The core of zero-dimensional monomial ideals

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.     

Some remarks on the identity between a variational integral and its relaxed functional

Summary Letf: (x, z)∈R ⁿ×Rⁿ→f(x, z)∈[0, +∞] be measurable inx and convex inz. It is proved, by an example, that even iff verifies a condition as|z| ^p≤f(x, z)≤Λ(a(x)+|z|^q) with 1<p<q,a∈L _loc ^s (R ⁿ),s>1, the functional that isL ¹(Ω)-lower semicontinuous onW ^1,1(Ω), does not agree onW ^1,1(Ω) with its relaxed functional in the topologyL ¹(Ω) given by inf

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Riassunto Siaf: (x, z)∈R ⁿ×Rⁿ→f(x, z)∈[0, +∞] misurabile inx e convessa inz. Si mostra con un esempio che anche sef verifica una condizione del tipo|z| ^p≤f(x, z)≤Λ(a(x)+|z|^q) con 1<p<q,a∈L _loc ^s (R ⁿ),s>1, il funzionale , che èL ¹(Ω)-semicontinuo inferiormente suW ^1,1(Ω), non coincide suW ^1,1(Ω) con il suo funzionale rilassato nella topologiaL ¹(Ω) definito da inf

     

New pi-extended water-soluble squaraines as singlet oxygen generators

[graph: see text] Condensation of squaric acid with a number of differently substituted 2-pyrrolyl derivatives afforded three new classes of squaraines. Their sharp and intense absorption bands in the biological window (700-900 nm), inherent singlet oxygen generation capabilities, together with proper functionalization allowing good water solubility make them suitable candidates as new non-porphyrinic singlet oxygen photosensitizers for photodynamic therapy (PDT).     

Are ring currents still useful to rationalize the benzene proton magnetic shielding?

[structure: see text] The conventional interpretation of proton NMR chemical shifts is supported by large basis set ab initio quantum mechanical calculations. The benzene protons are predicted to lie within the deshielding zone defined in terms of the out-of-plane magnetic shielding domain. However, ring currents by themselves are not sufficient to account quantitatively for the observed benzene proton downfield chemical shift. sigma-Electron contributions must also be taken into account. The conventional explanation for the ethyne proton chemical shift is valid.     

Stability boundaries, percolation threshold, and two-phase coexistence for polydisperse fluids of adhesive colloidal particles

We study the polydisperse Baxter model of sticky hard spheres (SHS) in the modified mean spherical approximation (mMSA). This closure is known to be the zero-order approximation C0 of the Percus-Yevick closure in a density expansion. The simplicity of the closure allows a full analytical study of the model. In particular we study stability boundaries, the percolation threshold, and the gas-liquid coexistence curves. Various possible subcases of the model are treated in details. Although the detailed behavior depends upon the particularly chosen case, we find that, in general, polydispersity inhibits instabilities, increases the extent of the nonpercolating phase, and diminishes the size of the gas-liquid coexistence region. We also consider the first-order improvement of the mMSA (C0) closure (C1) and compare the percolation and gas-liquid boundaries for the one-component system with recent Monte Carlo simulations. Our results provide a qualitative understanding of the effect of polydispersity on SHS models and are expected to shed new light on the applicability of SHS models for colloidal mixtures.     

The use of “actinometer” gases in optical diagnostics of plasma etching mixtures: SF6-O2

The spectroscopic emission intensities from excited F atoms in SF₆-O₂ discharges at 1 torr have been correlated to the densities of atoms in their ground electronic state by measuring the excitation efficiencies of the electrons in the energy range 11 to 17 eV with a method which essentially consists in the analysis of the emission of Ar or N₂, added as actinometer gases to the discharge mixtures. The general applicability of the method has been tested by a direct titration of F atoms with chlorine. The spectroscopic analysis has allowed the determination of useful information on the trends of both the electron densities and their energies as a function of the oxygen percent in the feed.     

On the use of symmetry in first-order perturbed HF theory. II

A method is described whereby molecular symmetry is employed to reduce the number of two-electron integrals in perturbed Hartree–Fock calculations of second-order properties. The method is a generalization of the Dacre–Elder procedure. First- and second-rank perturbing tensor operators are examined in the coupled HF approach to electric dipole polarizabilities, magnetic susceptibilities, quadrupole polarizabilities, and spin-dopolar contributions to spin–spin coupling constants. The procedure sketched here permits a large saving of computer efforts, which is shown by some illustrative examples.     

Di- and trinuclear Zn2+ complexes of calix[4]arene based ligands as catalysts of acyl and phosphoryl transfer reactions

The calix[4]arene scaffold, blocked in the cone conformation by proper alkylation of the lower rim hydroxyls, was used as a convenient molecular platform for the design of bi- and trimetallic Zn2+ catalysts. The catalytic activity of the Zn2+ complexes of calix[4]arenes decorated at the 1,2-, 1,3-, and 1,2,3-positions of the upper rim with 2,6-bis[(dimethylamino)methyl]pyridine units were investigated in the cleavage of ester 6 and of the RNA model compound HPNP. High rate enhancements, up to 4 orders of magnitude, were observed in a number of catalyst-substrate combinations. Interestingly the order of catalytic efficiency among regioisomeric dinuclear complexes in the cleavage of ester 6 is 1,2-vicinal > 1,3-distal, but it is reversed in the reaction of HPNP. The higher efficiency of trinuclear compared to dinuclear complexes provides an indication of the cooperation of three Zn2+ ions in the catalytic mechanism.