CUBIC (abbreviation for “clear, unobstructed brain/body imaging cocktails and computational analysis) is a histology method that allows tissues to be transparent (process called “tissue clearing”). As a result it makes investigation of large biological samples with microscopy easier and faster.
The method was published in 2014 by Etsuo A. Susaki and Hiroki R. Ueda, primarily for use in neurobiology research of brains from model organisms like rodents or small primates. But in upcoming years there were other works published, using CUBIC method on other tissues like lymph nodes or mammary glands. CUBIC can be also combined with CLARITY-based tissue clearing methods.
Homework Statement
If α, β and γ are roots of cubic polynomial and:
αβγ = 6
α2+β2+γ2=20
α3+β3+γ3=121
Find the equation of cubic polynomial
Homework Equations
vieta
The Attempt at a Solution
The equation is in the form:
x3 - (α+β+γ)x2 + (αβ + αγ + βγ) x - αβγ = 0
But I...
Given the function:
w=\sqrt[3]{(z-5)(z+5)}
which is fully-ramified at both the finite singular points and at infinity, how does one create the normal Riemann surface for this function? It's a torus but I do not understand how to map a triple covering onto the torus so that it's fully-ramifed...
The first part of the question asks to find the COG of the curve y=[1-x]*x^2 in the interval x=0 to x=1
I found that correctly as (0.6,0.0571)
The next part asks to find the COG of another cubic curve y=x[1-x]^2
But without using integration but by using the result of the first part of...
Homework Statement
The Attempt at a Solution
For Part A) I did the normal best fit straight line stuff, A^τAX=bA^τ etc, resulting in:
y= 31/26x -8/3
Now part B) is where I need a hand, I started with just cubing, squaring etc the terms given and doing row ops, which is where I'm at...
Is it possible to have a cubic polynomial (ax^3+bx^2+cx+d) which has three REAL roots, with one of them being +/- infinity?
If there is, can you give an example?
Thanks!
Cubic Population Model with steady states !
I am unsure as what this question means:
Consider the cubic population model: dN/dt = cN(N-k)(1-N) where c>0 and 0<k<1
If the the initial populations is N_0 describe without proof the future of the population, distinguish the various cases on...
Find the error bound of approximation of f using the cubic spline
want to find a cubic spline for f on the interval [a,b]
suppose we have n nodes with n-1 different intervals
I tried to find it using the Taylor expansion around any nodes say x_i \in [a,b]
f(x) - S(x) = f(x_i)-S(x_i) +...
Recently I came across this problem where it was stated:
"A cubic function y=ax3+bx2+cx+1 has only one tangent which has the slope of 4, and which touches the graph in x=-1/3"
I did the best I could to translate it into English. The problem went on ofcourse, but this is the part which...
Homework Statement
hey Forum! I had a question here I'm struggling with and was wondering if someone could take a look. its Dealing with calculus, specifically derivatives and behaviors of the graph:
http://i41.tinypic.com/mc6opj.jpg
I just started and part a) already has me stumped D...
Hey forum, I know this is an easy one, but it's been a while for me :P
thanks for your help!
Homework Statement
Given the following graph of h(x)
a) The intervals where h(x) is increasing and decreasing
b) The local maximum and minimum points of h(x)
c) The intervals where h(x) is...
I do not really understand this as you can probably tell, but What is the difference bewteen Linear and Cubic displacement deformation functions in beam bending? For example why would one be used over another to model or calculate beam bending? or how does either type effect what bending...
1. Homework Statement
x^3 +px^2 + 56x + q = 0
I've attempted the first part but I have no idea what to do next. I know usually you'd have 3 new roots inn terms of alpha, beta and gamma but they're not given.
2. Homework Equations
Given that the three roots are all positive and...
Homework Statement
x^3 +px^2 + 56x + q = 0I've attempted the first part but I have no idea what to do next. I know usually you'd have 3 new roots inn terms of alpha, beta and gamma but they're not given.
Homework Equations
Given that the three roots are all positive and are the first free...
Homework Statement
Hello there!
I'm trying to find the roots of the following cubic polynomial
x^3 - 10x + 18 = 0
The Attempt at a Solution
I did the following: I rewrite 18 as
18 = - (x^3 - 10x)
then I did back substitution and factored out
x^3 - 10x - x^3 + 10x = 0 or x(x^2-10) -...
Homework Statement
In a simple cubic lattice of spacing 0.2nm a phonon traveling in the {1 0 0} direction with wavelength 0.42nm collides with another phonon of the same wavelength which is traveling in the {1 1 0} direction. Draw a reciprocal space diagram to show the magnitude and...
Homework Statement
\frac{x^3+x^2-5x+3}{x^3-3x+2}
Homework Equations
The Attempt at a Solution
well I'm drawing that long division house with x^3-3x+2 on the outside and x^3+x^2-5x+3 on the inside.
I'm seeing that x^3 goes into x^3 one time, so i put a 1 on top of the...
Homework Statement
If f(x) is an irreducible cubic polynomial over a field F, is it ever possible that C_2 may occur as the \operatorname{Aut}(K/F) where K is the splitting field of f?
The Attempt at a Solution
It seems that this should be theoretically possible. In particular, if f is an...
Homework Statement
i) The average concentration of 222Rn in air inside a building is 20Bqm-3; what is the average concentration of Rn in atoms per cubic meter?
ii) In a sealed room of volume 50m3 what activity of 238U in a piece of porous rock would eventually give rise to this 222Rn...
Cubic Spline...what is the logic in constructing it?
Hey guys,
I am not trying to directly code a cubic spline computation, but I am writing a sub routine in VBA that takes input data, and outputs it to a text file in Maple syntax.
Anywho, my cubic spline actually produces LINEAR splines! I...
Homework Statement
what the questions asks is that i need to find the equation of a polynomial with these given points:
1,1
2,-3
3,5
4,37
5,105i know that one way to solve is by creating 5 equations then solve for ax^3+bx^2+cx+d using the elimination/substitution method.
however is there...
Hi,
I'm studying my algebra and I was trying this exercise:
Solve
z³+iz²-7z-iz-6-6i=0
I found the 2 real solutions (3 and -2) but i can't seem to find the complex one.
I tried this:
(z²-z)(i)=6(i) ==> z= -2 and 3
z³-7z=6==> z= -1, -2 and 3
I found that the complex solution is...
I'm trying to prove the following, which is left unproven in something I'm reading on ruler-and-compass constructions:
If ax^3+bx^2+cx+d is a polynomial over a subfield F of ℝ, and p+q\sqrt{r} is a root (with \sqrt{r}\notin F) then p-q\sqrt{r} is also a root.
The theorem immediately before...
Homework Statement
f(x) = |x+2|^3 -1
The Attempt at a Solution
- So, I know the formula is: d|x| / dx = x / |x|
- My guess would be: (x+2)^3 / |x + 2|^3 ?
I'm trying to find Increase and Decrease intervals for the graph..
Homework Statement
Hi all,
I was wondering if there is a procedure you can follow to calculate the complex roots of a cubic equation.Homework Equations
For example the equation
x3 - 1 = 0
has roots of x = 1
x = -0.5 + √3/2 i
x = -0.5 - √3/2 i
Admittedly, I got those solutions off wolfram...
Hi,
So I was working on a little project the other day and it was in regards to the cubic formula...
Which can be found here:
http://en.wikipedia.org/wiki/Cubic_formula#General_formula_of_roots
basically given an equation of the form:
ax3 + bx2 + cx + d = 0 the formulas on the...
The given problem:
The permitted energy values for a massless (or ultrarelativistic) particle (kinetic energy much larger than rest energy) in a 3-dimensional cubic box of volume V = L^3, can be expressed in terms of quantum numbers n_{x}, n_{y} and n_{z}:
\epsilon = \frac{hc\sqrt{n_x^2 +...
Hi. I posted this in the Homework question but after 152 views with no right answer, my question looks analytical and rigorous enough to be posted here.
Thank you...
----
I am asking about part iv).
[PLAIN]http://img715.imageshack.us/img715/7977/113ivb.jpg
Attempt at a solution...
Homework Statement
I am asking about part iv).
[PLAIN]http://img715.imageshack.us/img715/7977/113ivb.jpg
Homework Equations
I guess they would be the ones in the earlier parts...
The Attempt at a Solution
In the given fact, I think x^3 - x - m(x - a) distance from the...
Is there a good way to do this?
I have an equation, say x^3 - 4*x^2 + 2, so a=1, b=-4, c=0, d=2.
Is there an easy way to express the largest root of such an equation? In this case, the roots are:
3.8661982625090223
-0.65544238154983
0.7892441190408067
But I am trying to find an...
If each spline is given in the form of
gi(x) = ai(x-xi)3 + bi(x-xi)2 + ci(x-xi) + di
where i = 1 to N for N+1 data points.
Then given that b1 and bN+1 are zero (because the second derivatives are zero at the endpoints, due to this being a natural cubic spline), then there are N-1...
I am currently trying to solve for the metric function for a black hole in adS space with quasi-topological gravity. The details aren't too important, but the point is that I have to solve for a cubic at one point, and choose the correct solution, which is the one that reduces to a linear...
Hi all:
I encountered a problem when studying the diffusivity of Li atoms in Si crystals.
From the textbook, it is shown the diffusivity tensor in the cubic crystals (BCC FCC) is a diagonal matrix and the values along different directions are also the same (from the rotational symmetry), which...
This question is really out of curiosity, and also due to my very limited knowledge of basic physics(biomed sciences tend to not teach you this).
Say I wanted to create a vacuum inside a metal cubic casing with the following parameters:
-The case is a cube, that measure 1x1x1m, so has a...
Hi,
I'm new on this forum. We have some science days in our school, and there is a big 1.5x1.5x1.5m ice cube melting. There is a contest who will guess the aprox. time that it takes to melt.
I think it will be more than two days, but I would like to get a more concrete answer somehow... :)...
How can one derive the relationship for a cubic crystal:
d= \frac{a}{\sqrt{h^2 + k^2 + l^2}}
It is shown here.
This is probably trivial but I am having trouble proving it as the Miller indices are reciprocals but the reciprocal is not distributive. This isn't for homework by the way - I...
cubic bezier curve : get "sub curve" coordinates
Hi,
I have a standard cubic bezier curve defined by 4 points, what I'm trying to get is a "sub-curve" of this one (from the same point of origin, to one particular point on this curve, with the same curve).
For example, getting the first...
How can you prove that a cubic graph with a bridge cannot be 3-edge colored?
I guess one could try a proof by contradiction, so we assume a 3 edge coloring is possible for such a graph. But then I am not sure in which direction to continue. I have tried to draw such graphs, and clearly...
Hi,
I have a sensor going into a microcontroller via a adc.
I have worked out the conversion from the adc value into real terms.
Now the math takes too long in code to run this. and a look up table with 1024 elements will fill my program memory very quickly.
So I have put the results...
Hi,
I have the following population figures for a five year interval:
554.8, 609, 657.5, 729.2, 830.7, 927.8, 998.9, 1070, 1155.3, 1220.5
The graph has an exponential growth from the first value to the fourth value and then the population starts to decay.
I found that a Cubic...
Homework Statement
If the equations ax2+bx+c=0 and x3+3x2+3x+2=0 have two common solutions then show a=b=c.
Homework Equations
The Attempt at a Solution
first equation will be the factor of second.
taking out common from first equation.
how to show a=b=c??
please provide...
Hi, can you help me with this problem?
a = \sqrt[3]{1 - 4b - 4c}
b = \sqrt[3]{1 - 4c - 4a}
c = \sqrt[3]{1 - 4a - 4b}
Find \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}
Thanks
Homework Statement
θ^3 - pθ^2 +qθ - r = 0 such that p and r do not equal zero
If the roots can be written in the form ak^-1, a, and ak for some constants a and k, show that one root is q/p and that q^3 - rp^3 = 0. Also, show that if r=q^3/p^3, show that q/p is a root and that the product...
I am trying to teach myself some chemical thermodynamics, in particular some methods for fluid property evaluation. I am reading an excellent book which has helped a lot ("Introduction to Chemical Engineering Thermodynamics", Smith-Van Ness-Abbott, Ed. 7, ISBN: 007-124708-4).
One thing that...
Homework Statement
Solve the following equations Simultaneously:
y=x^3 and y=3x-2
My question is, how do I solve this? I've tried everything
The Attempt at a Solution
I've tried to isolate x in the linear equation and substitute it into the cubic. I don't know if that's wrong but it...
I have been seeing a few during in my practice questions which leaves me worrying.
If it is a quadratic function, the irrational numbers can be easily obtained using the equation.
However, I got a question today which eventually took this form:
28D3+36D2-41D2+4 = 0
(I reevaluated...
[B][B], Dear Fellows
I need to find the solution of cubic equation in exponential form which is written in a research article
If EQUATION is
(k^6-A k^4+B k^2+E)Y(z)=0
and solution given is as,
Y(z)=M exp(-k_1z)
where M is a constant and k_1 is solution of the above equation...