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.
The problem and solution are posted... no. 8
I may need insight on common difference ...
In my lines i have,
Let the roots be ##(b), (b-1)## and ##(b+1)##.
Then,
##x^3-3bx^2+3cx-d = a(x-b(x-b+1)(x-b-1)##
##x^3-3bx^2+3cx-d= a(x^3-3bx^2+3b^2x-x-b^3+b)##
##a=1##.
Let...
(i) I take the second derivative of Y: Y'' = 6X + 2A. Y'' = 0 when X = -A/3. Moreover, as Y'' is linear it changes sign at this X. Thus, it is the point of inflection.
(iii) After the substitution, the term x^2 appears twice: one, from X^3 as -3(x^2)(A/3), and another from AX^2 as Ax^2. They...
This is part of a longer exercise I struggled with. I checked the solutions manual, and there was a bit where they performed the following steps:
$$x^3=3a^2x-2a^3 \\$$
$$(x-a)^2(x+2a)=0$$
And then concluded that the roots were ##a## and ##-2a##, which is clear. What I can't work out is how...
If I have a air tank that is 1 cubic feet with the pressure gauge at 0 and I pump in air to 5000 psi how many cubic feet of a 100 psi would be in that tank? Any help would be appreciated
In terms of tetrahedral stacking, as occurs in diamond cubic, what I'm describing would be a system with additional tetrahedra in the empty cubes of that figure, but with their vertices on the opposite corners of the cubes that contain them to the "regular" diamond cubic arrangement.
Due to the...
For a state to be stationary it must be time independent.
Naively, I tried to find the values of c where I don't have any time dependency.
##e^{c \cdot L_z} \psi (r,t) = e^{c L_z} \sqrt{\frac{8}{l^3}} sin(\frac{2 \pi x}{l}) sin(\frac{2 \pi u}{l}) sin(\frac{2 \pi z}{l}) e^{-iEt/\hbar}##...
The context:
I created an educational resource, a set of interactive diagrams that allow the user to see how Hamilton's stationary action arrrives at the true trajectory. There is a diagram for each of the following three cases:
- Uniform force, hence the potential increases linear with...
Desmos.com is a great online graphing utility which I'm sure is familiar to many PF users. I wanted to experiment with the Newton-Raphson method using it so chose solution of cubic graphs as an example. The graph shows a variable cubic on which all turning points and intercepts are calculated...
Hi,
I was trying to find roots of the following cubic polynomial and there are only two roots. I believe there should be three roots. Could you please guide me why there are only two roots?
If you say that the "1" repeats itself as a root then I'd say the same could be said of "0.9". Thank...
If $\alpha,\,\beta,\,\gamma$ are the roots of the equation $x^3+ax+1=0$, where $a$ is a positive real number and $\dfrac{\alpha}{\beta},\,\dfrac{\beta}{\gamma},\,\dfrac{\gamma}{\alpha}$ be the roots of the equation $x^3+bx^2+cx-1=0$, find the minimum value of $\dfrac{|b|+|c|}{a}$.
Find a polynomial of degree 3 with real coefficients such that each of its roots is equal to the square of one root of the polynomial $P(x)=x^3+9x^2+9x+9$.
Hey! 😊
Show that the interpolation exercise for cubic splines with $s(x_0), s(x_1), , \ldots , s(x_m)$ at the points $x_0<x_1<\ldots <x_m$, together with one of $s'(x_0)$ or $s''(x_0)$ and $s'(x_m)$ or $s''(x_m)$ has exactly one solution.
Could you give me a hint how we could show that? Do...
##\sum ∝=3##
##\sum ∝β=0##
##∝βγ=-4##
##\sum2 ∝=6##
##\sum 2∝.2β##=4##\sum ∝β=0##
##2∝.2β.2γ=-32##
we then end up with
##x^3-6x^2+0x+32=0##
##x^3-6x^2+32=0##
i am looking for alternative methods ...
An equation $x^3+ax^2+bx+c=0$ has three (but not necessarily distinct) real roots $t,\,u,\,v$. For what values of $a,\,b,\,c$ are the numbers $t^3,\,u^3,\,v^3$ roots of an equation $x^3+a^3x^2+b^3x+c^3=0$?
The roots $x_1,\,x_2$ and $x_3$ of the equation $x^3+ax+a=0$ where $a$ is a non-zero real number, satisfy $\dfrac{x_1^2}{x_2}+\dfrac{x_2^2}{x_3}+\dfrac{x_3^2}{x_1}=-8$. Find $x_1,\,x_2$ and $x_3$.
Hi,
I was trying to solve the equation x³-2x-5=0. I solved it online and the real solution is x≈2.0946.
The following is an excerpt from the Wikipedia article on cubic equation.
The cubic equation, x³-2x-5=0, is a depressed cubic and in this case 4p³+27q²>0. But the real root of equation...
Suppose the system of equations (coming from invariance of the wave equation) :
$$B=-vE\\A^2-B^2/c^2=1\\E^2-c^2D^2=1\\AD=EB/c^2\\B=vA\\AE-BD=1$$
If one adds a lightspeed movement like
$$A=a+f\\B=b-cf\\D=d+h\\E=e-ch$$
Then solving equ 1 for f gives
$$f=(b+ve-vch)/c$$
Equ 4 for h implies...
Hi, Can someone please help me in understanding few parameters of cubic equation formula for solving polynomial of degree three. I attached the formula in the screenshot.
My questions are:
(1) what is ". " dot in the end of the formula and what does it mean?
(2) I want to use it only for real...
I created an array, where the first three entries of each column are the x,y, and z coordinates. The last entry in each column is the charge. I called this array PCQ.
l/2
l/2
-l/2
-l/2
-l/2
l/2
l/2
-l/2
-l/2
l/2
l/2
-l/2
-l/2
-l/2
l/2
l/2
l/2
l/2
l/2
l/2
-l/2
-l/2
-l/2
-l/2
q
-q
q
-q
q...
Hi PF!
Here equations 4 and 5 imply $$a^3=a_0^3+3 a_0 \Sigma \implies a_0 \approx a\left( 1- \frac{1}{a^2}\Sigma \right).$$ Can someone explain how this approximation is found?
Edit: I place in calculus thread because there must be some series expansion going on or a neglecting of terms.
So I am currently looking to work on some projects with my brother.
I have some questions regarding the usage of nitrogen.
We are looking at a 7.2 cubic metre cylinder of Nitrogen Pure compressed and wondering at what rate of pressure will equal roughly 30-60mins of use?
Nitrogen Bottle here...
The equation ## x^3-x+.1=0 ##, has 3 real roots that can be quickly approximated as follows: Writing the equation ## x=.1+x^3 ##, iterative methods quickly indicate that there is a root ## r_1 ## near ## x=+.1 ##, and more accurately ## r_1 \approx + .101 ##. ## \\## Doing an approximate...
I don't understand this.
a is not suppose to be -1; this is the only rule in the equation
The answer is the second picture, I just don't know the steps that lead to that answer.
Hi, this question was in a year 11 extension maths textbook in the enrichment section. I have the answer as k>17 and k<-11 because I graphed it on GeoGebra. The Graph can be found here: https://ggbm.at/xpegwwtq. While I know the answers I would like to know how to work it out using algebra...
Hey! :o
Let $S_{X,3}$ be the vector space of cubic spline functions on $[-1,1]$ in respect to the points $$X=\left \{x_0=-1, x_1=-\frac{1}{2}, x_2=0, x_3=\frac{1}{2}, x_4\right \}$$ I want to check if the function $$f(x)=\left ||x|^3-\left |x+\frac{1}{3}\right |^3\right |$$ is in $S_{X,3}$...
Hey! :o
I want to determine an approximation of a cubic polynomial that has at the points $$x_0=-2, \ x_1=-1, \ x_2=0 , \ x_3=3, \ x_4=3.5$$ the values $$y_0=-33, \ y_1=-20, \ y_2=-20.1, \ y_3=-4.3 , \ y_4=32.5$$ using the least squares method.
So we are looking for a cubic polynomial $p(x)$...
Homework Statement
We were given a tutorial to complete which I did complete.
Now the question is:
By modifying the appropriate lines in your script file, find the values of a, b, c, and d so that the cubic polynomial y = ax3 + bx2 + cx + d passes through the (x, y) pairs (-1, 3), (0, 8)...
Hello,
In general, any equation is a statement of equality between two expressions. In the 2D case, equations generally involve the two variables ##x## and ##y## or either variable alone if we require the other variable to be equal to zero.
The most general quadratic equation should be the...
Homework Statement
Hi, this is more of a review question and I'm just looking at solutions of natural cubic spline equations and some will give the cubic spline as:
1. s(x) = a + bx + cx^2 + dx^3
on Wolfram
while other pages will give:
2. s(x) = a + b(x - t) + c(x-t)^2 + d(x-t)^3
where...
I'm having hard time finding the center of inversion of cubic diamond structure.
At first I thought (2,2,2) would be the center of inversion, but (1,1,3), (3,3,3), (1,3,1), (3,1,1) (i.e. four atoms inside the cube) are not centrosymmetric about (2,2,2).
and survive for 24 hours.
That would be 4.16 cubic millimeters per mosquito!
These findings are due to testing of packing methods for shipping mosquitos around for disease prevention (like malaria which is mosquito transmitted.
I have a tank that is 250 Cubic Feet.
The tank is under vacuum (1x10-5 Torr).. which is actually 1.93368e-7 psia.
How much Argon, in cubic feet, does it take to back-fill to atmosphere or 14.7 psia?
Ambient temperature in tank is 90 degrees.
In case of simple cubic lattice relative magnetization is given by
\sigma=1-\frac{1}{S}\frac{v}{(2\pi)^3}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\mbox{d} k_x\mbox{d} k_y\mbox{d}k_z(\mbox{e}^{\frac{E(\vec{k})}{kT}}-1)^{-1}...
<<moderator: moved from a technical forum, no template>>
Hi ...
I have a question about a job in the material science courseWe give the hall petch type that denotes the dependence of the strength on the average grain diameter d, also has a value close to 1mpa. I have to show in a diagram σ-d ^...