Crosscap numbers of pretzel knots

The crosscap number of a knot in the 3-sphere is defined as the minimal first Betti number of non-orientable surfaces bounded by the knot. In this paper, we determine the crosscap numbers of a large class of pretzel knots. The key ingredient to obtain the result is the algorithm of enumerating all essential surfaces for Montesinos knots developed by Hatcher and Oertel.     

Transmission electron microscopy study of an AlN nucleation layer for the growth of GaN on a 7-degree off-oriented (0 0 1) Si substrate by metalorganic vapor phase epitaxy

We have investigated the morphology of the high-temperature-grown AlN nucleation layer and its role in the early stage of GaN growth, by means of transmission electron microscopy. The nitride was selectively grown on a 7-degree off-oriented (0 0 1) patterned Si substrate by metalorganic vapor phase epitaxy. AlN was deposited on the inclined unmasked (1 1 1) facet in the form of islands. The size of the islands varied along the slope, which is attributable to the diffusion of the growth species in the vapor phase. The GaN nucleation occurred at the region where rounded AlN islands formed densely. The threading dislocations were observed to generate in the GaN nucleated region.     

Development of self-indicating resin

Previously, we have reported the development and application of self-indicating resins (SIR), materials which can indicate presence or absence of amines in the reaction solution by the conspicuous color change of a phenolsulfophthalein type dye immobilized on resin beads [2a]. Although the functionality necessary for attaching the dye to the resins could be readily introduced by the Suzuki-Miyaura coupling during the synthesis of the SIR 1, this approach was only applicable to the dyes containing suitable functionality for the cross-coupling reaction. In this article we describe a new approach of immobilizing the indicating dyes onto the resin support. The dyes suitable for loading onto aminomethyl polystyrene (PS) resin were prepared by Friedel-Crafts reaction of 2-sulfoterephthalic anhydride with a wide range of phenols. Using this new route, the SIR 6c was readily prepared in >100g quantities. Use of the SIR 6c in the synthesis of a 144 member urea library was demonstrated and the SIR successfully indicated the endpoint of the reaction between amines and isocyanates.     

Captured and cross-linked palladium nanoparticles

Polystyrene-poly(ethylene glycol) resin-captured cross-linked palladium nanopaticles were prepared via a straightforward route, and their heterogeneous behavior was truly confirmed by various tests. They were applied to aqueous Suzuki cross-coupling reactions with various aryl bromides and recycled up to six times without loss of activity.     

Interconnections and Initial Conditions of Linear Systems With First-Order Representations

This paper considers the initial value problem of an interconnection composed of linear systems described by the first-order differential/algebraic equations (DAEs). An initial condition of the system variable for which the DAE has a solution is called admissible. For the interconnected system, we formulate the invariance of the admissible initial condition sets (AICSs) of the sub-systems under interconnection. Namely, the AICSs are said to be invariant if they remain unchanged even when additional constraints due to interconnection are imposed on the system variables. It is shown that the feedback and regular feedback structures of the interconnection guarantee the invariance of the AICSs in the senses of impulsive-smooth distributions and smooth distributions, respectively. The results in this paper justify the use of a feedback controller in the control system design.     

Duplicated ring enlargement of 4,9-methanothia[11]annulene to 6,11-methanothia[15]annulene

3,10-Dipyrrolidinyl-4,9-methanothia[11]annulene reacts with excess dimethyl acetylenedicarboxylate (DMAD) in refluxing toluene to give ring-enlarged 6,11-methanothia[15]annulene. X-ray crystallographic analysis of the product shows two different cis,trans-dienyl parts in the ring system. Product formation possibly involves π-facial selective addition of the enamine with DMAD and torque-selective ring opening of the intermediate cyclobutenes.     

Measurements of analyzing powers Ay, Axx, Ayy and Axz in dp elastic scattering at Ed = 56 MeV

The differential cross section and all components of the analyzing powers A_y, A_xx, A_yy and A_xz have been measured in dp elastic scattering at 56 MeV. This is the first measurement of A_xz in the cyclotron energy region. A_xz has been measured with the beam polarized in the horizontal plane using the polarization tagging method. Faddeev calculations have been performed for four cases of the NN interaction. The Coulomb correction gave smaller effects at the present energy than at lower energies. Three of them reproduce the experimental data well. The agreement between the calculations and data for A_xz was better than that reported at lower energy. The deuteron asymptotic D- to S-state ratio has been obtained and is consistent within the limits of uncertainty with previously obtained values.     

Alexander polynomials of doubly primitive knots

We give a formula for Alexander polynomials of doubly primitive knots. This also gives a practical algorithm to determine the genus of any doubly primitive knot.