scholarly journals On the exceptional locus of the birational projections of a normal surface singularity into a plane

2009 ◽  
Vol 321 (9) ◽  
pp. 2461-2473
Author(s):  
Jesús Fernández-Sánchez
Keyword(s):  
Surface Singularity ◽  
Normal Surface ◽  
Exceptional Locus

scholarly journals Some Numerical Criteria for the Nash Problem on Arcs for Surfaces

2008 ◽  
Vol 191 ◽  
pp. 1-19 ◽  
Author(s):  
Marcel Morales
Keyword(s):  
Topological Type ◽  
Resolution Of Singularities ◽  
Surface Singularity ◽  
List Type ◽  
Minimal Resolution ◽  
Normal Surface ◽  
Exceptional Set ◽  
Intersection Matrix ◽  
Irreducible Components ◽  
Almost All

AbstractLet (X, O) be a germ of a normal surface singularity, π: → X be the minimal resolution of singularities and let A = (ai,j) be the n × n symmetrical intersection matrix of the exceptional set of In an old preprint Nash proves that the set of arcs on a surface singularity is a scheme , and defines a map from the set of irreducible components of to the set of exceptional components of the minimal resolution of singularities of (X,O). He proved that this map is injective and ask if it is surjective. In this paper we consider the canonical decomposition •For any couple (Ei,Ej) of distinct exceptional components, we define Numerical Nash condition (NN(i,j)). We have that (NN(i,j)) implies In this paper we prove that (NN(i,j)) is always true for at least the half of couples (i,j).•The condition (NN(i,j)) is true for all couples (i,j) with i ≠ j, characterizes a certain class of negative definite matrices, that we call Nash matrices. If A is a Nash matrix then the Nash map N is bijective. In particular our results depend only on A and not on the topological type of the exceptional set.•We recover and improve considerably almost all results known on this topic and our proofs are new and elementary.•We give infinitely many other classes of singularities where Nash Conjecture is true.The proofs are based on my old work [8] and in Plenat [10].

ON -K2 FOR NORMAL SURFACE SINGULARITIES II

2000 ◽  
Vol 11 (09) ◽  
pp. 1193-1202
Author(s):  
HAO CHEN ◽  
SHIHOKO ISHII
Keyword(s):  
Accumulation Point ◽  
Surface Singularity ◽  
Normal Surface ◽  
Accumulation Points ◽  
Surface Singularities

In this paper we continue our study [1] of the set of nonzero -K2 of normal surface singularities. The main results are (1) Every accumulation point of the set is the sum of -K2 of several normal surface singularities; (2) There are accumulation points of the set which are not -K2 of any one normal surface singularity, which means that the set {-K2} is not closed.

The Effect of Benzene on Bluegill Olfactory Lamellae

1985 ◽  
Vol 43 ◽  
pp. 574-575
Author(s):  
D.R. Mattie ◽  
J.W. Fisher
Keyword(s):  
Surface Morphology ◽  
Soluble Fraction ◽  
Lepomis Macrochirus ◽  
Sublethal Concentration ◽  
Water Soluble ◽  
Major Constituent ◽  
Jet Fuels ◽  
Aquatic Biota ◽  
Normal Surface ◽  
Cacodylate Buffer

Jet fuels such as JP-4 can be introduced into the environment and come in contact with aquatic biota in several ways. Studies in this laboratory have demonstrated JP-4 toxicity to fish. Benzene is the major constituent of the water soluble fraction of JP-4. The normal surface morphology of bluegill olfactory lamellae was examined in conjunction with electrophysiology experiments. There was no information regarding the ultrastructural and physiological responses of the olfactory epithelium of bluegills to acute benzene exposure.The purpose of this investigation was to determine the effects of benzene on the surface morphology of the nasal rosettes of the bluegill sunfish (Lepomis macrochirus). Bluegills were exposed to a sublethal concentration of 7.7±0.2ppm (+S.E.M.) benzene for five, ten or fourteen days. Nasal rosettes were fixed in 2.5% glutaraldehyde and 2.0% paraformaldehyde in 0.1M cacodylate buffer (pH 7.4) containing 1.25mM calcium chloride. Specimens were processed for scanning electron microscopy.

Modeling Vibration-Induced Tire-Pavement Interaction Noise in the Mid-frequency Range

2020 ◽  
Author(s):  
Sterling McBride ◽  
Ricardo Burdisso ◽  
Corina Sandu
Keyword(s):  
Sound Intensity ◽  
Element Model ◽  
Dominant Frequency ◽  
Contact Forces ◽  
Surface Velocity ◽  
New Wave ◽  
Normal Surface ◽  
Radiated Noise ◽  
Physical Effects ◽  
Effects Of Rotation

ABSTRACT Tire-pavement interaction noise (TPIN) is one of the main sources of exterior noise produced by vehicles traveling at greater than 50 kph. The dominant frequency content is typically within 500–1500 Hz. Structural tire vibrations are among the principal TPIN mechanisms. In this work, the structure of the tire is modeled and a new wave propagation solution to find its response is proposed. Multiple physical effects are accounted for in the formulation. In an effort to analyze the effects of curvature, a flat plate and a cylindrical shell model are presented. Orthotropic and nonuniform structural properties along the tire's transversal direction are included to account for differences between its sidewalls and belt. Finally, the effects of rotation and inflation pressure are also included in the formulation. Modeled frequency response functions are analyzed and validated. In addition, a new frequency-domain formulation is presented for the computation of input tread pattern contact forces. Finally, the rolling tire's normal surface velocity response is coupled with a boundary element model to demonstrate the radiated noise at the leading and trailing edge locations. These results are then compared with experimental data measured with an on-board sound intensity system.

A STRENGTHENING OF RESOLUTION OF SINGULARITIES IN CHARACTERISTIC ZERO

2003 ◽  
Vol 86 (2) ◽  
pp. 327-357 ◽  
Author(s):  
A. BRAVO ◽  
O. VILLAMAYOR U.
Keyword(s):  
Characteristic Zero ◽  
Resolution Of Singularities ◽  
Closed Subscheme ◽  
Subject Classification ◽  
Invertible Sheaf ◽  
Simple Manner ◽  
Birational Morphism ◽  
Exceptional Locus

Let $X$ be a closed subscheme embedded in a scheme $W$, smooth over a field ${\bf k}$ of characteristic zero, and let ${\mathcal I} (X)$ be the sheaf of ideals defining $X$. Assume that the set of regular points of $X$ is dense in $X$. We prove that there exists a proper, birational morphism, $\pi : W_r \longrightarrow W$, obtained as a composition of monoidal transformations, so that if $X_r \subset W_r$ denotes the strict transform of $X \subset W$ then:(1) the morphism $\pi : W_r \longrightarrow W$ is an embedded desingularization of $X$ (as in Hironaka's Theorem);(2) the total transform of ${\mathcal I} (X)$ in ${\mathcal O}_{W_r}$ factors as a product of an invertible sheaf of ideals ${\mathcal L}$ supported on the exceptional locus, and the sheaf of ideals defining the strict transform of $X$ (that is, ${\mathcal I}(X){\mathcal O}_{W_r} = {\mathcal L} \cdot {\mathcal I}(X_r)$).Thus (2) asserts that we can obtain, in a simple manner, the equations defining the desingularization of $X$.2000 Mathematical Subject Classification: 14E15.

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