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.

We present a first-principles study of the effects of charging and perpendicular electric fields on hydroxyl groups, both of which mediate the reduction of graphene oxide through the formation of H2O and H2O2. Starting with an investigation of the interaction between the hydroxyl groups and graphene, we determine the equilibrium binding geometry, binding energy, and the diffusion path with a mi...

Close coordination between leaf gas exchange and maximal hydraulic supply has been reported across diverse plant life forms. However, it has also been suggested that this relationship may become weak or break down completely within the angiosperms. We examined coordination between hydraulic, leaf vein, and gas-exchange traits across a diverse group of 35 evergreen Australian angiosperms, spanni...

the aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. several characterizations and properties of these multifunctions along with their mutual relationships are established in $l$-fuzzy topological spaces

‎In this paper‎, ‎we propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraints‎. ‎We use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functions‎. ‎We also fo...

Multi-spins tunneling cross-relaxations in an ensemble of weakly-coupled Ho 3+ ions, mediated by weak anisotropic dipolar interactions, can be ev-idenced by ac-susceptibility measurements in a high temperature regime. Based on a four-body representation, including the rare-earth nuclear spin, two-ions tunneling mechanisms can be attributed to both dipolar-biased tun-neling and co-tunneling proc...

The co-elementary hierarchy is a nested ordinal-indexed sequence of classes of mappings between compacta, with each successor level being defined inductively from the previous one using the topological ultracopower construction. The lowest level is the class of continuous surjections; and the next level up, the coexistential maps, is already a much more restricted class. Co-existential maps are...

CONTEXT Non-islet-cell-tumor-induced hypoglycemia (NICTH) is caused on rare occasions by secretion of insulin from tumor cells that are reported to have a single tissue origin. CASE REPORT A 67-year-old male patient had cardia adenocarcinoma and concomitant lung adenocarcinoma with extensive metastases and repeated episodes of intractable hypoglycemia. Immunohistochemical staining for insulin...

Immunoprecipitation (IP) and Co-IP are common techniques for isolating proteins and identifying protein-protein interactions, respectively. Exclusion-based sample preparation (ESPTM) with EXTRACTMAN® (Figure 1) allows for rapid, yet gentle washing of protein solutions during these procedures. EXTRACTMAN has been shown to be ideal for isolating elusive, weakly-bound protein complexes by Co-IP us...

the interaction between nominal and real sectors is studied based on estimating a simultaneous co-integrated system including foreign and domestic prices, real output, liquidity and exchange rate variables. two co -integrating vectors namely augmented ppp and demand for money functions are identified. the results suggest that real output is a weakly exogeneous variable and relatively the leadin...