scholarly journals A Complex Surface Admitting a Strongly Plurisubharmonic Function but No Holomorphic Functions

2013 ◽  
Vol 25 (1) ◽  
pp. 329-335 ◽  
Author(s):  
Franc Forstnerič
Keyword(s):  
Plurisubharmonic Function ◽  
Holomorphic Functions ◽  
Complex Surface

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 The Uniformisation of the Equation $$z^w=w^z$$

2021 ◽  
Author(s):  
A. F. Beardon
Keyword(s):  
Positive Solutions ◽  
Complex Plane ◽  
Complex Variable ◽  
Holomorphic Functions ◽  
Parametric Form ◽  
Lambert Function ◽  
The Real ◽  
Complex Equation ◽  
Real Equation ◽  
Expository Paper

AbstractThe positive solutions of the equation $$x^y = y^x$$ x y = y x have been discussed for over two centuries. Goldbach found a parametric form for the solutions, and later a connection was made with the classical Lambert function, which was also studied by Euler. Despite the attention given to the real equation $$x^y=y^x$$ x y = y x , the complex equation $$z^w = w^z$$ z w = w z has virtually been ignored in the literature. In this expository paper, we suggest that the problem should not be simply to parametrise the solutions of the equation, but to uniformize it. Explicitly, we construct a pair z(t) and w(t) of functions of a complex variable t that are holomorphic functions of t lying in some region D of the complex plane that satisfy the equation $$z(t)^{w(t)} = w(t)^{z(t)}$$ z ( t ) w ( t ) = w ( t ) z ( t ) for t in D. Moreover, when t is positive these solutions agree with those of $$x^y=y^x$$ x y = y x .

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 Coefficients problems for families of holomorphic functions related to hyperbola

2020 ◽  
Vol 70 (3) ◽  
pp. 605-616
Author(s):  
Stanisława Kanas ◽  
Vali Soltani Masih ◽  
Ali Ebadian
Keyword(s):  
Unit Disk ◽  
Holomorphic Functions ◽  
Hankel Determinant ◽  
Coefficient Problem

AbstractWe consider a family of analytic and normalized functions that are related to the domains ℍ(s), with a right branch of a hyperbolas H(s) as a boundary. The hyperbola H(s) is given by the relation $\begin{array}{} \frac{1}{\rho}=\left( 2\cos\frac{\varphi}{s}\right)^s\quad (0 \lt s\le 1,\, |\varphi| \lt (\pi s)/2). \end{array}$ We mainly study a coefficient problem of the families of functions for which zf′/f or 1 + zf″/f′ map the unit disk onto a subset of ℍ(s) . We find coefficients bounds, solve Fekete-Szegö problem and estimate the Hankel determinant.

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