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.     

半质环的交换性条件

本文对满足可变恒等式的半质环在某种有界条件下给出了一个判断环Ｒ交换性的简便准则，使文献［２－２７］中所有相应结果均成为其直接推论．此外，对不限有界的情况，也得到较为广泛的结论．     

Uniform meyer solution to the three dimensional cauchy problem for laplace equation

We consider the three dimensional Cauchy problem for the Laplace equation uxx(x,y,z)+ uyy(x,y,z)+ uzz(x,y,z) = 0, x ∈ R,y ∈ R,0 z ≤ 1, u(x,y,0) = g(x,y), x ∈ R,y ∈ R, uz(x,y,0) = 0, x ∈ R,y ∈ R, where the data is given at z = 0 and a solution is sought in the region x,y ∈ R,0 z 1. The problem is ill-posed, the solution (if it exists) doesn't depend continuously on the initial data. Using Galerkin method and Meyer wavelets, we get the uniform stable wavelet approximate solution. Furthermore, we shall give a recipe for choosing the coarse level resolution.     

Toader型平均与几种经典平均的确界

给出了最佳参数α_1,α_2,α_3,β_1,β_2,β_3∈R,使得双向不等式α_1Q(a,b)+(1-α_1)G(a,b)0且a≠b成立.其中A(a,b)=(a+b)/2,H(a,b)=2ab/(a+b),G(a,b)=(ab)~(1/2),Q(a,b)=((a~2+b~2)/2)~(1/2),C(a,b)=(a~2+b~2)/(a+b),T(a,b)=2/π∫_0~(π/2)(a~2cos~2t+b~2sin~2)~(1/2)tdt分别是两个正数a和b的算术平均,调和平均,几何平均,二次平均,反调和平均和Toader平均.     

BOOK REVIEWS

Book reviewed in this article: The Origin of the Carolina Bays , by Douglas Johnson. A Guide to Naval Aviation , by Lt. Wallace W. Elton, USNR; Lt. Alfred H. Driscoll, USNR; Lt. Robert N. Burchmore, USNR; and Lt. Gray B. Larkum, USNR. Mathematics for Navigators , by Delwyn Hyatt, Commander, USN, (Ret.) and Bennett M. Dodson, Commander, USNR. The Text -Activity Books . Elementary Topography and Map Reading , by Samuel L. Greitzer. Earth Science , A Physiography, by Gustave L. Fletcher. Shopwork , by Edward C. Wicks, Instructor of Industrial Arts, Morristown High School, New Jersey, John Poljacik, Jr., Instructor of Industrial Arts, Morrislown High School, and John Ellberg, author of Tales of A Rambler. Shop Practice , by William J. Kennedy. Plane Trigonometry and Statics , by Norman Miller. The Story of Flying , by Archibald Black. Electricity for Everyone , by Joseph R. Lunt, late Professor of Science at Rhode Island College of Education, and William T. Wyman. Air Navigation for Beginners , A Ground School Primer for Aerial Navigators , by Scott G. Lamb, B.S., M.S. Essentials of Algebra (Complete Second Year Course ), by Walter W. Hart. Solid Geometry , by F. Eugene Seymour, Supervisor of Mathematics, New York State Department of Education, and Paul James Smith, Head of Department of Mathematics, East High School, Rochester, New York. Modern Science Series , by Charles E. Dull. Organic Chemistry , by C. W. Porter and T. D. Stewart. Man's Physical Universe , by Arthur Talbot Bawden. Man and His Physical Universe , by Frank Covert, Jean Ezra Clarence Harrah, and Fred Louis Herman. Elementary Electricity , by Edgar P. Slack.     

(3,2,1)-共轭r-正交拉丁方的存在性

如果两个v阶拉丁方L和M的重叠产生恰好r个不同的有序对,则称L和M是r-正交的.如果L还是M的(i,j,k)-共轭,则称L是(i,j,k)-共轭r-正交的,简记为(i,j,k)-r-COLS(v)((i,j,k)-r-conjugate orthogonal Latin square of order v),其中{i,j,k}={1,2,3}.本文研究(3,2,1)-r-COLS(v)的存在性问题.对于v 23,除去少数几个可能的例外值,本文给出关于(3,2,1)-r-COLS(v)的几乎完整的解.对于v23,如果r∈[v,v2]\{v+1,v+2,v+3,v+5,v+7,v2 1},除去可能的例外r=v2 3,都存在(3,2,1)-r-COLS(v).由于(3,2,1)-r-COLS(v)的存在性与(1,3,2)-r-COLS(v)的存在性是等价的,本文得到关于(1,3,2)-r-COLS(v)的同样结论.     

圈的$L(d_1,d_2,\ldots,d_t)$-数$\lambda(C_n;d_1,d_2,\ldots,d_t)$

An L（d0,d2,...,dt）-labeling of a graph G is a function f from its vertex set V（G） to the set {0,1,..., k} for some positive integer k such that If（x） - f（y）l ≥di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L（d1,d2,...,dt）-number λ（G;d1,d2,... ,dt） of G is the smallest integer number k such that G has an L（d1,d2,...,dr）- labeling with max{f （x）｜x ∈ V（G）} = k. In this paper, we obtain the exact values for λ（Cn; 2, 2, 1） and λ（Cn; 3, 2, 1）, and present lower and upper bounds for λ（Cn; 2,..., 2, 1,..., 1）     

Book reviews

L.N. TREFETHEN and D. BAU, III,Numerical Linear Algebra,SIAM, Philadelphia, 1997G.-C. ROTA,Indiscrete Thoughts,Birkhäuser, Boston, 1997D.E. KEYES, A. SAMEH and V. VENKATAKRISHNAN, eds.Parallel Numerical Algorithms,Kluwer, Dordrecht, 1997A. KIRSCH,An Introduction to the Mathematical Theory of Inverse Problems,Springer, New York, 1996L.F. SHAMPINE, R.C. ALLEN, Jr. and S. PRUESS,Fundamentals of Numerical Computing,Wiley, New York, 1997C.W. UEBERHUBERNumerical Computation, 2 vols.Springer, Berlin, 1997W.G. McCALLUM et al.Multivariate Calculus,Wiley, New York, 1997ZHI-QUAN LUO, JONG-SHI PANG and D. RALPH,Mathematical Programs with Equilibrium Constraints,Cambridge University Press, Cambridge, 1996P.R. POPIVANOV and D.K. PALAGACHEV,The Degenerate Oblique Derivative Problem for Elliptic and Parabolic Equations,Akademie Verlag, Berlin, 1997     

Codimension-Two Bifurcation,Chaos and Control in a Discrete-Time Information Diffusion Model

In this paper, we present a discrete model to illustrate how two pieces of information interact with online social networks and investigate the dynamics of discrete-time information diffusion model in three types: reverse type, intervention type and mutualistic type. It is found that the model has orbits with period 2, 4, 6, 8, 12, 16, 20, 30, quasiperiodic orbit, and undergoes heteroclinic bifurcation near 1:2 point, a homoclinic structure near 1:3 resonance point and an invariant cycle bifurcated by period 4 orbit near 1:4 resonance point. Moreover, in order to regulate information diffusion process and information security, we give two control strategies, the hybrid control method and the feedback controller of polynomial functions, to control chaos, flip bifurcation, 1:2, 1:3 and 1:4 resonances, respectively, in the two-dimensional discrete system.     

Non-Gaussian analysis and hypergroups

NANU Mathematical Institute, Kiev, Ukraine and MCS University, Lublin, Poland; NANU Mathematical Institute, Kiev, Ukraine and Bielefeld University, Germany. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 3, pp. 51–55, July–September, 1995.     

BOOK REVIEW

Life Cycles: Reflections of an Evolutionary Biologist, John Tyler Bonner, Princeton University Press, 41 William Street, Princeton, New Jersey, 08540, 1993, 209 pp., or UK: Princeton University Press, Chichester, West Sussex, ISBN 0-691-03319-6     

Exclusive traveling waves for competitive reaction-diffusion systems and their stabilities

We study the existence, uniqueness and asymptotic behavior, as well as the stability of a special kind of traveling wave solutions for competitive PDE systems involving intrinsic growth, competition, crowding effects and diffusion. The traveling waves are exclusive in the sense that as the variable goes to positive or negative infinity, different species are close to extinction or carrying capacity. We perform an appropriate affine transformation of the traveling wave equations into monotone form and construct appropriate upper and lower solutions. By this means, we reduce the existence proof to application of well-known theory about monotone traveling wave systems (cf. [A. Leung, Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering, MIA, Kluwer, Boston, 1989; J. Wu, X. Zou, Traveling wave fronts of reaction-diffusion systems with delay, J. Dynam. Differential Equations 13 (2001) 651-687] and [I. Volpert, V. Volpert, V. Volpert, Traveling Wave Solutions of Parabolic Systems, Transl. Math. Monogr., vol. 140, Amer. Math. Soc., Providence, RI, 1994]). Then, by using spectral analysis of the linearization over the profile, we prove the orbital stability of the traveling wave in some Banach spaces with exponentially weighted norm. Furthermore, we show that the introduction of some weight is necessary in the sense that, in general, traveling wave solutions with initial perturbations in the (unweighted) space C₀ are unstable (cf. [I. Volpert, V. Volpert, V. Volpert, Traveling Wave Solutions of Parabolic Systems, Transl. Math. Monogr., vol. 140, Amer. Math. Soc., Providence, RI, 1994] and [D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., vol. 840, Springer-Verlag, New York, 1981]).     

Book reviews

d'Alessandro, P., A Conical Approach to Linear Programming Scalar and Vector Optimization Problems, Gordon and Breach Science Publishers, Australia Canada China France Germany India Japan Luxembourg Malaysia The Netherlands Russia Singapore Switzerland Thailand United Kingdom 1997, 312 pp., ISBN 90- 5699-031-4.

Fang, S.-C., Rajasekera, J. R. and Tsao, H. S. J., Entropy Optimization and Mathematical Programming, Kluwer's International Series. Kluwer Academic Publishers, Boston London Dordrecht, 1997, pp. 343, US $120.00; ISBN 0-7923-9939-0.

Golshtein, E. G. and Tretyakov, N. V., Modified Lagrangians Monotone Maps in Optimization, John Wiley & Sons, New York Chicester Brisbane Toronto Singapore 1996,438 pp., £55.00, ISBN 0-471-54821-9.

Hoffmann, K.-H., Leugering, G. and Troltzsch, F. (Eds.), Optimal Control of Partial Differential Equations, International Confa-ence in Chemnitz, Germany, April 20-25, 1998; International Series of Numerical Mathematics ISNM, Vol. 133, Birkhauser Verlag AG, Basel*Boston-Berlin 1999, viii+323 pp., DM 188.00, ISBN 3-7643- 6151-4.     

Book Vignettes

Freeman, Ira M., Light and Radiation. Calder, Nigel, Violent Universe: An Eyewitness Account of the New Astronomy. Glasstone, Samuel, The Book of Mars. Randall, Charles A. Jr., Extra-Terrestrial Matter. Willerding, Margaret F. and Hoffman, Stephen, Modern Intermediate Algebra. Cohen, David, O'Neill, Brian J., and Bailey, John E., Geology: Rocks and Mincrals. Are You Unique? Careers In—Accounting, Banking, Business, Economics, Engineering, Finance Law, Mathematics, Other Professions. 0–319–339, U. S. Government Printing Office, Washington, D. C. 1969.     

逐次渐近Φ-强半压缩型有限算子簇的多步迭代程序的收敛性

对一致广义Lipschitz连续的逐次渐近Φ-强半压缩型有限算子簇,研究了一致光滑Banach空间中具误差的修正多步Noor迭代序列强收敛于该算子簇的公共不动点问题.作为所得结果的应用,得到了2007年Huang在相同空间框架中所建立的逼近具有有界值域的逐次Φ-强伪压缩算子的不动点具误差的修正Mann迭代和具误差的修正Ishikawa迭代两者的收敛是等价的这一结果,而且所用的方法不同于Huang.同时还改进和推广了Rhoades和Soltuz,Huang,Bu和Noor,Huang和Bu,Su,Yao,Chen和Zhou,Liu,Kim,Kim,Liu,Ni和Xu等人的近期相应结果.     

关于群中乘积元素的阶

讨论群中两个元素a,b的阶不相等时其乘积ab的阶的一类计算问题.设ㄧaㄧ=m,ㄧ bㄧ=n,若(m,n)=1,且存在k∈N使a=bk,则有ㄧabㄧ=mn/d1d2,其中d1=(m,k+1),d2=(n,k+1).若m≠n,ab=ba,且(m,n)ㄧm/(m,n),或(m,n)ㄧn/(m,n),则有ㄧabㄧ=[m,n].     

Market efficiency of the Post Communist East European stock markets

The stock markets from Post Communist East-European Countries are still considered highly speculative. For this reason, the previously performed tests often infirmed the efficient market hypothesis. However, especially in the past years, different studies revealed an improvement in the level of efficiency. In this context, our paper has tested the predictability of returns based on past records (as a proxy for the weak-form efficiency) for the market index and the most important stocks of 20 East European former communist countries: Bosnia-Herzegovina, Bulgaria, Croatia, Czech Republic, Estonia, Georgia, Hungary, Kazakhstan, Latvia, Lithuania, Former Yugoslav Republic of Macedonia, Moldova, Montenegro, Poland, Romania, Russia, Serbia, Slovakia, Slovenia, and Ukraine, for the period January 2008–December 2010, a period of financial crisis for most of these countries. Various methods for testing were used (unit root tests, runs test, variance ratio test, filter rules test and the January Effect). The tests have revealed that for some assets the efficient market hypothesis cannot be rejected. However, the results have shown that there are serious doubts concerning the stock market efficiency for all the countries in the analyzed period. Moreover, heterogeneity between the results for different countries was revealed. A higher level of market efficiency can suggest to decision-makers the use of passive portfolio management techniques while a lower level of efficiency implies the use of active portfolio management instruments.     

The structure of Hopf algebras

This survey considers work published between 1970 and 1990 on the algebraic aspects of Hopf theory. There are detailed discussions of the properties of antipodes, group and primitive elements, integrals, crossed products, Galois theory, Lie coalgebras, the category of Hopf algebras, quantum groups, etc.Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 29, pp. 3–63, 1991.     

De Bruijn-Good图的自同构和同态

<正> 所谓n级de Bruijn-Good图G_n是一个有向图:它有2~n个顶点,分别用2~N个二值n元素组 (a_1,a_2,…,a_n),a_i=0或1,来标记;它有2~(n+1)条弧,即对于任意两个以下形状的顶点