For each value of r ≥ 4, r even, we construct infinitely many r-regular, r-connected graphs whose cyclability is not greater than 6r − 4 if r = 0 (mod 4) and 8r − 5 if r ≡ 2 (mod 4).

Recently, Varshney and Singh [Rend. Mat. (6) 2 (1982), 219–225] have given sharper quantitative estimates of convergence for Bernstein polynomials, Szasz and Meyer-Konig-Zeller operators. We have achieved improvement over these estimates by taking moments of higher order. For example, in case of the Meyer-Konig-Zeller operator, they gave the following estimate

wherein ∥·∥ stands for sup norm. We have improved this result to

We may remark here that for this modulus of continuity ) our result cannot be sharpened further by taking higher order moments.

In this paper a new translation plane of order 81 is constructed. Its collineation group is solvable and acts on the line at infinity as a permutation group K which is the product of a group of order 5 belonging to the center of K with a group of order 48. A 2-Sylow subgroup of K is the direct product of a dihedral group of order 8 with a group of order 2. K admits six orbits. They have lengths 4, 6, 12, 12, 24, 24.

For each odd prime p this paper gives an example of a non-abelian p-group with a non-abelian automorphism group in which each automorphism is central.

A formula is given for the Möbius function of the poset Hom(P, Q) of all order-preserving maps between two finite posets P and Q. Two applications of the formula are presented.

In this paper we show that the countable sum theorem for locally-closed sets, for sheaf theoretic cohomological dimension over a given ring L, holds in all perfectly normal spaces as well as in all locally compact spaces.

Integral equations of Oseen type are first kind Fredholm equations whose kernels have a logarithmic singularity. They arise in exterior boundary value problems in fluid flow and heat transfer. Subject to the assumption of uniqueness of solutions of the parent exterior boundary value problem, solutions of the Oseen type integral equations are shown to exist.

Some time ago Barry [Proc. London Math. Soc. 12 (1962), 445–495] established the right connection between the smallest and largest values of small subharmonic functions on certain circles about the origin. The behaviour of functions extremal for this connection is investigated.

Let be analytic in the unit disc U(|z| <1) and let F(z) = (l-λ)f (Z) + λ(f(z)*h(z)) where with cn 's are known and are nonnegative, λ ≥ 0 In the present paper, using convolution methods we investigate the mapping properties of F(z) when f(z) belongs respectively to several subclasses of analytic functions with negative coefficients.

The Liapunov-Razumikhin technique has been employed to study Lp stability properties of solutions of functional differential equations of delay type where the delay becomes unbounded as t ↠ +∞. These results have been applied to investigate sufficient conditions for L2-stability of Volterra integro-differentlal equations.