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SmartSugarDaddy
@MexSugarDaddy
Sin filias ni fobias políticas ni religiosas. Gusto por la educación.
Katılım Mart 2024
138 Takip Edilen13 Takipçiler

@warfareanalysis Death to the satanic settlers. Allah with Al-Qassam
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On 07/07/2025,
Al-Qassam Brigades published footage of an ambush targeting Israeli soldiers in the Al-Ziraa area of Beit Hanoun, northern Gaza, in which two explosives were remotely detonated, the first targeting the initial force and the second targeting the rescue force.
Following the ambush, the Israeli army announced the killing of 5 soldiers and the injury of 20 others, all from Netzah Yehuda Battalion.
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Ve, @DiegoRuzzarin nos explica ese adefesio que llaman "democracia" en Estados Unidos:
"Estados Unidos tiene 435 personas en el Congreso. Todos los que están en negro y rojo reciben dinero de Israel. Sólo los que están en azul y verde no reciben dinero de Israel.
O sea, de los 435 miembros del Congreso, 324 representa los intereses del lobby sionista.
(...) Marx tenía razón, y no es por querer citar a Marx todo el puto tiempo, pero es que si, la realidad constantemente le da la razón a Marx, pues lean a Marx. No sé quién más recomendarles."
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Pascal’s Triangle is a triangular array of numbers where each number is the sum of the two numbers directly above it.
Where It’s Used
Probability & statistics
Combinatorics
Algebra
Computer science algorithms
#matrix #pascal #mathematics #math
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Warmup to Statistical Mechanics
What Exactly is a Hamiltonian A
System?
In ordinary Mechanics, you might begin with position and velocity. Hamiltonian Mechanics rewrites the same motion in a different language. Instead of position and velocity, it uses position and momentum. We write the position variables as q and the momentum variables as p. Then the full state of the system at one instant is
(q, p)
That pair is one point in phase space.
Why do we do this?
Because in these variables, the equations of motion take a remarkably clean form. Everything is generated by one single function, the Hamiltonian
H(q, p)
and in the simplest cases this Hamiltonian is just the total energy written in terms of position and momentum.
So if you know H, you know the dynamics.
You might wonder, but how can one function generate motion?
The rule is
dqᵢ/dt = ∂H/∂pᵢ
dpᵢ/dt = −∂H/∂qᵢ
These are Hamilton’s equations.
Now read them slowly 😄
The rate of change of position comes from differentiating H with respect to momentum. The rate of change of momentum comes from differentiating H with respect to position, with a minus sign.
This constitutes the whole engine.
A simple example makes this less abstract:
Take one particle of mass m moving in a potential V(q). Then the Hamiltonian is
H(q, p) = p²/(2m) + V(q)
The first term is kinetic energy. The second term is potential energy.
Now apply Hamilton’s equations.
First,
dq/dt = ∂H/∂p = p/m
So momentum tells you how position changes.
Second,
dp/dt = −∂H/∂q = −dV/dq
Thus, momentum changes because of force.
If you now combine these two equations, you recover ordinary Newtonian mechanics. Since p = m dq/dt, we get
m d²q/dt² = −dV/dq
So, Hamiltonian mechanics is not a different theory. It is the same mechanics, written in a form that exposes its geometric structure much more clearly.
The animation
The full 3D surface is the Hamiltonian itself, the energy landscape H(q, p). The floor underneath is phase space, marked by energy contours and the local flow field. The bright moving point is one actual state (q(t), p(t)) evolving under Hamilton’s equations. Its trail shows that the motion is not arbitrary. It is guided everywhere by the geometry of the same single function H. The render is doing more than illustrating a particle moving, it is showing how one function organizes the whole phase-space motion.
The math breakdown:
Start with one degree of freedom. The state is described by position q and momentum p. So the system lives in a two-dimensional phase space with coordinates
(q, p)
Now choose a Hamiltonian
H(q, p)
Think of H as the energy function. In many standard systems,
H(q, p) = kinetic energy + potential energy
For a particle of mass m in a potential V(q), this becomes
H(q, p) = p²/(2m) + V(q)
Hamilton’s equations say
dq/dt = ∂H/∂p
dp/dt = −∂H/∂q
Now substitute this specific H.
First compute the p derivative:
∂H/∂p = ∂/∂p (p²/(2m) + V(q)) = p/m
So
dq/dt = p/m
Now compute the q derivative:
∂H/∂q = ∂/∂q (p²/(2m) + V(q)) = dV/dq
So
dp/dt = −dV/dq
These two first-order equations completely determine the motion.
Now, connect this back to Newton’s law.
From
dq/dt = p/m
we get
p = m dq/dt
Differentiate both sides with respect to time:
dp/dt = m d²q/dt²
But Hamilton’s second equation gives
dp/dt = −dV/dq
So , together they imply
m d²q/dt² = −dV/dq
This is exactly Newton’s second law for motion in the potential V(q).
Thus, Hamilton’s equations do not replace mechanic, they reorganize it.
#HamiltonianMechanics #PhaseSpace #ClassicalMechanics #MathematicalPhysics #DifferentialEquations #Mathematics #Physics
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Ben G'vir de risas en un plató hablando de lanzar bombas de neutrones y de arrasar Irán. Son el Mal Absoluto. Nunca en la historia de la humanidad ha habido gente más peligrosa y abiertamente nociva que ésta.
Quienes lo justifican, lo minimizan, lo ocultan, lo edulcoran o lo niegan son como ellos, porque sin su apoyo tácito o explícito, no tendrían esa capacidad.
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