Topological invariants of isolated complete intersection curve singularities

In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.

Finite determinacy and Whitney equisingularity of map germs from C(n) to C(2n-1)

We show that a holomorphic map germ f : (C(n), 0) -> (C(2n-1), 0) is finitely determined if and only if the double point scheme D(f) is a reduced curve. If n >= 3, we have that mu(D(2)(f)) = 2 mu(D(2)(f)/S(2))+C(f)-1, where D(2)(f) is the lifting of the double point curve in (C(n) x C(n), 0), mu(X) denotes the Milnor number of X and C(f) is the number of cross-caps that appear in a stable deformation of f. Moreover, we consider an unfolding F(t, x) = (t, f(t)(x)) of f and show that if F is mu-constant, then it is excellent in the sense of Gaffney. Finally, we find a minimal set of invariants whose constancy in the family f(t) is equivalent to the Whitney equisingularity of F. We also give an example of an unfolding which is topologically trivial, but it is not Whitney equisingular.

Bipartite graphs and quasipositive surfaces

We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links and discuss its potential relation with the adjacency problem for plane curve singularities.

Cutting Arcs For Torus Links And Trees

Among all torus links, we characterise those arising as links of simple plane curve singularities by the property that their fibre surfaces admit only a finite number of cutting arcs that preserve fibredness. The same property allows a characterisation of Coxeter-Dynkin trees (i.e., An , Dn , E6 , E7 and E8 ) among all positive tree-like Hopf plumbings.

On Sandwiched Singularities

Sandwich-Singularitäten sind die Singularitäten auf derNormalisierung von Aufblasungen eines regulärenFlächenkeimes. In der Arbeit wird ein enger Zusammenhangzwischen Topologie und Deformationstheorie vonSandwich-Singularitäten einerseits und ebenenKurvensingularitäten andererseits dargestellt. NeueErgebnisse betreffen u.a. Deformationen vonnulldimensionalen komplexen Räumen in der Ebene, die durchvollständige Ideale beschrieben werden, z.B. wann'simultanes Aufblasen' der Fasern einer solchen Deformationmöglich ist. Zudem werden Glättungskomponenten und dieKollar-Vermutung für Sandwich-Singularitäten untersucht undim Zusammenhang damit numerische Kriterien für die Frage, obdie symbolische Algebra einer Raumkurve endlich erzeugt ist.

The logarithmic spiral, autoisoptic curve

In the Line of Investigation that in the department of “Technical Drawing” in the School of Agriculture Engineering of Madrid, we carry out on the study of The Technical Curves and his singularities, we demonstrate an interesting property of the Logarithmic Spiral. The demonstrated property consists of which the logarithmic spiral is a autoisoptic curve, that is to say that if from a point P anyone of the spiral tangent straight lines draw up to the previous arc, these form a constant angle α. This demonstration is novel and in addition we get to contribute a method to calculate the angle α given the equation of the spiral.

Treatment of singularities in 2-D domains using BIEM

The singularities which arise when there is a sudden change of boundary conditions are modelled using spectral shape interpolation functions. The procedure can be used for elasticity as well as potential theory and to any degree of accuracy with respect to the smooth part of the curve.

Results on singularities of pairs

Thesis (Ph.D.)--University of Washington, 2016-06

Computational adjustment technique for digital mammographic images based on the digitizer characteristic curve

We evaluated the performance of a novel procedure for segmenting mammograms and detecting clustered microcalcifications in two types of image sets obtained from digitization of mammograms using either a laser scanner, or a conventional ""optical"" scanner. Specific regions forming the digital mammograms were identified and selected, in which clustered microcalcifications appeared or not. A remarkable increase in image intensity was noticed in the images from the optical scanner compared with the original mammograms. A procedure based on a polynomial correction was developed to compensate the changes in the characteristic curves from the scanners, relative to the curves from the films. The processing scheme was applied to both sets, before and after the polynomial correction. The results indicated clearly the influence of the mammogram digitization on the performance of processing schemes intended to detect microcalcifications. The image processing techniques applied to mammograms digitized by both scanners, without the polynomial intensity correction, resulted in a better sensibility in detecting microcalcifications in the images from the laser scanner. However, when the polynomial correction was applied to the images from the optical scanner, no differences in performance were observed for both types of images. (C) 2008 SPIE and IS&T [DOI: 10.1117/1.3013544]

Rotation curve bifurcations as indicators of close recent galaxy encounters

Context. Rotation curves of interacting galaxies often show that velocities are either rising or falling in the direction of the companion galaxy. Aims. We seek to reproduce and analyse these features in the rotation curves of simulated equal-mass galaxies suffering a one-to-one encounter as possible indicators of close encounters. Methods. Using simulations of major mergers in 3D, we study the time evolution of these asymmetries in a pair of galaxies during the first passage. Results. Our main results are: (a) the rotation curve asymmetries appear right at pericentre of the first passage, (b) the significant disturbed rotation velocities occur within a small time interval, of similar to 0.5 Gyr h(-1), and, therefore, the presence of bifurcation in the velocity curve could be used as an indicator of the pericentre occurrence. These results are in qualitative agreement with previous findings for minor mergers and flybys.

Anisotropic singularities in modified gravity models

We show that the common singularities present in generic modified gravity models governed by actions of the type S = integral d(4)x root-gf(R, phi, X). with X = -1/2 g(ab)partial derivative(a)phi partial derivative(b)phi, are essentially the same anisotropic instabilities associated to the hypersurface F(phi) = 0 in the case of a nonminimal coupling of the type F(phi)R, enlightening the physical origin of such singularities that typically arise in rather complex and cumbersome inhomogeneous perturbation analyses. We show, moreover, that such anisotropic instabilities typically give rise to dynamically unavoidable singularities, precluding completely the possibility of having physically viable models for which the hypersurface partial derivative f/partial derivative R = 0 is attained. Some examples are explicitly discussed.

Analysis of the E-J Curve of HTS Tapes Under DC and AC Magnetic Fields at 77 K

The evaluation of the electrical characteristics of technical HTS tapes are of the key importance in determining the design and operational features of superconducting power apparatuses as well as to understand the external factors which affect the superconducting performance. In this work we report the systematic measurements of the electric field versus current density, E-J relation of short samples for three commercial HTS tapes (BSCCO-2223 tapes, with and without steel reinforcement, and YBCO-coated conductor) at 77 K. In order to get sensitive and noiseless voltage signals the measurements were carried out with DC transport current and subjecting the broad surface tape to DC (0-300 mT) and AC (0-62 mT, 60 Hz) magnetic fields. The voltage is measured by a sensitive nanovoltmeter and the applied magnetic field is monitored by a Hall sensor placed on the tape broad surface. The comparison between the results obtained from the three tapes was done by fitting a power-law equation for currents in the vicinity of the critical current. For the current regime below the critical one a linear correlation of the electric field against the current density is observed. The BSCCO samples presented the same behavior, i.e., a decreasing of n-index with the increasing DC and AC magnetic field strength. Under AC field the decreasing slope of n-index is steeper as compared to DC field. The n-index curve for the YBCO tape showed similar behavior for AC field, however under DC field in the 0-390 mT range exhibited a slight decreasing of the n-index.

Isotropic singularities in shear-free perfect fluid cosmologies

We investigate barotropic perfect fluid cosmologies which admit an isotropic singularity. From the General Vorticity Result of Scott, it is known that these cosmologies must be irrotational. In this paper we prove, using two different methods, that if we make the additional assumption that the perfect fluid is shear-free, then the fluid flow must be geodesic. This then implies that the only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic singularity are the FRW models.

Right adolescent idiopathic thoracic curve (Lenke 1 A and B): does cost of instrumentation and implant density improve radiographic and cosmetic parameters?

In adolescent idiopathic scoliosis (AIS) there has been a shift towards increasing the number of implants and pedicle screws, which has not been proven to improve cosmetic correction. To evaluate if increasing cost of instrumentation correlates with cosmetic correction using clinical photographs. 58 Lenke 1A and B cases from a multicenter AIS database with at least 3 months follow-up of clinical photographs were used for analysis. Cosmetic parameters on PA and forward bending photographs included angular measurements of trunk shift, shoulder balance, rib hump, and ratio measurements of waist line asymmetry. Pre-op and follow-up X-rays were measured for coronal and sagittal deformity parameters. Cost density was calculated by dividing the total cost of instrumentation by the number of vertebrae being fused. Linear regression and spearman`s correlation were used to correlate cost density to X-ray and photo outcomes. Three independent observers verified radiographic and cosmetic parameters for inter/interobserver variability analysis. Average pre-op Cobb angle and instrumented correction were 54A degrees (SD 12.5) and 59% (SD 25) respectively. The average number of vertebrae fused was 10 (SD 1.9). The total cost of spinal instrumentation ranged from $6,769 to $21,274 (Mean $12,662, SD $3,858). There was a weak positive and statistically significant correlation between Cobb angle correction and cost density (r = 0.33, p = 0.01), and no correlation between Cobb angle correction of the uninstrumented lumbar spine and cost density (r = 0.15, p = 0.26). There was no significant correlation between all sagittal X-ray measurements or any of the photo parameters and cost density. There was good to excellent inter/intraobserver variability of all photographic parameters based on the intraclass correlation coefficient (ICC 0.74-0.98). Our method used to measure cosmesis had good to excellent inter/intraobserver variability, and may be an effective tool to objectively assess cosmesis from photographs. Since increasing cost density only improves mildly the Cobb angle correction of the main thoracic curve and not the correction of the uninstrumented spine or any of the cosmetic parameters, one should consider the cost of increasing implant density in Lenke 1A and B curves. In the area of rationalization of health care expenses, this study demonstrates that increasing the number of implants does not improve any relevant cosmetic or radiographic outcomes.

Motor development curve from 0 to 12 months in infants born preterm

Aim: To trace a reference curve for motor development from birth up to 12 months of corrected chronological age in infants born preterm and low birth weight. Methods: This is a cross-sectional study with a sample of 308 preterm infants (53% boys) weighing < 2500 g at birth. The Alberta Infant Motor Scale (AIMS) was used for motor development assessment. Results: Comparing the motor performance of preterm infants with infants from a standardized sample on the AIMS, it was found that, except for the age group of the newborn, preterm infants showed lower motor development scores in comparison with the AIMS normative sample in all age groups between 1 and 12 months. The curve of motor development showed a continuous increase in the number of motor skills of preterm infants during their first 12 months of age. However, the average of motor acquisitions of preterm infants showed a nonlinear pattern with a standard indicator of stabilization between 8 and 10 months of age. Conclusion: Preterm infants, 1-12 months of age, showed motor development AIMS scores lower than the standards established in the normative sample. The findings may contribute as norm-reference for assessing the motor development of preterm infants in follow-up programmes in developing countries.