ORALS
SESSION:
MathematicsTuePM2-R9
| 6th Intl. Symp. on Sustainable Mathematics Applications |
| Tue. 28 Nov. 2023 / Room: Showroom | |
| Session Chairs: Ruggero Maria Santilli; Mike Mikalajunas; Session Monitor: TBA |
16:00: [MathematicsTuePM209] OS
THE USE OF A NUMERICALLY CONTROLLED SYSTEM OF ANALYTICS TABLE FOR SOLVING VARIOUS CASES OF THE NAVIER-STOKES EQUATIONS IN TERMS OF GENERALIZED ANALYTICAL SOLUTIONS ONLY Mike Mikalajunas1 ;
1CIME, iLe Perrot, Canada;
Paper Id: 118
[Abstract] The general application of Specialized Differential Forms in Science and Engineering has resulted into the creation of a very unique table called Numerically Controlled System of Analytics or (NCSA) for short by which any type of differential equation may now be completed integrated only in terms of generalized analytical solutions involving only the algebraic and elementary functions. Over time when such a new method of computational analysis is applied correctly then this would have the effect of reducing our excessive dependency on the use of many types of well known experimental based models in the Physical Sciences in favor of a more Universal Algebraic Theory.
In this talk I will begin by highlighting the importance of using a Numerically Controlled System of Analytics table in fluid dynamics and in mechanics of material for integrating the corresponding set of PDEs only in terms of generalized analytical solutions as a complete alternative to conventional methods of integration. I will be demonstrating how to correctly setup such a table that would lead to defining a very special type of database by which complete generalized analytical solutions to PDEs may be logically deduced only by computation.
I will also be revealing a very important mathematical property of Specialized Differential Forms that has led to redefining the whole concept of a composite function in terms of providing us with a very practical way of measuring its degree of composition regardless of whether or not they are defined in either explicit or in implicit form. This would make it possible while in the process of setting up our Numerically Controlled System of Analytics table for analysis on various cases of the Naiver-Stokes equations to extend the scope of new potential forms of analytical solutions to PDEs by including composite functions of various degree of compositions that can be defined in either explicit or in implicit form.
Under this new type of measure for the degree of composition for all composite functions, the simple wave equation for example that forms the basis of representation of solutions to the time dependent and independent Schrödinger equation for uni-electron and multi-electron structure may be elevated to include composite functions as well where the exact order of composition would have to be determined by computation only. This would have the potential of providing us with a much better understand on the exact physical structure of a wave when applied to many areas of the Physical and Biological Sciences as a result of solving for certain types of differential equations and systems of differential equations based on the method of Specialized Differential Form.
References:
Mikalajunas, M. (2022), “The Gradual Abandonment of many types of well known experimental based Physical Models in favor of a more Universal Algebraic Theory: A General Introduction”, Sustainability through Science and Technology (SIPS 2022), Nov 2022, Hilton Phuket Arcadia, Thailand.
Mikalajunas, M. (2022), “The Gradual Abandonment of many types of well known experimental based Physical Models in favor of a more Universal Algebraic Theory: Part I - General Framework”, Sustainability through Science and Technology (SIPS 2022), Nov 2022, Hilton Phuket Arcadia, Thailand.
Mikalajunas, M. (2022), “The Gradual Abandonment of many types of well known experimental based Physical Models in favor of a more Universal Algebraic Theory: Part II - Specific Examples”, Sustainability through Science and Technology (SIPS 2022), Nov 2022, Hilton Phuket Arcadia, Thailand.
Mikalajunas, M. (2023), “On the use of Multivariate Polynomials and the differential of Multivariate Polynomials as a means of establishing a more Universal Algebraic Theory for solving Differential Equations”, American Mathematical Society Spring Southeastern Sectional Meeting, Georgia Institute of Technology, Atlanta, GA, March 18-19, 2023.
SESSION:
MathematicsTuePM2-R9
| 6th Intl. Symp. on Sustainable Mathematics Applications |
| Tue. 28 Nov. 2023 / Room: Showroom | |
| Session Chairs: Ruggero Maria Santilli; Mike Mikalajunas; Session Monitor: TBA |
16:25: [MathematicsTuePM210] OS
UNIVERSAL ALGEBRAIC THEORY AND UNIFIED THEORY OF ANALYTICAL INTEGRATION - WORKSHOP #1 Mike Mikalajunas1 ;
1CIME, iLe Perrot, Canada;
Paper Id: 487
[Abstract] A solution of the limitation of Calculus in terms of not being able to establish some form of a unified theory of analytical integration was achieved by introducing an entirely new computational algorithm called specialized differential forms or (SDF) that involve the use of Multivariate Polynomials and the differential of Multivariate Polynomials, all defined in a very unique algebraic configuration. Such a unique algorithm would lead to some form of a unified theory of analytical integration that would be driven entirely by computation. This new universal theory in mathematics would be applicable for solving those DEs whose exact solution can only be expressed in terms of the algebraic and elementary functions. Concrete "numerical evidence" of this will be shown on a number of very simple mathematical models involving a first order ODE and a second order PDE. A series of Physical models have been carefully chosen just for demonstrating the applicability of the current unified theory of integration into the Physical Sciences. These will include the PDEs used for describing a very specific case of the Navier-Stokes equations corresponding to an incompressible fluid involving heat transfer and variable viscosity. To fundamentally illustrate the complete versatility of our unique algorithm for solving PDEs, we would be describing a general process for attempting to solve the set of PDEs that govern general linear elastic boundary value problems.
SESSION:
MathematicsTuePM2-R9
| 6th Intl. Symp. on Sustainable Mathematics Applications |
| Tue. 28 Nov. 2023 / Room: Showroom | |
| Session Chairs: Ruggero Maria Santilli; Mike Mikalajunas; Session Monitor: TBA |
16:50: [MathematicsTuePM211] OS
UNIVERSAL ALGEBRAIC THEORY AND UNIFIED THEORY OF ANALYTICAL INTEGRATION - WORKSHOP #2 Mike Mikalajunas1 ;
1CIME, iLe Perrot, Canada;
Paper Id: 488
[Abstract] A solution of the limitation of Calculus in terms of not being able to establish some form of a unified theory of analytical integration was achieved by introducing an entirely new computational algorithm called specialized differential forms or (SDF) that involve the use of Multivariate Polynomials and the differential of Multivariate Polynomials, all defined in a very unique algebraic configuration. Such a unique algorithm would lead to some form of a unified theory of analytical integration that would be driven entirely by computation. This new universal theory in mathematics would be applicable for solving those DEs whose exact solution can only be expressed in terms of the algebraic and elementary functions. Concrete "numerical evidence" of this will be shown on a number of very simple mathematical models involving a first order ODE and a second order PDE. A series of Physical models have been carefully chosen just for demonstrating the applicability of the current unified theory of integration into the Physical Sciences. These will include the PDEs used for describing a very specific case of the Navier-Stokes equations corresponding to an incompressible fluid involving heat transfer and variable viscosity. To fundamentally illustrate the complete versatility of our unique algorithm for solving PDEs, we would be describing a general process for attempting to solve the set of PDEs that govern general linear elastic boundary value problems.
SESSION:
MathematicsTuePM2-R9
| 6th Intl. Symp. on Sustainable Mathematics Applications |
| Tue. 28 Nov. 2023 / Room: Showroom | |
| Session Chairs: Ruggero Maria Santilli; Mike Mikalajunas; Session Monitor: TBA |
17:15: [MathematicsTuePM212] OS
UNIVERSAL ALGEBRAIC THEORY AND UNIFIED THEORY OF ANALYTICAL INTEGRATION - WORKSHOP #3 Mike Mikalajunas1 ;
1CIME, iLe Perrot, Canada;
Paper Id: 489
[Abstract] A solution of the limitation of Calculus in terms of not being able to establish some form of a unified theory of analytical integration was achieved by introducing an entirely new computational algorithm called specialized differential forms or (SDF) that involve the use of Multivariate Polynomials and the differential of Multivariate Polynomials, all defined in a very unique algebraic configuration. Such a unique algorithm would lead to some form of a unified theory of analytical integration that would be driven entirely by computation. This new universal theory in mathematics would be applicable for solving those DEs whose exact solution can only be expressed in terms of the algebraic and elementary functions. Concrete "numerical evidence" of this will be shown on a number of very simple mathematical models involving a first order ODE and a second order PDE. A series of Physical models have been carefully chosen just for demonstrating the applicability of the current unified theory of integration into the Physical Sciences. These will include the PDEs used for describing a very specific case of the Navier-Stokes equations corresponding to an incompressible fluid involving heat transfer and variable viscosity. To fundamentally illustrate the complete versatility of our unique algorithm for solving PDEs, we would be describing a general process for attempting to solve the set of PDEs that govern general linear elastic boundary value problems.
SESSION:
MathematicsTuePM3-R9
| 6th Intl. Symp. on Sustainable Mathematics Applications |
| Tue. 28 Nov. 2023 / Room: Showroom | |
| Session Chairs: Ruggero Maria Santilli; Session Monitor: TBA |
17:55: [MathematicsTuePM313] OS
UNIVERSAL ALGEBRAIC THEORY AND UNIFIED THEORY OF ANALYTICAL INTEGRATION - WORKSHOP #4 Mike Mikalajunas1 ;
1CIME, iLe Perrot, Canada;
Paper Id: 490
[Abstract] A solution of the limitation of Calculus in terms of not being able to establish some form of a unified theory of analytical integration was achieved by introducing an entirely new computational algorithm called specialized differential forms or (SDF) that involve the use of Multivariate Polynomials and the differential of Multivariate Polynomials, all defined in a very unique algebraic configuration. Such a unique algorithm would lead to some form of a unified theory of analytical integration that would be driven entirely by computation. This new universal theory in mathematics would be applicable for solving those DEs whose exact solution can only be expressed in terms of the algebraic and elementary functions. Concrete "numerical evidence" of this will be shown on a number of very simple mathematical models involving a first order ODE and a second order PDE. A series of Physical models have been carefully chosen just for demonstrating the applicability of the current unified theory of integration into the Physical Sciences. These will include the PDEs used for describing a very specific case of the Navier-Stokes equations corresponding to an incompressible fluid involving heat transfer and variable viscosity. To fundamentally illustrate the complete versatility of our unique algorithm for solving PDEs, we would be describing a general process for attempting to solve the set of PDEs that govern general linear elastic boundary value problems.
SESSION:
MathematicsTuePM3-R9
| 6th Intl. Symp. on Sustainable Mathematics Applications |
| Tue. 28 Nov. 2023 / Room: Showroom | |
| Session Chairs: Ruggero Maria Santilli; Session Monitor: TBA |
18:20: [MathematicsTuePM314] OS
UNIVERSAL ALGEBRAIC THEORY AND UNIFIED THEORY OF ANALYTICAL INTEGRATION - WORKSHOP #5 Mike Mikalajunas1 ;
1CIME, iLe Perrot, Canada;
Paper Id: 491
[Abstract] A solution of the limitation of Calculus in terms of not being able to establish some form of a unified theory of analytical integration was achieved by introducing an entirely new computational algorithm called specialized differential forms or (SDF) that involve the use of Multivariate Polynomials and the differential of Multivariate Polynomials, all defined in a very unique algebraic configuration. Such a unique algorithm would lead to some form of a unified theory of analytical integration that would be driven entirely by computation. This new universal theory in mathematics would be applicable for solving those DEs whose exact solution can only be expressed in terms of the algebraic and elementary functions. Concrete "numerical evidence" of this will be shown on a number of very simple mathematical models involving a first order ODE and a second order PDE. A series of Physical models have been carefully chosen just for demonstrating the applicability of the current unified theory of integration into the Physical Sciences. These will include the PDEs used for describing a very specific case of the Navier-Stokes equations corresponding to an incompressible fluid involving heat transfer and variable viscosity. To fundamentally illustrate the complete versatility of our unique algorithm for solving PDEs, we would be describing a general process for attempting to solve the set of PDEs that govern general linear elastic boundary value problems.
19:30 Dinner
