N′-[(E)-1-(5-Bromo-2-hydroxy­phen­yl)ethyl­idene]benzohydrazide

The C=N double bond in the title compound, C15H13BrN2O2, is trans E configured and the dihedral angle between the aromatic ring planes is 22.3 (1)°. The crystal structure is stabilized by intra­molecular O—H⋯O and inter­molecular N—H⋯O hydrogen bonds

(5-Bromo-2-hydroxy­phen­yl)(phen­yl)methanone

In the title compound, C13H9BrO2, the dihedral angle between the aromatic ring planes is 53.6 (1)°. The crystal structure is stabilized by intra­molecular O—H⋯O and inter­molecular C—H⋯O hydrogen bonding and C—H⋯π inter­actions

N′-[(E)-(5-Bromo-2-hydroxy­phen­yl)(phen­yl)methyl­idene]-4-chloro­benzo­hydrazide

The Schiff base, C20H14BrClN2O2, displays a trans conformation with respect to the C=N double bond. The aromatic rings at either end of the –C(=O)–NH–N=C– fragment are nearly parallel [dihedral angle = 3.4 (5)°]. The hydr­oxy group forms an intra­molecular hydrogen bond to the imino N atom

N′-[(E)-(5-Bromo-2-hydroxy­phen­yl)(phen­yl)methyl­ene]benzohydrazide

In the title compound, C20H15BrN2O2, the C=N double bond displays a trans configuration. The crystal structure features an intra­molecular O—H⋯N hydrogen bond

Quasi-Perron-Frobenius property of a class of saddle point matrices

The saddle point matrices arising from many scientific computing fields have block structure $W= \left(\begin{array}{cc} A & B\\ B^T & C \end{array} \right)$, where the sub-block $A$ is symmetric and positive definite, and $C$ is symmetric and semi-nonnegative definite. In this article we report a unobtrusive but potentially theoretically valuable conclusion that under some conditions, especially when $C$ is a zero matrix, the spectral radius of $W$ must be the maximum eigenvalue of $W$. This characterization approximates to the famous Perron-Frobenius property, and is called quasi-Perron-Frobenius property in this paper. In numerical tests we observe the saddle point matrices derived from some mixed finite element methods for computing the stationary Stokes equation. The numerical results confirm the theoretical analysis, and also indicate that the assumed condition to make the saddle point matrices possess quasi-Perron-Frobenius property is only sufficient rather than necessary

Proposal of Direct Search for Strongly Bound States of ppbar, npbar Systems with High Intensity and Collective pbar beam

In this letter, we discuss the possibility to look for the direct evidence of the existence of the ppbar and npbar bound states. Measurement of the single \gamma ray from the ppbar and npbar systems at rest can directly confirm whether the X(1860) and X(1835) are the resonances which are strongly coupled to ppbar. In addition to the neutral candidate, a charged resonance $X^-$ is also proposed to be searched for in npbar channel. We find that the data from the Crystal Barrel experiment at LEAR/CERN can be used to confirm the X(1835) observed by BES Collaboration. The possibility of measuring the $\gamma$ spectrum below 100 MeV at the new experiment with cold high intensity \pbar beam at GSI is discussed. These new techniques can be used to probe the structure of the X(1860) and X(1835) in the future.Comment: Accepted by Mod. Phys. Lett.