On a question of Arhangel'skiǐ

This paper settles a question proposed by A.V. Arhangel'skiǐ concerning the cardinality of a compact Hausdorff space and a strict bound on the character of its points.     

On a problem of Nicole Brillou?t-Belluot

We solve the problem posed by Nicole Brillou?t-Belluot (During the Forty-ninth International Symposium on Functional Equations, 2011) of determining all continuous bijections f : I → I satisfying $$f(x)f^{-1}(x) = x^2 \quad{\rm for\, every}\, x \in I,$$ where I is an arbitrary subinterval of the real line.     

On a conjecture of the Randi? index

The Randi? index of a graph G is defined as , where d(u) is the degree of vertex u and the summation goes over all pairs of adjacent vertices u, v. A conjecture on R(G) for connected graph G is as follows: R(G)≥r(G)−1, where r(G) denotes the radius of G. We proved that the conjecture is true for biregular graphs, connected graphs with order n≤10 and tricyclic graphs.     

The concept of a θ-refinable embedding

In this paper we prove a theorem concerning θ-refinable embeddings which unifies numerous results concerning θ-refinability principally by clarifying connections between spaces defined by sequences of open covers satisfying monotone type conditions and spaces defined by sequences of open covers satisfying finite intersection type conditions. We make numerous applications to spaces such as p-spaces and wΔ-spaces. Of particular interest are theorems concerning the distinction between monotone types of completeness and Čech-type completeness. A corollary of these is a characterization of complete Moore spaces as the semicomplete Moore spaces which are θ-refinably embedded in their Wallman compactifications. Some results on embeddings in H-extensions are given which elucidate the nature of Čech completeness.     

On a Theorem of Milin

Let S be class of functions f(z)=z a_2 z~2 … analytic and univalent in the unit disk D, and let 1.M.Milin proved that Theorem A. If f∈S and then where d_o(h)=1and In fact,the result is deduced from Milan′s Tauberian Theorem. Here     

On a Conjecture of Shapiro's

ＯｎａＣｏｎｊｅｃｔｕｒｅｏｆＳｈａｐｉｒｏ＇ｓ陈志国ＯｎａＣｏｎｊｅｃｔｕｒｅｏｆＳｈａｐｉｒｏ＇ｓ￥ＣｈｅｎＺｈｉｇｕｏ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ）Ａｂａｔｒａｃｔ：Ｔｈｉｓｐｒｏｂｌｅｍｗａｓ...     

On a Conjecture of Halperin

Ｏｎ　ａ　Ｃｏｎｊｅｃｔｕｒｅ　ｏｆ　ＨａｌｐｅｒｉｎＨｕａｎｇＨｕａｌｅ（黄华乐）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｃａｄｅｒｎｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ，１０００８０）Ａｂｓｔｒａｃｔ：Ｉｎ［１］，Ｈａｌｐｅｒｉｎｒａｉｓｅ...     

On a Problem of Hayman

ＯｎａＰｒｏｂｌｅｍｏｆＨａｙｍａｎＣｈｅｎＨｕａｉｈｕｉ（陈怀惠）ＦａｎｇＭｉｎｇｌｉａｎｇ（方明亮）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ，Ｊｉａｎｇｓｕ，２１００２４）Ｃ...     

On a Theorem of Drasin

D. Drasin in 1969 proved that a family of holomorphic functions is normal ifevery function in the family satisfies f' - af~3≠b, where a and b are two complexnumbers and a≠0. Now, we obtain two improvements of this criterion. Theorem 1 A family {f} of holomorphic functions is normal if every functionin {f} satisfies     

On solutions of a common generalization of the Go?a?b-Schinzel equation and of the addition formulae

Under some additional assumptions we determine solutions of the equation

f(x+M(f(x))y)=f(x)○f(y),     

On a modification of a problem of Bialostocki, Erd?s, and Lefmann

For positive integers m and r, one can easily show there exist integers N such that for every map Δ:{1,2,…,N}→{1,2,…,r} there exist 2m integers

x₁<?<x_m<y₁<?<y_m,     

On a Class of Additive Functions

ＯｎａＣｌａｓｓｏｆＡｄｄｉｔｉｖｅＦｕｎｃｔｉｏｎｓＺｈａｉｗｅｎｇｕａｎｇ（翟文广）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＳｈａｎｄｏｎｇＵｎｉｖ．，Ｊｉｎａｎ，Ｓｈｏｎｄｏｎｇ，２５０１Ｏ０）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＰａｎＣｈｅｎｇｂｉａｏＲｅｃｅｉ...     

On a Class of ��-Modules

Ukrainian Mathematical Journal - In [Int. Electron. J. Algebra, 15, 173 (2014)], Smith introduced maps between the lattice of ideals of a commutative ring and the lattice of submodules of an...     

On a Proof of Roth''''s Theorem

We denote by M_(n,m)(F) the set of all n×m matrices over the field F and by M_n(F) the set of all n×n matrices over the field F. W. E. Roth has shown the following theorem in 1952, [1]. Theorem Let A∈M_n(F),B∈M_m(F) and C∈M_(n,m)(F), then the matrix equation AX-YB=C (1) has a solution X, Y∈M_(n,m)(F) if and only if the matrices     

On a conjecture of ōshima

The set of homotopy classes of self maps of a compact, connected Lie group G is a group by the pointwise multiplication which we denote by H(G), and it is known to be nilpotent. ōshima [H. ōshima, Self homotopy group of the exceptional Lie group G₂, J. Math. Kyoto Univ. 40 (1) (2000) 177-184] conjectured: if G is simple, then H(G) is nilpotent of class ?rankG. We show this is true for PU(p) which is the first high rank example.     

On a question of T Mizokami

In the short note, we shall give a negative answer of a question which israised in[1].     

On a Case of James' Probelm

ＯｎａＣａｓｅｏｆＪａｍｅｓ＇ＰｒｏｂｌｅｍＸｕＭａｏｚｈｉ（徐茂智）（ＰｅｋｉｎｇＵｎｉυｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１００８７１，Ｐ．Ｈ．Ｃ）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＴｕａｎＨｓｉｏｆｕＲｅｃｅｉｖｅｄＤｅｃ．１５，１９９３ＯｎａＣａｓｅｏ...     

On a Trigonometric Inequality of Vinogradov

In this paper, we improve an inequality of Vinogradov by analysis method.     

On a Class of Univalent Functions

A sharp coefficient estimate,distortion theorem and the radius of convexityare determined for the class R(α,β,A,B)of function f(z)=z+sum from n=2 to∞a_nz~n satisfyingthe condition|f’(z)-1/Bf’(z)-[B+(A-B)(1-α)]|<βfor someα,β(0≤α<1,0<β≤1)and-1≤A相似文献