scholarly journals Crisis Deducing All Physics Laws, Solution to The Crisis and Its Applications to Improved Variational Principle, Improved Noether Theorem and so on

2020 ◽  
Author(s):  
C. Huang ◽  
Yong-Chang Huang
Keyword(s):  
Variational Principle ◽  
Extreme Values ◽  
Noether Theorem ◽  
Lagrange Equations ◽  
Famous Theorem ◽  
The Real ◽  
Equivalent Relation

This paper discovers that current variational principle and Noether theorem for different physics systems with (in)finite freedom systems have missed the double extremum processes of the general extremum functional that both is deduced by variational principle and is necessarily taken in deducing all the physics laws, but these have not been corrected for over a century since Noether's proposing her famous theorem, which result in the crisis deducing all the physics laws. This paper discovers there is the hidden logic cycle that one assumes Euler-Lagrange equations, and then he finally deduces Euler-Lagrange equations via the equivalent relation in the whole processes in all relevant current references. This paper corrects the current key mistakes that when physics systems choose the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current articles, reviews and (text)books. The real physics should be what after choosing the variational extreme values of physics systems, the general extremum functional of the physics systems needs to further choose the minimum absolute extremum zero of the general extremum functional, otherwise, the appearing processes of physics systems are still virtual processes. Using the double extremum processes of the general extremum functionals, the crisis and the hidden logic cycle problem in current variational principle and current Noether theorem are solved. Furthermore, the new mathematical and physical double extremum processes and their new mathematical and physical pictures for (in)finite freedom systems are discovered. The improved variational principle and improved Noether theorem are given, which would rewrite all relevant current different branches of science, as key tools of studying and processing them.

scholarly journals General variational principle, general Noether theorem, their classical and quantum new physics and solution to crisis deducing all physics laws

2020 ◽  
Author(s):  
C. Huang ◽  
Yong-Chang Huang
Keyword(s):  
Variational Principle ◽  
Extreme Values ◽  
New Physics ◽  
Noether Theorem ◽  
Lagrange Equations ◽  
Famous Theorem ◽  
The Real ◽  
Equivalent Relation

This paper discovers that current variational principle and Noether theorem for different physics systems with (in)finite freedom systems have missed the double extremum processes of the general extremum functional that both is deduced by variational principle and is necessarily taken in deducing all the physics laws, but these have not been corrected for over a century since Noether's proposing her famous theorem, which result in the crisis deducing relevant mathematical laws and all physics laws. This paper discovers there is the hidden logic cycle that one assumes Euler-Lagrange equations, and then he finally deduces Euler-Lagrange equations via the equivalent relation in the whole processes in all relevant current references. This paper corrects the current key mistakes that when physics systems choose the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current articles, reviews and (text)books. The real physics should be after choosing the variational extreme values of physics systems, the general extremum functional of the physics systems needs to further choose the minimum absolute extremum zero of the general extremum functional, otherwise, the appearing processes of physics systems are still virtual processes. Using the double extremum processes of the general extremum functionals, the crisis and the hidden logic cycle in current variational principle and current Noether theorem are solved. Furthermore, the new mathematical and physical double extremum processes and their new mathematical pictures and physics for (in)finite freedom systems are discovered. This paper gives both general variational principle and general Noether theorem as well as their classical and quantum new physics, which would rewrite all relevant current different branches of science, as key tools of studying and processing them.

scholarly journals General Canonical Variational Principle and Noether Theorem, Their New Classical and Quantum Physics, Solution to Crisis Deducing All Physics Laws in Phase Space

2020 ◽  
Author(s):  
C. Huang ◽  
Yong-Chang Huang
Keyword(s):  
Phase Space ◽  
Variational Principle ◽  
Quantum Physics ◽  
Extreme Values ◽  
New Physics ◽  
Extreme Value ◽  
Noether Theorem ◽  
First Time ◽  
Value Functional ◽  
General Extreme Value

This paper discovers that current canonical variational principle and canonical Noether theorem of (in)finite freedom systems for different physics systems have neglected doublet extreme value processes of the general extreme value functional that both is derived by variational principle and is necessarily be taken in deriving all ( quantum ) physics laws in phase space, but which have not been done for over one century since Noether's showing her distinguished theorem, which lead to the crisis deriving all (quantum) physics laws (necessary) in phase space. We discover there is the hidden logic cycle that people assume canonical equations, and then they finally deduce canonical equations by the equivalent relation in the whole processes in all current references. We correct the current key mistake concepts that when physics systems take the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current references. The real physics should be what after taking the physics systems' variational extreme values, the physics systems' general extremum functional needs to further take the general extremum functional's minimum absolute extremum zero, otherwise, the appearing processes of physics systems still are virtual processes. Conservation current equations and conservation currents, in phase space, of general canonical variational principle and general canonical Noether theorem are, respectively, deduced for the first time. Using the general extremum functionals' doublet extreme value processes, the hidden logic cycle and the crisis in current canonical variational principle and current canonical Noether theorem are solved. Consequently, the new mathematical pictures, classical and quantum new physics in phase space and the new mathematical and physical doublet extremum processes for (in)finite freedom systems are discovered. General canonical variational principle and general canonical Noether theorem naturally are given, which would rewrite all the different sciences in phase space, as key tools of studying and dealing with them.

scholarly journals Covariant brackets for particles and fields

2017 ◽  
Vol 32 (19) ◽  
pp. 1750100 ◽  
Author(s):  
M. Asorey ◽  
M. Ciaglia ◽  
F. Di Cosmo ◽  
A. Ibort
Keyword(s):  
Variational Principle ◽  
Geometrical Approach ◽  
Covariant Formulation ◽  
Lagrange Equations ◽  
Relativistic Systems

A geometrical approach to the covariant formulation of the dynamics of relativistic systems is introduced. A realization of Peierls brackets by means of a bivector field over the space of solutions of the Euler–Lagrange equations of a variational principle is presented. The method is illustrated with some relevant examples.

On the Nonuniqueness of Solutions Obtained With Simplified Variational Principles

1996 ◽  
Vol 63 (3) ◽  
pp. 820-827 ◽  
Author(s):  
H. Mang ◽  
P. Helnwein ◽  
R. H. Gallagher
Keyword(s):  
Variational Principle ◽  
Lagrange Multipliers ◽  
Variational Principles ◽  
Boundary Value ◽  
Geometrically Nonlinear ◽  
Lagrange Equations ◽  
Geometrically Nonlinear Theory ◽  
Nonuniqueness Of Solutions ◽  
Uniqueness Of The Solution ◽  
Bending Of Beams

The attempt to satisfy subsidiary conditions in boundary value problems without additional independent unknowns in the form of Lagrange multipliers has led to the development of so-called “simplified variational principles.” They are based on using the Euler-Lagrange equations for the Lagrange multipliers to express the multipliers in terms of the original variables. It is shown that the conversion of a variational principle with subsidiary conditions to such a simplified variational principle may lead to the loss of uniqueness of the solution of a boundary value problem. A particularly simple form of the geometrically nonlinear theory of bending of beams is used as the vehicle for this proof. The development given in this paper is entirely analytical. Hence, the deficiencies of the investigated simplified variational principle are fundamental.

scholarly journals LAWS OF MOTION IN THE FRAME THEORIES OF GRAVITY

2021 ◽  
Vol 2 (37) ◽  
pp. 73-79
Author(s):  
S. Samokhvalov
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Riemannian Space ◽  
Lagrange Equations ◽  
Remarkable Feature ◽  
Translational Invariance ◽  
Famous Theorem ◽  
Conservation Of Energy ◽  
Wide Range ◽  
Theories Of Gravity

One of the most striking features of the general relativity (GR) is the fact that the matter that generates gravitational field cannot move arbitrarily, but must obey certain equations that follow from equations of the gravitational field as a condition of their compatibility. This fact was first noted in the fundamental Hilbert's work, in which equations of GR saw the world for the first time as variational Lagrange equations. Hilbert showed that in the case when fulfilling equations of the gravitational field which were born by an electromagnetic field, four linear combinations of equations of the electromagnetic field and their derivatives are zero due to the general covariance of the theory. It is known that this is what stimulated E. Noether to invent her famous theorem. As for "solid matter", for the compatibility of equations of the gravitational field, it is necessary that particles of dust matter move along geodesics of Riemannian space, which describes the gravitational field. This fact was pointed out in the work of A. Einstein and J. Grommer and according to V. Fock it is one of the main justifications of GR (although even before the creation of GR it was known that the motion along geodesics is a consequence of the condition of covariant conservation of energy-momentum of matter). This remarkable feature of GR all his life inspired Einstein to search on the basis of GR such theory from which it would be possible to derive all fundamental physics, including quantum mechanics. Interest in this problem (following Einstein, we name it the problem of motion) has resumed in our time in connection with the registration of gravitational waves and analysis of the conditions of their radiation, i.e. the need for its direct application in gravitational-wave astronomy. In this article we consider the problem to what extent the motion of matter that generates the gravitational field can be arbitrary. Considered problem is analyzed from the point of view symmetry of the theory with respect to the generalized gauge deformed groups without specification of Lagrangians. In particular it is shown, that the motion of particles along geodesics of Riemannian space is inherent in an extremely wide range of theories of gravity and is a consequence of the gauge translational invariance of these theories under the condition of fulfilling equations of gravitational field. In addition, we found relationships of equations for some fields that follow from the assumption about fulfilling of equations for other fields, for example, relationships of equations of the gravitational field which follow from the assumption about fulfilling of equations of matter fields.

scholarly journals Sums and products of intervals in ordered semigroups

2021 ◽  
Vol 29 (2) ◽  
pp. 187-198
Author(s):  
T. Glavosits ◽  
Zs. Karácsony
Keyword(s):  
Real Line ◽  
Ordered Semigroup ◽  
Translation Invariant ◽  
Famous Theorem ◽  
Ordered Semigroups ◽  
The Real ◽  
Ordered Ring

Abstract We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]a, b[ + ]c, d[ = ]a + c, b + d[ for all a, b, c, d ∈ 𝕊 such that a < b and c < d, but the intervals are no translation invariant, that is, the equation c +]a, b[ = ]c + a, c + b[ is not always fulfilled for all elements a, b, c ∈ 𝕊 such that a < b. The multiplicative version of the above example is shown too. The product of open intervals in the ordered ring of all integers (denoted by ℤ) is also investigated. Let Ix := {1, 2, . . ., x} for all x ∈ ℤ+ and defined the function g : ℤ+ → ℤ+ by g ( x ) : = max { y ∈ ℤ + | I y ⊆ I x ⋅ I x } g\left( x \right): = \max \left\{ {y \in {\mathbb{Z}_ + }|{I_y} \subseteq {I_x} \cdot {I_x}} \right\} for all x ∈ ℤ+. We give the function g implicitly using the famous Theorem of Chebishev. Finally, we formulate some questions concerning the above topics.

scholarly journals Crisis Deducing All PhysicsLaws, Solution to The Crisis and Its Applications to Improved Variational Principle, Improved Noether Theorem and so on

2020 ◽  
Author(s):  
C. Huang ◽  
Yong-Chang Huang
Keyword(s):  
Variational Principle ◽  
Noether Theorem

This paper discovers that current variational principle and Noether theorem for both different physics systems and (in)finite freedom systems have missed the double extremum processes of the general extremum functional that is deduced by variational principle and necessarily taken in deducing all the physics laws, but these have not been corrected for over a century since Noether's proposing her theorem, which result in the crisis deducing all the physics laws. Using the double extremum processes of the general extremum functionals, the crisis and the hidden logic cycle problem in current variational principle and current Noether theorem are solved. Furthermore, the new mathematical and physical double extremum processes and their new mathematical and physical pictures for (in)finite freedom systems are discovered. The improved variational principle and improved Noether theorem are given, which are key useful to different branches of science.as key tools of studying and processing them.

scholarly journals Теорема Артина для f-колец

2015 ◽  
Author(s):  
A.G. Kusraev
Keyword(s):  
Rational Functions ◽  
Sum Of Squares ◽  
Famous Theorem ◽  
The Real ◽  
Complete Ring ◽  
Positive Polynomial ◽  
Ring Of Quotients ◽  
Real Closure ◽  
F Ring ◽  
17Th Problem

The main result states that each positive polynomial p in N variables with coefficients in a unital Archimedean f-ring K is representable as a sum of squares of rational functions over the complete ring of quotients of K provided that p is positive on the real closure of K. This is proved by means of Boolean valued interpretation of Artin's famous theorem which answers Hilbert's 17th problem affirmatively.

Hamiltonian Formulation for Continuous Third-order Systems Using Fractional Derivatives

2021 ◽  
Vol 14 (1) ◽  
pp. 35-47
Keyword(s):  
Variational Principle ◽  
Fractional Derivatives ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Lagrange Equations ◽  
Third Order ◽  
Derivative Operator ◽  
Hamilton Equations ◽  
Liouville Fractional Derivative ◽  
Continuous Field

Abstract: We constructed the Hamiltonian formulation of continuous field systems with third order. A combined Riemann–Liouville fractional derivative operator is defined and a fractional variational principle under this definition is established. The fractional Euler equations and the fractional Hamilton equations are obtained from the fractional variational principle. Besides, it is shown that the Hamilton equations of motion are in agreement with the Euler-Lagrange equations for these systems. We have examined one example to illustrate the formalism. Keywords: Fractional derivatives, Lagrangian formulation, Hamiltonian formulation, Euler-lagrange equations, Third-order lagrangian.

THE THERMODYNAMIC DESCRIPTION OF HETEROGENEOUS DISSIPATIVE SYSTEMS BY VARIATIONAL METHODS: II. A VARIATIONAL PRINCIPLE APPLICABLE TO NON-STATIONARY (UNCONSTRAINED) HETEROGENEOUS DISSIPATIVE SYSTEMS

1960 ◽  
Vol 38 (10) ◽  
pp. 1356-1365 ◽  
Author(s):  
J. S. Kirkaldy
Keyword(s):  
Variational Principle ◽  
Thermodynamic Description ◽  
Approximate Expression ◽  
Diffusion Reaction ◽  
Dissipative Systems ◽  
Lagrange Equations ◽  
Flow Process ◽  
Holonomic Constraint ◽  
Steady Growth ◽  
Phenomenological Equations

The variational principle[Formula: see text]involving the independent thermodynamic fluxes Ji and forces Xi and subject to the non-holonomic constraint, Xi = constant, gives an expression for the integral behavior of an unconstrained heterogeneous conduction–diffusion–reaction–viscous flow process. The validity of this expression can be checked by performing the variation with respect to the forces to obtain as Euler–Lagrange equations the phenomenological equations,[Formula: see text]This principle allows the unique mathematical specification of certain non-stationary systems which are not easily amenable to differential analysis.As an example, it is demonstrated that the principle generates an approximate expression for the steady growth velocity, v, of an isothermal segregation reaction in terms of the degree of advancement of the reaction, [Formula: see text], and its derivative with respect to v,[Formula: see text]

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