What is Cubic: Definition and 427 Discussions

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.

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  1. B

    Find roots of cubic polynomial with complex coefficient

    Homework Statement Find roots of $$ -\lambda ^3 +(2+2i)\lambda^2-3i\lambda-(1-i) = 0 $$ Homework EquationsThe Attempt at a Solution I tried my old trick I tried to separating the 4 terms into 2 pairs and try to find a common factor in the form of ##\lambda + z## between them, $$ -\lambda ^2...
  2. B

    Lagrange and cubic spline interpolate

    Homework Statement This is a bit unusual, I don't know whether I should post it here or math forum tbh. When I was doing numerical method home work, I am required to do perform both of these interpolation on a set of 4 data points. It turns out that the result of these 2 methods always agrees...
  3. shintashi

    B Equations vs. Functions Quadratic and Cubic?

    So if i take the rules that a straight vertical line drawn through the function with more than one intersection implies it is not a function, to mean that the quadratic equation for a circle is not a function. Furthermore, it also implies a cubic equation, such as x^3 can be a function, because...
  4. maistral

    Cubic equation of state near critical point (~0.95 < Tr < 1)

    Hi. I have read somewhere that cubic equations of state seem to have convergence issues when vapor pressure calculations are done near the critical point. Sadly, I have forgotten where I have have read it :( I would like to ask some knowledgeable people regarding this, or can people point me I...
  5. Clara Chung

    Question about a cubic crystal and its parameters

    Homework Statement Homework EquationsThe Attempt at a Solution So i got the answer by finding the diagonal of the square and then find the radius of A. ([(2x0.17)2 ]x2 )1/2 = 2a + 2x0.17 And find out a= 0.14 nm , however the answer is 0.124nm, please help
  6. lfdahl

    MHB Solve the cubic equation 4u^3+3u−3=0

    Given the depressed cubic equation: $4u^3+3u-3 =0$(1). Solve the equation with the substitution: $u = \sinh x$. (2). Solve the equation without this substitution.
  7. H

    Find the equation of a cubic graph

    Homework Statement ##x^3 - 4x^2 + ax + b## tangent to x-axis at x = 3 Homework EquationsThe Attempt at a Solution if the graph tangent at x = 3, means at x =3, y = 0 my questions is, is at x = 3 the graph's gradient (slope) = 0 ? if yes why? if yes then means dy/dx = 0 ##3x^2 - 8x + a = 0##...
  8. binbagsss

    Cubic positive solution exists analysis

    Homework Statement Question: For ##\Lambda^3+\Lambda^2+A=0## , show that for ##A<0## there is some real positive ##\Lambda## which solves this Homework EquationsThe Attempt at a Solution [/B] Attempt: Write ##-A=\hat{A} ##, then ##\hat{A} \in (0,\infty)## and...
  9. J

    Convert mg/s to SCCM (Standard Cubic Centimeters per Minute)

    Hello, Can anyone explain the procedure to convert mg/s to SCCM? I'm working with an Alicat Mass Flow Controller, which regulates Argon (Ar) mass flow from 1 to 6 mg/s at 27o C or 300 K (room temperature). For documentation purpose, I need mass flow in terms of mg/s, as well as, SCCM. Thank...
  10. M

    MHB How to Factor Cubic Terms in Algebraic Expressions?

    Factor the expression. (a - a^2)^3 + (a^2 - 1)^3 + (1 - a)^3 (a - a^2)(a - a^2)(a - a^2) + (a^2 - 1)(a^2 - 1)(a^2 - 1) + (1 - a)(1 - a)(1 -a) Is this the right approach thus far?
  11. M

    MHB How do you factor a cubic function?

    Precalculus by David Cohen, 3rd Edition Chapter 1, Section 1.3. Question 44b. Factor the expression. x^3 + 2x^2 + x x(x^2 + 2x + 1) x(x + 1)(x + 1) x(x + 1)^2 Correct?
  12. ElPimiento

    I How is it that the SPH cubic spline kernel in normalized?

    Hi, (This is more of a math question but I thought Astronomy people would be more familiar with the equation and how it's used) So in Monaghan 1992 (http://adsabs.harvard.edu/abs/1992ARA&A..30..543M, bottom of pg 554) a cubic spline in three dimensions is defined. I tried to integrate it (using...
  13. Ameer Bux

    How to Solve a Cubic Equation Involving Derivatives and Substitutions?

    Homework Statement Refer to attached image. Please help. It's due tomorrow. Homework Equations Doesn't state The Attempt at a Solution Refer to attached image
  14. R

    How do I convert cubic picometer to cubic centimeter?

    Part of the question says: An unit cell has a cell edge of 288 pm. I got to the part where volume (288 pm)^3 = (288 x 10^-10 cm)^3 I have no idea how that equals 2.39 x 10^-23 cm^3 Only the Bold part ^
  15. K

    Number of modes in Cubic Cavity

    Homework Statement Calculate the number of modes in a cubic cavity of length a=2.5 cm in the wavelength interval (λ1,λ2) where λ1=500 nm and λ2=501 nm. What's the total energy which radiates from the cavity if it's kept at a constant temperature of T=1500 K. Homework Equations I imagine these...
  16. S

    A Possible decay process for a cubic scalar self-interaction

    Consider the Lagrangian $$\mathcal{L}=\frac{1}{2}\partial_{\mu}h\partial^{\mu}h-\frac{1}{2}m^{2}h^{2}-\frac{\lambda}{3!}h^{3}$$ for a real scalar field ##h##. This is the Klein-Gordon Lagrangian with a cubic self-interaction term. Does this model allow the decay process $$h \rightarrow h +...
  17. J

    Solving for A in a Simple Cubic Lattice

    Homework Statement 1. For a simple cubic lattice with a lattice constant of a, the energy band can be expressed as:E = Acos(kxa)cos(kya)cos(kza) + B. (a) Suppose the effective mass for the electron at conduction band is m* = -ħ2/2a2, find A. Homework EquationsThe Attempt at a Solution I...
  18. E

    I Is it Possible to Index a Cubic Lattice with h^2+k^2+l^2=7?

    Hi everyone, I've been given a problem where I have to index reflections from a cubic lattice, the procedure is simple enough but I'm getting a case where I get : h^2+k^2+l^2=7 I've taken to many books, but most either don't mention the topic or say they are simply 'forbidden' reflections. I...
  19. F

    # of gas particles hitting one face of a cubic container

    Homework Statement [/B] 1 mol of gas at temperature T is contained in a cubic container of side L. Estimate the number of collisions per second between the atoms in the gas and one of the walls of the cubic container. My book gives this formula for that quantity \frac{N_A}{6L}\sqrt{\frac{3 k...
  20. R

    Calculating Dimensions of a Cylindrical Container with Given Volume

    The question reads, "Find the dimensions of a cylindrical tennis ball container which has the volume of V(x)=8πx3+17πx2+10πx+π such that the volume is exactly 825π cm3. Hint: V = πr2h." To start off, I set V(x)=825π and moved it to the right side, giving 0 = 8πx3+17πx2+10πx-824π. Factoring...
  21. stevendaryl

    Insights Solving the Cubic Equation for Dummies - Comments

    stevendaryl submitted a new PF Insights post Solving the Cubic Equation for Dummies Continue reading the Original PF Insights Post.
  22. A

    Fortran Calculating Cubic Root: Numerical Recipes & Cardino Method

    I tried to calculate the cubic root by using the method that are exist in Numerical receipes 77 but I got no answer and I don't know my mistake . Also, I tried by using Cardino method but Also I couldn't success to get an answer. Can any read my codes and tell me where is my errors or provide me...
  23. C

    9 components of strain for a cubic

    Homework Statement why the strain of εxy , εxz , εyx , εzx , εyz , εzy is γ_xy / 2 , γ_xz / 2, γ_yx / 2, γ_zx / 2 , γ_yz / 2 , and γ_zy / 2 ? how to get that ?. Homework EquationsThe Attempt at a Solution Taking an example of εxy , what does γ_xy / 2 mean ? [/B]
  24. Mr Davis 97

    B Showing all solutions to a cubic equation

    I am solving the following problem: Find all real x such that ##x^3 + 3x^2 + 3x = 1## I complete the cube by adding 1 to both sides, and get that ##(x + 1)^3 = 2## then ##x = 2^{1/3} - 1## What I'm asking is how can I be sure that I have found all real solutions? What if there are other solutions?
  25. Celestion

    Finding existence of zeros of cubic by multiplying y values?

    Homework Statement I can do the question, but in a different way to the worked solution which I don't understand. So my question is can anyone explain the worked solution which is in point 3 below. The question was to show there is exactly one zero to the function f(x) = Ax^3 - Ax + 1, with...
  26. H

    Cubic polynomial for the motion of a heavy symmetric top

    In the second paragraph after the expression of ##f(u)## below, it wrote "there are three roots to a cubic equation and three combinations of solutions". However, the combination of having three equal real roots was not mentioned. Why? In the next paragraph, in the second sentence, it wrote "at...
  27. anemone

    MHB Cos (π/7) is a root to a cubic equation

    Prove that $\cos \dfrac{\pi}{7}$ is a root of the equation $8x^3-4x^2-4x+1=0$.
  28. anemone

    MHB Possible integer values for coefficients of cubic equation with given root

    Given $a,\,b,\,c$ and $d$ are all integers such that $x=\sqrt[3]{\sqrt{8}+4}-\sqrt[3]{\sqrt{8}-4}$ is a root to the equation $ax^3+bx^2+cx+d=0$. Find the possible values for $(a,\,b,\,c,\,d)$.
  29. N

    MHB Finding relative extrema of a cubic function

    Find local maxima and minima for 6${x}^{3}$+6${x}^{2}$-8x. I found that (-1.08,8.08) is max, (0.41,-1.86) is min. Where i was wrong?
  30. G

    I General formulae for the roots of a cubic equation

    Hi everyone. I'm sorry for the long thread. If you don't want to read all the introductory stuff I will mark the part towards the end where my questions are located. I'm trying to find the general formulae for the roots of the equation $$ax^3 + bx^2 + cx + d = 0$$ By using some changes of...
  31. I

    A Can a Tree Visit Every Cell in a Cubic Lattice Blindly?

    I need to generate a tree in a cubic lattice that, from any cell, visits every other cell in the lattice just once. This visit must be blind, that is, it is not allowed to mark the cell as visited. Thanks in advance for any solution or reference.
  32. M

    I Partitions of Euclidean space, cubic lattice, convex sets

    If the Euclidean plane is partitioned into convex sets each of area A in such a way that each contains exactly one vertex of a unit square lattice and this vertex is in its interior, is it true that A must be at least 1/2? If not what is the greatest lower bound for A? The analogous greatest...
  33. anemone

    MHB Cubic Equation And Its Roots

    Let the function of $f$ be a cubic polynomial such that $f(x)=x^3-\frac{3}{2}x^2+ax+b=0$, with real roots lie in the interval $(0,\,1)$. Prove that $16a+24b\le 9$. Find the corresponding function of $f$ when the equality holds.
  34. Rumplestiltskin

    Solving Cubic Factorisation Homework

    Homework Statement The curve C with equation y = f(x) passes through the point (5, 65). Given that f'(x) = 6x2 -10x - 12, a) use integration to find f(x) b) Hence show that f(x) = x(2x+3)(x-4) The Attempt at a Solution I have no problem with this question, except it seems the given function...
  35. karush

    MHB Are local min/max of a cubic function determined by the zeros alone?

    Just curious are cubic functions dirvel from just having the zeros, does that always determine where the local min/max is. I notice many cubic graphs given on homework show where the zeros are but the local min/max is not given. For example...
  36. ellipsis

    Average number of photons in a cubic meter

    It seems to me that light travels (in a room) from everywhere, to everywhere else: A complicated, messy, interconnected network of photons of varying wavelengths which somehow avoid ever colliding with each other. This is what allows me to see things, and other people to see other things...
  37. B

    Can a 3x3 Matrix Represent a Quadratic, Cubic, or Quartic Function?

    I have a doubt... Look this matrix equation: \begin{bmatrix} A\\ B \end{bmatrix} = \begin{bmatrix} +\frac{1}{\sqrt{2}} & +\frac{1}{\sqrt{2}}\\ +\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{bmatrix} \begin{bmatrix} X\\ Y \end{bmatrix} \begin{bmatrix} X\\ Y \end{bmatrix} = \begin{bmatrix}...
  38. Dr. Strange

    What is the energy in a cubic km of empty space?

    If I have a 1 km cube of empty space at a constant temperature of 2.7 K, how much energy do I have? That is, if I know the total volume of space in the universe and I know what the average temperature of that space is, can I computer to total energy of the universe?
  39. anemone

    MHB Is $10^a\lt 127$ True for the Real Root of $x^3-3x-3=0$?

    Given $a$ is the real root for $x^3-3x-3=0$, prove that $10^a\lt 127$.
  40. TheOfficialAB

    Crystal phase transition, Diffraction peak splitting problem

    Homework Statement [/B] Hi there! This is a question from a practice problem sheet I got from the lecturer of my Condensed Matter 1 course. Below are the normal vectors to the {111} and {112} lattice planes: Homework Equations [/B] Bragg Condition: \begin{equation} n \lambda = d \sin...
  41. C

    Spins on a 3D cubic lattice

    Homework Statement Consider a system of rotors, each of them placed at one node of a 3D cubic lattice. The system is known as a Heisenberg spin model. Each rotor is represented by a vector of unit length ##\mathbf S(\mathbf r)##, where ##\mathbf r## is its position on the lattice. The...
  42. S

    Can a cubic polynomial be solved without arccos?

    I was reviewing the Cardano's method formula for a real cubic polynomial having 3 real roots. It seems that to do so, the arccos (or another arc*) of a term involving the p & q parameters of the reduced cubes must be done, and then followed by cos & sin of 1/3 of the result from that arccos -...
  43. teetar

    How to prove b^2 > 24c for a cubic with 1 max/1 min

    Homework Statement The cubic curve y = 8x^3 + bx^2 + cx + d has two distinct points P and Q, where the gradient is zero. Show that b^2 > 24c Homework Equations None that I can think of. The Attempt at a Solution There's two distinct points where the gradient is zero, since it's third degree...
  44. C

    MHB How can I show b^2 > 24c in a cubic with one maximum and one minimum?

    Hello, been thinking on this one for a little while, and can't seem to figure it out. Problem statement is: The cubic curve y = 8x^3 + bx^2 + cx + d has two distinct points P and Q, where the gradient is zero. Show that b^2 > 24c. It seems simple enough, but I can't logic it out. This...
  45. K

    Chemistry Need help finding how many molecules fill 1 cubic cm....

    Homework Statement The question I'm working on is: If a layer of oleic acid is considered to be one molecule thick and the molecules are assumed to be essentially cubes, how many molecules would fill one cubic centimeter? Homework Equations \[/B] I've found the volume and area of the acid so...
  46. C

    Converting cubic cm to cubic m and kg/m^3 to g/cm^3 etc

    Is the following correct? To convert cubic cm to cubic m we divide the cubic cms by 10^6, eg, 1cm^3 = 1/1,000,000th of 1m^3.. This is because we could fit 10^6 cubes, each measuring 1cm x 1cm x 1cm into a larger cube measuring 1m x 1m x 1m.
  47. B

    Cubic Formula: Is There a Unique Way to Write It?

    This formula: Is the unique form of write the cubic formula or exist other? OBS: Can be that other formula can be get through of some formula like this: source: https://pt.wikipedia.org/wiki/Bhaskara_II
  48. karush

    MHB How to Derive a Cubic Function with Horizontal Tangents at Given Points?

    $$y=ax^3+bx^2+cx+d$$ Find the cubic eq whose graph has horz tangent at the points$ (-2,6)$ and $ (2,0)$ $$y'=3a{x}^{2}+2bx+c$$
  49. B

    Body centered cubic arrangement and others

    3-D Why in bcc central atoms does not touch other atoms in that layers while in that of hcp and all others cases central atoms touch atoms in that layer..
  50. anemone

    MHB Summing a Series of Cubic Roots

    Sum the series below: \sum_{n=1}^{999}\dfrac{1}{a_n} where $a_n=\sqrt[3]{n^2-2n+1}+\sqrt[3]{n^2+2n+1}+\sqrt[3]{n^2-1}$.
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