✓ Space-Time

✓ The motion in Space-Time

✓ Fundamental concepts of physic ( Space, Time & Motion)

✓ Galileo’s Principle of Relativity(GPR)

✓ Review of Electrical Field

✓ Review of Magnetic Field

✓ Wave Equation

✓ Electromagnetic wave

✓ Maxwell & Electromagnetic wave

✓ Michelson – Morelli & Ether ,speed of light

✓ Principles of Einstein Relativity theorem

✓ Pythagorean Theorem

✓ Proof that time is not absolute

 Stretched time for the moving observer ✓

✓ Time dilation Factor

✓ Fundamental particles (Neutrinos, Electrons, Quarks)

✓ Compression of distance for the moving observer in addition to time compression

✓ Characteristics of an ideal Theory

✓ Invariant

✓ Facts

✓ Geodesic

✓ Interval

✓ Minkowski of Space-time

✓ Conjecture of Minkowski & Newton

✓ Hyperbolic Space

✓ Space-time concept

✓ Different speeds in Space & constant speed at Space-time

✓ Compression of Time due to motion in Space

✓ Concepts of Mass, Weight, Momentum

✓ Momentum Conservation Law

✓ Mass Conservation Law

✓ Momentum Equation at Space-time

✓ Einstein Equation (relationship between Mass & Energy)

✓ Energy Conservation Law

✓ Momentum’s Vector at Space-time

✓ Displacement 4-vector

✓ Energy Conservation Law

✓ Relationship between Energy & Mass

✓ Proving value of factor (or coefficient)

✓ Calculation of Light mass or photon mass

✓& its relationship with Creation of the world

✓ Principle of Energy Conversion

✓ Bonding Energy

✓ Ground state of Atom

✓ Excited state of Atom

✓ Strong Nuclear Force

✓ Levels of bonding two protons

✓ Fusion process

✓ Fractal Generation at Quantum Foam

✓ Hydrogen gas, the first element at the world

✓ Nuclear energy of Fission

✓ The process of White Dwarf, Black holes, Neutron star

formation

✓ The fate of the world in the future based on the famous equation

(Einstein, beautiful mind, exquisite idea) 

✓ Galileo’s experiment on falling bodies in a vacuum, independent of their mass in equal time

✓ Newton’s definition about Mass & Gravity

✓ Newton’s suggested relation between the Gravity & the Mass

✓ Gravitational Field

✓ Defining Weight

✓ The effect of gravity on the photon

✓ Inertial Mass

✓ Gravitational Mass

✓ Equivalence Principle

✓ The exact performance of Gravitational Force

✓ Curvature of the trajectory in space-time caused by the gravitational field

✓ Effect of energy on Curvature of space-time

✓ Measurement of space-time Curvature with Tensor calculus

✓ Achievements of the theory of relativity

✓ Obstacles of the theory of relativity

✓ Predictions of the theory came true

✓ Relationship between the theory of Relativity and the Quantum theory

✓ The cause of the tide phenomenon in the Earth’s surface waters

✓ The equation of measurement of the curvature of the geodesic

✓ Geodesic

✓ The measurement of the curvature of the geodesic equation

✓ A redefinition of gravity force with the theory of Relativity

✓ The effect of gravity on the photon that comes to Earth

✓ Blue shift

✓ Red shift

✓ Doppler effect about light wave

✓ Gravitational waves

✓ Relationship between the space-time and the fractal

✓ Danaki theory about Mass production

✓ Integration of special relativity theory and Quantum theory & Quantum field production

✓ Planck scale

✓Contradiction of the theory of Relativity with the atom of space

✓ Modified special Relativity

✓ The Fundamental changes in physics over the past 200 years

✓ Edward Lorenz’s Butterfly Effect

✓ Newton’s theory and its formation process

✓ The process of studying human by biology science

✓ Reductionism perspective for study of the world

✓ Calculus and its role in understanding the world

Lecture Two: Introduction to the theory of chaos and Danaki

✓ Three conditions for applicability of Calculus in study of functions

✓ Analytic functions

✓ Applicability range of calculus in study of the nature‘s phenomena

✓ The relationship between the components

✓ Danaki theory

✓ Is it possible to Study the human based on reductionism perspective or not?

✓ The structure of Danaki

✓ Synchronization phenomenon

✓ Fireflies

✓ Creation from chaos

✓ Structures of the Cantor set

✓ Diagram of Koch and self-similarity

✓ Really three-dimensional phenomena in nature!

✓ Fractal structures

✓ The space-time fractalness

✓ Trajectory

✓ Phase space

✓ Periodic motion of the system in phase space

✓ Zero Point of the diagram at analysis system (Attractor)

✓ Limiting Cycle Attractor

✓ Types of Attractor

✓ Initial condition

✓ Determining or prediction of trajectory via Evolutionary equations

✓ Geometric method of studying trajectories

✓ Trajectory’s impact on the universe

Lecture Six: Bifurcation in the phase space

✓ Investigating the causes and reasons for changes of Koch diagram

✓ Bifurcation Phenomenon

✓ stable and unstable Attractor

✓ Studying a system with equation in the phase space for different values of r

✓ Libchaberz experiment

✓ Describing the reality of the universe using simple mathematical equation

✓ Lorenz simple equations to study the atmosphere of Earth

Lecture Seven: Creation

✓ Generalization of Lybchaberz tests

✓ The interpretation of three tests of Lorenz

✓ drawing the diagram of the Lorenz equations

✓Amazing Results of drawing a diagram of the temperature difference between the Earth and the atmosphere in terms of time

✓ how to produce chaotic behavior from a calculable system

✓ Similarity between Robert May diagram and Lorenz diagram

✓ Butterfly strange attractor

✓ Difference between Libchberz and Lorenz works

✓ confirmed results Robert May by testing Malkvs

✓Lorenz’s butterfly effect

✓ The fractal structure generated by chaos in time

✓ Lorenz Attractor about air flow

✓ Rossler Attractor about chemical solutions

✓ Henon Attractor about astronomy and stars

✓ Strange Attractor Galactic

✓ Belousov- Zhabotinsky Reaction test

✓ Control and guidance of the behavior of particles in imaginary world, creation of bifurcation in the real world

✓ The re-emergence of imaginary numbers i

✓ The role of imaginary numbers

✓ The application of imaginary numbers for Understanding the world’s phenomena

✓ Chaotic behavior occurrence in pendulum swing test with three magnets

✓ Review of important theories

✓ The role of i in quantum and relativity

✓ Synchronization and benefits of using it

✓ The importance of real numbers with imaginary numbers

✓ The cause of doubling in Bifurcation

Iterative equations ✓

✓ Review of May’s diagram, space creation

✓ Different modes in fate of phenomena and particles in complex plain

✓ “Julia sets”, various applications, types of “Julia set” and the fate of each of them

✓ Mandelbrot set diagram & comparison with May diagram

✓ The general rule governing all phenomena and events in the world

✓ Creation of different worlds by “Julia sets”

✓ Decoding of doubling in bifurcation phenomenon

✓ Investigating different areas of May’s diagram: predictable zone, bifurcation zone, chaos zone

✓ Resolving the deterministic equation for different values of the control parameter by Feign bum

✓ The global Bifurcation constant

✓ An overview of the most important numbers in mathematics

✓ The role of global fixed number of processes of nature and science

✓ The role of negative numbers in the real world

✓ An overview of the most important and influential theory in the world (Newton’s theory, quantum theory, theory of relativity, the theory of chaos)

✓ Role of C coefficient in occurrence of different “Julia sets”

✓ connection of the coefficient C and DNA molecules

✓ General description of Danaki theory with applicable examples

✓ Harmonics series of Euler numbers

✓ The relationship between the natural numbers and prime numbers based on Euler equation

✓ Riemann zeta function

✓ Zeros of the Riemann zeta function

✓ Scope of application of physical theories compared to the size of the world

Scope of Newtonian physics✓

✓ The history of quantum theory

✓ JJ Thomson Experiment & his atomic model (Cakes with raisins)

✓ Rutherford’s atomic model 

✓ Rutherford’s experiment completed by Geiger and Mars-den

✓ The reason that electron does not  collapse 

✓ The reason that atomic nuclei with more than one proton do not decay

✓ The formation of Quantum theory

✓ Thomas Young’s experiment about the light (The Double Slit Experiment)

✓ Introducing Maxwell’s electromagnetic theory

✓ Ultraviolet catastrophe

✓ Unsolved problems in physics in the early twentieth century

✓ Black body

✓ Microwave background

✓ Solving ultraviolet catastrophe problem by Max Planck

✓ Einstein’s photoelectric effect

✓ Einstein’s masterpiece

✓ Spectrum phenomenon

The quantized angular momentum ✓

✓ Mathematical interpretation of dual nature of light

✓ The Heisenberg uncertainty principle

The electron cloud model of atom ✓

✓ Absorption Spectrum

✓ Standing wave oscillation of electrons around the nucleus

✓ Problems of De Broglie model

✓ Electrons and nuclei formations in different excited state

✓ Redirecting atomic path by energy of ultraviolet lights

✓ Heisenberg’s uncertainty principle on the quantity of energy and time

✓ Schrödinger’s well-known equation

✓ Wave function

✓ Pauli exclusion principle

✓ Fermion’s particles in physics

✓ Entanglement

✓ Quantum foam

✓ Investigating wave function changes according to Schrödinger

✓  Probability of finding electrons around the nucleus

✓ The general rules of quantum theory

✓ Observation creates Reality

✓ Superposition

✓ Distribution of electron cloud and its amplitude around the nucleus of atom

✓ Thomas Young’s Double Slit Experiment analysis by the wave function

✓ The difference between probability and possibility

✓The resulting interference pattern of atomic waves of one million     simultaneous observations

✓ Determining factor in behavior of atom

✓ Mathematical interpretation of wave function in a state of superposition

✓ Review of vector and its properties in Mathematics

The effects distance on the atomic wave interference pattern✓

✓ Reasons of Einstein and Schrödinger’s opposition to the principles of quantum theory

✓ The Einstein’s hidden variables

✓ Copenhagen interpretation

✓ De-coherence

✓ Suspicious connection

✓ Cardano solutions for equation 

✓ The birth of number “i”

✓ Imaginary dimension

✓ Complex numbers and a more complete understanding of the world by them

✓ The results of mathematical operations on imaginary numbers

✓ The probability amplitude of a state is an imaginary number and the probability of a state is a real number

✓ The role of imaginary numbers multiplication in happening of new things in nature

✓ Review of commutative property in vectors summation

✓ Different vectors multiplication & vector multiplication of two complex numbers

✓ The introduction to Quaternion mathematics

✓ Schrödinger’s cat

✓ The difference between Einstein, Schrödinger, Bohr and Heisenberg ideas about quantum principles

✓ Repeating Schrödinger’s cat experiment with the wave function

✓ Einstein Podolsky Rosen paradox (EPR)

Generalization of EPR experiment to the Quantum world✓

✓ Twin photons

✓ A review of the polarization property of light

✓ Quantum Entanglement

✓ The hidden information in Quantum physics

✓ EPR experiments with electron and positron

 ✓ Bell’s inequality

✓ Four tests of “Bell” on assumption of world’s reality and dependency of world’s reality to the observer

✓ Completing studies of “Bell” by “Henry steppe”

✓ Thomas Young’s test and the wave interference pattern

✓ The particle behavior of light in the double-slit experiment

✓ Thomas Young’s experiment in two forms:

A: In isolated box

B: Double-slit

✓ Delayed choice experiment

✓ The way of creating reality through observation

✓ Whole Knowledge or world knowledge

✓ Libet’s experiment on the brain and its results

✓ Equation of a two-dimensional surface in three dimensional space

✓ Vector spaces

✓ Converting important vector spaces

✓ Matrices

✓ Algebraic Geometry

✓ Determinant

✓ Affine Grid Geometry

✓ Base vectors

✓ Commutation

✓ Association

✓ Review of parallelogram properties based on Affine geometry

✓ linearly Independent

✓ Measuring the area in linear algebra based on Affine geometry

✓ Different observers

✓ Convert a vector’s data from one observer to another

✓ Equations related to it

✓ Definition of the Bi-vector

✓ Convert vector information from one observer to another

✓ Two linearly dependent vectors

✓ A solubility investigation of an equation

✓ The product of two matrices

✓ First method (column)

✓ The second method on the coordinate axis (linear)

✓ Third method by matrix method

✓ Hyper-plane

✓ New definition of linear algebra

✓ Zero Matrix and its application

✓ Identity Matrix

✓ The system of equations 

✓ Matrix 2 * 2

✓ Closed systems

✓ Linear transformation

✓ Affine grade definition in the circle

✓ Parameterization methods

✓ One equation, one unknown

✓ Two equations, two unknowns

✓ Multi-equation, several unknowns

✓ Two equations, three unknowns

✓ Two equations, four unknowns

✓ Linear vector space

✓ Study a set of vectors in vector space in the following states:

a: There is a space

b: Subspace

c: column space

d: Null space

✓ Application of column space

✓ Resolvable column space

✓ Rank

✓ Free Column

✓ Ether & Ether wind

✓ Time expansion coefficient

✓ The Michelson–Morley experiment

✓ Lorentz theory

✓ The Lorentz transformations

✓ The artificial time

✓ The fundamental structures

✓ Galileo’s principle of relativity (GPR)

✓ The constant “c”

✓ Galileo transformations

✓ Revision of the definition of basic concepts by Einstein

✓ Einstein’s proposed approach for time sync for two observers

✓ Time sync method for two or more observers based on the Maxwell law

✓ Effects of motion on the concept of simultaneity for different observers (relativity of simultaneity for different observers)

✓ References Frame

✓ The principle of the constancy of the laws of physics to all observers

✓ Einstein transformation equations based on the gamma factor γ and comparison with the Lorentz transformation equations

✓ The third method of obtaining the Lorentz transformation equations

✓ Transforming the coordinates of each observer to coordinates of other observer to get the same results

✓ Inertial Reference Frame

✓ The laws of physics are the same for all Inertial Frames

✓ Euler Number

✓ Exponential functions

✓ Euler Series & Euler function

✓ Hyperbolic Geometry

✓ Application of the Lorentz transformation equations

✓ Studying the Lorentz transformation equations about space, time and space-time

✓ Identicalization of units for all observers

 Principle of Least Action ✓

✓ Calculus of Variations

✓ Boundary-value Problem

✓ Time becomes slow for a moving person

✓ Time stops for an object moving at the speed of light

✓ Length of an object becomes shorter along its path

✓ Relativity of motion for different observers

✓ The twin paradox

✓ Orthogonality

✓ Space-time

✓ Proper-time

✓ The ranges in which motion of light is defined by its velocity

✓ Position 4-vector at Space-time

✓ Invariant quantity

✓ Velocity 4-vector

✓ Scaler quantity

✓ Momentum 4-vector

✓ Binomial Expansion

✓ 4-vector Characteristics

✓ Photon examination in terms of energy and momentum

✓ Obtaining Equation of Photon Energy Using 4-vector

✓ Inner product of 4-vector

✓ Signature of matrix

✓ Co-variant and contra-variant vectors

✓ Dynamic History

✓ Geometric method

✓ Dynamic System, oscillator & Non-linear equations

✓ Differential Equations and its Applications &difference with Difference equations

✓ The geometric method of Poincare

✓ The fixed point and its types

✓ discrete time equation

✓ Controllers

✓ Gradient of the curve of the system in different parts

✓ The definition of Bifurcation

✓ Equations of empirical relation

✓ The role of the control parameter in bifurcation

✓ Creational equations and its types

✓ Trans-critical bifurcation and its types

✓ Pitchfork bifurcation (third type)

✓ Super-critical pitchfork bifurcation and Sub-critical pitchfork bifurcation

✓ Investigating Effect of the control parameter in this type of situation bifurcation and state of the fixed points

✓ Drawing a diagram of and assessing its interesting results 

✓ The Hysteresis property

✓ Study of simple solid-state laser

✓ Hawken mathematical model for solid-state laser

✓ Laser Communications and bifurcation

✓ Co-phase moment

✓ Circular vector field

✓ Critical point

✓ The linear velocity, angular velocity

✓ Uniform oscillator system

✓ The phase difference

✓ Two-dimensional systems of linear equations in phase space

✓ Fixed Point properties in two-dimensional systems

✓ Saddle point

✓ Manifold, types & applications

✓ simple harmonic oscillator and solving equation via Poincare method

✓ Simple harmonic oscillator specifications and assessing direction of its manifold

✓ The impact of Ƭ and Δ changes in the type of fixed points of

✓ Linearization of non-linear equations

✓ Exceptions of  linearization

✓ Null cline

✓ Separator line

✓ Gravity domain

✓ competition model of Lokta- Volterra

✓ The study of energy changes in non-linear systems

✓ Jacobian matrix

✓ Homo-clinic trajectory

✓ Hetero-clinic trajectory

✓ Conservative systems

✓ Reversible systems

✓ Limit cycle, properties and types

✓ Limit cycle systems in biology and the human body

✓ The role of cycle control parameter (μ) of limit cycle

✓ Super-critical Hopf Bifurcation

✓ Sub-critical Hopf Bifurcation

✓ Vander-pol equation

✓ Relaxation oscillation

✓ Quantitative non-linear systems

✓ Duffing oscillator

✓ Phase space, state space, complex vector space

✓ Complex conjugate and its application

✓ Dual vector

✓ Introduction to Dirac notation

✓ Set theory

✓The concept of multi-dimensional vectors in complex space

✓ The concepts of probability amplitude and the probability of a state in the Quantum system

✓ The concepts of probability amplitude and the possibility of a state in the Quantum system

✓ Study of dimensions in the complex vector space, introduction of the unit vectors and unit vector based method of extending a vector

✓ Normalizing a vector

✓ Orthogonality of two vectors and its difference with perpendicularity of two vectors in linear algebra

✓ Orthonormal vectors and how to extend a “ket” based on its Orthonormal vectors

✓ Introduction to Quantum bit and its difference from classic bit

✓Review on the inner product of vectors, orthogonality and normalized length of each vector and the orthonormality concept

✓ The relationship between the electron spin and emitting photons and explaining this phenomenon by Quantum bit and linear superposition of states

✓ Relationship between Quantum physics and Chaos theory with purpose to incorporate these theories

✓ Symmetric matrix

✓ Hermitian matrix

✓ Expected value/ Average value

✓  Eigen values/ Eigen vectors

✓ Postulates of quantum mechanics

✓ Operator of Energy, Momentum & Position

✓ Spin operator and its characteristics

✓ The human brain and its relationship with electrons

✓ The projection operator and its characteristics

✓ Quantum Zeno Effect

✓ Justification of light’s polarization effect using projection operator and Zino quantum effect

✓ The position operator and its characteristics

✓ Mathematics of wave function and its collapse because of observation

✓ The Dirac’s delta function and its acts on the wave function

✓ completion of the delta – function and observation

✓ Unitary matrix and its difference with projection matrices and its applications

✓ presentation of a matrix operator and change of the base vectors

✓ The Similarity and the unitary matrices

✓Study of relationship between rotational matrix, unitary transformation and baseline change.

✓Study of the relationship between the uncertainty principle and commutativity property in operators

✓ Study of the relationship between statistics and the uncertainty principle and the concept of the mean value or expected value

✓ Differential operator and its relationship with the momentum operator

✓ The importance of i to achieve quantum operator

✓ Comparing the Eigen States of the momentum and position Operators – in relation to commutativity property

✓ De Broglie’s theory and the relation of momentum with matter waves

✓ The mathematical proof of Heisenberg’s uncertainty principle

✓Quantization of linear and angular momentum and its mathematical proof

✓ Completion of the discussion of the wave function

✓ A review of the study of the nature of light

✓ Birth of the photon

✓ Relationships of the “De Broglie”

✓ Schrödinger’s masterpiece

✓ Changes of time- evolution

✓ Where is the particle?

✓ Mathematical tools of Fourier transformations

✓ Interference pattern

✓ Double-slit experiment

✓ Calculating the Schrödinger equation based on the equation of nature

✓ The integration process of the theory of Relativity and Quantum theory

✓ Tayler series

✓ The MacLaurn series

✓ General definition of applied mathematics or Calculus of variation

✓ Difference between functional and function

✓ The history of mathematics Lagrangian

✓ Where does the famous equation “F = ma” come from?

✓ The equation and the principle of the least action

✓ Euler-Lagrange equation (the equation of nature)

✓ Conservative and non-conservative forces

✓ Gaining the equation “F = ma” according to the definition Lagrange provided

✓ Obtain the Euler-Lagrange equation through the Calculus of variation

✓ Applications of the Euler-Lagrange equation

✓ Equilibrium

✓ Configuration

✓ Use of the term “Extremum” in the “least” law of nature

✓ Principle of least action

✓ Principle of Fermet

✓ Maupertuis equation and its relation to the Euler equation

✓ What are the features of the system describing the principle of the least action?

✓ This law, why is there in the warp and woof of nature and space-time, where has come from, why does nature insist on dictating this law to all beings?

✓ Proof of the Euler-Lagrange equation in mathematical language

✓ Steps in the formation of a theory in physics

✓ The dis-advantage of physics theory (a flaw in the theory of physics)

✓ The ability and weakness of the Lagrangian

✓ Comparison of Lagrangian Formalism with Newtonian Formalism (Lagrange mechanics and Newtonian mechanics)

✓ Generalized coordinates

✓ Constraints

✓ A review of two facts in nature to obtain the Lagrangian equation

✓ Obtaining the Lagrangian equation for free fall and comparing it with the equation obtained by the Newtonian physics method

✓ Obtaining the Lagrangian equation for the pendulum and comparing it with the equation obtained by the Newtonian physics method

✓ Obtaining the Lagrangian equation for moving the object on a spherical surface and comparing it with the equation obtained by the Newtonian physics method

✓ General Momentum

✓ Obtaining the Lagrangian equation for moving an object on the ramp and comparing it with the equation obtained by the Newtonian physics method

✓ Holonomic system

✓ Study the configurations of a system

✓ The equation of motion of systems with 2-body problem

✓ Examining the reel with two weights and its Lagrangian equation

✓ Important factors that should be taken into account in the Lagrangian equation of 2-body problem

✓ Lagrange equation for compound pendulum

✓ Lagrange Multipliers

✓ Euler-Lagrange equation for conservative systems and non-conservative systems and friction systems

✓ Proof of the Lagrangian equations by mathematical method so far obtained using physical arguments.

✓ The reason for using g_(x) = 0 in the equation

✓ Obtaining the Euler-Lagrange equation based on the Principle of least action

✓ Symmetry

✓ Continuous symmetry

✓ Discrete symmetry

✓ Rotational symmetry

✓ Transnational symmetry

✓ Time Symmetry or temporal symmetry

✓ Active symmetry and passive symmetry

✓ Relationship of Lagrange with the Law of conservation

✓ The Nöether Theorem

✓ Continuous transnational symmetry

✓ Hamilton is the total energy of the system (in mathematical language)

✓ Equations of variations of coordination’s in two Transitional and Rotational states

Lecture Six: Relativity & Quantum

✓ Generator of linear s symmetry

✓  Conservation of Linear momentum’s law

✓ Conservation of Angular momentum’s law

✓ Conservation of Energy and time momentum’s law

✓ Constant of motion (COM)

✓ Definition of Lagrangian in the Cartesian Space

✓ Application of Lagrangian Formalism in proof the shortest path between two points

✓ Relationship of Lagrangian Formalism and relativity theory and obtaining equations of relativity theory using Lagrangian Formalism

✓ Obtain Einstein equation E = mc² by using Lagrangian Formalism

✓ Relationship between Lagrangian Formalism and Quantum theory and obtaining Quantum theory equations using Lagrangian Formalism

Lecture Seven: Hamiltonian Formalism

Hamiltonian Dynamical system

✓ An overview of Hamilton’s biography

✓ Hamiltonian Formalism

✓ Gradient system and its equations

✓ Symplectic gradient system

✓ Symplectic geometry

✓ Generator time evolution

✓ Constant of Motion (COM)

Lecture Eight: Hamiltonian Formalism 

Poisson Bracket 

✓ Dynamic variables

✓ Phase space flow

✓ Definitions and Reasons for Studying phase Space

✓ Difference between Quantum physics, Lagrangian Formalism and Hamiltonian Formalism in obtaining motion equations

✓ Hamilton’s connection H (q, p) with Lagrangian

✓ Acquire Hamiltonian “H” through Lagrangian “L” in mathematical language

✓ Proof that the Hamiltonian is a constant of motion or not?

✓Dependent  and Independent systems

✓ From Lagrangian Formalism to  symmetry’s system

✓ proof of the constant of motion of quantities other than Hamiltonian in the system

✓ Poisson bracket and its concept in mathematical language

✓ “Lie’s Algebra” and its role in the relationship between real world events and the events of the Quantum world

✓ Physical Concept of “Lie’s Algebra” Equation for Poisson bracket Operators

✓ Canonical Poisson Bracket

Lecture Nine: Hamiltonian Formalism

Liouville ˊs Theorem

✓ Some examples of obtaining equations of motion of the system using Hamiltonian Formalism

a: Pendulum equation, conservative system regardless of friction

b: Equations of system motion with multiple members and ‘n” degrees of freedom in the magnetic field

✓ Liouvilleˊs Theorem

✓ Are the flow lines compressible in the phase-space? What happens in both cases of compression or not?

Lecture Ten: Hamiltonian Formalism

Canonical Transformation

✓ An overview of the concepts of linear algebra

a: Matrix determinant

b: coordinate transformation

c: Jacobi Matrix

✓ Canonical transformation

✓ Time Evolution and its relation with canonical transformation and Hamiltonian system

✓ Application of Hamiltonian transformation

✓ A study of the Hamiltonian motion of a Hamiltonian system in a phase space with a degree of freedom

✓ Extended of the phase space

✓ A method of obtaining constant of motion for the studied systems

✓ Jacobi Identity

✓ Providing a method for systems that for any reason cannot solve the equations of motion of the system:

a: Hamiltonian system in a two-dimensional phase space with a degree of freedom

b: Hamiltonian system in a multidimensional phase space with “n” or “2n” degrees of freedom

c: System`s specific mode

Lecture Twelve: Hamiltonian Formalism

Periodicity & chaos

✓ Energy Surface, constant of motion of space, constant of motion of Surface

✓ Conditions that make it possible to integrate the system equations

✓ Solvable system

✓ Conditions that make a system solvable

✓ N-Torus

✓ Assessing the Solubility of a System with a 1-Torus degree of freedom

✓ Assessing the Solubility of a System with a 2-Torus degree of freedom

✓ Periodic behavior and quasi-periodic behavior of the system

✓ Assessing the Solubility of a System with a 3-Torus degree of freedom

✓ Study of completely chaotic systems

✓ Review of one-dimensional and two-dimensional harmonic oscillator in Hamiltonian system with a focus on being integrable or non-integrable

✓ Investigating the solubility of one-dimensional harmonic oscillator

✓ A spiral diagram, stable spiral and unstable spiral

✓ Investigating the solubility of two-dimensional harmonic oscillator

✓ Quasi-periodic behavior

✓ Lissajous figures Diagram

Lecture Thirteen: Hamiltonian Formalism

Quantum chaos/ Riemann Zeta Function

✓ Study of integrablity a system with one particle and one degree of freedom in a two-dimensional space

✓ Study of integrablity a system with two particles and two degrees of freedom in a two-dimensional space

✓ Study of integrablity a system with three degrees of freedom, single body

✓ Study of integrablity a 2-body system in a three-dimensional space

✓ Study of integrablity a 3-body system in a three-dimensional space

✓ Study of integrablity a 1-body system in a square two-dimensional space

✓ Study of integrablity a 1-body system in a circular double-dimensional space

✓ Study of integrablity a 1-body system in an ellipse enclosed two-dimensional space

✓ Study of integrablity a 1-body system in a polygonal enclosed two-dimensional space (with curvature in one of the sides)

✓ Introducing systems with specific boundaries known as “Bounimovich Stadiums” and their physically and mathematically integrable.

Lecture Fourteen: Hamiltonian Formalism

Symplectic Group/ Standard model

✓ Symplectic geometry and its relation with Hamiltonian Flow

✓ The Relationship of the symplectic transformation with Canonical transformation

✓ The equations obtained from the condition of the determinants of the Jacobian matrix = 1

✓ Orthogonal matrix and its features

✓ Identity Matrix

✓ Pauli Matrix

✓ Definition of group theory and its features

✓ Lie Group

✓ Abelian group

✓ Orthogonal matrix group

✓ Isotropic Harmonic oscillator

✓ Dynamical Symmetry Group

✓ Special unitary group

✓ Generating matrices all special unitary (z) matrices

✓ How to calculate the number of generators of a system

✓ Types of Quarks in nature and their transformations into each other

✓ Feynman Diagram

✓ The role of weak and strong nuclear forces on quarks

✓ Standard Model

✓ Bugs entered on the standard model

Lecture Fifteen: Hamiltonian Formalism

Semi- classical Quantization

✓ The study of the relationship between classical and semi-classical physics

✓ phase space

✓ The old Quantum theory

✓ Examination of oscillator systems

✓ Review of one-dimensional nonlinear oscillator:

a: In terms of energy

b: In terms of system period

✓ Two influential H (H Hamiltonian, ħ Planck’s constant coefficient)

Lecture Sixteen: Hamiltonian Formalism

Quantum vs classical

✓ “Louis De Broglie ” and New Quantum Theory

✓ The study of dynamical systems in Hamiltonian classical physics and Hamiltonian Quantum physics

✓ Describing the state system with a degree of freedom at any moment

✓ Comparison of these two physics in terms of:

a: State of system

b: Study space

c: The type of numbers

d: Trajectory

e: The relationship between” p & q” pairs

f: Trajectory equation

h: Volume preserving

Lecture Twelve: Hamiltonian Formalism

Periodicity & chaos

✓ Energy Surface, constant of motion of space, constant of motion of Surface

✓ Conditions that make it possible to integrate the system equations

✓ Solvable system

✓ Conditions that make a system solvable

✓ N-Torus

✓ Assessing the Solubility of a System with a 1-Torus degree of freedom

✓ Assessing the Solubility of a System with a 2-Torus degree of freedom

✓ Periodic behavior and quasi-periodic behavior of the system

✓ Assessing the Solubility of a System with a 3-Torus degree of freedom

✓ Study of completely chaotic systems

✓ Review of one-dimensional and two-dimensional harmonic oscillator in Hamiltonian system with a focus on being integrable or non-integrable

✓ Investigating the solubility of one-dimensional harmonic oscillator

✓ A spiral diagram, stable spiral and unstable spiral

✓ Investigating the solubility of two-dimensional harmonic oscillator

✓ Quasi-periodic behavior

✓ Lissajous figures Diagram

Lecture Thirteen: Hamiltonian Formalism

Quantum chaos/ Riemann Zeta Function

✓ Study of integrablity of a system with one particle and one degree of freedom in a two-dimensional space

✓ Study of integrablity of a system with two particles and two degrees of freedom in a two-dimensional space

✓ Study of integrablity of a system with three degrees of freedom, single body

✓ Study of integrablity a 2-body system in a three-dimensional space

✓ Study of integrablity a 3-body system in a three-dimensional space

✓ Study of integrablity a 1-body system in a square two-dimensional space

✓ Study of integrablity a 1-body system in a circular two-dimensional space

✓ Study of integrablity a 1-body system in an ellipse enclosed two-dimensional space

✓ Study of integrablity a 1-body system in a polygonal enclosed two-dimensional space (with curvature in one of the sides)

✓ Introducing systems with specific boundaries known as “Bounimovich Stadiums” and their physically and mathematically integrability assessment.

✓ Introduction to the Model Danaki

✓ Nonlinear oscillator behavior

✓ The role of separatrix in the dynamics of nonlinear systems

✓ Zero Point energy and formation of fundamental particles

✓ Stem Cells and Specialized cells

✓ Relationship of quantum field with stem cells biology

 ✓ Review of the dynamics of linear and nonlinear systems in the vector field

✓ Fixed Points and equilibrium points and their types

✓ Introducing a criterion for determining the type of fixed points based on the matrix (operator) derivative

✓ Fixed points and Orbits

✓ Limit cycles

✓ The theory of the index

✓ Engineering of Stem Cells

✓ Creation of living creatures from atoms

✓ A step in the direction of low-temperature Nuclear fission

✓ Control of the Phase space topology

✓ Changing the number and quality of phase space elements

✓ Imaginary dimension of phase space

✓ Bifurcation in one and multi-dimensional space

✓ Hysteresis phenomenon in phase space

✓ Birth and death of the limit cycles

✓ Hoff Bifurcations

✓ Infinite period Bifurcations

✓ Homo-clinic bifurcation

✓ Saddle-Node bifurcation of limit cycles

Lecture Nine: Bifurcation in Nature & Technology

Danaki Biology:Where have we come from?

✓ Start of the growth process from the initial zygote

✓ Gene expression and protein synthesis

✓ The role of the bifurcation in the gene expression

✓ Gene control and its relation with imaginary dimension of phase space

✓ The role of imaginary dimension in the production of specialized cells from stem cells

✓ The governing law (equation) of the zygote growth

✓ The Genetic code and Zero of the L-Functions and its Relationship with the Riemann Zeta Function

✓ How to determine the L-function of a cell

✓ Introduction of Danaki Medicine: The first step

✓ Danaki biology-the formation of organs from stem cells

✓ Regular structures in nature

✓ Turing pattern and morphogenesis

✓ Turing instability and Bios

✓ Oscillation and periodic behavior in biochemistry

✓ Belousv- Zhabothsky (BZ) reactions

✓ Non-equilibrium thermodynamics

✓ Hof bifurcation in Biochemistry

✓ Simultaneous creation of the Hof and Turing bifurcation

✓ Cell birth with periodic behavior from stem cells

✓ A new step in biochemistry and stem cells

✓ An overview of 14 sessions presented in Quantum theory –1

✓ Complex vector space

✓ Hilbert space

✓ Complex conjugate numbers

✓ Continuous system and discrete system

✓ Affine geometry

✓ Projective geometry

✓ Hyperbolic Geometry

✓ Rotational hyperbolic geometry

✓ Algebra, rotational Algebra, rational algebra

✓ Orthagonality

✓ Dirac notation

✓ Completing testing

✓ The postulates of Quantum systems

✓ wave function Collapse

✓ Quantum Zino Effect

✓ Schrödinger equation and its properties

✓ Application of the Schrödinger equation on the energy of a Quantum system

✓ Eigenvalues of Hamiltonian system

✓ Investigating the Time Evolution of a system in two states

✓ Wave function changes in time

✓ mathematical Characteristics of the wave function

✓ Remembering different types of operators

✓ Time Dependent Schrödinger’s Equation (TDSC)

✓ Time Independent Schrödinger’s Equation (TISC)

✓ Proof of the Time Dependent Schrödinger’s Equation in two states of “Free particle” and “Bounded particle” in vacuum space

✓ Solving Time-dependent Schrödinger’s Equation or general Schrödinger’s Equation (Quantum Dynamics)

✓ Eigen-Function and Eigen-Vector

✓ The Dynamic Quantum systems application

✓ Strum-Lioville Equation

✓ Infinite potential well

✓ Time Evolution with more details

✓ – Hamiltonian in more detail

✓ Relationship between Hilbert space or complex vector space with phase space in classical physics

✓ Time Evolution of a Quantum system in different states

✓ General steps of studying the of Time Evolution process of a system

✓ Justifying the Double-slit tests with a new perspective

✓ Time Evolution of wave packet

✓ The role of the Hamiltonian operator in studying the dynamical systems in classical physics

✓ The role of potential functions in the study of dynamical systems in phase space and Hilbert space

✓ The role of potential functions in solving Schrödinger equations and understanding Quantum systems

✓ Study of potential energy changes in space V (x) in the following conditions:

(E = Eigen Function)

a: V> E

b: V <E

c: V = E

(Examining different values of V(x ✓

a: Free particle

(b: Infinite potential well(hard

c: Potential Well (Soft)

✓ Checking the slope of the curve in V> E mode

✓ Drawing a diagram of the equation Z² + Y² = R² in the following modes:

a: Very small R

b: Very large R

c: Exception mode, energy in a certain size

d: Infinite limit of the potential wellhead depth → Y towards infinity

e: Large L size L → ∞

Example: well with low width and high depth so that the area of the well does not change

Density of probabilities ✓

Conservation of probability density ✓

The mass conservation equation in fluid mechanics ✓

✓ Investigating the motion equation of a particle, which initially has V = 0, then goes to a point at the level V> 0. In two modes:

a: Particle energy less than energy level V = a

b: The energy of the particle is greater than the energy level V = a

Special potential functions ✓

✓ Five types of potential function:

a: step function

a-1: E> V

a-2: E <V

b: The energy level is higher than V₀ → in both modes E> V

c: Potential well with specified depth → E> V

d: Potential Well Depth → ∞ Width → 0

e: Potential ∆- function

✓ Overview of two types of nuclear energy (nuclear fusion, nuclear fission)

✓ Connection between the mutation, the bifurcation and the Quantum tunneling

✓ The Heisenberg uncertainty principle in classical physics and Quantum physics

✓ Description of periodic phenomena based on classical physics

✓ Investigating the transmission coefficient for a particle that there is an obstacle on its path

 Application of two types of nuclear energy to produce fuel ✓

✓ Comparison of nuclear fusion function and nuclear fission functions

✓ The concept of harmonic motion or harmonic oscillator

✓ Harmonic oscillator equation

✓ Calculation of total energy of the classical harmonic oscillator (kinetic and potential energy)

✓ Is the pendulum motion a harmonic oscillator?

✓ The least amount of Quantum energy (zero-point energy)

✓ The distances of the Quantum energy levels and their differences with the classical world

✓ Schrödinger equation associated with oscillating motion in the Quantum world

✓ Deep Concept of Energy

✓ Hamiltonian general equation for Quantum harmonic oscillator

✓ Lowering operator

✓ Quantum vacuum

✓ Operator method

✓ Classical angular momentum

✓ Quantum angular momentum

✓ Comparison of Quantum Angular Momentum and Classical angular momentum

✓ Unitary operator

✓ Generator types

✓ Symmetry types

✓ Intrinsic angular momentum

✓ An overview of some important equation

✓ Raising operator and lowering operator

✓ Spin

✓ Types of angular momentum:

a: Spin angular momentum

b: Orbital angular momentum

✓ Elementary particle (Boson & Fermion)

✓ Möbius strip

✓ Stren- Gerlach experiment

✓ Magnetic Moment

✓ Magnetic Dipole

✓ Non-uniform Magnetic field

✓ Pauli matrices

✓ Obtaining Eigenvalues of  Ĺ_x & Ĺ_y

✓ Spinor

✓ An overview of the process of studying Quantum systems in a one-dimensional space

✓ Difference in the process of studying Quantum systems in three-dimensional space

✓ The Quantum system in Cartesian coordinates

✓ Quantum system in two-dimensional space

✓ Quantum system in three dimensional space

✓ Harmonic oscillator in three dimensional space

✓ Review of changes due to the presence of electrical charge in vacuum space

✓ Force or field around the electrical charge in the form of accelerated motion

✓ Centripetal acceleration

✓ Columbi Force

✓ Central potential function

✓ Spectrometer of hydrogen

✓ Einstein photoelectric phenomenon and its explanation with spectrometer

✓ Laplacian transformation from Cartesian coordinates to spherical coordinates and vice versa

✓ Standard Hamiltonian Equation

✓ Drawing the potential function of the hydrogen atom

✓ The concept of moving in the Quantum world

✓ Degeneracy

✓ Reducing the mass

✓ Introduction

✓ Review of the last two sessions of the theory of special relativity

✓ Biography Einstein

✓ Klein & Einstein Group Competition

✓ Human fundamental discoveries since creation

✓ General interpretation of General Theory of Relativity

✓ Quantum gravity

✓ Newtonian gravity

✓ Poisson equation

✓ Gravitational field and its comparison with Einstein field Equation

✓ Introducing the geodesic

✓ The height and speed of the satellites

✓ Compression of distance for the moving observer in addition to time compression

✓ Characteristics of an ideal Theory

✓ Invariant

✓ Facts

✓ Geodesic

✓ Interval

✓ Minkowski of Space-time

✓ Conjecture of Minkowski & Newton

✓ Hyperbolic Space

✓ Coordinates of free fall in the gravitational field and coordinates of inertia of special relativity

✓ Obtaining the geodesic equation of free fall with the help of coordinate transformation

✓ Review of the Pythagorean Theorem, rejection of different coordinates

✓ Generalization of Pythagorean theorem, from Euclidean geometry to Riemann geometry

✓ Define the surface metrics and examine their significance

✓ Introducing Christopher’s Symbol as a Coordinate Interface

✓ Flat surface metric (no curvature) in Cartesian, Polar, Cylindrical and Spherical coordinates

✓ Conversion of metrics

✓ Tidal force in no-uniform gravity

✓ The relationship between tidal force and the possibility of removing gravity in free fall

✓ Curved surface metric

✓ Manifold introduction, Riemannian manifold and Riemannian geometry

✓ The connection of the curved surface with the possibility of converting its metric into a flat surface metric

✓ Relationship between tidal force and surface curvature

Lecture Six: Mathematical language of General relativity (1)

A extrinsic and intrinsic geometric

✓ Riemannian surfaces, Riemannian geometry, manifolds

✓ Contra-variant axes and vectors and their relationship with the metric

✓ Converting the contra-variant to the co-variant and vice versa

✓ The vector length and the distance between two points in terms of the Contra-variant and Co-variant components

✓ Introduction of Differential Geometry

✓ Physical concept of tensor and ideal physical theory

Tensor 

✓ Definition of tensor and its application

✓ Coordinates Transformation

✓ Jacobian matrix and its role in transforming the observers

✓ Defining the co-variant base vectors

✓ Defining the metric of the manifold co-variant in terms of the corresponding base vectors

✓ The relationship between metric and co-variant and contra-variant

✓ The relationship between the contra-variant and the co-variant base vectors

✓ Tensor of covariant vectors components

✓ Tensors of rank 2 and higher and their conversion between two observers

✓ Operations on tensors

✓ Decreasing tensor’s rank

Christoffel Symbol

✓ Basic co-variant and contra-variant vectors as tensor

✓ Metric as tensor

✓ Christoffel Symbol, a symbol of Change of co-variant Vectors on Manifold

✓ The role of Christoffel Symbol in geodesics

✓ The derivation of tensors and its problems

Co-variant derivative 

✓ Continuation of the Christoffel Symbol

✓ The physical meaning of Christoffel Symbol

✓ Tensor derivative

✓ Co-variant Derivative

✓ co-variant Derivative of base vectors and metric

✓ Equation of motion in terms of co-variant derivative

✓ Geodesic equation in terms of co-variant derivative

 Riemann Curvature Tensor  

✓ Parallel transformation

✓ Geodesic as a parallel transformation of velocity vector

✓ Riemannian manifold curvature and parallel transformation

✓ Commutation of Co-variant Derivatives

✓ Riemann tensor and parallel transformation

✓ Riemann tensor and commutation of co-variant derivatives

 Tidal Force & Riemann tensor 

✓ Tidal Force and Geodesic Deviation in Newtonian Physics

✓ Tidal Force and Geodesic in differential geometry

✓ The relationship of the Tidal force (physics) with the manifold curvature (space-time geometry)

✓ Jacobian vector field

✓ Geodesic deviation equation

✓ Tidal Force Equation and Riemann Tensor

Ricci Tensor & Scalar

✓ Riemann tensor properties

✓ Degrees of freedom of Riemann tensor

✓ Bianchi relation

✓ Riemann normal coordinates (RNC)

✓ Ricci Tensor (Unique)

✓ Ricci Scalar

Einstein Field Equations

✓ Pseudo-Riemannian geometry

✓ Minkowski metric and Pseudo-Minkowski metric

✓ From Newton’s Theory to Special Relativity & General Relativity

✓ Co-variant derivative of Ricci tensor

✓ Conservation laws of Ricci Tensor

✓ Weak gravitational field and slow velocity movement

✓ Einstein Field equations in the vacuum

✓ Einstein tensor, its co-variant derivative and conservation laws

✓ Einstein Field Equations for a curved Spacetime

✓ Time curvature in weak gravitational field

✓ The physical cause of the non-linearity of Einstein’s field equations

✓ Gravitational field

✓ Another form of Einstein equations

✓ Cosmological constant entry and static universe

✓ Einstein’s main mistake in removing the cosmological constant of equations in 1929

✓ Dark energy and its possible source

✓ Einstein space

✓ De sitter Space

✓ An Introduction to solutions of Einstein Equations

✓ The non-linearity of Einstein’s equations and the possible role of chaos

✓ The principle of Plenitude

✓ Mathematical visualization and its realization to realization, especially in abstract algebra

✓ An overview of the Origin of Numbers and their applications in physics theory

✓ Cayley Algebra and the role of Al-Khazini in its formation

✓ The symmetry and symmetry breaking in Cayley algebra

✓ The first step in introducing of Group theory

✓ Symmetry

✓ The symmetry in art

✓ The symmetry from the Greek era to Kepler and Tycho-Brahe

✓ Abstract symmetry

✓ Permutation Formula

✓ The symmetry in the permutation process

✓ Triangle symmetries

✓ Relationship of triangle symmetries and Permutation of three items

✓  The mathematical definition of Group 

✓ Symmetry in nature and physics

✓ Symmetry in physics equations

✓ Symmetry in cell growth and in stem cells

✓  Definition of a Polynomial and its role in complex systems

✓ Polynomial roots and their relation to fixed points in complex space

✓ Roles of Babylonian civilization, Brahmaghita, Diaphanthos, Kharazmi, Khayyam, Tartaglia and Cardano in emergence of Group theory

✓ Permutation of Polynominal roots and the information that comes from the structure of the equations

✓Vita s FormulaS  and Girard, rules summing the powers of the roots of any equation

✓ Lagrange and permutation of the roots

✓ The roots of 5th degree polynomials (Quinties) and above

✓ Lagrange’s method for solving these polynomials

✓ French  mathematician, Galois, and Staring Group Theory

✓ Homomorphism, Isomorphism and Automorphism

✓ Group definition and algebraic structures

✓ Algebraic structure of the Field

✓ Important algebraic fields

✓  Field Extension

✓ Field Automorphism, Automorphism group of a field, Galois group

✓ The group and its subgroups

✓ Group lattice

✓ The group, living beings and other creatures

✓ Application of group theory cell division and its emergence process

✓ Cell division and emergence

✓ Cyclic group

✓ Group Generator

✓ Cyclic subgroups generator

✓ Lagrange Theorem for subgroups

✓ Relationship between cyclic and Abelian groups

✓ Definition of Klein Group

✓ Mathematical description of the emergence process

✓ How do the world and creatures emerge?

✓ Mathematics of emergence and genesis of every being

✓ Biology of emergence

✓ Studying stem cells and describing how they are formed and how do they differentiate  into specialized cells

✓ Mathematical explanation of cell division and cell differentiation

✓ Studying particle physics in the framework of the emergence model

✓ How mathematics of emergence can describe compound particles such as atoms and molecules

✓ Continuation of physics and biology of emergence

✓ Interaction of creatures with the environment

✓ Gene expression and protein synthesis affected by the interaction of the organism and its environment

✓ Normal subgroup

✓ Right and left co-sets side of subgroup

✓ Quotient group

✓ The role of subgroup interaction with the environment in Galois theory

✓ Brain and how to do develop new brain abilities

Lecture Zero: Emerging Universe

Introduction

✓ An introduction to the science of emergence

✓ Different branches of emergence science (mathematics, physics, biology, and philosophy of emergence)

✓ Goals of the academy

✓ Introducing  important theories their strengths and weaknesses and their relationships to each other

✓ Investigating why sciences, including biology, physics, medicine, and others have not remarkably progressed in recent decades.

✓ Theory of general relativity based on the Danaki model

✓ Danaki structure and Quantum Theory

✓ Relationship between components

✓ Description of physical reality by complex numbers

✓Absence of  “imaginary number (i)” in various branches of science

✓ The unity of universe Law that governs all phenomena and their process of growth (the unity of law of emergent universe)

Lecture One: Foundations of Mathematics- revisit

Axiomatic systems

✓ What is mathematics?

✓ How are mathematics and physics related?

✓ Pure mathematics & Applied mathematics

✓ The importance and position of human brain in a various studies

✓ Yoga and music

✓ Ramanujan

✓ Is the universe discrete or continuous?

✓ A tool for understanding time

✓ Formal Systems

✓ Algebra

✓ The Riemann zeta function

✓ 1+1=1 !!!

✓ Mirror symmetry and the perfect tool for studying it

✓An introduction to emergence Mathematics; Foundation and Frameworks

✓ Introducing three groups of organisms at the beginning of the genesis and exploring the cause of survival or extinction of each group

✓ Two mathematical models

✓ Five postulates of Euclidean geometry and their relationship to formal systems

✓ The seed of the universe

✓ Definition “Thing” as Vector Space

✓ Complex vector space

✓ The history of the Zero number

✓ Multiplication of two vectors

✓ Clifford Algebra feature

✓ Relationship between pure mathematics and physics

✓ Algebraic Geometry and Clifford Algebra

✓ Study Tools for micro-universe and the macro universe

✓ Seeking the right tool for studying the world seamlessly

✓ Root “uv”

✓ Differences in the nature of “uv” in pure mathematics and physics

✓ The relationship between”UV” & “VU” with “uv” & “vu”

✓ Finding the root of “uv” equation 

✓ Answer to two important (90 years old) questions in physics

✓ The role of multiplication in the formation and creation of the universe

✓ Where were the physical world and the creatures before the creation of the universe and its phenomena?

✓ The void space and the Quantum void

✓ What is the Time conception?

✓ The concept of time and its role in physics as well as in the  imaginary dimension

✓ What is Big-Bang and the nature of the universe before the Big-Bang

✓ Energy and its nature in space-time

✓ Space-time for every being

✓ The new definition of the imaginary dimension of time based on the Danaki model

✓ The new definition of motion based on space-time

✓ Curvature of space-time and gravity

✓” Ƭ ” (Tau) instead of “t” and “I” instead of “i”

✓ Justifying the moment of creation and the moment of death

✓ Multi-vector

✓ Emergence

✓ Emergence space and its relation to space-time

✓ What is the space-time and how is it formed?

✓ Point definition in mathematics space

✓ Scalar definition (unit-vector number)

✓ Pseudo-Scalar definition (bi-vector number)

✓ The entities introduced in the emergence space: (scalar, vector, bi-vector, multi-vector)

✓ Creating new beings by multiplying defined entities in the emergence space

✓ Degenerate systems

✓ So up, as below

✓ How does a creature emerge?

✓ Zero point  and bifurcation

✓ New definition of Zero point

✓ Re-study of Double-slit experiment: a new perspective

✓ Overview of how zygotes are formed and new axioms

✓ The role of “i” in the emergence and disappearance (birth and death)

✓ Types of attractors in different of May s diagram.

✓ The role of nonlinear systems and chaos theory in the creation

✓ Roles of multiplication and addition in a system

✓ Differences between numbers and “n” values

✓ Information and its importance in different systems

✓ The role of entropy in the creation

✓ The history of Clifford Algebra

✓  Complex Number properties

✓ Quaternion and its applications, especially in daily life

✓ Addition and multiplication of  Quaternions

✓  commuting Quaternions

✓ How do Quaternions represent rotation in a three-dimensions

✓ Invertse of Quaternion

Convert Quaternion to  the Matrix 4 * 4   ✓

Obtaining i, j, k based on the Matrix 4 * 4

✓ Types of attractors in different of May s diagram.

✓ The role of nonlinear systems and chaos theory in the creation

✓ Roles of multiplication and addition in a system

✓ Differences between numbers and “n” values

✓ Information and its importance in different systems

✓ The role of entropy in the creation

✓ The history of the formation of Clifford Algebra

✓  Complex Number properties

✓ Quaternion and its applications, especially in daily life

✓ Addition and multiplication of  Quaternions

✓  commuting Quaternions

✓ How do Quaternions represent rotation in a three-dimensions

✓ Inverted of Quaternion

Convert Quaternion transform to  the Matrix 4 * 4   ✓

Obtain i, j, k based on the Matrix 4 * 4

✓  Quaternion definition based on double number

✓ The idea of completing complex numbers

✓ Z_n application in rotation of unit Matrix in two-dimensional space

✓ Unit complex number

✓  Unit Dual number

✓ Definition of Derivatives Based on Unit Dual number

✓ Gibb’s Algebra (Vector Algebra)

✓ Hyper complex numbers

✓ The relationship between string theory and Quaternions

Introducing AL-Khazini and the importance of his work in the history of Quaternions

Euler Zeta function

✓ Fibonacci’s Identity equation

✓ Proof of Euler’s Identity

✓ Analysis for N-dimensional Quaternion

✓ A brief mention of Octanion & Sedenion

✓ Fanoo Diagram

✓ Cayley’s numbers

✓ Normed Algebra and Normed Division Algebra

✓ Ring → non-zero elements all have multiplicative inverse

✓ A brief mention of the difference between Group, Ring, Field

✓ Properties of Normed division Algebra

✓ The importance of associativity and commutativity in describing the reality of the universe and  Quantum physics

✓ Review of the following terms:

a:Commutative Algebra

b:Non- Commutative Algebra

c: Anti-Commutative Algebra

d:Associative Algebra

e:Non- Associative Algebra

f:Alternative Algebra

g:Lie Algebra

h:Jordan Algebra ←Jordan Identity

i:Power associative Algebra

j: Cayley-Dickson Algebra

  A few tips on Non- Associativity ✓