Measure Definition and 1000 Threads

If I have a linear actuator, how can I find out how much force it can move with a constant velocity?

Isothermal Titration Calorimetry measures the enthalpy of (e.g.) protein binding by measuring the amount of heat that must be added/removed to a solution in order to perfectly balance the heat generated/released by the gradual introduction of a protein's binding partner. My understanding is that...

How can I measure the phase angle between two signals of the same frequency without an oscilloscope? Thanks in advance

I don't know what is the principle of Fizeau's method. In the experiment a rotating toothed wheel is used.But why the toothed wheel is used? If the toothed wheel is not used,why the time for the light traveled cannot be measured?

I have read that, the light from a distant moving object is tested for doppler shift to calculate its velocity. My question is, we can only lay our hands on the modified frequency, not the original frequency. So how to calculate the doppler shift from that?

Hi, I'm doing a group investigation on external wall insulation for my school building. The walls do not have a cavity and thus it has been proposed to put insulation over the exterior render of the wall. This is a fairly common building procedure. However, my task is to investigate the...

Is entropy a measure of "disorder"? In textbooks I never saw a definition of entropy given in terms of a "measure of disorder", and am wondering where this idea comes from? Clausius defined it as an "equivalent measure of change", but I do not see the relation with a concept of "order" or...

I had a question regarding some text in a paper that I was reading. It had to do with ramsey interferometry, where they initialized a particle in spin up (lets say up along the z axis on the bloch sphere), after which they applied a pi/2 pulse to rotate it 90 degrees around the x-axis, they wait...

NASA's horizon system shows the angle (S-O-T) of Sun and planet from the view of Earth. Could you please tell me how one measure the angle of Sun and Mars when opposition nearly takes place. In other words, if S-O-T approaches 175/176/178 degrees, how does one from the view of Earth measure this...

I was wondering how the force of a Stirling engine was measured? I mean, for every degree Celsius that the temperatures differ. how much more force (or horse power) is the engine generating? Are there any other variables to this? What I'm getting is can Stirling engines power cars if enough heat...

I need help in below matter. During the classes on my college we used this type of testing stand with force gauges : http://www.qualityforcegauges.com/force-gauges/ Unfortunately the exam is coming in strides and I still don’t know how to measure the vibration frequency. So I’d like to ask you...

Hi people, I was wondering if anyone knows of any commercial device to measure directly Planck's constant. I mean no use of indirect measurements, just to press a button and for the number to appear in a screen. Thanks

Ok so I have a project and I have to measure the sidereal synodic rotation period of the sun using sun spots. I have included a diagram of what to do. but I will explain it too. you take 5 images with a common sunspot and track it's movement on those 5 days (on the diagram, the sunspot is...

Hi, I am a computer science engineer and I am trying to simulate the gravity on my computer; several objects with different masses randomly distributed in a Three-dimensional space. I would like to compute a global measure that describes the dynamic of that system at each instant T. My question...

Let K be a compact hausdorff space, and u a borel measure on K. You are given that if A is an open set in K with A and E disjoint, we have u(A)=0. (E is a certain closed set in K) Show that for a borel set A, we have that u(AE)=u(A), where AE is the intersection. we have that...

Here's the thing. I want to measure the surface charge of the alginate beads synthesized in our lab. It's about 400μm in diameter. I think most people uses zetasizer to examine the zeta-potential of small particles. But I think 400μm is probably too large for this kind of equipment to measure...

1. About how many cells were plated to count His+ revertant colonies? How was total cell number determined? I know that the mutation freq was out of 10^7 survivors. So they had to measure the total cell number and come up with 10^7 survivors? But I'm not sure how they got this...

Let \lambda(A) denote the measure of A and let \lambda^{*}(A) denote the outer measure of A and let \lambda_{*}(A) denote the inner measure of A Okay so the question is as follows: Suppose that A \cup B is measurable and that \lambda(A \cup B) = \lambda^{*}(A) + \lambda^{*}(B) < \infty Prove...

Figure 7.16 is a bird's-eye view of a smooth horizontal wire hoop that is forced to rotate at a fixed angular velocity co about a vertical axis through the point A. A bead of mass m is threaded on the hoop and is free to move around it, with its position specified by the angle \phi that it...

f_{k} \overset{m}{\rightarrow} f and g_{k} \overset{m}{\rightarrow} g over E. Then: a) f_{k} + g_{k} \overset{m}{\rightarrow} f+g over E b) If | E | < + \infty, then f_{k} g_{k} \overset{m}{\rightarrow} fg over E. Show that the hiphotesis | E | < + \infty is neccesary c) Let \{...

Hello there. The stochastic calc book I'm going through ( and others I've seen ) uses the phrase "\mathscr{F}-measurable" random variable Y in the section on measure theory. What does this mean? I'm aware that \mathscr{F} is a \sigma-field over all possible values for the possible values of...

Hello readers! I have a question for you: My father designs and builds post pounders (machines similar to pile drivers use to "pound" wooden fence posts into the ground). He has had great success building new and innovative pounders and would like to know just how hard they are capable of...

This is how I understand it: Bohr argued that universe was inherently unpredictable as was the spin of the particle, and it was only based on probabilities. Einstein argued that the spin of the particle was actually always the same, just that our physics is not capable of determining it. But...

Homework Statement I'm in a Year 10 physics class. We have been asked, for homework, to design an experiment to measure the velocity of a standing wave. No other information has been given other than that. I reproduce the exact instructions we were given, since the guidelines suggest I...

Suppose A is not a bounded set and m(A∩B)≤(3/4)m(B) for every B. what is m(A)?? here, m is Lebesgue Outer Measure My attemption is : Let An=A∩[-n,n], then m(A)=lim m(An)= lim m(An∩[-n,n]) ≤ lim (3/4)m([-n,n]) = infinite. is my solution right? I am confusing m(A) < infinite , it...

Homework Statement You and a friend each have one rope. You tie the two ropes together and stand as far apart as possible, each holding one end of the new longer rope and pulling to put it under tension. You then begin moving your arm in such a way as to produce a harmonic wave with a...

Hi all, I would like to ask for suggestions on how to measure the frequency from my main supply which is 240V? As i know the frequency varies very little, hence i would like to measure it as accurate as possible. The reason for this is because I'm doing a smart meter project with Arduino...

I have a question on sub-additivity. For sets ##E## and ##E_j##, the property states that if ##E=\bigcup_{j=0}^{\infty}E_j## then ##m^*(E) \leq \sum_{j=0}^{\infty}m^*(E_j)##, where ##m^*(x)## is the external measure of ##x##. Since ##E\subset \bigcup_{j=0}^{\infty}E_j##, by set...

Let us begin with a state belonging to the four dimensional tensor product of two particles. \sqrt {p_1}|+_x>|+_{x'}> + \sqrt {p_2}|+_x>|-_{x'}> + \sqrt {p_3}|-_x>|+_{x'}> + \sqrt {p_4}|-_x>|-_{x'}> We can compute the Von Neumann entropy by tracing out and taking the log of the matrix...

So the above is the problem and my idea of how to approach it. This problem comes from the section on the Countable Additivity of Integration and the Continuity of Integration, but I was not sure how to incorporate those into the prove, if you even need them for the result. I had no idea what...

Let us all pretend it 150 years in the future and we all have spaceships and can travel through space easily without disrupting time. Our only measure of location would be compared to Earth, and our measure of time would be Earth time (revolutions around the sun and rotations). What if we...

Homework Statement We have a metric space X=\cup X_k where X_k\subset X_{k+1} and each X_k is open. Show that for any Borel set E, there is an open set U such that \mu (U-E)<\epsilon . (Its supposed to be "U \ E".) Homework Equations \mu is a measure, so probably the important thing...

Hello everyone, I am running a physics class next week where I want to show to high school children the power of piezoelectricity. I want to let them see with their own eyes that if a crystal is squeezed the differential potential between two opposite faces will change accordingly to the...

Hi all, I understand some PDE is linear like \frac{\partial f}{\partial t}+\frac{\partial f}{\partial x}=0 while some PDE is nonlinear like \frac{\partial f}{\partial t}+f\frac{\partial f}{\partial x}=0 Some PDE is weak nonlinear and some is strong nonlinear. I am wondering whether...

Hi, I'm doing some work and keep coming across Enstrophy. Wikipedia gives a description that provides some insight, however I was hoping that someone could explain why its a measure that is used and what does it tell us?

we cannot measure the speed of light in a vacuum only in space, and since we are told that space is expanding it could be that the speed light varies through time.

Homework Statement Two parts to this question. a) Suppose ##S## is a bounded set and has an interior point ##Q##, prove that ##C(S) > 0##. ( Hint : Inside any neighbourhood of ##Q##, you can place a square ). b) For each integer ##n>0##, let ##L_n## be the line segment ##\{ (\frac{1}{n}, y)...

Ok, I don't think I'm on the right track here. I ASSUMED that the set of all countable collections \{I_k\}_{k = 1}^\infty of nonempty open, bounded intervals such that E \subseteq \bigcup_{k = 1}^\infty I_k is a countable set itself, which it probably isn't. I'm not even sure where to start...

Hello everybody, Eratosthenes of Cyrene ( 276 BC– 195 BC) was a Greek mathematician, geographer, poet, astronomer, and music theorist.The interesting thing about his biography,is that he was able to measure the Earth's circumference using only simple tools and good geometry .here is a video...

Hello, Is there a cheap device or someone that I can easily build that will let me know the speed of a moving object? Its for one of my son's project... Thank you in advance.

Would it be correct to call Voltage and Temperature intensive measures of Energy, and call Electric Field and Pressure intensive measures of the potential for Force generation? If so, is Voltage (Potential Energy) used to generate a force on a charged particle (by way of an Electrical...

can we measure ripple factor using same? again what is difference between ripple, ripple voltage and ripple factor?

Author: Donald Cohn Title: Measure Theory Amazon Link: https://www.amazon.com/dp/0817630031/?tag=pfamazon01-20

I have finally finished reading the proof of the Banach-Tarski paradox. I think the proof was the standard versoin I see around the internet, with the the group G of rotations phi and psi and so on. I was wondering how the proof fails as a result of lebesgue measure on the set?

Hi guys. I am using a servo motor in one of my projects. I would like to calculate the power the motor is inputting into my system. I will use the equation P=IV to calculate my power. Voltage across my motor will be constant. It's about 5V since that's the voltage required to run the motor...

Hello all, I'm a new Mechanical engineering graduate student who needs help using a photodiode. I'd like to rig up some kind of circuit that will let me measure the intensity of laser light. This is kind of a new area for me haven't really done anything like this before so forgive me if I come...

According to the QM postulates, when we measure momentum, we get an eigenvalue of the momentum operator and the system takes on a state that is the corresponding eigenket. Now, as I understand it, the eigenkets of the momentum operator are all Dirac delta functions corresponding to plane...

The cosmological principle says that on large scales the universe is homogeneous and isotropic. Therefore there should be a way to define and measure inhomogenities and anisotropies. Regarding the definition I see the following problem: Usually we would like to define ##M=\int_V dV\,\mu##...

Is there a formula or something? When I solve quadratic equation I get two roots of x1 and x2. how can I find out the length? Thank you

I don't understand what it means to have measure zero. Like I understand that the indicator functions is and what it does, but I am not exactly sure what measure zero is. Okay, I mean that I understand that: ## \int_{A} 1_{A} dx = \nu(A)## and this is the "volume" of some region A in...