Related papers: Central set Theorem near zero

Hindman and Leader first introduced the notion of Central sets near zero for dense subsemigroups of $((0,\infty),+)$ and proved a powerful combinatorial theorem about such sets. Using the algebraic structure of the Stone-$\breve{C}$ech…

N. Hindman and I. Leader introduced the set of ultrafilters 0+ on (0,1) and characterize smallest ideal of (0+,+) and proved the Central Set Theorem near zero. Recently Polynomial Central Set Theorem has been proved by V. Bergelson, J. H.…

In [B] Beiglb\"ock gave a Multidimension Central sets theorem. Recently, [GP] extended this result for polynomials. They proved the Multidimensional Polynomial Central sets theorem. Earlier, Hindman and Leader introduced the near zero…

The most powerful formulation of the Central Sets Theorem in an arbitrary semigroup was proved in the work of De, Hindman, and Strauss. The sets which satisfy the conclusion of the above Central Sets Theorem are called $C$-sets. The…

There are several notions of largeness in a semigroup. N. Hindman and D. Strauss established that if $u,v \in \mathbb{N}$, $A$ is a $u \times v$ matrix with entries from $\mathbb{Q}$ and $\psi$ is a notion of a large set in $\mathbb{N}$,…

Considering any dense subsemigroup of the additive semigroup of positive real numbers and a filter associated with it as the domain of thought, various concepts of sets like sets that forces recurrence near zero, sets that contains broken…

Furstenberg introduced the notion of Central sets in 1981. Later in 1990 V. Bergelson and N. Hindman proved a different but an equivalent version of the central set theorem. In 2008 D. De, N. Hindman and D. Strauss proved a stronger version…

In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

Motivated by situations in which the removal of a zero (a.k.a., an absorbing element) from a semigroup yields a subsemigroup with another zero, sets of quasi-zeros (a.k.a., quasi-absorbing elements) are introduced as well as primitive…

Hindman and Leader first introduced the notion of semigroup of ultrafilters converging to zero for a dense subsemigroups of $((0,\infty),+)$. Using the algebraic structure of the Stone-$\breve{C}$ech compactification, Tootkabani and Vahed…

The Central sets theorem was first introduced by H. Furstenberg [F] in terms of Dynamical systems. Later Hindman and Bergelson extended the theorem using Stone-$\v{C}$ech compactification $\beta$$\mathbb{N}$ of $\mathbb{N}$. In [SY]…

The Central Sets Theorem was introduced by H. Furstenberg and then afterwards several mathematicians have provided various versions and extensions of this theorem. All of these theorems deal with central sets, and its origin from the…

The Theorems of Hindman and van der Waerden belong to the classical theorems of partition Ramsey Theory. The Central Sets Theorem is a strong simultaneous extension of both theorems that applies to general commutative semigroups. We give a…

The Central Sets Theorem near zero was originally proved by Hindman and Leader. Later a version of Central Sets Theorem was proved by De, Hindman and Strauss known to be the stronger Central Sets Theorem. Subsequently many other versions of…

It is known that there are many notions of largeness in a semigroup that own rich combinatorial properties. In this paper, we focus on partition and almost disjoint properties of these notions. One of the most remarkable results with…

The notion of almost centralizer and almost commutator are introduced and basic properties are established. They are used to study $\widetilde{\mathfrak M}\_c$-groups, i. e.groups for which every descending chain of centralizers each having…

The Central Sets Theorem, a fundamental result in Ramsey theory, is a joint extension of both Hindman's theorem and van der Waerden's theorem. It was originally introduced by H. Furstenberg using methods from topological dynamics. Later,…

The notion of Image partition regularity near zero was first introduced by De and Hindman. It was shown there that like image partition regularity over $\mathbb{N}$ the main source of infinite image partition regular matrices near zero are…

In this article, we investigate the image and preimage of the important combinatorial sets such as central sets, $C$-sets, and $J_\delta$-sets which play an important role in the study of combinatorics under certain partial semigroup…

We prove results about uniform convergence of densities in the free central limit theorem without assumptions of boundedness on the support.