The commutator algebra of a nilpotent matrix and an application to the theory of commutative Artinian algebras

We show a number of properties of the commutator algebra of a nilpotent matrix over a field. In particular we determine the simple modules of the commutator algebra. Then the results are applied to prove that certain Artinian complete intersections have the strong Lefschetz property.     

Generic Initial Ideals,Graded Betti Numbers,and k-Lefschetz Properties

We introduce the k-strong Lefschetz property and the k-weak Lefschetz property for graded Artinian K-algebras, which are generalizations of the Lefschetz properties. The main results are:

1. Let I be an ideal of R = K[x ₁, x ₂,…, x _n ] whose quotient ring R/I has the n-SLP. Suppose that all kth differences of the Hilbert function of R/I are quasi-symmetric. Then the generic initial ideal of I is the unique almost revlex ideal with the same Hilbert function as R/I.

2. We give a sharp upper bound on the graded Betti numbers of Artinian K-algebras with the k-WLP and a fixed Hilbert function.     

The central simple modules of Artinian Gorenstein algebras

Let A be a standard graded Artinian K-algebra, with char K=0. We prove the following.

1.

A has the Weak Lefschetz Property (resp. Strong Lefschetz Property) if and only if has the Weak Lefschetz Property (resp. Strong Lefschetz Property) for some linear form z of A.

2.

If A is Gorenstein, then A has the Strong Lefschetz Property if and only if there exists a linear form z of A such that all central simple modules of (A,z) have the Strong Lefschetz Property.

As an application of these theorems, we give some new classes of Artinian complete intersections with the Strong Lefschetz Property.     

A new simple preparation of platinum-nickel alloy nanoparticles and their characterization as an electrocatalyst for methanol oxidation

Pt-Ni alloy nanoparticles were produced by casting 2 or 10 mM H₂PtCl₆ solutions on a Ni column. The apparent particle size for the resultant Pt-Ni alloys increased with the concentration of the H₂PtCl₆ solution, while the content of Pt in the alloy decreased. The potential sweeps of 5 cycles in an H₂SO₄ aqueous solution for Pt-Ni (2 mM)/Ni and Pt-Ni (10 mM)/Ni electrodes led to electrochemical behavior similar to a polycrystalline Pt electrode, suggesting the formation of a few thin Pt layers on each Pt-Ni alloy surface. In electrochemical measurements, both Pt-Ni/Ni electrodes showed more negative onset potential of methanol oxidation and slower degradation of oxidation current of methanol than the polycrystalline Pt electrode. X-ray photoelectron spectroscopy of both Pt-Ni/Ni electrodes showed the shift of Pt4f peaks to a higher binding energy, suggesting that the increase in the d vacancy in the balance band 5d orbital of Pt contributed to the improved electrocatalytic activity and durability of the Pt-Ni/Ni electrodes.     

A convenient synthesis of 2−–5− linked oligoribonucleotides

A general synthesis of 2?–5? linked oligoribonucleotides has been achieved on the basis of chemoselective formation of the 2?–5? internucleotide linkage using N-unblocked nucleosides.     

Generic initial ideals of some monomial complete intersections in four variables

Let R = K[x ₁, x ₂, x ₃, x ₄] be the polynomial ring over a field of characteristic zero. For the ideal (x₁^a, x₂^b, x₃^c, x₄^d) ì R{(x_1^a, x_2^b, x_3^c, x_4^d) \subset R}, where at least one of a, b, c and d is equal to two, we prove that its generic initial ideal with respect to the reverse lexicographic order is the almost revlex ideal corresponding to the same Hilbert function.     

New High-Performance Catalysts Developed at Mitsui Chemicals for Polyolefins and Organic Synthesis

This contribution reports Mitsui's R&D activities in the field of catalysis technology focusing on molecular catalysts. Examples of the high-performance molecular catalysts developed at Mitsui include bis(phenoxy-imine) group 4 transition metal complex catalysts (FI Catalysts), phosphazene catalysts (PZN catalysts) and b(beta)-ketoiminato Co(II) complex catalysts. Many of the materials stemming from these catalysts were either difficult or impossible to prepare using conventional catalysts.     

Host-guest interaction between swelling clay minerals and poorly water-soluble drugs. 1: Complex formation between a swelling clay mineral and griseofulvin

The formation of a complex between a swelling clay mineral and griseofulvin (GF), a poorly water-soluble drug, was examined. A strong host-guest interaction between the neutral drug molecules and the clay mineral was observed not only in the solid state but also in aqueous dispersion. The powder X-ray diffraction patterns revealed the disappearance of a crystalline phase of GF through host-guest interaction for samples having low GF contents. The complex formation was confirmed to be due to monolayer adsorption on the basis of quantitative thermochemical analyses. The strong interaction between GF and the clay was also detected when the complex powder was dispersed in an aqueous medium on the basis of the intensity changes of from free GF solution in CD and fluorescence spectra as compared with those observed for the free GF solution.     

Dynamic polymer blends--component recombination between neat dynamic covalent polymers at room temperature

Dynamic polymers based on acylhydrazone bonds in the linear main chains were found to show bond exchange leading to crossover component recombination as neat polymers even at room temperature under acid catalysis, thus generating randomized copolymers.