Curvature estimation of arbitrary discrete 3D surfaces using partial derivatives based on distance maps

2004 ◽  
Author(s):  
Xiangwei Zhang ◽  
Milan Sonka
Keyword(s):  
Partial Derivatives ◽  
Curvature Estimation ◽  
3D Surfaces

On the motion of comet P/d’Arrest

1974 ◽  
Vol 22 ◽  
pp. 145-148
Author(s):  
W. J. Klepczynski
Keyword(s):  
Equations Of Motion ◽  
Variational Equations ◽  
Partial Derivatives

AbstractThe differences between numerically approximated partial derivatives and partial derivatives obtained by integrating the variational equations are computed for Comet P/d’Arrest. The effect of errors in the IAU adopted system of masses, normally used in the integration of the equations of motion of comets of this type, is investigated. It is concluded that the resulting effects are negligible when compared with the observed discrepancies in the motion of this comet.

AlCu Pattern Generation on 3D StructuredWafer Using Multi Level Exposure Method on Electrodeposited Polymer Material

2003 ◽  
Vol 766 ◽  
Author(s):  
Vineet Sharma ◽  
Arief B. Suriadi ◽  
Frank Berauer ◽  
Laurie S. Mittelstadt
Keyword(s):  
Line Width ◽  
Metal Film ◽  
Focal Depth ◽  
Cost Effective ◽  
Pattern Generation ◽  
Promising Technique ◽  
Critical Dimensions ◽  
Exposure Method ◽  
Multi Level ◽  
3D Surfaces

AbstractNormal photolithography tools have focal depth limitations and are unable to meet the expectations of high resolution photolithography on highly topographic structures. This paper shows a cost effective and promising technique of combining two different approaches to achieve critical dimensions of traces on slope pattern continuity on highly topographic structures. Electrophoretically deposited photoresist is used on 3-D structured wafers. This photoresist coating technique is fairly known in the MEMS industries to achieve uniform and conformal photoresist films on 3D surfaces. Multi step exposures are used to expose electrophoretically deposited photoresist. AlCu (Cu-0.5%), 0.47-0.53 μm thick metal film is deposited on 3D structured silicon substrate to plate photoresist. By combining these two novel methods, metal (AlCu) traces of 75 μm line width and 150 μm pitch (from top flat to down the slope) have been demonstrated on isotropically etched 350 μm deep trenches with 5-10% line width loss.

2D periodic structures patterned on 3D surfaces by interference lithography for SERS

2018 ◽  
Vol 461 ◽  
pp. 171-174 ◽  
Author(s):  
Ivana Lettrichova ◽  
Agata Laurencikova ◽  
Dusan Pudis ◽  
Jozef Novak ◽  
Matej Goraus ◽  
...  
Keyword(s):  
Periodic Structures ◽  
Interference Lithography ◽  
3D Surfaces

scholarly journals Computerized image understanding system for reliable estimation of spinal curvature in idiopathic scoliosis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ananthakrishna Thalengala ◽  
Shyamasunder N. Bhat ◽  
H. Anitha
Keyword(s):  
Spinal Deformity ◽  
Medial Axis ◽  
Image Understanding ◽  
Spinal Curvature ◽  
Absolute Difference ◽  
Computer Assisted ◽  
Type I ◽  
Observer Variability ◽  
Curvature Estimation ◽  
Accuracy And Repeatability

AbstractAnalysis of scoliosis requires thorough radiographic evaluation by spinal curvature estimation to completely assess the spinal deformity. Spinal curvature estimation gives orthopaedic surgeons an idea of severity of spinal deformity for therapeutic purposes. Manual intervention has always been an issue to ensure accuracy and repeatability. Computer assisted systems are semi-automatic and is still influenced by surgeon’s expertise. Spinal curvature estimation completely relies on accurate identification of required end vertebrae like superior end-vertebra, inferior end-vertebra and apical vertebra. In the present work, automatic extraction of spinal information central sacral line and medial axis by computerized image understanding system has been proposed. The inter-observer variability in the anatomical landmark identification is quantified using Kappa statistic. The resultant Kappa value computed between proposed algorithm and observer lies in the range 0.7 and 0.9, which shows good accuracy. Identification of the required end vertebra is automated by the extracted spinal information. Difference in inter and intra-observer variability for the state of the art computer assisted and proposed system are quantified in terms of mean absolute difference for the various types (Type-I, Type-II, Type-III, Type-IV, and Type-V) of scoliosis.

scholarly journals 3D-surface MALDI mass spectrometry imaging for visualising plant defensive cardiac glycosides in Asclepias curassavica

2021 ◽  
Vol 413 (8) ◽  
pp. 2125-2134
Author(s):  
Domenic Dreisbach ◽  
Georg Petschenka ◽  
Bernhard Spengler ◽  
Dhaka R. Bhandari
Keyword(s):  
Mass Spectrometry ◽  
Mass Spectrometry Imaging ◽  
Cardiac Glycosides ◽  
Molecular Mechanisms ◽  
Plant Science ◽  
Primary Metabolism ◽  
Native Plant ◽  
Asclepias Curassavica ◽  
3D Surface ◽  
3D Surfaces

AbstractMass spectrometry–based imaging (MSI) has emerged as a promising method for spatial metabolomics in plant science. Several ionisation techniques have shown great potential for the spatially resolved analysis of metabolites in plant tissue. However, limitations in technology and methodology limited the molecular information for irregular 3D surfaces with resolutions on the micrometre scale. Here, we used atmospheric-pressure 3D-surface matrix-assisted laser desorption/ionisation mass spectrometry imaging (3D-surface MALDI MSI) to investigate plant chemical defence at the topographic molecular level for the model system Asclepias curassavica. Upon mechanical damage (simulating herbivore attacks) of native A. curassavica leaves, the surface of the leaves varies up to 700 μm, and cardiac glycosides (cardenolides) and other defence metabolites were exclusively detected in damaged leaf tissue but not in different regions of the same leaf. Our results indicated an increased latex flow rate towards the point of damage leading to an accumulation of defence substances in the affected area. While the concentration of cardiac glycosides showed no differences between 10 and 300 min after wounding, cardiac glycosides decreased after 24 h. The employed autofocusing AP-SMALDI MSI system provides a significant technological advancement for the visualisation of individual molecule species on irregular 3D surfaces such as native plant leaves. Our study demonstrates the enormous potential of this method in the field of plant science including primary metabolism and molecular mechanisms of plant responses to abiotic and biotic stress and symbiotic relationships. Graphical abstract

scholarly journals Slice holomorphic solutions of some directional differential equations with bounded L-index in the same direction

2019 ◽  
Vol 52 (1) ◽  
pp. 482-489 ◽  
Author(s):  
Andriy Bandura ◽  
Oleh Skaskiv ◽  
Liana Smolovyk
Keyword(s):  
Partial Differential Equations ◽  
Continuous Function ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Holomorphic Functions ◽  
Positive Continuous Function ◽  
Partial Differential ◽  
Partial Derivatives ◽  
Fixed Direction

AbstractIn the paper we investigate slice holomorphic functions F : ℂn → ℂ having bounded L-index in a direction, i.e. these functions are entire on every slice {z0 + tb : t ∈ℂ} for an arbitrary z0 ∈ℂn and for the fixed direction b ∈ℂn \ {0}, and (∃m0 ∈ ℤ+) (∀m ∈ ℤ+) (∀z ∈ ℂn) the following inequality holds{{\left| {\partial _{\bf{b}}^mF(z)} \right|} \over {m!{L^m}(z)}} \le \mathop {\max }\limits_{0 \le k \le {m_0}} {{\left| {\partial _{\bf{b}}^kF(z)} \right|} \over {k!{L^k}(z)}},where L : ℂn → ℝ+ is a positive continuous function, {\partial _{\bf{b}}}F(z) = {d \over {dt}}F\left( {z + t{\bf{b}}} \right){|_{t = 0}},\partial _{\bf{b}}^pF = {\partial _{\bf{b}}}\left( {\partial _{\bf{b}}^{p - 1}F} \right)for p ≥ 2. Also, we consider index boundedness in the direction of slice holomorphic solutions of some partial differential equations with partial derivatives in the same direction. There are established sufficient conditions providing the boundedness of L-index in the same direction for every slie holomorphic solutions of these equations.

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