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浙江师范大学学报（自然科学版） 1989年第1期23卷 39-44页

作者：张福泉

本文根据:任意整系数首1多项式,f(x)被整系数首1二次多项式g(x)整除的充分必要条件是余式为零。先找出f(x)含有x^2+a或x^2-x+a因式的条件。然后把因式以一次项系数偶、奇分为两类,通过平移,把结果推广到一般情形。

关键词： monic Polynomial Translation

On Conditional Probabilities of Factoring Quadratics

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Advances in Pure Mathematics 2020年第3期10卷 114-124页

作者： Thomas Beatty Gabriela von Linden Department of Mathematics Florida Gulf Coast University Fort Myers FL USA

Factoring quadratics over Z is a staple of introductory algebra and textbooks tend to create the impression that doable factorizations are fairly common. To the contrary, if coefficients of a general quadratic are selected randomly without restriction, the probability that a factorization exists is zero. We achieve a specific quantification of the probability of factoring quadratics by taking a new approach that considers the absolute size of coefficients to be a parameter n. This restriction allows us to make relative likelihood estimates based on finite sample spaces. Our probability estimates are then conditioned on the size parameter n and the behavior of the conditional estimates may be studied as the parameter is varied. Specifically, we enumerate how many formal factored expressions could possibly correspond to a quadratic for a given size parameter. The conditional probability of factorization as a function of n is just the ratio of this enumeration to the total number of possible quadratics consistent with n. This approach is patterned after the well-known case where factorizations are carried out over a finite field. We review the finite field method as background for our method of dealing with Z [x]. The monic case is developed independently of the general case because it is simpler and the resulting probability estimating formula is more accurate. We conclude with a comparison of our theoretical probability estimates with exact data generated by a computer search for factorable quadratics corresponding to various parameter values.

关键词： Factorization Polynomial Quadratic Integers Rational Numbers monic Modular Arithmetic Conditional Probability

Macroscopic 3D plasmonic superlattice arrays by evaporative self-assembly

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Science Foundation in China 2016年第2期24卷 48-48页

With the support by the National Natural Science Foundation of China and Science and Technology Key Project of Shenzhen,the research team led by *** Xuefeng(喻学锋)from Shenzhen Institutes of Advanced Technology,Chine... 详细信息

关键词： assembly macroscopic fabrication aligned ordered thereby coffee seriously collective monic

ARITHMETIC OF n-QUADRATIC ALGEBRAIC FUNCTION FIELDS

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Chinese Science Bulletin 1987年第17期32卷 1157-1161页

作者：张贤科 Department of Mathematics University of Science and Technology of China Hefei

Let K=F_q(t) be the rational function field with the transcendental element t over F_q, F_q the field of q elements of odd characteristic. Any finite extension of k is called an algebraic function field. In this note,... 详细信息

关键词： algebraic rational discriminant umber divisor formulae monic properly quadratic assume

Hom Functors from A Regular Category

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数学研究与评论 1986年第2期 1-4页

作者：于永溪 Suzhou University Suzhou

This paper aims to show the exactness of Hom functors with domain a regular category and codomain the category set. I°In [Ⅰ], we put forward a problem: To what degree and to which categories with ferminal objects can HAA (homological algebra in abelian categories)be naturally extended? By 'naturally'we mean that the generalized theory degenerate into the theory of HAA when the terminal objects are nullS.

关键词： Regular naturally category algebra exact degenerate commutative completed smoothly monic

A PROPERTY OF QUASIKERNEL FAMILIES

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Chinese Science Bulletin 1983年第12期28卷 1591-1594页

作者：于永溪吴利生 Dalian Institute of Technology Suzhou University

This note will discuss the problem about the structure of quasikernel families. Introducing self-bijective half-functors, we shall try to prove that the quasikernel families are their invariants. Then Theorem 3.8 of [... 详细信息

关键词： invariants suppose monic 月卜动环 morphism write 邝丽 holds brief

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可消半模的正合列

江西师范大学学报（自然科学版） 2008年第6期32卷 702-704页

作者：敖忠平陈培慈蔡述平石油大学计算机科学系广东广州510510 江西师范大学数学与信息科学学院江西南昌330027

设A和B是S-半模,f:A→B是半模同态.ΔA和Kf分别定义为ΔA={(a,b)∈A×A|a+m=b+m,存在m∈A}和Kf={(a,b)∈A×A|f(a)+m=f(b)+m,存在m∈B}.将Kf和ΔA同时缩小为所规定的Kerf和ΔA,重新给出了monic和epic不同的定义,从不同的角度对某类特殊... 详细信息

关键词：可消半模正合列 monic epic equivalance

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可消半模的五引理

新疆师范大学学报（自然科学版） 2008年第2期27卷 12-14页

作者：敖忠平蔡述平宋海燕广州石油大学计算机科学系广东广州510510

文章借鉴[1]中的方法与技巧,将[1]中的Kf和-ΔA分别缩小为本文所规定的Kerf和—ΔA,重新给出了monic和epic不同的定义,探讨了某类特殊的半模——可消半模的某些性质,以及从不同的角度对可消半模的五引理进行了刻画。

关键词：可消半模五引理 monic epic

TWO RESULTS ON KUHN'S ALGORITHM

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Chinese Science Bulletin 1982年第10期27卷 1131-页

作者：徐森林王则柯 University of Science and Techmology of China Hefei Zhongshan University

In finding roots of polynomials by Kahn’s algorithm, Prof. W. Harold Kuhn construeted the sequences (zjk, djk), where are all roots of a monic polynomial f（z） of degree n in the complex variable z with complex numb... 详细信息

关键词： polynomial monic roots finding 分日洲口赵川吕加