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Expanded Field Theory New Axioms, Laws and Consequences

- The present study attempts to expand the Classic Field Theory to a more general theory of the field. This more general field theory is named Expanded Field Theory. This new theory contains 2 new axioms and 8 laws. It predicts to include the gravitational field and other unknown and unexplored fields. As it Field Theory is described mostly by Theory of Electromagnetic Field. The Electromagnetic Field is described by Maxwell’s laws The Maxwell’s laws are certified by a single axiom which claims that the movement of a vector E in a closed loop (div rot E = 0) is evenly or velocity is constant . The author replaces this axiom with a new one, according to which the movement of a vector E in an open loop (div rot E ≠ 0) or an open vortex (div Vor E ≠ 0) is unevenly or velocity is variable. If the vortex is in plane (2D), it is named a cross vortex. If the vortex is in volume (3D), it is named a longitudinal vortex. Something more- each vortex can be decelerating (div (VorE) <0) or accelerating (div (VorE)> 0). Abstract- The present study attempts to expand the Classic Field Theory to a more general theory of the field. This more general field theory is named Expanded Field Theory. This new theory contains 2 new axioms and 8 laws. It predicts to include the gravitational field and other unknown and unexplored fields. As it is well known the Classic Field Theory is described mostly by Theory of Electromagnetic Field. The Electromagnetic Field is described by Maxwell’s laws (1864). The Maxwell’s laws are certified by a single axiom which claims that the movement of a vector E in a closed loop (div rot E = 0) is evenly or velocity is constant. The author replaces this axiom with a new one, according to which the movement of a vector E in an open loop (div rot E ≠ 0) or an open vortex (div Vor E ≠ 0) is unevenly or velocity is variable. If the vortex is in plane ( 2D ), it is named a cross vortex. If the vortex is in volume (3D), it is named a longitudinal vortex. Something more- each vortex can be decelerating (div (VorE) <0) or accelerating (div (VorE)> 0). After the first axiom are obtained immediately 4 types of movements – cross vortex, which can be accelerating or decelerating and longitudinal vortex , which can also be accelerating or decelerating. The results obtained: Abstract- It is accepted that three-dimensional physical space is a hypersurface with a Riemannian metric in four-dimensional space. The metric tensor of this three-dimensional space is defined by Einstein's equations. Another coordinate of four-dimensional space is time. In this space, the equations of the world line of a particle with a mass m are defined under certain initial conditions: the starting point of the space and the vector of the particle's initial velocity. This approach removes all the problems and contradictions noted in the monograph [1], and the resulting equations adequately describe, for example, the curvilinear motion of planets without energy change. Abstract-It is accepted that three-dimensional physical space is a hypersurface with a Riemannian metric in four-dimensional space. The metric tensor of this three-dimensional space is defined by Einstein's equations. Another coordinate of four-dimensional space is time. In this space, the equations of the world line of a particle with a mass m are defined under certain initial conditions: the starting point of the space and the vector of the particle's initial velocity. This approach removes all the problems and contradictions noted in the monograph [1], and the resulting equations adequately describe, for example, the curvilinear motion of planets without energy change. Abstract- The Earth is isolate on its orbit motion around the Sun. The thermal radiation on Earth determines climate warmer or colder. By Kirchhoff’s law, the thermal radian on Earth must be in an equilibrium state. Which equivalents to an optimum problem. This paper establishes an equilibrium equation of thermal radiation of Earth, transmits it to an optimum problem, and proves that the equilibrium of thermal radiation of Earth is an indifferent equilibrium, neither stable, nor un-stable, based on the Stefan- Boltzmann law and the emissivity formula. The result means that the climate neither getting warmer and warmer, nor getting colder and colder. Abstract- The Earth is isolate on its orbit motion around the Sun. The thermal radiation on Earth determines climate warmer or colder. By Kirchhoff’s law, the thermal radian on Earth must be in an equilibrium state. Which equivalents to an optimum problem. This paper establishes an equilibrium equation of thermal radiation of Earth, transmits it to an optimum problem, and proves that the equilibrium of thermal radiation of Earth is an indifferent equilibrium, neither stable, nor un-stable, based on the Stefan- Boltzmann law and the emissivity formula. The result means that the climate neither getting warmer and warmer, nor getting colder and colder. Abstract- Radiative cooling is the phenomenon responsible for dew formation on plants. Harvesting humidity from the air has two different pathways: fog and dew, but harvesting dew have not been sufficiently exploited. In this paper, we describe the resources for radiative cooling as well as lawsonite mineral for exploiting this natural phenomenon. Further, this paper describes the development of dew harvesting systems for use in the semi-arid mirleftsouth Morocco. Numerical simulations using the energy balance equation were performed. Harvesting dew can be used as a renewable complementary source of water both for drinking and agriculture in specific arid or semi- arid areas. In order to form global estimates of dew collection potential via a dew formation model, we combined meteorological parameters with radiative properties of a specific collector sheet (natural lawsonite, CaAl 2 Si 2 O 7 (OH) 2 •H 2 Odeposited on glass) to enhance the dew yield. The daily yields show that significant amounts of dew water can be collected. Abstract- Radiative cooling is the phenomenon responsible for dew formation on plants. Harvesting humidity from the air has two different pathways: fog and dew, but harvesting dew have not been sufficiently exploited. In this paper, we describe the resources for radiative cooling as well as lawsonite mineral for exploiting this natural phenomenon. Further, this paper describes the development of dew harvesting systems for use in the semi-arid mirleftsouth Morocco. Numerical simulations using the energy balance equation were performed. Harvesting dew can be used as a renewable complementary source of water both for drinking and agriculture in specific arid or semi- arid areas. In order to form global estimates of dew collection potential via a dew formation model, we combined meteorological parameters with radiative properties of a specific collector sheet (natural lawsonite, CaAl 2 Si 2 O 7 (OH) 2 •H 2 Odeposited on glass) to enhance the dew yield. The daily yields show that significant amounts of dew water can be collected. Abstract- The article starts from the natural phenomenon of sparks in the stone tip, analyzes the essence of frictional heat generation, and deduces the theory of pressure heat generation. Geocentric, geothermal, and solar source issues are explained. Abstract- The article starts from the natural phenomenon of sparks in the stone tip, analyzes the essence of frictional heat generation, and deduces the theory of pressure heat generation. Geocentric, geothermal, and solar source issues are explained. Abstract The abstract is the foundation of the research paper. It should be clear and concise and must contain the objective of the paper and inferences drawn. It is advised to not include big mathematical equations or complicated jargon. Many researchers searching for information online will use search engines such as Google, Yahoo or others. By optimizing your paper for search engines, you will amplify the chance of someone finding it. In turn, this will make it more likely to be viewed and cited in further works. Global Journals has compiled these guidelines to facilitate you to maximize the web-friendliness of the most public part of your paper. Abstract: This summary should be two hundred words or less. It should clearly and briefly explain the key findings reported in the manuscript and must have precise statistics. It should not have acronyms or abbreviations. It should be logical in itself. Do not cite references at this point. work development. the study, common approaches the problem, relevant results, significant conclusions or new questions.


Expanded Field Theory New Axioms, Laws and Consequences
Dr. Valentina Markova Abstract-The present study attempts to expand the Classic Field Theory to a more general theory of the field. This more general field theory is named Expanded Field Theory. This new theory contains 2 new axioms and 8 laws. It predicts to include the gravitational field and other unknown and unexplored fields.
As it is well known the Classic Field Theory is described mostly by Theory of Electromagnetic Field. The Electromagnetic Field is described by Maxwell's laws (1864). The Maxwell's laws are certified by a single axiom which claims that the movement of a vector E in a closed loop (div rot E = 0) is evenly or velocity is constant.
The author replaces this axiom with a new one, according to which the movement of a vector E in an open loop (div rot E ≠ 0) or an open vortex (div Vor E ≠ 0) is unevenly or velocity is variable. If the vortex is in plane ( 2D ), it is named a cross vortex. If the vortex is in volume (3D), it is named a longitudinal vortex. Something more-each vortex can be decelerating (div (VorE) <0) or accelerating (div (VorE)> 0).
After the first axiom are obtained immediately 4 types of movements -cross vortex, which can be accelerating or decelerating and longitudinal vortex , which can also be accelerating or decelerating.
The following results are obtained: evenly movement is replaced with unevenly movement (decelerating or accelerating); movement in a closed loop is replaced with movement in an open loop or vortex; a cross vortex in 2D generates a longitudinal vortex in 3D through a special transformation and vice versa-the longitudinal vortex in 3D through another special transformation generates a cross vortex in 2D; the decelerating vortex emits primary vortices to environment, but the accelerating vortex sucks into the same primary vortices from environment; the accelerating longitudinal vortices are attracted to one another, as the faster is inserted into the slower and thus form a funnel-this is the model of gravity funnel.
It should be noted, in particular, the results of the second axiom. It claims that two complex (cross-longitudinal) vortex objects in 3D that work in one direction as one complementary pair, are existed simultaneously. This way they are obtained 2 pairs of complementary objects in both directions.

Introduction The Essence of Axiom 1 a) The Classic Axiom
The classic axiom in the Theory of the Electromagnetic Field certifies Maxwell's laws (1864). It postulates that the movement of an electric vector E in a closed loop is evenly: where (rot E) is the movement of the vector E in a closed loop; div (rot E) is the divergence (the variation in increase or decrease) of the vector E during its movement in a closed loop (rot E); the movement of the vector E in a closed loop (rot E) with zero divergence (variation) of the vector E is equivalent to evenly movement or to movement with constant velocity V [1]. The defect of the classic axiom (1) is that it does not describe movements in an open loop or a vortex, or movements with a non-constant or variable velocity V.

b) The New Axiom for rotor
For the purpose of describing a larger range of movements, it is obviously necessary to expand the foundation of service theory. This means that such an axiom must be used which can certify wider set of movements.
The main motivation for altering the classic axiom (1) follows after the need to describe the causative relationships in uneven movements in open systems. It turns out that open vortices are the cause of closed vortices, which means that open vortices are more fundamental than closed ones [2].
So it is the necessity to change the existing axiom of the Classic Field Theory for close loop to axioms of Expanded Field Theory for open loops [3].
In order to expand the concepts, the notion (1) of movement of vector E in a closed loop (div (rot E) = 0) in 2D ( Figure 1A, a) is replaced by the notion (2) of movement in an open loop (div (rot E) ≠ 0 in 2D ( Figure  1A,b).
c) The extension of the term of vortex (vor) from Classic Fluid Theory − Unreal term of vortex: evenly vortex (vor) is used in Classic Theory: The term vortex (vor) is used in fluid dynamics and defined as "an area in fluids, where the flow rotates evenly along a spiral around an axis line, which can be straight or curved" [4]. Fluid movement is uniform (evenly) in 3D. To begin with, we can use this classic definition, having in mind that here the term (vortex, vor) is for a uniform vortex in the classical sense.
Real term of vortex: unevenly vortex (Vor) means that the velocity (V) is variable and as a resultthe steps are not constant.
For the purposes of the present study the the term must extend to both 3D and 2D and modified for an unevenly vortex or a vortex with uneven movement.
In fact, in nature it does not exist evenly vortex with the constant steps between the rotations. If a movement is evenly, it forms a closed circle rather than an open vortex. There is an unevenly vortex in nature, and because it is uneven it is not centered, but it is eccentric.
Thus the designation of an evenly vortex "vortex, vor" is replaced with a designation for an uneven vortex "Vortex, Vor" with a capital letter.

Definition: An unevenly cross vortex (E 2D ) is an unevenly vortex (E) spinning transversally in a 2D plain.
The cross open vortex in 2D is designated as Vortex E 2D or simply V or E 2D ( Figure 1A, b).

Definition: An unevenly longitudinal vortex (H 3D ) is an unevenly vortex (H) spinning in the volume of 3D.
The longitudinal open vortex in 3D is designated as Vortex H 3D or simply Vor H 3D ( Figure 1A,d).
Both definitions for natural unevenly vortices ignore the thickness of the vortex itself, be it cross or longitudinal. Differences in geometry reflect the difference in distance between the coils and the diameter of the coils.

d) The New Axiom for rotor and vortex
It exists a vortex div (VotE) ≠ 0 as an open loop (div (rotE) ≠ 0) in 2D or: div (VotE) ≠ 0.
The existence of an open loop means that it can exists a decelerating or an accelerating vortex in 3D: div (VorH) <0; div (VorH)> 0; 4b.
Axiom 1. The moving of vector E along an open loop is unevenly div(rotE) =/=0, or velocity is variable. Consequence (of moving in vortex) − Moving with monotone-decreasing or monotoneincreasing velocity becomes along an open vortex: div (VotE) ≠ 0 for vector E in 2D(in plane) that was named as cross vortex, or div (VotH) ≠ 0 for vector H in 3D(in volume) that was named as longitudinal vortex. 5. − The motion of vector E with monotone-decreasing or monotone-increasing velocity is along the open loop in 2D vortex : div (VotE) ≠ 0 , for which div (VorE) <0; div (VorE)> 0. The motion of vector H with monotone-decreasing or monotone-increasing velocity is along the open loop in 3D vortex: div (VotH) ≠ 0, for which div (VorH) <0; div (VorH)> 0.
Consequence (of variation of moving ): − The main result of Axiom 1 is that there have been 4 types of vortices: a cross vortex in 2D (E 2D ) that can be accelerated (E 2D+ ) or decelerated (E 2D-) and a longitudinal vortex in 3D (H 3D ) that can also be accelerated (H 3D+ ) or decelerated (H 3D-), (Figure1 А, c, d). − We immediately received 4 types of movementscross (3a), which can be accelerated or decelerating(4a) and longitudinal (3b) , which can also be accelerated or decelerating(4b).

Consequence (of visual perception)
It is known that light is spreading crosswise. − Therefore, the cross vortex will reflect the light rays, and an external observer will perceive the image of the cross vortex. − But the thread of the longitudinal vortex does not reflect the light. The light crosses the thread of longitudinal vortex, surrounds the thread, and continue its path without reflecting the longitudinal vortex. So it forms diffraction. Therefore, the longitudinal vortex is invisible to an external observer.

II.
The essence of Axiom 2

a) Two directions of pair of complementary objects
The reason is that the vector E is a complex vector. When E 1 = A + iV, the amplitude A is superimposed and as a result generates a velocity V (Figure1B, c). When E 2 = V + iA, the velocity V is transformed as a result of the amplitude A (Figure1B, b).
Definition: Pair of complementary objects is such pair of vortices which is generated by complementary vectors E 1 = A + iV, E 2 = V + iA, and as a result the objects have complementary actions.
If one object pushes (Figure1B, c), but the other pulls (Figure 1 B,   As is known from cybernetics, the system is a set of interconnected parts that work together through some process of control. The definition of a system includes simultaneity at unified internal time and bidirectional and also commitment to the exchange of matter and energy. "A system is called a multitude of objects and relationships between them, which are treated as one. A link can connect two or more objects. It can be information, material or energy. The set of connections defines the structure of the system. The management of an arbitrary system is studied by cybernetics using two approaches… "(Wikipedia). For comparison in the Electromagnetic Field, the electrical circuit contains one generator element and one or several passive consumers that only transform energy from one view(kinet.) to the other view (poten.).

III.
Expanding of Maxwell's Law a) The inconvenience of the first Classic Maxuell's Law According to the classic axiom (1), the first classic law of Maxwell named "the law of electromagnetic induction" is presented as follows: where (rot E) is the evenly movement of the electric vector E in a closed loop, µ is the coefficient of magnetic ( A ) Figure 1B: One pair (in one direction ) of complex vortices in 3D permeability, ∂ Н/∂t is the variation of the magnetic vector H in time t [1].On the one hand, a change in magnetic induction over time (∂H / ∂t) generates an evenly movement of the electric vector (rot E). It is named "the law of electromagnetic induction", where the sign""means generation: 7a.
-On the other hand, an evenly movement of the electric vector (rot E) must generate a magnetic induction vector (H) in the center of the closed loop (rotE is right proportional ̴ to H) : where the sign " ̴ " means proportionality.

a) Laws of the transformation of a cross vortex (E 2D ) into a longitudinal vortex (H 3D )
At every (i) point p(i) of a decelerating cross vortex E there are two simultaneous movements: velocity vector (-V) and amplitude of the cross vortex (-W). The two simultaneous movements (V and W) also exist at all points of longitudinal vortices. The cross vortex (E 2D -) is transformed into a longitudinal vortex (H 3D +). This is accomplished through a specific operator (Δ1) for cross-longitudinal transformation ( Figure 1B, b).
The cross (E 2D ) and the longitudinal (Н 3D ) vortex are not an original and an image by analogy with the well-known transformations of Laplace or Fourier. They are representatives of spaces with qualitatively different structures. Therefore the introduced operator (Δ1) connects the original in one type (transverse) of space with its image in another type (longitudinal) of space, i.e. the transformation Δ1 connects two spaces with different qualities. where Vor (for Vortex, meaning an unevenly vortex) replaces rot (for rotor, meaning closed loop); the cross vortex in 2D (E 2D ) continues its development in 3D as a longitudinal vortex (Н 3D ) (Figure1Bb). While Maxwell's law (7) states that vector E generates vector H, the present law (8) postulates that the cross vortex Vor (E 2D ) of E in 2D generates a longitudinal vortex Vor (H 3D ) of H in 3D. The sign (-) for Vor (H 3D ) 3D means that E 2D and H 3D have opposite dynamics. For example when div (Vor E 2D ) < 0 (is decelerated), div (Vor H 3D ) > 0(is accelerated).      Figure 6C).  -The Consequence (8b) of Law1 describes in 2D the model of electron (e-) as the accelerating inward vortex( acc(e-)) (Figure2c) in the chain of proton-electron (Figure 2d -Figure 2c). Every electron (e-) of this type pulsates in 3D in two modes of:" expanded cross vortex and a shortened longitudinal vortex" and "shrunken cross vortex and extended longitudinal vortex" ( Figure 6A, Figure 6C).
Consequence: It exists another two consequences (not described in the article), but they describe decelerating or accelerating cross vortices to outward. This is the 2 type of positrons: (dec(e+)) and (acc(e+)) positrons.

b) Laws of the transformation of a longitudinal vortex (H 3D ) into a cross vortex (E 2D ).
For the opposite transformation a new operator Δ2 is introduced to transform a longitudinal (H 3D ) into a cross (E 2D ) vortex. The physical nature of this Δ2 transformation is quite different in comparison with Δ1.
-Generally speaking, the transformations Δ1 and Δ2 are orthogonal rather than symmetrical to each other. 9b.
-The Consequence (9b) of Law2 describes in 2D the model of proton(p+) as the accelerating outward vortex dec(p+)) (Figure2d) in the chain of proton-electron ( Figure 2d -Figure 2c). Every proton (acc(p+)) of this type pulsates in 3D in two modes of:" expanded cross vortex and a shortened longitudinal vortex" and "shrunken cross vortex and extended longitudinal vortex" ( Figure 6A, Figure  6C).
Consequence: It exists another two consequences (not described in the article), but they describe decelerating or accelerating This is the 2 models of a ntiprotons (dec(p-)) and (acc(p)) ( Figure 6B).
-We immediately obtain 4 tipes of antiproton: (dec(p)) and (acc(p-)) that each of them pulsates in two modes:" expanded cross vortex and a shortened longitudinal vortex" and "shrunken cross  Figure 6C).

V.
Conclusions a) Two tipe electrons -The first type of electron( acc(e-)): when the electron is inside a proton-electron system(connected in the atom) has accelerating cross vortex (E2D+) inward that generates a decelerating longitudinal vortex(H3D-) upward.
Therefore, an electron ,bound into an atom (acc(e-)) is strongly linked to a cross component (E2D+) and poorly connected along a longitudinal component (H3D-).
-A second type of electron(dec(e-)): when the electron is free (outside of the atom) has decelerating cross vortex (E2D-) inward, which generates an accelerating longitudinal vortex upward (H3D+). When electron is free (second type (dec(e-)), the decelerating cross vortex (E2D-) is interrupted .
On account of that accelerating longitudinal vortex (H3D+) shoots a fast ingredient, tears in dashes (due to pulsation) and connects to the decelerating longitudinal vortex (H3D-) at input of the proton. Therefore, the free electron(dec(e-)) is poorly linked in cross component (E2D-) and highly bound to the longitudinal component(H3D+).
Consequence: There is a significant difference in the states of a bound electron (acc(e-)) and a free electron (dec(e-)).
Consequence: Scientists measure the mass of a free electron (dec(e-)) with a decelerating cross vortex (E 2D-) inward, and can't measure the mass of a connected electron (acc(e-)) with an accelerating cross vortex (E 2D+ ) inward.

Consequence:
The measured mass of free electrons is much more then the mass of linked in atom inside electrons. -The new extended meaning of the term" Complementarity" is when the two parts are generating and they act anti-phase -one push and the other pulls.

b) Electromagnetic and Gravity field
-The two transformations Δ1 (Law1) and Δ2 (Law2) are not symmetrical but rather form pairs of objects that complement each other in their action .So they form a pairs of complementary objects or they are mutually orthogonal. -The two vortices in the described above vortex pairs ( Figure 2c -Figure 2d) play the role of generators (!) -one push (Figure 2d), the other -pulls ( Figure  2c). Obviously in described above chain (Figure 2c - Figure 2d) there is not the consumer. Therefore this chain has not energy losses. It is well known that in every Electromagnetic chain has generator and one or more consumers. That's why Electromagnetic chain has energy losses.
-Both transformations, Δ1 (Law1) and Δ2 (Law2), are not regulated by external regulator or external parameters. Therefore the processes are regulated only by internal laws and are not determined by outside parameters.

VI. Law of Nonparametric Movement of the Vortex
Obviously the processes of acceleration and deceleration of the longitudinal vortex is a nonparametric process. Processes of accelerating and decelerating longitudinal vortices manifest both quantitative and qualitative changes [5].This mechanism of amplification is known in cybernetics as Positive Feedback. shows that velocity Vi increases by redistribution with cross vortices. There is also redistribution of mass The mass of the cross vortices is added in portions (quanta) with acceleration to the initial mass of the longitudinal vortex with velocity Vi and thus accelerates it more and more (Figure 3a).
-The accelerating longitudinal vortex sucks in more cross vortices from outside that accelerate further the longitudinal vortex with velocity Vi and so on. Thus the longitudinal vortex at output(Vi) increases its velocity and acceleration which returns at input. The reason is that it suck in more cross vortices and increases of the acceleration and mass to the entrance (Figure 3a). -This process runs avalanche until it reaches a saturation level where the acceleration becomes maximum (a max ) for a time slice (t 0 -t n ), (Figure 3b). VII. Law of the Constant Power of the Vortex As we saw above there are two qualitatively different movements at each (i) point p (i) of the decelerating vortex E: longitudinal vector velocity (V) and cross vortex with amplitude (W) ( Figure 1B, b).
The reason of that is the vector E is not a simple vector but it is a complex vector ( Figure 1B,d).
-It is well known that in Classic Mechanic the simultaneous operation of two independent vectors is equal to the sum of these vectors. -According to Law 3, the transforming one vector (V) into a vortex (W) and vice versa is a nonparametric process. Transformation is done by internal laws but not by setting parameters from outside. -The nonparametric transformation of two variables V (t) and W (t) is mathematically described by the product V (t) . W (t) of these variables. where i= 0 ÷ ∞ is current point from step to step; the product (Vi).(Wi) is proportional to the current power(P i) of the uneven vortex .

Consequence:
The simultaneous operation of two mutually -dependent vectors is equal to the product of these variables (in Expanded Field Theory) while the simultaneous operation of two independent vectors is equal to the sum of these variables (in Classic Mechanic). Consequence: At a decelerating vortex vector velocity (V) is transformed according to internal law (10) into the amplitude of the cross vortex (W) (Figure 4a, b).
Consequence: At a accelerating vortex vector velocity (V) is transformed according to internal law (10) into the amplitude of the cross vortex (W) (Figure 4a, c).

VIII.
Laws of the Velocity of the Longitudinal Vortex (V) and the Amplitude of the Cross Vortices (W) We saw in the previous point (p.6) that at a decelerating vortex vector velocity (V) is transformed according to into the amplitude of the cross vortex (W) (Figure 4a,b). More precisely-the reduction in speed (V) is transformed into an increase in the amplitude(W) of cross vortices. 11.

Law 5: The deceleration vortex in 2D is described with a system of 2 equations in which: longitudinal velocity (V) decreases in (n) portions (ψ n ) times; the amplitude (W) increases in (n) portions (ψ n ) times:
where v n , w n n are periodic roots with period n; v n , w n are mutual orthogonal that fulfill the requirement for orthogonality: v n. w n = V 0 .w 0 , v n. ω n = V 0 .W 0 ; n = 0 ÷ ∞; the roots v n , w n are expressed as: v n = (1/ψ n ).V 0 , ω n =ψ n .W 0 ; linear velocity V 0 is the starting value of V n , amplitude of cross vortex W 0 is the starting value of ω n ; ψ is a proportional that fulfills the requirement: ψ-1/ ψ =1.
Consequence: The deceleration vortex in 3D is described with a system of 4 equations in which: longitudinal velocity (V) decreases in (n) portions (ψ n ) times; the angular velocity (w) , the amplitude (W) and the number (N) of cross vortices increase in (n) portions (ψ n ) times: 11a.
I W 2 = W 0 (1 +W), where v n , w n are periodic roots with period n; v n , w n are mutual orthogonal that fulfill the requirement for orthogonality: v n. w n = V 0 .w 0 , v n. ω n = V 0 .W 0 ; n = 0 ÷ ∞; the roots v n , w n and ω n and n n are expressed as: v n = (1/ψ n ).V 0 , ω n =ψ n .W 0 ; w n = ψ n .W 0 , [n n ]=ψ n .N 0 ; linear velocity V 0 is the starting value of V n , amplitude of cross vortex W 0 is the starting value of ω n , angular velocity w 0 is starting value of w n , number N 0 is starting value of n n, [n n ] is the closest integer; ψ is a proportional that fulfills the requirement: ψ-1/ ψ =1.  Consequence: Because of increasing of the amplitude (W) the angular velocity ( w ) and the number of cross vortices (N) it forms decelerating, thickening and expanding left rotating Funnel in which: W max ; w max ; N max Consequence: Two or more decelerating longitudinal vortices repel each other. The reason is due to the emission of cross vortices from center to outside.
where v n ,w n are n periodic roots with period n; v n ,w n are mutual orthogonal that fulfill the requirement for orthogonality: v n. w n = V 0 .w 0 , v n. ω n = V 0 .W 0 ; n = 0 ÷ ∞; internal law the roots v n , w n are expressed as: v n = (ψ n ).V 0 , ω n = (1/ψ n ). W 0 ; linear velocity V 0 is the starting value of V n , amplitude of cross vortex W 0 is the starting value of ω n ,; ψ is a proportional that fulfills the requirement: ψ-1/ ψ =1.

Consequence:
The acceleration vortex in 3D is described with a system of 4 equations in which: longitudinal velocity (V) increases in (n) portions (ψ n ) times, the angular velocity (w) , the amplitude (W) and the number (N) of cross vortices decrease in (n) portions (ψ n ) times: 12a.
where v n , w n n are periodic roots with period n; v n , w n are mutual orthogonal that fulfill the requirement for orthogonality: v n. w n = V 0 .w 0 , v n. ω n = V 0 .W 0 ; n = 0 ÷ ∞; the roots v n , w n and ω n and n n are expressed as: v n =(ψ n ).V 0 , ω n =(1/ψ n ).W 0 , w n =(1/ψ n ).W 0 , n n =(1/ψ n ).N 0 ; linear velocity V 0 is the starting value of V n , amplitude of cross vortex W 0 is the starting value of ω n , angular velocity w 0 is starting value of w n , number N 0 is starting value of n n ; ψ is a proportional that fulfills the requirement: ψ-1/ ψ =1. Consequence: An accelerating vortex (E 2D +) with a velocity vector (V) sucks in accelerating vortices with decreasing amplitude (W) in perpendicular direction (because of sign -in second equation of system 12,12a).
According to the Consequence 8b of Law1 the accelerated cross vortex(E 2D +) generates (sucking) to its center a longitudinal vortex(H 3D-) from the outside to inside(to the right). At each point(n i ) a right rotating wheel is formed. The spiral vortex in 3D is formed as a right rotating spiral ( Figure 4c). Therefore, the acceleration vortex will twist to the right -clockwise (+), viewed against the movement ( Figure 4c). like: the vortex is inserted at the center with the maximum lineal speed, the minimum number of coils and the minimum distance, the slower vortex is with more coils and a longer way along the spiral and the vortex at the periphery is winding with a minimum lineal speed, maximum number of coils and a maximum spiral path. Because of acceleration this tube turns to the so called Gravity Funnel.

Laws of Continuity
In Euclidean geometry has an axiom that postulates that only one straight line passes through two points. The Axiom 2 for two complementary objects resemble an axiom in Euclidean geometry. But in essence Axiom 1 and Axiom 2 are physical, rather than geometrical. Instead of points as geometric objects there is a pair of vortices with different dynamics as physical objects: the both of them are generators-one pulls, the other pushes (Figure 2c, d).
Provisionally vortices can be classified as primary (W) and secondary (E) uneven vortices. The primary uneven vortices are micro cross vortices (W) (Figure 5c, d). The secondary uneven vortices are Expanded Field Theory New Axioms, Laws and Consequences macro cross vortices (E) (Figure 2c,d). The primary cross vortices exist as a free form or free cross vortices. They are also called as "free energy" (Figure 5 c,d).
Definition: Primary vortices are emitted to the environment or sucked in from environment by the secondary (main) vortex.

a) Law of continuity in a closed loop in 2D
According Law 5 (11) decelerating cross vortex (E2D-) emits decelerating primary cross vortices in perpendicular direction (Figure 5b).
-In general the primary micro vortices are derivatives of the main secondary macro vortices. -Since cross vortex objects are physical particle, they must fulfill the main Physical Law of continuity cycle of movement matter and energy. -In order to fulfill the fundamental law of continuity, the feedback must pass through empty space (feedback 2D).It contains elementary primary cross vortices generated and emitted by the secondary decelerating cross vortex( Figure 5c) and consumed and sucked in by the secondary accelerating cross vortex (Figure 5d). This feedback is closed through the so called "empty space". The feedback is in inverse direction to the direction of the main cross vortices. -Therefore, in order to satisfy this fundamental law in physics, apparently this space cannot be "empty", as we often call it. The imaginary space is filled with primary cross vortices. -The primary cross vortices are copies of the secondary cross vortices but at a much smaller scale. But their movement in the space between the two vortex objects in 2D is due to the sucking action of the accelerating main longitudinal vortex (E2D+) (the second vortex in the pair) (Figure 4c, Figure 5d).

b) Law of continuity in a closed loop in 3D
In order to fulfill the fundamental law of physics the feedback of the main longitudinal vortices in 3D must close through the space (feedback 3D). It contains elementary primary longitudinal vortices, generated and consumed by the main secondary longitudinal vortices.
-This imaginary space is filled with primary longitudinal vortices resembling copies of the secondary longitudinal vortices but at a much smaller scale. All longitudinal vortices (primary and secondary) create a new type of field that contributes to our knowledge of the field as a form of matter. As these longitudinal vortices are highly accelerated they attract, suck and form longitudinal packets as a micro funnels [6]. They move in the opposite direction as a feedback in 3D.

Consequence:
The reason for the emission of primary elementary longitudinal vortices is that the secondary longitudinal vortex tears in dashes by high frequency pulses (H3D+) (Figure 5c).
-The real links in 2D and 3D are simple, but the imaginary links in 2D (feedback 2D) and 3D (feedback 3D) are most likely multi ciphered. b) Two tips of electrons -The first type of electron (acc(e-)): when the electron is inside a proton-electron system(connected in the atom) has accelerating cross vortex (E2D+) inward that generates a decelerating longitudinal vortex (H3D-) upward.

Therefore, an electron, bound into an atom (acc (e-)) is strongly linked to a cross component (E2D+) and poorly connected along a longitudinal component (H3D-).
-A second type of electron (dec (e-)): when the electron is free (outside of the atom) has decelerating cross vortex (E2D-) inward, which generates an accelerating longitudinal vortex upward (H3D+). When electron is free (second type (dec (e-)), the decelerating cross vortex (E2D-) is interrupted.
On account of that accelerating longitudinal vortex (H3D+) shoots a fast ingredient, tears in dashes (due to pulsation) and connects to the decelerating longitudinal vortex (H3D-) at input of the proton.

Therefore, the free electron (dec (e-)) is poorly linked in cross component (E2D-) and highly bound to the longitudinal component (H3D+).
Consequence: There is a significant difference in the states of a bound electron (acc (e-)) and a free electron (dec (e-)).
Consequence: Scientists measure the mass of a free electron (dec (e-)) with a decelerating cross vortex (E 2D-) inward, and can't measure the mass of a connected electron (acc (e-)) with an accelerating cross vortex (E 2D+ ) inward.  x-axis and y-axis. The x-axis is pulling him to the accelerating vortex (2). The y-axis rotates decelerating vortex (1) (2) is much more than of decelerating vortex (1) and because this number determine much more mass of substance for accelerating vortex (2): m2>>m1 -In center (green) it has an accelerating longitudinal vortex(4) from down to up (direction of internal gravity wave). -In middle (red) because of resistance it has an decelerating longitudinal vortex that form internal "Back wave" (direction of external gravity wave). have mass as a substance. They exist alone or in a package such as a pipe or funnel (9). When the pipe (funnel)is not active, the energy inside the package exists as a standing wave. When it enters into denser environment of primary free cross vortices the funnel becomes active and it acts as a mixer. At the center (10) it turns to right, but at periphery (11) it turns to left. ii. Invisible -Main link in 2D is total invisible. Because of the thread of link form difraction to the light waves, this link does not reflect light waves and it is invisible. It is a model of so called "Black energy" -Feedback in 2D is invisible.Because of primary cross vortices emitted from decelerating particle (1) to accelerating particle (2) are commensurable with waves of light , they do not reflect the waves of light. They are the model of so called "Black matter". -Main link in 3D is total invisible too, because of the thread of link form difraction to the light waves too. -Feedback in 3D is invisible too . Because of primary longitudinal vortices emitted from accelerating longitudinal funnel (4) of decelerating particle (1) to the decelerating funnel (10) of accelerating particle (2) are proportional to diameter with waves of light , they do not reflect the waves of light. iii.

Conclusion
We see that there are many more invisible objects (95%) and very few actually (only two) visible objects (5%). in first quadrant is center in accelerating cross vortex (2), but in second-is center in decelerating cross vortex (1)(Law 5, Law 6), (Figure 6).
h) Some explanation of particle charge as direction and size of the acceleration -The direction (inward or outward)of cross vortex determines the charge (negative or positive) of cross objects. When direction is from out to in (1) -the" charge" is negative (E2D-)). When direction is from in to out (2) -the" charge" is positive (E2D+) (Figure 6). -The stationary mode describes creation of objects, but pulsating mode explains their work in time and pulsating and transmitting transverse waves at the speed of light. -It explains the cause for mass increasing of an elementary particle, described in Theory of Relativity of Einstein and confirmed by the experiment. For example an electron that moves at the speed of light, increases its mass (Law5, Law 6). The reason is in structure of electron as an vortex from outside to inside(1, Figure 6). When electron is not connected to the proton, it is in free form. The cross vortex of electron sucks inward the free primary vortices. The higher the speed -the more primary vortices are sucked in and are glued to the electron.

j) Some explanation of Gravity field
Gravity field participates in a stationary structure in the tube (at the entrance or at the exit) of Gravity funnel that generates the cross part of object. Gravity field participates and in a pulsating structure as a wrap around the object.  Geometry of Space (3 + 1) The tasks of GR mechanics can be divided into several levels: the cosmos as a whole, a galaxy, a binary star, and the last one is a point particle in a gravitational field, the scale of which is much larger than the size of the particle, and the particle's own field is much weaker than the external one. So you can consider a planet in the field of a star and a small body in the field of a planet. At each level, it can be assumed that the gravitational field is created by an object of a higher level and it can be considered stationary in those periods of time that are considered. Particle kinematics ˗ the simplest problem of mechanics ˗ describes the inertial world line of a point particle in the absence of any external force. For this, the differential geometry of the four-dimensional space-time is used, which takes into account the difference in the properties of time and space. The main features of this type of space follow from the formulation of the physical problem [1], but then the geometry is constructed purely mathematically. Consider the four-dimensional Euclidean space as the initial concept for describing the physical space-time. In some coordinate system, given by the starting point and four non-collinear axes, each point in space corresponds to four numbers ( ) The tangents to these lines are linearly independent and form a local frame. Any vector drawn from the point M can be decomposed with respect to this frame. Now the same Euclidean space is described in curvilinear coordinates. The transition to curvilinear coordinates is unambiguous and reversible. This is due to the fact that the Euclidean space is affine. In addition, in the geometry of the physical space-time, three spatial coordinates must be equivalent, and the time coordinate must differ in special properties. Therefore, we will call such a space not four-dimensional, but the space (3 + 1). Special Theory of Relativity (SR) is not described in four-dimensional Euclidean space, but in (3+1) Minkowski space, which is called "index one pseudo-Euclidean space". In this space, the time coordinate is a purely imaginary number. This made it possible to simply describe all the differences between the mechanics of the SR and classical mechanics. But with such a choice of one of the coordinate axes, the transition to curvilinear coordinates described above would lead to the fact that all coordinates i x′ become complex numbers and the selection of the time coordinate disappears.
The properties of the space (3+1) can be described by the properties of the metric tensor of this space. This possibility has long been used in describing the kinematics of the GR, but in well-known monographs Abstract-It is accepted that three-dimensional physical space is a hypersurface with a Riemannian metric in four-dimensional space. The metric tensor of this three-dimensional space is defined by Einstein's equations. Another coordinate of fourdimensional space is time. In this space, the equations of the world line of a particle with a mass m are defined under certain initial conditions: the starting point of the space and the vector of the particle's initial velocity. This approach removes all the problems and contradictions noted in the monograph [1], and the resulting equations adequately describe, for example, the curvilinear motion of planets without energy change.
Keywords: general theory of relativity, metric tensor, hypersurface, Riemannian geometry, geodesic line, gravitational field, equations of motion. espite its long history and the work of outstanding physicists, the general theory of relativity still contains a number of fundamental contradictions and unresolved issues. Attention is drawn to them in the monograph [1] in the chapters on the General Theory of Relativity (GR), which "is perhaps the most beautiful of all existing physical theories." In this work, we will show that all these problems are removed if, from the very beginning, changes are made to the mathematical definition of the properties of space, in which the GRelativity is described. As a sign that this is not a four-dimensional space, all of whose axes are mathematically the same, let's call it "space (3 + 1)".  1, 2, 3). The metric tensor G is a rank 4 symmetric non-singular matrix whose components generally depend on the coordinates. Like any real symmetric non-singular matrix, the metric tensor at each point in space can be reduced to a diagonal form, that is, there is such a real non-singular matrix D that the matrix diagonal (this is indicated by a bar over the matrix character). If the components of the metric tensor depend on the coordinates, then its diagonal components also depend on the coordinates. The matrix can also be reduced to a diagonal form by introducing a rectilinear orthogonal coordinate system at the selected point, which is called Galilean. Such a transformation reveals properties that are important for what follows. At the origin, located at a chosen point in space, generally speaking, inhomogeneous, the metric tensor will be exactly diagonal, as in the case of an algebraic transformation of the matrix but for small deviations from the origin, the off-diagonal components will be of the second order of smallness in deviations. If the space is Euclidean, then the metric tensor does not depend on the coordinates and can be reduced to a diagonal form by introducing Galilean coordinates throughout the space.
The matrix D or orientation of the Galilean coordinates frame can be chosen in an infinite number of ways. In this case, the metric tensor of the space (3+1) SR always has the form {see [1] formula (6.5)}:

Kinematics and Dynamics of a Particle in Gravitation Field
Further we will denote the metric tensor G and its components ij g .
Let us describe the difference in the physical meaning of the zero row and the remaining three rows of the metric tensor matrix. The theory should describe not the trajectory of a particle in three-dimensional space, Let us establish the rule that if the matrix is diagonal, then the rows whose diagonal element is positive are located in the upper part of the matrix. This rule was introduced in the monograph [1] and is called the signature. In the described case, the diagonal element is positive in the top row, and are negative in the remaining rows. This defines an important property of the space: a sequence of signs in an invariant quadratic form that describe the curve arc differential: The main axiom of the GR: in a gravitational field, it is possible to bring the metric tensor to a diagonal form only locally at each point in space. This geometry is called Riemannian geometry. The fundamental Einstein equation relates the curvature of space to the distribution and movement of mass in space. We consider a stationary gravitational field. Therefore, the energy-momentum tensor does not depend on time, and the zero value of the indices does not make sense. The geometry of three-dimensional space is determined by the Einstein equations, in which the indices take only the values 1, 2, 3. Here the constant k is the gravitational constant, αβ T are components of the energymomentum tensor of the mass that creates the gravitational field, the Ricci tensor R and its convolution R (scalar curvature) are expressed in terms of the metric tensor of three-dimensional space and its derivatives with respect to coordinates. If the space is flat, then the Ricci tensor is identically equal to zero. − + + +   g g g g g g g g g g g g g g g g g g g g g g g g Then, obviously, the energy-momentum tensor is also equal to zero. The converse is also true: if the energymomentum tensor is identically equal to zero, then the space is flat, i.e., Euclidean. Einstein's equations define the matrix of the metric tensor of the three-dimensional Riemannian This matrix must be cell-diagonal. This means that three-dimensional space is a hypersurface in fourdimensional space on which a Riemannian metric is defined.
This definition of the metric tensor in (3+1) space is the main new mathematical proposition in this paper. Further, we will show that if it is accepted, the entire further theory of the motion of a particle in a gravitational field is built logically sequentially. All the problems noted but not resolved in the monograph [1] disappear, and the limiting transition to the special theory of relativity becomes clear. In [1] the metric tensor of three-dimensional space was also introduced, but it was obtained as a result of a thought experiment, which is incorrect for geometry. As a result the formula expressing its components in terms of the components of the metric tensor of the four-dimensional space is incorrect. The identity 0 0 α ≡ g means that all components in this row and column, except for the diagonal one, are equal to zero; ( ) 00 = r g g is a scalar function of spatial coordinates. The coordinate r is a three-dimensional space vector; in contrast to 4-vectors, we will denote them by small letters. Let's move on to Galilean coordinates at a fixed spatial point r and reduce to diagonal form the matrix ( ) r G . To reduce to diagonal form a cell matrix of the fourth rank, it is necessary to reduce to diagonal form only the matrix of the third rank ( ) µν r g . The metric tensor of three-dimensional space defines by Einstein's equation (2.5) for three-dimensional space. This is a matrix of the third rank with components We will not present differential geometry. It is described in sufficient detail in the monograph [1]: §83, §85, §86. We give only some definitions and formulas necessary for further presentation. The space (3+1) is a special case of a fourdimensional space with a metric tensor defined by us. Therefore, general concepts and formulas can be used, taking into account formula (2.9). The curve in the space (3+1) is generally given in the form The general definition of a geodesic line is a line whose tangents are parallel at any point. In addition, the length of the tangent segment, given at one, arbitrarily chosen point, is preserved in the Riemannian space. Through any point in space in any direction it is possible to draw a geodesic and only one. In different sources, you can find different definitions of the equations of a geodesic line. Usually they are represented as the equality to zero of the sum of the derivative of the corresponding component of the vector U along the length of the arc and the term proportional to the connection coefficient, which is determined by a linear combination of the derivatives of the metric tensor with respect to the coordinates.
For our purposes, it is more convenient to use the form of differential equations of a geodesic line presented in the monograph [2]: Since we know the diagonal form of the matrix in this equality, using this, we get:

III.
Kinematics and Dynamics of a Particle in Space (3+1) The main task of mechanics in the macrocosm is to determine the world lines of particles in various conditions. In pseudo-Euclidean space, in the absence of forces, it is always a straight line, determined by the initial conditions: the starting point and the velocity vector. This is formulated in Newton's first law -the law of inertia: "A particle maintains a state of rest or uniform, rectilinear motion until an external force acts on it." In the Riemannian space in this law, only the words "... uniform, rectilinear ..." should be replaced by "... movement at a constant speed." In Euclidean space, these expressions are equivalent, the velocity vector can be moved along a straight line. In a Riemannian space, the parallel translation of a tangent vector from a certain starting point occurs along a geodesic line.
Let us pass in equations (2.13) from geometric quantities to physical ones, that is, observable, measurable and having dimensions. This is a system of four equations that differ only in the index value. But in the space (3 + 1), the equation for the time axis ( 0 i = ) has some differences due to the fact that the function ( ) ( ) g t r depends on time only through the dependence of coordinates on time, i.e. due to the motion of the particle. Then we get: On the right side of the equalities, we pass to differentiation with respect to time using formulas (2.11).
We obtain equations expressed in terms of coordinates and time: Here, as in formulas (2.11), v dx dt is a kinetic energy. If we multiply the equations by тс, where т is the mass of the particle, then the function ( ) mcg r plays the role of a potential.
Then it follows from equations a) and b) that in threedimensional space the gravitational force is perpendicular to the velocity. Therefore, this potential affects the form of the trajectory, but does not change the velocity modulus, that is, the kinetic energy. This is a well-known natural phenomenon: under the influence of gravity, planets move in closed orbits without changing their kinetic energy. In our theory, this happened due to the fact that it was accepted ( ) ( ) 00 . g = r r g Equations expressed in terms of impulses are written in line c). As is known (see [1]), kinetic energy can be expressed in terms of spatial impulses and rest energy. This function is called the Hamiltonian function This is the law of conservation of energy in a gravitational field. The remaining three equations describe Newton's second law: acceleration is proportional to the acting force.
The monograph [3] formulates the rules for projecting a Riemannian space onto a flat one. With this transformation, the geodesic line becomes a straight line. This is obvious, since the defining property of a geodesic is the constancy of direction.

Kinematics and Dynamics of a Particle in Gravitation Field
In the monograph [1] in the footnote to § 85: "It can be shown that by a suitable choice of the coordinate system it is possible to achieve the vanishing of all connection coefficients not only at one point, but also throughout the given world line." (The proof of this statement can be found in P. K. Rashevsky's book "Riemannian Geometry and Tensor Analysis". Nauka, (1964), §91.)". The solution of the above specific problem is a special case of the theorem proved in the monograph [3], therefore, using this theorem, one can consider the problem of the combined action of gravitational and electromagnetic fields.
The equations of motion of a particle in a gravitational field are obtained by sequentially taking into account the position that the physical fourdimensional space is a distinguished time axis and a three-dimensional hypersurface, the metric tensor of which is determined by the Einstein equations. This approach removes all the problems and contradictions noted in the monograph [1], and the resulting equations adequately describe, for example, the curvilinear motion of planets without energy loss.
Introduction limate change is one of the focus topics in the world [1]. On the one hand, NASA scientists (NASA 2009) [2] found that fast-flowing Glaciers and thin Greenland and Antarctic ice sheets are accelerating. Which shows that the earth is being warming. On the other hand, cold wave, heavy snowfall, freeing temperature, with new-record sweeping Europe, North America, and East Asia have been reported in srtcles [3,4], news reports [5]. These reports query the earth warming.

Which one is correct? Or both are in-correct/correct?
What is the criterion for judging the climate of Earth to be warmer or colder?
II. The Criterion for Judging the Climate of Earth to be Warmer or Colder Here, the "(Average) Earth's radian temperature T" is used as the criterion for judging the climate to be warmer or colder, based on reflecting the global factors of Earth's climate. It differs from that criteria based on local factors, such as local Glaciers, local temperature, local snowfall, etc. Where T is unknown, to be determined by the thermal radian equilibrium equation of Earth.

Energy Exchanging of Earth
The Earth is isolate on its orbit motion around the Sun. The energy exchanging of Earth through Thermal radiation. The thermal radiation on Earth determines climate warmer or colder.
A body emits radiation at a given temperature and frequency exactly as well as absorbs the same radiation. This was proved by Kirchhoff.
By Kirchhoff's law [6], the absorption of thermal radiation on Earth is equal to its emission. That means that the thermal radiation on Earth must be in an equilibrium state.

IV. The Study on Thermal Equilibrium is Transferred to the Study of Optimum Problem
The study on equilibrium state in mechanics often take placed to the study of some Principles, e.g., the Generalized Principles of Variation was used to mechanics [7]; the Principle of Minimum Potential Energy [8] was used to study static mantle density distribution, etc. Here, the study on the thermal radiation equilibrium of Earth is transferred to the study of an optimum problem.

T = F(T) = (min/max) T p(T).
(1) a) By Plank's law [9] , the emissivity ε is the function of (λ, T), Where λ=electromagnetic wavelenght, h=Plank's constant, c=speed of light, k=Boltzmann' sconstant, T=temperature of the radiator. For total wavelengths, improper integrating of (2) from 0 to infinity of radiation, we have Where the emissivity is the function only of T. There are many articles introducing S-B law [10] , etc. The S-B law, formulated by J. Stefan (1879) based on experiment and derived by L. Boltzmann (1884) based on thermal dynamic. It states that the total radiant heat power emitted from a surface is proportional to the fourth power of its absolute temperature. The S-B law gives: Where p=p(T)=the net radiant power per unit surface area of radiator. σ=Stefan's constant, σ = 5.6703 × 10 −8 ,watt/m 2 K 4 , K=absolute temperature, T= temperature of radiator, ε = ε(T)=emissivity.
c) Construction the thermal radian equilibrium equation of Earth = ( ) = ( / ) ( ). Let p=p(T) be an object functional of an optimum (min or max), then, the variation problem becomes: d) The necessary condition of the thermal radiation of Earth laying on an equilibrium state The thermal radiation laying on equilibrium, by (6), it must be: (6) is the necessary condition of an equilibrium state. The point at equilibrium is called a stationary point. (6) is expressed: Integrating both sides of (7), we have Where the integral constant C can be determined by the known condition between ε and T, that is: ε=1 (black body), T=0°K (black body), then, C=1 Then, we have (10) is called "emissivity formula".
Substituting (10) and (4) into (5), we have: That means operator F maps T into a constant. Or, F independents to temperature T. That is already shown in (6), the necessary condition of the thermal radiation of Earth laying on an equilibrium state.
e) The sufficient condition of the thermal radiation equilibrium of Earth to be an extreme point According to optimization theory [11]，the sufficient condition of an equilibrium state reaching to its extreme point depends on the sign of its higher order derivatives. By (4) and (10), we have By (4), we have Substituting (10), (12), (13) into (14), we have Similarly, we have d n F dT n = 0, (n = 1,2, … ∞) According to the third rule (p. 232 of [11]), (16) shows that no extreme point exists. The equilibrium is an indifferent equilibrium, neither stable, nor um-stable. The indifferent equilibrium holds for arbitrary temperature T.

VI. Discussion
Q=question, A=answer, Q1: There are many factors, influent climate of Earth, such as: Forest fire, heat energy emitted from inside of the Earth via earthquake [12][13][14][15][16], and volcano, and human activity caused density of CO 2 increasing, etc. Do these factors causing the Earth's radian temperature T going up? A1: Do not worry about hat. If the emissivity ε changingand causing T increasing, then, by the S-B law, more heat energy. With four power shall emitted to the space and keeps T unchanged.

Highlights:
• Energy release of Earthquake proportions to square of velocity of Earth rotation; • Earthquake happens in pulse-mode, the releasing energy storages in fasten rotation of Earth. Once the velocity of rotation of Earth returned to normal, the storage energy transfers to kinetic energy and disaster happening. People should get out from dangerous zone before the rotating velocity returned to normal. 3, On Earth Science[8 23 24], Highlight of series studies on "static mantle density distribution 1, equation, 2, solution, 3, application": • Why the Tibet-Qinghai high-land rising up? Why earthquakes happen frequently at the belt (about 35°of south & north latitudes)? The study of three papers found that the static mantle density distributes in "X-types", where the un-continuity of masses locates at the turning point of "X" (about 35°of south & north latitudes). Earthquakes happen frequently at this belt and the Tibet-Qinghai highland raising up can be viewed as supporting to the study.

VII. Conclusion
The thermal radian equilibrium equation of Earth is an indifferent equilibrium, neither stable, nor un-stable. Any temperature T satisfies the necessary condition, while does not satisfy the sufficient condition of an extreme point. Therefore, It has no unit solution T. Introduction ince1905, scientists has tried to collect dew to obtain water, using the so-called Ziboldcondensers [1][2][3]. Recently, many studies concerning natural condensation of water vapor are oriented towards agriculture (plants and animals), the source of drinking water and the study of the soil cooling [4][5][6][7][8].Dew is a type of precipitation where water molecules droplets form on the ground, which is usually not explicitly considered in hydrologic cycle, because the amounts are small. However, in semiarid and arid regions harvesting dew can reach or even exceed all other forms of precipitation for extended periods or indeed a whole year. Water scarcity well becomes especially severe in many countries of Africa (South Morocco, Senegal, Mali, etc). One possible solution lies in alternative water sources, such as nocturnal radiative cooling. Dew formation is the result of nocturnal radiation. Practically, Dew is a natural phenomenon that occurs under particular meteorological conditions and on a dew plate condenser with high radiative cooling properties specially designed for this purpose. Dew forms when the temperature of a surface (collector sheet or dew condenser) cools below the dew point temperature (T d ) of the surrounding air so that water vapor contained in this air condenses on the collector sheets. The cooling effect of a collector sheet is caused by a radiation loss. The importance of water vapor as a reservoir of heat can be seen by comparing the daily temperature ranges of a semi-arid environment to that of a humid area. Semi-arid and humid environments may heat up in the same manner during the day but, due to the relative absence of water molecules and dioxide the carbon to absorb and hold the heat energy, the semiarid region cools down much more at night than the humid region. How much it cools down depends on the meteorological data.
We attempt to create an efficient and cheap dew plate condenser has not yet been exploited. In this modeling study we focus on the harvesting dew onto lawsonite radiant mineral as a dew condenser, and investigate the potential for its collection. The planar dew condenser was set at an angle of 30° with respect to horizontal. Numerical simulations using the energy balance equation to identify the meteorological factors which determine the degree of cooling, and to assess their effect on harvesting dew were performed. These meteorological parameters were found to be ambient temperature (T amb ), cloud cover (N), wind speed (V w ), soil heat flux (G), and relative humidity (Hr). The temperature of the collector sheets (Ts) dew forms on is also important. The impact of water vapor on soil is important in arid or semi-arid environments.

a) Sample description and characterization
Lawsonite,CaAl 2 Si 2 O 7 (OH) 2 •H 2 O),is one of the key mineral used as an indicator of high-P and low-Z metamorphic environments like blueschists-facies metabasalts and metagreywackes [9][10]. Lawsonite can occur as isolated needle-like crystals, aggregates displaying a radiating pattern, or as tabular crystals. The structure, which contains both discretehydroxyl groups (OH) and H 2 O molecule, was first solved by Wickman [11].In addition to Si 2 O 7 groups, lawsonite contain also the SiO 4 unit. At ambient conditions, lawsonite is orthorhombic with space group 2ℎ 16 and the following designation of crystallographic axes has been adopted: a = 8.795 Å, b = 5.847 Å, c =13.142 Å. The structure consists of chains of edge sharing Al-O octahedra and which are linked by Si2O7 groups. The non-centred primitive unit cell (spectroscopic cell) is half as large and contains 38 atoms; hence, there are a total of 114 vibration modes at the centre of the Brillouin zone [12][13].A knowledge of atomic positions and symmetries leads to the following irreduciblere presentation of the 114 modes: Γ = 16 + 11 1 + 16 2 + 8 3 ( = 51 ) + 11 ( ) +18 1 + 13 2 + 18 3 ( = 49 )+1 1 + 1 2 + 1 3 ( ) It is assumed that the Si 2 O 7 polyhedra, OH and H 2 O groups are preserved as distinct structural units. The site symmetry of both Si 2 O 7 and water molecules H 2 O within lawsonite is mm (C 2v ) and that of hydroxyl groups OH is m (C s ). Labotka and Rossman [12] have assigned the bands of the vibrations of OH and H 2 O in lawsonite. The stretching motions of Si 2 O 7 polyhedra were assigned by Hofmeister et al [13].The stretching vibrations of one Si 2 O 7 unit can be divided into the vibrations of SiO 3 and the vibrations of Si-O-Si bridges [14].
Bending of water ( 2 )Stretching symmetric ( 2 )Stretching antisymmetric As shown in Fig. 1, we have presented the different vibrational modes stretching of natural lawsonite calculated by PM3 semi-empirical method. At most wavelengths, the atmospheric downward radiation is fairly similar to the energy flux emitted by a soil at the ambient temperature. However, this is not true for wavelengths between 769 and 1250 cm -1 (8-13 µm) where the atmosphere is partly transparent provided that the humidity is low. The transmittance in the wavelength region 769-1250 cm -1 , the "atmospheric window", is during the night responsible for the radiative cooling phenomenon of infrared (IR) emitting dew condensers. Harvesting dew occurs because the radiation emitted by a dew plate condenser at ambient temperature is not balanced by the atmospheric downward radiation. By exploiting this window (769-1250 cm -1 ) one can cool a dew condenser on the Earth's surface by radiating its heat (radiative mechanism) away into cold outer space. Therefore, we remark that the lawsonite as dew condenser presented seven absorption bands in the 769-1250 cm -1 region due to vibrational behavior of Si 2 O 7 structural group. The higher emissivity of lawsonite as dew condenser in the atmospheric window involves its higher rate of cooling by radiation [15]. In Table 1 are report summary Raman and IR vibration modes of natural lawsonite in the atmospheric window 769-1250 cm -1 .

b) Dew model description
The dew plate condenser in our model is an inclined collector sheet of natural lawsonite mineral (Fig.2) Table 2: Some parameters used in dew model [15] [16][17][18][19][20]. The heat energy balance as given by the following equation: where , and are the dew condenser's temperature, mass and specific heat capacity, respectively. The dew condenser's mass is given by = , where , and are its density, surface area (square meter) and thickness (see Table 1). and are the specific heat capacity and mass of water, representing the cumulative mass of dew water that has condensed onto the collector sheet (Fig. 2).
, , and describe the powers involved in the heat exchange processes. The radiation term, is given by where and are the incoming thermal infrared radiation flux from the atmosphere and the outgoing radiative power from the dew condenser, respectively. and are the condenser and the sky emissivity. Returning to Eq. (1), the term describes the conductive heat exchange between the dew condenser surface and the ground (blackbody). We assume perfect insulation; the conductive heat exchange is negligible.
The convective heat-exchange term , is given by: where is the ambient air temperature and is the heat transfer coefficient [21].
is the specific latent heat of condensation for water For the rate of condensation, we can write a mass balance equation by the following relationship: ( ) > ( ) ; If not = 0 α m is the mass transfer coefficient. P sat (T d ) is the saturation pressure at the dew point temperature.

Results and Discussion
The average of relative humidity (R H ) in the Mirleft region is about 80.6% for dry season but reaches 5% for the wet season. In table, 4 we present the key statistics of the daily average of the day and night average, maxima and minima [22]. Dew water is influenced by ambient temperature , dew temperature , dew condenser temperature and other metrological factors. Cumulative dew was calculated hourly for 12 h period (per night) as a function of temperature dew condenser is shown in Fig. 3. It shows that the effect of dew plate condenser temperature ( ) on dew formation ( ) per night is linear for all parameters combination employed. Fig.3 illustrates also that dew formation declines linearly with dew condenser temperature. The amount of condensed water obtained varied from 0.56 to 1.67 L/m 2 per night as a function of dew condenser temperature . For the given dew condenser, creating an imbalance between the incoming thermal radiation from the sun and the outgoing thermal radiation from the surface dew condenser through the transparency window (8-13µm), is key to achieving dew condensation. The algorithm imposes an approximate relation condition, with T a and T d , provides a reasonable estimation of dew occurrence [24][25]: This condition cannot be used to estimate the cumulative dew; however; it can give a good estimation of its occurrence. Condition (7) can be expressed as a condition on relative humidity ( − corresponds to relative humidity [25]) and condensation occurrence whenthe temperature of the dew condenser ( ) is below the dew point temperature ( ).  Table 5: The wind speed data during the dry and wet seasons [23].  [23]. Figure 4 illustrates the sensitivity of the modelled dew formation to changes in the dew condenser thickness at different values of dew condenser temperature. The effect of dew condenser temperature is more complex: increasing the dew condenser temperature reduces the collected dew, whereas decreasing the dew condenser temperature increases convective heating. Collected dew declines linearly with dew condenser thickness. It has a big influence on collected dew for both cases: decreases or increases.   Figure 5 shows that the effect of wind speed on dew formation is non-linear. The effect of wind speed on dew formation (Fig. 5) is more complicated that of the dew condenser thickness and dew condenser temperature parameters just discussed above. Beysens et al found that the wind speed of 0 m s -1 is the threshold for dew occurrence [25]. However, Monteith found that the dew formation is negligible when the wind speed drops below 0.5m s -1 , and that the dew formation increases when wind speed is 2-3m s -1 [26]. We observe that collected dew increases with wind speed up to a certain value of V=3 m s -1 and then decreases again. Similarly, the wind speed of 0.5m s -1 is the threshold for dew occurrence.

Conclusion
The numerical simulations for dew formation on lawsonite collector sheet were investigated by implementing a dew collection model bases on solving the energy balance equations. We show that dew collection yield depends on several meteorological factors such as relative humidity, cloud cover and wind speed. On the other hand, we observe that dew collection yield depends also on the dew condenser thickness and dew condenser temperature. The result obtained is that the lawsonite sheet condenser collected between 0.5 and 0.165L/m 2 /night of water. The lawsonite thin film has high emissivity across 8-13µm; which indicates that it can be used as good radiative cooling and dew water condenser mineral. Further experiments and numerical simulations are required for new minerals that can increase dew collection yields.  The Essence of Frictional Heat Generation hen we were young, we often played the game of smashing sparks at night, that is, smashing the small stone in our hand on the big stone, you will find that if there is sliding, the spark will be very small, and the spark will be when it touches will be great. This is in great contradiction with the theory of frictional heat generation that we have learned. Is there any other explanation? The current popular explanation, the energy transformation of objects. If we must understand in this way, we will further consider how these energies are converted from kinetic energy to heat energy of molecular motion.
To talk about the essence of frictional heat generation, we must first talk about the essence of friction. The relative motion of two objects forms friction. From a macro perspective, the relative motion of two objects is the relative displacement of the two contact surfaces. From the perspective of microscopic particles, it is the relative displacement of the two particle clusters. The contact surface of the two particle clusters has obvious unevenness, and friction is the mutual collision of the convex parts of the contact surface. And the essence of the collision, we can infer that it is the pressure generated by the particles in the contact part. It can be considered that the essence of friction is: the pressure generated by the collision between the particles of the convex parts of the two relative motion contact surfaces. From the point of view of weak gas pressure, the molecular kinetic energy is increased, the molecular oscillation is intensified, and the radiation energy is increased. From the perspective of highintensity pressure, just like the principle of proton collider, proton collision produces the same effect of splitting, resulting in great atomic splitting and releasing a lot of energy. Therefore, the heat generated by friction is generated by the strong pressure between the contact parts. When the pressure is strong, the particle structure can be broken and changed, resulting in breaking excitation, thereby releasing a large amount of energy.
From the calculation point of view, the frictional heat generation Q, is proportional to the contact surface pressure, P and speed V. It can be seen from this that pressure plays a decisive role in frictional heat generation. The pressure formula for the collision of moving objects, p=mv/st. m is the mass, V is the decrement in velocity, s is the contact area, and t is the action time.
Substituting the data in can calculate the pressure at the touch. This formula extends to collisions between small particles and can be transformed into p=mv 2 /r 2 . V is the velocity and r is the particle radius.
Why, when there is a lot of stress, energy is generated? This is the scope of solid-state physics research. Strictly speaking, I don't know. I only talk about my own feeling and understanding. 'We know that there are a large number of highspeed moving electrons around each atomic nucleus. Although two relatively stationary objects are stationary when viewed as a whole, they still have high-speed electrons at the level of the atoms in the contact surface and relative motion. As long as the pressure is large enough to make the two particles come into close contact with each other, breaking the respective laws of motion of electrons around their nuclei, the particle structure will change, resulting in mass-energy conversion to release energy. This is the essence of frictional heat generation.
We know that there is a large space around the nucleus, and there is a magnetic field generated by the movement of electrons. When the pressure on the material is greater than the binding energy, the normal feeling is that the object begins to change in shape or diffuse and slide around. But what happens if there is no room for activity? Let us boldly imagine that matter begins to compress space. At first, it compresses the circulation space of magnetic field lines around the nucleus. The magnetic cycle of a single atom cannot be completed, and the large cycle of the magnetic field of matter is forcibly completed, and the magnetic energy is collectively released to the outside, forming external magnetism. In the past, matter had no magnetism, because individual particles had their own magnetic cycles and exhibited random magnetism to the outside world, so there was no magnetism. Under the action of pressure, the magnetism is concentrated and released in a concentrated direction, so it appears magnetic to the outside. This is the principle of the formation of Author: e-mail: 1242604176@qq.com W magnetism, and the magnetism of geomagnetism and stars is formed in this way. This is my reasoned understanding of the formation of the Earth's magnetic field, and I hope you can refer to it.
Under the pressure of the magnetic cycle, the pressure continues to increase, and the electron circulation around the nucleus is blocked. In order to achieve the cycle, the atom releases a part of the energy ions to keep itself intact. Due to the release of heat energy, the object begins to heat up, and as the pressure continues to increase, the material slowly liquefies, then vaporizes, and finally completes ionization. Continuing, the ions begin to decompose. First, the large ions are decomposed into small ions, and the small ions continue to decompose into a soup composed of protons, neutrons, and quarks. Finally, the quantization is completely decomposed, and the energy generation process of a star is completed. The reaction of protons in the ion soup of proton quarks is the pattern in the proton collider. The ions collide with each other and break apart, forming smaller ions.
Triboelectricity is a phenomenon we all know, and the phenomenon of stone tip sparks shows that there is an ultra-high temperature energy release process at the stone tip. The power of one person completes the spark of the stone tip, the power of the earth's plates, produces a volcanic eruption, and the power of the earth has geothermal heat. This is what I know about the source of the earth's heat.

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