Geometrical analysis of a lens-like medium with higher-order aberration

The propagation of light rays in a slab-waveguide whose dielectric constant varies radially with a quadratic law but has fourth and sixth order terms in it is described. Exact solutions consisting of Jacobi elliptic functions are shown. The exact ray trajectory and delay time of an optical pulse, therefore, can be obtained. The results show that the optimum fourth-order and sixth-order coefficients are near 2/3 and 17/45, respectively.     

The effect of molecular weight heterogeneity on the second virial coefficient of linear polymers in good solvents

The effect of molecular weight heterogeneity on the second virial coefficient A₂ in good solvents is studied for binary mixtures of monodisperse poly(α-methylstyrenes). It is concluded that A₂ for polymer mixtures passes through a maximum with variation of the mixing ration. From comparison with the data, it is concluded that no available theory quantitatively explains both the molecular weight dependence of A₂ of monodisperse polymer and the variation of A₂ of mixtures with the mixing ratio. The interpenetration function for two polymer coils with different molecular weights is discussed on the assumption that the thermodynamic interaction between two polymer coils in good solvents can be approximated by a hard-sphere model.     

Dynamic flow properties of vinylon fibre and glass fiber reinforced polyethylene melts

An experimental study of the dynamic shear flow properties of polyethylene melts filled with glass fibers and vinylon fibers was carried out and comparison with the steady shear flow properties was made. The effects of loading level and the characteristics of the fibers on the rheological properties of the fiber-filled systems is discussed. The rigidity and complex viscosity of the fiber-filled systems is sensitive not only to the quantity of fibers but also to their length, distribution and properties. The Cox-Merz empirical law for complex viscosity and steady shear viscosity, and Roscoe's empirical relation for estimating the normal-stress coefficients are both able to be applied to pure polymer melts but not to fiber-filled systems.     

Electrical and thermal properties in CuV2S4

The successive phase transitions of the cubic spinel structure CuV₂S₄ have been studied by the electrical resistivity and the specific heat. In the resistivity and the specific heat two anomalies have been observed at T₁～91 K and T₃≈55 K. The specific heat indicates that the phase transition at T₁ is in the vicinity of a tricritical point, where the resistivity has a small sharp peak. On the other hand, the specific heat shows a step at T₃, where a hysteresis of the resistivity indicates the existence of the first-order phase transition.     

Fabrication of a new gradient-index rod lens with high performance

A gradient-index rod lens was fabricated by the new ion-exchange technique, in which another dopant was added to the fused salt. It was found that this dopant remained only in the merginal region of the glass rod and modified the improper refractive index distribution in this region. The lens has high numerical aperture of 0.6 and gives good results in the light focusing system and the light source coupling system.     

The spectrum of infinite regular line graphs

Let be an infinite -regular graph and its line graph. We consider discrete Laplacians on and , and show the exact relation between the spectrum of and that of . Our method is also applicable to -semiregular graphs, subdivision graphs and para-line graphs.

     

Recent development of ortho-C–H functionalization of aryl sulfoxides through [3,3] sigmatropic rearrangement

Sulfoxide-promoted ortho-C–H functionalization reactions of aromatic compounds have emerged as powerful tools for organic synthesis. Among them, [3,3] sigmatropic rearrangement induced by interrupted Pummerer reaction or electrophilic activation of sulfoxides has proved to be a fruitful strategy due to its versatility and high reaction efficiency. This digest paper mainly focuses on recent progress on C–H functionalization reactions of aryl sulfoxides via [3,3] sigmatropic rearrangement of sulfonium-tethered intermediates.     

Structural Phase Transitions of a Molecular Metal Oxide

The structural phase of a metal oxide changes with temperature and pressure. During phase transitions, component ions move in multidimensional metal–oxygen networks. Such macroscopic structural events are robust to changes in particle size, even at scales of around 10 nm, and size effects limiting these transitions are particularly important in, for example, high-density memory applications of ferroelectrics. In this study, we examined structural transitions of the molecular metal oxide [Na@(SO₃)₂(n-BuPO₃)₄Mo^V₄Mo^VI₁₄O₄₉]⁵⁻ (Molecule 1 ) at approximately 2 nm by using single-crystal X-ray diffraction analysis. The Na⁺ encapsulated in the discrete metal-oxide anion exhibited a reversible order–disorder transition with distortion of the Mo–O molecular framework induced by temperature. Similar order–disorder transitions were also triggered by chemical pressure induced by removing crystalline solvent molecules in the single-crystal state or by substituting the countercation to change the molecular packing.     

Chiral helicenoid diarylethene with large change in specific optical rotation by photochromism

A diarylethene possessing one [4]thiaheterohelicene and one benzothiophene, the latter with a chiral methoxymethoxyethyl group on its C-3 position, was proved to work as a switch of specific optical rotation at a wavelength at which both colored and colorless forms have no absorption in solution. The difference of the specific optical rotation was 1300 degrees between the open form and the photostationary state. The specific optical rotation of one of the isolated optically active major colored forms was -4680 degrees. The conversion to the colored form was 64%, and the diastereomeric excess of photocyclization was 47%.     

Ferrocenylpyrazole—A versatile building block for hydrogen-bonded organometallic supramolecular assemblies

The crystal architectures of 5-ferrocenylpyrazole (1) and its metal complexes were investigated. Compound 1 can form non-solvated and chloroform-solvated crystals. In both cases, 1 forms a zigzag one-dimensional architecture via NH?N hydrogen bonds. The hydrogen bond exhibits a twofold disorder, which was shown to be static by solid-state ¹³C NMR. In the solvated crystal, the chloroform is released at 415 K, associated with melting of the crystal. The reaction of 1 with metal salts provided metal-centered ferrocenyl clusters [Zn(NO₃)₂(1)₄] (4), [Co(NO₃)₂(1)₄] (5), [CoCl₂(1)₄] (6), [Zn(NCS)₂(1)₂] (7), cis-[Pt(NH₃)₂(1)₂](PF₆)₂ (8), and trans-[Pt(NH₃)₂(1)₄](PF₆)₂ (9). In all of these complexes, 1 acts as a monodentate ligand. In 4, 5, and 7, the multinuclear units are joined via hydrogen bonds to form supramolecular chains. Two polymorphs were found for the crystals of 4. Both are composed of the same hydrogen-bonded chains, but their arrangements are different. 5-Ferrocenyl-1-tritylpyrazole (2) and 4-ferrocenyl-1-methylpyrazole (3) were also crystallographically characterized.