On minimizing difference of a SOS-convex polynomial and a support function over a SOS-concave matrix polynomial constraint

2017 ◽  
Vol 169 (1) ◽  
pp. 177-198
Author(s):  
Jae Hyoung Lee ◽  
Gue Myung Lee
Keyword(s):  
Support Function ◽  
Matrix Polynomial ◽  
Polynomial Constraint

A Method to Describe the Process of Shaping Operational Effectiveness of Military Aircraft – An Outline

2013 ◽  
Vol 33 (1) ◽  
pp. 45-55
Author(s):  
Henryk Tomaszek ◽  
Ryszard Kaleta ◽  
Mariusz Zieja
Keyword(s):  
Support Function ◽  
Military Aircraft ◽  
Operational Effectiveness ◽  
Correct Operation ◽  
Operation And Maintenance

Abstract The paper deals with the process of shaping the operational effectiveness of military aircraft under some specific circumstances, i.e. while flying on missions. The term ‘effectiveness’ has been assumed to mean the probability of accomplishing an air mission by one of the aeronautical system’s components, i.e. the aircraft together with its pilot. There is a chance to improve the effectiveness, or make it worse, in subsequent flights, depending on how the maintenance support function. The correct operation and maintenance of the system’s components should provide that the following condition is satisfied: * Pk ≥ P , where Pk - effectiveness in the k-th flight, and P* - the lower demanded limit of effectiveness. The Authors drew their inspiration for this paper from publication [2].

Hawaiian Electric Advanced Inverter Grid Support Function Laboratory Validation and Analysis

2016 ◽  
Author(s):  
Austin Nelson ◽  
Adarsh Nagarajan ◽  
Kumar Prabakar ◽  
Vahan Gevorgian ◽  
Blake Lundstrom ◽  
...  
Keyword(s):  
Support Function

A general inverse matrix series relation and associated polynomials – II

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira
Keyword(s):  
Matrix Polynomial ◽  
Combinatorial Identities ◽  
Inverse Matrix ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Series Representations ◽  
The Matrix ◽  
Associated Polynomials ◽  
Matrix Pair ◽  
Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

scholarly journals An Ecological Service System Based Study on Suburban Rural Landscape Multifunction

Land ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 232
Author(s):  
Jie Zheng ◽  
Lisha Na ◽  
Binglin Liu ◽  
Tiantian Zhang ◽  
Hao Wang
Keyword(s):  
Rural Communities ◽  
Urban Areas ◽  
Support Function ◽  
Service System ◽  
Rural Landscape ◽  
Dual Function ◽  
The Sustainable Development ◽  
Ecological Service ◽  
Single Function ◽  
Data Constraints

Suburban rural landscape multifunction has received increasing attention from scholars due to its high demand and impact on main urban areas. However, few studies have been focused on suburban rural landscape multifunction because of data constraints. The present study quantified the four landscape services based on ecological service system, i.e., regulating function (RF), provision function (PF), culture function (CF), and support function (SF), determined the interaction through the Spearman correlation coefficient, and ultimately identified the landscape multifunction hotspots and dominant functions through overlay analysis. The result indicated that suburban rural communities have exhibited the characteristics of regional multifunction, and the landscape multifunction hotspots accounted for 64.2%; it should be particularly noted that, among single-function, dual-function, and multifunction hotspots, both support function, and culture function was dominant, while only one case was found in which the regulating function was dominant. Furthermore, all landscape functions other than SF-CF exhibited certain correlations. The study suggests that planning and management should be performed in future in combination with landscape multifunction to ensure the sustainable development of suburban rural communities.

scholarly journals A Schur-Cohn theorem for matrix polynomials

1990 ◽  
Vol 33 (3) ◽  
pp. 337-366 ◽  
Author(s):  
Harry Dym ◽  
Nicholas Young
Keyword(s):  
Unit Circle ◽  
Matrix Polynomial ◽  
Hermitian Matrix ◽  
Krein Space ◽  
Gram Matrix ◽  
Natural Basis ◽  
Test Matrix ◽  
Matrix Polynomials ◽  
Rational Vector ◽  
Square Matrix

Let N(λ) be a square matrix polynomial, and suppose det N is a polynomial of degree d. Subject to a certain non-singularity condition we construct a d by d Hermitian matrix whose signature determines the numbers of zeros of N inside and outside the unit circle. The result generalises a well known theorem of Schur and Cohn for scalar polynomials. The Hermitian “test matrix” is obtained as the inverse of the Gram matrix of a natural basis in a certain Krein space of rational vector functions associated with N. More complete results in a somewhat different formulation have been obtained by Lerer and Tismenetsky by other methods.

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