Date post: | 08-Apr-2016 |
Category: |
Documents |
Upload: | joseluisarmenta |
View: | 26 times |
Download: | 6 times |
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
111
222
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
555
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
666
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
222222
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:
333333
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