Non-level semi-standard graded Cohen–Macaulay domain with h-vector (h0,h1,h2)

Let $\mathbb{k}$ be an algebraically closed field of characteristic 0, and $A={?}_{i\in \mathbb{N}}{A}_i$ a Cohen–Macaulay graded domain with $A_0=\mathbb{k}$. If A is semi-standard graded (i.e., A is finitely generated as a $\mathbb{k}[A_1]$-module), it has the h-vector$(h_0,h_1,\dots ,h_s)$, which encodes the Hilbert function of A. From now on, assume that $s=2$. It is known that if A is standard graded (i.e., $A=\mathbb{k}[A_1]$), then A is level. We will show that, in the semi-standard case, if A is not level, then $h_1+1$ divides $h_2$. Conversely, for any positive integers h and n, there is a non-level A with the h-vector $(1,h,(h+1)n)$. Moreover, such examples can be constructed as Ehrhart rings (equivalently, normal toric rings).     

Synthesis and properties of a new fluorescent bicyclic 4-N-carbamoyldeoxycytidine derivative

[reaction: see text] A bicyclic 4-N-carbamoyldeoxycytidine derivative (1, dC(hpp)) geometrically locked was synthesized as a new fluorescent nucleobase. The hybridization properties of oligodeoxynucleotides containing dC(hpp) were investigated by use of T(m) analysis. It was found that dC(hpp) forms stable base pairs not only with the complementary guanine base, but also with the adenine base. Interestingly, the fluorescence of dC(hpp) was suppressed only when a dC(hpp)-dG base pair was formed.     

Design and synthesis of novel chiral spiro ionic liquids

[reaction: see text] Novel chiral imidazolium salts have been synthesized as examples of chiral ionic liquids with a spiro skeleton. Effects of N-substituents and counteranions on the melting point of spiro imidazolium salts and their chiral discrimination abilities are described.     

Anomalous heat evolution of deuteron implanted al upon electron bombardment III - try to observe the nuclear d-d reaction

In previous papers, one of the authors (K. K.) has observed the anomalous melting of the surface layer of deuteron implanted Al, containing so-called "tunnel structures", on the electron bombardment in transmission electron microscope. In the present paper, we intended to observe the evidence of the d-d nuclear reaction, expecting neutron emission, associated with the melting phenomenon. However, the result was rather unexpected. The melting phenomenon was certainly observed under the same experimental conditions as before. But, in spite of the melting, neutron emission associated with the nuclear reaction was not observed. And, more unexpectedly, X-ray emission of energy less than roughly 400 v keV was observed when specimens with a bubble structure, which never showed melting, were bombarded with electron beams. Several conceivable mechanisms are discussed which, however, are all not convincing to explain the melting. The melting is attributed to some excess energy generation. The error estimation of the radiation measurements was undertaken.     

The N = 16 Spherical Shell Closure in 24O

The unbound excited states of the most neutron-rich dripline oxygen isotope, ²⁴O, have been investigated by using the ²⁴O(p,p′)²⁴O^* reaction at the beam energy of 62 MeV/nucleon in inverse kinematics. The first and second unbound excited states of ²⁴O have been observed at ${E_{\rm x}= 4.63_{-0.14}^{+0.30}}$  MeV and ${E_{\rm x}= 5.13_{-0.24}^{+0.19}}$  MeV (preliminary) along with the evidence for another higher lying state at around 7.3 MeV. The quadrupole deformation parameter ${\beta_{2^+}}$ was deduced to be ${0.15_{-0.03}^{+0.08}}$ (preliminary) for the first time. The systematics of the ${\beta_{2^+}}$ and the ${E_{\rm x}(2_1^+)}$ in the Z = 8 isotopes shows the N = 16 spherical shell closure in ²⁴O.     

Fourier domain optical coherence tomography using optical demultiplexers imaging at 60,000,000 lines/s

We describe high-speed Fourier domain optical coherence tomography (OCT) using optical demultiplexers (ODs) for spectral dispersion. The OD enables separation of a narrow spectral band of 14 GHz (0.11 nm) from a broadband incident light at 256 different frequencies in 25.0 GHz intervals centered at 192.2 THz (1559.8 nm). OCT imaging of 60,000,000 axial scans per second was achieved through parallel signal acquisition using 256 balanced photoreceivers to simultaneously detect all the output signals from the ODs in a Fourier domain OCT system. OCT imaging at a 16 kHz frame rate, 1100 A-lines per frame, 3 mm depth range, and 23 microm resolution was demonstrated using a resonant scanner for lateral scanning.     

Magnetic structures of exchange bias Ni/FeF2(1 1 0) interface

Electronic and magnetic structures of ferromagnetic (FM)/antiferromagnetic (AFM), Ni/FeF₂(1 1 0), with a compensated AFM interface are investigated by using the full-potential linearized augmented plane-wave method. We find that magnetic structures at the AFM interface are perturbed by a contact with the FM material, where the superexchange interaction through the interface F excites and induces a small net moment at the AFM interface. These results predicted may play an important role for explaining the exchange bias in this system, and rule out the exchange bias mechanisms with the spin-flop coupling and the magnetic moment reorientation.     

Stereoinvertive C–C Bond Formation at the Boron-Bound Stereogenic Centers through Copper-Bipyridine-Catalyzed Intramolecular Coupling of α-Aminobenzylboronic Esters

Enantiospecific intramolecular Suzuki–Miyaura-type coupling with α-(2-halobenzoylamino)benzylboronic esters to give 3-substituted isoindolinones is achieved by using copper catalysts with 2,2′-bipyridine-based achiral ligands. Enantioenriched α-aminobenzylboron reactants bearing a hydrogen atom at the boron-bound stereogenic carbons undergo stereoinvertive coupling in the presence of a 6-phenyl-2,2′-bipyridine ligand with high enantiospecificity. α-Aminobenzylboronates bearing fully substituted boron-bound stereogenic centers also gave the 3,3-disubstituted isoindolinones with stereospecific stereochemical inversion in the presence of simple 2,2′-bipyridine as a ligand.