A remark on the irregularity complex

A Remark on Irregularity of the ∂-neumann Problem on Non-smooth Domains

It is an observation due to J.J. Kohn that for a smooth bounded pseudoconvex domain Ω in C there exists s > 0 such that the ∂-Neumann operator on Ω maps W s (0,1)(Ω) (the space of (0, 1)-forms with coefficient functions in L -Sobolev space of order s) into itself continuously. We show that this conclusion does not hold without the smoothness assumption by constructing a bounded pseudoconvex dom...

A remark on the means of the number of divisors

‎We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$‎, ‎where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎Also‎, ‎we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.

A short remark on the result of Jozsef Sandor

It is pointed out that, one of the results in the recently published article, ’On the Iyengar-Madhava Rao-Nanjundiah inequality and it’s hyperbolic version’ [3] by J´ozsef S´andor is logically incorrect and new corrected result with it’s proof is presented.

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

A Remark on Sums of Squares of Complex Vector Fields

Let {Zj} be a finite collection of vector fields, with smooth complex-valued coefficients, defined in an open subset U of Euclidean space. Let Z∗ j be the formal adjoint of Zj , with respect to the Hilbert space structure L2 associated to some measure with a smooth nonvanishing density. Consider the operator L = ∑ j Z ∗ jZj, which we shall refer to as a sum of squares. L is said to be hypoellip...