Stability for the Marcinkiewicz theorem. Case of a fourth-degree polynomial

1981 ◽  
Vol 16 (5) ◽  
pp. 1413-1424
Author(s):  
N. A. Sapogov
Keyword(s):  
Degree Polynomial ◽  
Fourth Degree ◽  
Marcinkiewicz Theorem

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.

BENDING OF ORTHOTROPIC RECTANGULAR CANTILEVER PLATE

2021 ◽  
pp. 2-9
Author(s):  
M.V. Sukhoterin ◽  
◽  
A.M. Maslennikov ◽  
T.P. Knysh ◽  
I.V. Voytko ◽  
...  
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Trigonometric Series ◽  
Bending Moment ◽  
Partial Solution ◽  
Numerical Results ◽  
Cantilever Plate ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Beam Function

Abstract. An iterative method of superposition of correcting functions is proposed. The partial solution of the main differential bending equation is represented by a fourth-degree polynomial (the beam function), which gives a residual only with respect to the bending moment on parallel free faces. This discrepancy and the subsequent ones are mutually compensated by two types of correcting functions-hyperbolic-trigonometric series with indeterminate coefficients. Each function satisfies only a part of the boundary conditions. The solution of the problem is achieved by an infinite superposition of correcting functions. For the process to converge, all residuals must tend to zero. When the specified accuracy is reached, the process stops. Numerical results of the calculation of a square ribbed plate are presented.

Complete Solution to the Eight-Point Path Generation of Slider-Crank Four-Bar Linkages

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Hafez Tari ◽  
Hai-Jun Su
Keyword(s):  
Complete Solution ◽  
Solution Process ◽  
Polynomial Equations ◽  
Homotopy Methods ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Augmented System ◽  
Polynomial Curve ◽  
Four Bar Linkage ◽  
Classical Homotopy

We study the synthesis of a slider-crank four-bar linkage whose coupler point traces a set of predefined task points. We report that there are at most 558 slider-crank four-bars in cognate pairs passing through any eight specified task points. The problem is formulated for up to eight precision points in polynomial equations. Classical elimination methods are used to reduce the formulation to a system of seven sixth-degree polynomials. A constrained homotopy technique is employed to eliminate degenerate solutions, mapping them to solutions at infinity of the augmented system, which avoids tedious post-processing. To obtain solutions to the augmented system, we propose a process based on the classical homotopy and secant homotopy methods. Two numerical examples are provided to verify the formulation and solution process. In the second example, we obtain six slider-crank linkages without a branch or an order defect, a result partially attributed to choosing design points on a fourth-degree polynomial curve.

Integrability of Hamiltonians with third‐ and fourth‐degree polynomial potentials

1983 ◽  
Vol 24 (9) ◽  
pp. 2289-2295 ◽  
Author(s):  
B. Grammaticos ◽  
B. Dorizzi ◽  
A. Ramani
Keyword(s):  
Degree Polynomial ◽  
Fourth Degree ◽  
Polynomial Potentials

scholarly journals Distribution of Trichinella infections in pigs and Trichinellosis in humans in Serbia from 1994 to 2018

2019 ◽  
Vol 73 (2) ◽  
pp. 133-143 ◽  
Author(s):  
Milorad Mirilovic ◽  
Nada Tajdic ◽  
Branislav Vejnovic ◽  
Spomenka Djuric ◽  
Nikola Mirilovic ◽  
...  
Keyword(s):  
Polynomial Function ◽  
Winter Season ◽  
Degree Polynomial ◽  
Surveillance Period ◽  
Mammal Species ◽  
Fourth Degree ◽  
Trend Line ◽  
Trichinella Infection ◽  
The World ◽  
The Republic

Introduction. Trichinellosis is a disease in humans caused by parasites of the genus Trichinella, and these roundworms can occur in a variety of animals (over one hundred mammal species). Members of the genus Trichinella are present in almost all continents and in all climate zones. Intensive studies on the eradication of this disease have been going on for a long period, but despite the finances invested in research projects, trichinellosis is still present in the 21st century and poses a major health issue all over the world. According to current scientific estimations, there are over 27 million Trichinellainfected people in the world. The aim of our study was to determine the distribution and trends for Trichinella infection in pigs and trichinellosis in humans in Serbia between 1994 and 2018. Materials and Methods. Data for the 25-year surveillance period of Trichinella cases registered in pigs and humans in Serbia was gathered from the Veterinary Directorate and from the Institute of Public Health of the Republic of Serbia. The data obtained was analysed with the relative numbers of structure and dynamics, indices and descriptive statistical indicators. Results and Conclusions. During the research period, 14,837 pigs were diagnosed as infected with Trichinella. Out of this number, 87.31% of pigs were identified in the five epizootiological regions, and only 12.69% were diagnosed in the non-epizootiological regions in Serbia. During the period 1994-2018 in Serbia, a total of 6,850 people were treated for Trichinella infection. Out of this number, 4,153 (60.63%) people were from the five epizootiological regions. The trend-line describing the presence of Trichinella in pigs was defined by a fourth degree polynomial function. Meanwhile, the trend-line describing the presence of trichinellosis in humans was defined by a sixth degree polynomial function. Trichinellosis in Serbia is most common during the winter season, from December to March.

Use of Resultant in the Dimensional Synthesis of Linkage Components: Motion Generation With Prescribed Timing

1992 ◽  
Author(s):  
Chuen-Sen Lin ◽  
Bao-Ping Jia
Keyword(s):  
Angular Displacement ◽  
Solution Process ◽  
Original System ◽  
Polynomial Equations ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Closed Form Solutions ◽  
Resultant Theory

Abstract Resultant theory is applied to derive closed-form solutions for the dimensional synthesis of linkage components for a finite number of precision positions for motion generation with prescribed timing. The solutions are in forms of polynomial equations of the exponential of a single unknown angular displacement. The degree of the derived polynomial depends on the number of links in the linkage component and the number of precision positions to be synthesized for, or the number of compatibility equations. The resultant theory is discussed in detail, and the procedure for the derivation of resultant polynomials is demonstrated. This paper shows that, for the case of two compatibility equations, the solution is a six-degree polynomial. For the case of three compatibility equations, the solution is a fifty-fourth degree polynomial. The Bernshtein formula is applied to check the exact number of solutions of the original system of polynomial equations and to verify the validity of the derived resultant polynomials. An algorithm is also proposed for screening out extra solutions which may be generated through the solution process.

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