omicron8251's channel
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14 hours ago
GT12. Aut(Z/n) and Fermat's Little Theorem
Abstract Algebra: We show that Aut(Z/n) is isomorphic to (Z/n)*, the group of units in Z/n. In turn, we show that the units consist of all m in Z...
omicron8251
commented:
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16 hours ago
Example of Group Automorphism 1 (Requires Linear Algebra)
Matrix Theory: We compute the automorphism groups of G = Z/10 and G=Z/2 x Z/2. The first case is a warm up for Part 2. The second case can be re...
omicron8251
commented:
Actually det(phi_3)=-1 and phi_3*phi_3 inverse is [[1,0][2,1]] different from the identity element.
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1 day ago
GARCH(1,1) to estimate volatility
GARCH(1,1) estimates volatility in a similar way to EWMA (i.e., by conditioning on new information) EXCEPT it adds a term for mean reversion: it sa...
omicron8251
commented:
the garch model seeems like it is an affine dependent set of vectors, v1 and v2 say.
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1 month ago
Analytical Mechanics Video #1: Calculus Of Variations Technique
Hundreds of FREE Problem Solving Videos And FREE REPORTS From
www.digital-university.org
omicron8251
commented:
at 12:02, the expression should've been multiplied by y' since power rule plus the chain rule is used.
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1 month ago
Did you know? Technology.
This is an amazing video about stuff we never knew.
Hope you enjoy!
By the way, the song used in the video is "Right Here, Right Now" by Fat boy...
omicron8251
commented:
It was very amazing how a 4 year old plays a videogame nowadays. I mean at this current rate, the next generation would be pretty good at computers. it's a little chilling at first in a sense, but this is not really unexpected. I guess computers do grow exponentially according to Moore's law with...
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1 month ago
MF69: Translating polynumbers and the Derivative
We begin moving towards calculus with polynumbers/polynomials by introducing the Derivative D=D_1 in a simple algebraic way. First we discuss compo...
omicron8251
commented:
a subderivative of a function f:I→R at a point x0 in the open interval I is defined to be a real number c such that
f(x)-f(x0)>c(x-x0).
So the subderivatives already exists as a inf(f'(x))
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1 month ago
Matlab Animation Droplets Final.avi
Animation Demo in Matlab using surface 3D plotting tools and movie tool.
omicron8251
commented:
how did you vary the periodicity of the droplets on matlab?
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1 month ago
Manifolds Part 1.wmv
What are Manifolds? Qualitative walk through of the definition of manifolds as topological spaces having differential structure. Coordinate functi...
omicron8251
commented:
Sorry, but what is the meaning of the picture that appeared in the beginning? System of how vectors operate on manifolds?
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1 month ago
Lec 15 | MIT RES.6-008 Digital Signal Processing, 1975
Lecture 15: Design of IIR digital filters, part 2
Instructor: Alan V. Oppenheim
View the complete course: http://ocw.mit.edu/RES6-008S11
License...
omicron8251
commented:
So passband frequency w and the preorder frequency are the same?
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1 month ago
Lec 16 | MIT RES.6-008 Digital Signal Processing, 1975
Lecture 16: Digital Butterworth filters
Instructor: Alan V. Oppenheim
View the complete course: http://ocw.mit.edu/RES6-008S11
License: Creative...
omicron8251
commented:
At 14;24, I think the the deviation is less than 2 db instead of 1 db.
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1 month ago
Lec 6 | MIT RES.6-008 Digital Signal Processing, 1975
Lecture 6: The inverse z-transform
Instructor: Alan V. Oppenheim
View the complete course: http://ocw.mit.edu/RES.6-008
License: Creative Common...
omicron8251
commented:
The condition for the contour integration is that the region considered is simply closed. Not triply doubly or multiply connected. If however, they are multiply connected then principle of deformation of path applies. With regard to the Cauchy integral formula used above, the region should be sim...
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1 month ago
Lec 11 | MIT RES.6-008 Digital Signal Processing, 1975
Lecture 11: Representation of linear digital networks
Instructor: Alan V. Oppenheim
View the complete course: http://ocw.mit.edu/RES6-008S11
Lic...
omicron8251
commented:
why is the arrow(current) pointing towards the left and not right in the bottom part of the circuit?
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1 month ago
Integral of x^n e^(-x) | MIT 18.01SC Single Variable Calculus, Fall 2010
Integral of x^n e^(-x)
Instructor: Christine Breiner
View the complete course: http://ocw.mit.edu/18-01SCF10
License: Creative Commons BY-NC-SA
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omicron8251
commented:
by the way, via the dominated convergence theorem which says that since e^x dominates x^n in the limit as x goes to infinity, the convergence of series is guaranteed?
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1 month ago
4J3, Diffusion of a Chemical | MIT 18.01SC Single Variable Calculus, Fall 2010
4J3, Diffusion of a Chemical
Instructor: Christine Breiner
View the complete course: http://ocw.mit.edu/18-01SCF10
License: Creative Commons BY-...
omicron8251
commented:
ln(1+R^2) at any time for the concentration of the chemical..
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1 month ago
Dual spaces #1: Intro; Independence
In this video I talk about a topic in linear algebra often downplayed in less theoretically-oriented linear algebra courses that I find pretty cool...
omicron8251
commented:
why is lambda in F and not in V?
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1 month ago
Vector Fields and Tensors Differential Geometry Part 4
Vector fields and the concept of parallel transport of a vector are introduced. Cartesian tensors are defined using the concept of tensor product ...
omicron8251
commented:
Wondering if that's the tangent space, what's a cotangent space? (i.e.)Tn*Mn.
About omicron8251's channel
actually bijectivity is already implied by homomorphism so pi is just homemorphic to whatever is in the bracket.