A note on a problem of Erdös and Hajnal

In [5], Erdös and Hajnal formulate the following proposition, which we shall refer to as Φ: If ? is an order-type such that $\text{|?| = ω}{}_2\text{but}\text{ω}{}_2\text{, ω}{}_2{}^1\text{? ?}$, there is ψ ? ?, |ψ| = ω₁, such that $\text{ω}{}_1\text{, ω}{}_1{}^1\text{? ψ}$. In [2], we showed that if V = L, then ?Φ. We do not know if the assumption V = L can be weakened to CH, or if, in fact, Φ is consistent with CH. However, in this note we show that, relative to a certain large cardinal assumption, Φ is consistent with 2^ω = ω₂, so that ?Φ is not provable in ZFC alone. Our proof has an interesting model-theoretic consequence, which we mention at the end.     

A Tauberian Theorem for Increasing Functions of Dominated Variation

We establish a Tauberian theorem for functions of dominated variation.     

A Variation of an Extremal Theorem Due to Woodall

We consider a variation of an extremal theorem due to Woodall [12, or 1, Chapter 3] as follows: Determine the smallest even integer (₃C₁,n), such that every n-term graphic sequence = (d₁, d₂,..., d_n) with term sum () = d₁ + d₂ + ... + d_n (₃C₁,n) has a realization G containing a cycle of length r for each r = 3,4,...,l. In this paper, the values of (₃C_l,n) are determined for l = 2m – 1,n 3m – 4 and for l = 2m,n 5m – 7, where m 4.AMS Mathematics subject classification (1991) 05C35Project supported by the National Natural Science Foundation of China (Grant No. 19971086) and the Doctoral Program Foundation of National Education Department of China     

Forcing axioms and the Galvin number

Periodica Mathematica Hungarica - We study the Galvin property. We show that various square principles imply that the cofinality of the Galvin number is uncountable (or even greater than $$\aleph...     

关于Misuirewing一个定理的注记

本文改进了Misuirewing的一个定理，并给出小熵猜测的一个新的证明。     

On certain indestructibility of strong cardinals and a question of Hajnal

A model in which strongness of is indestructible under ⁺ -weakly closed forcing notions satisfying the Prikry condition is constructed. This is applied to solve a question of Hajnal on the number of elements of { |2 <}.     

关于度量加的一个定理及一个矩阵不等式

关于度量加的一个定理及一个矩阵不等式苏化明（合肥工业大学数学力学系２３０００９）§１关于度量加的一个定理Ｒ。Ａｌｅｘａｎｄｅｒ在［１］中曾提出如下猜想：设两个单形的顶点分别为ｐ＿１，Ｐ＿２，…，Ｐ＿（ｎ＋１），和构作第三个单形，使得测应当有不等式这里...     

A Remark on a Theorem by Kodama and Shimizu

We prove a characterization theorem for the unit polydisc Δ ⁿ ⊂ℂ ⁿ in the spirit of a recent result due to Kodama and Shimizu. We show that if M is a connected n-dimensional complex manifold such that (i) the group Aut (M) of holomorphic automorphisms of M acts on M with compact isotropy subgroups, and (ii) Aut (M) and Aut (Δ ⁿ ) are isomorphic as topological groups equipped with the compact-open topology, then M is holomorphically equivalent to Δ ⁿ .      

A Note on a Theorem of Horst Sachs

In this note, we present an apparently new and rather short proof of a celebrated theorem of Horst Sachs characterizing bipartite finite graphs in term of their eigenvalue spectrum. Moreover, the simplicity of the proof allows us to establish this theorem and related results as a special instance of much more general assertions regarding the spectral theory of compact graphs. Finally, some intriguing possible generalizations to locally finite, yet not compact graphs suggested by Horst Sachs are discussed in the last section.Received December 8, 2003     

极限的一个定理及其应用

给出了一个极限定理,能较好地解决一类特殊“和式”的极限问题.同时,利用对数函数的性质,又能够用来解决一些“积式”的极限.     

A New Morera-Type Theorem on a Unit Disk

We present a new Morera-type theorem on a unit disk.     

A Note on a Continuous Approximate Selection Theorem

The purpose of this note is to show a new generalization of the continuous approximate selection theorem of F. Deutsch and P. Kenderov (1983, SIAM J. Math. Anal.14, 185–194).     

A Note on a Theorem of H. Cartan

We prove that if D C is a bounded domain with real analytic boundary, and D is either pseudoconvex or it satisfies condition (R), then the compact open topology in Aut(D), the group of holomorphic automorphisms of D is the topology of uniform convergence on D.     

d-集上的Besov空间的一个迹定理

In the paper we give a trace theorem of Besov spaces Bαp,p(Rn) on a d-set.It is a kind of extension of related results of Jonsson and Wallin,which has important applications on PDE theory.     

A Note on a Theorem of J. Szabados

In this note, we establish a companion result to the theorem of J. Szabados on the maximum of fundamental functions of Lagrange interpolation based on Chebyshev nodes.