for any lacunary sequence $theta = (k_{r})$, we define the concepts of $s_{theta}-$limit point and $s_{theta}-$cluster point of a sequence of fuzzy numbers $x = (x_{k})$. we introduce the new sets  $lambda^{f}_{s_{theta}}(x)$, $gamma^{f}_{s_{theta}}(x)$ and prove some inclusion relaions between these and the sets $lambda^{f}_{s}(x)$, $gamma^{f}_{s}(x)$ introduced in ~cite{ayt:slpsfn} by aytar [...

Logical Reasoning Systems derive sound conclusions from formal declarative knowledge. Such systems are usually deened by abstract rules of inference. For example, the rule of modus ponens states that given P , and \P implies Q" (usually written P ! Q), we can infer Q. Logical systems have a rich history starting with Greek syllogisms and continuing through the work many prominent mathematicians...

Graphical User Interfaces (GUIs) are composed of virtual objects, widgets, which respond to events triggered by user actions. Therefore, test inputs for GUIs are event sequences that mimic user interaction. The nature of these sequences and the values for certain widgets, such as textboxes, causes a two-dimensional combinatorial explosion. In this paper we present Barad, a GUI testing framework...

We show how the cross-disciplinary transfer of techniques from dynamical systems theory to number theory can be a fruitful avenue for research. We illustrate this idea by exploring from a nonlinear and symbolic dynamics viewpoint certain patterns emerging in some residue sequences generated from the prime number sequence. We show that the sequence formed by the residues of the primes modulo k a...

This work proposes a Markovian memoryless model for the DNA that simplifies enormously the complexity of it. We encode nucleotide sequences into symbolic sequences, called words, from which we establish meaningful length of words and groups of words that share symbolic similarities. Interpreting a node to represent a group of similar words and edges to represent their functional connectivity al...

Data compression is concerned with how information is organized in data. The size and importance of these databases will be bigger and bigger in the future; therefore this information must be stored or communicated efficiently though there are many text compression algorithms, they are not well suited for the characteristics of DNA sequences. There are algorithms for DNA compression which takes...

We characterize all the pairs of complementary non-homogenous Beatty sequences (An) n≥0 and (Bn) n≥0 for which there exists an invariant game having exactly {(An, Bn) | n ≥ 0} ∪ {(Bn, An) | n ≥ 0} as set of P-positions. Using the notion of Sturmian word and tools arising in symbolic dynamics and combinatorics on words, this characterization can be translated to a decision procedure relying only...