UNCERTAIN FOURTH-DEGREE EQUATION OF THREE VARIABLES

2019 ◽  
Author(s):  
L. L. Bokareva ◽  
N. L. Bokarev ◽  
Y. V. Buyakova
Keyword(s):  
Fourth Degree ◽  
Degree Equation

scholarly journals The accurate calculation of the geodetic heights of the celestial body’s surface points relative to the triaxial ellipsoid

2019 ◽  
Vol 486 (4) ◽  
pp. 489-493
Author(s):  
M. E. Fleis ◽  
M. V. Nyrtsov ◽  
M. M. Borisov ◽  
A. I. Sokolov
Keyword(s):  
Normal Equation ◽  
Triaxial Ellipsoid ◽  
Approximate Methods ◽  
Small Bodies ◽  
Fourth Degree ◽  
New Approach ◽  
Geodetic Height ◽  
Rectangular Coordinates ◽  
Ellipsoid Of Revolution ◽  
Degree Equation

A sphere or ellipsoid of revolution are usually used for approximation of the physical surface of the Earth. In some cases, a triaxial ellipsoid is used. The calculation of the geodetic height of points on the Earth’s surface is carried out mainly by approximate methods using the formulas for the dependence of spatial rectangular coordinates x, y, z on geodesics B, L, H. However, there are small bodies of the Solar system, for example, Eros 433 asteroid, for which such variants of the first approximation are incorrect, since in this case both first approximations are not small quantities. This article proposes a fundamentally new approach to calculating the geodesic height relative to the triaxial ellipsoid, based on the joint use of the normal equation for a surface passing through a given point and the equations of the surface itself. The method is reduced to solving the sixth-degree equation by the Sturm method and the fourth-degree equation by the Ferrari method.

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.

Geometry of the bifurcations of the normalized reduced Henon–Heiles family

1982 ◽  
Vol 382 (1783) ◽  
pp. 361-371 ◽  
Keyword(s):  
Bifurcation Diagram ◽  
Main Resonance ◽  
Fourth Degree ◽  
Global Geometry ◽  
Geometric Explanation ◽  
Hamiltonian Functions

This paper deals with the global geometry of the bifurcations of a family of Hamiltonian functions that arises from normalizing the Henon–Heiles family to fourth-degree terms and then performing a reduction. This gives a geometric explanation of the bifurcation diagram for the main resonance in the model of axisymmetric galaxies of Braun and Verhulst.

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

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