qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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50,802 | [
"https://quant.stackexchange.com/questions/50802",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/-1/"
] | I am having a slight brain meltdown because I do not seem to be able to understand the following basic thing.
Consider a BS economy, and two assets <span class="math-container">$X$</span> and <span class="math-container">$Y$</span>
<span class="math-container">$$
dX = \sigma X dW
$$</span>
<span class="math-container"... | Might you be using the tower law in a wrong way? I have the impression you derive your second equation by conditioning by the <span class="math-container">$\sigma$</span>-algebra generated by <span class="math-container">$(Y_t)_{t\geq0}$</span>, however note that:
<span class="math-container">$$\mathscr{F}_t\nsubseteq\... | Agreeing to your first observation: After orthogonalization, with independent W and W’, and using self explanatory notation for the new diffusion coefficients, which obviously depend on <span class="math-container">$\rho$</span>, we can show that, under <span class="math-container">$\mathbb{Q}_Y$</span>, we have:
<spa... | https://quant.stackexchange.com |
1,590,750 | [
"https://math.stackexchange.com/questions/1590750",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/145510/"
] | Does $\sum \limits _{k=1}^\infty \frac{3n+2}{n(n+1)}$ converges?
Well, I know that $\frac{3n+2}{n(n+1)} = \frac{3}{(n+1)} + \frac{2}{n(n+1)}$
and I know that $\sum \limits _{n=1}^\infty \frac{3}{(n+1)}$ < 3 and $\sum \limits _{n=1}^\infty \frac{2}{n(n+1)}$ < 2 Which implies that (with arithmetic limits) that $\... | You have
$$
\frac{3n+2}{n(n+1)}>\frac{3n}{n(n+1)}>\frac{1}{n+1} \quad \qquad n=1,2,\cdots,
$$ thus your initial series is <strong>divergent</strong> as is the harmonic series.
| Your statement: $\sum_{n=1}^{\infty} \frac{3}{n+1} < 3$ is incorrect as the LHS goes to infitiny.
$$\sum_{n=1}^{\infty} \frac{3n+2}{n(n+1)} = \sum_{n=1}^{\infty} \bigg (\frac{1}{n+1} + \frac{2}{n} \bigg) >\sum_{n=1}^{\infty} \frac{2}{n}$$
which means your series is divergent.
| https://math.stackexchange.com |
151,193 | [
"https://electronics.stackexchange.com/questions/151193",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/49115/"
] | I want to connect two PCBs with four wires: VCC, GND, 2x I2C. Which connector is best suited for this application? I was thinking about an USB connector (and wire), but I am not sure if that is the best possibility. Therefore I wanted to ask if there are better connector types than USB for this application? VCC is 5V.
| Some I2C interfaces on the market (MCC iPort for instance) use AMP 4-1761206-1 connectors, for which pre-fabricated cables are readily available.
<img src="https://i.stack.imgur.com/ScpYI.jpg" alt="enter image description here">
You could also go with RJ-11 if you're not worried about shielding (as long as no one con... | <img src="https://i.stack.imgur.com/rzkm5.jpg" alt="enter image description here">
I use this type of flat cables. They are reliable to use.
| https://electronics.stackexchange.com |
43,811 | [
"https://physics.stackexchange.com/questions/43811",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9662/"
] | In ordinary classical gauge theories the term $-\frac{1}{2}\mathrm{Tr}(F_{\mu\nu}F^{\mu\nu})=-\frac{1}{4}F^a_{\mu\nu}F_a^{\mu\nu}$ in the Lagrangian is completely natural. A somehow rare term would be a "cubic" one like $$L_c=\kappa \eta_{\mu\gamma}\mathrm{Tr}(F^{\mu\nu}F_{\nu\alpha}F^{\alpha\gamma}).$$ Is there a phys... | You can certainly write down a Lagrangian with $F^2$ and $F^3$ terms, and they will both contribute to the tree-level amplitudes involving three (Non-Abelian) gauge bosons. (You could also write additional terms with four or more factors of $F_{\mu\nu}$, but kinematics prevent them from contributing to the three-gauge-... | user1504 has already explained in terms of renormalization. Here I want to cast one idea on another aspect -- why Lagrangians you see in real physics always have quadratic dependence in velocity, i.e. $L\sim \dot{x}^2$ or $\mathcal{L}\sim \dot{\phi}^2$.
Let's talk about simple quantum mechanics, i.e. things are talked... | https://physics.stackexchange.com |
3,031 | [
"https://quant.stackexchange.com/questions/3031",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/2137/"
] | I am trying to write a highly optimised limit order book and I wondered what sort of size I can expect for:
<ul>
<li>Range of limit prices</li>
<li>Number of orders at each limit price</li>
</ul>
I am developing custom hardware (FPGA) and thus have very limited amounts of memory available and very different data stru... | A correct answer would depend on the instruments and markets you're trading, and whether this is for handling public or propietary orders. For example, if I were to design for the simple case, US equities and a public market, I'd want the queue size at <em>each</em> price level to be able to handle at least the maximu... | If you're writing a "highly-optimized" book then you should be tailoring that book to the venues from which you will be receiving data. Max price, for example, is published in NASDAQ's Itch spec: 200,000.0000.
If you plan on trading US equities you better go read each of the venues depth of book specs very carefully. ... | https://quant.stackexchange.com |
44,870 | [
"https://softwareengineering.stackexchange.com/questions/44870",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/16193/"
] | I am gathering questions and responses in math, science, and technology for a "Family Feud" style game for high school students. I am having trouble finding and thinking of questions, especially in the technology realm. Technology (programming or general tech) questions are preferred.
If you have never seen the game s... | The Family Feud questions are always in the form of "name something that ..." not "What are all the ...". so you could have "name a programming language" or "name a data type". You could also have "we asked 100 programmers, what is your monitor resolution" or "name an add-in for Visual Studio" or "name an editor for wo... | What common control structures exist in most programming languages?
<ol>
<li><code>if</code></li>
<li><code>while</code> loop</li>
<li><code>for</code> loop</li>
<li><code>goto</code></li>
</ol>
| https://softwareengineering.stackexchange.com |
658,234 | [
"https://physics.stackexchange.com/questions/658234",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/307328/"
] | I have a toy car and a battery. The barrery has a screen that shows how much energy it has left. Since kinetic energy is proportional to velocity squared, I need 1J of energy to go from 0m/s=>1m/s, but 3J of energy to go from 1m/s =>2m/s.
So I can surely use this to tell what absolute reference frame I am in! If ... | In all your figures, you are referring to the speed of the vehicle with respect to the surface of the earth. Since you cannot tell the speed of the earth, you do not have access to an absolute reference frame. You do have access to the relative speed of the vehicle, but of course that could be done as a speedometer a... | The work done by the battery is frame dependent. In order to make my point and to simplify the math, I'm assuming that the battery does work by applying the force on a single point, instead of applying forces on multiple charges to move the current. I'll also be doing things in 1d. You can think in this particular case... | https://physics.stackexchange.com |
597,810 | [
"https://electronics.stackexchange.com/questions/597810",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/301407/"
] | I am new to Verilog and I am trying to implement an asynchronous reset.
I have difficulties understanding the difference between using <code>always @ (posedge clk or posedge reset)</code> and <code>always @ (posedge clk or negedge reset)</code>.
What are the differences between them and which one should I use to imple... | <code>Posedge reset</code> reacts on positive edge of reset signal, that is transition from <code>0</code> to <code>1</code>. <code>Negedge</code> is transition from <code>1</code> to <code>0</code>.
Which to use depends on whether the reset signal is active high or low. If it is active high (<code>reset=1</code> mean... | I suspect that the source of your confusion is that in real life, the async reset input to a flip-flop is not actually edge-triggered, but level-triggered. (The reset happens continuously whenever the reset is active, not just at the edge.) So, the standard way of modeling flip-flops with async reset in Verilog is argu... | https://electronics.stackexchange.com |
45,952 | [
"https://physics.stackexchange.com/questions/45952",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9783/"
] | Where a force of 200N pulls two blocks together(as one system) across a horizontal table top(µ=0.800)
$m_A$ = 5.00kg, $m_B$ = 10.0kg
<ol>
<li>Find the acceleration of the system. </li>
<li>Find f$_k$ between B and A</li>
</ol>
I found a to be 5.485 m/s² which agrees with the textbook's 5.5m/s².
The textbook says b ... | If both block A, and B are moving together as a system, the two blocks will not have a kinetic friction between the two of them (because they are stationary to each other). Draw your free-body diagram of both blocks individually, and write an expression for all the forces acting on the each block. Share what you find b... | Ok I figured it out, sorry the fact that block A is on top of block B is important.
F$_a$ = 5.485m/s²(5kg) = 27.425N
$\Sigma F_x = 200N ∴ f_s= 200N - F_a = 200N -27.435 =172.575$
| https://physics.stackexchange.com |
604,173 | [
"https://physics.stackexchange.com/questions/604173",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/283512/"
] | A helicopter rotor blade is 7.80 m long and has a mass of 110 kg. (a) What force is exerted on the bolt attaching the blade to the rotor axle when the rotor is turning at 320 rev/min? (Hint: For this calculation the blade can be considered to be a point mass at the center of mass. Why?
| As said in the question, we can consider the blade as a point mass.
Now don't imagine that the blades are connected to the axle, rather think of them as the mass of the blade tied to a string 7.80 m/ 2 (distance of the center of mass and the axle) from the axle. Now, when the masses move in a circular motion the only t... | There are actually three important components of the bolt force: vertical, to keep the blade from falling, horizontal-tangential which pushes or pulls on the blade perpendicular to its length, and horizontal, to keep the blade from flying away from the rotor axle.
In order to calculate the vertical force you would need... | https://physics.stackexchange.com |
488,100 | [
"https://physics.stackexchange.com/questions/488100",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/235452/"
] | (From The Oxford Solid State Basics by Steven H. Simon [Chapter 2.1])
Reading through a condensed matter textbook and struggling to see how the author progresses with the calculation in the chapter where he discusses Einstein's calculation for a single harmonic oscillator in one dimension:
<span class="math-container"... | Rewriting <span class="math-container">$\sum_{n=0}^{\infty} e^{-\beta\hbar\omega(n+1/2)}$</span> as <span class="math-container">$\sum_{n=0}^{\infty} (e^{-\beta\hbar\omega(1/2)} * r)$</span> [where r = <span class="math-container">$e^{-\beta\hbar\omega n}$</span>] may expose the logic of the first step for you: As <spa... | For the first: Look at the maximal <span class="math-container">$n$</span>, and apply the partial sum of the geometric sum.<br>
For the second: Look at the definition of <span class="math-container">$\sinh(x)$</span>.
| https://physics.stackexchange.com |
16,953 | [
"https://stats.stackexchange.com/questions/16953",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/5405/"
] | Is there a specific method to detect change points(structural breaks) in a timeseries? (stocks prices).
| @Dail if you're more inclined to the applied rather than the theoretical behind detection of structural break, you might want try <code>http://cran.r-project.org/web/packages/cpm/index.html</code> this is the link for <code>CPM</code> package of <code>R</code>, where you can use <code>processStream</code> to find multi... | Change Points can arise from a number of possible causes. Each of the possible causes can be evaluated. In terms of increasing complexity : 1. detecting a change in the expected value is essentially Intervention Detection. Pursue the work of Ruey Tsay to understand what you need to do. His work does not cover detecting... | https://stats.stackexchange.com |
620,386 | [
"https://electronics.stackexchange.com/questions/620386",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/313877/"
] | Can a faulty HDMI-cable with damaged TDMS pins/wires still work to the extent that the computer can still detect the monitor, but the monitor just will not display anything (except for no signal)?
| HDMI sources use the DDC (I2C) channel to identify the monitor and its capabilities. So, yes, the source could identify the sink if TMDS were broken.
But it won’t be able to do HDCP since keying material is sent in-band over TMDS and managed by DDC.
| Yes. If monitor can detect 5V from PC, monitor will assert hotplug. If PC can detect monitor hotplug, PC knows monitor is connected tries to read EDID. If EDID can be read, PC knows monitor is connected and the information it has. The monitor does not have to be turned on or have any power to make this happen, and the ... | https://electronics.stackexchange.com |
5,934 | [
"https://chemistry.stackexchange.com/questions/5934",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/2164/"
] | I was linked to a Kickstarter for a cooling ball to be placed in drinks which claims with constant marketing hyperbole how much it relies on "Phase Change" ! which is a neat concept and seems not unreasonable, but in thinking about it I'm failing to imagine (as I'm no chemist, and of ill education) what refrigerant cou... | I tried to use the curated dataset from Mathematica to answer this question. You can ignore the following if you have no interest in Mathematica and just jump down to the end for my ideas.
The following code gets all of chemicals currently in the curated dataset and grabs the melting points and NFPA health rating. Th... | Jimmy,
There are most likely many chemicals that have a melting point range in that vicinity, but I can't comment on their toxicity. However, I can comment on some of the science here.
First of all, water is one of very few molecules that <em>expands</em> when it freezes. That has to do with the hydrogen bond networ... | https://chemistry.stackexchange.com |
350,435 | [
"https://softwareengineering.stackexchange.com/questions/350435",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/257969/"
] | I have an API which returns a list of articles. An article can have three status: Approved, Pending and Rejected. Now the front-end needs to hit the API in following scenarios:
<ol>
<li>Get all the articles irrespective of the status.</li>
<li>Get all articles added by an user.</li>
<li>Get all articles added by an us... | The answer to this depends how much you want the UI to cope with future requirement changes, such as additional buttons for different kinds of filterings. For trivial apps, most people will hard-code filtering object into each button. However, if you want the system to be extensible, and you have a total control over t... | Its a better solution to pass the expected values rather than hard code it in front end. In future, you may have another possible state/status. It will be far easier for the backend to pass this new value and the UI to handle it dynamically by displaying another button or a drop down.
| https://softwareengineering.stackexchange.com |
957,916 | [
"https://math.stackexchange.com/questions/957916",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/145922/"
] | How would I prove this?
I know that I must show <span class="math-container">$f(a)=f(b) \Rightarrow a = b$</span>
I also know I must use the definition of homomorphism, ie:
<span class="math-container">$f(a+b)=f(a)+f(b)$</span>
<span class="math-container">$f(ab)=f(a)f(b)$</span>
<span class="math-container">$f(1)... | Suppose <span class="math-container">$f(a) = f(b)$</span>, then <span class="math-container">$f(a-b) = 0 = f(0)$</span>. If <span class="math-container">$u = (a-b) \ne 0$</span>, then <span class="math-container">$f(u)f(u^{-1}) = f(1) = 1$</span>, but that means that <span class="math-container">$0 f(u^{-1}) = 1$</span... | A field homomorphism must in particular be a ring homomorphism, so its kernel is an ideal. The only ideals of a field are the zero ideal and the field itself.
| https://math.stackexchange.com |
538,454 | [
"https://physics.stackexchange.com/questions/538454",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/84158/"
] | In curved space time, there is a spin-connection term <span class="math-container">$\overline{\psi}\gamma^\mu\sigma^{ab}\omega^{ab}_\mu\psi$</span>.
Here's my apparent problem. If there were no Higgs field and no gravity, all particles would be massless. And hence the left-handed and right handed electrons would uncou... | Frankly, I cannot follow every tangent in the discussion, nor should I attempt to comment on it. But the basic brutal fact that should consistently fit with all the rest is that <strong><em>odd numbers of visible gamma matrices insulate left from right chiralities</em></strong> inside spinor bilinears. This is a repres... | From comment from Cosmas Zachos:
The gamma matrices in the Weyl representation are all of the form:
<span class="math-container">$$\gamma^\mu = \begin{bmatrix} 0 & A \\
B & 0
\end{bmatrix}$$</span>
Thus an even power of them will be diagonal and the equations will decouple into left and right-handed fermions... | https://physics.stackexchange.com |
182,994 | [
"https://mathoverflow.net/questions/182994",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14566/"
] | Suppose $f:\mathbb{R} \to \mathbb{R}$ has the property that for every fixed $t\in\mathbb{R}$ the function
$$
g_t : x \mapsto f(x) - f(x-t)
$$
is $C^\infty(\mathbb{R})$. Does it follow that $f$ is smooth?
Edit: The answer is no in generality (see answer below), but what if we impose the condition that $f$ is measur... | Here's a solution for $f\in L^1_{\mathrm{loc}}$, or even for $f$ a distribution, which avoids Fourier analysis by mollifying.
Let $\phi \in C^\infty_c(\mathbf{R})$ be a smooth bump function of total mass $1$. Define $\tilde{f} := \phi * f$. Then $f\in C^\infty(\mathbb{R})$. Moreover,
$$
(f-\tilde{f})(x) = \int (f... | At least under the axiom of choice the answer is negative: The are discontinuous additive functions $f;\mathbb R \to \mathbb R$ (as far as I remember, that's why Hamel inveted Hamel basis) and for such a function $g_t(x)=f(x)-f(x-t)$ is constant for all $t$.
| https://mathoverflow.net |
1,805,679 | [
"https://math.stackexchange.com/questions/1805679",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/253941/"
] | I have a series defined like this:
<span class="math-container">$$\sum_{n=1}^{\infty} (-1)^n \left(\cos \frac{1}{n}\right)^n$$</span>
and I need to find out whether it converges or diverges. I know that <span class="math-container">$\lim_{n\to\infty} |a_n| = 1$</span> but does it tell something about the series when th... | An infinite series $\sum\limits_{n} a_n$ will <em>never</em> converge if $a_n \not\to 0$. It doesn't matter if it is alternating or not.
| The original series diverges, as you end-up subtracting then adding $1$.
Anyway, by grouping the terms in pairs, you get a new series with the general term
$$\left(\cos\left(\frac1{2n}\right)\right)^{2n}-\left(\cos\left(\frac1{2n+1}\right)\right)^{2n+1}\\
=\left(1-\frac1{2(2n)^2}+\cdots\right)^{2n}-\left(1-\frac1{2(2... | https://math.stackexchange.com |
108,442 | [
"https://physics.stackexchange.com/questions/108442",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/44364/"
] | Mr.E is on a luxury spaceship travelling about 1/2 the speed of light and finds a cubic lump of unstable matter(attached to a bomb) in his cabin. He of course is an expert with bombs but this device is based on the unstable matter's critical mass. The lump of matter fluctuates a tiny amount constantly but if it is more... | Critical mass is actually more about 'the right number of nuclei in a specified space'. As we are talking about solid matter this equivalently translates to a given number of atoms (or molecules depending on your matter). And this furthermore translates to our everyday mass. But it's 'not about mass', it is just a prac... | The bomb doesn't "care" what its mass might look like to an observer in another frame.
If you calculate critical mass you don't worry how big it might seem to observers located in billions of other possible frames of reference. Local frame of reference is the only one valid for making calculations concerning the occu... | https://physics.stackexchange.com |
97,333 | [
"https://cs.stackexchange.com/questions/97333",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/93785/"
] | I am new to Huffman coding and I find myself facing a lot of confusion as to how to determine if a code is Huffman or not without having the probabilities associated to each codeword. I know one way is look at whether or not the code is prefix. If not, then it's not a Huffman code. If yes, then we need to check if it g... | If you have a Huffman code, and the codes have lengths $l_i$, then the sum over $2^{-l_i}$ must be equal to 1. In your case, that sum is 1/4 + 1/4 + 1/4 + 1/8 = 7/8 < 1, therefore not a Huffman code. You can replace the code 110 with 11.
(I am quite sure you can prove that for any prefix code, the sum is ≤ 1. And ... | When a frequency tree is built for a message upon its characters, the leaf nodes of the tree are the characters composing the message with their frequency and internal nodes just have a frequency sum of all its descendents. <br>
<strong>The characteristic property of frequency trees for Huffman encoding is that, all in... | https://cs.stackexchange.com |
27,960 | [
"https://mathoverflow.net/questions/27960",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6649/"
] | A set $M$ is called <em>amenable</em> if it is transitive and satisfies the following conditions:
<ol>
<li>For all $x,y\in M$, $\{x,y\}\in M$</li>
<li>For all $x\in M$, $\bigcup x \in M$</li>
<li>$\omega \in M$</li>
<li>For all $x,y \in M$, $x\times y \in M$</li>
<li>($\Sigma_0$ comprehension) Whenever $\Phi$ is a $\... | I think the following is a counterexample to your specific question. Let AH be the set of those $x$ such that (1) each element of $TC\{x\}$ has cardinality at most $\aleph_\omega$ and (2) all but finitely many elements of $TC\{x\}$have cardinality strictly smaller than $\aleph_\omega$. (By $TC\{x\}$, I mean the trans... | I agree with Andreas Blass's solution. The problem, or difficulty, with the definition
of amenable is highlighted with this example: $\Sigma_0$-comprehension in this questioner's
scheme is not really adequate.
For this reason it is sometimes replaced with $\Sigma_0$- (or `rudimentary') -closure for
$\Delta_0$ formulae... | https://mathoverflow.net |
393,802 | [
"https://electronics.stackexchange.com/questions/393802",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/196688/"
] | Assume that I have a 220 to 12 volts transformer with a nominal output current of 3 A (marked "12 V 3 A"). Now what does happen if I connect the two output wires to each other or to a load with very low impedance? Does the current exceed 3 A by a large margin? I don't think so. But is the secondary coil designed to wi... | If you short the output of a good/efficient transformer, the secondary current will be very high, and the transformer will likely overheat and be damaged.
However, there are intentionally lossy ("impedance protected") transformers that will limit the load current to a safe value to prevent damage to the transformer in... | There's no upper limit to the current that will flow in that case. The transformer will cheerfully draw, up to its impedance and inductive limits, until it melts the secondary down into copper slag. Or, the thin primary wires will overheat and blow like a fuse.
We see it a lot where people think a component has bui... | https://electronics.stackexchange.com |
315,271 | [
"https://mathoverflow.net/questions/315271",
"https://mathoverflow.net",
"https://mathoverflow.net/users/127118/"
] | For <span class="math-container">$\sigma \in \mathrm{GL}_n(\mathbb C)$</span> and <span class="math-container">$f(x_1,...,x_n)\in \mathbb C[x_1,...,x_n]$</span>, let <span class="math-container">$f^ \sigma (x):=f(\sigma^{-1}x)$</span>, for <span class="math-container">$x=(x_1,...,x_n)$</span>.
For a subgroup <span cl... | <strong>Note added on 26 Nov 2018:</strong> I have corrected my answer, which had a serious mistake.
For simplicity of notation, let <span class="math-container">$(x,y,z) = (x_1,x_2,x_3)$</span>. The Hessian form associated to <span class="math-container">$f_0 = {x_1}^3+{x_2}^3+{x_3}^3+6x_1x_2x_3$</span> is
<span cl... | It is known that the linear transformation fixing <span class="math-container">$f_0$</span> are exactly the transformations <span class="math-container">$(x_1,x_2,x_3)\mapsto (\lambda x_{\sigma(1)}, \mu x_{\sigma(2)}, (\lambda\mu)^{-1}x_{\sigma(3)})$</span>, where <span class="math-container">$\sigma\in\mathfrak{S}_3$<... | https://mathoverflow.net |
21,148 | [
"https://physics.stackexchange.com/questions/21148",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/447/"
] | I'm a physics tutor. I'm stuck up with this question. I've no clue about how to proceed with this question. Can any one help?
<blockquote>
A 2 Kg block moving with 10 m/s strikes a spring of constant π^2 N/m attached to 2 Kg block at rest kept on a smooth floor. The time for which rear moving block remain in contact... | Switch to a reference frame which moves with the center of mass the system. Consider a point on the spring at the COM of the system. Split the spring into two springs (use the fact that $k\propto 1/l$) at this point. Now, you have a point which is stationary (in com frame), and two blocks attached to it, both of which ... | It may help to use a frame of reference where the center of mass of the system is at rest.
| https://physics.stackexchange.com |
463,724 | [
"https://physics.stackexchange.com/questions/463724",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8916/"
] | <img src="https://i.stack.imgur.com/e3x8j.jpg" alt=""Blowing someone else's candle out won't make yours shine brighter." ">
Is the claim in this sign correct? Would a candle shine slightly brighter with slightly more oxygen in the room?
And what do you mean "The candles aren't literal."?
| The claim is certainly true for candles in different rooms. Even in the same room, the effect of one candle on another in terms of oxygen consumption is with all likelihood completely negligible, and the candles could thus be treated as completely separate systems.
As to your question about how the candles are not lit... | It doesn't burn brighter but rather longer. Given the desity of air in that system remain constant, the amount of oxygen consumed by the candle per unit time is constant and consistent regardless of the number of candles in the system. To put that into perspective, blowing on a flame brightens it because setting air in... | https://physics.stackexchange.com |
136,698 | [
"https://softwareengineering.stackexchange.com/questions/136698",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/34069/"
] | This is an abstract question to clarify a refactoring concept in the ruby language. Assume in the real world that there would be many more variables and method in the Furniture Class and Refinish method.
I have a Class called Furniture.
It has a method called '<code>refurnish(VarnishToUse, TimeToTake)</code>'.
This ... | They'll have to learn the proper terms eventually, the sooner the better.
Use them correctly, and explain them whenever you get a blank stare. Just try to send the right signals, that it's OK to ask about anything they don't understand - the only stupid questions are those you don't ask.
| <h2>In general</h2>
When a person doesn't understand you, you have two alternatives:
<ol>
<li>Adapt the vocabulary according to what the person knows or not,
</li>
<li>Explain to the person the terms she doesn't understand.
</li>
</ol>
The first case works well when the person knows already the technical vocabulary qui... | https://softwareengineering.stackexchange.com |
108,033 | [
"https://mathoverflow.net/questions/108033",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14579/"
] | Suppose <span class="math-container">$(M,g)$</span> is a compact Riemannian manifold with totally geodesic boundary. Its <em>double</em> is given by
<span class="math-container">$$
D(M) = M\cup_fM
$$</span>
where <span class="math-container">$f:\partial M\to\partial M$</span> is the identity map. In general <span class... | It <em>is</em> a $C^\infty$ manifold if you define charts properly (e.g. using geodesics normal to the boundary as coordinate lines).
The <em>metric</em> of the double is $C^2$ (but not always $C^3$). Indeed, since the boundary is totally geodesic, the normal derivative of the metric tensor (in the above mentioned coo... | You can give $D(M)$ a $C^k$ structure, $k=0,\ldots,\infty,\omega$ if $M$ has one.
Take a $C^k$ function $f$ on $M$ that is $1$ on the boundary with positive normal derivative, and $0\leq f<1$in the interior.
Then you can take $D(M)=\{(x,t)\in M\times\mathbb{R}: f(x)+t^2=1\}$.
Do you want $D(M)$ to be a <em>riem... | https://mathoverflow.net |
156,789 | [
"https://physics.stackexchange.com/questions/156789",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/52949/"
] | Let's say we have a hollow cylinder with a charge $q$, radius $r$ and height $h$ as in the figure below.
<img src="https://i.stack.imgur.com/Evu3C.png" alt="enter image description here">
I am trying to find the electric field perpendicular to the surface of the hollow cylinder. I think the easiest way is Gauss' law w... | I'm assuming here that the cylinder is "infinitely long", or at least very long so that <span class="math-container">$h >> r$</span>. Otherwise, there are complicated non-integrable "end effects", but it doesn't look like you're interested in those.
As you said, you need Gauss's law. You're ... | Your answer is right but the cylinder is of infinite length so you have to express the Electric field in terms of aerial charge density, not in terms of total charge.
<span class="math-container">$$ E=\frac{\sigma}{\epsilon_0}\frac{r}{R}$$</span>
| https://physics.stackexchange.com |
604,612 | [
"https://physics.stackexchange.com/questions/604612",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/275190/"
] | <blockquote>
When a football rolls down a hill, the potential energy of the ball turns into kinetic
energy at the bottom. However, if you carry the ball down and stand with it at the
bottom, the ball has no kinetic energy. Explain what has happened to the energy.
</blockquote>
I am completely stuck on this one. Any ide... | the gravitational potential energy of the ball has been converted into heat in the leg and arm muscles of the person carrying the ball downhill.
| When a person carried a ball to the bottom, the ball got a force from that person. So, you've got displacement (the ball moved from the top to the bottom) and you've got force. Remember what is force times displacement? Yes, that is work. For F constant, work is W = F x s (F is force and s is displacement). So, the wor... | https://physics.stackexchange.com |
372,886 | [
"https://softwareengineering.stackexchange.com/questions/372886",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/195338/"
] | I work in a traditional software development environment. A team of developers work on a product in 2-4 week Sprints and then hand the results over to an operations team to be deployed and managed. Our operations team runs our PreProd and Prod environments under an ITIL framework.
We’ve been trying to include operatio... | The answer above about finding a common ground would be the best advice, and in keeping with the spirit of devops - but personally, the idea to bring operations and development closer together for me means to stop thinking of personnel as 'dev' or 'ops' in the first place, and to bring everyone's strengths to the fore ... | <strong>Don’t shoot… I come in peace ;)</strong>
I can relate to the other side of the coin as I used to be one of those Operations People.
Just imagine that you(the Dev) are being pulled into Operation meeting where there is nothing for you to say or relate to and you have to sit there for a number of hours. And th... | https://softwareengineering.stackexchange.com |
17,257 | [
"https://mechanics.stackexchange.com/questions/17257",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/401/"
] | While replacing my calipers and their mounting brackets, I passed a tap through the bolt holes on the wheel hub assembly that secure the bracket, to clean up the threads. The tap's movement felt unusual: it didn't seem to be hitting any thread once past a certain point in the hole (which is about 3/4" deep in total).
... | Well, this was me being an idiot. Or, more charitably, not thinking the situation through.
When I got around to reassembly, I realized that this hub assembly is between the head of the bolt and the support bracket, and it's the bracket itself that has the threaded hole. This bolt hole felt so loose because <strong>the... | From the look of the picture I would say that there is not much 'meat' left for the threads of the bolt to grab against. The amount of corrosion leads me to believe there were threads all the way through at some point.
Drilling/tapping can get complicated and expensive if you don't have the tap. Also the bigger bolt m... | https://mechanics.stackexchange.com |
266,450 | [
"https://mathoverflow.net/questions/266450",
"https://mathoverflow.net",
"https://mathoverflow.net/users/107004/"
] | Let $\mu$ be a finite measure on $\mathbb{R}$. Define the measures $(\mu_n)_{n\geq 1}$ by $\mu_{n+1}=\mu\ast \mu_n$ and $\mu_1=\mu$
Is there a singular (with respect to the Lebesgue measure) continuous measure $\mu$ on $\mathbb{R}$ such that for all $n\geq 2$, $\mu_n$ is also singular continuous ?
| Here is a simple explicit example of a measure $\mu$ with all convolution powers singular: let $\mu$ be the distribution of
$$
\sum_{k=1}^\infty X_k 2^{-k!},
$$
where the $X_k$ are IID taking values $0$ and $1$ with equal probability. The support of $\mu$ is the set $A$ of points whose binary expansion has non-zero di... | Yes, indeed. You can build a one dimensional family of non-atomic singular measures on $[0,1]$ simply by pushing the Bernoully measure with parameter $p$ with the help of the dyadic decomposition of real numbers.
Start with $X_i$ iid random variables such that $P(X_i = 1) = p = 1 - P(X_i = 0)$ and define
$$
Y_p = \sum... | https://mathoverflow.net |
10,759 | [
"https://astronomy.stackexchange.com/questions/10759",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/7313/"
] | I have seen different pictures in a different community to showcasing the Milky Way. I can never tell whether it's edited or it's the real picture. Actually, I can never see any galaxy as such by with my naked eye. But can the Milky Way be seen with the naked eye? If yes, then I would really like to know when and how t... | Most photographs you will see of the Milky Way are long exposure photographs (often around 30 seconds exposure, whatever the limit is before star trails become noticeable at their focal distance; sometimes longer if they use a tracking mount) at a very wide aperture. This is done to capture the maximum amount of light... | There are a few nearby galaxies that can be seen with the naked eye, but clear & dark skies are essential. Most notable for northern-hemisphere viewers is the Andromeda Galaxy also known as M31, best viewed in late summer and fall; from the southern hemisphere the Magellanic Clouds, irregular satellites of our own ... | https://astronomy.stackexchange.com |
53,372 | [
"https://electronics.stackexchange.com/questions/53372",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5517/"
] | <img src="https://i.stack.imgur.com/C51oP.gif" alt="enter image description here">
This is the basic common emitter amplifier.I have read that polarized capacitors should have proper polarity connected to terminals of DC voltage source and they may blow off if they are connected in a wrong way and the polarized capaci... | Polaized capacitors must <i>always</i> have 0 or greater volts on them from the positive terminal to the negative. However, that does not mean there can't be a AC component to the voltage, only that the lowest peaks don't go negative. Put another way, you are fine as long as the cap has a DC bias at least as large as... | It's pretty straight forward, there is an AC voltage which rides on top of the DC voltage. Ideally the combined voltages should never go negative, which means that for the most negative portion of the AC voltage it will still have a lower magnitude than the DC component. SO the fact that the capacitors block DC voltag... | https://electronics.stackexchange.com |
98,631 | [
"https://softwareengineering.stackexchange.com/questions/98631",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/30757/"
] | Have you always been fundamentally correct in the software designs you proposed? When you give out some design that was fundamentally wrong, you tend to lose the respect of your fellow team members. No matter what you do after that you end up being crosschecked for everything thing you propose after that incident. This... | Once, the vp of a fortune 500 cost the company 1 million dollars with a bad business decision. When he turned in his resignation to the C.E.O the response he was given was, "I just invested One Million dollars in your education and now you are trying to leave? I do not accept."
I grow tired of managers and other worke... | I've been doing this a long time (15+ years), and I still don't get it right the first time. The best designs come out of an iterative, collaborative process. When you have been working on a design for a while, it is easy to get trapped in thinking that it is the only way that it can be done. A fresh perspective is ... | https://softwareengineering.stackexchange.com |
18,596 | [
"https://earthscience.stackexchange.com/questions/18596",
"https://earthscience.stackexchange.com",
"https://earthscience.stackexchange.com/users/18410/"
] | I had participated in a quiz recently and one of the questions was 'which is the largest island in the world?'. I wrote Australia as the answer remembering that it was the 5th largest country in the world and none of the top 4 were islands.
However (and rather dreadfully) the answer given was Greenland.I took this up ... | Australia does get widely referred to as an island as well as as a continent - an island-continent sometimes. My understanding is that "continent" in terms of geology refers to the largest land mass of a continental plate and is more a matter of convention - a general agreement - than precise definition. Such definitio... | Australia can be seen as a very "continenty" continent. It contains very old stable continental lithosphere in cratons, like for instance the Pilbara or the Yilgarn craton.
I fear, the quiz makers were correct with classifying Australia as a continent.
| https://earthscience.stackexchange.com |
438,150 | [
"https://electronics.stackexchange.com/questions/438150",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/141113/"
] | The shaft of an unconnected motor is easy to rotate relative to a motor with shorted terminals. If a resistive load is connected to the terminals, the turning difficulty is somewhere in between.
Why is this? (I'm using a BLDC motor.)
| I have to start with some terminology -- sorry if it's esoteric, but this will bring things into line with how folks talk about this subject.
When you turn a permanent-magnet DC machine*, the armature generates a voltage internally. This is called the "EMF"** of the armature, or the "back EMF" if the machine is runni... | "applying a resistive load" to a running motor is <strong>essentially how an electric brake works</strong>. As a first approximation, the torque produced by the motor is proportional to the current, that's turning the motor is harder as the load resistance gets smaller. When you short the terminals, there's only the in... | https://electronics.stackexchange.com |
489,660 | [
"https://electronics.stackexchange.com/questions/489660",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/146624/"
] | I was reading about telephone lightning arrestors in my ARRL RFI Book (first edition, copyright 1998), in chapter 9 "Telephone RFI" (by Pete Krieger, previously WA8KZH, now K8COM) and on page 9.6, the following is stated (emphasis mine):
<blockquote>
<strong>The Lightning Arrestor</strong>
Telephone service en... | The carbon block becomes exactly like a high power TRIAC (with a trigger voltage (<250V), when sufficient voltage and time duration for ionization exists.
There is an incremental negative resistance when triggered (avalanche effect) and is inversely proportional to the current.
Line inductance limits the Re-r... | There are many different kinds of lighting arrestors -- and all of them work differently, age differently, and fail differently.
A lighting arrestor diverts the high voltage lighting strike to ground instead of allowing the voltage to pass through to your radio equipment.
Some are simply devices that are basically s... | https://electronics.stackexchange.com |
217,923 | [
"https://dba.stackexchange.com/questions/217923",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/56050/"
] | I got A cursor with some ifs like this one:
<pre><code> IF @ROLE='RW'
BEGIN
SET @COMMAND ='
USE '+QUOTENAME(@DATABASE)+'
CREATE USER '+QUOTENAME(@LOGIN_ACESSO)+' FOR LOGIN '+QUOTENAME(@LOGIN_ACESSO)+' WITH DEFAULT_SCHEMA=[DBO]'+CHAR(13)+CHAR(10)+'
... | We strongly suspect that this issue may have been related to the numerous connection errors highlighted in the SQL Server Error log (see original post above) which preceded the issue. The maximum number of connections may have been exceeded.
We have since restarted the database server and have resolved the connection ... | When applying any changes to the SQL Server services it is advisable to do this via the <strong>SQL Server xxxx Configuration Manager</strong> to guarantee that any related permissions (files / directories / databases / instances) and policies are set correctly.
<hr>
<h2>Fixing Service Accounts (Permissions and All)<... | https://dba.stackexchange.com |
1,570,914 | [
"https://math.stackexchange.com/questions/1570914",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/287775/"
] | The formula for sum of all numbers formed with all the given digits is:
<pre><code>(Sum of digits) (n-1)!(1111....ntimes)
</code></pre>
<em>n</em> stands for number of digits.
For ex:
Sum of all numbers formed with 1,2,3 and 4 is
10 × 3! × 1111 = 66660.
Can anyone figure out how this was derived?
| I figured the answer out.
If you fix 1 in the thousands place, all other numbers can be arranged in 3! Ways.
Therefore 1 occurs in thousands place 3! Times. Same for all the numbers. Therefore for thousands place, total sum= 1000(sum) 3!.
But same thing occurs for all other positions. Therefore sum= 1111...×(sum) ×(... | This can also be done in another method — we get 10 if we add the digits 1,2,3,4. 4! is 24 and the number of digits is 4 so, if we divide 24 by 4 we get 6. 10×6=60. 60 will be taken in all ones tens, hundreds, thousands, ten thousands... if we add in this method w... | https://math.stackexchange.com |
1,111,856 | [
"https://math.stackexchange.com/questions/1111856",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/192814/"
] | $$x^{2}+y^{2}-5x-15y+30=0$$
I'm supposed to rewrite this equation so that you can easily see the centre and radius of the circle. I don't even know where to start. According to Mathematica the centre is $(5/2, 15/2)$ and the radius is $\sqrt{65/2}$.
| Answer:
$$x^2 +y^2 -5x-15y+30 = 0$$
$$x^2 -5x +(\frac{5}{2})^2 +y^2 -15x +(\frac{15}{2})^2 -(\frac{5}{2})^2-(\frac{15}{2})^2+30 = 0$$
$$(x-\frac{5}{2})^2+(y-\frac{15}{2})^2 = \frac{225+25}{4}-30$$
$$(x-\frac{5}{2})^2+(y-\frac{15}{2})^2 =(\sqrt{\frac{65}{2}})^2$$
Center$$ (\frac{5}{2},\frac{15}{2})$$and the radius $... | I will do $x$. Please do $y$.
$$x^2+y^2-5x-15y+30=0$$
$$x^2-5x+25/4-25/4+y^2-15y+30=0$$
$$(x-5/2)^2+y^2-15y+30-25/4=0$$
| https://math.stackexchange.com |
294,932 | [
"https://electronics.stackexchange.com/questions/294932",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/139503/"
] | So in our lab, we are working with an oscilloscope, an Analog to be precise. It is the Tektronix 2205. My question is if it is analog, then why would it have "20 MHz" written on its box.
| Being an analog scope the signal is limited by the BW of the amplifier of this unit to 20MHz.
This in turn implies it's minimum rise time from 10 % to 90 % defined as approx 0.35/BW or 17.5ns according to manual.
This is often defined by the -3dB bandwidth for a low pass filter. The attenuation slope beyond this is ... | Probably the single most important parameter that tells you whether a particular scope is suitable for a particular job is its analog bandwidth. Signals that fall within this bandwidth will be displayed properly, while signals that exceed this bandwidth (even if just in their harmonics) will be distorted.
Since the ba... | https://electronics.stackexchange.com |
125,883 | [
"https://cs.stackexchange.com/questions/125883",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/4911/"
] | I am trying to show that the <em>best case</em> time complexity of Quicksort is <span class="math-container">$\Omega(n \log n)$</span>.
The following recurrence describes the best-case time complexity of Quicksort:
<span class="math-container">$$T(n) = \min_{0 \le q \le n-1} \left(T(q) + T(n-q-1) \right) + \Theta(n).... | Let us replace <span class="math-container">$\Theta(n)$</span> with <span class="math-container">$n$</span>, for concreteness, and assume a base case of <span class="math-container">$T(0) = 0$</span>. Let's try to prove inductively that <span class="math-container">$T(n) \geq cf(n)$</span>, where <span class="math-cont... | You can use the recursion tree method.
The amount of work on the level at depth <span class="math-container">$0$</span> is at least <span class="math-container">$c n$</span> for some constant <span class="math-container">$c$</span> (from the <span class="math-container">$\Theta(\cdot)$</span> notation). The amount of ... | https://cs.stackexchange.com |
659,124 | [
"https://physics.stackexchange.com/questions/659124",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/311272/"
] | The earth pulls all bodies towards it at <span class="math-container">$9.8\ \mathrm{m/s^2}$</span>. I would like to imagine that the ground is accelerating up at <span class="math-container">$9.8\ \mathrm{m/s^2}$</span> (just as an analogy). So this means that a rocket going up should have a greater acceleration than ... | <blockquote>
But the universe expands faster than light-speed, and this expansion was caused by the big bang. Doesn't this demonstrate that the speed of light cannot be the speed of causality?
</blockquote>
No, because the big bang happened everywhere. So there is no spatial distance between any point in the universe a... | Your mistake is to have assumed that the expansion of the Universe is in itself a cause of something else. Nothing is 'caused' by the expansion.
| https://physics.stackexchange.com |
1,404,709 | [
"https://math.stackexchange.com/questions/1404709",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/263444/"
] | Please help me out;
I need to specify a function satisfying these conditions:
$$ f(0)=1 \;\;;\;\lim_{x \to \infty}f(x)=0$$
Hopefully does there exist a simple answer? Thanks a lot!
| $$f(x) = \begin{cases}1 & \text{ if } x\leq 0 \\ 0&\text{ if }x>0\end{cases}$$
is one such function. Also, for any $\alpha > 0$, the function
$$\frac 1{(x + 1)^\alpha}$$
satisfies your conditions.
Furthermore, take any function $f(x)$ which is not identically equal to $0$ and is defined on $(a, \infty... | There are many trillions of answers. The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = 0$ except for $f(0) = 1$ will do.
| https://math.stackexchange.com |
37,536 | [
"https://electronics.stackexchange.com/questions/37536",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5259/"
] | Please edit this since I'm too ignorant of electronics and electrical equipment to explain this well.
I'm looking for a device that I can create that would take AC or DC current from a power source and send it into my home and possibly upstream to the power company (if I have a net supply in my home). For instance, if... | To me it looks like you've connected the power backwards.
If the green clips are input power and the unconnected lead is where you're measuring the voltage (and I'm assuming this, since there's no additional information in the question), then you've connected input voltage to the output of the regulator.
Next, how is... | Your photo only shows two clip leads of the same color with no indication what you have done with the other ends or about the third connection.
But generally speaking, linear regulators require capacitors placed near them for proper operation. Try placing .1 uF and 10 uF capacitors in parallel across the output, an... | https://electronics.stackexchange.com |
4,234,340 | [
"https://math.stackexchange.com/questions/4234340",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/438367/"
] | In John Lee's book on "Introduction to smooth manifolds", he proves the following result:
<blockquote>
Let <span class="math-container">$G$</span> be a Lie group and <span class="math-container">$M$</span> be a smooth manifold. Suppose that <span class="math-container">$G$</span> acts smoothly, freely and pro... | It goes to infinity for all <span class="math-container">$a$</span> and <span class="math-container">$b$</span> that are greater than <span class="math-container">$0$</span>. This is because the exponential grows faster than any polynomial eventually. This holds also for <span class="math-container">$b\leq 1$</span>.
| Use L'Hopital's rule <span class="math-container">$\lceil b \rceil$</span> times to get <span class="math-container">$$\lim_{x\to\infty}C\frac{e^{ax}}{x^{b-\lceil b\rceil}}=0.$$</span>
| https://math.stackexchange.com |
443,413 | [
"https://physics.stackexchange.com/questions/443413",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/153014/"
] | I have read the following sentence in a section which is explaining why particle accelerators need such high energy:
<blockquote>
As we require high precision position measurement, the Heisenberg uncertainty principle tells us that the standard deviation of momentum <span class="math-container">$\sigma_p$</span> mus... | For any measurement there is no general relationship between the measurement (average) itself and the uncertainty (standard deviation) of that measurement. The bold statement is about measurements in general.
We usually report a measurement as
<span class="math-container">$$p\pm\Delta p$$</span>
where <span class="mat... | The misconception here is that there is an actual momentum, and not a superposition of momenta. Moreover, the average momentum (or expectation value) is not relevant.
What the book is saying is that if <span class="math-container">$\Delta p$</span> is large, then there must be high momentum states in the actual state.... | https://physics.stackexchange.com |
564,950 | [
"https://physics.stackexchange.com/questions/564950",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/261792/"
] | Suppose I let a block fall from a height above a vertical spring. Any air drag is ignored. I want to find the maximum compression the spring will undergo. <strong>Is it possible to use the work-energy theorem over the Course of the entire motion?</strong>
The confusion is due to the fact that the spring force doesn't a... | <blockquote>
I want to find the maximum compression the spring will undergo. Is it
possible to use the work-energy theorem over the Course of the entire
motion?
</blockquote>
Yes it is. But you will have to apply it in two parts.
The work energy theorem states that the net work done on an object equals its change in ki... | You can apply work energy theorem.
Work energy theorem states that Work done by all forces = <span class="math-container">$\Delta KE$</span>
Edit : My earlier answer was wrong. I am trying to treat spring-block as a system .
I am assuming change in potential energy from the equilibrium of the spring.
So if the distan... | https://physics.stackexchange.com |
149,866 | [
"https://physics.stackexchange.com/questions/149866",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/65750/"
] | Visualizing the double slit experiment, there are light lines and dark lines. The dark lines I understand are caused by the interference cancelling waves. What I don't understand is where the energy of the cancelled waves goes. What happens to the energy of those waves?
| An intuitive way to see it: Intensity of light in constructive interference: $I_{max} = \left(\sqrt{I_1} + \sqrt{I_2}\right)^2$. Intensity of light in destructive interference: $I_{min} = \left(\sqrt{I_1} - \sqrt{I_2}\right)^2$. One slit has intensity $I_1$ and another slit has intensity $I_2$. And the "total intensity... | The interference pattern has parts were the wave cancel (destructive interference) and parts where they are added (constructive interference), so the energy gets redistributed, there are no losess.
| https://physics.stackexchange.com |
124,085 | [
"https://cs.stackexchange.com/questions/124085",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/119451/"
] | For a practical task, we are asked to provide the transition table for a Turing machine that validates the number of open brackets is equal to the number of closing brackets.
The only tape symbols allowed are ( ) E B
If the number of brackets is equal (opening brackets = closing brackets) then the machine must halt in... | When analyzing algorithms it makes little sense to consider the best-case scenario as it is very often trivial and not very informative.
You can convince yourself that almost every algorithm can be adapted to have a best-case complexity of <span class="math-container">$O(n)$</span>, where <span class="math-container">... | "lower bound" can be applied for each scenario and individually not meaningful! (lower bound of what?) As we analyzed the worst-case scenario most of the time as time complexity of an algorithm, hence, "lower bound" is applied for the worst-case scenario (not the best case).
In other words, as the time complexity is e... | https://cs.stackexchange.com |
47,815 | [
"https://security.stackexchange.com/questions/47815",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/36301/"
] | Whether I use openssll or gnutls's certtool, I end in a single threaded part which take several minutes.<br>
When I try to compile the libraries with auto-parallelizer advanced efficient tools. It sill stay single threaded.
I would like to understand more before diving in large part of code for manual rewrite...
| Checking for primality of the two required primes usually takes the longest. Note that the time required to find a prime depends a lot on luck. If the prime is close to the starting point it can be almost instantaneous. If it is much further away it may take quite a bit of time.
There is however one other component th... | This looks weird. An anemic laptop from 2005 generates 4096-bit RSA keys (i.e. huge, overkill keys) in less than 10 seconds. "Several minutes" would indicate that there is something wrong in your system. Or that you are aiming for ridiculously large RSA keys (2048 bits are very fine; 3072 bits are understandable if you... | https://security.stackexchange.com |
343,529 | [
"https://softwareengineering.stackexchange.com/questions/343529",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/264594/"
] | I have come up with the following design for my requirement and want know if there is a better way to do it or if you have any feedback on the design.
<strong>Requirement</strong>
Assume that an app provides different add-ons and each of these add-ons have a licence. The user is given a license key and he can activat... | I think that the design is well oriented but I would sugggest the folowing:
<ul>
<li>Licences and add-ons are mapped via the <code>$addon_name</code> property but a <code>matches(add_on_name)</code> method should be added to the base class in order to know if a licence belongs to a given add-on, or better yet not pass... | A license is basically a document. It strikes me as odd that your license has methods like Activate() and Deactivate(). I would expect a LicenseManager class that does these things. The License class should do no more than encapsulate the license. It might have Read() and Write() methods to read the license from or wri... | https://softwareengineering.stackexchange.com |
598,490 | [
"https://math.stackexchange.com/questions/598490",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/17139/"
] | Need help trying to evaluate this limit that is clearly related to the difference quotient and/or the Funda. Theorem of Calc (derivative of the integral is the function)
Anyone know how to close the deal here? I am trying to translate what I have into the difference quotient so I can determine the f(x)
Am I ba... | Hints for you to understand and justify:
Define
$$F(x):=\int\limits_1^x (e^t+2)dt\implies F'(x)=e^x+2$$
and thus
$$\lim_{h\to 0}\frac1h\int\limits_1^{1+h}(e^t+2)dt=\lim_{h\to 0}\frac{F(1+h)-F(1)}h=:F'(1)=e+2\;\ldots$$
| Looks right up to
$$\lim_{h \to 0}\frac{e^{1+h}+2h-e}{h}.$$
This can be re-written as
$$\lim_{h \to 0}\frac{e^{1+h}-e^1}{h}+2.$$
(where I mean the final $2$ included in the limit, but then the limit of 2 is just 2.)
Now the fraction part of the limit is the derivative definition of the derivative of $e^x$ at $x=1$. B... | https://math.stackexchange.com |
655,350 | [
"https://electronics.stackexchange.com/questions/655350",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/320586/"
] | If 208 V three phase is constructed of three 120 V lines, what is the most simple and safe way to get either 208 V, single phase, or 240 V, single phase?
| 120V is from phase to neutral. The difference between phases is 208V rather than 240V because they are 120 degrees out of phase, not 180. You have 208V single phase between any 2 phases. To get 240V you need a transformer
| Connect your load between two of the phases. To keep the system as balanced as possible, connect different loads between different pairs of phases.
Since neither connection to your load is a neutral, overcurrent protection and isolation needs to be double pole.
| https://electronics.stackexchange.com |
289,466 | [
"https://math.stackexchange.com/questions/289466",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/60042/"
] | One typically studies analysis in <span class="math-container">$\mathbb{R}^n$</span> after studying analysis in <span class="math-container">$\mathbb{R}$</span>. Why can't the same be said of <span class="math-container">$\mathbb{C}$</span>?
| I would say that the main reason that several complex variables is rarely seen in the undergraduate curriculum (and even not that often in the graduate curriculum unless the department has some specialists in SCV) is that you can't get very far without lots of prerequisites.
You can for example start by proving Cauchy... | The typical progression goes ${\bf R},{\bf R}^n,{\bf C},{\bf C}^n$. Different individuals get to different places along the progression.
| https://math.stackexchange.com |
806,636 | [
"https://math.stackexchange.com/questions/806636",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Let $p$ be an odd prime and $\omega$ be a primitive $p$<sup>th</sup> root of unity. The question is to prove that:
$$(1-\omega)(1-\omega^2) \cdots (1-\omega^{p-1})=p$$
<hr>
What I have done so far is:
I can see that this is true for $p=3$
$$(1-\omega)(1-\omega^2)=1-(\omega+\omega^2)+w^3=1-(-1)+1=3=p$$
I am not ab... | Recall the formula for the summation $1+x+x^2+\cdots+x^n = {x^{n+1}-1 \over x-1}$ when $x\neq 1$.
In particular, this shows that $f(x)=x^{p}-1 =(1+x+x^2+\cdots+x^{p-1})(x-1)$.
Since $\omega$ is a root of unity, we have $f(\omega^k) = 0$ for $k=0,...,p-1$.
Since $\omega$ is primitive, $\omega^0,...,\omega^{p-1}$ are ... | Hint: what does $x^n-1$ look like factored?
| https://math.stackexchange.com |
203,730 | [
"https://dba.stackexchange.com/questions/203730",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/136910/"
] | How to get how many times my PostgreSQL database restarted and how to get each restart time?
I do not want to get the details from the log file. Is there any other way to get those details?
| I would like to comment but couldn't due to the lack of reputation.
Is your secondary node being enabled read-only? And if so, did you check if there's any blockings on the secondary node?
Another thing that you could check is if there's any maintenance jobs running.
And... could you try to make everything asynchr... | I have the same problem on a few databases in an Availability Group (AG) in SQL Server 2016. I tried the following steps and it seems to truncate the Transaction Log file.
<ol>
<li>Take a Transaction Log backup of the DB in Secondary Node of AG (I have set the Secondary Node as my primary backup Node)</li>
<li>Execut... | https://dba.stackexchange.com |
17,033 | [
"https://mechanics.stackexchange.com/questions/17033",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/3823/"
] | I drive a <strong>1988 Mazda RX-7 non-turbo 5spd</strong>.
The previous owner claims the clutch was done last July(little under a year ago) and I have no reason to doubt such claims. I do believe the clutch release bearing was not installed correctly. When the clutch is not pushed in, there is a spaceship kind of noi... | The noise you describe is a VERY common issue with the transmission in the model of RX-7 you are driving. As a matter of fact, my current RX-7 (1991, 220k miles) has this exact same issue.
Based on your description, the noise is almost certainly coming from the transmission's input shaft bearing - not any part of the ... | If the noise is only happening when the clutch is engaged (pedal out), it's not the throw out bearing. You'd only hear the noise when you push on the pedal. This is because the only time the throw out bearing is being used is when you are pushing the pedal down. It won't contact the clutch fingers any other time, and t... | https://mechanics.stackexchange.com |
384,293 | [
"https://physics.stackexchange.com/questions/384293",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/183700/"
] | Suppose You were put into a box with all the instruments you might require.<br>
The box moves with constant velocity on the surface of the earth.<br>
We are asked to detect inside the box whether we are moving or not.
This question was asked by our physics teacher and thrown to discussion to the class.<br>
I know Ei... | Lets tackle each argument one at a time...
<blockquote>
When a policeman fires his 'speed tracking instrument' at a car the light produced reflects from the car and according to the speed of the car frequency changes to an apparent observed frequency. (Doppler Effect)
So we could just fire up a light beam to a wal... | Assuming that you are moving in a straight line at constant velocity, you would be unable to detect your own motion. In the Doppler Effect argument, you forget that the police officer is at rest relative to the moving object in his frame, but because there is no motion in your frame, and thus and Doppler Effect measure... | https://physics.stackexchange.com |
946,678 | [
"https://math.stackexchange.com/questions/946678",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/178921/"
] | I'm currently trying to solve an example that goes as follows:
<blockquote>
Determine the value of <span class="math-container">$c$</span> so that each of the following functions can serve as a probability distribution of the random variable <span class="math-container">$x$</span>.
<span class="math-container">$p(x) = ... | The sum
$$\sum_1^\infty c(0.3)^{x-1}\tag{1}$$
of all the probabilities has to be equal to $1$.
But the series (1) is an infinite geometric series. By a standard formula, it has sum $\frac{c}{1-0.3}$.
Thus $c=0.7$.
<strong>Remark:</strong> Suppose that a certain experiment has probability of success $p$. Repeat the ... | The series
$$
c\sum_{x=1}^\infty(0.3)^{x-1}
$$
must be equal to $1$.
We have that
$$
\sum_{x=1}^\infty(0.3)^{x-1}=\sum_{x=0}^\infty(0.3)^{x}=\frac1{1-0.3}=\frac{10}7
$$
so $c$ must be equal to $0.7$.
| https://math.stackexchange.com |
68,990 | [
"https://dsp.stackexchange.com/questions/68990",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/51382/"
] | In physics, the total energy of a system is the summed energy of its component subsystems, and energy must be conserved, ie, adding the energy of the components gives the total energy.
In signal analysis (discrete time signals), one would expect that the energy of a signal would be defined in such a way that energy wou... | This question goes deep into the notion of selecting "invariant" features between representations.
From your first paragraph, I understand that your component subsystems are mutually exclusive (they don't overlap), and their union yields the whole system. This decomposition can be called covering, or segment... | Say you decompose the signal <span class="math-container">$x(t)$</span> into two components: <span class="math-container">$$s(t) = x(t) + y(t).$$</span> As you say, there are myriad ways to do this. The energy of <span class="math-container">$s(t)$</span> is <span class="math-container">$$E_s = \int_{-\infty}^\infty s^... | https://dsp.stackexchange.com |
49,690 | [
"https://mathoverflow.net/questions/49690",
"https://mathoverflow.net",
"https://mathoverflow.net/users/344/"
] | Let $X$ be a topological space. In elementary algebraic topology, the cup product $\phi \cup \psi$ of cochains $\phi \in H^p(X), \psi \in H^q(X)$ is defined on a chain $\sigma \in C_{p+q}(X)$ by $(\phi \circ \psi)(\sigma) = \phi(_p\sigma)\psi(\sigma_q)$ where $p_\sigma$ and $\sigma_q$ denote the restriction of $\sigma$... | Via the Dold-Kan correspondence, the category of cosimplicial abelian groups
is equivalent to the category of nonpositively graded chain complexes of abelian groups
(using homological grading conventions). Both of these categories are symmetric monoidal:
chain complexes via the usual tensor product of chain complexes, ... | One such example comes from Steenrod squares. Let $C^{*}(X)$ be the singular cochain algebra of a topological space $X$ with coefficients mod 2. The cup product $\smile$ is not commutative, but there are operations $\smile_i:C^{*}(X)\otimes C^{*}(X)\to C^{*}(X)$ of degree $-i$ such that $\smile_0=\smile$ and $\smile_i$... | https://mathoverflow.net |
27,127 | [
"https://stats.stackexchange.com/questions/27127",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2912/"
] | I have a bunch of related datasets. The pearson correlations between pairs of them are typically definitely larger than the spearman correlations. That suggests any correlation is linear, but one might expect that even if the pearson and spearman were the same. What does it mean when there is a definite gap between the... | The Spearman correlation is just the Pearson correlation using the ranks (order statistics) instead of the actual numeric values. The answer to your question is that they're not measuring the same thing. Pearson: linear trend, Spearman: monotonic trend. That the Pearson correlation is higher just means the linear corre... | The Pearson Correlation assumes several assumptions for it to be accurate: 1) Each variable is normally distributed; 2) Homoscedasticity, the variance of each variable remains constant; and 3) Linearity, meaning that a scatter plot depicting the relationship shows data points clustering symmetrically around the regress... | https://stats.stackexchange.com |
617,854 | [
"https://physics.stackexchange.com/questions/617854",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/290631/"
] | A body is starting from rest. A force is acting on it for a short period of time. In that given time, power delivered to it at any instance <span class="math-container">$t$</span> is given
<span class="math-container">$$P = F \cdot v_1 = ma \cdot v_1 = mv_1^2/t,$$</span>
where <span class="math-container">$v_1$</span> ... | <blockquote>
Can someone please explain where I went wrong?
</blockquote>
You haven't been rigorous enough.
Newton's second law tells us:
<span class="math-container">$$F=ma$$</span>
<span class="math-container">$$a=\frac{F}{m}$$</span>
Because the force applied is constant we can write:
<span class="math-container">$$... | The equation <span class="math-container">$P=Fv$</span> (or more precisely <span class="math-container">$P=\mathbf F\cdot\mathbf v$</span>) gives you the <strong>instantaneous</strong> power supplied by the force <span class="math-container">$F$</span>.
The equation <span class="math-container">$P=\Delta\text{KE}/\Delt... | https://physics.stackexchange.com |
198,184 | [
"https://dba.stackexchange.com/questions/198184",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | A common problem placing databases on one server Instance is they all share same tempdb. Is it possible to allocate tempdb file/and filegroups for separate databases. Does Resource Governor allow this?
Database 1, only gets access to one file/filegroup 1 in tempdb.
Database 2, only gets access to one file/filegroup 2... | No.
Resource Governor is for throttling CPU, query workspace memory, and storage throughput, but there is no feature in SQL Server that restricts which files/filegroups a database can access in TempDB.
Plus, think about cross-database queries - if you had a cross-database query, how would that even work?
| If you need that level of granularity, you should setup multiple SQL Server instances; that is the only way to have multiple tempdb databases.
| https://dba.stackexchange.com |
285,831 | [
"https://softwareengineering.stackexchange.com/questions/285831",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/106048/"
] | My personal approach to a git commit is that every commit should include a <strong>unit of change</strong>, in its completness.
When I develop, I usually focus on such units. But sometimes, my attention strays someplace else and I work for a while on a different unit. This is probably not optimal, but I have learned t... | Commit history is vitally important, but for 3 reasons:
<ol>
<li>merging to somewhere else. You need to pick the pieces out of a branch and stick them elsewhere, its important to have all the pieces you want in there and nothing you don't want. So if your 'messy' commit contains changes intended for the feature you're... | When this does happen, it's not a huge deal to simply revert the change in the next commit. Add a proper commit message (<code>Removing the XYZ that I accidentally added in C92A891</code>) will be enough for other developers to understand in code review.
Rather than worrying about fixing any specific incident, try to ... | https://softwareengineering.stackexchange.com |
95,096 | [
"https://mathoverflow.net/questions/95096",
"https://mathoverflow.net",
"https://mathoverflow.net/users/825/"
] | Let $X_1,\dots,X_n$ denote i.i.d. standard Gaussian random variables. My question is: Do there exist absolute constants $C,c>0$ such that for every $\epsilon>0$ and positive real numbers $a_1,\dots,a_n>0$, we have the following bound
$\quad \Pr(\sum_{i=1}^n a_i X_i^2 \le \epsilon \sum_{i=1}^n a_i)\le C\epsilo... | We can show that
$$
\mathbb{P}\left(\sum_ia_iX_i^2\le\epsilon\sum_ia_i\right)\le\sqrt{e\epsilon}
$$
so that the inequality holds with $c=1/2$ and $C=\sqrt{e}$.
For $\epsilon\ge1$ the right hand side is greater than 1, so the inequality is trivial. I'll prove the case with $\epsilon < 1$ now.
Without loss of general... | I also would strongly suspect it holds with $c = 1/2$. Here's an argument which, if I haven't made a mistake, gives the upper bound $O(\epsilon^{1/2} \ln^{1/2}(1/\epsilon))$.
Assume without loss of generality that $a_1 \geq a_2 \geq \cdots \geq a_n$ and that $a_1 + \cdots + a_n = 1$. Divide into two cases:
<strong... | https://mathoverflow.net |
83,299 | [
"https://physics.stackexchange.com/questions/83299",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/30751/"
] | I have got this problem where I have been given the following wave function: $$\Psi = 0\quad\text{if}~|x| > a\quad\text{and}\quad A(a^2-x^2)\quad \text{if} \quad |x|< a$$
Now the first question is "Determine the time-dependent wave-function. Your answer should be expressed as an infinite sum." How do i express it... | Set $x = r \cos \theta$, $y = r \sin \theta$. Taking the total differentials, $$\mbox{d}x = \mbox{d}r \cos \theta - r \sin \theta \mbox{d} \theta,$$
$$\mbox{d}y = \mbox{d}r \sin \theta + r \cos \theta \mbox{d} \theta.$$
Squaring and simplifyng
$$\mbox{d}s^2 = {\mbox{d}x}^2 + {\mbox{d}y}^2 = {\mbox{d}r}^2 + r^2 {\mbo... | For the polar coordinates expression. simply "divide" the line element in polar coordinates by <span class="math-container">$dt^2$</span> to obtain
<span class="math-container">\begin{align}
\left(\frac{ds}{dt}\right)^2 = \left(\frac{dr}{dt}\right)^2 + r^2\left(\frac{d\theta}{dt}\right)^2
\end{align}</span>
so in pol... | https://physics.stackexchange.com |
444,573 | [
"https://physics.stackexchange.com/questions/444573",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/171371/"
] | I am starting to read General Relativity, and from what i have understood, in this theory, time is a derived notion. An event is not associated with a particular time.
But then what is the physical meaning of an event?
And if time is a derived notion, then the four dimensions in our manifold are all spatial?
| There is no physical meaning associated to an event. An event is a point in the spacetime manifold, where the manifold itself is a mathematical structure allowing to retrieve the effect of gravity as seen by an arbitrary observer.
To say it otherwise: any observer will see spacetime as split between space and time, w... | You are correct in saying a particular event is not associated with a particular time.
This does not mean that time is <em>derived</em>, though. It's just different for observers travelling at different speeds.
An event is just a point in spacetime. Usually, we care about interesting events, like a lightening strike... | https://physics.stackexchange.com |
386,315 | [
"https://electronics.stackexchange.com/questions/386315",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/170041/"
] | Moved here from SE Physics.
Do MRI magnets oscillate during charging or even during persistant mode due to parasitic capacitance? What problems can this cause?
I am planning a low temp superconducting toroid inductor with multiple layers operating in persistent mode under liquid Helium. I am considering if I have to ... | The only problem that an LC resonance would introduce is some ringing at discontinuities.
You may rest assured that we treat changing the field of a superconducting magnet in much the same way that you would do dental work on a nuclear polecat; very, very carefully and slowly. The economic cost, and physical danger, o... | I don't think so. The Q will not be infinite, so any ringing would die off.
You obviously cannot increase the current quickly in the coil. The only moment of discontinuity is when the charging is complete but the delta in inductance (from the heat switch) is small so there might a small amount of ringing. While it is... | https://electronics.stackexchange.com |
17,439 | [
"https://dsp.stackexchange.com/questions/17439",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/10591/"
] | I am building a morse code decoder in Python. I am using SciPy and Numpy for FFT, filter, etc. It is coming along ok, but the signal is noisy. I am extracting the dominant frequency from the FFT of the input signal (which is audio from a wav file), and sampling at a rate great enough to detect whether a signal is pr... | The bandwidth of the message content of a CW signal in Hz is roughly at least 4 times the WPM at which the dots and dashes of each Morse Code character are being keyed. The actual signal may take up a several multiples of that bandwidth, depending on the envelope shaping or the rise/fall time of the CW transmitter use... | When I did this once I did use a bandpass filter around the estimated tone frequency. I used a fairly large passband. You can use your favorite type of bandpass filter. One thing to check is that if the transmission rate is very fast compared to the tone frequency there may not be that many cycles of the tone when tran... | https://dsp.stackexchange.com |
281,349 | [
"https://mathoverflow.net/questions/281349",
"https://mathoverflow.net",
"https://mathoverflow.net/users/114580/"
] | Suppose that there exist continuous maps $f:Y\longrightarrow Z$ and $g:Z\longrightarrow Y$ so that $g\circ f\simeq 1_Y$. Also, let $h :X\longrightarrow Y$ be a continuous map which induces an isomorphism of
fundamental groups. We know that $M_{h}\simeq Y$ and $M_{f\circ h}\simeq Z$, where $M_{h}=\frac{X\times I \cup Y... | I think you can do the following : factor your map $F\colon M_h\to M_{f\circ h}$ as the inclusion $i\colon M_h\hookrightarrow M_h\cup_Y M_f$ followed by a map $q\colon M_h\cup_Y M_f\to M_{f\circ h}$. Then, construct a retract $r\colon M_h\cup_Y M_f\to M_h$. It is then enough to prove that the map $M_h\cup_Y M_f\to M_{f... | This is a comment with a commutative diagram rather than a full answer.
Let $H\colon Y\times I\to Y$ be a homotopy between $\operatorname{id}_Y$ and $g\circ f$.
I though defining $G$ using the diagram
$$\require{AMScd}\begin{CD}
X\times I@>H\circ(h\times\operatorname{id}_I)>>Y\times I\\
@VVV@VVV\\
M_{f\circ h... | https://mathoverflow.net |
308,916 | [
"https://physics.stackexchange.com/questions/308916",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/143341/"
] | Everything I read says that "heat 'flows' from 'hot' to 'cold'" or "thermal energy is transferred from 'high' to 'low'" So my question is: <strong>why isn't the 'transfer' or 'flow' considered equal/simultaneous?</strong>
By this I mean if we put two objects together one 'hot' and one 'cold' the 'cold' one heats up a... | <blockquote>
"Everything I read says that "heat 'flows' from 'hot' to 'cold'" or "thermal energy is <strong>transferred</strong> from 'high' to 'low''"
</blockquote>
emphasis mine
Transfer is to move from one place to another. When we talk about heat transfer it is known that the transfer involves a heat loss and ... | <blockquote>
So is it just convention that we say the fast one transferred speed to the slow one rather than saying the slow one reduced the speed of the fast one?
</blockquote>
No, convention has nothing to do with it, it's probability.
There is more chance that a particle moving faster than a particle moving sl... | https://physics.stackexchange.com |
932,427 | [
"https://math.stackexchange.com/questions/932427",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/176213/"
] | I have to show: $\displaystyle\frac{1}{1^4}+\frac{1}{2^4}+...+\frac{1}{n^4} \le 2-\frac{1}{\sqrt{n}}$ for natural $n$
I tried to show it by induction (but I think it could be possible to show it using some ineqaulity of means) so for $n=1$ we have $1=1$ so inequality holds then I assume it's true for $n$ and for $n+1$... | You want to show that
$$2-\frac{1}{\sqrt{n}}+\frac1{(n+1)^4}\le 2-\frac1{\sqrt{n+1}}.\tag{1}$$
If (1) is true, then using induction hypothesis one gets
$$1+\frac1{2^4}+\cdots+\frac{1}{n^4}+\frac{1}{(n+1)^4}\le 2-\frac1{\sqrt{n}}+\frac1{(n+1)^4}\le 2-\frac1{\sqrt{n+1}},$$
and we are done by induction.
Showing (1) shoul... | You should show its:
$\displaystyle2-\frac{1}{\sqrt{n}}+\frac{1}{(n+1)^4}\le2-\frac{1}{\sqrt{n+1}}$
The other ways does not help your proof (think about it for a while)
| https://math.stackexchange.com |
126,206 | [
"https://math.stackexchange.com/questions/126206",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/24117/"
] | <blockquote>
How can we show that if $R$ is an infinite commutative ring and $R/I$ is finite for every nonzero $I \unlhd R$, then $R$ is an integral domain?
</blockquote>
I tried proceeding by contradiction: assume $a$,$b$ $\in R \backslash \{0\}$ and $ab=0$; then $R/(a)$ and $R/(b)$ must be finite, say $R/(a)=\{k_i... | If $ab=0$, and if $k_i$, $1\leq i\leq m$, are representatives mod $a$, then $(b)=\{bk_1,\dots,bk_m\}$, i.e. $(b)$ is finite and hence $R/(b)$ infinite.
| I give a solution when $R$ is commutative and noetherian.
Suppose absurdly that $R$ is not a domain, hence $0$ is not a prime ideal. Therefore, for every prime ideal $\mathfrak{p}$ of $R$, the domain $R / \mathfrak{p}$ is finite, hence a field. So every prime ideal of $R$ is maximal, i.e. $R$ is artinian. Therefore $... | https://math.stackexchange.com |
1,078,713 | [
"https://math.stackexchange.com/questions/1078713",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/81706/"
] | What I am trying to prove is that if $f$ is entire and $e^f$ is constant $f$ is constant. This is my attempt but I just can't go forward to get anything meaningful. $$e^{f(z)}=c$$ where $c\in \mathbb{C}$ is a constant. Then the set of solutions for $f(z)$ is {$\log|c|+i(Arg(c)+2k\pi)|k\in \mathbb{Z}$}. But then how do ... | <strong>Hint</strong>: Since $c$ can't be zero, it helps to consider the derivative of both sides.
| By the chain rule, we can take the derivative of both sides to get
$$e^{f(z)} = c$$
$$f'(z)e^{f(z)}=0$$
$$f'(z)\cdot c = 0$$
$$f'(z)=0$$
This implies $f(z)$ is constant.
| https://math.stackexchange.com |
705,437 | [
"https://physics.stackexchange.com/questions/705437",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/259664/"
] | I'm currently taking a course in Quantum-optics, focusing primarily on the book <em>Introductory to quantum optics</em> by C. Gerry & P. Knight. In the book they first present the quantization of a single mode of the EM field, and the electric field operator is set to be(page 12, equation 2.15) <span class="math-co... | Why do you think <span class="math-container">$\hat E_2$</span> is a standing wave mode? There is no multiplicative separation of <span class="math-container">$\vec r$</span> and <span class="math-container">$t$</span> dependence in the operator. On the contrary, they are always grouped in the expression <span class="m... | Expand the sinusoidal term in <span class="math-container">$E_1$</span> and we'll directly see the difference in the spatial dependence:
<span class="math-container">$$E_1=\sqrt{\frac{\hbar \omega}{\epsilon_0 V}}\frac{1}{2i}\left(a e^{ikz}-a e^{-ikz}+a^\dagger e^{ikz}-a^\dagger e^{-ikz}\right)\vec{e}.$$</span> There ar... | https://physics.stackexchange.com |
310,937 | [
"https://physics.stackexchange.com/questions/310937",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/84724/"
] | If I by some mean threw lunar soil in the earths direction, and used it to power some turbines, would the turbines generate more energy than it took to get the lunar soil out of the moons orbit?
For example:<br>
Assuming I can convert all the kinetic energy from the moon dust to electricity.<br>
If I had an x amount... | At a pure physics level, you're correct. The potential energy of the earth-moon system is decreased by moving a small mass from the moon to the earth. Therefore you can construct some mechanism to extract the energy from that different state.
But at an engineering level, this is very difficult. There's no cable or ... | It's not a scheme that I would invest in.
Energy Expenditure
<ol>
<li>Get the digging gear to the moon. To make the process efficient, you need lots of equipment, that's lot of energy required.</li>
<li>Energy required to dig up the regolith, where will that come from?</li>
<li>Energy required to get a large amount o... | https://physics.stackexchange.com |
672,531 | [
"https://physics.stackexchange.com/questions/672531",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/251805/"
] | Now, I know. The question is silly. Why would there be friction if the object is at rest with no force acting upon it?
However, by the inequality <span class="math-container">$f_s \le \mu_s F_n$</span>, shouldn't there be friction regardless? Because the normal force always has a magnitude, so shouldn't friction have a... | <span class="math-container">$\mu_s F_n$</span> gives the <em>maximum</em> force of friction. The current force of friction is always less than or equal to this, and <span class="math-container">$0$</span> is clearly <span class="math-container">$\leq \mu_s F_n$</span>.
| <span class="math-container">$0\leq\mu_sF_n$</span> is still a true inequality since both <span class="math-container">$\mu_s$</span> and <span class="math-container">$F_n$</span> are non-negative, real numbers, so the mathematics allows for zero static friction.
| https://physics.stackexchange.com |
265,857 | [
"https://security.stackexchange.com/questions/265857",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/62071/"
] | Lets say my password is <code>AppleDogFire642!</code>.
What would be the potential security consequences if my password hint was <code>BananaCatSmoke123@</code>?
| If I saw <code>BananaCatSmoke123@</code> and it didn't work, then I would most certainly start replacing words, numbers, and symbols.
You not only give away your pattern, but the context behind each word. You reduce the entropy for the attacker considerably. So instead of <code>Apple</code> providing 5 characters from ... | A password hint should be just that: A hint.
For example, if you have 3 passwords with high entropy, which you use on systems where using a password manager isn't possible, then the password hint should be something that hints you towards <em>which</em> password you have chosen.
For example, say you have the following ... | https://security.stackexchange.com |
3,041,516 | [
"https://math.stackexchange.com/questions/3041516",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/470941/"
] | Consider two integrals of the form <span class="math-container">$$I_{xx}=\int x^2 f(r)d^3r,~~I^\prime=\int xy ~f(r)d^3r$$</span> where <span class="math-container">$f(r)$</span> is a function of <span class="math-container">$r=|\vec{r}|$</span> only and has no dependence on <span class="math-container">$\theta,\phi$</s... | <blockquote>
Any hints on how to proceed to find zmod5?
</blockquote>
Do it the <em>EXACT</em> same way.
<span class="math-container">$5 -1 = X$</span>
And <span class="math-container">$2018\div X = Q$</span> with <span class="math-container">$R$</span> remaider.
So <span class="math-container">$7^{2018}-1 = (7^{... | We have:
<span class="math-container">$$(7^2)^{1009} - 1 \pmod 5$$</span>
<span class="math-container">$$\equiv (-1)^{1009} - 1$$</span>
<span class="math-container">$$\equiv -2 \equiv \bbox[5px,border:2px solid black]3 \pmod 5$$</span>
| https://math.stackexchange.com |
182,673 | [
"https://dba.stackexchange.com/questions/182673",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/131459/"
] | I am using a db.currentOp() to check the current connection in Mongodb.
How can I get the total number of all record and how can I get all the "client" IP in a one column?
Thanks
<pre><code>db.currentOp()
{
"inprog" : [
{
"desc" : "WT RecordStoreThread: local.oplog.rs",... | This will help to aggregate the information -
<strong>Connection Count by ClientIP, with Total</strong>
For Mongo Shell:
<pre><code>db.currentOp(true).inprog.reduce((accumulator, connection) => { ipaddress = connection.client ? connection.client.split(":")[0] : "unknown"; accumulator[ipaddress] = (accumulator[ip... | You can try:
<pre><code>db.currentOp().inprog.forEach(function(x) { print(x.client) })
172.16.0.1:42768
172.16.0.4:59984
172.16.0.2:50643
172.16.0.1:20183
</code></pre>
If you want to remove the port add a regex:
<pre><code>db.currentOp().inprog.filter(x => x.ns === 'local.oplog.rs').forEach(function(x) { print(x... | https://dba.stackexchange.com |
1,736,273 | [
"https://math.stackexchange.com/questions/1736273",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/329909/"
] | While in class, we were proving a limit problem using the Squeeze Theorem, but when I was reviewing my notes, I came up with a problem,,
The first question was to prove that
$$\lim_{n\to \infty}(1+n)^\frac{1}{n}=1$$
Okay, this was easy.
The next question was to use the limit proven above to evaluate the following l... | For all $n,$ $1\le 1+n + n\cos n \le 3n$ and $1/(2n + n\sin n) \le 1/n.$ Thus
$$ 1 \le (1+n + n\cos n)^{1/(2n + n\sin n)}\le (3n)^{1/n} \to 1.$$
By the squeeze theorem, the limit is $1.$
| What do you get if you put $n=2k +k\sin k$ in the first "easy" limit? Also, can you approximate $|\cos n-\sin n|$?
| https://math.stackexchange.com |
3,411,351 | [
"https://math.stackexchange.com/questions/3411351",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/453033/"
] | Here is my question:
<blockquote>
Let <span class="math-container">$G$</span> be a group and <span class="math-container">$\mathbb{K}$</span> be a field. Let <span class="math-container">$\mathbb{K}[G]$</span> be the group ring of <span class="math-container">$G$</span> over <span class="math-container">$\mathbb{K}$</s... | Short answer: No.
Let <span class="math-container">$G=\Bbb{Z}/n\Bbb{Z}$</span>. Then define <span class="math-container">$\newcommand\CC{\Bbb{C}}\CC[G] \to \CC[G]$</span>
by <span class="math-container">$g \mapsto \zeta_n^g g$</span>. This is an automorphism of <span class="math-container">$\CC[G]$</span> which doesn... | The answer is no. Take for example the group ring <span class="math-container">$\mathbb K[\mathbb Z] $</span>, which is isomorphic to <span class="math-container">$\mathbb K[t, t^{-1}]$</span>. If the characteristic of the field is not <span class="math-container">$2$</span>, we can send <span class="math-container">$t... | https://math.stackexchange.com |
4,368,942 | [
"https://math.stackexchange.com/questions/4368942",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/965463/"
] | I am trying to study if there can be a SES of the following form
<span class="math-container">$$0 \to \mathbb Z_4 \xrightarrow{f} \mathbb Z_8 \oplus \mathbb Z_2 \xrightarrow{g} \mathbb Z_4 \to 0.$$</span>
So, I know if there is one, <span class="math-container">$f$</span> must be injective and <span class="math-contain... | Note that we have <span class="math-container">$a+b=0$</span>, so <span class="math-container">$b=-a$</span>. Using that, we have <span class="math-container">$a+b+c=a-a+c$</span>.
In general, <span class="math-container">$a+b+c=a-a+c$</span> is not true. It is true only if we know <span class="math-container">$b=-a$... | From second inner product : <span class="math-container">$$\begin {pmatrix} a & b & c \end{pmatrix} . \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} = a.1+b.1+c.0$$</span>
As the above two vectors are orthogonal then <span class="math-container">$a+b=0$</span>
So substitute <span class="math-container">$b=-a$</span>... | https://math.stackexchange.com |
30,699 | [
"https://stats.stackexchange.com/questions/30699",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/10164/"
] | I have been calculating p-values for correlations using bootstrapping. I've just been using the same p-value cutoff regardless of the number of pair-wise calculations. Intuitively, it seems to me that the more correlations that I perform, the more likely I am to obtain a spurious correlation due to random chance.
<str... | I also don't follow your situation 100%, but I suspect it doesn't matter. The problem of multiple comparisons arises simply due to the mathematics of looking at lots of random things. That is, each statistical test can be understood as a Bernoulli trial. If the null hypothesis holds in every case, you have a Binomia... | But bootstrapping does offer a simple way to do multiple comparisons (including simultaneous intervals if you don't like testing) in a way that incorporates dependence structures in an asymptotically consistent way. The statement that "bootstrapping does not get you out of this fact" is misleading because it follows a ... | https://stats.stackexchange.com |
15,694 | [
"https://security.stackexchange.com/questions/15694",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/9616/"
] | How can I know that a network card in a server was infected by a virus or not? Are there any methods to check it?
| While it's theoretically possible to insert malicious code into flash memory on peripheral equipment like network cards, it's more likely to see the use of videocard GPU systems to do rainbow table cracks for special purpose hackware, etc.
Specialized programming is needed that would be nation-state level targeted att... | Very few viruses will infect the network card on your server. Viruses typically infect your OS or other application software. Therefore, for most purposes you don't need to worry about viruses in your network card. If you're worried about viruses, take standard steps to harden your server; search the archives for se... | https://security.stackexchange.com |
423,271 | [
"https://softwareengineering.stackexchange.com/questions/423271",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/120909/"
] | I would like to know how manage a type of pull requests. One of my reviewers ask me for a lot and a lot of changes (3 or 4 days doing changes), all related with possible improvements in the code that I thought it is too much and it ends up in a "perfect" and "smart" code. It is difficult to discuss ... | Do you need to do <em>everything</em> that your reviewer asks of you? Usually, you don't. A good code review process has some back-and-forth. A reviewer might suggest a change, the developer might explain why that is or is not a good idea. If the reviewer's suggestions really improve the code, you should consider them.... | If such major issues arise at the code review stage, it is too late. It shows that your development process has problems. In a normal process first the main design decisions should be defined and discussed within a team. Then there is not much space for discussion.
Then I see 3 major cases.
<ol>
<li>If you followed the... | https://softwareengineering.stackexchange.com |
121,228 | [
"https://mathoverflow.net/questions/121228",
"https://mathoverflow.net",
"https://mathoverflow.net/users/31271/"
] | Given the group ring $\mathbb{Z}[G]$ of a finite group $G$ over $\mathbb{Z}$, is there a way to generalize the notion of the "frobenius algebra" in some cases? One can show that every group ring $\mathbb{Q}[G]$ is a frobenius algebra and thus the projektive and injective modules correspond. This seems to be wrong in ge... | I claim that if $R$ is a left Noetherian ring and $M$ a finitely generated left $R$-module, then $M$ is injective as an $R$-module iff it is injective in the category of finitely generated $R$-modules.
Suppose $M$ is injective in the category of f.g. $R$-modules. Then for any left ideal $I$ of $R$ and any left $R$-mo... | The notion of Frobenius algebra is still useful in the general case, but then group rings that are Frobenius algebras aren't necessarily quasi-Frobenius rings, as your example notes. However if $M$ is a noetherian Frobenius $A$-algebra where $A$ is a commutative and self-injective ring then $M$ itself is a quasifrobeni... | https://mathoverflow.net |
16,507 | [
"https://security.stackexchange.com/questions/16507",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/10891/"
] | I play in a game which includes normal risks, but also a wide range of supernatural powers which could affect the security of a network. These may be as prosaic as a retrieving data directly from a device's memory with a touch or as dramatic as sending one's mind directly into a network or constructing a small alternat... | Modern day security holds the belief that you cannot make a network infinitely secure - build a better mousetrap and you'll encourage the evolution of mice. Any security system will have to be bounded by the expected capabilities of the attackers, and will have to employ a threat based risk remediation strategy that p... | You've hit on the basic premise of IT Security: you can't predict or stop everything, and to try might cost more than what you are trying to protect. Your character is concerned with Mastery of skill to overcome higher-level obstacles, but the race to create obstacles that are higher than other people's skills is fooli... | https://security.stackexchange.com |
93,554 | [
"https://cs.stackexchange.com/questions/93554",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/89689/"
] | Lets say Problem A,B are in NP.
Can we reduce Problem A to B? Meaning A $≤_p$ B? or A $≤_t$ B
Is there a difference in "hardness" of a Problem even in NP?
Or must Problem B at least be NP-Complete?
| The $n$ isn't indexing how many <em>references to</em> variables there are, it's indexing how many free variables are able to be referred to.
You can think of $0,1,\dots,n-1$ as being variables $v_0,v_1,\dots,v_{n-1}$. A term in $\mathcal T_n$ is a term that is allowed to refer to variables $v_0$ through $v_{n-1}$. If... | This is crucial:
<blockquote>
It further clarifies that the elements of $\mathcal{T}_n$ are terms with <em>at most</em> $n$ free variables, numbered between $0$ and $n-1$.
</blockquote>
Then, in the rest of your argument, you forgot the "numbered between $0$ and $n-1$" part.
Item 3 states that, if $t_1$ has its fr... | https://cs.stackexchange.com |
42,256 | [
"https://quant.stackexchange.com/questions/42256",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/15283/"
] | It's readily verified mathematically that <span class="math-container">$V=S$</span> and <span class="math-container">$V=e^{rt}$</span> are solutions to the Black-Scholes PDE <span class="math-container">$\frac{\partial V}{\partial t}
+ \frac{\sigma^2 S^2}{2} \frac{\partial^2 V}{\partial S^2}
+ r S \frac{\partial V}{\pa... | The VIX Index is computed from option prices on S&P Index.
A VIX-like Index for other industries would first require to have a liquid option market.
| In theory that would be possible. However, liquidity in industries could in some instances be substantially less than liquidity in the SPX thus making the hedging of volatility derivatives such as vol futures more difficult. Also, there may not be sufficient interest from investors to make the launching of industry/sec... | https://quant.stackexchange.com |
472,969 | [
"https://physics.stackexchange.com/questions/472969",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/228346/"
] | Now I am reading a Weinberg's book "Quantum theory of field". Vol.1 page: 55
Сould you explain me the following things?
<blockquote>
Einstein's principle of relativity states the equivalence of certain 'inertial' frames of reference. It is distinguished from the Galilean principle of relativity, obeyed by Newtonian... | In the first equation you have <span class="math-container">$\eta_{\mu\nu}$</span> at both sides because you define the Lorentz transformations as those leaving the metric <span class="math-container">$\eta_{\mu\nu}$</span> invariant. So <span class="math-container">$\eta'_{\mu\nu}=\eta_{\mu\nu}$</span>.
You can obtai... | I hope this is useful for you. This has to do with how to measure distances in Minkowski space. This is done through the metric, an amount that in principle depends on the point in space but in this case, special relativity, is constant. These equations that you have written tell us precisely about that. In the first, ... | https://physics.stackexchange.com |
139,279 | [
"https://electronics.stackexchange.com/questions/139279",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/58651/"
] | Basically I need heating element which can heat up small volume of air (lets say shoes box size) up to about 60 C degrees. I am going to use 25 V source supply with 2 A current.
What I thought about doing is:
<pre><code>Cp= 1.00 J/gK (air specific heat)
q=1275g/m^3 (density of air)
V=0.05m^3 (volume of air I need to ... | <blockquote>
I am going to use 25 V source supply
</blockquote>
If your supply voltage source is 25 volts then you need to use this to calculate the resistance needed.
\$Power = \dfrac{volts^2}{resistance}\$
Resistance = \$25^2 / 21.25 = 29.4\$ ohms
The error you made was to assume that your power supply will alw... | I would work with what @user56801 suggested.
I would select a resistor that will use all of the 50W your PSU can supply and use a thermostat to control the temperature and it will be maintained at 60 degC much more accurately than hoping the external convection, radiation and conduction losses are going to be zero or ... | https://electronics.stackexchange.com |
501,507 | [
"https://electronics.stackexchange.com/questions/501507",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/251254/"
] | I want to ask about wall adapter (switching) with 2.5mm jack
let's assumed its label as 9V 2A.
I saw many tutorial even some product use normal adapter (2.5mm jack) with BMS module to charge Li-ion cells. (for this function BMS just over voltage protect and balance for each cell) So BMS module it's self don't have fu... | <blockquote>
Q1: What happen when load draw current more than 2A? (Will it preform constant current mode?)
</blockquote>
It could go into current limit. It might not and depending on the (lack of quality) could overheat and go on fire.
<blockquote>
Q2: Is it safe to use wall adapter to charge battery? (Can we co... | the current on the label is not an automatic limit, attempting to exceed it may cause a temporary voltage reduction, or cause the adaptor to shut-down, or even cause it to break.
The 2A limit will not prevent yout battery from being over chanrged, that is why a battery mamangemnt systrem is needed,
If you can set th... | https://electronics.stackexchange.com |
4,343,829 | [
"https://math.stackexchange.com/questions/4343829",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/727735/"
] | Assume <span class="math-container">$\theta \sim U[0,1]$</span>.
Fix <span class="math-container">$x\in \mathbb{R}$</span> and consider the following random variable:
<span class="math-container">$ g_{x}\left(\theta\right)=\begin{cases}
2-|x| & |x|\leq\theta\\
0 & \text{else}
\end{cases} $</span>
How can I calc... | <blockquote>
We must to calculate <span class="math-container">$$\lim_{x\to \pi/2}\frac{\sin x-1}{2x-\pi}$$</span>
</blockquote>
If we use a change of variables <span class="math-container">$\ h = x - \frac{\pi}{2},\ $</span>then this becomes:
<span class="math-container">$$\lim_{h\to \ 0}\frac{\sin\left(\frac{\pi}{2} ... | Another way to rewrite it is<br />
<span class="math-container">$$ \frac{\sin(t + \pi/2) - 1}{2t} = \frac{\sin t\cos(\pi/2) + \sin(\pi/2)\cos t - 1}{2t} = \frac{\cos t - 1}{2t}. $$</span>
| https://math.stackexchange.com |
187,794 | [
"https://physics.stackexchange.com/questions/187794",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/82906/"
] | I know the relation between specific heat at constant volume and pressure and I also know how to calculate it.
Thing is, I don't understand its concept
I want to know why at constant pressure, specific heat is always greater than at constant volume
| At constant volume, all the heat that goes into the system goes into raising the temperature of the system, and no external work is done.
At constant pressure, some of the heat goes into expanding the system, which does external work, and therefore leaves less energy available for raising the temperature.
| Specific heat at constant volume represents the heat supplied to a unit mass of the system to raise its temperature through 1K, keeping the volume constant. Since, V= Constant, dV = 0 and the work done by the system W = PdV = 0. The first law of thermodynamics says: Q = (dU+W) = (dU+PdV) = dU.
Specific heat at constan... | https://physics.stackexchange.com |
142,016 | [
"https://electronics.stackexchange.com/questions/142016",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/59989/"
] | I am trying to replace a broken cable on my headphones(Sennheiser HD 280 PRO) but I can't figure the type of cable so that I can order it online. I think it is pretty standard as it seems other headphones have similar cables. However searching for headphones cable only helps to find replacing connector cable(i.e. the o... | I'd use speaker wire, as it's probably best combination of cheap and readily available. Places that sell speakers may sell it by the foot, from a spool.
I believe if you reclaim wire from a different dead device, you run the risk of it being lacquered, making it hard to work with (namely, hard to solder).
| If this is the cable that runs between the two earpieces, all you need is two conductors.
The original cable uses enamelled wire of two different colors. The enamel coating with burn off when you tin the conductors. Simply twist all of the strands of one color together, then hold the twisted wires in a ball of molten... | https://electronics.stackexchange.com |
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