.: Unconditional Substrates are the Key to Innovation

This post comes with complementary information to the two earlier posts of “True Bose Einstein Condensed System Phase( 3)”.

Definitions:

1-In quantum mechanics, the uncertainty principle: is any of a variety of mathematical inequalities asserting a fundamental lower bound on the precision with which certain pairs of physical properties of a particle, such as position (x) and momentum p, can be simultaneously known. The more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. The original heuristic argument that such a limit should exist was given by Werner Heisenberg in 1927.

Mathematically, the uncertainty relation between position and momentum arises because the expressions of the wave function in the two corresponding bases are Fourier transforms of one another (i.e., position and momentum are conjugate variables). A similar tradeoff between the variances of Fourier conjugates arises wherever Fourier analysis is needed, for example in sound waves. A pure tone is a sharp spike at a single frequency. Its Fourier transform gives the shape of the sound wave in the time domain, which is a completely delocalized sine wave. In quantum mechanics, the two key points are that the position of the particle takes the form of a matter wave, and momentum is its Fourier conjugate, assured by the de Broglie relation.

2- The Fourier transform, named for Joseph Fourier, is a mathematical transform with many applications in physics and engineering. Very commonly, it expresses a mathematical function of time as a function of frequency, known as its frequency spectrum. The Fourier integral theorem details this relationship. For instance, the transform of a musical chord made up of pure notes (without overtones) expressed as amplitude as a function of time, is a mathematical representation of the amplitudes and phases of the individual notes that make it up. The function of time is often called the time domain representation, and the frequency spectrum the frequency domain representation. The inverse Fourier transform expresses a frequency domain function in the time domain. Each value of the function is usually expressed as a complex number (called complex amplitude) that can be interpreted as a magnitude and a phase component. The term "Fourier transform" refers to both the transform operation and to the complex-valued function it produces.

3- In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat propagation.

4- Harmonic analysis: is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms. In the past two centuries, it has become a vast subject with applications in areas as diverse as signal processing, quantum mechanics, and neuroscience.

5- In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform.

6- Time frequency transform: In signal processing terms, a function (of time) is a representation of a signal with perfect time resolution, but no frequency information, while the Fourier transform has perfect frequency resolution, but no time information. As alternatives to the Fourier transform, in time–frequency analysis, one uses time–frequency transforms to represent signals in a form that has some time information and some frequency information – by the uncertainty principal, there is a trade-off between these. These can be generalizations of the Fourier transform, such as the short-time Fourier transform, the Gabor transform or fractional Fourier transform, or can use different functions to represent signals, as in wavelet transforms and chirplet transforms, with the wavelet analog of the (continuous) Fourier transform being the continuous wavelet transform.

7- The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (t) is:

where:

A, the amplitude, is the peak deviation of the function from its center position.

ω, the angular frequency, specifies how many oscillations occur in a unit time interval, in radian per second

φ, the phase, specifies where in its cycle the oscillation begins at (t = 0).

When the phase is non-zero, the entire waveform appears to be shifted in time by the amount φ/ω seconds. A negative value represents a delay, and a positive value represents an advance.

7-1 This wave pattern occurs often in nature, including ocean waves, sound waves, and light waves.

A cosine wave is said to be "sinusoidal", because it is also a sine wave with a phase-shift of (π/2). Because of this "head stars", it is often said that the cosine function leads the sine function or the sine lags the cosine.

7-2 In two or three spatial dimensions, the same equation describes a travelling plane wave if position (x) and wave number (k) are interpreted as vectors, and their product as a dot product. For more complex waves such as the height of a water wave in a pond after a stone has been dropped in, more complex equations are needed.

7-3 In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number obtained by multiplying corresponding entries and then summing those products. The name "dot product" is derived from the centered dot " $\cdot$ " that is often used to designate this operation; the alternative name "scalar product" emphasizes the scalar (rather than vector) nature of the result.

When two Euclidean vectors are expressed in terms of coordinate vectors on an orthonormal basis, the inner product of the former is equal to the dot product of the latter. For more general vector space, while both the inner and the dot product can be defined in different contexts (for instance with complex numbers as scalars) their definitions in these contexts may not coincide.

In three dimensional space, the dot product contrasts with the cross product, which produces a vector as result. The dot product is directly related to the cosine of the angle between two vectors in Euclidean space of any number of dimensions.

8- Signal processing: is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, or measurements of time-varying or spatially-varying physical quantities. Signals of interest can include sound, images, and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals, and many others.

9- The goals of signal processing can roughly be divided into the following categories.

9-1 Signal acquisition and reconstruction, which involves measuring a physical signal, storing it, and possibly later rebuilding the original signal or an approximation thereof. For digital systems, this typically includes sampling and quantization.

9-1-1 Data acquisition: is the process of sampling signals that measure real world physical conditions and converting the resulting samples into digital numeric values that can be manipulated by a computer. Data acquisition systems (abbreviated with the acronym DAS or DAQ) typically convert analog waveforms into digital values for processing. The components of data acquisition systems include:

a) Sensors that convert physical parameters to electrical signals.

b) Signal conditioning circuitry to convert sensor signals into a form that can be converted to digital values.

c) Analog-to-digital converters, which convert conditioned sensor signals to digital values.

9-2 Quality improvement, such as noise reduction, image enhancement, and echo cancellation.

9-3 Signal compression, including audio compression, image compression, and video compression.

9-4 Feature extraction, such as image understanding and speech recognition.

9- 5 In communication systems, signal processing may occur at OSI layer (1), the Physical Layer (modulation, equalisation, multiplexing, etc.) in the seven layer OSI model, as well as at OSI layer (6), the Presentation Layer (source coding, including analog-to-digital conversion and data compression).

10- The Open Systems Interconnection (OSI) model: is a product of the Open Systems Interconnection effort at the International Organization for Standardization. It is a prescription of characterising and standardising the functions of communication system in terms of abstraction layers. Similar communication functions are grouped into logical layers. A layer serves the layer above it and is served by the layer below it.

According to recommendation X.200, there are seven layers, labelled (1) to (7), with layer (1) at the bottom. Each layer is generically known as an (N) layer. An "N+1 entity" (at layer N+1) requests services from an "N entity" (at layer N).

10-1 The (OSI) seven layers:

OSI Model
Polymer.doc	Data unit	Layer	Function
Host layers	Data	7. Application	Network process to application
		6. Presentation	Data representation, encryption and decryption, convert machine dependent data to machine independent data
		5. Session	Interhost communication, managing sessions between applications
	Segments	4. Transport	End-to-end connections, reliability and flow control
Media layers	Packet/Datagram	3. Network	Path determination and logical addressing
	Frame	2. Data link	Physical addressing
	Bit	1. Physical	Media, signal and binary transmission

11- Line vector: A line vector is a vector, such as a force, that is constrained to lie along a given line.

12- A transistor: is a semiconductor device used to amplify and switch electronic signals and electrical power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current flowing through another pair of terminals. Because the controlled (output) power can be higher than the controlling (input) power, a transistor can amplify a signal. Today, some transistors are packaged individually, but many more are found embedded in integrate circuit.

13-1 Semiconductor devices: are electronic components that exploit the electronic properties of semiconductor materials, principally silicon, germanium, and gallium arsenide, as well as organic semiconductor. Semiconductor devices have replaced thermionic devices (vacuum tubes) in most applications. They use electronic conduction in the solid state as opposed to the gaseous or thermionic emission in a high vacuum.

13-2 An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice. It is different from the positron, which is an actual particle of antimatter, whereas the hole is just a fiction, used for modelling convenience.

The electron hole was introduced into calculations for the following two situations:

If an electron is excited into a higher state it leaves a hole in its old state. This meaning is used in Auger electron spectroscopy (and other x-ray techniques), in computational chemistry, and to explain the low electron-electron scattering-rate in crystals (metals, semiconductors).

In crystals, band structure calculations lead to an effective mass for the charge carriers, which can be negative. Inspired by the Hall Effect, Newton's law is used to attach the negative sign onto the charge.

13-3 In quantum mechanics, and in particular quantum chemistry, the electronic density is a measure of the probability of an electron occupying an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typically denoted as either ρ(r) or n(r). The density is determined, through definition; by the normalized N-electron wave function which itself depends upon (4N) variables (3N spatial and N spin coordinates). Conversely, the density determines the wave function modulo a phase factor, providing the formal foundation of density functional theory.

13-4 An integrated circuit: or monolithic integrated circuit (also referred to as IC, chip, or microchip) is an electronic circuit manufactured by lithography, or the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material. Additional materials are deposited and patterned to form interconnections between semiconductor devices.

13-5 Electrical mobility: is the ability of charged particles (such as electrons or protons) to move through a medium in response to an electric field that is pulling them. The separation of ions according to their mobility in gas phase is called Ion mobility spectrometry, in liquid phase it is called electrophoresis.

13-6 Semiconductor materials: are nominally small band gap insulators. The defining property of a semiconductor material is that it can be doped with impurities that alter its electronic properties in a controllable way.

Because of their application in devices like transistors (and therefore computers) and lasers, the search for new semiconductor materials and the improvement of existing materials is an important field of study in materials science.

Most commonly used semiconductor materials are crystalline inorganic solids. These materials are classified according to the periodic table groups of their constituent atoms.

14- An organic semiconductor is an organic material with semiconductor properties. Single molecules, short chain (oligomers) and organic polimers can be semiconductive. Semiconducting small molecules (aromatic hydrocarbins) include the polycyclic aromatic compounds pentacene, anthracene, and rubrene. Polymeric organic semiconductors include poly(3-hexylthiophene), poly(p-phenylene vinylene), as well as polyacetylene and its derivatives. There are two major overlapping classes of organic semiconductors. These are organic charge-transfer complexes and various linear-backbone conductive polymers derived from polyacetylene. Linear backbone organic semiconductors include polyacetylene itself and its derivatives polypyrrole, and polyaniline. At least locally, charge-transfer complexes often exhibit similar conduction mechanisms to inorganic semiconductors.

15- A charge-transfer complex (CT complex) or electron-donor-acceptor complex is an association of two or more molecules, or of different parts of one very large molecule, in which a fraction of electronic charge is transferred between the molecular entities. The resulting electrostatic attraction provides a stabilizing force for the molecular complex. The source molecule from which the charge is transferred is called the electron donor and the receiving species is called the electron acceptor.

The nature of the attraction in a charge-transfer complex is not a stable chemical bond, and is thus much weaker than covalent forces. The attraction is created by an electronic transition into an excited electronic state, and is best characterized as a weak electron resonance. The excitation energy of this resonance occurs very frequently in the visible region of the electro-magnetic spectrum, which produces the usually intense color characteristic for these complexes. These optical absorption bands are often referred as charge-transfer bands (CT bands). Optical spectroscopy is a powerful technique to characterize charge-transfer bands.

Conclusion from definitions:

The line vector function is the shortest function with respect to time. The uncertainty principle missed to use this function to deal with time frequency, in contradiction the principle was based on Fourier transform which makes the time frequency more complicated and less fast, means a loss of time during the process. The consequences are to limit the development of applications in many domains of technologies such as instruments of measurement used in quantum mechanics, and in the computer based applications.

I already introduced three materials (TiCuO, DyCuO, and SiCuO), these materials are compounds of copper and oxygen called cuprates, they are a new family of high temperature superconductor, and can resolve the problem of room temperature superconductor and also they could be the solution to resolve the problem cited above. Once a chip and a transistor are built using these materials; efficiency in time frequency will be corrected at 100%. This is a huge gain of time by achieving C in E =MC2. The problem of the observer of particles and wave like particles will be resolved; means it will be possible to see a particle as a particle and as a wave in the same time. Also most of the persisting problems within the OSI model will be resolved by adding an 8^th layer which is chips and transistors based on (TiCuO, DyCuO and SiCuO).

The suggested materials are organic metals designed in molecule shape, and they are superconductors formed illegally to the human known physics laws.