Encyclopedia - Harmonic Convergence: Encyclopedia - Harmonic Convergence
The Harmonic Convergence was a loosely-organized new age spiritual event that occurred on 1987, August 17th, when groups of people gather...   » Read the article

Dictionary - Harmonic Convergence: New Age Dictionary On Harmonic Convergence
Harmonic Convergence - N The assembly of New Age meditators gathered at the same propitious astrological time in different locations t...   » Read the article

Dictionary - Harmonic Convergence: New Age Spiritual Dictionary On Harmonic Convergence
Harmonic Convergence New Age day of international prayer and ceremony, August 16 - 17, 1987   (See also: Harmonic Convergence...   » Read the article

Article - Harmonic Concordance, November 8th 2003, The Real 2012?
There is a lot of talk about the importance of 2012 as the ending of the Mayan Calendar but some say that November 8th 2003 is the correc...   » Read the article

Article - Harmonic Concordance November 8 2003 And Its Spiritual Significance.
Harmonic Concordance and its spiritual significance.   » Read the article

Article - Venus Transit & Quetzalcoatl: The Venus Transit And The Return Of The Energy Of Christ And Of Quetzalcoatl
Carl-Johan Calleman, one of the leading authorities on the Mayan Calendar, presents a radical theory about the coming Venus Transit. Does...   » Read the article

Article - Mayan Calendar As Our Guide To The Future
This is the foreword by José Argüelles to Carl Johan Calleman's latest book: Enlightenment: The Mayan Calendar as Our Guide to the Future...   » Read the article

Article - Spiritual Awakening: Two Streams Of Future Probability
Kiara Windrider is a therapist, poet, astrologer, healer, explorer of mystic and shamanic paths and the author of the award-winning book ...   » Read the article

Article - Harmonic Concordance: A Bird's Eye View
Harmonic Concordance: An overview and perspective on the Harmonic Concordance.    » Read the article

Article - Harmonic Concordance Perspective: November 8th Lunar Exclipse Grand Sextile
Harmonic Concordance: An astrological perspective on the Harmonic Concordance.    » Read the article

Article - Mayan Calendar: Mayan Calendar And The Cycles Of The Goddess
Humanity’s path towards retrieving the Mayan calendar system really started with the Harmonic Convergence, August 16-17, 1987, when large...   » Read the article

Article - Year 2012: Stargates Preparing For Spiritual Awakening Year 2012
More and more lightworkers are taking their place in the cosmic scheme of things and assisting in the spiritual awakening of our world. W...   » Read the article

Encyclopedia - Jose Arguelles: Encyclopedia - Jose Arguelles
Jose Arguelles (b. 1939) is the New Age spiritual leader for the Planet Art Network and the Foundation for the Law of Time. He holds a Ph...   » Read the article

Encyclopedia - Divergent Series: Encyclopedia - Divergent Series
In mathematics, a divergent series is an infinite series that does not converge. That is, divergent series and convergent series are anto...   » Read the article

Encyclopedia - Convergence: Encyclopedia - Convergence
In the absence of a more specific context, convergence denotes the approach toward a definite value, as time goes on; or to a definite po...   » Read the article

Encyclopedia - Arithmetic-geometric Mean: Encyclopedia - Arithmetic-geometric Mean
In mathematics, the arithmetic-geometric mean M(x, y) of two positive real numbers x and y is defined as follows: we first form the ari...   » Read the article

Encyclopedia - Exemplar: Encyclopedia - Exemplar
Exemplar, in the sense developed by philosopher of science Thomas Kuhn, is a well known usage of a scientific theory. According to Kuhn, ...   » Read the article

Encyclopedia - Mathematical Analysis: Encyclopedia - Mathematical Analysis
Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies cl...   » Read the article

Encyclopedia - Geometric Mean: Encyclopedia - Geometric Mean
The geometric mean of a set of positive data is defined as the product of all the members of the set, raised to a power equal to the reci...   » Read the article

Dictionary - Harmonic Convergence: New Age Spirituality Dictionary On Harmonic Convergence
Harmonic Convergence An assembly of millions of New Agers gathered at spiritual sites (vortexes) around the world. to usher in peace o...   » Read the article

Dictionary - Harmonic Convergence: New Age Spirituality Dictionary On Harmonic Convergence
Harmonic Convergence An assembly of millions of New Agers gathered at spiritual sites (vortexes) around the world. to usher in peace o...   » Read the article

Dictionary - Harmonic Convergence: New Age Spirituality Dictionary On Harmonic Convergence
Harmonic Convergence An assembly of millions of New Agers gathered at spiritual sites (vortexes) around the world. to usher in peace o...   » Read the article

Encyclopedia - Fourier Series: Encyclopedia Ii - Fourier Series - Definition Of Fourier Series
Suppose that f(x), a complex-valued function of a real variable, is periodic with period 2Ï€, and is square-integrable over the interval ...   » Read the article

Encyclopedia - Harmonic Number: Encyclopedia Ii - Harmonic Number - Introduction
The generalized harmonic number of order n of m is given by . Note that n may be equal to , provided m > 1. And If , while , the har...   » Read the article

Encyclopedia - Convergence: Encyclopedia Ii - Convergence - Mathematics
In mathematics, convergence describes limiting behaviour, particularly of an infinite sequence or series toward some limit. To assert con...   » Read the article

Encyclopedia - Harmonic Number: Encyclopedia Ii - Harmonic Number - Applications
The harmonic numbers appear in several calculation formulas, such as the digamma function: where γ is the Euler-Mascheroni constant 0...   » Read the article

Encyclopedia - Fourier Series: Encyclopedia Ii - Fourier Series - Convergence Of Fourier Series
While the Fourier coefficients an and bn can be formally defined for any function for which the integrals make sense, whether the series ...   » Read the article

Encyclopedia - Fourier Series: Encyclopedia Ii - Fourier Series - Example
Let f(x) = x be the identity function for x from −π to Ï€. Outside this domain, the Fourier series implicitly requires that we define ...   » Read the article

Encyclopedia - Fourier Series: Encyclopedia Ii - Fourier Series - Orthogonality
The Fourier basis functions are orthogonal in the discrete space where δ(x) is the Dirac delta function and δT(x) is the Dirac comb ...   » Read the article

Encyclopedia - Fourier Series: Encyclopedia Ii - Fourier Series - Plancherel's And Parseval's Theorem
Another important property of the Fourier series is the Plancherel theorem Parseval's theorem, a special case of the Plancherel theore...   » Read the article

Encyclopedia - Fourier Series: Encyclopedia Ii - Fourier Series - Some Positive Consequences Of The Homomorphism Properties Of Exp
Because "basis functions" eikx are homomorphisms of the real line (more precisely, of the "circle group") we have some useful identities:...   » Read the article

Encyclopedia - Square Wave: Encyclopedia Ii - Square Wave - Examining The Square Wave
In contrast to the sawtooth wave, which contains all integer harmonics, the square wave contains only odd integer harmonics. Using Fourie...   » Read the article

Encyclopedia - Digamma Function: Encyclopedia Ii - Digamma Function - Taylor Series
The digamma has a rational zeta series, given by the Taylor series at z=1. This is , which converges for |z|<1. Here, ζ(n) is the R...   » Read the article

Encyclopedia - Khinchin's Constant: Encyclopedia Ii - Khinchin's Constant - Series Expressions
Khinchin's constant may be expressed as a rational zeta series in the form or, by peeling off terms in the series, where N is an in...   » Read the article

Dictionary - Jose Arguelles: New Age Spirituality Dictionary On Jose Arguelles
Jose Arguelles (1939 - ) New Age author whose book The Mayan Factor, published early 1987, argued that during a critical time (August ...   » Read the article

Dictionary - Motion: Spiritual - Theosophy Dictionary On Motion
Motion The essential characteristic of abstract motion, whether in space, time, or consciousness, commonly manifesting as change. Abso...   » Read the article

Dictionary - Zuvuya: Mysticism Magick Dictionary On Zuvuya
ZUVUYA José Argüelles' word that he says is what the Maya called "the memory circuit hotline." Earth lies within...   » Read the article

Dictionary - Mayan Calendar: Mysticism Magick Dictionary On Mayan Calendar
MAYAN CALENDAR The Mayan year, beginning always on July 26, called a tun consisting of 360 days (called kin ) and 5 or 6 epagomenals c...   » Read the article

Dictionary - Apo Pantas Kakodaimones!: Mysticism Magick Dictionary On Apo Pantas Kakodaimones!
APO PANTAS KAKODAIMONES! False banishing mantram ("Away all evil demons!")   APOCALYPSE We are aware that the muslims i...   » Read the article

Encyclopedia - Potential Theory: Encyclopedia Ii - Potential Theory - Inequalities
A fruitful approach to the study of harmonic functions is the consideration of inequalities they satisfy. Perhaps the most basic such ine...   » Read the article

Encyclopedia - Convergence Of Fourier Series: Encyclopedia Ii - Convergence Of Fourier Series - Absolute Convergence
We say about a function f that it has an absolutely converging Fourier series if Obviously, if this condition holds then SN(t) converg...   » Read the article

Encyclopedia - Convergence Of Fourier Series: Encyclopedia Ii - Convergence Of Fourier Series - Summability
Does the sequence 0,1,0,1,0,1,... converge to ½? This does not seem like a very unreasonable generalization of the notion of convergence...   » Read the article

Encyclopedia - Series Mathematics: Encyclopedia Ii - Series Mathematics - Absolute Convergence
A series is said to converge absolutely if the series of absolute values converges. In this case, the original series, and all reor...   » Read the article

Encyclopedia - Convergence Of Fourier Series: Encyclopedia Ii - Convergence Of Fourier Series - Convergence At A Given Point.
There are many known tests that ensure that the series converges at a given point x. For example, if the function is differentiable at x....   » Read the article

Encyclopedia - Potential Theory: Encyclopedia Ii - Potential Theory - Symmetry
A useful starting point and organizing principle in the study of harmonic functions is a consideration of the symmetries of the Laplace e...   » Read the article

Encyclopedia - Series Mathematics: Encyclopedia Ii - Series Mathematics - Power Series
Several important functions can be represented as Taylor series; these are infinite series involving powers of the independent variable a...   » Read the article

Encyclopedia - Convergence Of Fourier Series: Encyclopedia Ii - Convergence Of Fourier Series - Norm Convergence
The simplest case is that of L2. According to the Riesz-Fischer theorem, if f is square-integrable then i.e. SN converges to f in the ...   » Read the article

Encyclopedia - Convergence Of Fourier Series: Encyclopedia Ii - Convergence Of Fourier Series - Convergence Almost Everywhere
The problem whether the Fourier series of any continuous function converges almost everywhere was posed by Nikolai Lusin in the 1920s and...   » Read the article

Encyclopedia - Series Mathematics: Encyclopedia Ii - Series Mathematics - Infinite Series
The sum of an infinite series is a limit of partial sums of infinitely many terms. Such a limit can have a finite value; if it has, the s...   » Read the article

Encyclopedia - Harmonic Number: Encyclopedia Ii - Harmonic Number - Generalizations
Euler's integral formula for the harmonic numbers follows from the integral identity which holds for general complex-valued s, for the...   » Read the article

Encyclopedia - Convergence Of Fourier Series: Encyclopedia Ii - Convergence Of Fourier Series - Order Of Growth
The order of growth of Dirichlet's kernel is logarithmic, i.e. See Big O notation for the notation O(1). It should be noted that the a...   » Read the article

Encyclopedia - Characterizations Of The Exponential Function: Encyclopedia Ii - Characterizations Of The Exponential Function - Why Each Characterization Makes Sense
Each characterization requires some justification to show that it makes sense. For instance, when the value of the function is defined by...   » Read the article

Encyclopedia - Convergence Of Fourier Series: Encyclopedia Ii - Convergence Of Fourier Series - Preliminaries
Consider f an integrable function on the interval [0,2Ï€]. For such an f the Fourier coefficients defined by the formula It is common...   » Read the article

Encyclopedia - Set Of Uniqueness: Encyclopedia Ii - Set Of Uniqueness - Definition
A subset E of the circle is called a set of uniqueness, or a U-set, if any trigonometric expansion which converges to zero outside E i...   » Read the article

Encyclopedia - Gibbs Phenomenon: Encyclopedia Ii - Gibbs Phenomenon - Description
The three pictures on the right demonstrate the phenomenon for a square wave whose Fourier expansion is More precisely, this is the fu...   » Read the article

Encyclopedia - Gibbs Phenomenon: Encyclopedia Ii - Gibbs Phenomenon - Formal Mathematical Description Of The Phenomenon
Let be a piecewise continuously differentiable function which is periodic with some period L > 0. Suppose that at some point x0, the ...   » Read the article

Encyclopedia - Gibbs Phenomenon: Encyclopedia Ii - Gibbs Phenomenon - The Square Wave Example
We now illustrate the above Gibbs phenomenon in the case of the square wave described earlier. In this case the period L is 2Ï€, the disc...   » Read the article

Encyclopedia - Series Mathematics: Encyclopedia Ii - Series Mathematics - Generalizations
Asymptotic series, otherwise asymptotic expansions, are infinite series that do not converge. But they are useful as sequences of approxi...   » Read the article

Encyclopedia - Laplace Transform: Encyclopedia Ii - Laplace Transform - Region Of Convergence
The Laplace transform F(s) typically exists for all complex numbers such that Re{s} > a, where a is a real constant which depends on t...   » Read the article

Encyclopedia - Series Mathematics: Encyclopedia Ii - Series Mathematics - History Of The Theory Of Infinite Series
Series mathematics - Convergence criteria. The investigation of the validity of infinite series is considered to begin with Gauss. Eule...   » Read the article

Encyclopedia - Proof That The Sum Of The Reciprocals Of The Primes Diverges: Encyclopedia Ii - Proof That The Sum Of The Reciprocals Of The Primes Diverges - The Harmonic Series
First, we describe how Euler originally discovered the result. He was considering the harmonic series He had already used the followin...   » Read the article

Encyclopedia - Sturm-liouville Theory: Encyclopedia Ii - Sturm-liouville Theory - Example
We wish to find a function u(x) which solves the following Sturm-Liouville problem: where the unknowns are λ and u(x). As above, we m...   » Read the article

Encyclopedia - Pontryagin Duality: Encyclopedia Ii - Pontryagin Duality - Examples
A character on the infinite cyclic group of integers Z under addition is determined by its value at the generator 1. Thus for any charact...   » Read the article

Encyclopedia - Sturm-liouville Theory: Encyclopedia Ii - Sturm-liouville Theory - Application To Normal Modes
Suppose we are interested in the modes of vibration of a thin membrane, held in a rectangular frame, 0 < x < L1, 0 < y < L2. ...   » Read the article

Encyclopedia - Polynomial Interpolation: Encyclopedia Ii - Polynomial Interpolation - Convergence Properties
It is natural to ask, for which classes of functions and for which interpolation nodes the sequence of interpolating polynomials converge...   » Read the article

Encyclopedia - Set Of Uniqueness: Encyclopedia Ii - Set Of Uniqueness - Early Research
The empty set is a set of uniqueness. This is just a fancy way to say that if a trigonometric series converges to zero everywhere then it...   » Read the article

Encyclopedia - Hypergeometric Series: Encyclopedia Ii - Hypergeometric Series - Introduction
A hypergeometric series could in principle be any formal power series in which the ratio of successive summands is a rational function...   » Read the article

Encyclopedia - Geometric Mean: Encyclopedia Ii - Geometric Mean - Calculation
In a formula: the geometric mean of a1, a2, ..., an is , which is . The geometric mean of a data set is always smaller than or equal to t...   » Read the article

Encyclopedia - Group Algebra: Encyclopedia Ii - Group Algebra - The Convolution Algebra L1g
It is a standard theorem of measure theory that the completion of Cc(G) in the L1(G) norm is isomorphic to the space L1(G) of functions w...   » Read the article

Encyclopedia - Pontryagin Duality: Encyclopedia Ii - Pontryagin Duality - Non-commutative Theory
Such a theory cannot exist in the same form for non-commutative groups G, since in that case the appropriate dual object G^ of isomorphis...   » Read the article

Encyclopedia - Laplace Transform: Encyclopedia Ii - Laplace Transform - Inverse Laplace Transform
The inverse Laplace transform is the Bromwich integral, which is a complex integral given by: where is a real number so that the cont...   » Read the article

Encyclopedia - Lp Space: Encyclopedia Ii - Lp Space - Lp Spaces
The concept of Lp space can be extended to vectors having an infinite number of components. For an infinite sequence of real (or complex...   » Read the article

Encyclopedia - De Rham Cohomology: Encyclopedia Ii - De Rham Cohomology - Related Ideas
The de Rham cohomology has inspired many mathematical ideas, including Dolbeault cohomology, Hodge theory, and the Atiyah-Singer index th...   » Read the article

Encyclopedia - Taylor Series: Encyclopedia Ii - Taylor Series - Properties
If this series converges for every x in the interval (a − r, a + r) and the sum is equal to f(x), then the function f(x) is called anal...   » Read the article

Encyclopedia - Pontryagin Duality: Encyclopedia Ii - Pontryagin Duality - The Dual Group
If G is a locally compact abelian group, a character of G is a continuous group homomorphism from G with values in the circle group T. It...   » Read the article

Encyclopedia - Group Algebra: Encyclopedia Ii - Group Algebra - Group Algebras Of Topological Groups: Ccg
For the purposes of functional analysis, and in particular of harmonic analysis, one wishes to carry over the group ring construction to ...   » Read the article

Encyclopedia - Potential Theory: Encyclopedia Ii - Potential Theory - Definition And Comments
The term "potential theory" arises from the fact that, in 19th century physics, the fundamental forces of nature were believed to be deri...   » Read the article

Encyclopedia - Zeta Distribution: Encyclopedia Ii - Zeta Distribution - Moments
The n-th raw moment is defined as the expected value of kn: The series on the right is just a series representation of the Riemann zet...   » Read the article

Encyclopedia - Exponential Function: Encyclopedia Ii - Exponential Function - Numerical Value
To obtain the numerical value of the exponential function. The infinite series can be rewritten as : This expression will conver...   » Read the article

Encyclopedia - Taylor Series: Encyclopedia Ii - Taylor Series - Taylor Series For Several Variables
The Taylor series may also be generalised to functions of more than one variable with A second-order Taylor series expansion of a scal...   » Read the article

Encyclopedia - Taylor Series: Encyclopedia Ii - Taylor Series - List Of Taylor Series Of Some Common Functions
Several important Taylor/Maclaurin series expansions follow. All these expansions are also valid for complex arguments x. Exponential fun...   » Read the article

Encyclopedia - Set Of Uniqueness: Encyclopedia Ii - Set Of Uniqueness - Singular Distributions
A closed set is a set of uniqueness if and only if there exists a distribution S supported on the set (so in particular it must be singul...   » Read the article

Encyclopedia - Multipole Expansion: Encyclopedia Ii - Multipole Expansion - Multipole Expansion For Magnetic Vector Potentials
Suppose we have a current loop with a current I in it. Then the vector potential of the induced magnetic field is and as before we can...   » Read the article

Encyclopedia - Particle In A Spherically Symmetric Potential: Encyclopedia Ii - Particle In A Spherically Symmetric Potential - Spherical Square Well
Let us now consider the potential V(r) = V0 for r < r0, i.e., inside a sphere of radius r0 and zero outside. We first consider bound s...   » Read the article

Encyclopedia - Pontryagin Duality: Encyclopedia Ii - Pontryagin Duality - Fourier Transform
The dual group of a locally compact abelian group is introduced as the underlying space for an abstract version of the Fourier transform....   » Read the article

Encyclopedia - Pontryagin Duality: Encyclopedia Ii - Pontryagin Duality - The Group Algebra
The space of integrable functions on a locally compact abelian group G is an algebra, where multiplication is convolution: if f, g are in...   » Read the article

Encyclopedia - Pontryagin Duality: Encyclopedia Ii - Pontryagin Duality - Bohr Compactification And Almost-periodicity
One important application of Pontryagin duality is the following characterization of compact abelian topological groups: Theorem. A local...   » Read the article

Encyclopedia - Pontryagin Duality: Encyclopedia Ii - Pontryagin Duality - Categorical Considerations
It is useful to regard the dual group functorially. In what follows, LCA is the category of locally compact abelian groups and continuous...   » Read the article

Encyclopedia - Sturm-liouville Theory: Encyclopedia Ii - Sturm-liouville Theory - Sturm-liouville Form
The differential equation is said to be in Sturm-Liouville (or self-adjoint) form. All second-order linear ordinary differential equat...   » Read the article

Encyclopedia - Riemann Zeta Function: Encyclopedia Ii - Riemann Zeta Function - Definition
The Riemann zeta function ζ(s) is defined for any complex number s with real part > 1 by the Dirichlet series: In the region {s in...   » Read the article

Encyclopedia - Group Algebra: Encyclopedia Ii - Group Algebra - Group Algebra Of A Finite Group
Given a finite group G, define the group algebra CG as the vector space over the complex numbers, with basis vectors {eg} corresponding t...   » Read the article

Encyclopedia - Laplace Transform: Encyclopedia Ii - Laplace Transform - Bilateral Laplace Transform
When one says "the Laplace transform" without qualification, the unilateral or one-sided transform is normally intended. The Laplace tran...   » Read the article

Encyclopedia - Laplace Transform: Encyclopedia Ii - Laplace Transform - Laplace Transform Of A Function's Derivative
It is often convenient to use the differentiation property of the Laplace transform to find the transform of a function's derivative. For...   » Read the article

Encyclopedia - International Financial Reporting Standards: Encyclopedia Ii - International Financial Reporting Standards - Adaptation And Convergence
IFRS are used in many countries in the world, including Hong Kong and Russia, certain European countries, and recently Australia. In Afri...   » Read the article

Encyclopedia - Mathematical Analysis: Encyclopedia Ii - Mathematical Analysis - History
Greek mathematicians such as Eudoxus and Archimedes made informal use of the concepts of limits and convergence when they used the method...   » Read the article

Encyclopedia - Hilbert Space: Encyclopedia Ii - Hilbert Space - Definition
Every inner product <.,.> on a real or complex vector space H gives rise to a norm ||.|| as follows: We call H a Hilbert space i...   » Read the article

Encyclopedia - Pontryagin Duality: Encyclopedia Ii - Pontryagin Duality - Haar Measure
A topological group is locally compact if and only if the identity e of the group has a compact neighborhood. This means that there is so...   » Read the article

Encyclopedia - Pontryagin Duality: Encyclopedia Ii - Pontryagin Duality - Plancherel And Fourier Inversion Theorems
As we have stated, the dual group of a locally compact abelian group is a locally compact abelian group in its own right and thus has a H...   » Read the article

Encyclopedia - Hypergeometric Series: Encyclopedia Ii - Hypergeometric Series - Notation
The standard notation for the general hypergeometric series is Here, the integers m and p refer to the degree of the polynomials P and...   » Read the article

Article - Popular Topic Pages I - 12
This is a sitemap for popular topic pages at Global Oneness. Click on a link and you will find multiple articles related to the topic: ...   » Read the article