Complete ideals and singularities of space curves

We consider complete ideals supported on finite sequences of infinitely near points, in regular local rings with dimensions greater than two. We study properties of factorizations in Lipman special *-simple complete ideals. We relate it to a type of proximity, linear proximity, of the points, and give conditions in order to have unique factorization. Several examples are presented. Received: 2 February 2000 / in final form: 14 March 2001 / Published online: 18 January 2002     

Diastereoselective Electrophilic Amination of Chiral 1‐Benzoyl‐2,3,5,6‐tetrahydro‐3‐methyl‐2‐(1‐methylethyl)pyrimidin‐4(1H)‐one for the Asymmetric Syntheses of α‐Substituted α,β‐Diaminopropanoic Acids

The chiral compounds (R)‐ and (S)‐1‐benzoyl‐2,3,5,6‐tetrahydro‐3‐methyl‐2‐(1‐methylethyl)pyrimidin‐4(1H)‐one ((R)‐ and (S)‐ 1 ), derived from (R)‐ and (S)‐asparagine, respectively, were used as convenient starting materials for the preparation of the enantiomerically pure α‐alkylated (alkyl=Me, Et, Bn) α,β‐diamino acids (R)‐ and (S)‐ 11 – 13 . The chiral lithium enolates of (R)‐ and (S)‐ 1 were first alkylated, and the resulting diasteroisomeric products 5 – 7 were aminated with ‘di(tert‐butyl) azodicarboxylate’ (DBAD), giving rise to the diastereoisomerically pure (≥98%) compounds 8 – 10 . The target compounds (R)‐ and (S)‐ 11 – 13 could then be obtained in good yields and high purities by a hydrolysis/hydrogenolysis/hydrolysis sequence.     

Critical points in a relativistic bosonic gas induced by the quantum structure of spacetime

It is well known that phase transitions arise if the interaction among particles embodies an attractive as well as a repulsive contribution. In this work it will be shown that the breakdown of Lorentz symmetry, characterized through a deformation in the relation dispersion, plus the bosonic statistics predict the emergence of critical points. In other words, in some quantum gravity models the structure of spacetime implies the emergence of critical points even when no interaction among the particles has been considered.     

Structural Effects in Visible‐Light‐Responsive Metal–Organic Frameworks Incorporating ortho‐Fluoroazobenzenes

The ability to control the interplay of materials with low‐energy photons is important as visible light offers several appealing features compared to ultraviolet radiation (less damaging, more selective, predominant in the solar spectrum, possibility to increase the penetration depth). Two different metal–organic frameworks (MOFs) were synthesized from the same linker bearing all‐visible ortho‐fluoroazobenzene photoswitches as pendant groups. The MOFs exhibit different architectures that strongly influence the ability of the azobenzenes to isomerize inside the voids. The framework built with Al‐based nodes has congested 1D channels that preclude efficient isomerization. As a result, local light–heat conversion can be used to alter the CO₂ adsorption capacity of the material on exposure to green light. The second framework, built with Zr nodes, provides enough room for the photoswitches to isomerize, which leads to a unique bistable photochromic MOF that readily responds to blue and green light. The superiority of green over UV irradiation was additionally demonstrated by reflectance spectroscopy and analysis of digested samples. This material offers promising perspectives for liquid‐phase applications such as light‐controlled catalysis and adsorptive separation.     

Physics of compaction of fine cohesive particles

Fluidized fractal clusters of fine particles display critical-like dynamics at the jamming transition, characterized by a power law relating consolidation stress with volume fraction increment [sigma--(c) proportional, variant(Deltaphi)(beta)]. At a critical stress clusters are disrupted and there is a crossover to a logarithmic law (Deltaphi = nu logsigma--(c)) resembling the phenomenology of soils. We measure lambda identical with- partial differentialDelta(1/phi)/ partial log(sigma--(c) proportional, variant Bo(0.2)(g), where Bo(g) is the ratio of interparticle attractive force (in the fluidlike regime) to particle weight. This law suggests that compaction is ruled by the internal packing structure of the jammed clusters at nearly zero consolidation.     

Asymptotic properties of two interacting maps

In this paper we consider a system whose state x changes to (x) if a perturbation occurs at the time t, for . Moreover, the state x changes to the new state (x) at time t, for . It is assumed that the number of perturbations in an interval (0, t) is a Poisson process. Here and are measurable maps from a measure space into itself. We give conditions for the existence of a stationary distribution of the system when the maps and commute, and we prove that any stationary distribution is an invariant measure of these maps.     

Effectiveness of Photodynamic Therapy in Elimination of HPV‐16 and HPV‐18 Associated with CIN I in Mexican Women

This study aimed to determine the effectiveness of photodynamic therapy (PDT), using δ‐aminolevulinic acid (5‐ALA), in the elimination of premalignant cervical lesions in Mexican patients with human papillomavirus (HPV) infection and/or cervical intraepithelial neoplasia (CIN). Thirty women diagnosed with CIN I and/or positive for HPV participated in the study. Topical 6% 5‐ALA in gel form was applied to the uterine cervix; after 4 h, the lesion area was irradiated with a light dose of 200 J cm^?2 at 635 nm. This procedure was performed three times at 48‐h intervals. Clinical follow‐up was performed at 3, 6, and 12 months after the initial PDT administration, by colposcopy, cervical cytology, histopathological analysis, polymerase chain reaction, and hybrid capture. Of HPV‐infected patients without evidence of CIN I, 80% cleared the infection, while HPV associated with CIN I was eliminated in 83% of patients (P < 0.05). At 12 months, CIN I had regressed in 57% of patients, although this response was not statistically significant. PDT using 6% 5‐ALA is concluded to be effective in eliminating HPV infection associated or not with CIN I.     

Algorithm for the Semigroup of a Space Curve Singularity

The semigroup of values of irreducible space curve singularities is the set of intersection multiplicities among hypersurfaces and the given curve. It is an invariant of the singularity, and for plane curves it characterizes the equisingularity type considered by Zariski. For space curve singularities the semigroup of values is a numerical semigroup and it can not be computed by means of the exponents of any Puiseux parametrization, as in the plane case. We obtain an algorithm for calculating the semigroup of values of a space curve singularity, which determines the generators of the semigroup and the valuation ideals associated with the semigroup. We give a Maple version of the algorithm.