Simetries in physics and mathematicsVersión 1

Is about the chirst milacres and physics mathematics and chemistry, equalties between formulas ,i also add some articles that were not accepted in physics reviews and oxford papers online for mathematics, in england

Jose luis Armenta becerra22/08/2013

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Index

1.- variational principle in cilindrics coordinates ..................................5,6

2.- arquimedes plasma.................................................................7,8

3.- debroglie wave and the paralels moments...........................................9

4.-Sparalell exponential series of spin ..............................................10

5.-Taylor serie integral form.........................................................11

6.-lenght diferential and proyections ................................................12

7.-delta de dirac delta and the relation with inertia tensor..........................13

8.-period inverse and the angular velocity............................................14

9.-gradient and the relations with top polarizated waves..............................15

10.- matemathics angles and south hemisphere...........................................16

11.-a falting constant need to check the volume of a sphere in the drop liquid model..17

12.-drop liquid model and the term sen as it need to be...............................18

13.-trinomium squared perfect and the klein gordon equation...........................19

14.-tridimensional box in a cilinder made by two particles............................20

15.-special frames of references in special relativity and the third angle............21

16.-cone light croise product.........................................................22

17.-euler poincare tetrahedron and teh quarks.........................................23

18.-trasquilation of a sheep and the third angle on special relativity................24

19.-hiperboloid of two sheets and the first and third term on the exponential.........25

20.-nabla.dl=1 by the function........................................................26

21.-Stokes theorem and the dreams of a schizo about me................................27

22.-poisson bracket and the end of the universe.......................................28

23.-a matrix is a space..............................................................29

24.-the apostrophe equal to the matrix A..............................................30

25.-constants directions on tropics of cancer and capricorn...........................31

333

26.-four particles made a brane.......................................................32

27.-nanohands made by nanotubes in medicine...........................................33

28.-the correct form of serve a glass of water........................................34

29.-the quantum cookie................................................................35

30.-the laser sword...................................................................36

31.-the perpetual machine on the sun to prevent a brown darf..........................37,38

32.-endothermic process and an incress of inner energy................................39

33.-quantum onion and the aids vacumm.................................................40,41

34.-the capacitancy as a vector.......................................................42

35.-energy greater than mass..........................................................43

36.-endothermic process more available in earth suface................................44

37.-the armentanian notation..........................................................45

38.-all equations with 2 members is convergent........................................46

39.-the gradient for a tall people will be more slow than a short ....................47

40.-electrodynamic moment of inertia..................................................48

41.-fathers with acidity will have sons fat cause they need more food in less time....49

42.-linear transformation equal to alfa...............................................50

43.-laplace equation is 1 like the poisson is j.......................................51

44.-the fibered as 2 su(1)............................................................52

45.-the helmholtz free energy as function of vocals...................................53

46.-the gibbs free energy as function of consonants...................................54

47.-dual space and linear transformations.............................................55

48.-the sustituion of dl as product croice and ds as dot product......................56

49.-the pseudo eter dimensional.......................................................57

50.-2 terms z´2 in the drop liquid model..............................................58

51.-legendre polynmial 5 n and 3 x....................................................59

444

52.-covariant and contravariant in gauge theory.......................................60

53.-spin at the side made a pseudo brane..............................................61

54.-the both vector...................................................................62

55.-a refrigerator have condensators and evaporators..................................63

56.-quantum pins......................................................................64

57.-white holes and crist ascension...................................................65

58.-laplace transformation and gamma function.........................................66

59.-no univocal as the set 2 is greater in connections................................67

60.-univocal as set 1 is greater in connections.......................................68

61.-biunivocal as i=j.................................................................69

62.-kaluza same grade properties......................................................70

63.-binomial expansion and the bessel equation........................................71

64.-coulomb and biot savart similities................................................72

65.-clips magnetitaion as cars chaos..................................................73

66.-the hypercube have 2 wedges.......................................................74

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Variational principle in cilindrics coordenates:

A variational principle is a scientific principle used within the caculus of variations, which develops general methods for finding functions which minimize or maximize the value of quantities that depend upon those functions. For example, to answer this question: "What is the shape of a chain suspended at both ends?" we can use the variational principle that the shape must minimize the gravitational potential energy.

According to cornelius lanczos, any physical law which can be expressed as a variational principle describes an expression which is self adjuntion These expressions are also called hermitian. Such an expression describes an invariant under a Hermitian transformation.

Fleix klein's erlanged program attempted to identify such invariants under a group of transformations. In what is referred to in physics as noether theorem, the poincare group of transformations (what is now called a gauge group) for general relativity defines symmetries under a group of transformations which depend on a variational principle, or action principle

Cartesian coordinates

For the conversion between cylindrical and Cartesian coordinate co-ordinates, it is convenient to assume that the reference plane of the former is the Cartesian x–y plane (with equation z = 0), and the cylindrical axis is the Cartesian z axis. Then the z coordinate is the same in both systems, and the correspondence between cylindrical (ρ,φ) and Cartesian (x,y) are the same as for polar coordinates, namely

in one direction, and

in the other. The arcsin function is the inverse of the sine function, and is assumed to return an angle in the range [−π/2,+π/2] = [−90°,+90°]. These formulas yield an azimuth φ in the range [−90°,+270°].

Many modern programming languages provide a function that will compute the correct azimuth φ, in the range (−π, π], given x and y, without the need to perform a case analysis as above. For example, this function is called by atann (y,x) in the C programming language, and atan (y,x) in common lisp

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Were x is subtituided by the correspondent in cilindrical coordinates.

777

Archimedes plasma

is useful for a spachip who need a pseudo gravity

1.-Introduction. My idea cames with a conference in the semana xalapeña de física 2007 cause i see that turning one umbrela to the right or left will cause a archimedes spiral so i think inmediatly that a plasma of archimedes could give a motion of gravity in the edge of the spiral; So now we have to do the experiment

2.-Spiral equation for a slinky the equation give us a meter by second so we have to multiply this for 9.8? how will be the Hamiltonian? Were the kinetics energy is: K=1/2mv2 And the potential energy will be: U=mgh Were h means high and is given by the archimedes spiral: h=r We pass to polar coordenates X=rcos Y=rsen

3.-The lagrangian The lagrangian is given by:

L=T-V L=1/2mr 2-mg(a+b ) And the Hamiltonian will be given by:

H= ˙qP−L

Were the generalized coordinates are θ and r Are escleronomas not holonomas coordinates .

Were the generalizated momentum is P= ∂L∂ qWere q1= θ and q2= rThereby p1=-mgb θAnd p2= rClearing the velocity in p1: θ=-p1/mg Clearing the velocity in p2 p2=0 For the coordinate θH= Σθ Pθ=−Pθ

2 /mg-1/2mr2-mg(a+b )

888

Remembering the Hamilton equations:

∂h∂qi

=− pi

∂H∂ pi

=q i

∂H∂ t

=∂ L∂t =k

Solving: ∂H∂θ -mgb =- pθ∂H∂r =0= pr

∂ H∂ pθ

=-2 pθr

∂ H∂ pr

= pr

∂H∂ t

=∂ L∂t =o

4.-aplications Will give the centripetal acceleration a rectangular área of gravity like this:

999

Parallels moments in theory of wavelenght of debroglie

where is the wavelenght, is the plank constant, is the moementum, is the rest mass, is the velocity and is the speed of light in a vacuum.

A theory of moments will be if pi∁ pk

Were a moment belongs to another space of moments of dim n+1

101010

Exponential series and the parallel spins

The exponential function ex can be characterized in a variety of equivalent ways. In particular it may be defined by the following power series

As we can se one factor is positive the second factor is positive so all the factors are positive so all

are with the same spin to the right are positive like in a rect line

111111

Integral form of the taylor serie

The Taylor series of a real or complex valued function ƒ(x) that is infinite diferentiable at a real or comples number a is the power series

which can be written in the more compact sigma notation as

where n! denotes the factorial of n and ƒ (n)(a) denotes the nth derivative of ƒ evaluated at the point a. The derivative of order zero ƒ is defined to be ƒ itself and (x − a)0 and 0! are both defined to be 1. In the case that a = 0, the series is also called a Maclaurin series.

So if we put a limit when the summatory tends to infinite lim n→∞:

∫ (a) f n

n !(x-a)n

121212

Projection and length diferential

Were f is dl i mean the length diferential

131313

The inertia tensor and the relation with dirac delta

Let [R] be the skew symmetric matrix associated with the position vector R=(x, y, z), then the product in the inertia matrix becomes

were the principal diagonal tends to 1 in dirac delta

141414

angular velocity and the inverse of period

In two dimensions the angular velocity ω is given by

So ω=dpdϕ

151515

Top polarized waves and the relationship with a gradient

And the gradient is:

In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is that rate of increase. In simple terms, the variation in space of any quantity can be represented (e.g. graphically) by a slope. The gradient represents the steepness and direction of that slope.

A generalization of the gradient for functions on a euclidean space that have values in another Euclidean space is the jacobian. A further generalization for a function from one banach space to another is the frechet derivative.

161616

South hemisphere and the mathematical angles

In the south hemisphere turn from right to left as the angle in a cuadrant or a Euclidean plane

171717

Drop liquid model and the volume of a sphere

The semi-empirical mass formula states that the binding energy will take the following form:

If we put 3/4πr3 as the total volumen of that drop not exactly in the inner volume but ouside

181818

Sin in the semiempirical formula

The semi-empirical mass formula states that the binding energy will take the following form:

We need a sen as a new constant cause it will move like a wave:

191919

The klein –gordon equation and the perfect trynomy cuadratic

The Klein–Gordon equation is

Were m2

ħ2 c2ψ= Ax2

And by + c are the others characters for get Ax2+by+c

202020

Suitables particles in a squared box

If each beer is a cylinder made by two particles

We have to calculate the system

212121

Special frames of reference and the third angle

A third angle

Inertial frame second angle

Frame of reference first angle

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Croise product in the light cone

As we can see in the present line exist a croice product cause will

Give a new direction a worm hole

232323

Tetrahedron figure in euler Poincare and the quarks

As the quarks cames from 3 from 3 2 ups and 1 down or 2 downs and 1 up

The Euler characteristic was classically defined for the surfaces of polyhedra, according to the formula

where V, E, and F are respectively the numbers of vertices (corners),edges and faces in the given polyhedron. Any convex polyhedron's surface has Euler characteristic

This result is known as Euler's polyhedron formula or theorem. It corresponds to the Euler characteristic of the sphere (i.e. χ = 2), and applies identically to spherical polyhedral as this tetrahedron

242424

Trasquilation of a sheep and the third angle of special relativity

As we see the third angle opers see (page 15) under a third frame of reference

252525

The third and first term expanded is the hiperbolid of two sheets

The exponential function ex can be characterized in a variety of equivalent ways. In particular it may be defined by the following power series

And the hyperboloid is:

(hyperboloid of two sheets).

Figure of the hyperboloid of two sheets:

262626

The nabla dot diferential of length

∇ . dl=1

And this is multiplied by the function as well know before in any problem suitable

272727

The stokes theorem and the dreams

One dream= =

This classical Kelvin–Stokes theorem relates the suface intergal of the curl of a vector field F over a surface Σ in Euclidean three-space to the line integral of the vector field over its boundary ∂Σ:

282828

The poisson bracket and the end of the universe

In canonical coordinates (also known as darboux coordinates) on the space phase, given

two functions and , the Poisson bracket takes the form

The first member with respect to q is the end of a space and the second is the end of the moment

configuration later interchange p and q

292929

A matrix is a space

In mathematic, a space is a set with some added structure

Were the set are the vector column or vector raw and the structure are the brases as see below:

303030

Apostrophe and the matrix A

The result of a transformation: Tx = x′

Tx=A

313131

Tropics of cancer and Capricorn as constant directions

As well know are normal vectors n1 and n2

Were a normal vectos is:

323232

Four particles made a brane

Each particle in each corner will made a wall if we turn the wall we will see this:

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Nanohand made by nanotubes in medicine

This will be one finger we only need to made a palm and unite the five fingers

343434

The correct form to serve a glass of water

Were the half of the top cylinder is have to be the half to the bottom clinder half and half, half in x and half of y

353535

The quantum cookie

363636

The laser sword

Is a laser device with a upper right little wall of plome

373737

The perpetual machine transforming hydrogen into helium

If the device is absorbing electrons to moving to upward level will oxidize like in chemistry is say the beta desintegration is:

In β− decay, the weak interaction converts an atomic nucleus into a nucleus with one higher atomic number while emitting an electron (e-) and an electron antineutrino (νe):

A

ZN → A

Z+1N’ + e− + ν

e

where A and Z are the mass number and atomic number of the decaying nucleus.

383838

The device of that machine will be

393939

Endothermic process will gained the incressed of inner energy

In thermodynamics, the word endothermic describes a process or reaction in which the system absorbs energy from its surroundings in the form of heat. It is a modern coinage from Greek roots. The prefix endo- derives from the Greek word "endon" (ἔνδον) meaning "within," and the latter part of the word comes from the Greek word root "therm" (θερμ-) meaning "hot." The intended sense is that of a reaction that depends on taking in heat if it is to proceed. The opposite of an endothermic process is an exothermic process, one that releases, "gives out" energy in the form of heat. Thus in each term (endothermic & exothermic) the prefix refers to where heat goes as the reaction occurs. The term endothermic was coined by Marcellin Berthelot (25 October 1827 – 18 March 1907).

404040

Quantum onion and the aids vacumm

This is the quantum onion by an fullerene:

414141

and this is the aids cell:

As you can see have the same form so if we put a medicine inside the fullerene will disappear the virus

424242

Capacitance as a vector

Capacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. A common form of energy storage device is a parallel-plate capacitor. In a parallel plate capacitor, capacitance is directly proportional to the surface area of the conductor plates and inversely proportional to the separation distance between the plates. If the charges on the plates are +q and −q, and V gives the voltage between the plates, then the capacitance C is given by

If we have two charges will be :

c=q21

v2=q1−q2

v2

434343

energy greater than mass

As is noted above, two different definitions of mass have been used in special relativity, and also two different definitions of energy. The simple equation E = mc2 is not generally applicable to all these types of mass and energy, except in the special case that the total additive momentum is zero for the system under consideration. In such a case, which is always guaranteed when observing the system from either its center of mass frame or its center of momentum fram E = mc2 is always true for any type of mass and energy that are chosen. Thus, for example, in the center of mass frame, the total energy of an object or system is equal to its rest mass times c2, a useful equality. This is the relationship used for the container of gas in the previous example. It is not true in other reference frames where the center of mass is in motion. In these systems or for such an object, its total energy will depend on both its rest (or invariant) mass, and also its (total) momentum.

In inertial reference frames other than the rest frame or center of mass frame, the equation E = mc2 remains true if the energy is the relativistic energy and the mass the relativistic mass. It is also correct if the energy is the rest or invariant energy (also the minimum energy), and the mass is the rest mass, or the invariant mass. However, connection of the total or relativistic energy (Er) with the rest or invariant mass (m0) requires consideration of the system total momentum, in systems and reference frames where the total momentum has a non-zero value. The formula then required to connect the two different kinds of mass and energy, is the extended version of Einstein's equation, called the relativistic energy–momentum relation-

And of course if there are 1 factor in energy in the first member of , E = mc2 the second member is< E so the mass are lower than E and the velocity squared is <E the multiplication of both made the equalty

444444

Process endothermic more available in the earth

In thermodynamics, the word endothermic describes a process or reaction in which the system absorbs energy from its surroundings in the form of heat. It is a modern coinage from Greek roots. The prefix endo- derives from the Greek word "endon" (ἔνδον) meaning "within," and the latter part of the word comes from the Greek word root "therm" (θερμ-) meaning "hot." The intended sense is that of a reaction that depends on taking in heat if it is to proceed. The opposite of an endothermic process is an exothermic process, one that releases, "gives out" energy in the form of heat. Thus in each term (endothermic & exothermic) the prefix refers to where heat goes as the reaction occurs. The term endothermic was coined by marcellin bethelot (25 October 1827 – 18 March 1907).

Cause the surroundings give energy like in a asteroid collition

454545

The armentanian notation

For the first member the sign will be:

Ax+By+c=

for the second member:

=Dx+EY-+c

So jointed the both parts we have

=

for the functions is the same f(x)=

=g(x)

464646

Convergent series as 2 members equations

In matheatics, a series is the sum of the terms of a sequence of numbers.

Given a sequence  , the nth partial sum   is the sum of the first n terms of the sequence, that is,

A series is convergent if the sequence of its partial sums   converges; in other words, it approaches a given number. In more formal language, a series converges if there exists a limit   such that for any arbitrarily small positive number  , there is a large integer such that for all  ,

A series that is not convergent is said to be divergent.

As we can see 2 members is convergent 3 or more member is not convergent so is divergent

474747

The rotational will be more slow in a tall people than in a short

The gradient In the three-dimensional cartesian coordinates system this is given by

So f will be more complex in a tall people so is more longer and have more muscles so going down

a slope will make more slow the walk

484848

Moment of inertia electrodynamic

and define the moment of inertia relative to the center of mass IC as

Were in electrodinamic Δ ri is the distance rest r2-r1 were the first is the observator charge and the second proob charge

And m is the mass of the electron

494949

fathers with acidity will have sons fat cause they need more food in less time

Acids play important roles in the human body. The hydrochloric acid present in the stomach aids in digestion by breaking down large and complex food molecules. Amino acids are required for synthesis of proteins required for growth and repair of body tissues. Fatty acids are also required for growth and repair of body tissues. Nucleic acids are important for the manufacturing of DNA and RNA and transmitting of traits to offspring through genes. Carbonic acid is important for maintenance of pH equilibrium in the body.

505050

Linear transformation equal to alfa

Were the homogeneity is also alfa in the sum of the first chart

Let V and W be vector spaces over the same field K. A function f: V → W is said to be a linear map if for any two vectors x and y in V and any scalar α in K, the following two conditions are satisfied:

additivity

Homogeneity of degree 1

The Laplace equation is i like the poisson is j

In mathematics, Laplace's equation is a second-order partial diferential equation named after pierre simon laplace who first studied its properties. This is often written as:

The Poisson Equation is

where   is the laplace opertor, and f and φ are real or complex-valued functions on a manifold. When the manifold is euclidean space, the Laplace operator is often denoted as ∇2 and so Poisson's equation is frequently written as

515151

525252

The fibered as two manifolds su(1)

Were E is one SU(1) and B will be the other

In diferential geometry in the category of differentiable manifolds, a fibered manifold is

a surjective submersion   i.e. a surjective differentiable mapping   such

that at each point   the tangent mapping   is surjective (equivalently its rank equals dim B).

535353

Helmholtz free energy and A(U)

Is the function of intern energy

The Helmholtz energy is defined as:

where

A  is the Helmholtz free energy (SI joules, CGS: ergs), U  is the internal energy of the system (SI: joules, CGS: ergs), T  is the absolute temperature (kelvins), S  is the entropy (SI: joules per kelvin, CGS: ergs per kelvin).

The Helmholtz energy is the legendre transformation of the internal energy, U, in which temperature replaces entropy as the independent variable.

This mean is the vocals formula A(U)

545454

Gibbs free energy as function of enthalpy

for a possible process. Let the change ΔG in Gibbs free energy be defined as

 

G(h) this mean the consonats are in this formula

555555

Dual space and transformation linear

one transformation linear is:

Let V and W be vector spaces over the same field K. A function f: V → W is said to be a linear map if for any two vectors x and y in V and any scalar α in K, the following two conditions are satisfied:

additivity

homogeneity of degree 1

This is equivalent to requiring the same for any linear combination of vect

And one dual space is:

Given any vector space V over a field F, the dual space V* is defined as the set of all linear mapsφ: V → F (linear functionals). The dual space V*itself becomes a vector space over F when equipped with the following addition and scalar multiplication:

for all φ, ψ ∈ V*, x ∈ V, and a ∈ F. Elements of the algebraic dual space V* are sometimes called covectors or one-forms

565656

dl and croice product and dot product as ds

Now is:

Now the dot product:

Is equal to:

575757

The pseudo eter dimensional as antipology and radiation

Topology has many subfields.

Point-set topology establishes the foundational aspects of topology and investigates concepts inherent to topological spaces (examples include compactness and connecteds).

Algebraic topology tries to measure degrees of connectivity using algebraic constructs such as homology and homotropy groups.

Geometric topology primarily studies manifolds and their embeddings (placements) in other manifolds. A particularly active area is low dimensional topology, which studies manifolds of four or fewer dimensions.

585858

There is only 2 terms z squared in the drop liquid model

Is the third and fourth element

595959

Five n´s and 3 x in the legendre polynomial

In mathematics, Legendre functions are solutions to Legendre's differential equation:

606060

Gauge theory is a covariant and a contravariant

Noether theorem implies that invariance under this group of transformations leads to the conservation of the currents

616161

The spin at a side and the pseudo brane

Will made wall if the spin go to right righter will appear a side of the brane or the left more to

left after dl will appear a brane

626262

The both vector

f(x) g(x)

636363

a refrigerator have condensers and evaporators

646464

Quantum pins

For holds magnetic camps is no optical pinzes

656565

White holes and crist ascension

A white hole, in general relativity, is a hypothetical region of space time which cannot be entered from the outside, but from which matter and light have the ability to escape. In this sense, it is the reverse of a black hole, which can be entered from the outside, but from which nothing, including light, has the ability to escape. White holes appear in the theory of eternal black holes. In addition to a black hole region in the future, such a solution of the Einstein field equations has a white hole region in its past. However, this region does not exist for black holes that have formed through gravitational collapse, nor are there any known physical processes through which a white hole could be formed.

666666

Gamma function and laplace transformed

The gamma function is defined for all complex numbers except the negative integers and zero. For complex numbers with a positive real part, it is defined via an impropel integral that converges:

If we change t by st we have:

The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), defined by:

The parameter s is a complex numbers

Were f (t) is tz-1

676767

No univocal as set 2 greater in connections:

686868

Univocal as set 1 are greater in connections

696969

Biunivocal as i=j

If set 1=I and set2 =j we have:

707070

Kaluza same grade properties

Were mxc is one grade and m is from the same grade

717171

Bessel and theorem of binomial

Bessel functions, first defined by the mathematician Daniel bernoulli and generalized by Friedrich bessel, are the canonical solutions y(x) of Bessel' diferenttial equation

The third term and the first member of expantion binomial

For natural numbers (taken to include 0) n and k, the binomial coefficient   can be defined as the coefficient of the monomial Xk in the expansion of (1 + X)n. The same coefficient also occurs (if k ≤ n) in the binomial formula

727272

Biot and savart law and coulumb law similities

The biot savart is:

Were the therm inside the integral is have the same vectors r like in the coulomb law

Coulomb's law can also be stated as a simple mathematical expression. The scalar and vector forms of the mathematical equation are

   and ,   respectively,

737373

Clips as magnetic cars

If we have magnetic cars due to chaos if they turn to the right the queue will go to the left

747474

Hypercube as a 2 wedges

One to left and to the right wall