The paper aims to establish a new sharp Burkholder-type maximal inequality in Lp for a class of stationary sequences that includes martingale sequences, mixingales and other dependent structures. The case when the variables are bounded is also addressed, leading to an exponential inequality for a maximum of partial sums. As an application we present an invariance principle for partial sums of c...

The keyboard problem is an optimization problem asking how many characters can be placed into a blank document using N keystrokes. The question is representative of a larger class of output maximization problems where there is the opportunity to expand output capacity by replicating the existing output as a single unit. Here I define a generalized keyboard sequence as an integer sequence repres...

A concept of variational dimension is introduced for a random sequence with stationary increments. In Gaussian case the variational dimension in the limit coincides with the Hausdorff dimension of a proper random process. Applications of the concept are illustrated by examples of neurological data and network traffic analysis.

The Ziv-Lempel complexity is a well-known complexity measure. In our paper we consider the Ziv-Lempel complexity for p'eriodic sequences as well as for pseudorandom number sequences. Further on, we will look at i ts cryptographic significance and compare it with other complexity measures such as the linear complexity.

We investigate the complete convergence of partial sums of randomly weighted extended negatively dependent (END) random variables. Some results of complete moment convergence, complete convergence and the strong law of large numbers for this dependent structure are obtained. As an application, we study the convergence of the state observers of linear-time-invariant systems. Our results extend t...

In this article, ITS sequences of 20 species in Osmanthus were cloned and researched. It was found that length of ITS sequences ranged from 614bp to 619bp, in which ITS-1 is obviously longer than ITS-2, 5.8S of 20 species is composed of 163bp, and the percentage of G+C in ITS sequence of 20 species is 54.24%-64.56%. Alignment between ITS sequences from 20 species of Osmanthus was performed, and...

Based on the detailed hydrophobic-hydrophilic(HP) model of amino acids, we propose dual-vector curve (DV-curve) representation of protein sequences, which uses two vectors to represent one alphabet of protein sequences. This graphical representation not only avoids degeneracy, but also has good visualization no matter how long these sequences are, and can reflect the length of protein sequence....

in this paper we introduce entire sequence spaces defined by a sequence of modulus functions . we study some topological properties of these spaces and prove some inclusion relations.

as an aromatic and colorful plant of substantive taste, saffron (crocus sativus l.) owes such properties of matter to growing class of the secondary metabolites derived from the carotenoids, apocarotenoids. regarding the critical role of micrornas in secondary metabolic synthesis and the limited number of identified mirnas in c. sativus, on the other hand, one may see the point how the characte...