Summary of determining extreme points and inflection points

2019 ◽  
Vol 6 (1) ◽  
pp. 19-23
Author(s):  
Hailing Li ◽  
Tengxiao Xu ◽  
Yijia Liu
Keyword(s):  
Extreme Points ◽  
Inflection Points

Tasks of Building Materials from the Viewpoint of Control Theory

2017 ◽  
Vol 737 ◽  
pp. 578-582 ◽  
Author(s):  
Irina Garkina ◽  
Alexander Danilov
Keyword(s):  
Control Theory ◽  
Building Materials ◽  
Mechanical Characteristics ◽  
Extreme Points ◽  
Parametric Identification ◽  
Technological Parameters ◽  
Inflection Points ◽  
The Cauchy Problem ◽  
Object Of Control ◽  
Physical And Mechanical Characteristics

From the viewpoint of control theory is given the synthesis of building materials. A control of structure and properties of the material is carried by changing the relevant technological parameters. Material is regarded as an object of control in mathematical modeling. The model is presented as a solution to the Cauchy problem for an ordinary differential equation fourth-order. The synthesis is based on parametric identification of mathematical models. The parameters are typical points of the kinetic processes of the formation of physical and mechanical characteristics of the material. Among them: roots of the characteristic polynomial; inflection points; the extreme points, etc. Applications of this approach to the synthesis of building materials for special purposes are given.

Identifying Market Inflection Points

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

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

Extreme Points and Majorization: Economic Applications

2020 ◽  
Author(s):  
Andreas Kleiner ◽  
Benny Moldovanu ◽  
Philipp Strack
Keyword(s):  
Extreme Points ◽  
Economic Applications

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 A short note on extreme points of certain polytopes

2020 ◽  
Vol 8 (1) ◽  
pp. 36-39
Author(s):  
Lei Cao ◽  
Ariana Hall ◽  
Selcuk Koyuncu
Keyword(s):  
Short Proof ◽  
Convex Polytopes ◽  
Short Note ◽  
Convex Polytope ◽  
Extreme Points ◽  
Alternative Proof ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem

AbstractWe give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly sub-stochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

scholarly journals Investigation of ancestral alleles in the Bovinae subfamily

BMC Genomics ◽  
2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Maulana M. Naji ◽  
Yuri T. Utsunomiya ◽  
Johann Sölkner ◽  
Benjamin D. Rosen ◽  
Gábor Mészáros
Keyword(s):  
Extreme Points ◽  
Genetic Mutation ◽  
Zebu Cattle ◽  
Ancestral State ◽  
Initial State ◽  
High Count ◽  
Environmental Pressures ◽  
Ancestral States ◽  
Productive Traits ◽  
Species Specific

Abstract Background In evolutionary theory, divergence and speciation can arise from long periods of reproductive isolation, genetic mutation, selection and environmental adaptation. After divergence, alleles can either persist in their initial state (ancestral allele - AA), co-exist or be replaced by a mutated state (derived alleles -DA). In this study, we aligned whole genome sequences of individuals from the Bovinae subfamily to the cattle reference genome (ARS.UCD-1.2) for defining ancestral alleles necessary for selection signatures study. Results Accommodating independent divergent of each lineage from the initial ancestral state, AA were defined based on fixed alleles on at least two groups of yak, bison and gayal-gaur-banteng resulting in ~ 32.4 million variants. Using non-overlapping scanning windows of 10 Kb, we counted the AA observed within taurine and zebu cattle. We focused on the extreme points, regions with top 0. 1% (high count) and regions without any occurrence of AA (null count). High count regions preserved gene functions from ancestral states that are still beneficial in the current condition, while null counts regions were linked to mutated ones. For both cattle, high count regions were associated with basal lipid metabolism, essential for survival of various environmental pressures. Mutated regions were associated to productive traits in taurine, i.e. higher metabolism, cell development and behaviors and in immune response domain for zebu. Conclusions Our findings suggest that retaining and losing AA in some regions are varied and made it species-specific with possibility of overlapping as it depends on the selective pressure they had to experience.

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.

Determination of catastrophic sets of a tubular chemical reactor by two-parameter continuation method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Marek Berezowski
Keyword(s):  
Continuation Method ◽  
Extreme Points ◽  
Chemical Reactor ◽  
Stationary States ◽  
Parameter Continuation Method ◽  
It Systems ◽  
Parametric Continuation ◽  
Parameter Continuation ◽  
Two Parameter

AbstractThe work relates to development and presentation a two-parameter continuation method for determining catastrophic sets of stationary states of a tubular chemical reactor with mass recycle. The catastrophic set is a set of extreme points occurring in the bifurcation diagrams of the reactor. There are many large IT systems that use the parametric continuation method. The most popular is AUTO’97. However, its use is sometimes not convenient. The method developed in this work allows to eliminate the necessity to use huge IT systems from the calculations. Unlike these systems, it can be inserted into the program as a short subroutine. In addition, this method eliminates time-consuming iterations from the calculations.

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