Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module $M$ over an Artin algebra $\Lambda$, there exists a positive integer $n_M$ such that for all finitely generated $\Lambda$-modules $N$, if \Ext_{\Lambda}^i(M,N)=0 for all $i\gg 0$, then \Ext_{\Lambda}^i(M,N)=0 for all $i\geq n_M$. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.Comment: 16 page

Electron momentum distribution of a single mobile hole in the t-J model

We investigate the electron momentum distribution function (EMDF) for the two-dimensional t-J model. The results are based on the self-consistent Born approximation (SCBA) for the self-energy and the wave function. In the Ising limit of the model we give the results in a closed form, in the Heisenberg limit the results are obtained numerically. An anomalous momentum dependence of EMDF is found and the anomaly is in the lowest order in number of magnons expressed analitycally. We interpret the anomaly as a fingerprint of an emerging large Fermi surface coexisting with hole pockets.Comment: M2S - submitted to Physica

Kinetic and ion pairing contributions in the dielectric spectra of electrolyte aqueous solutions

Understanding dielectric spectra can reveal important information about the dynamics of solvents and solutes from the dipolar relaxation times down to electronic ones. In the late 1970s, Hubbard and Onsager predicted that adding salt ions to a polar solution would result in a reduced dielectric permittivity that arises from the unexpected tendency of solvent dipoles to align opposite to the applied field. So far, this effect has escaped an experimental verification, mainly because of the concomitant appearance of dielectric saturation from which the Hubbard-Onsager decrement cannot be easily separated. Here we develop a novel non-equilibrium molecular dynamics simulation approach to determine this decrement accurately for the first time. Using a thermodynamic consistent all-atom force field we show that for an aqueous solution containing sodium chloride around 4.8 Mol/l, this effect accounts for 12\% of the total dielectric permittivity. The dielectric decrement can be strikingly different if a less accurate force field for the ions is used. Using the widespread GROMOS parameters, we observe in fact an {\it increment} of the dielectric permittivity rather than a decrement. We can show that this increment is caused by ion pairing, introduced by a too low dispersion force, and clarify the microscopic connection between long-living ion pairs and the appearance of specific features in the dielectric spectrum of the solution

Entanglement of two delocalised electrons

Several convenient formulae for the entanglement of two indistinguishable delocalised spin-1/2 particles are introduced. This generalizes the standard formula for concurrence, valid only in the limit of localised or distinguishable particles. Several illustrative examples are given.Comment: 4 page

Synthesis, Conformational Studies and Enantioselective Homogeneous Catalytic Hydrogenation with CRC-PHOS, and Some Congeners

The lactone of (1S,3R)-1-hydroxy-1-diphenylphosphino metyl- 2,2,3-trimethylcyclopentan-3-carboxylic acid (8, CRC-PHOS), and (1R,3R)-bis(diphenylphosphinoxymethyl)-2,2,3-trimethylcyclopentane (16), were prepared starting from ( + )-camphanic and (-)- isocamphoric acid, respectively. Their complex salts [Rh(norbornadiene) lactone of (1S,3R)-1-hydroxy-1-diphenylphosphinomethyl- 2,2,3-trimethylcyclopentan-3-carboxylic acid] perchlorate (27), and [Rh(norbornadiene (1R,3R)-1,2,2-trimethyl-1,3-bis ( diphenylphosphinoxymethyl) cyclopentane)] perchlorate (28) were isolated and their catalytic and enantioselective ability tested on some model prochiral carboxylic acids. The asymetric bias did not exceed 35°/o e. e. in either case. Attepmts at preparation of the diphosphine congener of 16, i.e. 21, as well as isolation of the phosphinite congener of 8, i. e. 22, failed. NMR LIS study of the conformation in solution of 8, and model compounds 6 and 9 revealed that 6 and 8 possess in their most stable conformations a dihedral angle 1P of 165°, (Figure 4.) while for 9 two stable conformations with 1P 200° and 350° are found. These results indicate that bidentate binding of metal to heteroatom X (0, P) in the side chain, and to the tetrahedral oxygen within lactone group is scarcely possible

Electron Spin Resonance of SrCu2(BO3)2 at High Magnetic Field

We calculate the electron spin resonance (ESR) spectra of the quasi-two-dimensional dimer spin liquid SrCu2(BO3)2 as a function of magnetic field B. Using the standard Lanczos method, we solve a Shastry-Sutherland Hamiltonian with additional Dzyaloshinsky-Moriya (DM) terms which are crucial to explain different qualitative aspects of the ESR spectra. In particular, a nearest-neighbor DM interaction with a non-zero D_z component is required to explain the low frequency ESR lines for B || c. This suggests that crystal symmetry is lowered at low temperatures due to a structural phase transition.Comment: 4 pages, 4 b&w figure

Layer-by-layer formation of oligoelectrolyte multilayers: a combined experimental and computational study

For the first time, the combination of experimental preparation and results of fully atomistic simulations of an oligoelectrolyte multilayer (OEM) made of poly(diallyl dimethyl ammonium chloride)/poly(styrene sulfonate sodium salt) (PDADMAC/PSS) is presented. The layer-by-layer growth was carried out by dipping silica substrates in oligoelectrolyte solutions and was modeled by means of atomistic molecular dynamics simulations with a protocol that mimics the experimental procedure up to the assembly of four layers. Measurements of OEM thickness, surface roughness and amount of adsorbed oligoelectrolyte chains obtained from both approaches are compared. A good agreement between simulated and experimental results was found, with some deviations due to intrinsic limitations of both methods. However, the combination of information extracted from simulations to support the analysis of experimental data can overcome such restrictions and improve the interpretation of experimental results. On the other hand, processes dominated by slower kinetics, like the destabilization of adsorbed layers upon equilibration with the surrounding environment, are out of reach for the simulation modeling approach, but they can be investigated by monitoring in situ the oligoelectrolyte adsorption during the assembly process. This demonstrates how the synergistic use of simulation and experiments improves the knowledge of OEM properties down to the molecular scale

FePO(4)NPs Are an Efficient Nutritional Source for Plants: Combination of Nano-Material Properties and Metabolic Responses to Nutritional Deficiencies

Phosphorous and iron are a macro- and micronutrient, respectively, whose low bioavailability can negatively affect crop productivity. There is ample evidence that the use of conventional P and Fe fertilizers has several environmental and economical disadvantages, but even though great expectations surround nanotechnology and its applications in the field of plant nutrition, little is known about the mechanisms underlying the uptake and use of these sub-micron particles (nanoparticles, NPs) by crop species. This work shows that cucumber and maize plants both use the nutrients borne by FePO(4)NPs more efficiently than those supplied as bulk. However, morpho-physiological parameters and nutrient content analyses reveal that while cucumber plants (aStrategy Ispecies with regard to Fe acquisition) mainly use these NPs as a source of P, maize (aStrategy IIspecies) uses them preferentially for Fe. TEM analyses of cucumber root specimens revealed no cell internalization of the NPs. On the other hand, electron-dense nanometric structures were evident in proximity of the root epidermal cell walls of the NP-treated plants, which after ESEM/EDAX analyses can be reasonably identified as iron-oxyhydroxide. It appears that the nutritional interaction between roots and NPs is strongly influenced by species-specific metabolic responses

A Chiral Phosphine (CRC-PHOS) Derived from ( + )-Champhanic Acid. A New Ligand for Homogeneous Asymmetric Hydrogenation

The lactone of 1S,3S-1-hydroxy-1-diphenylphosphinomethyl- 2,2,3-tri-methyl-cyclopentan-3-carboxylic acid (4, CRC-PHOS) was prepared from ( + )-camphanic acid methylester 1, and its complex salt [Rh(CRC-PHOS)2NBD] · CI04 • THF (5) was isolated. The latter exhibited rather a high rate, but low enantioselectivity in the first attempt at asymmetric hydrogenation