The Polynomial Analogue of a Theorem of Rényi

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

On the $s^{th}$ Derivative of a Polynomial-II

The paper presents an $L^{r}-$ analogue of an inequality regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle of arbitrary radius but greater or equal to one. Our result provides improvements and generalizations of some well-known polynomial inequalities.

?-Independent and Dissociate Sets on Compact Commutative Strong Hypergroups

In this paper we define ?-independent (a weak-version of independence), Kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and Sidon sets. These sets have the lacunarity or thinness property and are very useful indeed. For example Varopoulos used the Kronecker sets to prove the Malliavin theorem. In t...

Looking for an Analogue of Rice's Theorem in Circuit Complexity Theory

Rice’s Theorem says that every nontrivial semantic property of programs is undecidable. In this spirit we show the following: Every nontrivial absolute (gap, relative) counting property of circuits is UP-hard with respect to polynomial-time Turing reductions. For generators [31] we show a perfect analogue of Rice’s Theorem. Mathematics Subject Classification: 03D15, 68Q15.

Almost multiplicative linear functionals and approximate spectrum

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...