Explanation Definition and 992 Threads

Why is the E[ Y - f(x) ]^2 minimized when choosing f(x) = E[Y|X] ?

Please, I need you to teach me how to write the equations from the Karnaugh map and then how to draw the NAND circuits. Here's the sample that I have but I don't understand :( I know the basic of writing SOP and POS from the Karnaugh map but that's all. I don't get how it is converted to get the...

Hi all, I'm looking for some help in understanding one of the theorems stated in section 20 of Munkres. The theorem is as follows: The uniform topology on ##\mathbb{R}^J## (where ##J## is some arbitrary index set) is finer than the product topology and coarser than the box topology; these...

For every force exerted by object A on object B, an equal and opposing force is exerted by object B on object A. I need help understanding the principle. I understand it when dealing with a completely stationary object: pushing on a solid wall, it exerts an equal force back to your hand...

Hi people, I'm new here, so, if there's anything wrong with my post, please tell-me =) So, if we have a recipient, with a cavity and a small hole, and imagine that we have a sudden expansion of the gas inside the recipient(we assume the volume increase was ΔV, and the duration of the...

Hi All, The question is rather simple: Why a plane mirror image exchanges right with left but does not interfere with up and down? Best wishes, DaTario

Hello All, I am new to GR, studying slowly. I am little bit confused between the following terms and their usage: (a) Co & contra variant vectors - Do they help in transformation? (b) What is a co-ordinate free system? Do co & contra variant vectors help it? (c) What is parallel...

Hello, Why people use semi-log and log-log plots? What are they advantage? Linear plots are more convenient as they show the direct relationship between x and y variables, aren't they? Thanks.

1. Question: Find the directional derivatives of f(x, y, z) = x2+2xyz−yz2 at (1, 1, 2) in the directions parallel to the line (x−1)/2 = y − 1 = (z−2)/-3. 2. Solution: We have ∇f = (2x + 2yz)i + (2xz - z2)j + (2xy - 2yz)k. Therefore, ∇f(1, 1, 2) = 6i - 2k. The given line is...

Hey all, I was wondering if someone could explain the difference between isothermal and adiabatic processes. I know that in isothermal process, there is no temperature change in the system, and in adiabatic process, there is no heat transfer. However, can someone explain to me what each one is...

Homework Statement If the magnitude of the Earth's momentum is P, what is the magnitude of the impulse that the sun applies to the Earth during six months? Homework Equations The Attempt at a Solution I know the solution is 2P, and I'm pretty sure it's just due to the change in...

The derivative of sin(ax²) is 2axcos(ax²). Why is that? I understand the cos(ax²) part of the derivative but I don't understand where the 2ax is coming from.

I wish to know why and how does hysteresis occur from a purely mathematical perspective, using analytical functions and multivariable calculus. Thank you!

I need explanations at the last part of this math solution. Question: Solve the differential equation: y' = (1 + 2/x)y Answer: ln|y| = x+ln(x^2)+c |y| = e^c.x^2.e^x y = Cx^2.e^x (C = +/-e^c is any constant that is not equals to 0) What I don't understand is this part where ...

I get confused when I read that the Energy of wave in classical mechanics is correlated to the amplitude E ~ A^2 (pls. point me to a doc which shows that, couldn't find any exact formula on internet), but then when we are talking about atoms,photons,electrons they say it is dependent on the...

I understand that in order for a space to be conformally flat that the vanishing of the Weyl tensor is a necessary condition. I was wondering if the following arguments are also (if not the same) in arguing that Robertson-Walker spacetime is conformally flat. Starting with the...

Homework Statement Every bounded sequence has a convergent subsequence. Homework Equations Suppose that closed intervals I_0 \supset I_1\supset ... \supset I_m and natural numbers n_{1} < n_{2} < ... < n_{m} have been chosen such that for each 0 \leq k \leq m, (2) |I_{k}| =...

Homework Statement Every bounded sequence has a convergent subsequence. Homework Equations Suppose that closed intervals I_0 \supset I_1\supset ... \supset I_m and natural numbers n_{1} < n_{2} < ... < n_{m} have been chosen such that for each 0 \leq k \leq m, (2) |I_{k}| =...

Hello, I need your help in clarifying some points from Normal Distribution Theorem: What does this expression exactly says: P(Z<=z) ? Z is random variable? z is deviation?

I'm reading the Wikipedia page for the Dirac equation I am not sure how one gets a new \rho and J^\mu. How does one do to derive these two? And can anyone show me why the expression for density not positive definite?

Homework Statement https://dl.dropbox.com/u/66988308/Capture.JPG Homework Equations V=rWThe Attempt at a Solution I tried to plug in the forumla , and algebras but I keep getting rc/rf as answer instead of rf/rc as the book says. Work: Vf=(rf)W W=Vf/rf W=Vc/rc Vc/rc = Vf/rf (Vc)(rf) = (Vf)...

what's the most illustration explanation or reason why a shear can pass from positive to negative in say a beam?

Homework Statement There is time-pass game, "Coin in a Bucket". In this game, we take a bucket full of water, and in the middle there is a small cup. We are asked to put the coin in the small cup from above the bucket. Now the point is, that whenever we place the coin from top of the...

Hi, So I recently worked out a problem in my mechanics class about two people jumping off a frictionless railroad cart at speed u. The result is that the cart will move faster if they each jump off separately than it would have if they both jumped at the same time. I've been trying to...

Homework Statement http://img507.imageshack.us/img507/6493/f7868b61c6cb4d6084fa5ba.png Homework Equations The Attempt at a Solution I've tried to deduct how my textbook has actually done this Thevenin Equivalent. No one in my class (that I've come into contact with anyway)...

Homework Statement I have two separate problems with the same issue; I don't grasp what information the equation of state is giving me. a. A system with l=1 is in the state ψ> = (1/√2) 1> - (1/2) 0> + (1/2) -1> Find Ly. b. A spin 1/2 is in the state ψ> = (1+i)/3 +> + (1/√3) ->...

Thinking of a restrictive pipe as an analogy of a resistor, which converts electrical energy to heat, would a pipe demonstrate a rise in temperature related to the loss of energy in the water, . (theoretically - and assuming conditions which did not have other influences - so water at ambient...

This is from section 2.3 in Griffith's book on the harmonic oscillator, and apparently this differential equation should be obvious (to move on in my reading, I need to understand this first). I'm not quite sure how to solve a second order ODE without constant coefficients, so help to get to the...

Alright in class, my teacher can factorize quadratics almost instantly. I wanted to know if anyone can tell me how to do it his way... Like if you had 5x^2 + 14x - 3 (x+3)(5x-1) He writes that instantly, I kind of figured out in the first term, you put the sign that the b term...

Homework Statement A proposed ride at the amusement part launches a roller coaster car up an inclined track. Near the top of the track, the car reverse direction and rolls backwards into the station...Homework Equations My question is: What is the difference between, "Sketch a graph of the...

Hey guys I'm a new member and I will be mostly asking questions :P Anyways ... Physics subjects in my school are about electricity now and my teachers aren't very good, so I can't clearly understand what they're saying. To get to the bottom line, our lesson was about electrons and...

hello PF community i'm looking for help in understanding the classification and observed behaviour of some DIY voltaic (?) cells and their associated circuits with which I've been tinkering for a couple of years the cell operation seems to belong somewhere between galvanic and the original...

I had this elaborate example all set up to lay my question out. and I can hear my x wife in my head. "you over think everything" So here is my question. I do not understand free falls 93feet/sec /second. this sounds to me that Tim would be doing 279 feet per second after only 3 seconds...

Homework Statement Okay I have to write an EEI (Extended Experimental Investigation) for physics in relation to which radiator coolant is best from a thermodynamics point of view, thus the specific heat of the coolant is the main focus. But to incorporate more depth into the report, I was going...

Hello, The following problem appears in my number theory text: The answer: I have tried to trace the reasoning in reverse. I understand how we get to the finish (by showing that the number is divisible by all of the relatively prime factors of n, but I don't understand how we...

PLEASE NOTE: When replaying these animations, click on the circular arrow in the bottom left corner of the video window. If you click inside the video, you may end up running a different video. We start during the era before Einstein when most of the great scientists believed in an absolute...

I've known this fact for a long time and have thought about an explanation for it for just as long. I've observed its effects such as in the shower: as the water flows down it moves the air with it causing the curtain to move inward into the shower. It just seems that with a moving fluid that...

hello, I can't seem to make sense out of amper/meter...one amp flowing throw a wire with a length of 0.5m would be 2A/m ? how does relate to the magnetic field?

So I have been dealing with the modulus function for almost a year now , I didn't ran into it many times so didn't really tried to understand it well . But it has started to get a little bit confusing . So if someone helps me I will be really happy . From what I know f(x) = |x| = { x ; x >=...

After looking into the Tacoma Narrows Bridge collapse, I tried to find out what this thing called aeorelastic flutter is and what causes it. Unfortunately, I didn't get a very good answer for either question, especially the latter one, and was hoping someone could help me out.

Just a bit confused & I am in need of a simple explanation of how energy flows in a battery. This was my thinking: Cathode: positive terminal, current flows OUT Anode: negative terminal, current flows IN Is this correct? And if so, why do many battery diagrams depict energy flowing out...

Energy Conversion Explanation I have a ball behind suspended at the top of a ramp. The ball rolls down the ramp and triggers a switch. The switch is connected to a 9V battery and a motor and turns on once the switch is pressed. The motor acts as a fan because it has "blades" attached to it...

Homework Statement The following data has been collected: Gas volume: V = 0.8 m3 Gas pressure: p = 160 kPa Compression index: n = 1.4 Pressure/volume relationship: pV^n = C Work done = ∫ TOP=V2 BOTTOM =V1 You first need to work out C, the value of the pressure/volume relationship...

i understand how sin90-theta is cos , but i am having trouble with sin 90+theta = cos ...please explain

Although the uncertainty principal can be written without quantum harmonic oscillators, it still happens when you consider them. Can the reason for the uncertainty principal be explained in terms of changing the equation? If I have a completely undetermined momentum, I should have something...

http://singlephoton.wikidot.com/single-photon-detection-experiment I was browsing the web earlier, and noticed that the page above said that recently there was a semi-classical (wave) explanation of the photoelectric effect (End of 2nd-3rd Line). I was wondering how this was, as I can't seem...

This is a graph from an article from last November on the search for the Higgs with the Atlas detector. It shows the cross section for a Higgs process relative to the standard model prediction. And then the upper limit of this, at the 95% confidence level. And this for different Higgs...

Absolutely Stunning Plot of a "Random" Sequence (Picture Included)--Need Explanation So I created 10000 waves of varying heights, 50% of the waves were 2 feet, 30% 1 foot, 15% 3 feet, 4% 4 feet, and 1% 5 feet tall. I generated 10000 "random" numbers with the statement "=Rand()" (this generates...

Hey all, This newb needs help understanding the posted circuit. Real quick, I'm going to post what I understand from left to right. R53 and R62 = Voltage Divider D2 = Clamping Diode (Clamping to 3.3V) R45 = R1 in basic (R2/R1)Vin = Vout op amp formula This is where I get stuck. Let's...

We know that an object with lower density than the medium it's in will float, and higher density will sink. Could someone provide proof of this in an equation format? I've been trying to use Bernoulli's theorem, but I feel like I'm doing something wrong. Thanks.