Double point curves for corank 2 map germs from C-2 to C-3

We characterize finite determinacy of map germs f : (C-2, 0) -> (C-3, 0) in terms of the Milnor number mu(D(f)) of the double point curve D(f) in (C-2, 0) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs f(t) : (C-2, 0) -> (C-3, 0) is equivalent to the constancy of both mu(D(f(t))) and mu(f(t)(C-2)boolean AND H) with respect to t, where H subset of C-3 is a generic plane. (C) 2011 Elsevier B.V. All rights reserved.

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are computed using only their weights and degree of homogeneity. A key point of the main theorem is to find the number called polar ratio of this polynomial class. An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneity. The constancy of the L numbers in families formed by such arrangements is shown, with the deformed terms having weighted degree greater than the weighted degree of the initial germ. Moreover, using the results of Massey applied to families of function germs, we obtain the constancy of the homology of the Milnor fibre in this family of semi-weighted homogeneous arrangements.

TOPOLOGY OF SINPLE SINGULARITIES OF RULED SURFACES IN R-p

In this work we compare the simple singularities of germs from R-2 to R-p with multiplicity 2 or 3 with the singularities appearing in the set of 2-ruled surfaces. We also study the topological type of all finitely determined singularities by studying generic projections of these singularities in R-3. (C) 2011 Elsevier B.V. All rights reserved.

Counting singularities via fitting ideals

The stable singularities of differential map germs constitute the main source of studying the geometric and topological behavior of these maps. In particular, one interesting problem is to find formulae which allow us to count the isolated stable singularities which appear in the discriminant of a stable deformation of a finitely determined map germ. Mond and Pellikaan showed how the Fitting ideals are related to such singularities and obtain a formula to count the number of ordinary triple points in map germs from C-2 to C-3, in terms of the Fitting ideals associated with the discriminant. In this article we consider map germs from (Cn+m, 0) to (C-m, 0), and obtain results to count the number of isolated singularities by means of the dimension of some associated algebras to the Fitting ideals. First in Corollary 4.5 we provide a way to compute the total sum of these singularities. In Proposition 4.9, for m = 3 we show how to compute the number of ordinary triple points. In Corollary 4.10 and with f of co-rank one, we show a way to compute the number of points formed by the intersection between a germ of a cuspidal edge and a germ of a plane. Furthermore, we show in some examples how to calculate the number of isolated singularities using these results.

Molecular epidemiology of extended-spectrum-beta-lactamase-producing Klebsiella pneumoniae over a 10 year period in Calgary, Canada

A study was designed to investigate the molecular epidemiology of extended-spectrum -lactamase (ESBL)-producing Klebsiella pneumoniae isolated in a centralized region over a 10 year period (200009). Molecular characterization was done using isoelectric focusing, PCR and sequencing for bla(CTX-M), bla(TEM) and bla(SHV) genes and plasmid-mediated quinolone resistance determinants. Genetic relatedness was determined with PFGE using XbaI and multilocus sequencing typing. A total of 89 patients with incident infections were identified; the majority presented with hospital-onset urinary tract infections. The absolute number of ESBL-producing isolates remained very low until 2003, increased slightly in 2004, remained stable until 2008 and then in 2009 there was an abrupt increase in the numbers of ESBL producers identified. The majority of K. pneumoniae produced CTX-M-14 and -15, and have replaced SHV-12-producing isolates since 2005. We identified four different major sequence types (STs) among 32 of isolates (i.e. ST17, ST20, and the new ST573 and ST575) and provided insight into their clinical and molecular characteristics. The ST isolates were more likely to produce community-onset infections, were associated with bla(CTX-M) and emerged during the latter part of the study period. ST17 produced CTX-M-15 and SHV-12, and was more likely to be positive for qnrB; ST20 produced CTX-M-14 and was positive for qnrS. The multiresistant ST575 that produced CTX-M-15 appeared in 2009. Our study highlights the importance of molecular epidemiology in providing insight into the emergence, characteristics and distribution of STs among ESBL-producing K. pneumoniae.

Colistin Resistance in Escherichia coli and Salmonella enterica Strains Isolated from Swine in Brazil

Reports about acquired resistance to colistin in different bacteria species are increasing, including E. coli of animal origin, but reports of resistance in wild S. enterica of different serotypes from swine are not found in the literature. Results obtained with one hundred and twenty-six E. coli strains from diseased swine and one hundred and twenty-four S. enterica strains from diseased and carrier swine showed a frequency of 6.3% and 21% of colistin-resistant strains, respectively. When comparing the disk diffusion test with the agar dilution test to evaluate the strains, it was confirmed that the disk diffusion test is not recommended to evaluate colistin resistance as described previously. The colistin MIC 90 and MIC 50 values obtained to E. coli were 0.25 mu g/mL and 0.5 mu g/mL, the MIC 90 and MIC 50 to S. enterica were 1 mu g/mL and 8 mu g/mL. Considering the importance of colistin in control of nosocomial human infections with Gram-negative multiresistant bacteria, and the large use of this drug in animal production, the colistin resistance prevalence in enterobacteriaceae of animal origin must be monitored more closely.

Crown dilaceration in permanent teeth after trauma to the primary predecessors: report of three cases

Crown dilaceration of permanent teeth occurs due to the non-axial displacement of the already formed hard tissue portion of the developing crown at an angle to their longitudinal axis due to trauma to the primary predecessors. This is a rare condition, representing only 3% of the total of injuries to developing teeth and usually occurs in permanent maxillary incisors because of the close proximity of their tooth germs to the primary incisors, which are more susceptible to trauma. This alteration frequently results from the intrusion of a primary tooth when the child is around 2 years of age, at which time half of the crown of the permanent successor is already formed. Teeth with dilacerated crowns may either erupt with buccal or lingual displacement or remain impacted. The treatment may involve endodontic, orthodontic, restorative and prosthetic procedures. This paper reports the restorative treatment proposed to reestablish the esthetics and function of the affected teeth in three cases of crown dilaceration in permanent maxillary incisors after trauma to their primary predecessors.

Lê–Greuel type formula for the Euler obstruction and applications

The Euler obstruction of a function f can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we establish several Lê–Greuel type formulas for germs f:(X,0)→(C,0) and g:(X,0)→(C,0). We give applications when g is a generic linear form and when f and g have isolated singularities.

Projections of hypersurfaces in 'R POT.4' with boundary to planes

We study orthogonal projections of generic embedded hypersurfaces in 'R POT.4' with boundary to 2-spaces. Therefore, we classify simple map germs from 'R POT.3' to the plane of codimension less than or equal to 4 with the source containing a distinguished plane which is preserved by coordinate changes. We also go into some detail on their geometrical properties in order to recognize the cases of codimension less than or equal to 1.

Order induced charge carrier mobility enhancement in columnar liquid crystal diodes

Discotic molecules comprising a rigid aromatic core and flexible side chains have been promisingly applied in OLEDs as self-organizing organic semiconductors. Due to their potentially high charge carrier mobility along the columns, device performance can be readily improved by proper alignment of columns throughout the bulk. In the present work, the charge mobility was increased by 5 orders of magnitude due to homeotropic columnar ordering induced by the boundary interfaces during thermal annealing in the mesophase. State-of-the-art diodes were fabricated using spin-coated films whose homeotropic alignment with formation of hexagonal germs was observed by polarizing optical microscopy. The photophysical properties showed drastic changes at the mesophase-isotropic transition, which is supported by the gain of order observed by X-ray diffraction. The electrical properties were investigated by modeling the current−voltage characteristics by a space-charge-limited current transport with a field dependent mobility.