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Contents

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The theory of nuclear sets

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**§1.** Nuclear set.** 2

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§2. ****Systematic Definitions**. 4

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§3. Common structural features. 6**

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§4. Regularity. Tabular systematization. 6**

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§5. Structuring. Linear decomposition. 7**

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§6. Symmetry ratios. The symmetry of the form. 8**

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§7. The basis of the nuclear space. 11**

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§8. Properties of nested structures. 15**

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§9. Inter-element connection and symmetry. 20**

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§10. Quantum interactions. The energy of the nucleus. 21**

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§11. Matrix of table and core. 22**

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§12. Rebuilding cores of set. 24**

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§13. Association and decay of nuclei. 25**

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§14. The basic structure of the excited state. 27**

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§15. Table of basic dynamic states. 29**

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§16. The symmetry of the atomic nuclei. 32**

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§17. Tunnel interaction 35**

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§18. Exchange interactions. 37**

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§19. Interactions in dynamic conditions 39**

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§20. Shards and chips. 39**

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§21. Mons. The structure of the shards. 40**

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§22. Mons cosmology. 41**

* Summary.*

In
this work the CLOSED ENUMERABLE SETS are submitted by the elementary
mechanical, evident, appreciable models. Such simplicity allows to
construct and check up adequate mathematical model, i.e. to systematize
and generalize characteristic properties of models and parts making her
and, having distributed these methods on natural objects, to offer a new
way of the description and research of the last. Symmetry of atomic nucleus there is one of consequences of the constructed theory.

**1. The closed enumerable set**: models, mathematics, physics.

The closed enumerable sets of two-dimensional models (structures) M, having form P_{m} and consisting of internal elements such as N_{m} and D_{m}= f(P_{m}, N_{m}) is studied, i.e.: M(P_{m}, D_{m}, N_{m }). For N_{m} from 0 to 111 set of models M can be placed in cells of some periodic table. The set ordered on the table, allocates internal elements of model N_{m}
which of concrete physical properties: A, B, C, E such, that
inter-element interactions in each of structures are completely
described by nine quantum of interaction: A^A, A^B, A^C, B^B, B^C, B^E,
C^C, C^E, E^E. These sizes form triangular 4х4 matrix T = [t_{ i, j}] which is a constant of the table.

Each
model is characterized by 15 sizes, and only 4 of them: e, g, b, and k
are independent and determine structural symmetry. Through the allocated
factors all other properties of model are expressed: structural – N_{m}, P_{m}, etc.; mathematical – coordinate system, coordinates N_{m}, etc.; physical – properties_{ }N_{m}, number of quantum’s of interaction n_{ AA}, n_{ AB},... The Last form a symmetric triangular matrix 4х4 [n _{j,k}] _{m} which is a constant of concrete model.

The trace from multiplication of matrix constants of the table and model determines energy of model:

Tr ([t _{i}_{, j}] · [n _{j, k}] _{m}) = D_{m }· Δ

Here Δ - the energy constant of the table and all quantum of interaction are proportional to her value. The
structure is dynamical object with the big number of the static and
excited conditions. Transition from one static condition in another
occurs through the excited condition. For concrete structure with set_{ }N_{m},_{ }static conditions differ in sizes_{ }P_{m}, D_{m},_{ }factors
of symmetry and a set of quantum of interaction. The energy spectrum of
model is discrete and is caused by change of number D_{m} at
transitions between conditions. Presence of opposite conditions of
models (static and excited) promotes their disorder and association.

The
excited conditions of structures submit to the same tabulated laws and
are characterized by numbers of filling a - layers (orbits): n (1-6) and
m (1-a). The similar behaviors characterize also the subsequent of
excitation. The maximal number excited each structure is determined by
difference N-P.

2. **Correlation**. Structural symmetry of atomic nucleus is physical example of the UMTAE.

**The
studied CLOSED ENUMERABLE SETS of models is a real set of physical
objects and is similar on a structure to molecules and atoms nucleus.
Therefore it is possible to admit, that the laws revealed for one
objects, are the general. For an example it is possible to take some
elements from Periodic system of elements of D.I. Mendeleyev and using
modeling formulas to reveal structures conterminous to them from the
modeling table. Really, let N coincides with a serial number of an
element or number of protons, then D or number of neutrons will be
determined by a difference between integer atoms mass A and N, i.e.
D=A-N. In such representation of 27 elements of Periodic system coincide
with structures from the modeling table under characteristics N, P, D,
but differ in factors of symmetry e, g, b, and k. If to take into
account isotopes, then the much more elements coincide. Nucleuses of
atoms have lower symmetry, i.e. insufficient number of neutrons. Assuming,
that the space outside of a nucleus has the neutron nature, does a
concept about expansion of the universe is more clearly. This
expansion occurs due to deformation of nucleus and disappearance of
heavy chemical elements. It is possible to tell, that the nucleus has a
planetary structure. Further, ***the Periodic system of elements of D.I. Mendeleyev should be characterized: matrix - *T* and energy - ***Δ*** constants, and each chemical element* *- coefficients of symmetry of atomic nucleus*. The electronic environment of atom is determined by structure of a nucleus, also his symmetry.

3. **The purposes**. Algebra of the closed enumerable set is a rebus for intellectuals.

The
special place in becoming and development of the theory is occupied
with mathematical methods. Internal space of model this closed
enumerable set N_{m} with the actions w, i.e. algebra* **N*_{m }= [N_{m}, w] - Sector; and not structural space this open integer set N with the actions W, i.e. algebra* N*
= {N, W} - Natural algebra. Presences of two algebras are the objective
need, caused by existence of vacuum, which shares and unites models.
Then the theory of radiation and interaction of structures is reduced to
the decision of boundary tasks in system of two algebras. Energy of the
model is written down in a ring above system of real numbers, in other
algebra this record will look in another way. New algebraic systems
through a set of new actions display new types of interactions and their
properties. On this way it is possible to open new material forms:
fields, essences, appearances.

§1. Ядерное
множество. 2

§2. Систематизация.
Определения. 4

§3. Общие структурные
характеристики. 6

§5. Структуризация.
Линейные разложения . 7

§6. Коэффициенты
симметрии. Симметрия формы. 8

§7. Базис ядерного
пространства. 11

§8. Свойства
вложенных структур. 15

§9. Межэлементные
связи и симметрия. 20

§10. Квант
взаимодействия. Энергия ядра. 21

§11. Матрицы таблицы
и ядра. 22

§12. Перестройка
ядер множества. 24

§13. Объединение и
распад ядер. 25

§14. Основное
возбужденное состояние структуры. 27

§15. Таблица основных
динамических состояний. 29

§16. Симметрия
атомных ядер. 32

§17. Туннельные
взаимодействия 35

§18. Обменные
взаимодействия. 37

§19. Взаимодействия в
динамических состояниях 39

§20. Осколки и чипы. 39

§21. Моны. Структура
осколка. 40