jinlong;Zhang, Yuduo;Ye, Jianxiong;Xie, Jun;Teo, Kok Lay;...
期刊：
Applied Mathematical Modelling ,2017年46:554-571 ISSN：0307-904X
通讯作者：
Zhu, Xi
作者机构：
[Yin, Hongchao; Yuan, Jinlong] Dalian Univ Technol, Sch Energy & Power Engn, Dalian 116024, Liaoning, Peoples R China.;[Yuan, Jinlong; Feng, Enmin] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Liaoning, Peoples R China.;[Xiu, Zhilong; Yuan, Jinlong] Dalian Univ Technol, Sch Life Sci & Biotechnol, Dalian 116024, Liaoning, Peoples R China.;[Zhang, Yuduo] Dalian Nationalities Univ, Coll Sci, Dalian 116600, Liaoning, Peoples R China.;[Ye, Jianxiong] Fujian Normal Univ, Sch Math & Comp Sci, Fuzhou 350007, Fujian, Peoples R China.
通讯机构：
[Zhu, Xi] T;Tianjin Univ Technol, Sch Management, Tianjin 300384, Peoples R China.
关键词：
Nonlinear time-delayed switched system;Biological robustness;Parallel optimization;Batch culture;Convergence analysis
摘要：
In this paper, a nonlinear enzyme-catalytic time-delayed switched dynamical system is considered to describe batch culture of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumoniae. This system can not only predict the exponential growth phase but also the lag and the stationary growth phases of batch culture since it contains two switching times for representing the starting moment of lag growth phase and the time when the cell specified growth rate reaches the maximum. The biological robustness is expressed in terms of the expectation and variance of the relative deviation. Our aim is to identify the switching times. To this end, a robust parameter identification problem is formulated, where the switching times are decision variables to be chosen such that the biological robustness measure is optimized. This problem, which is governed by the nonlinear system, is subject to a quality constraint and continuous state inequality constraints. Using a hybrid time-scaling transformation to parameterize the switching times into new parameters, an equivalently robust parameter identification problem is investigated. The continuous state inequality constraints are approximated by a conventional inequality constraint, yielding a sequence of approximate robust parameter identification subproblems. The convergence analysis of this approximation is also investigated. Owing to the highly complex nature of these subproblems, a parallel algorithm, based on simulated annealing, is proposed to solve these subproblems. From an extensive simulation study, it is observed that the obtained optimal switching times are satisfactory. © 2017 Elsevier Inc.
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英文
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On the Diophantine system f(z)=f(x)f(y)=f(u)f(v)
作者：
Zhang, Yong* ;Shen, Zhongyan
期刊：
Periodica Mathematica Hungarica ,2017年75(2):295-301 ISSN：0031-5303
通讯作者：
Zhang, Yong
作者机构：
[Zhang, Yong] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.;[Shen, Zhongyan] Zhejiang Int Studies Univ, Dept Math, Hangzhou 310012, Zhejiang, Peoples R China.
通讯机构：
[Zhang, Yong] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.
关键词：
Diophantine system;Positive integer solution;Rational solution;Elliptic curve
摘要：
We show that the Diophantine system f(z)=f(x)f(y)=f(u)f(v)has infinitely many nontrivial positive integer solutions for f(X) = X2- 1 , and infinitely many nontrivial rational solutions for f(X) = X2+ b with nonzero integer b. © 2017, Akadémiai Kiadó, Budapest, Hungary.
语种：
英文
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The Shifted Classical Circulant and Skew Circulant Splitting Iterative Methods for Toeplitz Matrices
作者：
Liu, Zhongyun* ;Qin, Xiaorong;Wu, Nianci;Zhang, Yulin
期刊：
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES ,2017年60(4):807-815 ISSN：0008-4395
通讯作者：
Liu, Zhongyun
作者机构：
[Liu, Zhongyun] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410076, Hunan, Peoples R China.;[Wu, Nianci; Qin, Xiaorong; Zhang, Yulin] Univ Minho, Ctr Matemat, P-4710057 Braga, Portugal.
通讯机构：
[Liu, Zhongyun] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410076, Hunan, Peoples R China.
关键词：
15A23;65F10;65F15;Hermitian positive definite;CSCS splitting;Gauss-Seidel splitting;iterative method;Toeplitz matrix
摘要：
<jats:title>Abstract</jats:title><jats:p>It is known that every Toeplitz matrix <jats:italic>T</jats:italic> enjoys a circulant and skew circulant splitting (denoted CSCS) i.e., <jats:italic>T = C−S</jats:italic> with <jats:italic>C</jats:italic> a circulantmatrix and <jats:italic>S</jats:italic> a skew circulantmatrix. Based on the variant of such a splitting (also referred to as CSCS), we first develop classical CSCS iterative methods and then introduce shifted CSCS iterative methods for solving hermitian positive deûnite Toeplitz systems in this paper. The convergence of each method is analyzed. Numerical experiments show that the classical CSCS iterative methods work slightly better than the Gauss–Seidel (GS) iterative methods if the CSCS is convergent, and that there is always a constant α such that the shifted CSCS iteration converges much faster than the Gauss–Seidel iteration, no matter whether the CSCS itself is convergent or not.</jats:p>
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英文
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Right triangle and parallelogram pairs with a common area and a common perimeter
作者：
Zhang, Yong*
期刊：
Journal of Number Theory ,2016年164:179-190 ISSN：0022-314X
通讯作者：
Zhang, Yong
作者机构：
[Zhang, Yong] Changsha Univ Sci & Technol, Coll Math & Comp Sci, Changsha 410114, Hunan, Peoples R China.;[Zhang, Yong] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China.
通讯机构：
[Zhang, Yong] C;Changsha Univ Sci & Technol, Coll Math & Comp Sci, Changsha 410114, Hunan, Peoples R China.
关键词：
Right triangle;Parallelogram;Common area;Common perimeter;Elliptic curve
摘要：
By the theory of elliptic curves, we show that there are infinitely many integer right triangle and integer parallelogram pairs with a common area and a common perimeter. © 2016 Elsevier Inc.
语种：
英文
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SOME OBSERVATIONS ON THE DIOPHANTINE EQUATION f(x)f(y) - f(z)(2)
作者：
Zhang, Yong*
期刊：
COLLOQUIUM MATHEMATICUM ,2016年142(2):275-283 ISSN：0010-1354
通讯作者：
Zhang, Yong
作者机构：
[Zhang, Yong] Changsha Univ Sci & Technol, Coll Math & Comp Sci, Changsha 410114, Hunan, Peoples R China.;[Zhang, Yong] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China.
通讯机构：
[Zhang, Yong] C;[Zhang, Yong] Z;Changsha Univ Sci & Technol, Coll Math & Comp Sci, Changsha 410114, Hunan, Peoples R China.;Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China.
关键词：
Diophantine equation;Integer solutions;Pell’s equation;Rational solutions
摘要：
Let f is an element of Q[X]be a polynomial without multiple roots and with deg(f) >= 2. We give conditions for f(X) - AX(2) + BX + C such that the Diophantine equation f(x)f(y) = f(z)(2) has infinitely many nontrivial integer solutions and prove that this equation has a rational parametric solution for infinitely many irreducible cubic polynomials. Moreover, we consider f(x)f(y) = f(z)(2) for quartic polynomials.
语种：
英文
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MINIMIZATION PROBLEMS FOR CERTAIN STRUCTURED MATRICES
作者：
Liu, Zhongyun* ;Ralha, Rui;Zhang, Yulin;Ferreira, Carla
期刊：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA ,2015年30:613-631 ISSN：1537-9582
通讯作者：
Liu, Zhongyun
作者机构：
[Liu, Zhongyun] Changsha Univ Sci & Technol, Sch Math & Comp Sci, Changsha 410076, Hunan, Peoples R China.;[Ralha, Rui; Ferreira, Carla; Zhang, Yulin] Univ Minho, Ctr Math, P-47110057 Braga, Portugal.;[Ralha, Rui; Ferreira, Carla; Zhang, Yulin] Univ Minho, Math & Applicat Dept, P-47110057 Braga, Portugal.
通讯机构：
[Liu, Zhongyun] C;Changsha Univ Sci & Technol, Sch Math & Comp Sci, Changsha 410076, Hunan, Peoples R China.
关键词：
Least-squares approximation;Centralizer of J;Anticentralizer of J;Moore-Penrose inverse
摘要：
For given Z, B is an element of C-nxk, the problem of finding Lambda is an element of C-nxn, in some prescribed class W, that minimizes parallel to AZ - B parallel to (Frobenius norm) has been considered by different authors for distinct classes W. Here, this minimization problem is studied for two other classes, which include the symmetric Hamiltonian, symmetric skew-Hamiltonian, real orthogonal symplectic and unitary conjugate symplectic matrices. The problem of minimizing parallel to A - (A) over tilde parallel to, where (A) over tilde is given and A is a solution of the previous problem, is also considered ( as has been done by others, for different classes W). The key idea of this contribution is the reduction of each one of the above minimization problems to two independent subproblems in orthogonal subspaces of C-nxn. This is possible due to the special structures under consideration. Matlab codes are developed, and numerical results of some tests are presented.
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英文
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On products of consecutive arithmetic progressions
作者：
Zhang, Yong;Cai, Tianxin*
期刊：
Journal of Number Theory ,2015年147:287-299 ISSN：0022-314X
通讯作者：
Cai, Tianxin
作者机构：
[Zhang, Yong] Changsha Univ Sci & Technol, Coll Math & Comp Sci, Changsha 410114, Hunan, Peoples R China.;[Cai, Tianxin; Zhang, Yong] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China.
通讯机构：
[Cai, Tianxin] Z;Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China.
关键词：
Consecutive arithmetic progression;Diophantine equation;Elliptic curve;Pell's equation;Primary;Secondary
摘要：
In this paper, first, we show the Diophantine equation. x(x+b)y(y+b)=z(z+b) has infinitely many nontrivial positive integer solutions for b≥. 3. Second, we prove the Diophantine equation. (x-b)x(x+b)(y-b)y(y+b)=(z-b)z(z+b) has infinitely many nontrivial positive integer solutions for b=. 1, and the set of rational solutions of it is dense in the set of real solutions for b≥. 1. Third, we get infinitely many nontrivial positive integer solutions of the Diophantine equation. (x-b)x(x+b)(y-b)y(y+b)=z2 for even number b≥. 2. At last, we raise some unsolved questions. © 2014 Elsevier Inc.
语种：
英文
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Asymptotic stability of solution to nonlinear neutral and Volterra functional differential equations in Banach spaces
作者：
Wang, Wansheng* ;Fan, Qin;Zhang, Yuan;Li, Shoufu
期刊：
Applied Mathematics and Computation ,2014年237:217-226 ISSN：0096-3003
通讯作者：
Wang, Wansheng
作者机构：
[Fan, Qin; Wang, Wansheng; Zhang, Yuan] Changsha Univ Sci & Technol, Sch Math & Computat Sci, Hunan 410114, Peoples R China.;[Li, Shoufu] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China.
通讯机构：
[Wang, Wansheng] C;Changsha Univ Sci & Technol, Sch Math & Computat Sci, Hunan 410114, Peoples R China.
关键词：
Asymptotic stability;Banach spaces;Delay integro-differential equations of "Hale's" form;Neutral functional differential equations;Volterra functional differential equations;Volterra partial functional differential equations
摘要：
This paper is concerned with the asymptotic stability properties of the solution to nonlinear neutral and Volterra functional differential equations. Some sufficient conditions for the asymptotic stability of the systems are given. As an illustration of the applications of these investigations, the contractivity and asymptotic stability results of the solution to Volterra partial functional differential equations and delay integro-differential equations of “Hale’s” form are obtained respectively. These results form the basis for obtaining insight into the analogous properties of their numerical solutions.
语种：
英文
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STRUCTURE-PRESERVING SCHUR METHODS FOR COMPUTING SQUARE ROOTS OF REAL SKEW-HAMILTONIAN MATRICES
作者：
Liu, Zhongyun* ;Zhang, Yulin;Ferreira, Carla;Ralha, Rui
期刊：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA ,2012年23:845-865 ISSN：1537-9582
通讯作者：
Liu, Zhongyun
作者机构：
[Liu, Zhongyun] Changsha Univ Sci & Technol, Sch Math, Changsha 410076, Hunan, Peoples R China.;[Ralha, Rui; Ferreira, Carla; Zhang, Yulin] Univ Minho, Ctr Matemat, P-4710057 Braga, Portugal.
通讯机构：
[Liu, Zhongyun] C;Changsha Univ Sci & Technol, Sch Math, Changsha 410076, Hunan, Peoples R China.
关键词：
Matrix square root;Skew-Hamiltonian Schur decomposition;Structure-preserving algorithm
摘要：
The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W. Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W, skew-Hamiltonian and Hamiltonian square roots. Compared to the standard real Schur method, which ignores the structure, this method requires significantly less arithmetic. © 2012, International Linear Algebra Society. All rights reserved.
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英文
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