In 2020, Roger Baker proved a result on the exceptional set of moduli in prime number theorem for arithmetic progressions following kind. Let $\mathcal {S}$ be pairwise coprime $q\le x^{9/40}$. Then primes $l\le x$ distribut

We examined mitochondrial DNA (COI) variability and distribution of Stereotydeus spp. in Victoria Land and the Transantarctic Mountains, and constructed Neighbour Joining (NJ) and Maximum Likelihood (ML) phylogenetic trees using all publicly available COI sequences for the three Stereotydeus species present (S. belli, S. mollis and S. shoupi). We also included new COI sequences from Miers, Mars...

this research proposes a methodology for ranking decision making units byusing a goal programming model.we suggest a two phases procedure. in phase1, by using some dea problems for each pair of units, we construct a pairwisecomparison matrix. then this matrix is utilized to rank the units via the goalprogramming model.

Even though the logratio methodology provides a range of both generic, mostly exploratory, and purpose-built coordinate representations compositional data, simple pairwise logratios are preferred by many for multivariate analysis in geochemical practice, principally because their simpler interpretation. However, systems that incorporate them predominantly oblique, resulting conceptual practical...

A number of space-time codes have been recently proposed for the quasi-static, flat-fading, multipleantenna wireless channel with coherent receiver. In this paper we will focus on design of space-time codes that are linear in the scalar input symbols. We provide design criteria that take into account both the error probability and the channel capacity. We consider the error probability via the ...

We give a new asymptotic upper bound on the size of a code in the Grassmannian space. The bound is better than the upper bounds known previously in the entire range of distances except very large values. the problem of estimating the number of planes whose pairwise distances are bounded below by some given value δ, for a suitably defined distance function d(p, q). This problem has attracted att...

SVM-Pairwise was a major breakthrough in remote homology detection techniques, significantly outperforming previous approaches. This approach has been extensively evaluated and cited by later works, and is frequently taken as a benchmark. No known work however, has examined the gap penalty model employed by SVM-Pairwise. In this paper, we study in depth the relevance and effectiveness of SVM-Pa...

In classical coding theory, different types of extendability results of codes are known. A classical example is the result stating that every (4, q − 1, 3)-code over an alphabet of order q is extendable to a (4, q, 3)-code. A constant dimension subspace code is a set of (k− 1)-spaces in the projective space PG(n− 1, q), which pairwise intersect in subspaces of dimension upper bounded by a speci...