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. E

    Conditions for Cubic Equation to Represent Curve

    Homework Statement 2) Given a cubic equation y = (x+5)(ax^2 + bx - 2). Give conditions on a and b for the equation to represent the following curve. The curve is attached to the email. http://img35.imageshack.us/img35/8246/question2o.png Homework Equations The Attempt at a Solution...
  2. Chiclayo guy

    20 Liters per cubic meter of rain?

    20 Liters per cubic meter of rain? A weather report for Chiclayo Peru said we received 20 liters per cubic meter of rain yesterday. How many inches of rain would a New York weather report say we received? Thanks. Tom
  3. L

    Develop Cubic equation with a few points

    Homework Statement Write the equation of the cubic function with a y-intercept at 1, a local minimum of (3,1) and through point (2,5) Homework Equations The Attempt at a Solution I know that d= +1 and that's about it. I am really stuck and needs to know this for my summative on...
  4. J

    How to get Formula from a Cubic Graph

    Homework Statement The figure shows the graph of a cubic polynomial. The function graphed is f(x)= Hint: You may write the function as f(x) = a(x-b)(x-c)(x-d) where b, c, and d, are integers and a is a fraction. Homework Equations The Attempt at a Solution I'm lost...
  5. J

    Cubic Polynomials: Solving w/o Rational Roots

    Homework Statement I think I saw another thread answer this question, but I was a little lost whilst reading it. I have just recently learned of the rational root theorem and was using it quite happily; figuring out what possibly answers went with cubic and quartic polynomials gave new...
  6. Mentallic

    Rational Coefficients & Non-Rational Roots: A Puzzling Cubic Polynomial

    Homework Statement Not so much a homework problem, but a problem that is annoying me because of its simplicity. Not all cubic polynomials with rational coefficients can be factorized by the rational root theorem (or is this false?). What I am finding hard to comprehend is how a cubic with...
  7. Char. Limit

    Proof of the Cubic Formula

    The proof of the quadratic formula was so simple, I moved to the proof of the cubic formula with supreme confidence. And found myself awash in as and cs and cubic roots. Can you turn this equation into a cubic? x=-\frac{b}{3a}...
  8. I

    Eigen values and cubic roots question

    So I found the characteristic equation of a matrix, and I know the roots of the equation are supposed to be the eigenvalues. However, my equation is: \lambda^3-2\lambda^2 I have double checked different row expansions to make sure this answer is correct. So don't worry about how I came to get...
  9. T

    How can one solve cubic functions?

    x3 - 12x + 1 = 0 How does one solve for x?
  10. S

    New solving cubic and quartic equations

    Cubic equation f=a x+b x^2+c x^3 Solving: A=\frac{-(a b+9 c f)+\sqrt{(a b+9 c f)^2-4 \left(b^2-3 a c\right) \left(a^2+3 b f\right)}}{2 \left(b^2-3 a c\right)} G=a+2 b A+3 c A^2 H=a A+b A^2+c A^3-f F=G^3-27cH^2 B=\left\{F^{1/3}\,,-(-1)^{1/3} F^{1/3}\,,(-1)^{2/3}F^{1/3}\right\}...
  11. A

    Question about coordination number of face centered cubic.

    May i know how to count the coordination number of fcc? i know coordination number is count by the number in contact. i can understand the coordination number of bcc which is 8 , becoz that is 8 number in contact . but why fcc is 12 , not 13? i counted it as 13 if we take one face atom as...
  12. S

    Reciprocal of a cubic function

    Is it possible to have the reciprocal of a cubic function that does not have any vertical asymptotes?
  13. D

    Interpreting Cubic Spline Coefficients for spline(theta, R)

    theta and R are of equal size and contain the points i want to fit to a spline. What really has me perplexed is the coefficients that are produced. How do i interpret these coefficients; I originally assumed that they were the coefficients of a polynomial in standard form, however after...
  14. L

    How can I factor a cubic equation?

    Homework Statement g(x)= x^4-2x^3-3x^2+2x+2 Homework Equations The Attempt at a Solution After using synthesized division, got x^3-x^2-4x-2 I need help in factoring from here please
  15. V

    Calculating Bragg Angle from Unit Cell in Cubic Crystal

    Homework Statement The unit cell in a cubic crystal is 2.74Å. Determine the Bragg angle for reflections from the planes (200), (212) and (-112). [sorry i don't know how to put a bar on top of the numbers] if the x-ray wavelength used is 1.54Å Homework Equations Given Bragg's condition as 2d...
  16. P

    How Can We Visualize the Primitive Vectors of a Basic Cubic Lattice?

    Do yoh have some nice picture to show why the primitive vectors of basic cubic lattice are \vec{a}_1=\frac{a}{2}(-\vec{e}_x+\vec{e}_y+\vec{e}_z) \vec{a}_2=\frac{a}{2}(\vec{e}_x-\vec{e}_y+\vec{e}_z) \vec{a}_3=\frac{a}{2}(\vec{e}_x+\vec{e}_y-\vec{e}_z) Thanks!
  17. J

    How can I find the roots of a cubic equation?

    I've been looking at some practise exams for the University I would like to apply to, I have to sit the exam on 4th November. We have never done finding the roots of a cubic equation before and I cannot figure it out from looking on the internet, the formulas are all horrible to understand...
  18. J

    Derivative of a sum of functions, also cubic graph roots

    Derivative of a sum of functions What would you interperate this as? It is one of the subsections of Differentiation from the syllabus of a University entrance Exam in November but I cannot think what it is referring to. Differentiation: Derivative of xa, including for fractional...
  19. J

    Solving Cubic Equations with Chebyshev Roots

    Say I have a monic polynomial, x^3 + ax^2 + bx + c with a=-2.372282, b=1.862273, c=-0.483023 The discriminant is given by a^2 b^2 - 4 b^3 - 4 a^3 c - 27 c^2 + 18 ab c which is < 0, indicating 1 real root and 2 complex conjugates. A method for solving a general cubic using the...
  20. J

    Solving cubic roots (with imaginary number)

    Homework Statement (0.1 - 0.3j)^(1/3) = a + bj, where j is the imaginary number or more specifically sqrt(-1). Does anyone know how to solve for a and b? Homework Equations I've looked at cubic function equations, along with some polar equations. However, the latter requires some angle...
  21. O

    Solving Cubic Spline Interpolation with Conditions and Coefficients

    Homework Statement Consider the use of cubic splines to interpolate a set of data. Suppose at some stage in the calculation we arrive at the following spline functions for two consecutive intervals \tilde{f_{0}} = x^{3} + ax^{2} + bx + c over the interval -1 \leq x \leq 1 \tilde{f_{1}} =...
  22. B

    Finding the equation of the line of a cubic function

    Hello, I am trying to find the equation in the form ax^3+bx^2+cx+d for the curve passing through the origin and (40 sq root 6, -20). How do I find the a, b, c, and d values?
  23. E

    If you want to solve a cubic equation

    There is a very handy numerical solution for cubic equations like ## x^3+ax^2+bx+c=0## with ##x_i \in R## while a^2-3b \neq 0. Though it makes use of the method of Newton, the starting point for the algorithm gives it a great advantage to the normal algorithm. And you can use MS Excel as an...
  24. E

    Graphical solution of cubic equations

    The following set of equations is believed to be unknown but it is very hard to become sure of that. If it is really new it might be published in Wikipedia. Does anybody know of a graphical solution of cubic equations that meets this one? I am very interested to hear from you. Given an...
  25. H

    Constructible root from cubic polynomial

    Does x^3 - 3x + 3sqrt(3) = have a constructible root? my solution: suppose a is a constructible root of the equation above. we square both sides to get x^6 - 6x^4 + 9x^2 = 27. since a is constructible, a^2 is constructible as well and we can turn this equation into cubic poly with rational...
  26. E

    Analytical solutions of cubic equations

    I hope somebody will help me with the following problem. Analytical solutions of cubic equations make use of the method of Cardano. Those solutions give roots that are functions of the coefficients of the equations, being functions where cubic roots are involved. Generally speaking cubic roots...
  27. M

    What Are Some Tips for Factorising Cubic Functions?

    Hello again. :smile: I'm having more trouble with my homewrork, but this one really isn't fair. We haven't done the work in class, and as far as I can tell it isn't on the syllabus, but we're still expected to do it. Homework Statement http://img17.imageshack.us/img17/4379/questions7.jpg...
  28. D

    How can -x^3 + 27 be factored?

    Homework Statement factor -x^3 + 27 Homework Equations The Attempt at a Solution Nothing, I have no idea how to factor it.
  29. Z

    Trying to find the equation of a cubic

    1. Find an equation that best fits the data? Data 2 16.40 3 15.70 4 15.30 5 15.20 6 15.21 7 15.40 8 15.80 9 16.30 10 16.80 11 17.50 12 18.18 13 18.70 14 19.36 15 19.88 16 20.40 17 20.85 18 21.22 19 21.60 20 21.65 I have narrowed it...
  30. H

    Face-centered cubic lattice.

    Homework Statement An element crystallises in a face-centered cubic lattice with a basis group of two atoms at [000] and [1/4 1/4 1/4]. The lattice constant is 3.55 x 10^-10 m (Q1) How many nearest and second-nearest neighbours does each atom have? (Q2) Calculate the average volume per...
  31. H

    Shear deformation of diamond cubic lattice

    I'm doing MD calculations and I am having trouble providing a satisfactory explanation for the following to my profs. I am trying to calculate c44 for a diamond cubic crystal (Si), and to do that I have to calculate energy vs shear strain. For each value of the shear strain, I have to do...
  32. S

    Calculating Mass of 1 Cubic Meter of Water in Kilograms

    Homework Statement Assuming that each cubic centimeter of water has a mass of exactly 1.00 g, find the mass of one cubic meter of water in kilograms. Homework Equations well i just changed everything from grams to kilograms and cm to m The Attempt at a Solution Well if there is 1g...
  33. T

    How can I factorise cubic equations using a simple method?

    Homework Statement Factroise equation Homework Equations The Attempt at a Solution Can anyone help shopw me the best way to factorise cubic equations? I am doing a question on matrices, and have a 3x3 matrix, which ends up giving me a cubic equation: -x^3 +10x^2 - 27x + 18...
  34. N

    Solving a Cubic Equation: Finding x

    Hey, I have a cubic of this form: \\ax^{3}-bx-c=0\\ how do I solve for x?
  35. R

    How can I find a cubic function with specific local maximum and minimum values?

    Homework Statement find a cubic function g(x)=ax^3 +bx^2+cx +d that has a local maximum value of 3 at -7 and a local minimum value 0f -9 at 12. Homework Equations The Attempt at a Solution I know the derivative should equal zero for a max or min to occure. So i got f...
  36. M

    Distance between copper atoms in cubic crystal lattice

    Homework Statement The atomic mass number of copper is A = 64. Assume that atoms in solid copper form a cubic crystal lattice. To envision this, imagine that you place atoms at the centers of tiny sugar cubes, then stack the little sugar cubes to form a big cube. If you dissolve the sugar, the...
  37. E

    Proove that the cubic root of 2 + the square root of 2 is irrational

    How do you show that the cubic root of two + the square root of two is irrational? I can easily show that each of these numbers is irrational, but not the sum :/.
  38. R

    Proving Positive Roots of a Cubic Equation: 0<3ab<=1 & b>= 3^0.5

    Homework Statement Suppose 'a' and 'b' are real numbers such that the roots of the cubic equation ax^3-x^2+bx-1=0 are all positive real numbers. Prove that: i) 0<3ab<=1 ii) b>= 3^0.5 Homework Equations Let x,y,z be the roots: x+y+z=1/a xy+yz+zx=b/a xyz=1/a The Attempt at a...
  39. R

    Solve By Factoring, and Equation of Cubic Function whose graph passes thru

    Homework Statement I am stuck on these two pre-cal problems... can anyone help? Solve By Factoring: 2x^3 + 2x^2 = 4x + 4 This next one I have no idea how to do Find an equation of the cubic function whose graph passes through the points (3,0) and (1,4) and is tangent to the x-axis...
  40. O

    Cubic formula and vietes formulas

    First, Is there a way to convert a complex number to polar form without using boolean commands? And now, my real question: Do all of viete's formulas hold true when the coefficients of a cubic formula are complex? I wrote a script that finds the roots of a cubic formula with complex...
  41. K

    Is a Negative Real Root Possible for a Fifth Degree Equation?

    If 1/a^3+ a^2+ 9=0 , is ''a'' greater than/less than or equal to -1/3. This a GRE question. Thanks!
  42. F

    Total resistance through cubic circuit

    Homework Statement Suppose a resistor R lies along each edge of a cube (12 resistors in all) with connections at the corners. Find the equivalent resistance between two diagonally opposite corners of the cube Homework Equations \SigmaI = 0 at a node (a junction) \SigmaV = 0...
  43. P

    Solving Cubic Equations: Finding the Roots

    Find the roots of the equation x^3 - 3x^2 - 10x +24 = 0 I personally, have never done cubic equations so can you please explain what should i do here. Should i try with GCF, even though i don't see one yet, or is there a method to do this?
  44. F

    Parallel Tangents to Cubic Graph

    Homework Statement I have the graph of a function f(x)=(x+1)(x+4)(x+6). I've found the tangent at x=-6, the equation of which is y=10x+60. I then need to algebraically find the equation of another tangent on the curve which is parallel to the first. Homework Equations No idea.The Attempt at...
  45. W

    Exploring Slip Systems of Face Centered Cubic Metals

    Hello, Recently,I study about the slip systems of metals which regarding to the material science subject. For face centered cubic(FCC),it slip system is {111}<110>.Hence the number of slip systems is 12.The{111}is the family for (111), (-111), (1-11), (11-1),(sorry！-1 means a bar line on top...
  46. C

    Packing fraction of body-centered cubic lattice - solid state physics

    packing fraction of body-centered cubic lattice -- solid state physics Homework Statement This is part of a series of short questions (i.e. prove everything in Kittel Ch. 1, Table 2): Prove that the packing fraction of a BCC (body-centered) cubic lattice is: 1/8 * pi * \sqrt{3}...
  47. P

    Solving Cubic Equations with Cardano's Method: A Complete Guide

    Homework Statement Find the solutions of: x^3-3x-2=0 using the Cardano's method. Homework Equations The Attempt at a Solution x=u+v (u+v)^3-3(u+v)-2=0 u^3+v^3+(u+v)(3uv-3)-2=0 3uv-3=0 uv=1 u^3v^3=1 u^3+v^3=2 u^3=v^3=1 Now u=v=\sqrt[3]{1}. I found...
  48. P

    Why is 3AB+P Set to Zero in Cardan's Cubic Equation?

    X^3+PX+Q=0 X_0 = A + B (A+B)^3 + P(A+B) + Q = 0 A^3 + B^3 + (3AB+P)(A+B) + Q = 0 The next step is 3AB+P=0 What make Cardano drop 3AB+P? Why it is zero?
  49. W

    Solving Hermite Cubic Elements Equation Using Fortran - Get Help Now!

    Homework Statement I desperately need help, cause I cannot find anything about hermite cubic elements and I need to make fortran program who solves this equation with hermite cubic elements: please explain to me how to solve this equation need answer fast for semestral signature...
  50. T

    Proof of a limit of a cubic like sequence.

    Now this is an example in my book that I don't really understand. It says prove that the limit of (4n^(3)+3n)/(n^(3)-6))=4 as n goes to infinity. Basically the definition of a limit of a sequence as n->infinity is as follows. Lim{a}=L For any epsilion>0 there is a N>0 such that n>N=>...
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