Number i versus number j for a piece of Pi in economics

in #number-i6 years ago (edited)

What is the number J?

The "unit" Imaginary Number (the equivalent of 1 for Real Numbers) is √(−1) (the square root of minus one). In mathematics we use i (for imaginary) but in electronics they use j (because "i" already means current, and the next letter after i is j).

The book of Numbers to the Sri Yantra power of a Mayan Mersenne

Pi (/paɪ/; uppercase Π, lowercase π; Greek: πι [pi]) is the sixteenth letter of the Greek alphabet, representing the sound [p].

What is Pi in economics?

Profitability index (PI), also known as profit investment ratio (PIR) and value investment ratio (VIR), is the ratio of payoff to investment of a proposed project. It is a useful tool for ranking projects because it allows you to quantify the amount of value created per unit of investment.

The lower-case letter π is used as a symbol for:

-The mathematical real transcendental (and thus irrational) constant π = 3.14159..., the ratio of a circle's circumference to its diameter in Euclidean geometry. The letter "π" is the first letter of the Greek words "περιφέρεια" 'periphery' and "περίμετρος" 'perimeter', i.e. the circumference.

-The hadron called the pi meson or pion.

-Economic profit in microeconomics.

-Inflation rate in macroeconomics.

-A type of chemical bond in which the P-orbitals overlap, called a pi bond.


chasm K clique number v. schism clan complex network

In abstract algebra, a split complex number (or hyperbolic number, also perplex number, double number) has two real number components x and y, and is written z = x + yj, j2 = +1 . The conjugate of z is z∗ = x − yj. Since j2 = +1, the product of a number z with its conjugate is z z∗ = x2 − y2, an isotropic quadratic form, N(z) = x2 − y2.

The Conscious of a Liberal
The Conscience of a Liberal
Paul Krugman - New York Times Blog
Mathematics and economics

Conscience
adjective
aware of and responding to one's surroundings; awake.

The words 'con' as well 'science' are ingredients for the word 'conscience'.

The children's' prison parents labor-pool development

Conscious
noun
an inner feeling or voice viewed as acting as a guide to the rightness or wrongness of one's behavior.

The Business Cycle and the Future

By Martin A. Armstrong

Princeton Economic Institute

Our Local Correspondents
October 12, 2009 Issue
The Secret Cycle
Is the financier Martin Armstrong a con man, a crank, or a genius?

September 2013
What Are the "Ingredients" for Economic Growth?

Stop Making Sense: Music from the Perspective of the Real (2015) by Scott Wilson: Music from the Perspective of the Real

Stop Making Sense offers an original and compelling theory of music ‘from the perspective of the real’ as this term is understood according to the Lacanian orientation in psychoanalysis. Located in a mediating position between the subject and the real, music is here regarded as a form of social bond analogous to but quite distinct from the language of speech, operating ‘outside sense’. Music, like mathematics, is often regarded as a ‘language’ of the real in two senses: as a particulate system of essentially meaningless notes and tones that nevertheless provide regularities offering structure and orientation; and as the ‘language of love’, a means of mediating jouissance or the agonies and ecstasies that result from the ‘real’ of sexual difference.

The first part of the book explains its theoretical and methodological underpinnings that are based in a reading of subjects and symptoms such as amusia. The second and third parts focus on contemporary examples that look at how music has become both a powerful locus of discontent and also a form of orientation in an age of generalized psychosis imposed by neoliberalism as a form of governance. This has been accelerated by the regime of digital telecommunications since the early 1990s, which has seen the emergence of various new symptoms related to the autistic jouissance to which we have been confined with our gadgets and networked computers. Specific examples and cases discussed include Freud’s melophobia or fear of music, Che Guevara’s revolutionary a-rhythmia, John F. Nash’s obsession with ‘Bach’s Little Fugue’, Talking Heads and Asperger’s Syndrome/Autism, Yoko Ono and the sense of 'lack' in the Beatles, the role of ‘Imagine’ in the murder of John Lennon, Brian Eno and the digital auto-generation of Freud’s ‘oceanic feeling’, Aphex Twin and the brain-dance of the hikikomori, and the utopian promise of Merzbow.

A mathematical constant is a special number that is "significantly interesting in some way". Constants arise in many areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory, and calculus.

"You don't have to be a mathematician to have a feel for numbers. A movie, by the way, was made — sort of a small-scale offbeat movie — called Pi recently. I think it starts off with a big string of digits running across the screen, and then there are people who get concerned with various things, and in the end this Bible code idea comes up. And that ties in with numbers, so the relation to numbers is not necessarily scientific, and even when I was mentally disturbed, I had a lot of interest in numbers." - John Forbes Nash, Jr., in a statement of 2006, quoted in Stop Making Sense: Music from the Perspective of the Real (2015) by Scott Wilson, p. 117

Pi (also titled π), is a 1998 film about a paranoid mathematician who searches for a key number that will unlock the universal patterns found in nature.

Directed by Darren Aronofsky and written by Darren Aronofsky, Sean Gullette, and Eric Watson.

Isaac Asimov: Becoming Educated

Pi Day is celebrated on March 14th (3/14) around the world. Pi (Greek letter “π”) is the symbol used in mathematics to represent a constant — the ratio of the circumference of a circle to its diameter — which is approximately 3.14159.

Save money on pizza and pie on National Pi Day

John Lewis (civil rights leader)
John Robert Lewis (born February 21, 1940) is an American politician and is a civil rights leader. He is the U.S. Representative for Georgia's 5th congressional district, serving since 1987, and is the dean of the Georgia congressional delegation. His district includes three-quarters of Atlanta.

Lewis, who as chairman of the Student Nonviolent Coordinating Committee (SNCC) was one of the "Big Six" leaders of groups who organized the 1963 March on Washington, played many key roles in the Civil Rights Movement and its actions to end legalized racial segregation in the United States. He is a member of the Democratic Party leadership in the U.S. House of Representatives and has served as a Chief Deputy Whip since 1991 and Senior Chief Deputy Whip since 2003.

Lewis has been awarded many honorary degrees and is the recipient of numerous awards from eminent national and international institutions, including the highest civilian honor of the United States, the Presidential Medal of Freedom.

The product and the multiplicative inverse of two nth roots of unity are also nth roots of unity. Therefore, the nth roots of unity form a group under multiplication. Given a primitive nth root of unity ω, the other nth roots are powers of ω. This means that the group of the nth roots of unity is a cyclic group.


True or False

Numbers do not lie.

Numerical Dynamic Programming in Economics
John Rust
Yale University

Davidsson, Per and Honig, Benson (2003)
The role of social and human capital among nascent entrepreneurs.
Journal of Business Venturing

What is hysteresis and hysteresis loss?

The energy lost as heat, which is known as the hysteresis loss, in reversing the magnetization of the material is proportional to the area of the hysteresis loop. Therefore, cores of transformers are made of materials with narrow hysteresis loops so that little energy will be wasted in the form of heat.

Condensed Matter > Materials Science
Theory of Hysteresis Loop in Ferromagnet

Magnetic Hysteresis: This effect is called a Coercive Force, HC . ... Then by constantly changing the direction of the magnetising current through the coil from a positive direction to a negative direction, as would be the case in an AC supply, a Magnetic Hysteresis loop of the ferromagnetic core can be produced.

(True or False, Numbers do not lie.)

Possible Answers

In mathematics, a Lie algebra (pronounced /liː/ "Lee") is a vector space together with a non-associative, alternating bilinear map , called the Lie bracket, satisfying the Jacobi identity.

In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. When the matrix is a square matrix, both the matrix and its determinant are referred to as the Jacobian in literature.

What is the Jacobi method?

In numerical linear algebra, the Jacobi method (or Jacobi iterative method) is an algorithm for determining the solutions of a diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges.

What is an AC, in a circuit?

Direct current (DC) circuits involve current flowing in one direction. In alternating current (AC) circuits, instead of a constant voltage supplied by a battery, the voltage oscillates in a sine wave pattern, varying with time as: In a household circuit, the frequency is 60 Hz.

Who were the Hessians in the Revolutionary War?

The term "Hessians" refers to the approximately 30,000 German troops hired by the British to help fight during the American Revolution. They were principally drawn from the German state of Hesse-Cassel, although soldiers from other German states also saw action in America.

How Cars Divide America
Car dependence not only reduces our quality of life, it’s a crucial factor in America’s economic and political divisions.

What is the Hessian matrix?

In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and later named after him. Hesse originally used the term "functional determinants".
In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables.

What is eddy current and hysteresis losses?

Eddy current loss= The ohmic losses in a metal body, due to the eddy currents flowing through it, induced by an alternating magnetic field. Hysteresis loss= The loss in form of heat when magnetisation of the material is made to alternate with respect to time.

Deep Eddy Pool is a historic, man-made swimming pool in Austin, Texas. Deep Eddy is the oldest swimming pool in Texas and features a bathhouse built during the Depression era by the Works Progress Administration. The pool began as a swimming hole in the Colorado River, became a resort in the 1920s, and is today a popular swimming pool operated by the City of Austin.

A Commodity pool operator (CPO) is an individual or organization that solicits or receives funds to use in the operation of a commodity pool, syndicate, investment trust, or other similar fund, specifically for trading in commodity interests.

After an initial “transient time,” an AC current will flow in the circuit as a response in Transient Analysis:

Alternating Current(AC) and AC Steady State Analysis
Complex Numbers and Phasors

What are the 26 states with Native American names?

What does it mean for a circuit to be at steady state?

In electronics, steady state is an equilibrium condition of a circuit or network that occurs as the effects of transients are no longer important. Steady state determination is an important topic, because many design specifications of electronic systems are given in terms of the steady-state characteristics.

Trump proposal would end California's tougher car emission standards
It would also halt an ongoing bid to boost fuel efficiency.

What does it mean to be going steady?

If two people are going steady, they are having a long, fairly serious romantic relationship. [informal] She's been going steady with Randolph for almost a year now. Synonyms: go out, court, be seeing someone, be in a relationship More Synonyms of go steady. steady.

Seen in some magnetic materials, saturation is the state reached when an increase in applied external magnetic field H cannot increase the magnetization of the material further, so the total magnetic flux density B more or less levels off. (It continues to increase very slowly due to the vacuum permeability.)

What is the point of saturation?

saturation point. Examples Word Origin. the point at which a substance will receive no more of another substance in solution, chemical combination, etc. a point at which some capacity is at its fullest; limit: After a while she reached the saturation point and could absorb nothing more from the lectures.

Is water a dielectric material?

In an electric field the water molecules are polarized. But they are not at rest and can't induce charges to produce electric field like a solid dielectric. The motion of water molecules varies the capacity of a capacitance constantly. Therefore water can't be used as dielectric in a capacitor

What is the saturation temperature?

Saturation temperature means boiling point. The saturation temperature is the temperature for a corresponding saturation pressure at which a liquid boils into its vapor phase. The liquid can be said to be saturated with thermal energy.

The relative permittivity of a material is its (absolute) permittivity expressed as a ratio relative to the permittivity of vacuum.

What is permittivity of dielectric?

Relative permittivity is the factor by which the electric field between the charges is decreased relative to vacuum. Likewise, relative permittivity is the ratio of the capacitance of a capacitor using that material as a dielectric, compared with a similar capacitor that has vacuum as its dielectric.

MERCURY STILL RISING: Record-breaking temperatures jump to 110 degrees in Austin

What do you mean by saturation pressure?

Definition of saturation pressure. : the pressure of a vapor which is in equilibrium with its liquid (as steam with water); specifically : the maximum pressure possible by water vapor at a given temperature.

Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past.

What is dielectric material give two examples?

Examples include porcelain (ceramic), mica, glass, plastics, and the oxides of various metals. Some liquids and gases can serve as good dielectric materials. Dry air is an excellent dielectric, and is used in variable capacitors and some types of transmission lines. Distilled water is a fair dielectric.

How does dielectric affect capacitance?

The capacitance of a set of charged parallel plates is increased by the insertion of a dielectric material. The capacitance is inversely proportional to the electric field between the plates, and the presence of the dielectric reduces the effective electric field.

What is Debye relaxation in the dielectric materials?

Magnetostratigraphy is a geophysical correlation technique used to date sedimentary and volcanic sequences. Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from the Earth's interior out into space, where it meets the solar wind, a stream of charged particles emanating from the Sun.

What is saturation temperature and pressure?

Saturation temperature means boiling point. The saturation temperature is the temperature for a corresponding saturation pressure at which a liquid boils into its vapor phase. The liquid can be said to be saturated with thermal energy.

OOPs, concepts, OPs, SoD concepts and a separation of concerns

hysterical
adjective
deriving from or affected by uncontrolled extreme emotion. 2. relating to, associated with, or suffering from hysteria.

In thermodynamics and solid state physics, the Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat (heat capacity) in a solid. It treats the vibrations of the atomic lattice (heat) as phonons in a box, in contrast to the Einstein model, which treats the solid as many individual, non-interacting quantum harmonic oscillators.

The magnetic moment is a quantity that represents the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current (such as electromagnets), permanent magnets, elementary particles (such as electrons), various molecules, and many astronomical objects (such as many planets, some moons, stars, etc).

More precisely, the term magnetic moment normally refers to a system's magnetic dipole moment the component of the magnetic moment that can be represented by an equivalent magnetic dipole: a magnetic north and south pole separated by a very small distance. The magnetic dipole component is sufficient for small enough magnets or for large enough distances. Higher order terms (such as the magnetic quadrupole moment) may be needed in addition to the dipole moment for extended objects.

The Grüneisen parameter, γ, named after Eduard Grüneisen, describes the effect that changing the volume of a crystal lattice has on its vibrational properties, and, as a consequence, the effect that changing temperature has on the size or dynamics of the lattice. The term is usually reserved to describe the single thermodynamic property γ, which is a weighted average of the many separate parameters γi entering the original Grüneisen's formulation in terms of the phonon nonlinearities.

Kids around the world are suing governments over climate change—and it’s working

When was the book of Joel written in the Bible?

Ninth century BC, particularly in the reign of Joash – a position especially popular among nineteenth-century scholars (making Joel one of the earliest writing prophets) Early eighth century BC, during the reign of Uzziah (contemporary with Hosea, Amos, and Jonah)

“The sun shall be turned into darkness, and the moon into blood, before the great and terrible day of the Lord,” – Joel 2:31. “The sun shall be turned into darkness, and the moon into blood, before the great and notable day of the Lord.” – Acts 2:20

Symbolic interpretations of 'Army of Locusts' and 'Horse' has a number of 'irrational' tangents that may be considered:

Fractal financial
fluctuations;
do they threaten
sustainability?

The full moon on the night of July 27-28, 2018, presents the longest total lunar eclipse of the 21st century (2001 to 2100).

2.5 billion pounds of meat is piling up in the US as exports slow down
Possible price cuts due to record amounts of meat

Can the dielectric constant be less than 1?

E is always less than or equal to Eo, so the dielectric constant is greater than or equal to 1. The larger the dielectric constant, the more charge can be stored. ... The capacitance is maximized if the dielectric constant is maximized, and the capacitor plates have large area and are placed as close together as possible.

Scientists confirm Einstein's supermassive black hole theory
Reuters Staff

With Eisenstein-Jacobi integers, Every nonzero Eisenstein integer has a unique (up to ordering) factorization up to associates, where associates are Eisenstein integers related to the given Eisenstein integer by rotations of multiples of 60 degrees in the complex plane.

What is the meaning of cube root of unity?

The word "root" in the term refers to square roots, cube roots, and any other roots you might happen to need. For any integer n, the nth root of a number k is a number that, when multiplied by itself n times, yields k. The word "unity," perhaps a bit anticlimactically, just means "one."

What is the difference between saturated and superheated steam?

Saturated (dry) steam results when water is heated to the boiling point (sensible heating) and then vaporized with additional heat (latent heating). If this steam is then further heated above the saturation point, it becomes superheated steam (sensible heating).

What is a Cyclotomic polynomial?

The cyclotomic polynomials are monic polynomials with integer coefficients that are irreducible over the field of the rational numbers. Except for n equal to 1 or 2, they are palindromics of even degree.

Deposition, sublimation, Shoe lace method, Green's function, octonions into quaternions, Ford Circles... Nash Equilibrium and Operational Hydrology...

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