The almost alternating diagrams of the trivial knot

Bankwitz characterized the alternating diagrams of the trivialknot. A non-alternating diagram is called almost alternatingif one crossing change makes the diagram alternating. We characterizethe almost alternating diagrams of the trivial knot. As a corollary,we determine the unknotting number one alternating knots withthe property that the unknotting operation can be done on itsalternating diagram. Received July 3, 2007. Revised September 29, 2008.     

Simple Synthesis of a Heterocyclophane Exhibiting Anti-c-Met Activity by Acting as a Hatch Blocking Access to the Active Site**

A simple approach to the synthesis of heterocyclophane consisting of two 4,4’-bithiazoles has been developed in mild conditions. The heterocyclophane with two short chains was conveniently prepared by Hantzsch thiazoles synthesis using the reaction of 3-tert-butoxycarbonyl-3-azapentanethiocarboxamide with 1,4-dibromobutane-2,3-dione in methanol under reflux for only 15 min. Amino groups at the linkers of this heterocyclophane can be functionalized to give acylated and carbamate derivatives. Their properties as protein kinase inhibitors were investigated, and one of the heterocyclophanes exhibited specific anti-activity for c-mesenchymal epithelial transition factor (IC₅₀=603 nm ), among seven types of protein kinases investigated. The computational site identification by ligand competitive saturation method was used to determine why the one heterocyclophane exhibited strong anti-activity for c-mesenchymal epithelial transition factor.     

Magnetic properties of La-Co substituted M-type strontium hexaferrites prepared by polymerizable complex method

Magnetic properties of La-Co substituted M-type strontium hexaferrites were studied. The samples were prepared by polymerizable complex method. Crystal structure of samples has been investigated by powder X-ray diffraction (XRD). Single-phase M-type strontium hexaferrites with chemical composition of Sr_1.05−xLa_xFe_12−xCo_xO₁₉ (x=0-0.4) were formed by heating at 1173 K for 24 h in air. Magnetic properties were discussed by measurements of M-H curves with vibrating sample magnetometer (VSM). La-Co substituted M-type strontium hexaferrites prepared by polymerizable complex method showed typical magnetic hysteresis of hard ferrite. The coercive force increased significantly by La-Co substitution with polymerizable complex method. Maximum coercive force achieved in this study is 8.0 kOe (640 kA/m). Scanning electron microscopy revealed that the prepared ferrite particles have plate-like shape of diameter range between 20 and 500 nm.     

Synthesis of a Pentacene‐Type Silaborin via Double Dehydrogenative Cyclization of 1,4‐Diboryl‐2,5‐disilylbenzene

A new pentacene‐type silaborin, in which three benzene rings are bridged by silicon and boron atoms, has been synthesized and characterized by using NMR spectroscopy and X‐ray crystallographic analysis. The precursor, 1,4‐bis(dimesitylboryl)‐2,5‐bis(phenylsilyl)benzene ( 4 ), was prepared by stepwise introduction of a silyl group and a boryl group to a benzene ring starting from 1,4‐dibromobenzene. Double cyclization of 4 proceeds by a H‐Mes exchange and a B‐H/C‐H dehydrogenative condensation to afford pentacene‐type silaborin 5 . X‐ray crystal structure analysis reveals that 5 adopts a bent structure rather than a planar one. UV/Vis spectra and DFT calculations for 5 reveal a lowering of the LUMO energy level compared with corresponding anthracene‐type 3 .     

Weyl Pseudo-Differential Operator and Wigner Transform on the Poincaré Disk

The purpose of this paper is to investigate some relations between the kernel of a Weyl pseudo-differential operator and the Wigner transform on Poincaré disk defined in our previous paper [11]. The composition formula for the class of the operators defined in [11] has not been proved yet. However, some properties and relations, which are analogous to the Euclidean case, between the Weyl pseudo-differential operator and the Wigner transform have been investigated in [11]. In the present paper, an asymptotic formula for the Wigner transform of the kernel of a Weyl pseudo-differential operator as 0 is given. We also introduce a space of functions on the cotangent bundle T ^* D whose definition is based on the notion of the Schwartz space on the Poincaré disk. For an S ¹-invariant symbol in that space, we obtain a formula to reproduce the symbol from the kernel of the Weyl pseudo-differential operator.     

Crystal Phases of TiO2 Ultrafine Particles Prepared by Laser Ablation of Solid Rods

Titanium dioxide ultrafine particles (UFPs) are produced by pulsed laser ablation of titanium or titanium dioxide (anatase and rutile) rods in an atmosphere of He or O₂/He mixture. The collected UFPs on cellulose membrane filters at the exit of the ablation chamber are analyzed by X-ray diffraction (XRD) and transmission electron microscopy (TEM). The TiO₂ particles produced are composed of very small particles (diameter: 10–50nm) that are completely anatase, irrespective of the rod material, and relatively large particles (diameter: 100nm–1m) that are a mixture of anatase and rutile. The large particles consist of the direct strip-off fragments coming from the rod surface. The particles obtained from the laser ablation on TiO₂ rods in an atmosphere of He contains gray particles that are supposed to be amorphous TiO₂ (x < 2). In the presence of O₂ in the ablation chamber, these oxygen defects in amorphous TiO₂ are stabilized and anatase UFPs are formed. These results suggest that the crystal phase of the products can be controlled by adjusting the rod material and the gases used in the ablation process.     

A Characterization of Some Minihypers and its Application to Linear Codes

Any {f,r- 2+s; r,q}-minihyper includes a hyperplane in PG(r, q) if fr-1 + s 1 + q – 1 for 1 s q – 1, q 3, r 4, where i = (qi + 1 – 1)/ (q – 1 ). A lower bound on f for which an {f, r – 2 + 1; r, q}-minihyper with q 3, r 4 exists is also given. As an application to coding theory, we show the nonexistence of [ n, k, n + 1 – qk – 2 ]q codes for k 5, q 3 for qk – 1 – 2q – 1 < n qk – 1 – q – 1 when k > q – q - \sqrt q + 2$$ " align="middle" border="0"> and for when , which is a generalization of [18, Them. 2.4].     

Novel synthesis of carbohydrates using electroreduction as key reactions

Glyceraldehyde was transformed to threose, erythrose, and erythrose using electro-reduction as key reactions.