Complex rays in transient scattering from smooth targets with inflection points

1988 ◽  
Vol 36 (9) ◽  
pp. 1272-1280 ◽  
Author(s):  
H. Ikuno ◽  
L.B. Felsen
Keyword(s):  
Inflection Points ◽  
Transient Scattering ◽  
Complex Rays

Real and complex rays for scattering from a target with inflection points

Radio Science ◽  
1987 ◽  
Vol 22 (6) ◽  
pp. 952-958 ◽  
Author(s):  
H. Ikuno ◽  
L. B. Felsen
Keyword(s):  
Inflection Points ◽  
Complex Rays

Nonspecular reflections from a curved interface

Geophysics ◽  
1991 ◽  
Vol 56 (8) ◽  
pp. 1203-1214 ◽  
Author(s):  
J. Schleicher ◽  
P. Hubral ◽  
M. Tygel
Keyword(s):  
Observation Point ◽  
Ray Theory ◽  
Seismic Section ◽  
Specular Reflections ◽  
Nonspecular Reflection ◽  
Incident Plane ◽  
Inflection Points ◽  
Arbitrary Velocity ◽  
Curved Interface ◽  
Complex Rays

If an incident wavefield hits a curved interface that possesses certain inflection points, there may exist “nonspecular” events in the reflected field that cannot be explained by real ray theory. The magnitude of such events can reach the order of the specular ones and can be expressed in terms of specular reflections at certain points on the analytic continuation of the interface. In fact, specular reflected “complex rays,” connecting complex reflection points with the observation point, are used to explain such events. Previous results obtained for acoustic calculations, involving an incident plane wave and a perfectly soft reflector, are extended to arbitrary velocity and density contrasts, as well as to an incident far‐field cylindrical wavefield. Moreover, the agreement between analytic results and independent computations using a finite‐differences scheme is shown. It confirms the existence of nonspecular reflections. The interpreter of a seismic section should, therefore, be aware of not attributing a subsurface interface to a nonspecular reflection, e.g., at a flank of a saltdome.

Identifying Market Inflection Points

CFA Digest ◽  
2010 ◽  
Vol 40 (1) ◽  
Author(s):  
Russell Napier
Keyword(s):  
Inflection Points

A Novel Thyroid Ultrasound Proficiency Metric Designed Through a Multidisciplinary Delphi Approach

2021 ◽  
pp. 000313482110111
Author(s):  
Yinin Hu ◽  
Alex D. Michaels ◽  
Rachita Khot ◽  
Worthington G. Schenk ◽  
John B. Hanks ◽  
...  
Keyword(s):  
Learning Curves ◽  
Delphi Panel ◽  
Thyroid Ultrasound ◽  
Point Scale ◽  
Image Capture ◽  
Delphi Approach ◽  
Inflection Points ◽  
Operative Planning ◽  
Positioning Technique ◽  
Formally Trained

Background Thyroid ultrasounds extend surgeons’ outpatient capabilities and are essential for operative planning. However, most residents are not formally trained in thyroid ultrasound. The purpose of this study was to create a novel thyroid ultrasound proficiency metric through a collaborative Delphi approach. Methods Clinical faculty experienced in thyroid ultrasound participated on a Delphi panel to design the thyroid Ultrasound Proficiency Scale (UPS-Thyroid). Participants proposed items under the categories of Positioning, Technique, Image Capture, Measurement, and Interpretation. In subsequent rounds, participants voted to retain, revise, or exclude each item. The process continued until all items had greater than 70% consensus for retention. The UPS-Thyroid was pilot tested across 5 surgery residents with moderate ultrasound experience. Learning curves were assessed with cumulative sum. Results Three surgeons and 4 radiologists participated on the Delphi panel. Following 3 iterative Delphi rounds, the panel arrived at >70% consensus to retain 14 items without further revisions or additions. The metric included the following items on a 3-point scale for a maximum of 42 points: Positioning (1 item), Technique (4 items), Image Capture (2 items), Measurement (2 items), and Interpretation (5 items). A pilot group of 5 residents was scored against a proficiency threshold of 36 points. Learning curve inflection points were noted at between 4 to 7 repetitions. Conclusions A multidisciplinary Delphi approach generated consensus for a thyroid ultrasound proficiency metric (UPS-Thyroid). Among surgery residents with moderate ultrasound experience, basic proficiency at thyroid ultrasound is feasible within 10 repetitions.

scholarly journals How Many Inflections are There in the Lyapunov Spectrum?

2021 ◽  
Author(s):  
O. Jenkinson ◽  
M. Pollicott ◽  
P. Vytnova
Keyword(s):  
Piecewise Linear ◽  
Lyapunov Spectrum ◽  
Stat Phys ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Expanding Map ◽  
Lyapunov Spectra ◽  
Linear Maps ◽  
Inflection Points ◽  
Piecewise Linear Maps

AbstractIommi and Kiwi (J Stat Phys 135:535–546, 2009) showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture in Iommi and Kiwi (2009) by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.

Collaborative Study of a Titrimetric Method for the Assay of Amitrole Formulations

1967 ◽  
Vol 50 (3) ◽  
pp. 568-572
Author(s):  
J Russell Bishop
Keyword(s):  
Collaborative Study ◽  
Statistical Analyses ◽  
Standard Samples ◽  
Titrimetric Method ◽  
Inflection Points ◽  
Good Agreement

Abstract titrimetric method for the assay of dry and liquid amitrole formulations was studied by 10 collaborators. In the method, acid is added to the prepared amitrole sample, the solution is titrated potentiometrically with standard alkali, and the amitrole content is measured as the amount of alkali consumed between the first and second inflection points. Collaborative results on standard samples of a dry 90% formulation, a dry 50% formulation, and a liquid 2 lb/gallon formulation showed good agreement between samples and laboratories. Statistical analyses of the results were satisfactory, and the method for the assay of amitrole formulations is recommended for adoption as official, first action

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