Solving the Quintic: A New Approach to Bring's Transformation

2021 ◽  
Author(s):  
Jorge Franco
Keyword(s):  
General Solution ◽  
New Approach ◽  
Solvable Equation

Applying a procedure similar to that of E.S. Bring, by using a 4th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2nd, 4th and 6th terms which was transformed into a cubic (solvable) equation. By applying a 6th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2nd, 3rd, 4th and 5th terms) form was obtained.

scholarly journals Solving the Quintic: A New Approach to Bring's Transformation

2021 ◽  
Author(s):  
Jorge Franco
Keyword(s):  
General Solution ◽  
New Approach ◽  
Solvable Equation

Applying a procedure similar to that of E.S. Bring, by using a 4th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2nd, 4th and 6th terms which was transformed into a cubic (solvable) equation. By applying a 6th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2nd, 3rd, 4th and 5th terms) form was obtained.

scholarly journals A General Solution to the Different Formulations of the Second Law of Thermodynamics

2021 ◽  
Vol 82 (2) ◽  
pp. 61-71
Author(s):  
Saeed Shahsavari ◽  
Mehran Moradi
Keyword(s):  
General Solution ◽  
Second Law Of Thermodynamics ◽  
The Other ◽  
Second Law ◽  
Energy Structure ◽  
New Approach ◽  
General Physics ◽  
Classical Thermodynamics ◽  
Physical Laws ◽  
Energy Components

The second law of thermodynamics is one of the most important physical laws that has been extracted by different formulations. In this paper, a new approach to study different formulations of the second law is extracted based on the energy components of the system as well as introducing the independent and dependent energy components concepts. Also, two main formulations of classical thermodynamics, and also entropy from the perspective of general physics are discussed based on the energy components of the system for constant applied energy to the system in different conditions. Kelvin-Plank and Clausius formulations, as two main classical formulations, are all assertions about impossible processes. Considering the energy structure equation of the system, as an equation to formulate the performed process using activated energy components, it is shown that different formulations of the second law of thermodynamics represent the same concept in the perspective of the energy structure. Finally, a new general formulation to the second law, based on the energy structure of the system is extracted, and the equivalence as the other formulations is shown. The presented formulation is extracted based on the dependent and independent activated energy components, and in fact, shows all possible paths in the considered energy applying to the system.

scholarly journals Solution of the Quintic and Sextic by Radicals

2021 ◽  
Author(s):  
Jorge A. Franco
Keyword(s):  
General Solution ◽  
Solvable Equation

Applying a procedure similar to that of E.S. Bring, by using a 4th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2nd, 4th and 6th terms which was transformed into a cubic (solvable) equation. By applying a 6th degree Tschirnhaus transformation to the BJSp (normal septic) equation its Bring-Jerrard binormal (without the 2nd, 3rd, 4th and 5th terms) form was obtained.

Axisymmetric Inclusion in a Half Space

1990 ◽  
Vol 57 (1) ◽  
pp. 74-77 ◽  
Author(s):  
H. Y. Yu ◽  
S. C. Sanday
Keyword(s):  
General Solution ◽  
Half Space ◽  
Transformation Method ◽  
Dislocation Loops ◽  
Hankel Transformation ◽  
New Approach ◽  
Elastic Fields ◽  
Special Cases

An alternate method of approach for solving the axisymmetric elastic fields in the half space with an isotropic spheriodal inclusion is proposed. This new approach involves the application of the Hankel transformation method for the solution of prismatic dislocation loops and Eshelby’s solution for ellipsoidal inclusions. Existing solutions by other methods for the inclusion with pure dilatational misfit in a half space are shown to be special cases of the present, more general solution.

scholarly journals A New Approach to Hyers-Ulam Stability of r -Variable Quadratic Functional Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Vediyappan Govindan ◽  
Porpattama Hammachukiattikul ◽  
Grienggrai Rajchakit ◽  
Nallappan Gunasekaran ◽  
R. Vadivel
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Quadratic Mapping ◽  
Ulam Stability ◽  
New Approach

In this paper, we investigate the general solution of a new quadratic functional equation of the form ∑ 1 ≤ i < j < k ≤ r ϕ l i + l j + l k = r − 2 ∑ i = 1 , i ≠ j r ϕ l i + l j + − r 2 + 3 r − 2 / 2 ∑ i = 1 r ϕ l i . We prove that a function admits, in appropriate conditions, a unique quadratic mapping satisfying the corresponding functional equation. Finally, we discuss the Ulam stability of that functional equation by using the directed method and fixed-point method, respectively.

Teoria wartości Alexiusa Meinonga

Etyka ◽  
1973 ◽  
Vol 12 ◽  
pp. 57-78
Author(s):  
Hanna Buczyńska-Garewicz
Keyword(s):  
General Solution ◽  
Emotional Experience ◽  
Philosophical Foundation ◽  
Emotional Experiences ◽  
New Approach

The article discusses Meinong’s theory of values in its later version as laid down in his studies Über emotionale Präsentation and Zur Grundlegung der allgemeinen Werttheorie. His early psychological works are omitted. The principal purpose aim of the article is to show that Meinong’s axiology was essentially antipsychological in its character. For the philosophical foundation of his theory of values Meinong took the theory of object which furnishes a general solution of the question of relations between emotional experience, its content and its object. The intentional interpretation of feelings as emotional experiences relating to objects suggested to Meinong a new approach to values – to treat them as correlates of those experiences.

scholarly journals Solution of the Quintic and Sextic by Radicals

2021 ◽  
Author(s):  
Jorge A. Franco
Keyword(s):  
General Solution ◽  
Solvable Equation

Applying a procedure similar to that of E.S. Bring, by using a 4th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2nd, 4th and 6th terms which was transformed into a cubic (solvable) equation. By applying a 6th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2nd, 3rd, 4th and 5th terms) form was obtained.

The O–C diagrams of minor planets − a new approach to modelling the rotation

1999 ◽  
Vol 173 ◽  
pp. 185-188
Author(s):  
Gy. Szabó ◽  
K. Sárneczky ◽  
L.L. Kiss
Keyword(s):  
Error Analysis ◽  
Time Dependence ◽  
Theoretical Work ◽  
Minor Planet ◽  
Minor Planets ◽  
New Approach ◽  
Preliminary Results ◽  
Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

The Role of VLBI in the Establishment of Coordinate Systems

1975 ◽  
Vol 26 ◽  
pp. 293-295 ◽  
Author(s):  
I. Zhongolovitch
Keyword(s):  
General Solution ◽  
Future Development ◽  
Rational Approach ◽  
Radio Telescopes ◽  
Coordinate Systems ◽  
Tectonic Plates ◽  
Astronomical Observations ◽  
Optical Instruments ◽  
Fundamental Polyhedron

Considering the future development and general solution of the problem under consideration and also the high precision attainable by astronomical observations, the following procedure may be the most rational approach:1. On the main tectonic plates of the Earth’s crust, powerful movable radio telescopes should be mounted at the same points where standard optical instruments are installed. There should be two stations separated by a distance of about 6 to 8000 kilometers on each plate. Thus, we obtain a fundamental polyhedron embracing the whole Earth with about 10 to 12 apexes, and with its sides represented by VLBI.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

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