For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

For d ≥ 1 and m ≥ 1, a graph has property Pd ,m if there exist at least m vertex-disjoint paths of length at most d between each pair of vertices. Property Pd ,m , which has a strong connection to wide diameter, is one way of measuring the reliability of a network. In this article, we first examine the relationship of Pd ,m to other similar properties and then we prove several results regarding...

Program: 1. Fabrizio Durante (Free University of Bozen–Bolzano, Italy) Multivariate copulas with hairpin support 2. Piotr Jaworski (University of Warsaw, Poland) Copulas of self–similar Ito diffusions 3. Franco Pellerey (Politecnico di Torino, Italy) Univariate stochastic orders and joint stochastic orders: conditions on the copula for mutual relationships 4. Giovanni Puccetti (University of Fi...

the present note is devoted to establish some extremal results for the zeroth-order general randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

The present note is devoted to establish some extremal results for the zeroth-order general Randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

In this paper, we deal with a coupled system of nonlinear fractional differential equations, which involve the Riemann-Liouville derivatives of different fractional orders. By using the monotone iterative technique combined with the method of upper and lower solutions, we not only obtain the existence of extremal system of solutions, but also establish iterative sequences for approximating the ...

for a bounded linear operator on hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎we study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎also we show that any quasinilpotent operator $t$ has an hypernoncyclic vector‎, ‎and so $t$ has a nontrivial hyperinvariant subspace‎.

Orderings of one sort or another arise naturally whenever there is a notion of size or precedence among objects in a musical space. Paying attention to the order properties of the space can lead to new musical insights. In this paper we study two musical orders that illustrate this point. In the first, we show that many of the most familiar chord and scale types in Western music appear as extre...

The statistical significance of gapped local alignments is characterized by analyzing the extremal statistics of the scores obtained from the alignment of random amino acid sequences. By identifying a complete set of linked clusters, "islands," we devise a method which accurately predicts the extremal score statistics by using only one to a few pairwise alignments. The success of our method rel...