Constants Definition and 486 Threads

Are the cosmological constant and the universal constant essentially the same?

Hi. My colleagues and I are doing a research on transformers (single-phase) and we stumbled across the following equations involving hysteresis and eddy current losses: Wh = ηBmaxxfV where Wh = hysteresis losses η = Steinmetz hysteresis constant Bmax = maximum flux density x = constant...

Homework Statement Suppose that the characteristic equation to a second order, linear, homogeneous differential equation with constant coefficients yielded two complex roots: \begin{array}{l} {\lambda _1} = a + bi\\ {\lambda _2} = a - bi \end{array} This would yield a general solution of: y =...

I have heard that ST can calculate the masses of the particles species of some vacuum and also its decay rate, charge and so on, but I have not seen any clear paper on the subject. Can anyone point me to one? Are "hbar" and "c" the same in all the vacuums?why or why not? Can ST predict the...

The commutation relations for the ##\mathfrak{so(n)}## Lie algebra is:##([A_{ij},A_{mn}])_{st} = -i(A_{j[m}\delta_{n]i}-A_{i[m}\delta_{n]j})_{st}##.where the generators ##(A_{ab})_{st}## of the ##\mathfrak{so(n)}## Lie algebra are given by:##(A_{ab})_{st} =...

Hey! :o Each element of the ring $\mathbb{C}[z, e^{\lambda z} \mid \lambda \in \mathbb{C}]$ is of the form $\displaystyle{\sum_{k=1}^n α_kz^{d_k}e^{β_kz}}$. A differential equation in this ring is of the form $$Ly = \sum_{k=0}^m \alpha_k y^{(k)}(z)=\sum_{l=1}^n C_lz^{d_l} e^{\beta_l z} , \ \...

Hi, I was just wondering if you have a cross product can you multiply out the constants and put them to one side. So ik x ik x E is equal to i^2(k x k x E) therefore is equal to -k x k x E. Is that correct?

Variable; A symbol for a number we don't know yet. It is usually a letter like x or y. Example: in x + 2 = 6, x is the variable. [mathsisfun.com] Q. Why is it called the variable? This seems to me to imply that its value varies. In the above example it seems to me to simply be the unknown...

Homework Statement A nonconducting disk of radius R has a uniform positive surface charge density sigma. Find the Electric field at a point along the axis of the disk at a distance x from its center. Assume that x is positive Homework Equations E=kq/r The Attempt at a Solution I know I'm...

I am reading gravitation and spacetime by Hans Ohanian and he is discussing the possibility of the constants, such as proton mass, fine structure constant, etc, actually changing over time. He makes the claim that since the universe is ~10^10 years old the expected change should be...

Homework Statement ##y' = \frac{cos x}{sin y}## ##y' = \frac{6x^2}{y(1 + x^3)}## Homework EquationsThe Attempt at a Solution So I was working through some textbook problems and there's something about the solutions of the above equations I don't quite understand. The first one: ##\int sin...

Now a days i am working on this paper...

Homework Statement A sinusoidal wave traveling in the –x direction (to the left) has an amplitude of 20.0 cm, a wavelength of 35.0 cm and a frequency of 12.0 Hz. The transverse position of an element of the medium at t = 0, x = 0 is y = –3.00 cm and the element has a positive velocity here. (a)...

Homework Statement Suppose, the following equation describes the relation between an independent and a dependent variable physical quantities(that will be measured by experiments; for example, temperature, current, voltage etc) x & y : ##y = ax^2 + bx + c## We have to find the values of the...

I wanted to ask how are the values of proportionality constants in physical relations determined. How do we come to know their exact values ? An explanation with an example please...

Homework Statement determine the constants a,b,c, and d so that the function f(x)=ax^3+bx^2+cx+d has its first derivative equal to 4 at the point (1,0) and its second derivative equal to 5 at the point (2,4) Homework EquationsThe Attempt at a Solution I found the first and second derivative...

i suppose matrices of the form $$A_i=\left(\begin{array}[cc] ccos(x_i)&sin(x_i)\\sin(x_i)&-cos(x_i)\end{array}\right)$$ And i consider the matrix $$C=A1\otimes A2\otimes 1_4-A1\otimes 1_4\otimes A2$$ I would like to show that the eigenvalues of C are independent of the x i tried with...

Homework Statement What is the difference between a dimensional physical constant and dimensionless physical constant? Homework EquationsThe Attempt at a Solution

How many of the 26 basic constants of nature and more (beyond the standard model) where the values range can be said to be quantum eigenvalues and the exact constant being the *collapsed* one? In other words, Can you refer to the exact value as collapsed (quantum) one from the eigenvalues (or...

Homework Statement I need help for this kinetics question: Chlorination of butene at 0 degrees c, liquid phase, dichloromethane as solvent. initial concentration of butene is 0.1M conversion of 47.71% achieved after 3.1 hours. an additional 0.5M of hot butene was added at this point, which...

Homework Statement Okay, here's the deal:I have been given a second order nonlinear differential equation, and I have also been given the general solution with constants A and B. I am supposed to find the constants A and B. The solution represents a fermion at rest, since the solution does not...

I'll post a picture of the equation and a picture of the problem I'm being asked. My problem is I can't get the units to cancel. This is a ratio, so the final answer is supposed to be unitless. The exponential term obviously needs the units to cancel, so I chose the correct Boltzmann constant...

Homework Statement The velocity of a particle is related to its position by: v2 = w2 (A2 - x2) where w and A are constants. Show that the acceleration is given by: a=-w2x[/B]Homework EquationsThe Attempt at a Solution a= v* dv/dt v=(A2w2-x2w2)1/2 dv/dt= 1/2 (A2w2-x2w2)-1/2 * -2xw2 v *...

Homework Statement For the following arrangement of two springs, determine the effective spring constant, keff. This is the force constant of a single spring that would produce the same force on the block as the pair of springs shown for this case. (Spring 1 is attached to Spring 2 which is...

Homework Statement Homework Equations DifEqs The Attempt at a Solution y ' = 4C1e-4xSinX - 4C2e-4xCosX y'(0) = -1 -1 = 0 - 4C2 Therefore C2 = 1/4 Not correct. What am I doing wrong?

Homework Statement In 2000 the population of a country was estimated to be 8.23 million. In 2010 the population was 9.77 million. Assume that the number of people P(t) in millions at time t (in years since 2000) is modeled by the exponential growth function. P(t) = Aekt Find P(t) giving the...

Find constants $P,\,Q,\,R,\,S, a,\,b$ such that $P(x-a)^2+Q(x-b)^2=5x^2+8x+14$ $R(x-a)^2+S(x-b)^2=x^2+10x+7$

Homework Statement So I'm calculating the gravitational potential of a sphere at at point P. R = radius of sphere, r = distance from center of sphere to point P. I'm looking at two scenarios; r > R (1) and r < R (2). So I have the following integral: \begin{equation} V(r) = \int...

A common equation (attributable to Fred Hoyle) for the mass of the observable universe is: c3/(2GH0). Despite that the whole universe is vastly larger than the observable universe, we can create an equation to calculate the mass of the observable universe, using the standard constants of...

So, I know that there are already three absolutely mandatory physical constants, like the gravitational constant, the Planck constant, and the speed of light. But what if you only changed the value of one constant? For example, if you changed the value of the gravitational constant to 4.4663 x...

Homework Statement ∫y1(x)^2dx from - to + infinity=1 and ∫y2(x)^2dx from - to + infinity=1 Homework Equations None that I know of. The Attempt at a Solution I evaluated the integrals and got that c1 is equal to c2 but I think that's wrong.

Homework Statement The ground, 1st excited state and 2nd excited state wave functions for a vibrating molecules are: Ψ0(x) = a e-α2/2 Ψ1(x) = b (x+d) e-α2/2 Ψ2(x) = c (x2 + ex + f) e-α2/2 respectively, with constants: a, b, c, d, e and f. Use the fact that these wave functions are part of an...

I'm jut not sure how to solve this problem in general, I tried a couple ways, but I keep getting wrong answers and I only have 2 attempts left. Please give me a direction to go in! A spring is 17.1cm long when it is lying on a table. One end is then attached to a hook and the other end is...

Homework Statement If you change the diameter of a spring does it affect the spring constant? Assume the spring length, if fully extended, was kept constant. Homework Equations F=kx; F=mg The Attempt at a Solution From my research the spring constant (k) is measured by applying a mass and...

Consider the following generic equilibrium: aM + bN ⇌ cO + dP An equilibrium constant, K, can be defined as: $$K = \frac{[O]^c [P]^d}{[M]^a [N]^b}$$ But couldn't we also define another equilibrium constant similarly with coefficients that are in the same ratio as our original equation? For...

I have a question on quantities that 'run' under the renormalization group flow. What's clear is that the properties through which particles couple -- such as charge, isospin, color etc -- change in their strengths as the energy increases. But this running is also true of the mass, which is a...

Homework Statement If acceleration=dV/dt, V=def.integal from t1 to t2 of a*dt,=at+C. At t=0, C=V0. Why do we have a constant C, as a definite integral was calculated. Won't C2 and C1 cancel out? Homework Equations Definite integral from x1 to x2 of dx is x2-x1 without any constant, right? The...

How would I go about calculating the units for the van der waals constants if I have 2 unknowns? (a and b) (P + a (n/V)^2) (V - n b) = n R T p=Pressure v=Volume n=moles R=gas constant T=temperature

I was looking through Zee's 'Quantum Field theory in a Nutshell" and he says that c and \hbar are "not so much fundamental constants as conversion factors." I've heard other physicists say this as well. I understand that these constants are used in some equations to give units of energy so...

I've noticed that the vast majority of named or important mathematical constants, are what you might call small numbers. Their modulus lies very often in the range [0,5]. Here's two examples of tables: http://en.wikipedia.org/wiki/Mathematical_constant#Table_of_selected_mathematical_constants...

My textbook says the extreme value theorem is true for constants but I don't buy it. I mean I suppose that every value over a closed interval for a constant would be a maximum and a minimum technically but it seems like BS to me. Can anyone explain why this BS is true?

The wave function solution psi is a function of time and position. Hence the integral of its square over all x will, in general, give a function of time. To normalize this, we must multiply with the inverse of the function. Therefore it seems that the normalization constant does not remain...

Hi guys, so we currently ran an experiment where we calculated the verdet constant when laser light passed through a glass rod then through an analyzer to a photodetector. The experiment worked great for us but I wanted to know if anyone has ever calculated the verdet constant for any other...

Homework Statement Find the differential equation of ln y = ax^2 + bx + c by eliminating the arbitrary constants a, b and c. Homework Equations Wrosnkian determinant. The Attempt at a Solution I've solved a similar problem (y=ax^2+bx+c --> y'''=0), but couldn't do the same with...

I am reading Joseph Rotman's book Advanced Modern Algebra. I need help with Problem 2.21 Part (i) on page 94. Problem 2.21 Part (i) reads as follows: -------------------------------------------------------------------- Let R be a domain. Prove that if a polynomial in R[x] is a unit, then it...

In classical electromagnetism, Coulomb's constant is derived from Gauss's law. The result is: ke = 1/4πε = μc^2/4π = 8987551787.3681764 N·m2/C2 Where ε is the electric permittivity of free space, μ is the magnetic permeability of free space, c is the speed of light in a vaccuum, and 4π is...

Homework Statement Eliminate the arbitrary constants of the equation: ax2 + bx + cHomework Equations (Concept) According to my instructor, having n arbitrary constants makes an nth-order differential equation.The Attempt at a Solution I tried to differentiate 'til I get a third derivative so I...

If in a typical complete circuit (RLC) we have a resistor with resistence R, an inductor with inductance L and a capacitor with capacitance C, so the generator has which constants? And in second place, I was searching about the math of generators in series and parallel and I found something...

Recently I have taken an interest in physical constants (and, through it, an interest in SI units and the upcoming redefinition of the kilogram). I actually have a list of almost all of them now, standard uncertainties included. After a bit, I decided to have a bit of fun messing around with the...

What exactly is ∏? I've never quite understood why it is apparent in so many different equations and formulas. Why is it there? Why is it apparent in nature so much? And ∏ it's just a infinite set of numbers why is it any more relevant than any other set of infinite numbers. Why is 3.14... so...