scholarly journals Properties of the Set of Hadamardized Hurwitz Polynomials

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Baltazar Aguirre-Hernández ◽  
Edgar-Cristian Díaz-González ◽  
Carlos-Arturo Loredo-Villalobos ◽  
Faustino-Ricardo García-Sosa
Keyword(s):  
Hadamard Product ◽  
Differential Topology ◽  
Fourth Degree ◽  
Hurwitz Polynomial ◽  
Interval Polynomial ◽  
Hurwitz Polynomials ◽  
Connected Set ◽  
Polynomial Family

We say that a Hurwitz polynomialptis a Hadamardized polynomial if there are two Hurwitz polynomialsftandgtsuch thatf∗g=p, wheref∗gis the Hadamard product offandg. In this paper, we prove that the set of all Hadamardized Hurwitz polynomials is an open, unbounded, nonconvex, and arc-connected set. Furthermore, we give a result so that a fourth-degree Hurwitz interval polynomial is a Hadamardized polynomial family and we discuss an approach of differential topology in the study of the set of Hadamardized Hurwitz polynomials.

DESIGN OF STABLE 3D RECURSIVE DIGITAL FILTERS USING 3-VARIABLE VERY STRICTLY HURWITZ POLYNOMIAL

2000 ◽  
Vol 10 (05n06) ◽  
pp. 219-228
Author(s):  
I. EL-FEGHI ◽  
M. AHMADI ◽  
W. C. MILLER ◽  
M. A. SID-AHMED ◽  
V. RAMACHANDRAN
Keyword(s):  
Digital Filters ◽  
Three Dimensional ◽  
Hurwitz Polynomial ◽  
Hurwitz Polynomials ◽  
Recursive Digital Filters

In this paper, methods for generating 3-variable Very Strictly Hurwitz Polynomials (VSHP's) are presented. It is shown that the derived 3-variable VSHP's could be used to design stable three-dimensional digital filters satisfying prescribed magnitude specifications.

A Monoparametric Family of Piecewise Linear Systems to Generate Scroll Attractors via Path-Connected Set of Polynomials

2021 ◽  
Vol 31 (03) ◽  
pp. 2150034
Author(s):  
J. A. López-Rentería ◽  
E. Campos-Cantón ◽  
B. Aguirre-Hernández ◽  
G. Fernández-Anaya
Keyword(s):  
Linear Systems ◽  
Structural Stability ◽  
Piecewise Linear ◽  
Numerical Examples ◽  
Piecewise Linear Systems ◽  
Connected Set ◽  
The Stability ◽  
Path Connected ◽  
Roots Of A Polynomial ◽  
Polynomial Family

In this work, we present a monoparametric family of piecewise linear systems to generate multiscroll attractors through a polynomial family defined by path curves that connect to the roots. The idea is to define path curves where the roots of a polynomial can take values by determining an initial and a final polynomial. As a consequence, structural stability and bifurcation of the system can be obtained. Structural stability is obtained by preserving the same stability of the initial and final polynomials. However, the system bifurcates by changing the stability of the final polynomial with respect to the initial polynomial. The aim is achieved by the design of a piecewise linear controller that is applied to affine linear systems. Our results are mathematically proved and numerical examples are also provided to illustrate the approach.

scholarly journals Stable Factorization of Strictly Hurwitz Polynomials

2010 ◽  
Vol 5 (5) ◽  
pp. 701
Author(s):  
Ömer Eğecioğlu ◽  
B. Siddik Yarman
Keyword(s):  
Positive Function ◽  
Quadratic Equations ◽  
Root Finding ◽  
Real Frequency ◽  
Hurwitz Polynomial ◽  
Hurwitz Polynomials ◽  
Starting Point ◽  
Factorization Technique ◽  
Multiple Variables ◽  
Selection Of

We propose a stable factorization procedure to generate a strictly Hurwitz polynomial from a given strictly positive even polynomial. This problem typically arises in applications involving real frequency techniques. The proposed method does not require any root finding algorithm. Rather, the factorization process is directly carried out to find the solution of a set of quadratic equations in multiple variables employing Newton’s method. The selection of the starting point for the iterations is not arbitrary, and involves interrelations among the coefficients of the set of solution polynomials differing only in the signs of their roots. It is hoped that this factorization technique will provide a motivation to perform the factorization of two-variable positive function to generate scattering Hurwitz polynomials in two variables for which root finding methods are not applicable.

scholarly journals On the Existence of Hurwitz Polynomials with no Hadamard Factorization

2020 ◽  
Vol 36 (36) ◽  
pp. 210-213
Author(s):  
Stanisław Białas ◽  
Michał Góra
Keyword(s):  
Hadamard Product ◽  
Stable Polynomial ◽  
Stable Polynomials ◽  
Hurwitz Polynomials

A Hurwitz stable polynomial of degree $n\geq1$ has a Hadamard factorization if it is a Hadamard product (i.e., element-wise multiplication) of two Hurwitz stable polynomials of degree $n$. It is known that Hurwitz stable polynomials of degrees less than four have a Hadamard factorization. It is shown that, for arbitrary $n\geq4$, there exists a Hurwitz stable polynomial of degree $n$ which does not have a Hadamard factorization.

scholarly journals Stability and Multiscroll Attractors of Control Systems via the Abscissa

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Edgar-Cristian Díaz-González ◽  
Baltazar Aguirre-Hernández ◽  
Jorge Antonio López-Rentería ◽  
Eric Campos-Cantón ◽  
Carlos Arturo Loredo-Villalobos
Keyword(s):  
Control Systems ◽  
Lower Bounds ◽  
Piecewise Linear ◽  
Dissipative Systems ◽  
Linear Type ◽  
Hurwitz Matrix ◽  
Hurwitz Polynomial ◽  
Hurwitz Polynomials ◽  
Starting Point ◽  
Linear Differential

We present an approach to generate multiscroll attractors via destabilization of piecewise linear systems based on Hurwitz matrix in this paper. First we present some results about the abscissa of stability of characteristic polynomials from linear differential equations systems; that is, we consider Hurwitz polynomials. The starting point is the Gauss–Lucas theorem, we provide lower bounds for Hurwitz polynomials, and by successively decreasing the order of the derivative of the Hurwitz polynomial one obtains a sequence of lower bounds. The results are extended in a straightforward way to interval polynomials; then we apply the abscissa as a measure to destabilize Hurwitz polynomial for the generation of a family of multiscroll attractors based on a class of unstable dissipative systems (UDS) of affine linear type.

EVALUATION OF LONGO’S HEMORRHOIDECTOMY AT HUE UNIVERSITY HOSPITAL

2012 ◽  
pp. 79-85
Author(s):  
Van Lieu Nguyen ◽  
Doan Van Phu Nguyen ◽  
Thanh Phuc Nguyen
Keyword(s):  
Hospital Stay ◽  
Perioperative Complications ◽  
University Hospital ◽  
Anal Pain ◽  
Stapled Hemorrhoidectomy ◽  
Fourth Degree ◽  
Duration Of Hospital Stay ◽  
The Mean ◽  
Good For

Introduction: Since Longo First described it in 1998, Stapled Hemorrhoidectomy has been emerging as the procedure of choice for symtomatic hemorrhoid. Several studies have shown it to be a safe, effective and relative complication free procedure. The aim of this study was to determine the suitability of (SH) as a day cas procedure at Hue University Hospital. Methods: From Decembre 2009 to April 2012, 384 patients with third- degree and fourth-degree hemorrhoids who underwent Stapled Hemorrhoidectomy were included in this study. Parameters recorded included postoperative complications, analegic requirements, duration of hospital stay and patient satisfaction. Follow-up was performed at 1 month and 3 months post-operative. Results: Of the 384 patients that underwent a Stapled Hemorrhoidectomy 252 (65,7%) were male and 132 (34,3%) were female. The mean age was 47,5 years (range 17-76 years. Duration of hospital stay: The mean day was 2,82 ± 1,15 days (range 1-6 days). There were no perioperative complications. There was one case postoperative complication: hemorrhage; Follow-up after surgery: 286 (74,4%) patients had less anal pain, 78 (20,3%) patients had moderate anal pain, 3 (0,8%) patients had urinary retention; Follow-up after one month: good for 325 (84,6%) patients, average for 59 (15,4%) patients; Follow-up after three months: good for 362 (94,3%) patients, average for 22 (5,7%) patients. Conclusion: Our present study shows that Stapled Hemorrhoidectomy is a safe, reduced postoperative pain, shorter hospital stay and a faster return to unrestricted daily activity

scholarly journals Simulation Tests of a Cow Milking Machine—Analysis of Design Parameters

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1358
Author(s):  
Ewa Golisz ◽  
Adam Kupczyk ◽  
Maria Majkowska ◽  
Jędrzej Trajer
Keyword(s):  
Mathematical Model ◽  
Simplified Model ◽  
Design Parameters ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Local Loss ◽  
Linear Drag ◽  
Milking Machine ◽  
Machine Analysis ◽  
The Impact

The objective of this paper was to create a mathematical model of vacuum drops in a form that enables the testing of the impact of design parameters of a milking cluster on the values of vacuum drops in the claw. Simulation tests of the milking cluster were conducted, with the use of a simplified model of vacuum drops in the form of a fourth-degree polynomial. Sensitivity analysis and a simulation of a model with a simplified structure of vacuum drops in the claw were carried out. As a result, the impact of the milking machine’s design parameters on the milking process could be analysed. The results showed that a change in the local loss and linear drag coefficient in the long milk duct will have a lower impact on vacuum drops if a smaller flux of inlet air, a higher head of the air/liquid mix, and a higher diameter of the long milk tube are used.

scholarly journals Effect of Differentiated Nitrogen Fertilization on the Enzymatic Activity of the Soil for Sweet Potato (Ipomoea batatas L. [Lam.]) Cultivation

Agronomy ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 1970
Author(s):  
Barbara Sawicka ◽  
Barbara Krochmal-Marczak ◽  
Piotr Pszczółkowski ◽  
Elżbieta Jolanta Bielińska ◽  
Anna Wójcikowska-Kapusta ◽  
...  
Keyword(s):  
Enzymatic Activity ◽  
Total Nitrogen ◽  
Nitrogen Fertilization ◽  
Ipomoea Batatas ◽  
Polynomial Regression ◽  
Sandy Loam ◽  
C:N Ratio ◽  
Soil Reaction ◽  
Research Station ◽  
Fourth Degree

The experiment was conducted between 2015–2017 in the Research Station for Cultivar Testing in Uhnin (51°34′ N, 23°02′ E), in Luvisols developed from sandy loam soils. Soil samples for the tests of enzymatic activity were collected after the crop was harvested. The measurements included: the content of dehydrogenases, phosphatases, urease and protease, as well as total organic carbon, total nitrogen and mineral nitrogen in soil, based on standard methods. The research results point to changes in the enzymatic activity of light soil under the influence of varied nitrogen fertilization. In objects fertilized with this ingredient, the activity of the analysed enzymes was significantly higher than in the control soil, except for combinations fertilised with 150 kg ha−1 N characterised by the highest accumulation of N-NO3− in soil. The activity of dehydrogenases, phosphatases and urease changed as the nitrogen dose increased. The polynomial regression analysis enabled a better understanding of those dependences. In the case of dehydrogenases, phosphatases and urease, a third-degree curvilinear relation of enzymatic activity to nitrogen fertilisation was observed (a fourth-degree relation was found, with a coefficient R2 in those equations amounting to =0.958, 0.977, 0.979, respectively) and in the case of protease activity, a fourth-degree relation, with coefficient R2 = 0.989. However, soil acidity did not have a significant influence on either the enzymatic activity or physico-chemical characteristics of soil under the cultivation of sweet potatoes. The C:N ratio turned out to be significantly negatively related to the content of the enzymes dehydrogenase (Adh), phosphatase (AF), urease (AU) and protease (AP) as well as the content of total nitrogen, especially its ammonium form (N-NH4). The obtained results indicate the usefulness of research on enzymatic activity as an indicator of soil reaction to nitrogen fertilization and will enable maintenance of the optimal biological balance of cultivated soils.

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