平面凸体的完全不等式组

对于平面凸体，分别用A、p、r、R、d表示它的面积、周长、内径、外径、直径．本文分别给出了其中的三元组合(A，r，R)，(p，r．R)，(p，r，d)，(A，r，d)所满足的不等式，并给出了相应的极值集．     

关于概率空间与次线性期望空间中的随机变量一致可积性的一个注记（英文）

在这篇注记中我们讨论随机变量的一致可积性.在概率空间中,我们引进了随机变量一致可积性的两个新的定义,并证明了他们与经典定义等价.在次线性期望空间中,我们给出了随机变量一致可积性的德拉瓦利普桑准则,并作了一些其它讨论.     

A supersingular coincidence

The Ramanujan Journal - The 15 primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71 are called the supersingular primes: they occur in several contexts in number theory and also,...     

PROPERTIES OF SOME SETS OF SEQUENCES DEFINED BY A MODULUS FUNCTION

In this article, the author introduces the generalized difference paranormed sequence spaces c （△v^m, f, p, q, s）, c0 （△v^m, f, p, q, s）, and l∞ （△v^m, f, p, q, s） defined over a seminormed sequence space （X, q）. The author also studies their properties like completeness, solidity, symmetricitv, etc.     

关于K4同胚图色唯一性的几个新结果

本文证得:如果i,j,k,l,m,n中有四个数相等,而另外二个数不小于此数,则K_4(i,j,k,l,m,n)是色唯一的.此外,我们还得到了另外两族具有色唯一性的K_4同胚图.     

Describing Neighborhoods of 5-Vertices in a Class of 3-Polytopes with Minimum Degree 5

Lebesgue proved in 1940 that each 3-polytope with minimum degree 5 contains a 5-vertex for which the set of degrees of its neighbors is majorized by one of the following sequences(6, 6, 7, 7, 7), (6, 6, 6, 7, 9), (6, 6, 6, 6, 11)(5, 6, 7, 7, 8), (5, 6, 6, 7, 12), (5, 6, 6, 8, 10), (5, 6, 6, 6, 17)(5, 5, 7, 7, 13), (5, 5, 7, 8, 10), (5, 5, 6, 7, 27), (5, 5, 6, 6,∞), (5, 5, 6, 8, 15), (5, 5, 6, 9, 11)(5, 5, 5, 7, 41), (5, 5, 5, 8, 23), (5, 5, 5, 9, 17), (5, 5, 5, 10, 14), (5, 5, 5, 11, 13).We prove that each 3-polytope with minimum degree 5 without vertices of degree from 7 to 10 contains a 5-vertex whose set of degrees of its neighbors is majorized by one of the following sequences: (5, 6, 6, 5, ∞), (5, 6, 6, 6, 15), and (6, 6, 6, 6, 6), where all parameters are tight.     

泛系分析:数学·方法论·相对论·辩证思维

基于对广义系统、泛导、泛对称、泛箱原理、泛系相对性提出了新的分析模式与新的相对数学化的简化强化的定义,发展了泛系方法论与泛系相对论的框架与理法,具体内容涉及:相对普适的数学化的泛系,200类对偶,对偶转化,泛对称转化,泛系辩证,八畴方法,泛系数学方法,广义量化,逼近转化原则,泛等价定理,供求分析,思维实验,广义灰色系统,等等.     

Trivial nuclear ideals of alternative algebras

Let A be a free alternative Φ-algebra, where Φ is an associative commutative ring with 1, containing 1/6, and g(y, z, t, v, x, x)=2[J_({[y, z], t, x}_, x, v)+J_({[y,x], z, x}_, t, v)], where [x, y]=xy−yx, J_(x, y, z)=[[x, y], z]+[[z, x], y]+[[y, z], x], {x, y, z}_=J_(x, y, z)+3[x, [y, z]]. We construct trivial nuclear ideals of A, that is, nonzero ideals with zero multiplication, lying in the associative center of A. In particular, it is shown that if G and B are fully invariant ideals of A on k≥7 free generators, generated by a function g and by double commutators, respectively, then GB+BG is a nuclear ideal of A. This implies that an unmized alternative algebra satisfies GB=BG=0. If an unmixed algebra is finitely generated, then G=0. In addition, we prove that if R is an unmixed solvable alternative algebra then (R^N)²=0 for some N. Translated fromAlgebra i Logika, Vol. 36, No. 1, pp. 97–115, January–February, 1997.     

GRPIA: a new algorithm for computing interpolation polynomials

Numerical Algorithms - Let x0,x1, ? , xn, be a set of n + 1 distinct real numbers (i.e., xm ≠ xj, for m ≠ j) and let ym,k, for m = 0, 1, ? , n, and k = 0, 1, ? , rm,...     

BOOK REVIEWS

Book reviewed in this article: Atoms in Action, by George Russell Harrison Earth's Adventures, by Carroll Lane Fenton Hackh's Chemical Dictionary, Third Edition, revised and edited by Julius Grant Physics of the 20th Century, by Pascual Jordan. Translated by Eleanor Oshry. Our Air-Ace Would, by Leonard O. Packard, Head of the Department of Geography, Teachers College, of the City of Boston, Bruce Overton, formerly of the Male High School, Louisville, Kentucky, and Ben Wood Columbia College, Columbia University. Organic Chemistry for the Laboratory, by C. W. Porter and T. D. Stewart Vital Mathematics, by Edwin Brown Allen, Head of The Department of Mathematics, Rensselaer Polytechnic Institute, Troy, N. Y., Dis Maly, Instructor in Mathematics, Rensselaer Polytechnic Institute, and S. Herbert Starkey, Jr., Head of Mathematics Department, Madison High School, Madison, N. J. Plane and Spherical Trigonometry, by William C. Brenke, University of Nebraska. Spherical Trigonometry With Tables, by Donald H. Ballou, Ph.D. Assistant Professor of Mathematics, Middlebury College, and Frederick H. Steen, Associate Professor of Mathematics, Allegheny College. Riddles in Mathematics, A Book of Paradoxes, by Eugene P. Northrop. Mathematics For Mariners, by Chester E. Dimick, Captain USGG; and Cuthbert C. Hurd, Lieutenant, USCGR Basic Mathematics, by Paul H. Daus, Professor of Mathematics, University of California, Los Angeles; John M. Gleason, Assistant Professor of Mathematics, San Diego State College, San Diego; and William M. Whyburn, Professor of Mathematics and Educational Supervisor, ESMWT, University of California, Los Angeles. Biology and Man, by Benjamin C. Gruenberg, Consultant of Social Security; Formerly Chairman, Biology Departments, Commercial and Julia Richman High Schools, New York City; and N. Eldred Bingham, Horace Mann-Lincoln School Elements of Biology, by Perry D. Strausbaugh, Professor of Botany, West Virginia University and Bernal R. Weimer.     

关于广义Thue－Mahler方程的解数

设ａ，ｂ是非零整数，ｐ１，…，ｐｒ是不同的素数，Ｐ＝｛±｜ｍ１，…，ｍｒ是非负整数｝．设Ｋ是ｎ（ｎ≥３）次代数数域，α１，…，αｍ∈ｋ（１＜ｍ＜ｎ），△（α１，…，αｍ）是α１，…，αｍ的判别式，ｆ（ｘ１，…，ｘｍ）＝αＮｋ／Ｑ（α１ｘ１＋…＋αｍｘｍ）∈ｚ［ｘ１，…，ｘｍ］．本文证明了：当ｆ（ｘ１，…，ｘｍ）非退化且Ｐｉ△（α１，…，αｍ）（ｉ＝１，…，ｒ）时，方程ｆ（ｘ１，…，ｘｍ）＝ｂｙ，ｘ１，…，ｘｍ∈ｚ，ｇｃｄ（ｘ１，…，ｘｍ）＝１，ｙ∈Ｐ至多有（４Ｓｄ２）（Ｓｄ）组解（ｘ１，…，ｘｍ，ｙ），其中ｄ＝ｎ！，Ｓ＝ｒ＋ω是ｂ的不同素因数的个数，ｈＡ是Ｋ的类数．     

A fully invariant ideal of alternative algebras

Let ϕ be an associative commutative ring with 1, containing 1/6, and A be an alternative ϕ-algebra. Let D be an associator ideal of A and H a fully invariant ideal of A, generated by all elements of the form h(y, z, t, x, x)=[{[y, z], t, x}-, x]+[{[y, x], z, x}-, t], where [x, y]=xy−yx, {x, y, z}-=[[x, y], z]−[[x, z], y]+2[x,[y, z]]. Here we consider an ideal Q=H∩D and prove that Q⁴=0 in the algebra A. If A is unmixed, then HD=0, DH=0, and Q²=0 in particular. If A is a finitely generated unmixed algebra, then the ideal H lies in its associative center and Q=0. It follows that any finitely generated purely alternative algebra satisfies the identity h(y,z,t,x,x)=0. We also show that a fully invariant ideal H₀ of the unmixed algebra A, generated by all elements of the form h(x, z, t, x, x), lies in its associative center and H₀∩D=0. Consequently, every purely alternative algebra satisfies the identity h(x,z,t,x,x)=0. Translated fromAlgebra i Logika, Vol. 36, No. 3, pp. 323–340, May–June, 1997.     

Periodic solutions of second-order systems with one-sided restrictions to the growth of the right-hand side with respect to the first derivative

For the system a periodic solution exists if for each i one of the following inequalities holds: $$\begin{array}{*{20}c} {f_i (t,u_1 , \ldots ,u_n ,p_1 , \ldots ,p_n ) \leqslant A(p_1 , \ldots ,p_{i - 1} )p_i^2 + B(p_1 , \ldots ,p_{i - 1} ),} \\ {f_i (t,u_1 , \ldots ,u_n ,p_1 , \ldots ,p_n ) \geqslant - A(p_1 , \ldots ,p_{i - 1} )p_i^2 - B(p_1 , \ldots ,p_{i - 1} ),} \\ {f_i (t,u_1 , \ldots ,u_n ,p_1 , \ldots ,p_n )signp_i \leqslant A(p_1 , \ldots ,p_{i - 1} )p_i^2 + B(p_1 , \ldots ,p_{i - 1} ),} \\ {f_i (t,u_1 , \ldots ,u_n ,p_1 , \ldots ,p_n )signp_i \geqslant - A(p_1 , \ldots ,p_{i - 1} )p_i^2 - B(p_1 , \ldots ,p_{i - 1} ),} \\ {f_i (t,u_1 , \ldots ,u_n ,p_1 , \ldots ,p_n )signu_i \geqslant - A(p_1 , \ldots ,p_{i - 1} )p_i^2 - B(p_1 , \ldots ,p_{i - 1} )} \\ \end{array} $$ for α(t)≤u≤β(t). Here α(t) and β(t) are the lower and upper vector functions for system (1) and the periodic conditions; A≥0, B≥0. Bibliography: 1 titles.     

广义Fibonacci序列的有限和

通过定义广义的Fibonacci序列{Hn,m}:Hn,m=p1Hn-1,m+p2Hn-2,m+…+pmHn-m,m,其中H1,m=a1,H2,m=a2,…,Hm,m=am,n≥m+1,m 2.给出了序列{Hn,m}一些有限和Un,m=∑ni=1Hi,m、U′n,m=∑ni=1(-1)iHi,m、Vn,m=∑ni=1iHi,m、Vn′,m=∑ni=1(-1)iiHi,m的计算公式.     

赋予hit—or-miss拓扑超空间动力系统的拓扑熵

设（X,d,f）为拓扑动力系统,其中X为局部紧第二可数Hausdorff空间,d为紧型度量,f为完备映射,用2^x和f分别表示由X的所有非空闭子集和所有闭子集构成的集族,（2^x,ρ,2^f）和（f,ρ,2^f）为由（X,d,f）诱导的赋予hit—or—miss拓扑的超空间动力系统．本文研究了h（X,d,f）和h（2^...     

关于阶乘的Erds-Stewart猜想

摘要:设n是正整数;P_0=1,P_i(i=1,2,…)是第i个素数.本文证明了:方程 n!+1=P_k~aP_(k+1)~b,P_(k-1)0,b>0,仅有解(n,P_k,P_(k+1),a,b)=(1,1,2,1,0),(2,3,5,1,0),(3,5,7,0,1),(4,5,7,2,0),(5,7,11,0,2).上述结果证实了Erds和Stewart提出的一个猜想.     

Characterization of the core in full domain marriage problems

In this paper, we study the core of two-sided, one-to-one matching problems. First, in a model in which agents have strict preferences over their potential mates and are allowed to remain single, we characterize the core as the unique solution that satisfies individual rationality, Pareto optimality, gender fairness, consistency, and converse consistency. Next, in a model that relaxes the constraint that agents have strict preferences over their potential mates, we show that no solution exists that satisfies Pareto optimality, anonymity, and converse consistency. In this full domain, we characterize the core by individual rationality, weak Pareto optimality, monotonicity, gender fairness, consistency, and converse consistency.     

Ma jorization Results and Coefficients Bounds for a Class of Univalent Functions Asso ciated with Operator

In this paper we introduce a new general subclass n,g ∑ a,λ(A, B,α) of univalent func-tions related the known integral operator and differential operator. Some majorization re-sults for n,g ∑ a,λ(A, B, 1) as well as the other functions are given. Furthermore, we find the coefficients bounds on|a2|and|a3|for functions in?n,g ∑ a,λ(A1, B1, A2, B2,α1,α2), which is the bi-univalent functions defined by n,g ∑ a,λ(A, B,α) and subordination. By giving specific values of the parameters of our main results, several(known or new) consequences of main results are also discussed.     

中心静脉血氧饱和度对心肺复苏后血流动力学不稳定患者容量反应性的预测价值

目的 分析影响子宫腺肌病发病的影响因素,寻找子宫腺肌病的防治及干预措施,从而减少子宫腺肌病的发病风险。方法 采用病例对照研究的方法,以128 例患者为实验组,同期入院的非子宫腺肌病的患者256 例为对照组。收集可能影响子宫腺肌病的影响因素,包括一般情况、生育及月经情况、生物学指标情况。采用SPSS18.0 统计软件进行统计分析,先行单因素因素分析,根据单因素分析有统计学差异的因素进行多因素logistic 回归分析。结果 单因素分析发现年龄、职业、早产、人工流产次数、剖宫产、痛经、ER、PR 和CA125 阳性为危险因素。多因素logistic 回归分析证实年龄、职业、早产、剖宫产、人工流产次数、FR 阳性、ER 阳性和CA125 阳性为子宫腺肌病的影响因素。结论 年龄、职业、早产、剖宫产、人工流产次数、FR 阳性、ER 阳性和CA125阳性为子宫腺肌病的影响因素,对其危险因素进行干预,可为防治方式提供参考。