Complete description of invariant Einstein metrics on the generalized flag manifold SO(2n)/U(p)?× U(n ? p)

We find the precise number of non-K?hler SO(2n)-invariant Einstein metrics on the generalized flag manifold M = SO(2n)/U(p)×U(n−p) with n ≥ 4 and 2 ≤ p ≤ n−2. We use an analysis on parametric systems of polynomial equations and we give some insight towards the study of such systems. We also examine the isometric problem for these Einstein metrics.     

A descent method for submodular function minimization

We show a descent method for submodular function minimization based on an oracle for membership in base polyhedra. We assume that for any submodular function f: ?→R on a distributive lattice ?⊆2 ^V with ?,V∈? and f(?)=0 and for any vector x∈R ^V where V is a finite nonempty set, the membership oracle answers whether x belongs to the base polyhedron associated with f and that if the answer is NO, it also gives us a set Z∈? such that x(Z)>f(Z). Given a submodular function f, by invoking the membership oracle O(|V|²) times, the descent method finds a sequence of subsets Z ₁,Z ₂,···,Z _k of V such that f(Z ₁)>f(Z ₂)>···>f(Z _k )=min{f(Y) | Y∈?}, where k is O(|V|²). The method furnishes an alternative framework for submodular function minimization if combined with possible efficient membership algorithms. Received: September 9, 2001 / Accepted: October 15, 2001?Published online December 6, 2001     

Z(2) gauge neural network and its phase structure

We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable _Si=±1$S_i=\pm 1$ on the i$i$-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable _Jij=±1$J_{ij}=\pm 1$ describes a state of the synaptic connection between j$j$-th and i$i$-th neurons. The gauge symmetry allows for a self-coupling energy among _Jij$J_{ij}$’s such as _JijJjkJki$J_{ij}{J}_{jk}{J}_{ki}$, which describes reverberation of signals. Explicitly, we consider the three models; (I) an annealed model with full and partial connections of _Jij$J_{ij}$, (II) a quenched model with full connections where _Jij$J_{ij}$ is treated as a slow quenched variable, and (III) a quenched three-dimensional lattice model with the nearest-neighbor connections. By numerical simulations, we examine their phase structures paying attention to the effect of the reverberation term, and compare them with each other and with the annealed 3D lattice model which has been studied beforehand. By noting the dependence of thermodynamic quantities upon the total number of sites and the connectivity among sites, we obtain a coherent interpretation to understand these results. Among other things, we find that the Higgs phase of the annealed model is separated into two stable spin-glass phases in the quenched models (II) and (III).     

Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs

We propose to use a two-species Fermi gas with the interspecies s-wave Feshbach resonance to realize p-wave superfluidity in two dimensions. By confining one species of fermions in a two-dimensional plane immersed in the background three-dimensional Fermi sea of the other species, an attractive interaction is induced between two-dimensional fermions. We compute the pairing gap in the weak-coupling regime and show that it has the symmetry of p_x+ip_y. Because the magnitude of the pairing gap increases toward the unitarity limit, it is possible that the critical temperature for the p_x+ip_y-wave superfluidity becomes within experimental reach. The resulting system has a potential application to topological quantum computation using vortices with non-Abelian statistics. We also discuss aspects of our system in the unitarity limit as a “nonrelativistic defect conformal field theory (CFT)”. The reduced Schrödinger algebra, operator-state correspondence, scaling dimensions of composite operators, and operator product expansions are investigated.     

Computer-Generated Holograms Based on the Three-Dimensional Fourier Spectrum

A method to synthesize a computer-generated hologram (CGH) of real-existing objects from projection images is proposed. Different from other similar methods, our method enables the synthesis of a CGH with only one-dimensional (1-D) mechanical scanning of the objects. Our method is connected with the three-dimensional (3-D) Fourier spectrum of the objects by the 3-D central slice theorem (CST). Two efficient recording techniques for projection images and numerical experiments to verify our principle is discussed. A comparison between the two techniques is also presented from the viewpoint of diffraction efficiency. © 2005 The Optical Society of Japan     

Preparation of Na+-selective electrodes by ion-implantation of lithium and silicon into single-crystal alumina wafer and its application to the production of ISFET

Summary Sodium ion-selective electrodes (Na⁺-ISE) were prepared by implanting Si⁺ and Li⁺ into alumina wafers and their characteristics were investigated. The alumina wafer had a thickness of 100 m and a diameter of 1.40 cm. The ionselective membrane was produced by ion-implanting of Li⁺ and Si⁺ on both sides of a single-crystal alumina wafer. The total doses of Li⁺ and Si⁺ were controlled to be the same, viz. 10¹³–10¹⁵ ions/cm². The ion-implanted alumina wafer with 10¹⁴ or 4×10¹⁴ ions/cm² of Li⁺ and Si⁺ showed better characteristics than the others.The response curves of the 10¹⁴ ions/cm² implanted alumina wafer had a slope of 42 mV/pNa in a concentration range from 1–10^–4mol/l. The full response achieved after about 1 min was reproducible. The proposed idea of producing Na⁺-ISE by ion-implantation technique was applied to functuate the gate surface of the field effect transitor to sodium ion. The sodium ion-sensitive FET (Na⁺-ISFET) prepared by implanting Li⁺ and Al⁺ at a dose of 5×10¹⁴ ions/cm² showed a slope of 30 mV/pNa in a concentration range from 1–10^–4mol/l.

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Herstellung Na⁺-ionenselektiver Elektroden durch Einbau von Lithium und Silicium in Einkristall-Alumniumoxidblättchen und Anwendung zur Erzeugung von ISFET

Zusammenfassung Na⁺-selektive Elektroden wurden durch Einbau von Si⁺ und Li⁺ in Aluminiumoxidblättchen hergestellt und ihre Charakteristiken untersucht. Die Blättchen hatten eine Dicke von 100 m und einen Durchmesser von 1,40 cm. Ebenso wurde die Membran für einen ISFET hergestellt. Die Gesamtmenge von Li⁺ und Si⁺ wurde auf 10¹³–10¹⁵ Ionen/cm² eingestellt, wobei sich bei 10¹⁴ oder 4×10¹⁴ Ionen/cm² die beste Charakteristik ergab.Die Responsekurven der mit 10¹⁴ Ionen/cm² versehenen Aluminiumoxidplättchen hatten eine Neigung von 42 mV/pNa in einem Konzentrationsbereich von 1–10^–4mol/l. Der nach 1 min erhaltene volle Response war reproduzierbar. Die vorgeschlagene Technik wurde zur Einstellung der Gate-Oberfläche des Feldeffekt-Transistors auf Natriumion benutzt. Der Na⁺-sensitive FET (Na⁺-ISFET), der durch Einbau von Li⁺ und Al⁺ mit 5×10¹⁴ Ionen/cm² hergestellt wurde, zeigte eine Neigung der Signalkurve von 30 mV/pNa in einem Bereich von 1–10^–4mol/l.

     

Inclusive η production at high pT at the ISR

The inclusive η production cross section at the CERN ISR has been measured for p_T values of up to 11 GeV/c. We find that the $\text{η}\text{π}{}^0$ cross-section ratio has an average value of 0.55 ± 0.07 and varies little with p_T.     

Hydrogenation of olefins by π-arene ruthenium complexes : A role of π-arene ligand in catalytic activity

The divalent ruthenium complexes bearing benzene, mesitylene triphenylbenzene as a π-ligand were prepared and their catalytic activity for olefin hydrogenation was examined. They showed activity in the presence of a small amount of base. Particularly, the complex with triphenylbenzene was found to have extremely high activity. Discussion here is on a role of a π-arene ligand in the activity.     

Ruthenium-catalyzed hydrogenation of alkynylstannanes with migration of the stannyl group

Molecular hydrogen adds to aliphatic and aromatic alkynylstannanes in the presence of a ruthenium catalyst, pushing the stannyl group to the adjacent carbon atom to give alpha-substituted vinylstannanes. This is the first achievement of hydrogenation of alkynylstannanes, which is applicable also to the deuteration affording precursors for an important class of deuterium-labeled compounds.