Linear components of the tangent cone in the Nash modification of a complex surface singularity

2011 ◽  
Vol 3 ◽  
pp. 83-88
Author(s):  
Jawad Snoussi
Keyword(s):  
Tangent Cone ◽  
Complex Surface ◽  
Surface Singularity ◽  
Nash Modification

scholarly journals Contact structures on AR-singularity links

2018 ◽  
Vol 29 (03) ◽  
pp. 1850019
Author(s):  
Çağrı Karakurt ◽  
Ferı̇t Öztürk
Keyword(s):  
Contact Structure ◽  
Complex Surface ◽  
Surface Singularity ◽  
Reverse Direction ◽  
Contact Structures ◽  
Rational Singularity ◽  
Existence Problem ◽  
The Way

An isolated complex surface singularity induces a canonical contact structure on its link. In this paper, we initiate the study of the existence problem of Stein cobordisms between these contact structures depending on the properties of singularities. As a first step, we construct an explicit Stein cobordism from any contact 3-manifold to the canonical contact structure of a proper almost rational singularity introduced by Némethi. We also show that the construction cannot always work in the reverse direction: in fact, the U-filtration depth of contact Ozsváth–Szabó invariant obstructs the existence of a Stein cobordism from a proper almost rational singularity to a rational one. Along the way, we detect the contact Ozsváth–Szabó invariants of those contact structures fillable by an AR plumbing graph, generalizing an earlier work of the first author.

New replica method with plasma polymerized film by glow discharge

1988 ◽  
Vol 46 ◽  
pp. 414-415
Author(s):  
A. Tanaka ◽  
M. Yamaguchi ◽  
T. Hirano
Keyword(s):  
Power Supply ◽  
Plasma Polymerization ◽  
Vacuum Chamber ◽  
Complex Surface ◽  
Replica Method ◽  
Metal Extraction ◽  
High Voltage Power Supply ◽  
Negative Glow ◽  
Hydrocarbon Gas ◽  
Hydrocarbon Molecules

The plasma polymerization replica method and its apparatus have been devised by Tanaka (1-3). We have published several reports on its application: surface replicas of biological and inorganic specimens, replicas of freeze-fractured tissues and metal-extraction replicas with immunocytochemical markers.The apparatus for plasma polymerization consists of a high voltage power supply, a vacuum chamber containing a hydrocarbon gas (naphthalene, methane, ethylene), and electrodes of an anode disk and a cathode of the specimen base. The surface replication by plasma polymerization in negative glow phase on the cathode was carried out by gassing at 0.05-0.1 Torr and glow discharging at 1.5-3 kV D.C. Ionized hydrocarbon molecules diffused into complex surface configurations and deposited as a three-dimensionally polymerized film of 1050 nm in thickness.The resulting film on the complex surface had uniform thickness and showed no granular texture. Since the film was chemically inert, resistant to heat and mecanically strong, it could be treated with almost any organic or inorganic solvents.

scholarly journals Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1054
Author(s):  
Rozaimi Zakaria ◽  
Abd. Fatah Wahab ◽  
Isfarita Ismail ◽  
Mohammad Izat Emir Zulkifly
Keyword(s):  
Complex Surface ◽  
Complex Data ◽  
Fuzzy Data ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
Data Control ◽  
Surface Data ◽  
Model Complex

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

scholarly journals Non Kählerian surfaces with a cycle of rational curves

2021 ◽  
Vol 8 (1) ◽  
pp. 208-222
Author(s):  
Georges Dloussky
Keyword(s):  
Deformation Theory ◽  
Complex Surface ◽  
Rational Curves ◽  
Intersection Form ◽  
Connected Component ◽  
Hirzebruch Surface ◽  
Compact Complex Surface ◽  
A Chain

Abstract Let S be a compact complex surface in class VII0 + containing a cycle of rational curves C = ∑Dj . Let D = C + A be the maximal connected divisor containing C. If there is another connected component of curves C ′ then C ′ is a cycle of rational curves, A = 0 and S is a Inoue-Hirzebruch surface. If there is only one connected component D then each connected component Ai of A is a chain of rational curves which intersects a curve Dj of the cycle and for each curve Dj of the cycle there at most one chain which meets Dj . In other words, we do not prove the existence of curves other those of the cycle C, but if some other curves exist the maximal divisor looks like the maximal divisor of a Kato surface with perhaps missing curves. The proof of this topological result is an application of Donaldson theorem on trivialization of the intersection form and of deformation theory. We apply this result to show that a twisted logarithmic 1-form has a trivial vanishing divisor.

scholarly journals Non-Destructive Fuel Volume Measurements Can Estimate Fine-Scale Biomass across Surface Fuel Types in a Frequently Burned Ecosystem

Fire ◽  
2021 ◽  
Vol 4 (3) ◽  
pp. 36
Author(s):  
Quinn A. Hiers ◽  
E. Louise Loudermilk ◽  
Christie M. Hawley ◽  
J. Kevin Hiers ◽  
Scott Pokswinski ◽  
...  
Keyword(s):  
Bulk Density ◽  
Pinus Palustris ◽  
Field Measurements ◽  
Complex Surface ◽  
Fuel Type ◽  
Field Methods ◽  
Volume Measurements ◽  
Woody Litter ◽  
Non Destructive ◽  
Surface Vegetation

Measuring wildland fuels is at the core of fire science, but many established field methods are not useful for ecosystems characterized by complex surface vegetation. A recently developed sub-meter 3D method applied to southeastern U.S. longleaf pine (Pinus palustris) communities captures critical heterogeneity, but similar to any destructive sampling measurement, it relies on separate plots for calculating loading and consumption. In this study, we investigated how bulk density differed by 10-cm height increments among three dominant fuel types, tested predictions of consumption based on fuel type, height, and volume, and compared this with other field measurements. The bulk density changed with height for the herbaceous and woody litter fuels (p < 0.001), but live woody litter was consistent across heights (p > 0.05). Our models predicted mass well based on volume and height for herbaceous (RSE = 0.00911) and woody litter (RSE = 0.0123), while only volume was used for live woody (R2 = 0.44). These were used to estimate consumption based on our volume-mass predictions, linked pre- and post-fire plots by fuel type, and showed similar results for herbaceous and woody litter when compared to paired plots. This study illustrates an important non-destructive alternative to calculating mass and estimating fuel consumption across vertical volume distributions at fine scales.

scholarly journals KNOT SINGULARITIES OF HARMONIC MORPHISMS

2001 ◽  
Vol 44 (1) ◽  
pp. 71-85 ◽  
Author(s):  
Paul Baird
Keyword(s):  
Riemann Surface ◽  
Complex Surface ◽  
Subject Classification ◽  
Harmonic Morphisms ◽  
Singular Set ◽  
Harmonic Morphism ◽  
Complex Curves ◽  
Analytic Curve ◽  
Primary 57M25 ◽  
Straight Lines

AbstractA harmonic morphism defined on $\mathbb{R}^3$ with values in a Riemann surface is characterized in terms of a complex analytic curve in the complex surface of straight lines. We show how, to a certain family of complex curves, the singular set of the corresponding harmonic morphism has an isolated component consisting of a continuously embedded knot.AMS 2000 Mathematics subject classification: Primary 57M25. Secondary 57M12; 58E20

Sign in / Sign up

Export Citation Format

Share Document