scholarly journals Order-Independent Algorithm for the Asymptotic Stability of Complex Polynomials

2021 ◽  
Vol 13 (5) ◽  
pp. 24
Author(s):  
Ziad Zahreddine
Keyword(s):  
Asymptotic Stability ◽  
Natural Extension ◽  
Current Work ◽  
Algebraic Operation ◽  
Stability Testing ◽  
Complex Polynomials ◽  
Large Order ◽  
Real Polynomials ◽  
Alternative Algorithm

The Extended Routh Array (ERA) settles the asymptotic stability of complex polynomials. The ERA is a natural extension of the Routh Array which applies only to real polynomials. Although the ERA is a nice theoretical algorithm for stability testing, it has its limitations. Unfortunately, as the order of the polynomial increases, the size of calculations increases dramatically as will be shown below. In the current work, we offer an alternative algorithm which is basically equivalent to the ERA, but has the extra advantage of being simpler, more efficient, and easy to apply even to large order polynomials. In all the steps required in the construction of the new algorithm, only one single and simple algebraic operation is needed, which makes it a polynomial order-independent algorithm.

scholarly journals Nonnegativity of uncertain polynomials

1998 ◽  
Vol 4 (2) ◽  
pp. 135-163 ◽  
Author(s):  
Dragoslav D. Šiljak ◽  
Matija D. Šiljak
Keyword(s):  
Robust Stability ◽  
Sufficient Conditions ◽  
Multivariable Systems ◽  
Complex Polynomials ◽  
Matrix Polynomials ◽  
Real Polynomials ◽  
General Parameter ◽  
Positive Realness ◽  
Exclusion Condition ◽  
Parameter Dependent

The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.

scholarly journals Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Mawardi Bahri
Keyword(s):  
Fourier Transform ◽  
Natural Extension ◽  
Orthogonality Relation ◽  
Current Work ◽  
Linear Canonical Transform ◽  
Uncertainty Principles ◽  
Complex Conjugation ◽  
Inversion Theorem ◽  
Windowed Fourier Transform

AbstractThe windowed linear canonical transform is a natural extension of the classical windowed Fourier transform using the linear canonical transform. In the current work, we first remind the reader about the relation between the windowed linear canonical transform and windowed Fourier transform. It is shown that useful relation enables us to provide different proofs of some properties of the windowed linear canonical transform, such as the orthogonality relation, inversion theorem, and complex conjugation. Lastly, we demonstrate some new results concerning several generalizations of the uncertainty principles associated with this transformation.

High-resolution electron microscopy of Cu2O surfaces

1986 ◽  
Vol 44 ◽  
pp. 396-397
Author(s):  
V. Castano ◽  
W. Krakow
Keyword(s):  
High Resolution ◽  
Natural Extension ◽  
High Resolution Electron Microscopy ◽  
Point Of View ◽  
Initial Oxidation ◽  
System A ◽  
Resolution Electron ◽  
Surface Reconstructions ◽  
Atomic Surface ◽  
Au Thin Films

In non-UHV microscope environments atomic surface structure has been observed for flat-on for various orientations of Au thin films and edge-on for columns of atoms in small particles. The problem of oxidation of surfaces has only recently been reported from the point of view of high resolution microscopy revealing surface reconstructions for the Ag2O system. A natural extension of these initial oxidation studies is to explore other materials areas which are technologically more significant such as that of Cu2O, which will now be described.

Universal ESEM

1993 ◽  
Vol 51 ◽  
pp. 786-787
Author(s):  
G.D. Danilatos
Keyword(s):  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
High Vacuum ◽  
Natural Extension ◽  
Necessary Condition ◽  
Environmental Scanning ◽  
Detection Systems ◽  
Small Gain ◽  
Detection Medium ◽  
Scanning Electron

The environmental scanning electron microscope (ESEM) has evolved as the natural extension of the scanning electron microscope (SEM), both historically and technologically. ESEM allows the introduction of a gaseous environment in the specimen chamber, whereas SEM operates in vacuum. One of the detection systems in ESEM, namely, the gaseous detection device (GDD) is based on the presence of gas as a detection medium. This might be interpreted as a necessary condition for the ESEM to remain operational and, hence, one might have to change instruments for operation at low or high vacuum. Initially, we may maintain the presence of a conventional secondary electron (E-T) detector in a "stand-by" position to switch on when the vacuum becomes satisfactory for its operation. However, the "rough" or "low vacuum" range of pressure may still be considered as inaccessible by both the GDD and the E-T detector, because the former has presumably very small gain and the latter still breaks down.

Impairment Tutorial: Rating Facial Disfigurement After an Injury

1998 ◽  
Vol 3 (4) ◽  
pp. 6-6
Author(s):  
Marc T. Taylor
Keyword(s):  
Current Work ◽  
Workers Compensation ◽  
Loss Of Function ◽  
Facial Disfigurement ◽  
Work Related ◽  
Work Related Injury ◽  
Compensation Claim ◽  
Impairment Ratings

Abstract This article discusses two important cases that involve the AMA Guides to the Evaluation of Permanent Impairment (AMA Guides). First, in Vargas v Industrial Com’n of Arizona, a claimant had a pre-existing non–work-related injury to his right knee as well as a work-related injury, and the issue was apportionment of the pre-existing injury. The court held that, under Arizona's statute, the impairment from the pre-existing injury should be subtracted from the current work-related impairment. In the second case, Colorado courts addressed the issue of apportionment in a workers’ compensation claim in which the pre-existing injury was asymptomatic at the time of the work-related injury (Askey v Industrial Claim Appeals Office). In this case, the court held that the worker's benefits should not be reduced to account for an asymptomatic pre-existing condition that could not be rated accurately using the AMA Guides. The AMA Guides bases impairment ratings on anatomic or physiologic loss of function, and if an examinee presents with two or more sequential injuries and calculable impairments, the AMA Guides can be used to apportion between pre-existing and subsequent impairments. Courts often use the AMA Guides to decide statutorily determined benefits and are subject to interpretation by courts and administrative bodies whose interpretations may vary from state to state.

Structuring Situational Information

2015 ◽  
Vol 20 (3) ◽  
pp. 176-189 ◽  
Author(s):  
John F. Rauthmann
Keyword(s):  
Statistical Analyses ◽  
Current Work ◽  
Common Language ◽  
Road Map ◽  
Taxonomic Approach ◽  
Situational Information

Abstract. There is as yet no consensually agreed-upon situational taxonomy. The current work addresses this issue and reviews extant taxonomic approaches by highlighting a “road map” of six research stations that lead to the observed diversity in taxonomies: (1) theoretical and conceptual guidelines, (2) the “type” of situational information studied, (3) the general taxonomic approach taken, (4) the generation of situation pools, (5) the assessment and rating of situational information, and (6) the statistical analyses of situation data. Current situational taxonomies are difficult to integrate because they follow different paths along these six stations. Some suggestions are given on how to spur integrated taxonomies toward a unified psychology of situations that speaks a common language.

Measuring the Situational Eight DIAMONDS Characteristics of Situations

2016 ◽  
Vol 32 (2) ◽  
pp. 155-164 ◽  
Author(s):  
John F. Rauthmann ◽  
Ryne A. Sherman
Keyword(s):  
Psychological Characteristics ◽  
Current Work

Abstract. It has been suggested that people perceive psychological characteristics of situations on eight major dimensions ( Rauthmann et al., 2014 ): The “Situational Eight” DIAMONDS (Duty, Intellect, Adversity, Mating, pOsitivity, Negativity, Deception, Sociality). These dimensions have been captured with the 32-item RSQ-8. The current work optimizes the RSQ-8 to derive more economical yet informative and precise scales, captured in the newly developed S8*. Nomological associations of the original RSQ-8 and the S8* with situation cues (extracted from written situation descriptions) were compared. Application areas of the S8* are outlined.

The Russian ruble crisis of December 2014

2016 ◽  
pp. 66-86
Author(s):  
A. Obizhaeva
Keyword(s):  
Microstructure Analysis ◽  
Future Market ◽  
Effective Response ◽  
Large Order ◽  
Short Period ◽  
The Face ◽  
Front Running ◽  
Futures And Options

The paper presents a microstructure analysis of the crash of the Russian ruble in mid-December 2014. The author shows that the market break probably happened due to the execution of a large order that converted Russian rubles into U.S. dollars over a short period of a few days. Expirations of futures and options as well as possible front-running could have exacerbated the collapse of the Russian currency. The paper discusses measures taken by the Moscow Exchange and Bank of Russia during the episode and makes several recommendations to prevent a repetition of the similar events and provide an effective response in the face of future market breaks.

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