Related papers: Rough Statistical Convergence of Double Sequences …
Statistical convergence was introduced in connection with problems of series summation. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with…
In this paper we consider the notion of strong $I$-statistically pre-Cauchy double sequences in probabilistic metric spaces in line of Das et. al. [6] and introduce the new concept of strong $I^*$-statistically pre-Cauchy double sequences…
The purpose of this paper is to define statistically convergent sequences with respect to the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties of this statistical form of convergence.
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
We continue the study of ideal convergence for sequences $(x_n)$ with values in a topological space $X$ with respect to a family $\{F_\eta:\eta\in X\}$ of subsets of $X$ with $\eta\in F_\eta$, where each $F_\eta$ measures the allowed…
Doubly stochastic learning algorithms are scalable kernel methods that perform very well in practice. However, their generalization properties are not well understood and their analysis is challenging since the corresponding learning…
The notion of rough set captures indiscernibility of elements in a set. But, in many real life situations, an information system establishes the relation between different universes. This gave the extension of rough set on single universal…
Statistical limits are defined relaxing conditions on conventional convergence. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with other…
In this paper using a non-negative regular summability matrix $\mathcal{A}$ and a non-trivial admissible ideal $\mathcal{I}$ in $\mathbb{N}$ we study some basic properties of strong $\mathcal{A}^{\mathcal{I}}$-statistical convergence and…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
Now a days, data mining and knowledge discovery methods are applied to a variety of enterprise and engineering disciplines to uncover interesting patterns from databases. The study of Sequential patterns is an important data mining problem…
In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering…
Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct…
Mapping of spatial hotspots, i.e., regions with significantly higher rates of generating cases of certain events (e.g., disease or crime cases), is an important task in diverse societal domains, including public health, public safety,…
In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, approximation theory worked as a…
Here we have introduced the idea of rough Cauchyness of sequences in a cone metric space. Also here we have discussed several basic properties of rough Cauchy sequences in a cone metric space using the idea of Phu.
In this paper ideas of different types of convergence of a sequence of random variables in probability, namely, statistical convergence of order $\alpha$ in probability, strong $p$-Ces$\grave{\mbox{a}}$ro summability of order $\alpha$ in…
A statistical description of heavy particles suspended in incompressible rough self-similar flows is developed. It is shown that, differently from smooth flows, particles do not form fractal clusters. They rather distribute inhomogeneously…