Mathematical Analysis of Nanostructured Surfaces: The Period-Scale Transform

This work has been motivated by the urgent need for accurate and complete characterization of patterns consisting of almost periodic arrangements of specific features (trenches, bumps, holes, spikes, and so on) amply used in the industries of nanotechnology, microelectronics, and photonics. The quantitative characterization of such surface structures demands mathematical methods able to reveal both period- and feature-scale aspects. Given that the conventional approaches (Fourier or wavelet transform) are limited to either periodicity or feature-scale characterization, our work contributes with the proposal of a transformation which combines Fourier and wavelet merits to quantify simultaneously the period and feature scale of a periodic or almost periodic surface pattern. The output of our study has been (a) a detailed investigation of the mathematical properties of the proposed period-scale transform (PST) along with its relationship with other well-known transforms, (b) a presentation of some examples of PST of model 1D periodic surfaces to identify its benefits, and (c) first applications of PST in real profiles extracted from experimental polymer surfaces after plasma treatment.

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Erratum to "Complete Characterization of Trees with Maximal Augmented Zagreb Index"

MATCH Communications in Mathematical and in Computer Chemistry ◽

10.46793/match.87-1.171x ◽

2021 ◽

Vol 87 (01) ◽

pp. 171-176

Author(s):

Xiaoshi Xiao ◽

◽

Xiuliang Qiu ◽

Wenshui Lin

Keyword(s):

Complete Solution ◽

Complete Characterization ◽

Zagreb Index ◽

The Past ◽

Mathematical Properties ◽

Augmented Zagreb Index

The augmented Zagreb index (AZI) has attracted more and more attentions in the past years. Some significant mathematical properties of AZI were obtained. In particular, Lin et al. [MATCH Commun. Math. Comput. Chem. 83 (2020) 167] recently claimed a complete solution to the problem of characterizing n-vertex tree(s) with maximal AZI. In this note we correct some errors in the paper.

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Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites

Tire Science and Technology ◽

10.2346/1.2150974 ◽

1982 ◽

Vol 10 (1) ◽

pp. 37-54 ◽

Cited By ~ 11

Author(s):

M. Kumar ◽

C. W. Bert

Keyword(s):

Response Characteristic ◽

Cord Compression ◽

Complete Characterization ◽

Strain Response ◽

Strain Gages ◽

Experimental Characterization ◽

Rubber Composites ◽

Stress Strain ◽

Strain Data

Abstract Unidirectional cord-rubber specimens in the form of tensile coupons and sandwich beams were used. Using specimens with the cords oriented at 0°, 45°, and 90° to the loading direction and appropriate data reduction, we were able to obtain complete characterization for the in-plane stress-strain response of single-ply, unidirectional cord-rubber composites. All strains were measured by means of liquid mercury strain gages, for which the nonlinear strain response characteristic was obtained by calibration. Stress-strain data were obtained for the cases of both cord tension and cord compression. Materials investigated were aramid-rubber, polyester-rubber, and steel-rubber.

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H∞ performance of weighted interval plants: complete characterization of vertex results

1993 American Control Conference ◽

10.23919/acc.1993.4792931 ◽

1993 ◽

Cited By ~ 3

Author(s):

C. V. Hollot ◽

R. Tempo

Keyword(s):

Complete Characterization ◽

Interval Plants

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Characterization of CMOS Structures (0.6 µm process) Submitted to HBM and COM ESD Stress Tests

ISTFA 1997: Conference Proceedings from the 23rd International Symposium for Testing and Failure Analysis ◽

10.31399/asm.cp.istfa1997p0315 ◽

1997 ◽

Author(s):

G. Meneghesso ◽

E. Zanoni ◽

P. Colombo ◽

M. Brambilla ◽

R. Annunziata ◽

...

Keyword(s):

Electron Microscopy ◽

Electrostatic Discharge ◽

Stress Test ◽

Complete Characterization ◽

Stress Tests ◽

Test Procedures ◽

Emission Microscopy ◽

Fast Rise ◽

Scanning Electron

Abstract In this work, we present new results concerning electrostatic discharge (ESD) robustness of 0.6 μm CMOS structures. Devices have been tested according to both HBM and socketed CDM (sCDM) ESD test procedures. Test structures have been submitted to a complete characterization consisting in: 1) measurement of the tum-on time of the protection structures submitted to pulses with very fast rise times; 2) ESD stress test with the HBM and sCDM models; 3) failure analysis based on emission microscopy (EMMI) and Scanning Electron Microscopy (SEM).

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Faculty Opinions recommendation of Large-scale characterization of HeLa cell nuclear phosphoproteins.

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.1022012.251640 ◽

2004 ◽

Author(s):

Andrew Emili

Keyword(s):

Hela Cell ◽

Large Scale ◽

Scale Characterization ◽

Nuclear Phosphoproteins

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Integrated, Multi-Scale Characterization of Imbibition and Wettability Phenomena Using Magnetic Resonance and Wide-Band Dielectric Measurements

10.2172/927607 ◽

2007 ◽

Author(s):

Mukul M. Sharma ◽

Steven L. Bryant ◽

Carlos Torres-Verdin ◽

George Hirasaki

Keyword(s):

Magnetic Resonance ◽

Wide Band ◽

Dielectric Measurements ◽

Multi Scale ◽

Scale Characterization

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POTENTIALS OF VHF SOUNDING RADARS FOR LARGE-SCALE CHARACTERIZATION OF GROUNDWATER MOUNDING UNDER HYPER-ARID CONDITIONS

10.1130/abs/2018am-323129 ◽

2018 ◽

Author(s):

Abotalib Z. Abotalib ◽

◽

Essam Heggy

Keyword(s):

Large Scale ◽

Arid Conditions ◽

Scale Characterization

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Complete characterization of spin chains with two Ising symmetries

EPL (Europhysics Letters) ◽

10.1209/0295-5075/125/10008 ◽

2019 ◽

Vol 125 (1) ◽

pp. 10008 ◽

Cited By ~ 1

Author(s):

Bat-el Friedman ◽

Atanu Rajak ◽

Emanuele G. Dalla Torre

Keyword(s):

Complete Characterization ◽

Spin Chains

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On the star forest polytope for trees and cycles

RAIRO - Operations Research ◽

10.1051/ro/2018076 ◽

2019 ◽

Vol 53 (5) ◽

pp. 1763-1773

Author(s):

Meziane Aider ◽

Lamia Aoudia ◽

Mourad Baïou ◽

A. Ridha Mahjoub ◽

Viet Hung Nguyen

Keyword(s):

Undirected Graph ◽

Dominating Set ◽

Discrete Math ◽

Complete Characterization ◽

Facial Structure ◽

Maximum Weight ◽

Single Node ◽

End Node ◽

Vertex Disjoint

Let G = (V, E) be an undirected graph where the edges in E have non-negative weights. A star in G is either a single node of G or a subgraph of G where all the edges share one common end-node. A star forest is a collection of vertex-disjoint stars in G. The weight of a star forest is the sum of the weights of its edges. This paper deals with the problem of finding a Maximum Weight Spanning Star Forest (MWSFP) in G. This problem is NP-hard but can be solved in polynomial time when G is a cactus [Nguyen, Discrete Math. Algorithms App. 7 (2015) 1550018]. In this paper, we present a polyhedral investigation of the MWSFP. More precisely, we study the facial structure of the star forest polytope, denoted by SFP(G), which is the convex hull of the incidence vectors of the star forests of G. First, we prove several basic properties of SFP(G) and propose an integer programming formulation for MWSFP. Then, we give a class of facet-defining inequalities, called M-tree inequalities, for SFP(G). We show that for the case when G is a tree, the M-tree and the nonnegativity inequalities give a complete characterization of SFP(G). Finally, based on the description of the dominating set polytope on cycles given by Bouchakour et al. [Eur. J. Combin. 29 (2008) 652–661], we give a complete linear description of SFP(G) when G is a cycle.

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