On a result of M. Kanda

Probability Theory and Related Fields -     

A note on a result by W. Hoeffding

The Hoeffding assertion about weak convergence of the distributions of the expected values of the order statistics based on i.i.d. observations is extended to the case of dependent sample data.     

On a fixed point theorem of Kirk

W.A. Kirk [J. Math. Anal. Appl. 277 (2003) 645-650] first introduced the notion of asymptotic contractions and proved the fixed point theorem for this class of mappings. In this note we present a new short and simple proof of Kirk's theorem.     

On a conjecture of W.E. Clark and M.E.H. Ismail

W.E. Clark and M.E.H. Ismail conjectured the inequality

On a problem of A. M. Vasil'ev

Vilnius Pedagogical University, Studentu 39, 2034 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 34, No. 3, pp. 388–407, July–September, 1994.     

On a result of G. Brosch

We prove a uniqueness theorem for non-constant meromorphic functions f, g which share three values 0, 1, ∞ and f−a, g−b share the value 0 for a,b∉{0,1,∞}. Our theorem improves a result of G. Brosch.     

On a result of R. R. Hall

An upper bound for the mean value of a non-negative submultiplicative function by R. R. Hall [3] is sharpened and generalised. Hall's inequality implies a certain rather accurate upper sieve estimate, and this aspect of Hall's result is exploited in deriving good lower bounds for π(x) via the sieve.     

Remarks to a new result of P. L. Ul'yanov

P. L. Ul'yanov has recently proved a new type of equivalence theorems in connection with the classical equivalence theorem by A. Plessner. Making use of certain results proved by us more than thirty years ago, we extend Ul'yanov's results into more general equivalence theorems.     

On a result of C. Mueller and E. Perkins

Summary. The equation du=(au”+bu′+cu) dt+νu ^γ W(dx,dt) is considered for γ∈(0,1). It is proved that u(t,·) has compact support for all t≥0 if u(0,·) does. This result extends a result of C. Mueller and E. Perkins who considered the case a=1,b=c=0. The proof does not use the nonstandard analysis unlike the one by C. Mueller and E. Perkins. Received: 6 September 1996 / In revised form: 12 February 1997     

A note on a result by M. Bognár concerning the Hahn--Mazurkiewicz Theorem

Summary In this note we use Theorem 2.4 in<span lang=EN-US style='font-size:10.0pt;mso-ansi-language:EN-US'>[1]to give a very short proof of a recent result due to M. Bognár (Theorem A in [3]). We also prove that Bognár's result is in fact equivalent to the classical Hahn-Mazurkiewicz Theorem. Finally we give generalizations in the non-compact setting.     

On a conjecture of W. Veys

In this work we show a singular K3 surface S of such that producing a counter-example to a conjecture of Veys. Received: 22 October 1999     

On a result of Avramov

We obtain some consequences in Commutative Algebra of a result of L.L. Avramov concerning deviations of local rings.     

On a result of Riemenschneider

O. Riemenschneider has recently exhibited a class of normal 2-dimensional analytic singularities for which some deformations of the minimal resolution cannot be blown down to deformations of the singularity. In this note we identify the obstructions to doing so, using algebraic techniques introduced by Schlessinger and the author.Partially supported by National Science Foundation under grant GP 32843 to Columbia University.