A remark on a paper of B. R. Gelbaum

Summary In this paper the following generalization of a theorem by B.R. Gelbaum is proved:Let (K, d) be a compact, connected metric space. Let B denote the Borel sets of (K, d), and P be a probability measure on B with P(G)O for any nonempty open G, f, gC(K,d) independent random variables on (K,B,P) and let g satisfy the following assumption:There is an y _o such that g ^–1(y₀) is a finite nonempty set. Then f is a constant function.Examples show that the assumptions of this theorem are essential.     

A remark on a paper of J. Prada

We would like to thank the Turkish Scientific and Technical Research Council for partial support, and Prof. Dr. T. Terziolu for suggesting the problem and useful comments, and Prof. Dr. V. P. Zahariuta of drawing our attention to Fishman's result [5].     

A remark on a paper of Luca

Summary It is proved that the set of those natural numbers which cannot be written as n-Ω(n) is of positive lower density. Here Ω(n) is the number of the prime power divisors of n. This is a refinement of a theorem of F. Luca.     

A remark on the preceding paper by L. Gross

It is the purpose of this note to present a slight extension of the Perron-Frobenius type theorems in the preceding paper (Thms. 1 and 3 of [1]).     

A remark on a paper of F. Luca and A. Sankaranarayanan

We generalize a result of F. Luca and A. Sankaranarayanan by proving that the set of n for which ϕ(1) + ⃛ + ϕ(n) is squareful is of zero density. A similar statement holds for σ (n) instead of ϕ(n) and for some other multiplicative functions. Dedicated to Professor Eugenijus Manstavičius on his 60th anniversary     

A remark on the paper “elastic equilibrium of a multiply connected isotropic plate with cracks” by S. A. Kaloerov

A remark on the paper “elastic equilibrium of a multiply connected isotropic plate with cracks” by S. A. Kaloerov     

A remark on a paper of Ibukiyama and Skoruppa

It was proved by Ibukiyama and Skoruppa that the spaces J _1,m (l) of Jacobi forms of weight 1, index m and level l vanish if gcd (l,m)=1. We will show that the result holds without the gcd hypothesis.     

A remark to the preceding paper by Chernoff

It is shown that the method of Chernoff developed in the preceding paper can be modified to prove the essential self-adjointness on C₀^∞(R^m) of all positive powers of the Schrödinger operator T = ? Δ + q if q real and in C^∞(R^m) and if $\text{T ? ?a ? b ¦ x ¦}{}^2\text{on}\text{C}{}_0{}^{\mathrm{\infty }}\text{(R}{}^{\mathrm{m}}\text{)}$.     

A remark on the paper of Dwivedi

In the present paper the method of Dwivedi and Trivedi in solving the dual integral equations, has been modified by presenting a very comprehensive and lucid solution, based on the analysis suggested by Fox.