scholarly journals Reduced Triangular Form of Polynomial 3-by-3 Matrices with One Characteristic Root and Its Invariants

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
B. Z. Shavarovskii
Keyword(s):  
Characteristic Root ◽  
Reduced Form ◽  
Polynomial Matrices ◽  
Triangular Form

In this paper the semiscalar equivalence of polynomial matrices is investigated. We introduce the notion of the so-called reduced triangular form with respect to semiscalar equivalence for the 3-by-3 matrices with one characteristic root and indicate the invariants of this reduced form.

scholarly journals Canonical Form of Reduced 3-by-3 Matrix with One Characteristic Root and with Some Zero Subdiagonal Elements

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
B. Z. Shavarovskii
Keyword(s):  
Canonical Form ◽  
Characteristic Root ◽  
Polynomial Matrices

A canonical form for a reduced matrix of order 3 with one characteristic root and with some zero subdiagonal elements is constructed. Thus, the problem of classification with respect to semiscalar equivalence of a selected set of polynomial matrices is solved.

On the semi-scalar equivalence of polynomial matrices over a field

2021 ◽  
pp. 80-82
Author(s):  
Volodymyr M. Prokip
Keyword(s):  
Present Report ◽  
Nonsingular Matrix ◽  
Invertible Matrix ◽  
Polynomial Matrices ◽  
Triangular Form

Polynomial matrices  and  of size  over a field  are semi-scalar equivalent if there exist a nonsingular  matrix  over  and an invertible  matrix  over  such that . The aim of the present report is to present a triangular form of some nonsingular polynomial matrices with respect to semi-scalar equivalence.

scholarly journals Reduction to a Canonical Form of a Third-Order Polynomial Matrix with One Characteristic Root by means of Semiscalarly Equivalent Transformations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
B. Z. Shavarovskii
Keyword(s):  
Canonical Form ◽  
Polynomial Matrix ◽  
Characteristic Root ◽  
Canonical Forms ◽  
Third Order ◽  
Polynomial Matrices ◽  
Order Polynomial

For the selected class of polynomial matrices of order three with one characteristic root with respect to the transformation of semiscalar equivalence, special triangular forms are established. The theorems of their uniqueness are proved. This gives reason to consider such canonical forms.

scholarly journals ON THE CONDITIONAL LIKELIHOOD RATIO TEST FOR SEVERAL PARAMETERS IN IV REGRESSION

2009 ◽  
Vol 25 (2) ◽  
pp. 305-335 ◽  
Author(s):  
Grant Hillier
Keyword(s):  
Likelihood Ratio ◽  
Cumulative Distribution Function ◽  
Characteristic Root ◽  
Cumulative Distribution ◽  
Reduced Form ◽  
Ratio Test ◽  
Efficient Simulation ◽  
Endogenous Variables ◽  
Lr Test ◽  
The Right

For the problem of testing the hypothesis that all m coefficients of the right-hand-side endogenous variables in an instrumental variables (IV) regression are zero, the likelihood ratio (LR) test can, if the reduced form covariance matrix is known, be rendered similar by a conditioning argument. To exploit this fact requires knowledge of the relevant conditional cumulative distribution function (c.d.f.) of the LR statistic, but the statistic is a function of the smallest characteristic root of an (m + 1)-square matrix and is therefore analytically difficult to deal with when m > 1. We show in this paper that an iterative conditioning argument used by Hillier (2009) and Andrews, Moreira, and Stock (2007 Journal of Econometrics 139, 116–132) to evaluate the c.d.f. in the case m = 1 can be generalized to the case of arbitrary m. This means that we can completely bypass the difficulty of dealing with the smallest characteristic root. Analytic results are obtained for the case m = 2, and a simple and efficient simulation approach to evaluating the c.d.f. is suggested for larger values of m.

Aerodynamic Shape Influence and Optimum Thickness Distribution Analysis of Perceptive Wind Turbine Blade

2018 ◽  
Vol 7 (3) ◽  
pp. 1
Author(s):  
J. V. Muruga Lal Jeyan ◽  
Akhila Rupesh ◽  
Jency Lal
Keyword(s):  
Wind Energy ◽  
Wind Turbine ◽  
Thickness Distribution ◽  
Turbine Blades ◽  
Reduced Form ◽  
Load Factor ◽  
Strong Impact ◽  
Theory Approach ◽  
Distribution Analysis ◽  
Optimum Thickness

The aerodynamic module combines the three-dimensional nonlinear lifting surface theory approach, which provides the effective propagated incident velocity and angle of attack at the blade section separately, and a two-dimensional panel method for steady axisymmetric and non-symmetric flow has to be involved to obtain the 3D pressure and velocity distribution on the wind mill model blade. Wind mill and turbines have become an economically competitive form of efficiency and renewable work generation. In the abroad analytical studies, the wind turbine blades to be the target of technological improvements by the use of highly possible systematic , aerodynamic and design, material analysis, fabrication and testing. Wind energy is a peculiar form of reduced form of density source of power. To make wind power feasible, it is important to optimize the efficiency of converting wind energy into productivity source. Among the different aspects involved, rotor aerodynamics is a key determinant for achieving this goal. There is a tradeoff between thin airfoil and structural efficiency. Both of which have a strong impact on the cost of work generated. Hence the design and analysis process for optimum design requires determining the load factor, pressure and velocity impact and optimum thickness distribution by finding the effect of blade shape by varying thickness on the basis of both the aerodynamic output and the structural weight.

Type 2 diabetes mellitus in patients with acute ischemiс stroke is associated with a decrease in plasma glutathione levels

2020 ◽  
Vol 25 (5) ◽  
pp. 29-35
Author(s):  
M. Yu. Maksimova ◽  
A. V. Ivanov ◽  
K. A. Nikiforova ◽  
F. R. Ochtova ◽  
E. T. Suanova ◽  
...  
Keyword(s):  
Diabetes Mellitus ◽  
Type 2 Diabetes ◽  
Type 2 Diabetes Mellitus ◽  
Redox Status ◽  
Reduced Form ◽  
Glutathione Level ◽  
Total Glutathione ◽  
Diabetes Mellitus Group ◽  
Reduced Forms

Ischemic stroke (IS) and type 2 diabetes mellitus are factors that affect the homeostasis of low-molecularweight aminothiols (cysteine, homocysteine, glutathione etc.). It has already been shown that IS in the acute period led to a decrease a level of reduced forms of aminothiols, but it is not clear whether type 2 diabetes mellitus has a noticeable effect there. Objective: to reveal the features of homeostasis of aminothiols in patients with type 2 diabetes mellitus in acute IS. Material and methods. The study involved 76 patients with primary middle cerebral artery IS in the first 10–24 hours after development of neurological symptoms. Group 1 included 15 patients with IS and type 2 diabetes mellitus, group 2 — 61 patients with IS and stress hyperglycemia. Their total plasma levels of cysteine, homocysteine, and glutathione, their reduced forms, and redox status were determined at admission (in the first 24 hours after IS). Results. There was a decrease in the level of total glutathione level (1.27 vs. 1.65 μM, p = 0.021), as well as its reduced form (0.03 vs. 0.04 μM, p = 0.007) in patients with IS and type 2 diabetes mellitus. Patients with type 2 diabetes mellitus who had a low redox status of homocysteine (0.65–1.2%) and glutathione (0.7–2.0%) were also characterized by a decrease in total glutathione level (p = 0.02; p = 0.03). Conclusion. Thus, type 2 diabetes mellitus is associated with a decrease in the level of total glutathione in acute IS. Probably, type 2 diabetes mellitus is characterized by a particular relationship between the metabolism of homocysteine, glutathione and glucose. Therefore, the search for homocysteine-dependent approaches to correct glutathione metabolism in type 2 diabetes mellitus may be of interest as an adjuvant therapy for IS.

Fault Tolerant Guidance of Under-Actuated Satellite Formation Flying Using Inter-Vehicle Coulomb Force

2019 ◽  
Vol 2 (1) ◽  
pp. 43-52
Author(s):  
Alireza Alikhani ◽  
Safa Dehghan M ◽  
Iman Shafieenejad
Keyword(s):  
Fault Tolerance ◽  
Formation Flying ◽  
Fault Tolerant ◽  
Coulomb Force ◽  
Control Law ◽  
Triangular Form ◽  
Satellite Formation Flying ◽  
Satellite Formation ◽  
Guidance Law ◽  
Tolerance Approach

In this study, satellite formation flying guidance in the presence of under actuation using inter-vehicle Coulomb force is investigated. The Coulomb forces are used to stabilize the formation flying mission. For this purpose, the charge of satellites is determined to create appropriate attraction and repulsion and also, to maintain the distance between satellites. Static Coulomb formation of satellites equations including three satellites in triangular form was developed. Furthermore, the charge value of the Coulomb propulsion system required for such formation was obtained. Considering Under actuation of one of the formation satellites, the fault-tolerance approach is proposed for achieving mission goals. Following this approach, in the first step fault-tolerant guidance law is designed. Accordingly, the obtained results show stationary formation. In the next step, tomaintain the formation shape and dimension, a fault-tolerant control law is designed.

The Logical Square and the Table of Oppositions

2012 ◽  
Vol 15 (1) ◽  
pp. 400-416
Author(s):  
Wolfgang Kienzler
Keyword(s):  
Reduced Form ◽  
Square Of Opposition ◽  
Logical Square ◽  
Long Time ◽  
The Square Of Opposition ◽  
The Way

The way Frege presented the Square of Opposition in a reduced form in 1879 and 1910 can be used to develop two distinct versions of the square: The traditional square that displays inferences and a “Table of Oppositions” displaying variations of negation. This Table of Oppositions can be further simplified and thus be made more symmetrical. A brief survey of versions of the square from Aristotle to the present shows how both aspects of the square have coexisted for a very long time without ever being properly distinguished.

Prevention of developing experіmental dіabetes by reduced form of glutathіone

2019 ◽  
Vol 95 (3) ◽  
pp. 21-27
Author(s):  
G.G. Meyramov ◽  
◽  
A.Zh. Shaybek ◽  
K.-D. Kohnert ◽  
G.T. Kartbayeva ◽  
...  
Keyword(s):  
Reduced Form
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