Eigenvalues of Two Parameter Polynomial Operator Pencils of Waveguide Type

The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a connection between the energetic stability condition and a perturbation problem for the coefficients is given.     

Synthesis and structure of cyclopropano-annelated homosesquinorbornene derivatives containing pyramidalized double bonds: evidence for the sterical effect of a cyclopropyl group on the degree of C=C double-bond pyramidalization

[reaction: see text] endo- and exo-2,3,4,7-tetrahydro-1H-1,4-methanobenzocycloheptene-7-carboxylic acid ethyl esters have been synthesized, and their Diels-Alder cycloaddition reactions with maleic anhydride, dimethyl acetylenedicarboxylate and singlet oxygen have been investigated. The X-ray analysis of four adducts indicated the pyramidalization of the central double bond. Density functional theory calculations on the isolated products and model compounds showed excellent agreement between the experimental and theoretical determined butterfly angles. Furthermore, it has been shown that a cyclopropyl group fused to [2.2.2] system decreases significantly the degree of the pyramidalization which is attributed to the steric interactions between the cyclopropyl group and ethano bridge of the norbornene systems. Due to the instability of the bicyclic endoperoxides, their X-ray analysis could not be carried out. DFT calculations on model compounds showed increased bending in the case of the product obtained by the addition of singlet oxygen to endo-2,3,4,7-tetrahydro-1H-1,4-methanobenzocycloheptene-7-carboxylic acid ethyl ester.     

Are oxygen rings (On) and their negative ions (O) unstable?

Oxygen clusters of the equilateral ring types O_n and their negative ions O are studied by the recently developed pictorial-topological quantum chemistry method, VIF (valency interaction formulas), of this author. The species are found to be of high energy relative to separated oxygen atoms, the cause being evident from the VIF pictures. The odd n rings should be at local minima but are not likely to have observable negative ions. The even n rings have distortional instabilities, yet their negative ions are more likely to be observed as transients in beam experiments.     

Recognition-induced transformation of microspheres into vesicles: morphology and size control

Polystyrene functionalized with diamidopyridine (DAP) recognition units self-assembles in nonpolar media to form thermally reversible micrometer-scale spherical aggregates. The size and the thermal stability of these microspheres can be controlled by the molecular weight of the polymer. The addition of thymine-functionalized polymer to these self-assembled microspheres converted them into vesicular aggregates with a controlled size. The morphology change was reversible: the addition of DAP-functionalized polymer converted the vesicles back to microspheres.     

Hydrophobic cryogels for DNA adsorption: Effect of embedding of monosize microbeads into cryogel network on their adsorptive performances

As alternative hydrophobic adsorbent for DNA adsorption, supermacroporous cryogel disks were synthesized via free radical polymerization. In this study, we have prepared two kinds of cryogel disks: (i) poly(2‐hydroxyethyl methacrylate‐N‐methacryloyl‐l ‐tryptophan) [p(HEMA‐MATrp)] cryogel containing specific hydrophobic ligand MATrp; and (ii) monosize p(HEMA‐MATrp) particles synthesized via suspension polymerization embedded into p(HEMA) cryogel structure to obtain p(HEMA‐MATrp)/p(HEMA) composite cryogel disks. These cryogel disks containing hydrophobic functional group were characterized via swelling studies, Fourier transform infrared spectroscopy, elemental analysis, surface area measurements and scanning electron microscopy. DNA adsorption onto both p(HEMA‐MATrp) cryogel and p(HEMA‐MATrp)/p(HEMA) composite cryogels was investigated. Maximum adsorption of DNA on p(HEMA‐MATrp) cryogel was found to be 15 mg/g polymer. Otherwise, p(HEMA‐MATrp)/p(HEMA) composite cryogels significantly increased the DNA adsorption capacity to 38 mg/g polymer. Composite cryogels could be used repeatedly without significant loss on adsorption capacity after 10 repetitive adsorption–desorption cycles. Copyright © 2013 John Wiley & Sons, Ltd.