In this paper we prove new results about the extremal structure of paths in directed graphs. Say we are given a directed graph G = (V,E) on n nodes, a set of sources S ⊆ V of size |S| = n, and a subset P ⊆ S × V of pairs (s, t) where s ∈ S, of size O(n), such that for all pairs (s, t) ∈ P , there is a path from s to t. Our goal is to remove as many edges from G as possible while maintaining the...

Given a domain $I\subset\Bbb{C}$ and an integer $N>0$, function $f: I\to\Bbb{C}$ is said to be {\it entrywise positivity preserving} on positive semidefinite $N\times N$ matrices $A=(a_{jk})\in I^{N\times N}$, if the application $f[A]=(f(a_{jk}))$ of $f$ $A$ for all such $A$. Such preservers in dimensions have been classified by Schoenberg Rudin as being absolutely monotonic. In fixed dimension...

background: the objective of this study is to establish raman signatures from pure cultures of different candida species using raman spectroscopy (rs) and use these signatures for rapid identification of unknown candida species. methods: pure cultures of five candida species were evaluated using rs to build a limited signature library. ‘raman processing’ (rp) software was used for principal com...

The realities of the modern city dictate conditions for expansion human habitats. A number industrial buildings erected in last century occupies large territories, often center cities. This causes environmental and aesthetic problems. In historical centers cities Kazakhstan, problem zones renovation is especial urgent. At same time, it necessary to consider economic feasibility such activities,...

Water is unique in its role as a life preserver. It is important to all members of a society. However, if one is looking for quality data in India to make data-driven decisions, one is lost. This is surprising given that there is a rich history of data collection in the country and looks forward to adopting real-time water sensing in a big way. In this paper, we first explore issues around data...

In this paper we investigate the structure of maps on classes of Hilbert space operators leaving the determinant of linear combinations invariant. Our main result is an infinite dimensional version of the famous theorem of Frobenius about determinant preserving linear maps on matrix algebras. In that theorem of ours, we use the notion of (Fredholm) determinant of bounded Hilbert space operators...