BACKGROUND One of the main concerns for archaeo-metallurgists and archaeologists is to determine to what extent ancient craftsmen understood the effect of metal alloy composition and were able to control it in order to produce objects with the most suitable features. This problem can be investigated by combining compositional analyses of a high number of ancient artefacts with correlation analy...

Compositional data are nonnegative carrying relative, rather than absolute, information—these often with a constant-sum constraint on the sample values, for example, proportions or percentages summing to 1% 100%, respectively. Ratios between components of composition important since they unaffected by particular set chosen. Logarithms ratios (logratios) fundamental transformation in ratio appro...

the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

The estimation of a mean of a proportion is a frequent task in statistical survey analysis, and often such ratios are estimated from compositions such as income components, wage components, tax components, etc. In practice, the weighted arithmetic mean is regularly used to estimate the center of the data. However, this estimator is not appropriate if the ratios are estimated from compositions, ...

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...

in the present paper, we introduce the sequence space [{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},] where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. we investigate its topological properties and inclusion relations. moreover, we consider the problem of fin...

a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...

matrix metalloproteinases (mmps) are a family of neutral proteinases that are important in normal development, cellular differentiation or migration, angiogenesis, neurogenesis, wound repair, and a wide range of pathological processes such as oxidative stress and neuroinflammation. mmps have been demonstrated to increase the permeability of the blood–brain barrier (bbb) by degrading the compone...

the purpose of the present study is to introduce the sequence space[{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left| sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},]where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. the topological properties and inclusion relations of this space are studied. moreover, the prob...