scholarly journals Appendix C: Mathematical Relations

2006 ◽  
pp. 231-238
Keyword(s):  
Mathematical Relations

A Bayesian View on the Hilbert Transform and the Kramers-Kronig Transform of Electrochemical Impedance Data: Probabilistic Estimates and Quality Scores

2020 ◽  
Author(s):  
Jiapeng Liu ◽  
Ting Hei Wan ◽  
Francesco Ciucci
Keyword(s):  
Power Generation ◽  
Electrochemical Impedance Spectroscopy ◽  
Hilbert Transform ◽  
Electrochemical Impedance ◽  
The Self ◽  
Impedance Data ◽  
The Hilbert Transform ◽  
Validation Tests ◽  
Self Consistency ◽  
Mathematical Relations

<p>Electrochemical impedance spectroscopy (EIS) is one of the most widely used experimental tools in electrochemistry and has applications ranging from energy storage and power generation to medicine. Considering the broad applicability of the EIS technique, it is critical to validate the EIS data against the Hilbert transform (HT) or, equivalently, the Kramers–Kronig relations. These mathematical relations allow one to assess the self-consistency of obtained spectra. However, the use of validation tests is still uncommon. In the present article, we aim at bridging this gap by reformulating the HT under a Bayesian framework. In particular, we developed the Bayesian Hilbert transform (BHT) method that interprets the HT probabilistic. Leveraging the BHT, we proposed several scores that provide quick metrics for the evaluation of the EIS data quality.<br></p>

Semiconductors

2018 ◽  
Author(s):  
L. Solymar ◽  
D. Walsh ◽  
R. R. A. Syms
Keyword(s):  
Crystal Growth ◽  
Molecular Beam ◽  
Vapour Deposition ◽  
Energy Levels ◽  
Chemical Vapour ◽  
Optical Excitation ◽  
Organic Chemical ◽  
Metal Organic ◽  
Mathematical Relations ◽  
Semiconductor Properties

Both intrinsic and extrinsic semiconductors are discussed in terms of their band structure. The acceptor and donor energy levels are introduced. Scattering is discussed, from which the conductivity of semiconductors is derived. Some mathematical relations between electron and hole densities are derived. The mobilities of III–V and II–VI compounds and their dependence on impurity concentrations are discussed. Band structures of real and idealized semiconductors are contrasted. Measurements of semiconductor properties are reviewed. Various possibilities for optical excitation of electrons are discussed. The technology of crystal growth and purification are reviewed, in particular, molecular beam epitaxy and metal-organic chemical vapour deposition.

scholarly journals MATHEMATICAL RELATIONS OF CERTAIN CHEST MEASUREMENTS.

JAMA ◽  
1904 ◽  
Vol XLIII (12) ◽  
pp. 787
Author(s):  
WINFIELD S. HALL
Keyword(s):  
Mathematical Relations

scholarly journals The Weighted Arithmetic Mean–Geometric Mean Inequality is Equivalent to the Hölder Inequality

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 380 ◽  
Author(s):  
Yongtao Li ◽  
Xian-Ming Gu ◽  
Jianxing Zhao
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Hölder Inequality ◽  
Power Mean ◽  
Weighted Arithmetic ◽  
Mathematical Equivalence ◽  
Power Mean Inequality ◽  
Mathematical Relations

In the current note, we investigate the mathematical relations among the weighted arithmetic mean–geometric mean (AM–GM) inequality, the Hölder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the weighted AM–GM inequality, the weighted power-mean inequality and the Hölder inequality are fully achieved. The new results are more generalized than those of previous studies.

scholarly journals Cluster analysis of knowledge sources in standardized electrical engineering subfields

2016 ◽  
Vol 13 (3) ◽  
pp. 405-422
Author(s):  
Marija Blagojevic ◽  
Zivadin Micic ◽  
Momcilo Vujicic
Keyword(s):  
Neural Networks ◽  
Cluster Analysis ◽  
Electrical Engineering ◽  
Financial Resources ◽  
Knowledge Sources ◽  
Knowledge Source ◽  
Innovation Intensity ◽  
Future Work ◽  
Analysis Of Knowledge ◽  
Mathematical Relations

The paper presents a cluster analysis of innovation of knowledge sources based on the standards in the field of Electrical Engineering. Both local (SRPS) and global (ISO) knowledge sources have been analysed with the aim of innovating a Knowledge Base (KB). The results presented indicate a means/possibility of grouping the subfields within a cluster. They also point to a trend or intensity of knowledge source innovation for the purpose of innovating the KB that accompanies innovations. The study provides the possibility of predicting necessary financial resources in the forthcoming period by means of original mathematical relations. Furthermore, the cluster analysis facilitates the comparison of the innovation intensity in this and other (sub)fields. Future work relates to the monitoring of the knowledge source innovation by means of KB engineering and improvement of the methodology of prediction using neural networks.

scholarly journals On Vessel to Vessel Interaction during Head-on encounter

10.18048/5303 ◽  
2017 ◽  
Vol 53 (1) ◽  
pp. 35-52
Author(s):  
David Brčić ◽  
Mate Barić ◽  
Robert Mohović
Keyword(s):  
Interaction Force ◽  
Post Processing ◽  
Strong Force ◽  
Main Factors ◽  
Force Components ◽  
Mathematical Relations ◽  
Relevant Factors ◽  
Interaction Phenomenon

Interaction of two vessels during head-on encounter acts as short and strong force. Consequences can reflect on vessels’ handling causing unwanted effects. This phenomenon was elaborated in the paper, considering influence of interaction force and its dependence on main recognized factors: mutual vessels’ distance, speed and depth under the keel. Besides interaction force components, analyses comprised other relevant factors as vessel’ heading, course alterations and drift of vessel due to interaction. Planned and, according to main factors, defined scenarios were conducted in navigational simulator with usage of navigational areas creation tools. After simulations and data post-processing, obtained results were summarized. Correlation of results with mathematical relations describing interaction was conducted. In the conclusion chapter, final inferences are stated, with some of observations which in the opinion of authors are significant. Conducted analyses, obtained results and derived conclusions represent basis for further research, thus future activities regarding interaction phenomenon are proposed.

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