Star partial order on B(H)

Let H be an infinite-dimensional complex Hilbert space and let B(H) be the algebra of all bounded linear operators on (H). In the paper the equivalent definition of the star partial order on B(H), using selfadjoint idempotent operators, is introduced. Also some properties of the generalized concept of order relations on B(H), defined with the help of idempotent operators, are investigated.     

The orthogonality relation classifies finite-dimensional formally real simple Jordan algebras

Abstract

It is shown that a finite-dimensional formally real simple Jordan algebra is completely determined by the relation of Jordan-orthogonality.

Communicated by Prof. Alberto Elduque     

Ring‐Shaped Silafluorene Derivatives as Efficient Solid‐State UV‐Fluorophores: Synthesis,Characterization, and Photoluminescent Properties

Four ring‐shaped silafluorene‐containing compounds ( 1 – 4 ) were synthesized and characterized as potentially promising monomers for fluorescent polymers. Their optical properties in solution and solid state (thin film and powder) were studied. These compounds have low quantum yields in solution (Φ_fl=0.13‐0.15) with fluorescence maxima at about 355 nm, but high quantum yields in the solid state (powder, Φ_fl=0.35‐0.54) with fluorescence maxima at about 377 and 488 nm. Influence of the substituents and the number of silafluorene units in 1 – 4 on their optical properties was investigated. Extensive study of the X‐ray crystal structures of 1 – 4 was undertaken to analyze and qualitatively estimate the role, extent, and influence of silafluorene moieties’ interactions on solid‐state fluorescent properties. Excited state UV/Vis and theoretical molecular orbital (MO) calculations were performed to explore possible fluorescence mechanisms and differences in quantum yields among these compounds.     

Fiber coupler for generating orbital angular momentum modes

We propose a fiber coupler consisting of a central ring and four external cores to generate up to ten orbital angular momentum (OAM) modes. Four coherent input lights are launched into the external cores and then coupled into the central ring waveguide to generate OAM modes. By changing the size of the external cores, one can selectively excite a high-order OAM mode. The quality of the generated OAM modes can be enhanced by adjusting the polarization state and the phase of input lights. We show the generation of OAM modes with odd charge numbers of -9 to +9 (i.e., 10 modes totally) with mode purity of >99% using <2?mm long fiber. This fiber coupler design can be extended to enable all-fiber spatial-mode (de)multiplexing.     

On the gibson barrier for the pólya problem

We study lower bounds on the number of nonzero entries in (0, 1) matrices such that the permanent is always convertible to the determinant by placing?±?signs on matrix entries.     

Formation of kinetically trapped nanoscopic unilamellar vesicles from metastable nanodiscs

Zwitterionic long-chain lipids (e.g., dimyristoyl phosphatidylcholine, DMPC) spontaneously form onion-like, thermodynamically stable structures in aqueous solutions (commonly known as multilamellar vesicles, or MLVs). It has also been reported that the addition of zwitterionic short-chain (i.e., dihexanoyl phosphatidylcholine, DHPC) and charged long-chain (i.e., dimyristoyl phosphatidylglycerol, DMPG) lipids to zwitterionic long-chain lipid solutions results in the formation of unilamellar vesicles (ULVs). Here, we report a kinetic study on lipid mixtures composed of DMPC, DHPC, and DMPG. Two membrane charge densities (i.e., [DMPG]/[DMPC] = 0.01 and 0.001) and two solution salinities (i.e., [NaCl] = 0 and 0.2 M) are investigated. Upon dilution of the high-concentration samples at 50 °C, thermodynamically stable MLVs are formed, in the case of both weakly charged and high salinity solution mixtures, implying that the electrostatic interactions between bilayers are insufficient to cause MLVs to unbind. Importantly, in the case of these samples small angle neutron scattering (SANS) data show that, initially, nanodiscs (also known as bicelles) or bilayered ribbons form at low temperatures (i.e., 10 °C), but transform into uniform size, nanoscopic ULVs after incubation at 10 °C for 20 h, indicating that the nanodisc is a metastable structure. The instability of nanodiscs may be attributed to low membrane rigidity due to a reduced charge density and high salinity. Moreover, the uniform-sized ULVs persist even after being heated to 50 °C, where thermodynamically stable MLVs are observed. This result clearly demonstrates that these ULVs are kinetically trapped, and that the mechanical properties (e.g., bending rigidity) of 10 °C nanodiscs favor the formation of nanoscopic ULVs over that of MLVs. From a practical point of view, this method of forming uniform-sized ULVs may lend itself to their mass production, thus making them economically feasible for medical applications that depend on monodisperse lipid-based systems for therapeutic and diagnostic purposes.     

Elastic deformations in hexagonal phases studied by small-angle X-ray diffraction and simulations

In this study we present experimental and theoretical results which concern the deviations from circularity of the pivotal plane in the inverse hexagonal phases (H(II)) of phospholipid self-assemblies. Due to packing constraints, the cross-section of the polar/apolar interface deviates from a circle, which we studied in minute detail by analysing small-angle X-ray diffraction data of dioleoyl-phosphatidylethanolamine (DOPE) and stearoyl-oleoyl-phosphatidylethanolamine (SOPE), respectively. On this structural basis, Monte Carlo (MC) simulated annealing variations of the free energy were carried out, both on the formation of the H(II)-phase and on the particular shape of the cross-section in the H(II)-phase. The equilibrium of the H(II)-phase pivotal plane contour and the corresponding values of the mean intrinsic curvature, H(m), and the hydrocarbon chain stiffness, τ, were determined from MC calculations. The results of these calculations were tested by solving the corresponding system of non-linear differential equations derived using variational calculus. Here our main aim is to predict the range of possible values of H(m) and τ. Comparing the measured structural data with predictions from MC calculations including lipid anisotropy, and accounting for the elastic deformations of the pivotal plane allowed us to determine a relationship between the bending deformation and stretching of hydrocarbon chains.