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Hilbert space with an inner product (f,g)
With a norm defined by square root of (f,f)
Turns the Hilbert space into an inner product space.
Thursday, July 12, 2012
a norm defined
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Hilbert space with an inner product (f,g)
With a norm defined by square root of (f,f)
Turns the Hilbert space into an inner product space.
Helicoidal which
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A developing surface is a ruled surface
The only ruled surface are the plane and
Helicoidal which is the only ruled minimal surface
Other than plane
The helicoid is the only non-rotary surface
Which can glide along itself.
Helicoidal which
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A developing surface is a ruled surface
The only ruled surface are the plane and
Helicoidal which is the only ruled minimal surface
Other than plane
The helicoid is the only non-rotary surface
Which can glide along itself.
Wednesday, July 11, 2012
is in the set
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In a set of numbers containing zero
And successor of numbers
Every number is in the set
is in the set
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In a set of numbers containing zero
And successor of numbers
Every number is in the set
Tuesday, July 10, 2012
infinity
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Existence of natural numbers set
Is defined in the complex axiom of infinity
Of existence of an empty set and for all primes of naturals
Also generates sets of naturals.
infinity
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Existence of natural numbers set
Is defined in the complex axiom of infinity
Of existence of an empty set and for all primes of naturals
Also generates sets of naturals.
tame the knots
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Objects of amphichiral superposable with mirror image,
Closed non-self intersecting curve
Not to be untangled in 3D to produce a simple loop:
Polygonal are not able to tame the knots.
tame the knots
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Objects of amphichiral superposable with mirror image,
Closed non-self intersecting curve
Not to be untangled in 3D to produce a simple loop:
Polygonal are not able to tame the knots.
Cycles of transversal
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Cycles of transversal intersection
On smooth manifold,
Though intersections are not well defined
In the boundary of higher dimensional mapped manifold.
Cycles of transversal
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Cycles of transversal intersection
On smooth manifold,
Though intersections are not well defined
In the boundary of higher dimensional mapped manifold.
inside a closed
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Topological spaces giving property to
Non compact-subspaces as
Compact inside a closed disk
Within Euclidian topology
inside a closed
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Topological spaces giving property to
Non compact-subspaces as
Compact inside a closed disk
Within Euclidian topology
Atlases
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Consistent charts on manifolds
Which are abstract in condition
Of topological spaces with
Atlases of coordinate charts.
Atlases
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Consistent charts on manifolds
Which are abstract in condition
Of topological spaces with
Atlases of coordinate charts.
genuine infinitesimals
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Nonstandard analysis and transfer principle
Gives to superstructures a nonstandard enlargement
To hyperreal numbers of genuine infinitesimals
In which Banach spaces are of interest.
genuine infinitesimals
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Nonstandard analysis and transfer principle
Gives to superstructures a nonstandard enlargement
To hyperreal numbers of genuine infinitesimals
In which Banach spaces are of interest.
Monday, July 09, 2012
cusp map
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Resulting cusp map:
Implies function of square root module;
The Invariant density is spending
The difference of half Unity.
cusp map
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Resulting cusp map:
Implies function of square root module;
The Invariant density is spending
The difference of half Unity.
Elliptical fixed
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Elliptical fixed points initiating
Centers of islands into hyperbolic
Media of infinite rational values.
Perturbed system goes dramatically to
Infinite island chains.
Elliptical fixed
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Elliptical fixed points initiating
Centers of islands into hyperbolic
Media of infinite rational values.
Perturbed system goes dramatically to
Infinite island chains.
Dissipative
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Contracting the volume
Of phase space
During trajectory is consequence of
Negative Divergence.
Dissipative
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Contracting the volume
Of phase space
During trajectory is consequence of
Negative Divergence.
itself
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Surface of section
In n-dimensional phase space
Presents itself in (n-1) dimensional.
Be aware of the phase plane
With two degrees of freedom.
itself
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Surface of section
In n-dimensional phase space
Presents itself in (n-1) dimensional.
Be aware of the phase plane
With two degrees of freedom.
Initial point
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Seeds has double meaning:
Startle of a algorithm which
Will generate randomness
And
Initial point in orbiting
In dynamical system.
Initial point
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Seeds has double meaning:
Startle of a algorithm which
Will generate randomness
And
Initial point in orbiting
In dynamical system.
into real and complex
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Cascades generated by vector
Flowing into real and complex
In a single map of
Events in invertible
into real and complex
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Cascades generated by vector
Flowing into real and complex
In a single map of
Events in invertible
orbits chaotically
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Beyond the accumulation point
Periodic orbits chaotically
Interact
In a the limitlessness of specific maps.
orbits chaotically
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Beyond the accumulation point
Periodic orbits chaotically
Interact
In a the limitlessness of specific maps.
Sunday, July 08, 2012
group in favor
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Torus fiber bundle in circuit:
Actions to be made on Galois group
In favor of polynomial roots;
Vector spaces - invertible maps
On linear assumptions.
group in favor
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Torus fiber bundle in circuit:
Actions to be made on Galois group
In favor of polynomial roots;
Vector spaces - invertible maps
On linear assumptions.
Characters
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Commutative Banach algebra conducting
To the complex operators
To function within their full
Imperativeness:
Within characters of continuity
And homomorphism
Characters are continuous.
Characters
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Commutative Banach algebra conducting
To the complex operators
To function within their full
Imperativeness:
Within characters of continuity
And homomorphism
Characters are continuous.
even naturally
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Hyperfinites sets allowing
Superstructures even naturally numbered
Will conduct to infinity
Analysis of structures subject to
Finiteness conditions.
even naturally
Image from 1x.com
Hyperfinites sets allowing
Superstructures even naturally numbered
Will conduct to infinity
Analysis of structures subject to
Finiteness conditions.
modules battle
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Hyperral number in confrontation
With finite infinity of definition;
Integers are the escapes
Into modules battle.
modules battle
Image from 1x.com
Hyperral number in confrontation
With finite infinity of definition;
Integers are the escapes
Into modules battle.
Saturday, July 07, 2012
Homotopy
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Homotopic transformation
Offers the instrumental
Of mathematical deformation:
As metamorphosis
In the nature of Ideas
When altering a concept into
The conjugate one.
Homotopy
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Homotopic transformation
Offers the instrumental
Of mathematical deformation:
As metamorphosis
In the nature of Ideas
When altering a concept into
The conjugate one.
Its wings
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Butterfly Effect extends
Its wings - in theory - in Chaos.
Graphs cannot control the
Possible Catastrophe
Attested by theorems.
Its wings
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Butterfly Effect extends
Its wings - in theory - in Chaos.
Graphs cannot control the
Possible Catastrophe
Attested by theorems.
collider
Image from 1x.com
Attractors in phase space
Of which basins of attraction
Are asymptotically tangible
Don’t think of only a kind of
Attractors, they are strange also
With erratic trajectories in fractal
Dimension.
I think on that in terms of smashing particles in
A collider of rationality
Within nonlinearity limits.
collider
Image from 1x.com
Attractors in phase space
Of which basins of attraction
Are asymptotically tangible
Don’t think of only a kind of
Attractors, they are strange also
With erratic trajectories in fractal
Dimension.
I think on that in terms of smashing particles in
A collider of rationality
Within nonlinearity limits.
Bifurcation
Image from 1x.com
Bifurcation in dynamical appearance
Periodically onsets the chaos
With fold characteristic
Saddle enough to cause
Nonlinearity of the system
Bifurcation
Image from 1x.com
Bifurcation in dynamical appearance
Periodically onsets the chaos
With fold characteristic
Saddle enough to cause
Nonlinearity of the system
Isomorphism
Subjective and measurable
An ergodic endomorphism
Homeomorphic in finding the right
Isomorphism
Isomorphism
Subjective and measurable
An ergodic endomorphism
Homeomorphic in finding the right
Isomorphism
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