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Abstracts unpublishedA delivery of cience divulgation
Here is the 2nd delivery in second edition of my books of science divulgation the first is simettries in physics and mathematics
Jose luis armenta11/09/2013
1
1.the upper first member and second member will be bottom and viceversa..........................4
2.hermite derivative and dipheomorphism..............................................................................5
3.legendre polynomials have 2 brackets...................................................................................6
4.binomial expansion begin with zero factorial.........................................................................7
5.infinite potential is the charge electric potential....................................................................8
6.if in the denominator is there a rest so in the numerator not.................................................9
7.davisson germer experiment.................................................................................10
8.cosine of pitheta plus cosine of theta is one revolution........................................11
9.the shortest lenght in artificial intelligence............................................................12
10.colittion between quarks produce spin at sides....................................................13
11.first columns later raws in matrix (mathematics)..................................................14
12.paraboloid of 1 sheets in the past, paraboloid of 2 sheets in the future and more big bangs………………………………………………………………………………………………………………………..15
13.un tranfixed phi by another phi in gauge theory....................................................16
14.in a gauge transformed there is a tendry later an equalty......................................17
15.and ii = true ij = false in truth values......................................................................18
15.the complex conjugate is outside the bracket neither the dage operator...............19
16.epicycloid and trebol of 3 sheets.............................................................................20,21
17.one hipociclod with a real value is a fractal.................................................................22
18.first the universe was bijective later not bijective surjective........................................23
19.transformation of legendre as add and diference equal to an product.........................24
20.range is the number of solved equations.....................................................................25
21.matrix singular as ij=ji or simetric................................................................................26
22.matrix conjugate if the same but using complex conjugate..........................................27
23.quantum webs form a worm hole................................................................................28
24.a function is monotonic and derivative exist in measure theory...................................29
2
25.if a function have derivative one limit function is measurable............................30
26.a integral function is also measurable.................................................................31
28.a maximum or minimum is also measurable.......................................................32
29.A.dl pass to be rotational of A.............................................................................33
30.when to use a derivative of the wave function....................................................34
31.diference between B and H.................................................................................35
32.christoffel simbols and easy way to remember...................................................36
33.the variable more used is the one who is take the form of dx..............................37
34.a lie parenthesis is a quantum bracket.................................................................38
35.wavefunctions as gaussian numbers.....................................................................39
36.so together we have 48 mb in 2 cores.....................................................................40
37.the delta of armenta...............................................................................................41
37.fa di bruno formula and binomial coefficient...........................................................42
38.similities between groups and rings.........................................................................43,44,45
39.lipmann equation and boseeinstein statistic...........................................................46
40.the maxwell boltzmann statistics have the boltzmann constant...............................47
41.the linear independent are equal to zero .................................................................48
42.Toeplitz matrix and percolation................................................................................49,50
42.the numbers of elements of the principal diagonal is the second index.....................51
43.centroid and third newton law..................................................................................52
44.enthalpy and inner energy are tds.............................................................50
45.ampere law have both magnetic and electric fields.............................................51
46.the gauge transformed have 2 transfixed.............................................................55
47.dirac´s delta and laurent serie..............................................................................56
48.legendre polynomial and beta function simetries.................................................57
49.cauchy schwarz inequality as the parts are big that the all....................................58
3
50.simetries between cauchy schwarz and triangule inequality.....................................59
51.the armenta inequality.............................................................................................60
52.lagrange identity and some cross products.....................................................61
53.grosspitaevskii and schrodinger equation......................................................62
54.groospitaevskii and the sphere volume..........................................................63
55.continuos delay and convolution integral....................................................... 64
56.capacity heat at volume and pressure constant................................................65
56.inner energy was first and later appear the enthalpy.........................................66
57.capacity at volume and pressure constant and a inverse proportional maxwell equation...................................................................................................................67
58.gibbs enthalphy...................................................................................................68
59.helmholtz inner energy........................................................................................69
60.helmholtz free energy is  and ............................................................................70
61.gibss free energy is + and  and +..........................................................................71
62. Gibbs free energy is enthalphy and tds equation (both)……………………………………..72
63. A morphism is an eigenvalue………………………………………………………………………………73
4
Tensor derivative means if is bottom in the first member the denominator will be upper
the metric on M:
Were g is the metric on M
the tangent space at is spanned by the vectors:
all spaned vectors are contravariant this mean upper
5
hermite polynomials and dipheomorphism
a hermite polynomial is given by:
There are two different ways of standardizing the Hermite polynomials:
(the "probabilists' Hermite polynomials"), and
And a homemorphims is given when the inverse can be derivative so if a hermite polynomial have the derivative itself will have a inverse too
6
Legendre polynomials have 2 brackets
In mathematics, Legendre functions are solutions to Legendre's differential equation:
7
Binomial expansion begin with 0 factorial
According to the theorem, it is possible to expand any power of x + y into a sum of the form
The coefficient of xn−kyk is given by the formula
,Were k factorial is zero factorial in the first member
8
Potential of a charge in infinite is the electric potential
9
If in the denominator there is a rest in the numerator doesn´t
, respectively,
Were here the numerator is the distance from 1 to 2
10
Davisson germer experiment
11
Cosine of pi theta + cosine of theta = one revolution
12
The shortest way to arrive to a parallel way in artificial intelligence
We have two parallel ways
The shortest way to arrive to the other side is continue in a till b is clear to pass and pass in rect line don´t in 45 degress
A
B
13
Quarks produce spin at sides
A quark is
So in u to u is 0 degress
U red to down green is 60 degress
Down green to u blue is 120 degress
14
First columns later raws in matrix (mathematics)
15
In the future more big bangs will occur
since the hyperboloid of one sheets formula is
And the figure is:
The hyperboloid of 2 sheets formula is:
We see in the past we have a 1 and in the future we will have a +1; In the present we have a 0
16
One transfixed phi by one phi in gauge theory
The Lagrangian (density) can be compactly written as
17
In gauge theory there is a tends later an equalty
In fact gauge theory is the translation to prime field from an not prime field
18
In true values ij=0 = false and ii= 1 equal to true
19
The operator conjugate complex is inside the bracket neither the sword operator
The determinant of a Hermitian matrix is real:
Proof:
Therefore if
20
Epicyloid and trebols
In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle — called an epicycle — which rolls without slipping around a fixed circle. It is a particular kind of roulette
If the smaller circle has radius r, and the larger circle has radius R =kr, then the parametric equations for the curve can be given by either:
or:
An epicycloid is a trebol:
21
Image of the trebol see page 17
22
One hypocycloid is a fractal if is real part the integer part I mean the mantize
And a fractal will be:
23
First the universe was bijective later not bijective surjective
First
Later with an disc of acretion:
24
Add and diference in legendre transformation
From these, it is evident that Df and Df * are inverses, as stated. One may exemplify this by considering f(x) = expx and hence g(p) = p logp − p.
They are unique, up to an additive constant, which is fixed by the additional requirement that
The symmetry of this expression underscores that the Legendre transformation is its own inverse (involutive).
In some cases (e.g. thermodynamic potentials), a nonstandard requirement is used, amounting to an alternative definition of f * with a minus sign,
25
Range is equal to numbers of incognites solved
Standard mathematical notation allows a formal definition of range.
In the first sense, the range of a function must be specified; it is often assumed to be the set of all real numbers, and {y  there exists an x in the domain of f such that y = f(x)} is called the image of f.
In the second sense, the range of a function f is {y  there exists an x in the domain of f such that y = f(x)}. In this case, the codomain of f must be specified, but is often assumed to be the set of all real numbers.
In both cases, image f ⊆ range f ⊆ codomain f, with at least one of the containments being equality.
26
Singular matrix as ij=ji is too named simetric matrix
In linear algebra an nbyn (square) matrix A is called invertible (some authors use nonsingular or nondegenerate) if there exists an nbyn matrixB such that
27
The same that above but with complex conjugate is a conjugate matrix
In mathemathics, the conjugate transpose, Hermitian transpose, Hermitian conjugate, bedaggered matrix, or adjoint matrix of an mbyn matrix Awith complex entries is the nbym matrix A* obtained from A by taking the transpose and then taking the complex conjugate of each entry (i.e., negating their imaginary parts but not their real parts). The conjugate transpose is formally defined by
where the subscripts denote the i,jth entry, for 1 ≤ i ≤ n and 1 ≤ j ≤ m, and the overbar denotes a scalar complex conjugate. (The complex conjugate of , where a and b are reals, is .)
This definition can also be written as
28
Quantum webs form a worm hole
Formula of the worm hole:
Were 8pi is 4 spheres
Here is the web design:
29
A function is measure if exist the derivative I mean is monotonic
A measure μ is monotonic: If E1 and E2 are measurable sets with E1 ⊆ E2 then
Were E1 is the derivative and E2 is the function
30
if a function have derivative one limit function is measurable
A measure μ is monotonic: If E1 and E2 are measurable sets with E1 ⊆ E2 then
31
A function integral is also measurable
If the packing ring exist also exist the integral of all the surface adding part by part
32
A maximum and minimum is also a measurable
Were here the minimum is the 3rd adding
33
The factor A.dl pass to be rotational of A
and now we see the change of .dl to:
34
When to use complex and when to use wave function
Euler´ formula states that, for any real number x,
And we have a polarization we derivative the formula from above and we use the real term
This 3D diagram shows a plane linearly polarized wave propagating from left to right with the same wave equations where E = E0 sin(−ωt + k ⋅ r)and B = B0 sin(−ωt + k ⋅ r)
35
Differences between B and H
B refers to magnetic flux density, and H to magnetic field strength. Magnetic flux density is most commonly defined in terms of the Lorentz force it exerts on moving electric charges.
So this means that H is for material devices and B not
36
The christoffel symbols an easy way to remember
I i
M K  m k
L l
37
The derivative more used takes the form of dx
(commutativity )
Were tau is the variable who appears more times here
38
a parenthesis of lie is a quantum bracket
For a matrix Lie group, smooth vector fields can be locally represented in the corresponding Lie algebra. Since the Lie algebra associated with a Lie group is isomorphic to the group's tangent space at the identity, elements of the Lie algebra of a matrix Lie group are also matrices. Hence the Jacobi–Lie bracket corresponds to the usual commutator for a matrix group:
where juxtaposition indicates matrix multiplication.
Where the x is the wave function and y is the complex conjugate
39
A wave function is also a Gaussian number
Formally, Gaussian integers are the set
Were the complex conjugate is the wave function complex
40
We have 48 mb in two cores
In quantum computing we have the quantum circuits; this is because in first core we have 16 mb in second core we have 32 mb soo 16+32=48
41
The delta of armenta
in the second figure is the delta of armenta; Look like the delta of dirac but is mine, here is the formula:
42
Faa di Bruno formula and binomial coefficient
The faa di Bruno formula says:
And the binomial coefficient is:
According to the theorem, it is possible to expand any power of x + y into a sum of the form
The coefficient of xn−kyk is given by the formula
,Were k is mn and (nk)! is n!m n
43
Groups and rings
A ring have this properties:
Addition is abelian, meaning:
1. (a + b) + c = a + (b + c) (+ is associative)
2. There is an element 0 in R such that 0 + a = a (0 is the zero element)
3. a + b = b + a (+ is commutative)
4. For each a in R there exists −a in R such that a + (−a) = (−a) + a = 0 (−a is the inverse
element of a)
Multiplication ⋅ is associative:
5. (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c)
Multiplication distributes over addition:
6. a ⋅ (b + c) = (a ⋅ b) + (a ⋅ c)
7. (a + b) ⋅ c = (a ⋅ c) + (b ⋅ c).
For many authors, these seven axioms are all that are required in the definition of a ring (such a structure is also called pseudoring, or a rng). For others, the following additional axiom is also required:
Multiplicative identity
8. There is an element 1 in R such that a ⋅ 1 = 1 ⋅ a = a
44
And the group axioms are:
1. The closure axiom demands that the composition b • a of any two symmetries a and bis also a symmetry. Another example for the group operation is
r3 • fh = fc,
i.e. rotating 270° right after flipping horizontally equals flipping along the counterdiagonal (fc). Indeed every other combination of two symmetries still gives a symmetry, as can be checked using the group table.
2. The associativity constraint deals with composing more than two symmetries: Starting with three elements a, b and c of D4, there are two possible ways of using these three symmetries in this order to determine a symmetry of the square. One of these ways is to first compose a and b into a single symmetry, then to compose that symmetry with c. The other way is to first compose b and c, then to compose the resulting symmetry witha. The associativity condition
(a • b) • c = a • (b • c)means that these two ways are the same, i.e., a product of many group elements can be simplified in any order. For example, (fd • fv) • r2 = fd • (fv • r2) can be checked using the group table at the right
(fd • fv) • r2 = r3 • r2 = r1, which equalsfd • (fv • r2) = fd • fh = r1.
While associativity is true for the symmetries of the square and addition of
numbers, it is not true for all operations. For instance, subtraction of numbers is
not associative: (7 − 3) − 2 = 2 is not the same as 7 − (3 − 2) = 6.
3. The identity element is the symmetry id leaving everything unchanged: for any symmetry a, performing id after a (or a after id) equals a, in symbolic form,
id • a = a,
a • id = a.4. An inverse element undoes the transformation of some other element. Every symmetry
can be undone: each of the following transformations—identity id, the flips fh, fv, fd, fc and the 180° rotation r2—is its own inverse, because performing it twice brings the square back to its original orientation. The rotations r3 and r1 are each other's inverses, because rotating 90° and then rotation 270° (or vice versa) yields a rotation over 360° which leaves the square unchanged. In symbols,
45
5.
fh • fh = id,
r3 • r1 = r1 • r3 = id.
46

lippman Schwinger and bose Einstein distribution
In quantum mechanics the Lippmann–Schwinger equation (named after Bernard A . lippman and Julian schwinger, Phys. Rev. 79, p. 469, 1950) is of importance to scatering theory. The equation is
And the bose Einstein statistics is:
B–E statistics was introduced for photons in 1924 by bose and generalized to atoms by einstein in 1924–25.
The expected number of particles in an energy state i for B–E statistics is
47
Mawell boltzmann distribution have the bolztmann constant
In statistical mechanics Maxwell–Boltzmann statistics describes the average distribution of noninteracting material particles over various energy states in termal equilibrium and is applicable when the temperature is high enough or the particle density is low enough to render quantum effects negligible.
The expected number of particleswith energy for Maxwell–Boltzmann statistics is where:
where:
is the number of particles in state i is the energy of the ith state is the degenarcyof energy level i. i.e. no. of states with energy μ is the chemical potential k is boltzmann constant T is absolute temperature N is the total number of particles
Z is the partition function
e(...) is the exponential function
48
is linear independent if is equal to zero
A subset S of a vector space V is called linearly dependent if there exist a finite number of distinct vectors u 1, u 2,..., un in S and scalars a1, a2,..., an, not all zero, such that
49
Toeplitz matrix and percolation
A toeplitz matrix is this:
.
50
And percolation is this:
51
Matrix L have the principal diagonal numbers in the first index
A matrix of the form
is called a lower triangular matrix or left triangular matrix, and analogously a matrix of the form
52
Centroid and third newton law
And the third law of newton says that an f1 have a f2 of same magnitude but in reverse
sense
53
Enthalpy and inner energy are tds
54
Ampere law have both magnetic and electric fields
In the first member we see magnetics fields and in second member we see electric fields
55
he gauge transformation have 2 tranfixed
The Lagrangian (density) can be compactly written as
56
Laurent series and dirac delta´s
A laurent serie means:
In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be applied. The Laurent series was named after and first published by Pierre Alphonse Laurent in 1843. Karl Weierstrass may have discovered it first in 1841 but did not publish it at the time.
The Laurent series for a complex function f(z) about a point c is given by:
And a delta of dirac is: The integral of the timedelayed Dirac delta is given by:
57
Legendre polynomial and beta function
A beta function is:
In mathematics, the beta function, also called the Euler integral of the first kind, is a special function defined by
And the legendre polynomial is:
In mathematics, Legendre functions are solutions to Legendre's differential equation:
If we sustitute x2 by t we have a simetry
58
Cauchy Schwarz inequality as the part are bigger that the all
the inequality is written as
59
Triangule inequality and Cauchy Schwarz simetries
Absolute value as norm for the real line. To be a norm, the triangle inequality requires that the absolute value satisfy for any real numbers x and y:
which it does.
And cauchy schwarz is dot product:
the inequality is written as
60
The armenta inequality
The armenta inequality we have 2 vectors, we apply croice product and later we drawn it, here is the formula
ǀ<x,y>ǀ≤ǀǀxǀǀxǀǀyǀǀ
And the drawn will be
X
Y
XxY
61
Lagrange identitie and some cross products
A lagrange identitie is :
The relation:
And have a relation with the cross point identitie
62
Groos pitaevskii and schrodinger equation
Groos pitaevskii is:
The pseudopotential model Hamiltonian of the system is given as
And schrodinger is:
Timedependent Schrödinger equation (single nonrelativistic particle)
63
Gross pitaevskii is one sphere area over radio
The pseudopotential model Hamiltonian of the system is given as
Were 4πr2 is the sphere area but δ (r i−r j) is the division between r2 and over r
64
Continuos delay and convolution integral
Continuous delay
And convolution is:
The convolution of f and g is written f∗g, using an asterisk or star. It is defined as the integral of the product of the two functions after one is reversed and shifted. As such, it is a particular kind of integral transform:
(commutativity)
65
Capacity heat at volumen and pressure constant
At volume constant is:
And in pressure constant is:
66
inner energy was first in the universe and enthalpy later
We have the inner energy like this:
And the enthalpy like this:
67
Capacity heat at volume and pressure constant and the first Maxwell relation
First we have:
And secondly we have
And the Maxwell relation is at v constant in two maxwell relations and in two p in two maxwell
relations note that all appear in second member
68
Enthalphy of gibbs
G(p,T) = H – TS
69
Hemmoltz inner 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 transform of the internal energy, U, in which temperature replaces entropy as the independent variable.
70
The Helmholtz free energy is minus minus
71
The gibbs free energy is plus, minus, plus
G(p,T) = U + pV – TS
72
Gibbs free energy is enthalphy and tds equation (both)
73
A morphism is an eigenvalue
A category C consists of two classes, one of objects and the other of morphisms.
There are two operations which are defined on every morphism, the domain (or source) and the codomain (or target).
If a morphism f has domain X and codomain Y, we write f : X → Y. Thus a morphism is represented by an arrow from its domain to its codomain. The collection of all morphisms from X to Y is denoted homC(X,Y) or simply hom(X, Y) and called the homset between X and Y. Some authors write MorC(X,Y) or Mor(X, Y). Note that the term homset is a bit of a misnomer as the collection of morphisms is not required to be a set.
For every three objects X, Y, and Z, there exists a binary operation hom(X, Y) × hom(Y, Z) → hom(X, Z) called composition. The composite off : X → Y and g : Y → Z is written g ∘ f or gf. The composition of morphisms is often represented by a commutative diagram. For example,
So this is also an eigenvalue