Distances between classes in $$W^{1,1}(\Omega ;{\mathbb {S}}^{1})$$

We introduce an equivalence relation on the space \(W^{1,1}(\Omega ;{\mathbb {S}}^1)\) which classifies maps according to their “topological singularities”. We establish sharp bounds for the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. Similar questions are examined for the space \(W^{1,p}(\Omega ;{\mathbb {S}}^1)\) when \(p>1\).     

Halving Steiner 2-designs

A Steiner 2-design S(2,k,v) is said to be halvable if the block set can be partitioned into two isomorphic sets. This is equivalent to an edge-disjoint decomposition of a self-complementary graph G on v vertices into K_ks. The obvious necessary condition of those orders v for which there exists a halvable S(2,k,v) is that v admits the existence of an S(2,k,v) with an even number of blocks. In this paper, we give an asymptotic solution for various block sizes. We prove that for any k?5 or any Mersenne prime k, there is a constant number v₀ such that if v>v₀ and v satisfies the above necessary condition, then there exists a halvable S(2,k,v). We also show that a halvable S(2,2ⁿ,v) exists for over a half of possible orders. Some recursive constructions generating infinitely many new halvable Steiner 2-designs are also presented.     

Self-regulated Ni cluster formation on the TiO2(1 1 0) terrace studied using scanning tunneling microscopy

We have studied the growth mode and morphology of Ni clusters on a TiO₂(1 1 0) surface with a wide terrace using scanning tunneling microscopy (STM) at a low coverage (less than 3 atoms nm⁻²). The Ni clusters are formed on the terrace at the low coverage of 0.2 atoms nm⁻². Their average dimensions are constant in three directions up to 1 atoms nm⁻². The Ni clusters have an oval shape with average sizes of 1.8 nm (along [0 0 1]) × 1.4 nm (along (in the [1 1 0] directions). Above the coverage of 1.0 atoms nm⁻², an increase in the cluster height occurs, retaining an almost constant lateral size. It is proposed that the interaction of the Ni cluster and the support surface regulates the Ni cluster size.     

KPZ in One Dimensional Random Geometry of Multiplicative Cascades

We prove a formula relating the Hausdorff dimension of a subset of the unit interval and the Hausdorff dimension of the same set with respect to a random path matric on the interval, which is generated using a multiplicative cascade. When the random variables generating the cascade are exponentials of Gaussians, the well known KPZ formula of Knizhnik, Polyakov and Zamolodchikov from quantum gravity [KPZ88] appears. This note was inspired by the recent work of Duplantier and Sheffield [DS08] proving a somewhat different version of the KPZ formula for Liouville gravity. In contrast with the Liouville gravity setting, the one dimensional multiplicative cascade framework facilitates the determination of the Hausdorff dimension, rather than some expected box count dimension.     

Tactile impression and friction of water on human skin

Water has a unique touch as well as characteristic physical properties. However, nobody knows the real identity of its touch. Here, we show that water creates a stick-slip feel when a small amount is rubbed using fingertip on an artificial skin that mimics the structure of human skin. The results of frictional analyses predict that this stick-slip feel is caused by a drastic change in frictional resistance. The present result is valuable for biologists and robot engineers as well as cognitive scientists and tribologists, because it is a new example of stick-slip phenomena on biological surfaces. The tactile texture of this most familiar material could also be applied to consumer products or virtual reality systems.     

Optical modulator using metal-oxide-semiconductor type Si ring resonator

Electric-field drive optical modulators using a Si ring resonator were fabricated on silicon-on-insulator (SOI) wafers. The fabricated resonators consisted of Si waveguides with width and thickness of 1.0 and 0.3 μm, respectively. In order to induce the linear electro-optic (EO) effect in the Si core layer, the strain was applied by covering the layer with Si₃N₄ film (0.26 μm thick) deposited by low pressure chemical vapor deposition (LPCVD) at 750 °C. The vertical electric-field was applied to the Si waveguide through the top and bottom cladding layers, and the optical output from the drop port at the resonance wavelength was measured. At a wavelength of 1501.6 nm, the optical modulation of 33% was obtained at 200V (electric-field at the silicon surface ∼3 × 10⁵ V/cm, nearly the breakdown field). The resonance wavelength was shifted toward the short wavelength side by applying both positive and negative voltages, this shift was explained by carrier concentration modulation. The linear EO effect in the Si core layer was not observed, presumably because the strain in the Si core layer was too small.     

Stereoselective synthesis of the C14-C24 degraded fragment of symbiodinolide

Symbiodinolide is a polyol macrolide isolated from the marine dinoflagellate Symbiodinium sp. in 2007. The C14-C24 fragment of symbiodinolide possessing the 17R/18R/21R absolute configuration, which was obtained as one of the degraded products of symbiodinolide, was synthesized stereoselectively from cis-2-butene-1,4-diol. The detailed comparison of the synthetic product with the degraded product in the spectroscopic data confirmed that the stereostructure of the C14-C24 fragment was 17R, 18R, and 21R.     

Influence of adding carbon nanotubes on photoelectric conversion properties of dye-doped titania gel

Multiwalled carbon nanotubes (MWCNTs) were incorporated into amorphous dye-doped titania gel by the sol?Cgel method at room temperature. The working electrodes were prepared by coating the ITO glass with the sol?Cgel titania precursor containing the dye and MWCNTs. The photoelectric conversion properties of the electrodes were examined by simple spectroscopic and electric measurements. The photocurrent spectrum originated from the absorption of the dye. The short circuit photocurrent was enhanced by adding a small amount of MWCNTs evenly to the amorphous dye-doped titania gel. The open circuit voltage was due to the semiconducting characteristics property of the titania gel. The experimental results indicated the electron transport from the dye excited states to the MWCNTs through the titania gel. The MWCNTs functioned as bridges between the titania and ITO. Steam treatment of the titania gel electrodes significantly increased the photoelectric performance due to crystallization of the titania and enhancement of the dye?Ctitania interaction forming the chelate complex on the titania particle surface.     

Chiral phosphinooxathiane ligands for catalytic asymmetric Diels-Alder reaction

Chiral cationic palladium[bond]phosphinooxathiane complexes have been found to be effective catalysts for enantioselective Diels-Alder (DA) reaction of cyclopentadiene with acyl-1,3-oxazolidin-2-ones to give the corresponding DA adducts in good yield and high enantioselectivity up to 93% ee.