The mathematical operations are defined for the improper element  ∞ 

 

∞.0, non meaning;  

 

Definition of a limit, by Augustin-Louis Cauchy and a proof that, for 0 < x < 1, 

 

 

Infinity is an unbounded quantity that is greater than every real number:

1∞=0

A statement the limit concept,

limx→∞1x=0

0⁺ :from the positive side of the real line.

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Fields researched
Version : 09/06/2013 

This is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of varous orders.It play a prominent role in engineering, physics, economics, and other disciplins.
E=MC2
Where:\
E = Energy\
m = mass\
c = speed of light

Einstein's field equations

Gμν≡Rμν−12Rgμν≐8πGc4Tμν

Last theorem of Pierre de FERMAT

Xn+yn=zn

Equation and constant of Ludwig BOLTZMANN

S=klogeWk=RNa

In quantum statistical mechanics, th H-function is the function:
H=∑iPilnpi

 

The Max PLANCK Constant

E=hνBλ(T)=2hc2λ51ehcλkBT−1
Where : \
λ : wavelength \
B : spectral radiance of th black body, \
T : absolute temperature, \
v : frequency of the emitted radiation \
KB : Boltzmann constant \
h: Planck constant \
c : Speed of light

Niels BOHR Atom Model

1λ=RH(122−1n2)forn=3,4,5,...

RZ=2π2meZ2e4h3
Where: 
me = the electron's mass 
e = electron's charge 
h = = Planck's constant 
Z = atom's atomic number (e.g. 1 for Hydrogen) 

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Quantum Mechanics

See  KB Physics 'What Is Quantum Mechanics?'

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Uncertainty principle

One consequence of the basic quantum formalism is the uncertainty principle. In its most familiar form, this states that no preparation of a quantum particle can imply simultaneously precise predictions both for a measurement of its position and for a measurement of its momentum. Both position and momentum are observables, meaning that they are represented by Hermitian operators. The position operator

X^

and momentum operator

P^

do not commute, but rather satisfy the canonical commutation relation:

[X^,P^]=iℏ

Given a quantum state, the Born rule lets us compute expectation values for both 

X 

and 

P,

and moreover for powers of them. Defining the uncertainty for an observable by a standard deviation, we have

σX=⟨X2⟩−⟨X⟩2,

and likewise for the momentum:

σP=⟨P2⟩−⟨P⟩2.

The uncertainty principle states that

σXσP≥ℏ2.

Either standard deviation can in principle be made arbitrarily small, but not both simultaneously. This inequality generalizes to arbitrary pairs of self-adjoint operators 

A  

and

B

The commutator of these two operators is

[A,B]=AB−BA,

and this provides the lower bound on the product of standard deviations:

σAσB≥12|⟨[A,B]⟩|.

Another consequence of the canonical commutation relation is that the position and momentum operators are Fourier transforms of each other, so that a description of an object according to its momentum is the Fourier transform of its description according to its position. The fact that dependence in momentum is the Fourier transform of the dependence in position means that the momentum operator is equivalent

up to an iℏ factor

to taking the derivative according to the position, since in Fourier analysis differentiation corresponds to multiplication in the dual space. This is why in quantum equations in position space, the momentum

Pi

is replaced by

 iℏ∂∂x,

 

and in particular in the non-relativistic Schrödinger equation in position space the momentum-squared term is replaced with a Laplacian times

−ℏ2

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The time evolution of a quantum state is described by the Schrödinger equation:

 iℏddtψ(t)=Hψ(t)

 The solution of this differential equation is given by

ψ(t)=e−iHt/ℏψ(0)

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Information Theory

Information theory is based on a measure of uncertainty known as entropy (designated “H”). For example, the entropy of the stimulus S is written H(S) and is defined as follows:

 

H(S)=−∑sP(s)log2P(s)

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Qubit Concept

 

It might, at first sight, seem that there should be four degrees of freedom in {\displaystyle |\psi \rangle =\alpha |0\rangle +\beta |1\rangle \,}, as {\displaystyle \alpha } and {\displaystyle \beta } are complex numbers with two degrees of freedom each. However, one degree of freedom is removed by the normalization constraint |α|² + |β|² = 1. This means, with a suitable change of coordinates, one can eliminate one of the degrees of freedom. One possible choice is that of Hopf coordinates:

α=eiψcos⁡θ2,β=ei(ψ+ϕ)sin⁡θ2.

Additionally, for a single qubit the overall phase of the state e^{i ψ} has no physically observable consequences, so we can arbitrarily choose α to be real (or β in the case that α is zero), leaving just two degrees of freedom:

{\displaystyle {α=cos⁡θ2,β=eiϕsin⁡θ2,}}

where {\displaystyle e^{i\phi }} is the physically significant relative phase.

The possible quantum states for a single qubit can be visualised using a Bloch sphere.

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the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter. Since the 17th century, mathematics has been an indispensable adjunct to the physical sciences and technology, and in more recent times it has assumed a similar role in the quantitative aspects of the life sciences...

 

Mathematics is the abstract study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.

Mathematicians seek out patterns (Highland & Highland, 1961, 1963) and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

None of this is entirely wrong, but it is also not satisfactory. Let us just point out that the fact that there is no agreement about the definition of mathematics, given as part of a definition of mathematics, puts us into logical difficulties that might have made Gödel smile...

 

If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this also the case of the objects that are studied in mathematics. In addition to that, the methods of investigation of mathematics differ markedly from the methods of investigation in the natural sciences. Whereas the latter acquire general knowledge using inductive methods, mathematical knowledge appears to be acquired in a different way: by deduction from basic principles. The status of mathematical knowledge also appears to differ from the status of knowledge in the natural sciences. The theories of the natural sciences appear to be less certain and more open to revision than mathematical theories. For these reasons mathematics poses problems of a quite distinctive kind for philosophy. Therefore philosophers have accorded special attention to ontological and epistemological questions concerning mathematics.

 

Mathematics at MIT is administratively divided into two categories: Pure Mathematics and Applied Mathematics. They comprise the following research areas:

Pure Mathematics

Algebra & Algebraic Geometry
Algebraic Topology
Analysis & PDEs
Geometry
Mathematical Logic & Foundations
Number Theory
Probability & Statistics
Representation Theory

Applied Mathematics

In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications.

Combinatorics
Computational Biology
Physical Applied Mathematics
Computational Science & Numerical Analysis
Theoretical Computer Science
Theoretical Physics

 

 Prefered links :Math zb Source (Karlsruhe), EncyMath, WolFram,

 

 

 

 

 

 

 

 

 

 

CERN, NASA, 

 

 

 

 

 

 

 

The essential composants of life are :Carbon, Hydrogen, Nitrogen, Oxygen, Phosphorus and Sulfur (CHNOPS).

 

Where are its from : 

-From a chemical process, under the Oceans?

 

-Or its was brought by meteorite collision?

...

 

Formation of life:

DNA sequencing : Fact Sheet by .gov, Nature,

 

 

Nature of container

The composant of life are throw By B.H.

 

 

4th revolution  vision of solar

The Centre is earth,

The Centre is Sun

Sun is the ....

https://nautil.us/issue/64/the-unseen/the-fourth-copernican-revolution

 

 

 

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Electromagnetic Spectrum

 

Notes,  

 

The three phenomenon electricity, magnetism, and light are the the different manifestations of the same phenomenon.

This confirmation is made possible by James Clerk Maxwell's researchs.

.

[ continue research from Britannica, Nasa, Wikipedia]

 

This is a electromagnetic radiation is as a stream of photons, where each traveling in a wave-like pattern, carrying energy and moving at the speed of light.

 

Tthe only difference between radio waves, visible light and gamma rays is the energy of the photons.

 

Radio waves have photons with the lowest energies.

Microwaves have a little more energy than radio waves.

Infrared has still more, followed by visible, ultraviolet, X-rays and gamma rays.