ELISEEV V.I. Introduction to the methods of the theory of functions of complex spatial variable Published: Moscow, 2003. |

Contents:

CHAPTER 1. BASIC CONCEPTS

1. Spatial complex system of numbers

1. Extracting a root of the number in complex space

2. Solving the quadratic equation in the space of numbers

3. Fundamental theorem of algebra

4. Spatial complex numbers

5. Geometric illustration of the spatial complex number

6. The space of zero divisors. Geometric illustration

7. The operation of division in a complex space

8. Consistency and self-containment of spatial complex algebra

2. Analytical functions of spatial complex variable

1. Differentiability of functions

2. Elementary functions

A. Power function

B. Fractional linear function

C. Consideration of the element of the space (v)

D. Exponential function

E. Logarithmic function

F. Elementary trigonometric functions

G. Trigonometric and hyperbolic functions

H. The function of argument (v)

3.Table of derivatives of elementary functions of classical analysis, as defined in complex space

3. Cauchy integral theorem in complex space

1. Connectedness of complex space

2. Integral and antiderivative

3. Distribution of integral theorems on multi-connected areas

4. Cauchy's integral equation

5. Integral Cauchy's theorems

6. Surface integrals

4. Numeric rows in the space

1. Abel's Theorem

2. Laurent row

5. Isolated singular points in space

6. Residues in space. Computation of integrals using the residue

7. Double integral

1. Area element in the complex space

2. The integral of rational functions (17 April 2001)

3. Computation of certain double integrals using the residue

4. Lemma (K. Jordan)

8. Conformal mappings in space

1. The concepts of conformal mapping in the space

CHAPTER 2. Calculation of lift force acting on the body of finite size in a stream continuum

Methods of classical solutions in the Z-plane

Methods of classical solutions in the space

CHAPTER 3. THEORY OF RELATIVITY IN COMPLEX SPACE

1.Lorentz

2.The energy in the space

3.Self-consistency of the interacting spaces

4.Interval of the theory of relativity in complex space

1. General introduction

2. Interval in form of complex expression

3. Isolated line

4. Time relativity

5. Michelson-Morley experiment analysis by the means of complex space algebra.

CHAPTER 4. PHYSICAL INTERPRETATION OF COMPLEX SPACE

1. Wave equation in complex space

2. Critical lines in the flow

3. Vortex model of the energy interaction in space. The physical interpretation of Cauchy integrals

4. Model of complex structural formation

CHAPTER 5. Vortex model of atomic nuclei. Binding energies equation of atomic nuclei

1. The correspondence between the periodic system of elements and the formation of cyclonic vortices in the atomic nucleus

2. Energy assessment of hypothesis of cyclone structure of nuclear matter

3. Space Nuclear Forces

4. Derivation of the binding energy of atomic nuclei equation

Table 1: Electronic configuration of the ground states of atoms

Table 2: The binding energy of atomic nuclei.

Table 3: The binding energy of light nuclei

5. Diagrams of th sate of atomic nuclei of elements

CHAPTER 6. Proove of cyclone model of atomic nuclei in accordance with the structure of space at distances of nuclear forces. Calculation of decay of radiactive nuclei.

1. Models of atomic nuclei.

2. Calculation of the electron and positron decay of nuclei. Conditions of electron and positron decay from the standpoint of structure of complex space.

3. Alpha decay.

4. The fallacy of the theory of the Coulomb barrier

5. Generalization of the results of alpha decay. Calculation of radioactive series.

CHAPTER 7. Physical space deformation from standpoint of complex space algebra. Particles as a result of binding of fundamental masses.

1. Physical constants, the fundamental mass and length.

2. Einstein's general relativity and the RTG Logunov contain methods of complex variable theory in hidden form.

3. Schwarzschild gravitational field in a complex space.

4. Complex space gravity.

5. Interaction operator in the structural formation.

6. Eelementary particles mass equation.

7. Gravitational-electromagnetic potential in complex space. Particles and microparticles models. Electric charge and spin of particles.

8. Calculation model of the hydrogen atom.

9. A proof of Planck hypothis about quants of energy.

CHAPTER 8. Classification of microparticles. Structure of physical space of microparticle s bound to the structure of the complex space

1. Models of microparticles in the gravitational electric and leptonic complex space. The correspondence between the isolated directions in the complex space and charge conjugation of microparticles. The quantum numbers of microparticles reflect multi-dimensional complex space.

2. Quantum numbers of quarks are result of space multi-connectedness.

3. The growth of the multi-connectedness of space determines the charges of S, C, B, t of quarks. Quark model

4. Leptons, mesons, baryons as a linear combination of quarks u, D

5. The structure of the gluon field.Calculation of the masses of microparticles

6. The system of equations for the calculation of the gluon field

Table 8.1. Calculation of the mass of microparticles.

7. Evaluation of the calculation of gluon fields and the mass of microparticles

8. The amount of single gluon vortices with the weights determine the structure of the field of microparticles

9. The calculation of masses microparticle by quark compositions and modes of decay. Computation of the quantum numbers of microparticles, the study of the spin, isospin, parity with the mass of microparticles. Realization of quantum CPT theorem. Study of the law of non-conservation of parity.

10. Calculation of the binding energy of atomic nuclei of the periodic table of elements and their isotopes, based on the structure of the gluon field of the proton and the neutron.

Таблица 8.2. Determinant of the weights of the proton, neutron, electron, positive pion.

Таблица 8.3. Calculation of the mass of atomic nuclei of the periodic table of elements and their isotopes.

CHAPTER 9. SUPERCONDUCTIVITY

1. General Provisions.

2. Necessary and sufficient conditions for the transition into conducting and the superconducting state

3. Research of field of critical temperatures of transition into the superconducting state for known compounds.

CHAPTER 10. CONCLUSION

1. Expansion of field of complex numbers. Study of necessary and sufficient conditions for the expansion of the field of complex numbers.

2. Extracting the square root of 1.

3. Spatial representation of complex number.

4. Complex spatial coordinates.

5. Study the implementation of the fundamental theorem of algebra.

6. Features of spatial system of spatial coordinates.

7. Particular areas in the complex space

8. Comparison of the structure of the complex space with the structure of the periodic table of elements.

9. Interaction operator interaction in the complex space

10.Basic prerequisites for the calculation of multicomponent chemical compounds.

11. The new numerical system - a new settlement unit in theoretical physics.

12. The gravitational interaction in the complex space-time. The structure of the ether.

13. The ratio between the inertial and gravitational mass. Calculation of the gravitational effect.

14. The mechanism of interaction of gravitational fields.

15. Structure of the complex space.

16. The identification of combinations of complex subspaces with the microparticles, classification of microparticles in accordance with the dimensions of space.

17. Ether and the physical vacuum.

18. The results of the Michelson experiment proof of the complexity of real space.