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3,946,224 | [
"https://math.stackexchange.com/questions/3946224",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/861329/"
] | I'm just going to write out the steps for an equation I use at a restaurant and I hope you in the community wouldn't mind answering by showing how the equation should be written properly.
I use this math process, or equation when dividing the quantity of cashew milk out for bottling at a restaurant I work at.<br />
BEG... | Indeed the two representations are equivalent. Substituting <span class="math-container">$x_i = e^{y_i}$</span>, we note that
<span class="math-container">$$ \prod_{i=1}^{n} \max\{1,x_i\} < d
\quad\Leftrightarrow\quad \prod_{i=1}^{n} \max\{1,e^{y_i}\} < d
\quad\Leftrightarrow\quad \sum_{i=1}^{n} \max\{0,y_i\} <... | Assume <span class="math-container">$d>1$</span> (otherwise the volume is <span class="math-container">$0$</span>). Call the volume <span class="math-container">$V_n(d)$</span> so<span class="math-container">$$V_n(d)=\int_0^1V_{n-1}(d)\mathrm{d}x+\int_1^dV_{n-1}(d/x)\mathrm{d}x=V_{n-1}(d)+\int_1^dV_{n-1}(x)\frac{d}{... | https://math.stackexchange.com |
568,087 | [
"https://math.stackexchange.com/questions/568087",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/65955/"
] | $$\displaystyle \lim_{x\to 0}f(x)=0$$
$$\displaystyle \lim_{x\to 0}\frac{f(2x)-f(x)}{x}=0$$
Prove, that $$\lim_{x\to 0}\frac{f(x)}{x}=0$$
So, I have some ideas:
<ol>
<li>Do $\lim_{x\to 0}\frac{f(x+x)-f(x)}{x+x-x}=0$ and $\lim_{x\to 0}f(x)=0$ imply that $f'(0)$ exist and $f'(0)=0$? If yes, than $lim_{x\to 0}\frac{f(... | Using OP's second technique, we have $$f(x) = f(x/2^{n}) + x\sum_{k = 0}^{n - 1}\frac{\gamma(x/2^{k + 1})}{2^{k + 1}}$$ where $\gamma(x) \to 0, f(x) \to 0$ as $x \to 0$. Letting $n \to \infty$ we get $$\frac{f(x)}{x} = \sum_{k = 0}^{\infty}\frac{\gamma(x/2^{k + 1})}{2^{k + 1}}$$ Also given any $\epsilon > 0$ we have... | For prime number $p$ and any nonzero integer $k$, define $f(\frac{k}{p})=\frac{1}{p}$. For irrational number $a$,$f(a)=0$. Then $f$ is well-defined on $\mathbb{R}$. You may check that it is a counterexample. What happens if we add the condition that $f$ is continuous? I will leave it as your exercise.
| https://math.stackexchange.com |
2,899,964 | [
"https://math.stackexchange.com/questions/2899964",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/467519/"
] | The problem I am working on is stated as follows.
<blockquote>
Let $A \subset R^2$ be open and $(a_1,a_2)\in A$. Suppose $f:A\to R$ satisfies that $\frac{\partial f}{\partial x_1}(a_1, a_2)$ exists,
and that $\frac{\partial f}{\partial x_2}$ is continuous in $A$. Prove that $f$ is differentiable at $(a_1, a_2)$.
<... | I hope you don't mind if I change the notation a bit.
Let $a = (a^1,a^2) \in A$. Let $h = (h^1,h^2) \in \mathbb{R}^2$. The partial derivatives of $f$ will be denoted by $D_1 f$ and $D_2 f$, instead of $\partial f/\partial x_1$ and $\partial f/\partial x_2$. For example, $D_1 f(a)$ denotes the partial derivative of $f$... | I'll use $D_1,D_2$ to denote partial derivatives with respect to the first and second variables. Suppose for simplicity that $a=(0,0)$ and $B((0,0),r)\subset A.$ For $|(x,y)|<r,$ we have
$$f(x,y) - f(0,0) = f(x,y) - f(x,0)+ f(x,0)-f(0,0).$$
By the MVT,
$$f(x,y) - f(x,0) = D_2f(0,c(x,y))y$$ $$ = D_2f(0,0)y +[D_2f(... | https://math.stackexchange.com |
328 | [
"https://physics.stackexchange.com/questions/328",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/41/"
] | <img src="https://i.stack.imgur.com/9ak7P.png" alt="alt text">
I'm stuck on number 5. The answers to the first 4 are correct, but I dont know how to set up number 5. Any idea that I would have would require me having some kind of time information, but thats not given. Any suggestions?
| I'm not sure I totally understand the question, but I can make an educated guess. Firstly, I envisage a person sitting on the merry-go round with their body pointed tangentially to the circle, in which cases <em>no</em> force <em>in that direction</em> is required.
However, if the person is free to move radially (can ... | Think about these:
<ol>
<li>What is the shape of the path the person takes?</li>
<li>What force is needed to keep the person traveling along that path?</li>
</ol>
| https://physics.stackexchange.com |
205,055 | [
"https://softwareengineering.stackexchange.com/questions/205055",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12697/"
] | I am writing a RESTful service in Java, of course it's typical HTTP based interface.
I am wondering should the service provide Java interface which has same semantic to the RESTful interface? I think Java interface will ease other Java code to call the service. (Client Java code doesn't need to use HTTP client to trig... | <blockquote>
The problem is it's difficult to write same semantic Java interface to a RESTful one, I mean same semantic.
</blockquote>
What is difficult about it? The standard way of doing REST interfaces in Java consists of writing a Java interface and adding some JAX-RS annotations, that's all.
| I don't write in Java, but the same concepts apply.
For most projects I work on, I try to do both. Basically my project is set up such that the REST interface just uses the underlying API. Basically the flow is:
<pre><code>REST -> Front-end API -> Useful code
</code></pre>
This way I can write additional front... | https://softwareengineering.stackexchange.com |
58,225 | [
"https://dsp.stackexchange.com/questions/58225",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/43105/"
] | We are working on LTE Uplink CFO Correction for 3 MHz band. The time domain CFO correction is easy, which depends on the processing of 3840 samples step by step multiply by <span class="math-container">$\exp(-j 2\pi f_\text{offset}t)$</span>. . What will be the equivalent frequency domain correction?
| Well, when <span class="math-container">$m=k$</span> the integral is:
<span class="math-container">$$
\int_0^T e^{j(m-k)\Omega_0t} dt =
\int_0^T e^{j \cdot 0 \cdot\Omega_0t} dt = \int_0^T dt = T
$$</span>
So as Juancho says in the comments, it's the same signal and so can't be orthogonal to itself.
| The text is a bit cumbersome, in that it states "things" before defining them. And the zero-signal (or vector) is considered orthogonal to every other vector. This is why the sentence "If <span class="math-container">$I=0$</span> for..." seems unnecessarily complicated to me. And the <span class="math-container">$m$</s... | https://dsp.stackexchange.com |
113,063 | [
"https://electronics.stackexchange.com/questions/113063",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/38853/"
] | I'm trying to drive a device that uses 12-0V levels for serial communication. I decided to use LS7407N, a buffer with open-collector, so that I can use Arduino's TTL levels to send commands to the device. The problem is that the device doesn't seem to get any messages. I am almost certain that the circuit is connected ... | Turns out it wasn't a design flaw.
tl;dr: <strong>Devices parity was set to EVEN</strong>.
Because of that, the messages from Arduino (with parity set to NONE) were coming in distorted. In case of loss of data the device simply doesn't provide any feedback.
My biggest mistake was assuming that the device parity wa... | Edit: I noticed there's no connection between the collector and the cap. Don't know what I was thinking so disregard my answer.
[A 100nF capacitor on the secondary side of the optocoupler gives a time constant of t = R*C = 4,7k * 100n = 0,47ms. Is this an OK rise time for the baud rate you are using?]
//Hank
| https://electronics.stackexchange.com |
15,074 | [
"https://astronomy.stackexchange.com/questions/15074",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/4160/"
] | Recently, <strong>over a thousand exoplanets were confirmed in one huge sweep</strong> which is a huge achievement and in the mix <strong>a dozen or so possibly habitable planets were confirmed</strong> as well. This made me wonder, Are there any common characteristics of (possibly) habitable planets? If so, what are t... | I think I will answer your question from two vantage points. Firstly, what do we have to measure about a new exoplanet to consider it potentially habitable? Keep in mind that in detecting these 1000 or so new exoplanets, we've only gone so far as to show that they (statistically) exist and to measure some very very bas... | Some of the possible characteristics are listed below.
<ol>
<li>Distance of planet from its host star. Is the planet in Goldie-lock zone?</li>
<li>Atmospheric composition. Presence of Oxygen, Nitrogen, CO2, water vapors.
Thick atmosphere can shield from radiation from host star.</li>
<li>Mass of the planet. surface g... | https://astronomy.stackexchange.com |
3,347,540 | [
"https://math.stackexchange.com/questions/3347540",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/546770/"
] | This problem came up in my homework for an online class and try as I might, I can't find a solution.
<span class="math-container">$(x-1)^3+2016(x-1)=-1$</span>
<span class="math-container">$(y-1)^3+2016(y-1)=1$</span>
Find <span class="math-container">$x+y$</span>
So far, I've tried letting <span class="math-conta... | From your point you have that or <span class="math-container">$a+b=0$</span> or <span class="math-container">$a^2-ab+b^2+2016=0$</span>. But <span class="math-container">$a^2-ab+b^2+2016=(a-\frac b2)^2 +b^2-\frac{b^2}4+2016>0\forall a,b\in\Bbb R$</span>. So you have <span class="math-container">$a+b=0\implies x+y=2$... | <strong>Hint</strong>
What can be concluded from <span class="math-container">$$(a+b)(a^2-ab+b^2+2016)=0\\a^2-ab+b^2\ge 0\quad,\quad \forall a,b\in\Bbb R$$</span>?
| https://math.stackexchange.com |
152,953 | [
"https://mathoverflow.net/questions/152953",
"https://mathoverflow.net",
"https://mathoverflow.net/users/36688/"
] | Is there a Riemannian metric on $\mathbb{R}^{2}=\mathbb{R} \times \mathbb{R}$ which is not conformally equivalent to a product metric?
More generally, assume that $M$ and $N$ are two manifolds. What obstructions are there for a metric $g$ on $M \times N$ to be conformally equivalent to a product metric for metrics
... | I'll give a partial answer to the OP's second question, which I take to be asking for the obstructions for a metric in dimensions greater than $2$ to be conformal to a product metric.
This is, first of all, a local question, since, even locally, most metrics in dimension $3$ or more are not conformally equivalent to... | Every metric on $R^2$ is conformally equivalent to either the standard metric on $R^2$ or to the standard metric on the unit disc. Thus there are only two conformal equivalence classes. As every class contains a metric which is a product, every metric on $R^2$ is conformally equivalent to a product metric. Of course, t... | https://mathoverflow.net |
2,514,617 | [
"https://math.stackexchange.com/questions/2514617",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/488910/"
] | I am struggeling with figuring out how to stat with this proof. I understand how to go about this if I need to prove that R is a partition of A. But the quotient set is confusing me.
Prove that:
IF $R$ is an equivalence relation on set $A$. Then A modulo R,
$A/R = \{[x]_R|x\in A\}$, is a partition of A.
Any hints o... | You need to check 3 things:
<ol>
<li>The equivalence classes are non-empty.</li>
<li>The union of the set of equivalence classes is $A$.</li>
<li>The equivalence classes are mutually disjoint.</li>
</ol>
Now, to give a hint, compare the above three conditions you have to check with the definition of an equivalence re... | If $R$ is an equivalence relation on set $A$, then $A$ modulo $R$,
$A/R=\{[x]_R:x\in A\}$, is a partition of $A$.
$\textbf{Proof}$. The family $\{[x]_R:x\in A\}$ of sets does not contain the empty set since for each equivalence class $[x]_R$, $x\in [x]_R$. So each $[x]_R\not=\varnothing$.
Secondly, we need to show ... | https://math.stackexchange.com |
146,154 | [
"https://security.stackexchange.com/questions/146154",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/134150/"
] | I am implementing a solution with set of Micro Services (Spring Rest Services) with Rabbit MQ as the message broker. The Edge server is Authenticated using OAuth based Identity server. Internal Micro Sevices calls are not Authorized or Authenticated.
My objective is to secure all internal Micro Services with Au... | Reusing the edge token is a really bad idea as it simply gives more opportunities for it to be intercepted and wrongly used.
You should identify any risk boundaries first. So which services/data actually require additional or separate protection. Then you can create security boundaries that match. You should not gene... | I agree with Julian's answer that you need to first understand the risks and classify data in your system.
I respectfully disagree using an edge token is a bad idea in all circumstances. If the token just specifies identity (who the caller is) and leaves authorization (what the caller can and cannot do) up to each ser... | https://security.stackexchange.com |
15,028 | [
"https://chemistry.stackexchange.com/questions/15028",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/7278/"
] | I wonder if sublimation can be done only on certain substances like iodine, or it can be done on all substances.
In other words, can sublimation be done, for example, on water? If it cannot, then why?
| Look up the term “phase diagram”. At different temperatures and pressures different phases are favored. Think about water. At 0 °C and 1 atm water and ice are equally favorable. There can be freezing or melting. At other temperatures and pressures there can be sublimation and deposition.
The sublimation of water is in... | Sublimation refers to molecules passing from the solid to the gas state without going through the liquid state. This happens all the time to every solid, including water, it's just a question of at what rate it sublimes and how that rate compares to its rate of melting in the same conditions.
Snow, for example, often ... | https://chemistry.stackexchange.com |
12,552 | [
"https://security.stackexchange.com/questions/12552",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/8298/"
] | I am writing an application for smartphones to provide very limited SSH usage. The user cannot perform arbitrary actions when logged in. They can run a specific script(s) only.
For various reasons it is not possible to implement passwordless login so the password must be provided from the smartphone for login. Howeve... | Giving all users a shared account is not something I would consider. You would not be able to know for certain which user did what on the system, multiple people will be sharing the same account concurrently... All in all, it's bound to get messy at some point.
Imagine if one of them loses their phone, and you are for... | Are you constrained to allowing the users direct access to SSH?<br>
That does put you in a pretty difficult spot, both with authenticating the users as was mentioned, and with restricting the actual actions they can perform.
I would suggest a different solution - have a server component, that emulates SSH, and then... | https://security.stackexchange.com |
133,493 | [
"https://stats.stackexchange.com/questions/133493",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/58450/"
] | For example, I have a population density map of a 100 x 100 km square region.
Each part of the rectangular region represents the population density i.e. (1,1) -> 128 people, (100,100) -> 50 people
I plug this square matrix into MATLAB using the "imagesc" command and it generates an image presenting the population de... | Use the raw data!
If I understand your problem correctly, you've got a matrix of data points where the (x,y) coordinates indicate a location and the value is the population density at that location. In other words $\textrm{data}(50,75)=100$ indicates that the area at position (50,75) has a population density of 100 p... | Using RGB images is to expensive. 100x100 matrix of data means that you must design network which contains 10000 inputs. For RGB format of data must be three times more inputs, because you use 3 parameters for every point in matrix, so you need 3x100x100 or 30000 inputs and in first layer your computations will be proc... | https://stats.stackexchange.com |
70,668 | [
"https://mathoverflow.net/questions/70668",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8176/"
] | An affine manifold is a topological manifold which admits a system of charts such that the coordinate changes are (restrictions of) affine transformations. Let $M$ be a compact affine manifold. Let $G$ be the fundamental group of $M$ and $\tilde M$ be its universal cover. One can show that each $n$-dimensional affine m... | There is a conjecture due to Markus which states that any compact affine manifold has parallel volume (<em>i.e.</em> the linear part of $\varphi$ lies in $\mathrm{SL}(n;\mathbb{R})$) if and only if it is complete. To the best of my knowledge, this conjecture is still open, which goes towards saying that there should be... | An answer to questions <b>1</b> and <b>3</b> is prodvided by $(\mathbb R^n\setminus\{0\})\big/\lambda^{\mathbb Z}$, where $\lambda^{\mathbb Z}$ acts by scalings.
That manifold is diffeomorphic to $S^{n-1}\times S^1$, and fails to be aspherical for $n\ge 3$.
The case $n = 2$ of the above construction can be used to pro... | https://mathoverflow.net |
2,158 | [
"https://quant.stackexchange.com/questions/2158",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/1204/"
] | My data source for end of day prices only gives the prices of the trades during the day. If a stock stops trading/goes out/moves to another exchange|changes symbol. I never hear about this.
My question(s) are:
<ol>
<li>Is there a way to determine that a stock is no longer trading? Most stocks that I have, have daily... | You can use changepoint analysis to identify regime change.
You can also look at large angle differences in the eigenvectors between your most up-to-date/recent covariance matrix and the covariance matrix from the prior window.
Another way to identify regime change is using a factor model. If the returns on a partic... | I would suggest a multivariate garch model as a possibility. We aren't exactly overrun with wonderful software for that, but with just bivariate data I would think that the in-sample correlation estimates would be reasonably robust over models and estimation.
It would be good to try two or three ways of doing it to m... | https://quant.stackexchange.com |
420,162 | [
"https://mathoverflow.net/questions/420162",
"https://mathoverflow.net",
"https://mathoverflow.net/users/148161/"
] | <ol>
<li>Is it true that if <span class="math-container">$A_1 \vee A_2 \vee .. \vee A_n = B_1 \vee B_2 \vee .. \vee B_m$</span>, where <span class="math-container">$A_i, B_j$</span> are homotopy types of complexes not decomposable into a bouquet, then the multisets <span class="math-container">$A_i$</span> and <span ... | In Hilton&Roitberg paper "On principal <span class="math-container">$S^3$</span>-bundles over spheres" it's proven that if you have a prime order <span class="math-container">$p \neq 2,3$</span> class <span class="math-container">$\alpha$</span> in <span class="math-container">$\pi_k(S^n)$</span> that is ... | There is a substantial literature on the subject. You should probably start with
C. W. Wilkerson, Genus and cancellation, Topology {\bf 14}
(1975), 29-36.
In particular, he shows
<strong>Definition</strong>:
Let <span class="math-container">$X$</span> be a 1-connected <span class="math-container">$p$</span>-local spa... | https://mathoverflow.net |
187,949 | [
"https://mathoverflow.net/questions/187949",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11966/"
] | Recently I come cross a question about deficient values of entire functions.
I find that many examples in the book about functions $f$ whose deficient values are singularities of the inverse $f^{-1}$.
I want to know whether there exist an example with the following property (in some sense it aks whether the concept... | The book of Goldberg and Ostrovskii MR2435270 contains several examples of functions whose
deficient value is not asymptotic. And in fact there are such functions
without asymptotic values at all. But deficient value must be in the closure
of the singular set.
This follows from a theorem of E. Collingwood, which has ... | I like to advocate differentiating between the <strong>singularities of the inverse function</strong>, which are denoted by $\operatorname{sing}(f^{-1})$, and the set of <strong>singular values</strong> of $f$, which I denote by $S(f)$. The latter set can be defined as the closure of $\operatorname{sing}(f^{-1})$, thou... | https://mathoverflow.net |
3,251 | [
"https://dba.stackexchange.com/questions/3251",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/154/"
] | A materialized view<sup>(MV)</sup> log can be used to allow a MV to do a fast refresh which only modifies the data that has changed. However, various conditions prevent the MV from using the log and therefore require a complete refresh. Oracle implemented an atomic complete refresh as a delete and insert of every rec... | This is just intended to demonstrate redo usage of various <code>insert</code> operations rather than answer the whole question. Results on my 10g instance are not 100% deterministic, but the broad picture remained the same each time I ran through.
For the heap tables, I do not know why the <code>insert /*+ append */<... | Good question. I "solved" this problem for my situation a while back by making the MV's and any indexes on them NOLOGGING. There was no point to it my situation - I was doing a full refresh of the view anyway, why would I need redo?
| https://dba.stackexchange.com |
657,512 | [
"https://math.stackexchange.com/questions/657512",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/46347/"
] | Suppose we are dealing with a discrete probability distribution and we are looking to find the value of $E[X]$.
$E[X] = \sum_x xP(X = x)$
I read that as take the value of each $x$ multiplied the probability of getting that value $x$, then sum all the values. And this gives us the mean, ie. the expected value of the ... | Note that if you have a general experiment with random variable $X$ it may be of interest to get the expected value of a certain function $f(X)$, for example if you get one credit more than you toss heads in a game and the number of heads is your random Variable $X$, then the amount of credit gained is given by $f(X) =... | The average of a constant is a constant. Also,
note that $\sum_x P(X = x) = 1$.
| https://math.stackexchange.com |
365,154 | [
"https://softwareengineering.stackexchange.com/questions/365154",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/294993/"
] | I am trying to make some version control locally on my Android project. It is just to have control about my changes, but I do not want to upload them to any external repository. Neither I want to create infernal folders with dates of updates...
I would want to use Git, in which I am a bit familiar. I am also familiar ... | Git can be used 100% locally, without any servers. The value of using a Git hosting service is
<ul>
<li>that this allows multiple developers to collaborate more easily, and</li>
<li>the web interface, with features like issue trackers, pull requests, code search, …, and</li>
<li>integrations with other services you'd ... | Git can be used locally, but you really should push major progress to a repository outside the working directory and preferably on a different disk/machine.
That is because the <code>.git</code> folder <em>within</em> the working directory where all the git objects and tracking data are by default stored is not partic... | https://softwareengineering.stackexchange.com |
22,984 | [
"https://mathoverflow.net/questions/22984",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4910/"
] | Let $K$ be a compact oriented 3-dimensional handlebody of genus $g$. The group $H_g$ of isotopy classes of diffeomorphisms of $K$ is called the <em>handlebody group</em>. (It embeds as a subgroup of the mapping class group of the genus $g$ surface $\partial K$.) The fundamental group of $K$ is a free group of rank $g... | This result is due to Luft; see "Actions of the homeotopy group of an orientable 3-dimensional handlebody".
McCullough, in "Twist groups of compact 3-manifolds", proves that the twist group is not finitely generated and gives further references.
EDIT. Ninja'ed (well, at least the first sentence).
| The answer is yes. I'm not sure who this is due to, but one nice reference is section 3.9 of Fomenko-Matveev's book "Algorithmic and Computer Methods for 3-Manifolds". It's not stated in precisely the form you stated it, but it can be easily extracted from there.
| https://mathoverflow.net |
123,804 | [
"https://cs.stackexchange.com/questions/123804",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/-1/"
] | So suppose I have a graph consisting of a tuple <span class="math-container">$(V,E,A,g)$</span> where <span class="math-container">$V$</span> denotes vertices, <span class="math-container">$E$</span> denotes edges, <span class="math-container">$A$</span> denotes a subset of <span class="math-container">$V$</span> (i.e.... | <blockquote>
I see that the language is equivalent to <span class="math-container">$L = \{aa^nbbb^mccccc^n\}$</span>,
</blockquote>
Indeed
<blockquote>
but I'm not sure if that helps at all.
</blockquote>
Well, maybe not. How about if we write the equivalent language ever-so-slightly differently:
<span class="m... | The ways to prove a language context free are to (1) exhibit a context free grammar for it; (2) exhibit a PDA accepting it; (3) construct it using closure properties. Here I'll go for (1).
Words in the language have a number of <span class="math-container">$a$</span> at the beginning and end that almost match, and an ... | https://cs.stackexchange.com |
212,609 | [
"https://dba.stackexchange.com/questions/212609",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/156592/"
] | Below query need to return multiple values
<pre><code>select
CASE WHEN LTRIM(RTRIM([Order].ClientProject_Id))!=''
THEN (SELECT StationeryClientProject.ImpFile from StationeryClientProject
WHERE StationeryClientProject.ClientProject_Id = [Order].ClientProject_Id)
ELSE (SELECT Stationery.ImpFile from Statione... | This should work:
<pre><code>select
CASE WHEN LTRIM(RTRIM([Order].ClientProject_Id))!=''
THEN StationeryClientProject.ImpFile
ELSE Stationery.ImpFile
END AS ImpFile
FROM [Order]
LEFT OUTER JOIN ClientProject ON ClientProject.ClientProject_Id = [Order].ClientProject_Id
LEFT OUTER JOIN StationeryClient... | A <em>subquery</em> used in scalar context like yours -- the <code>CASE</code> expression must return a single (scalar) value, -- should also return a single value. It's hard to guess what you want, since you did not explain your problem in human language, nor did you supply table structures or sample data, but I think... | https://dba.stackexchange.com |
904,516 | [
"https://math.stackexchange.com/questions/904516",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/170815/"
] | I think I did something wrong, so I was hoping someone might be able to show me the solution
Two functions <span class="math-container">$V (x, y)$</span> and <span class="math-container">$U (x, y)$</span> are connected by the equation
<span class="math-container">$$V (x, y) = U (x, y)e^{−ax−by}$$</span>
where <span cla... | You remembered to use the chain rule, but apparently forgot the product rule. Use it once:
$$
V_x=e^{-ax-by}U_x-a e^{-ax-by}U
$$
then use it again:
$$
V_{xx}=e^{-ax-by}U_{xx}- a e^{-ax-by}U_x - a e^{-ax-by}U_x + a^2 e^{-ax-by}U
$$
You may notice the same term appearing in the middle twice; it saves a bit of time to r... | Let $\alpha=c_1$, $\beta=c_2$ and $U=f$(completely for shortening the latex solution, no real need to do that)$\frac{d}{dx}(f(x, y)e^{-(c_1 x)-c_2 y)}$
$\cdot \frac{d}{dx}(uv) = v \frac{du}{ dx}+u\frac{dv}{dx}$, where $u = e^{c_1 (-x)-c_2 y}$ and $v = f(x, y)$
$=f(x, y) (\frac{d}{dx}(e^{-(x c_1)-y c_2}))+e^{-x c_1-y c... | https://math.stackexchange.com |
134,540 | [
"https://chemistry.stackexchange.com/questions/134540",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/94318/"
] | I'm going back through my notes from a chemistry class, which I did well in despite not having a very good conceptual understanding, in order to hopefully develop that understanding, but there's something I can't find in the book or online. Why is it that, when solving for the pH of a solution that results from the mix... | <strong>The strategy of major species</strong>
You correctly describe the strategy. First, let reactions go to completion (in the direction that makes sense, i.e. weak base and strong acid forms weak acid and spectator ion - never the other way around). Then, check what the major species are and estimate the pH. Final... | Given the following problem:
<blockquote>
25.0 mL of 0.30 M hydrochloric acid is added to 40.0 mL of 0.50 M ammonia. Calculate the pH, and concentrations of <span class="math-container">$\ce{NH3 \text{and} NH4+}$</span>.
</blockquote>
To solve such problem you must make some assumptions. Some of which are good, so... | https://chemistry.stackexchange.com |
53,228 | [
"https://chemistry.stackexchange.com/questions/53228",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/30772/"
] | <blockquote>
<strong>Question:</strong> Justify the use of phenolphthalein $(\mathrm{p}K_\ce{in}=9.4)$ as a indicator for the titration of benzoic
acid $(K_\mathrm{a}=6.3\times 10^{-5})$ with $\ce{NaOH}$.
</blockquote>
<hr>
<strong>My attempt:</strong>
I can calculate the $K_\mathrm{b}$ of $\ce{NaOH}$ from the a... | As far as I have understood, I have to compare the $\mathrm{p}K_\mathrm{b}$ of sodium benzoate with the $\mathrm{p}K_\mathrm{ind}$ of phenolphthalein.
Thus what I get is:
$K_\mathrm{b}$ of sodium benzoate $=\frac{K_\mathrm{w}}{K_\mathrm{a}}=1.59\times 10^{-10}$
$\mathrm{p}K_\mathrm{b}$ of sodium benzoate $=9.79$
$\... | You have to take two reactions into account.
First the protolysis of benzoic acid
$$\ce{HA + H2O <=> H3O+ + A-}$$
$$k_A = \frac{[\mathrm{H_3O^+}] [\mathrm{A^-}]}{[\mathrm{HA}]} \tag{1}$$
and second the (simplified) protolysis of phenolphthalein
$$\ce{HInd + H2O <=> H3O+ + Ind-}$$
$$k_{Ind} = \frac{[\mat... | https://chemistry.stackexchange.com |
2,904,029 | [
"https://math.stackexchange.com/questions/2904029",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/589599/"
] | Me and a mate of mine are having a small debate, because I don't know if I'm being incredibly stupid or not.
If you take a term, $ax^b$, does the exponent '$b$' apply to the entirety of $ax$, making it $(ax)^b$, or just $x$, making it $a(x^b)$?
It's silly to debate over something that is probably basic mathematical l... | Generally:
$$ax^b\equiv a\cdot x^b$$
while:
$$(ax)^b\equiv a^b\cdot x^b$$
| Do the product after the exponent, unless brackets tell you otherwise
| https://math.stackexchange.com |
2,727,239 | [
"https://math.stackexchange.com/questions/2727239",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/547813/"
] | I understand the meaning of $\frac{dy}{dx}$ and $\int f(x)dx$, but outside of that what do $dy, du, dx$ etc.. mean?
When I took calc I, derivatives and integrals were given a definition, but these things were kind of skipped over. When we started using du substitution we had to start using them but they were still nev... | This is a common problem with Leibniz's notation; people often treat the "<span class="math-container">$dx$</span>" as something that can be moved around as though it were a variable, and <span class="math-container">$\frac{dy}{dx}$</span> as a fraction, rather than as a symbol denoting one singular quantity. The other... | These are notations and you learn them by practice.
$dx$ means change in $x$ when you talk about derivatives and it means with respect to $x$ when you talk about integrals.
$dy$ means the linear change in $y$ when we talk about derivative and it means with respect to $y$ when we talk about integrals.
$dy/dx$ is ano... | https://math.stackexchange.com |
433,444 | [
"https://stats.stackexchange.com/questions/433444",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/208700/"
] | I have a discrete time series <span class="math-container">$x(t)$</span> <span class="math-container">$ t = \{0,\Delta t,2\Delta t\dots\}$</span> in which every point comes with a confidence value <span class="math-container">$c(t)$</span> arising from the measurements. You may think of is as the variance or volatility... | <blockquote>
Is there such a thing as having too large a sample when it comes to trying to estimate the population distribution?
</blockquote>
<strong>No.</strong> The closer the sample size is to the population size, the better. Ideally you would take a full census of the population, which occurs when the sample ... | I think that the researcher used sloppy language, at best. Their second sentence appears to be incorrect.
I might summarize the relevant points as follows. As sample size increases towards infinity:
<ul>
<li>The distribution of the sample mean (a random variable) converges to a Normal distribution, by the Central Li... | https://stats.stackexchange.com |
2,942,601 | [
"https://math.stackexchange.com/questions/2942601",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/552634/"
] | under what conditions on a topology we have: <span class="math-container">$cl(U_1 \cap U_2)=cl(U_1) \cap cl(U_2)$</span> if <span class="math-container">$U_1,U_2$</span> is open
| By definition, the space spanned by <span class="math-container">$S$</span> is the set of matrices of the form
<span class="math-container">$$
\left(
\begin{matrix}
2\lambda & -\lambda \\
-\mu & \mu
\end{matrix}
\right)
$$</span>
for some coefficients <span class="math-container">$\lambda, \mu$</span> living i... | Simply, <span class="math-container">$\{s\cdot\begin{pmatrix}2&-1\\0&0\end{pmatrix}+t\cdot\begin{pmatrix}0&0\\-1&1\end{pmatrix}| s,t\in\mathbb F\} $</span> where <span class="math-container">$\mathbb F$</span> is the base field. By definition.
| https://math.stackexchange.com |
278,805 | [
"https://softwareengineering.stackexchange.com/questions/278805",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/165064/"
] | I was wondering why Java and other programming languages implement (seemingly) redundant functions such as:
<pre><code>"foobar".startsWith("bar", 3);
// same as
"foobar".substring(3).startsWith("bar");
// or even indexOf(str, offset), regionMatches(...)
</code></pre>
Is there a reason behind this?
| There are few possible reasons for this sort of thing:
<ol>
<li>As in JacquesB's answer it may simply be <strong>convenience</strong> for the library user to call a single method rather than two methods and keep their code more succinct.</li>
<li><strong>Performance</strong> may be a consideration. Calling <code>.subs... | These are called convenience functions. They are included so users can write shorter and simpler code.
Note that almost every library is "redundant" in the sense that users could write the same code themselves outside of the library. However the point of using libraries is that you save time and code, and you can reus... | https://softwareengineering.stackexchange.com |
77,330 | [
"https://cs.stackexchange.com/questions/77330",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/24642/"
] | I have the following problem:
Given an unsorted array A of size n, print the first k elements in A larger than its median.
Here's my approach to the problem:
<pre><code> 1. Create a minHeap and a maxHeap
2. Iterate over elements in A // O(n)
- if maxHeap.count < minHeap.count
insert ... | Answering your second question:
<ol>
<li>Find the median $m$, and partition the set into $L_1 = \{x | x \in S \wedge x < m\}$ and $L_2 = \{x | x \in S \wedge x > m\}$.</li>
<li>Find the $k$th largest element $x_k$ in $L_2$, and partition the set into $L_2' = \{x | x \in L_2 \wedge x \leq x_k\}$ and $L_3 = \{x |... | The k elements following the median can be retrieved in O(n). To get them in sorted order, an additional O(k log k) sorting step is required.
<h3>Quickselect</h3>
From a high-level perspective, the Quickselect algorithm takes an array and an integer k. It then places the k-th largest number in the correct place, smal... | https://cs.stackexchange.com |
108,520 | [
"https://chemistry.stackexchange.com/questions/108520",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/73822/"
] | <blockquote>
At STP, the density of a gas in a vessel is <span class="math-container">$0.9002$</span>. If the gas is a mixture of argon and helium, what percentage of the gas is argon?
</blockquote>
I am stuck on this. From what I can gather, the only influencing characters would be moles and grams. This idea is bas... | Well, I can see all the relations you require knowledge of in the question itself!
Calculate the effective molecular mass from
<span class="math-container">$$M = \frac{dRT}{P}$$</span>
<span class="math-container">$R$</span> is known, <span class="math-container">$d$</span> given. <span class="math-container">$P$<... | I'd start the solution with this equation:
<span class="math-container">$n_{Ar}d_{Ar}/(n_{Ar} + n_{He}) + n_{He}d_{He}/(n_{Ar} + n_{He}) = d_{avg}$</span>
where I emphasize that the density of the gas is a <em>molar average</em> value, and rewrite it as
<span class="math-container">$\chi_{Ar} d_{Ar} + (1-\chi_{Ar})... | https://chemistry.stackexchange.com |
203,371 | [
"https://softwareengineering.stackexchange.com/questions/203371",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/95405/"
] | I'm developing a pipeline for processing text that will go into production. The question I keep asking myself is: should I stick to one language for the project when I'm looking for a tool to do a particular task (e.g. NLTK, PDFMiner, CLD, CRFsuite, etc.)?
Or is it OK to mix and match languages on the project? So I ... | In a perfect world, we'd all be using the One True Language™. The reality is somewhat different.
<ol>
<li>If you insist on a single language, you may be be excluding many tools from your toolbelt, regardless of the language you choose.</li>
<li>Some applications are impossible or impractical to write in a single la... | I have found that large multi-programmer, multi-year projects are best served with a single language, while small, one-person projects are best served with a "whatever works" policy.
The issue is maintenance and bringing in new programmers. If you have a large project that spans many years, then you have a significan... | https://softwareengineering.stackexchange.com |
479,412 | [
"https://physics.stackexchange.com/questions/479412",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57218/"
] | I have seen the derivation of the high temperature heat capatcity sing integration of the density of states. The heat capacity is <span class="math-container">$C=3Nk_B$</span> with <span class="math-container">$N$</span> the number of atoms in the lattice. According to my lecturer 'this is in agreement with the equipar... | There are actually six quadratic degrees of freedom per atom: the three vibrational <em>potential</em> energies, which are quadratic in displacement, and the three <em>kinetic</em> energies, which are quadratic in velocity. This gives you the proper specific heat.
| Each mode is an independent harmonic oscillator. Thus, there is a quadratic kinetic energy term <strong>and</strong> a quadratic potential energy term in the Hamiltonian of each normal mode. Therefore the average total energy is <span class="math-container">$3Nk_BT$</span>.
| https://physics.stackexchange.com |
13,478 | [
"https://mathoverflow.net/questions/13478",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3238/"
] | This may be a silly question - but are there interesting results about the invariant: the minimal size of an open affine cover? For example, can it be expressed in a nice way? Maybe under some additional hypotheses?
| Consider for simplicity smooth projective varieties defined over $\mathbb C$. In this case, the minimal size equals $n+1$ where $n$ is the dimension of the variety.
Proof. Let $M^n$ be such a variety. Take $n+1$ generic very ample divisors $D_0,...,D_n$. Then such divisors don't have a common intersection. At the sam... | In fact this is a difficult question in general, I believe. For example, if $X$ is a closed subvariety of ${\mathbb P}^n$, then asking for the minimal number of affine opens that cover
the complement ${\mathbb P}^n\setminus X$ is the same as asking for the minimal number of hypersurfaces
whose (set-theoretic) intersec... | https://mathoverflow.net |
15,873 | [
"https://softwareengineering.stackexchange.com/questions/15873",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4280/"
] | Are there any systematic differences between software developers (sw engineers, architect, whatever job title) with an electronics or other engineering background, compared to those who entered the profession through computer science?
By electronics background, I mean an EE degree, or a self-taught electronics tink... | Having an EE minor and a CS major, I've worked with both groups academically. I've never held a job where I designed EE style products, but I've consumed a lot of them doing work for companies with things like PLC, and so having been able to understand (from an educational background) what as occurring was nice. So I c... | If I had to generalize, here's what my experience has been:
<ul>
<li>Engineers (or just EE's) tend to do better in the "perfection of the small". Given a small programming task, they think very long and hard about all the edge cases, and are more likely to end up building a piece of software that's very robust. It's... | https://softwareengineering.stackexchange.com |
73,725 | [
"https://chemistry.stackexchange.com/questions/73725",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/44105/"
] | Is it possible for a compound to act as a Lewis acid but NOT act as a Brønsted acid? When would this happen? Could you please give a few examples where/why this happens ?
| Certainly. There are many compounds that can accept a pair of electrons from a Lewis base, yet don't have any Brønsted-Lowry acid (proton) moiety. The two are really rather different things, although there are of course many compounds that are both Lewis and Brønsted-Lowry acids ($\ce{Al(OH)3}$ for example).
Some e... | In addition to above nice answers, there is a trick that can be used to confuse students: A compound for example $\ce{Al2O3}$;
It can acts as a Lewis acid and Brønsted base <strong>but not as Brønsted acid</strong>
Consider these reactions:
Recall the <strong>Lewis Theory of acids and bases</strong> which states th... | https://chemistry.stackexchange.com |
196,482 | [
"https://dba.stackexchange.com/questions/196482",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/41240/"
] | Unlike tables, a table type cannot be altered by a simple command. I need to do the following:
<ol>
<li>Rename existing table type</li>
<li>Create the new table type</li>
<li>Open each affected objects (i.e. ALTER SP) and execute it again so that the reference to table type will be updated.</li>
</ol>
But this is a t... | Instead of
<blockquote>
Open each affected objects (i.e. ALTER SP) and execute it again so
that the reference to table type will be updated
</blockquote>
you can just find all the affected objects and refresh them using <code>sp_refreshsqlmodule</code>.
Here is the code to find the modules:
<pre><code>select o... | For some reference, based on <code>@sepupic</code>'s answer, I can further enhance it to be:
<pre><code>-- First, rename existing table type to something else
EXEC sp_rename 'TT_MY_TABLE_TYPE', 'TT_MY_TABLE_TYPE_1'
-- Create the new table type
CREATE TYPE [dbo].[TT_MY_TABLE_TYPE] AS TABLE(
[MY_FIELD] [varchar](20... | https://dba.stackexchange.com |
28,319 | [
"https://quant.stackexchange.com/questions/28319",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/22424/"
] | I always understood implied volatility as a volatility I need to plug into BS in order to get the market price.
My question is if I am using different model, does it mean that implied volatility is the volatility I need to plug into pricing equation of the new model in order to get market price or am I still referrin... | In practice, an implied volatility always refers to the volatility that you need to plug into the Black-Scholes', or Black's, pricing formula to obtain the market price. You may have a different model (e.g., a Heston style stochastic variance model), for which you are able to calibrate the parameters by matching your m... | Ok, there is a basic misconception about Implied Volatility. IV is derived <strong>from</strong> the price of the options in the market. Not the other way around. We do use different IVs to estimate option prices in other conditions, but that is just bringing the equations full circle. The Black-Scholes and many other ... | https://quant.stackexchange.com |
355,343 | [
"https://electronics.stackexchange.com/questions/355343",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/176824/"
] | <strong>TL,WR:</strong> Why do we use signal energy as a measurement of an approximation's error, and not something "simpler" like the absolute value of the error?
<hr>
<strong>Background:</strong> I'm reading through my textbook for my introduction to signals class, and they have just gotten to a point where they ar... | Using all the area under a data bit signal (integrating) and its energy gives the maximum signal when compared to the noise error. Less performing methods use peak signal and then peak noise may apply but gives worse SNR and higher BER. Good demodulators may be harder than center peak sample but integrating the entire... | We very likely do our calculations in frequency domain because Fourier series and transforms are handy. Unfortunately they do not present signals exactly, there can be large large error spikes if we transform our Fourier series back to the time domain. But mathematicians have shown that those error spikes have less and... | https://electronics.stackexchange.com |
8,569 | [
"https://physics.stackexchange.com/questions/8569",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2499/"
] | I am studying how animals (including the human beings) can perceive distances thanks to their eyes and their ears. I am focusing on the fact that they always go in pairs: two eyes, two ears, etc.
About the sight, I think our eyes use the parallax. But is this enough? Is this the only way we can perceive distances with... | With vision depth is determined by parallax. This largely works for objects out to 100m or less. Depth beyond that distance is assessed by familiarity with these objects, say large mountains or vistas, and experience with them.
Depth with hearing is determined by two means. A tone which is perceived louder in one... | Adding to Lawrence's answer, apart from the monocular cues like depth from shading, lighting, haze, geometrical structure and familiarity of objects, you also have binocular cues from the eye motor convergence system (eyes point at the spot you are looking at in 3d space) as well as the feedback from the lens focusing ... | https://physics.stackexchange.com |
13,085 | [
"https://quantumcomputing.stackexchange.com/questions/13085",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/11868/"
] | I know that when a qubit is described in a superposition state as <span class="math-container">$\alpha|0⟩ + \beta|1⟩$</span>, then the probability of measuring <span class="math-container">$|0⟩$</span> is <span class="math-container">$\alpha^2$</span> and probability of measuring <span class="math-container">$|1⟩$</spa... | Just to add, I sometime come accros notion of negative probability in quantum mechanics. However, this misunderstanding. As you mentioned, each qubit can be writen as
<span class="math-container">$$
|q\rangle = \alpha|0\rangle + \beta|1\rangle,
$$</span>
where <span class="math-container">$\alpha, \beta \in \mathbb{C}$... | The probability is <span class="math-container">$|\alpha|^2$</span>, not <span class="math-container">$\alpha^2$</span>, and thus always non-negative.
| https://quantumcomputing.stackexchange.com |
365,390 | [
"https://physics.stackexchange.com/questions/365390",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/166166/"
] | I've recently come across a strange result when comparing the Hamiltonian and Lagrangian formulations of classical mechanics.
Suppose we are working in the regime where we can say the Hamiltonian $H$ is equal to the total energy $$H=T+V.\tag{1}$$ That is, the constraints are holonomic and time-independent, and the pot... | The problem is that the Lagrangian and the Hamiltonian are functions of different variables, so you must be exceedingly careful when comparing their partial derivatives.
Consider the differential changes in $L$ and $H$ as you shift their arguments:
$$dL = \left(\frac{\partial L}{\partial q}\right) dq + \left(\frac{\... | If you look at the values of the functions:
$$
H(q,p) = T(q,p) + V(q,p)\\
L(q, \dot{q}) = T(q, \dot{q}) - V(q,\dot{q})
$$
with
$$
T(q, \dot{q}) = T(q, p)
$$
The kinetic Energy as a function of $q$ and $\dot{q}$ and the kinetic Energy as a function of $q$ and $p$ are supposed to have the same value. BUT that doesn't mea... | https://physics.stackexchange.com |
8,676 | [
"https://physics.stackexchange.com/questions/8676",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/3124/"
] | How big would a hollow rigid object need to be to float, (not in water but in air) if all of the air was vacuumed out and the container sealed?
| Another way to look at this is to solve for what weight/area you are allowed to use. Assume a spherical craft. Surface area goes up in proportion to r^2. Volume (which will generate your lift) is proportional to r^3. If you do the math, you find that you are allowed to use (r x 0.4)kg/m^2, or about (r x 0.88) lbs/m... | Just to flesh out Jim's answer.
Assume you made a cube (makes the math easier!) 1m x 1m x 1m<br>
Aluminium has a density of 2700kg/m^3<br>
And you need the cubeto have a mass of less than 1.2Kg<br>
- so can use (1.2/2700) m^3 of material
The surface area is 6m^2 then you can have a thickness of (1.2/2700)m^3 / 6m^2... | https://physics.stackexchange.com |
122,175 | [
"https://mathoverflow.net/questions/122175",
"https://mathoverflow.net",
"https://mathoverflow.net/users/30081/"
] | Can anything be said about connectedness of a smooth manifold M from some property of Diff(M) in an analogous way Like C(X) has no idempotents iff X is connected.
| Let $M$ be a compact oriented manifold. The following hold if and only if $M$ is connected.
1) $\text{Diff}_0(M)$ is simple.
This was proven by Thurston if $M$ is connected; see
MR1445290 (98h:22024)
Banyaga, Augustin(1-PAS)
The structure of classical diffeomorphism groups. (English summary)
Mathematics and its... | $M$ is connected if and only if the connected component of $Diff(M)$ (equivalently, of $Diff_c(M)$) acts transitively on $M$.
Edit: I just remembered, that the Lie algebra of compactly supported vector fields determines the base manifold up to diffeomorphism, see:
MR0064764 (16,331a) Reviewed
Shanks, M. E.; Pursell, ... | https://mathoverflow.net |
138,828 | [
"https://physics.stackexchange.com/questions/138828",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/45557/"
] | Consider a wire being stretched from two ends with equal forces. We know that both of these forces collectively participate in elongating the wire; had there been one force the wire would have accelerated in the direction of force. Why can't then the stress be calculated using the two forces (knowing that the vector re... | Tricky question. Basically you would think the total force is 0 on any plane intersecting the cylinder at right angles, hence there would be no pressure, right? Well, the first point (0 net force) is correct, second is not.
Imagine being physically pulled by two equally strong friends in opposite directions. Total for... | Yes, we <strong>can</strong> calculate the stress in the case you have given, and that stress is still given by F/A.
Why is the stress for the case in which the wire is attached to ceiling at one end and pulled with a force F at the other also F/A? In the ceiling case, the net force is zero just as in your case. So t... | https://physics.stackexchange.com |
1,526,798 | [
"https://math.stackexchange.com/questions/1526798",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/239207/"
] | <blockquote>
Theorem:
Let $U \subseteq \mathbb{R}^m, f: U \to \mathbb{R}^n$. Then $f$ is
continuous on $U \Leftrightarrow$ For all closed sets $T \subseteq \mathbb{R}^n$, there exists a closed set $S \subseteq \mathbb{R}^m$
such that $f^{-1}(T) = S \cap U$.
</blockquote>
How to prove this theorem? If the wo... | Asumming $x\in\mathbb{R}$:
$$\int\left|\cos(2x)+\sin(2x)i\right|\space\space\text{d}x=$$
$$\int\sqrt{\left(\cos(2x)\right)^2+\left(\sin(2x)\right)^2}\space\space\text{d}x=$$
$$\int\sqrt{\cos^2(2x)+\sin^2(2x)}\space\space\text{d}x=$$
$$\int\sqrt{\frac{1}{2}\left(\cos(4x)+1\right)+\frac{1}{2}\left(1-\cos(4x)\right)}\spa... | Notice that $|x + yi| = \sqrt{x^2 + y^2}$.
By the Pythagorean identity $\cos^2\theta+\sin^2\theta=1$, the modulus of $\cos 2x + i\sin 2x$ is therefore $1$.
| https://math.stackexchange.com |
2,895,228 | [
"https://math.stackexchange.com/questions/2895228",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/587367/"
] | Problem is as follows
<blockquote>
Find the anti-derivative of the function $$f(x) = \frac{8}{\sqrt{36-4x^2}}$$
</blockquote>
Started Calc 2 last week and we are doing $u$-substitution review. However, no matter what I try, I have no clue how to even begin this problem. $u$-subbing the denominator gets me stuck.
... | Hint:
Let $$ x=3\sin(u),\ dx= 3\cos(u)$$
| $$\int \frac{8}{\sqrt{36-4x^2}}dx$$
put $x=3 \sin t$ thus $dx=3 \cos t dt $ and $t=\sin^{-1}(x/3)$
$$\int \frac{8\cdot3 \cos t dt }{6\cdot \cos t}=\int 4 dt$$
| https://math.stackexchange.com |
71 | [
"https://dsp.stackexchange.com/questions/71",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/69/"
] | In Image/Signal processing context we have seen/we know that if there are say 4 samples and if we take an average of those 4 samples, then we say that the result sample is a low pass filtered output sample. This is very relevant in Image processing context. Now then, what is the operation which implies a high pass filt... | The example you gave of taking 4 samples and taking the average of it is sort of a poor-man's low-pass filter. Generally things aren't as simple as that. But for understanding sake there is some value in using these simple examples.
A low pass filter is indeed like taking 4 samples and taking an average of it. Ex:
<p... | Firstly, an average is a very specific low-pass filter.
High-pass filtering means keeping fast-changes and discarding the "gradual changes". Differentiation is one classic mathematical way of doing this.
In the discrete domain, if you convolve a signal vector with $(\begin{matrix} 1 & -1 \end{matrix})$ you see p... | https://dsp.stackexchange.com |
337,781 | [
"https://physics.stackexchange.com/questions/337781",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/157496/"
] | I don't really understand the difference and the relation between work and kinetic energy. When you move an object a distance you do work (or does the object work?), what's the object's kinetic energy? Is the kinetic energy the work you've put in to the box all gathered up at the end of the distance given the box keeps... | The kinetic energy is indeed the work you have done (assuming no change in potential energy), however this is also neglecting the effect of friction. In real life, the kinetic energy of the box is going to be constant if its moving at a constant velocity even if you are exerting a force on the box and hence doing work ... | Work translates directly into kinetic energy unless there is a potential field or friction. In the case of a potential the energy of work may be shared between kinetic energy and potential energy. When friction is present some or all of the energy of work may go into heating the environment.
| https://physics.stackexchange.com |
401,034 | [
"https://softwareengineering.stackexchange.com/questions/401034",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/350903/"
] | I am developing an application that has some features which are only meant to be available to members of the company while the majority of the application is for public use.
Having two separate repositories is a nightmare, since many bugs, feature requests etc. related to one are relevant to the other. Is there any g... | Since you are using git, there is nothing preventing you from merging changes. What you really have is an internal and external fork. Even if there repositories started out with completely different history as long as the file structure is the same you can combine the two histories. The first merge will be kind of pain... | This is what configuration is for. Simply add an environment variable or other configuration variable that is set on the deployment of the code. Something like:
<pre><code>FEATURE_SET=internal
</code></pre>
The code looks for the environment variable and not found defaults to a value. Then only one repository is r... | https://softwareengineering.stackexchange.com |
25,540 | [
"https://quant.stackexchange.com/questions/25540",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/18715/"
] | I am trying to find a dataset (oil prices, S&P index, DAX returns etc.) in order to visualize the high volatility and low volatility periods in a plot.
So far, I have not found a dataset that has this trend.
For example, the price of a Apple stock has so far only increased with small swings and cannot be modeled ... | Spx is perfect for that. But for regime switching you need samples that span many years.
| I think the VIX index is a good example of what you are looking for.
| https://quant.stackexchange.com |
40,777 | [
"https://mechanics.stackexchange.com/questions/40777",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/25100/"
] | I am installing new spark plugs in my 2013 Chevy Cruze and I dropped a spark plug in the well upside down. I tried to get it out with 8" needle noose pliers but it will not budge. Any help would be appreciated.
| I have a telescopic magnet which is invaluable for this very scenario. It even has a light built into the end of the magnet. I bought it because I saw it in the tool shop and it's gotten me out of a mess so many times that I can't even think how I coped without it.
| The first thing to do it to be sure that the well is wide enough to allow the pliers to open up enough to actually grip the plug, you may only be able to grab it by the electrode. You probably don't want to try to grab it by the outside of the threads because there may not be enough room for you to pull it up if you do... | https://mechanics.stackexchange.com |
3,307 | [
"https://mechanics.stackexchange.com/questions/3307",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1704/"
] | My car had been sitting for a while without being driven. The battery now has a weak charge but it can get the engine started (barely). I would like to charge the battery by running the engine, but because my brakes are currently not working, I cannot take it for a drive.
Assuming the battery is still viable, while ... | There are a few variable involved.Namely the size of the battery and its general health. and to what extent you want it charged.Do you want it charged 100% or enough to start it the next time.The charging capacity of the alternator and the quality of the connections.The engine RPM won't really matter as anything from j... | Perhaps an alternate suggestion: purchase, borrow or rent a battery charger. I bought mine for about $20 US and it will easily charge a nearly dead battery up to an acceptable level in about an hour (going from memory).
If you do the math, the car is a terribly inefficient battery charging system. It's pretty good i... | https://mechanics.stackexchange.com |
730,509 | [
"https://physics.stackexchange.com/questions/730509",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/347348/"
] | So i was interested if i could make A B C monitors lets say and ive a b c glasses for all of them. My question was that is it physicly possible to make 3 same screens in a way that when i put on a glass it will be able to see only A monitor screen and b glasses only B monitor and c only C monitor.for example if i ise a... | If you only consider polarization of light, I cannot see a way how this could be achieved for more than two displays – for each display there is only one angle at which no light is (theoretically) transmitted. If there are more than two pairs of glasses and displays, the third one will necessarily transmit some light.
... | As an alternative to the solution by Martin Baláž:
Filter glass that allows only narrow-bands (i.e. colours) would enable the wearer to see only the image in the corresponding colour. The screen would need to represent the images by producing them in that wavelength.
Qualification:
Many screens have only three primary ... | https://physics.stackexchange.com |
312,907 | [
"https://softwareengineering.stackexchange.com/questions/312907",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/219569/"
] | <strong>Background</strong>
<em>Construction</em>
Note that I am using C# here, but it may not be necessary to provide input to my conceptual questions about design. Consider the following design methodology...
I work at a place where we have a number of different versions of a particular product. Recently I was giv... | The best practice should be "limit the length of a line so that you, all your colleagues, and all the tools that you are using are happy with it", plus some common sense. 80 characters seems to be very low and tends to reduce readability. I have once been totally tricked by a line like this:
<pre><code>/* Very long co... | Yes, it does look better. That is why the "Don't use overlong lines!" maxim is so very strong.
As for best practice, I never, ever use these horribly long constructor expressions. I would always use
<pre><code>public class MyClass {
public void myMethod() {
final Map<String, List<MyInterfaceHere&... | https://softwareengineering.stackexchange.com |
11,628 | [
"https://dba.stackexchange.com/questions/11628",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/6595/"
] | How to get the free temporary memory available in a server
For example:- I am running one SSIS package to upload data to tables. First it will move all the data to temporary table and then it will upload to actual Tables. So before executing this package is there any way to get the available remaining temporary memory... | There is no such a thing in sql server as <strong>temporary memory</strong>. Temp tables and table variables created in <code>tempdb</code> and may use shared buffer pool of sql server as any other objects do
<strong>But</strong>
if you still insist on <em>knowing everything about server memory</em> use the following... | I assume you mean tempdb? There is no such concept as "temporary memory size"
If so..
You can subtract allocated data from tempdb data file size, but you won't see all objects because of "Metadata visibility" and the fact that temporary tables are local to a connection
And the data files should grow to accommodate ... | https://dba.stackexchange.com |
18,407 | [
"https://physics.stackexchange.com/questions/18407",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/6724/"
] | <blockquote>
Suppose a block with mass <span class="math-container">$3\ \mathrm{kg}$</span> is on a frictionless table and a force of <span class="math-container">$15\ \mathrm N$</span> pulls it from an angle of <span class="math-container">$38^\circ$</span> above the horizontal.
1) What is the apparent weight ... | You're correct that the vertical component of Newton's second law should be
$$\sum F_y = ma_y$$
You set $a_y = 0$ because the block is not flying up off the table. This is implied by the wording of the problem: usually blocks are assumed not to be flying up off their tables unless it is explicitly stated that that is... | The vertical acceleration will be less than the acceleration due to gravity, hence the block will stay on table. For this reason the vertical acceleration is taken to be zero.
| https://physics.stackexchange.com |
279,191 | [
"https://physics.stackexchange.com/questions/279191",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/45742/"
] | Yoshioka (Ch. 3.1) uses the following reasoning to explain why the heat bath can be considered to be at a fixed temperature.
<blockquote>
Since the heat capacity of the heat bath (reservoir) is much larger
than that of the system under consideration (sample), the amount of
energy exchanged between the systems ... | Let the heat capacity of the bath be $C_0$ and the heat capacity of your test system $C_1$. If we transfer some quantity of heat between the two systems then the changes in temperatures are:
$$\begin{align}
\Delta T_0 &= \frac{Q}{C_0} \\
\Delta T_1 &= -\frac{Q}{C_1}
\end{align}$$
If we take the ratio the heat... | Heat capacity $C$ is the amount of energy needed to raise the temperature 1 degree (actually 1 Kelvin).
<ul>
<li>If the object added to the bath has a low $C$, little energy is required from the bath to heat it up to the new temperature.</li>
</ul>
But "little" is relative.
<ul>
<li>If the bath has a low $C$ as well... | https://physics.stackexchange.com |
849 | [
"https://mechanics.stackexchange.com/questions/849",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/538/"
] | I realize this may be a silly question to those of you on here who are proper petrol-heads and this may even be a repeat question, but I could not find anything on it on here, so here goes:
What are the advantages and disadvantages between cars with petrol engines vs those with diesel engines?
I've heard people say t... | As an everyday buyer you won't be interested in the high performance end of diesel or petrol, so here goes:
<ul>
<li>Diesel engines typically rev lower and have more low speed torque - so you are less likely to stall off the line, for example.</li>
<li>Petrol engines usually rev higher and get more power at 3-4 thousa... | In short, diesel engines tend to be more reliable and more robust. They're also far more fuel efficient than their petrol counterparts.
Also, diesel engines may be down on power but what they lose in power they make up for in torque. Torque is more noticeable in an urban environment because of the stop and go nature ... | https://mechanics.stackexchange.com |
20,675 | [
"https://electronics.stackexchange.com/questions/20675",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2824/"
] | I'm building a relay board which I'll eventually control using an Arduino. I'm using an IEC socket so that I can use a simple kettle lead for my AC input. The appliance the relay is controlling might be drawing 13Amp. Can I still use this IEC socket?
According to my calculations I can't because at 13amp it's 2.9Kw not... | It's hard to compute this since you don't know for sure where the poles and zeros of the LM324 are.
I would add the components to provide a little immediate negative feedback around the opamp. Sometimes this is called "compensation" feedback. It basically slows down the opamp so that it can't get ahead of the system... | An old rule, that often works, is just put a 100 ohm resistor in series with the load.
| https://electronics.stackexchange.com |
21,307 | [
"https://engineering.stackexchange.com/questions/21307",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/15268/"
] | If we are able to see an object in a certain color,that means it reflects the color.A blackbody is one which has zero reflectivity.Then how come it is not black always?
| Your assumption is incorrect. The color we see is the combination of reflected light, if any, and radiated light. All objects radiate photons of one wavelength or another. All objects absorb photons of one wavelength or another. These two spectral curves (absorption and radiation) are the same, but the spectral pow... | There is no Perfect black body (including black hole see hawkings radiation for details) that is why you can see a small light coming up from every black body and hence no body have emissivity of 1. This means true black is not yet discovered.
| https://engineering.stackexchange.com |
226,699 | [
"https://stats.stackexchange.com/questions/226699",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/12147/"
] | I am taking part in a classification challenge (classes are 0 and 1) where the inputs are encrypted (because these are expensive financial data).
As the encryption is order-preserving I can only use the fact that e.g.
$$
x_1 > x_2
$$
but not
$$
d = x_1-x_2
$$
Besides trees, which machine learning algorithms give ... | In order to better understand the problem I think it is worth explaining the main idea of how order-preserving cryptography works.
Imagine that we have column vector $\mathbf{x}$ than we want to encrypt. The encryption function is $f(\cdot)$ and it is monotonically increasing, and potentially with varying slope.
T... | I don't think you should use order to predict the binary outcome since if a model trained on your data is applied to totally unseen data which was collected in a slightly different way (not sure how that data was collected) then it's going to perform very badly.
Moreover, such "golden features" based on data ordering... | https://stats.stackexchange.com |
43,681 | [
"https://mathoverflow.net/questions/43681",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3106/"
] | In grad school I learned the isomorphism between de Rham cohomology and singular cohomology from a course that used Warner's book <i>Foundations of Differentiable Manifolds and Lie Groups</i>. One thing that I remember being puzzled by, and which I felt was never answered during the course even though I asked the prof... | Here is a really "trivial" application. Since a volume form (say from a Riemannian metric) for a compact manifold $M$ is clearly closed (it has top degree) and not exact (by Stoke's Theorem), it follows that the cohomology is non-trivial, so $M$ cannot be contractible.
| There is quite a number of surprising and deep statements that can be proven using de Rham. The examples I list are not elementary in any sense, but give a glimpse at the power of the theory. They all have in common that they employ features of the de Rham theory that are not at hand in singular theory.
Often de Rham ... | https://mathoverflow.net |
1,562,038 | [
"https://math.stackexchange.com/questions/1562038",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/190287/"
] | Prove that any $\sigma \in $ Aut$(\mathbb{R/\mathbb{Q}})$ takes squares to squares and takes positive reals to positive reals. Conclude that $a < b$ implies $\sigma a < \sigma b$ ,$\forall a,b
\in R$.
proof: Suppose $\sigma: a → b$, such that $a = c^2$ where $b$ is a square.
Then $\sigma(a) = \sigma(c^2) = \si... | It's not isomorphic to $\mathbb Z$ because it has characteristic 3.
| $\mathbb{Z}$ is not isomorphic to any ring of the form $R[x]$. In particular, note that every nonzero element in $\mathbb{Z}$ can be written as either:
$$ 1+1+...+1$$
Or
$$(-1)+(-1)+...+(-1)$$
But in a polynomial ring, the element $p(x)=x$ cannot be written in either form.
| https://math.stackexchange.com |
281,363 | [
"https://mathoverflow.net/questions/281363",
"https://mathoverflow.net",
"https://mathoverflow.net/users/114633/"
] | I encountered the following question in my studies:
Let us assume we have a real anlaytic solution to an ODE on $\mathbb{R}$ of Schr\"odinger type
$-\psi''(x)+V(x)\psi(x)=\lambda \psi(x)$
but we assume that $V$ is well-behaved (a bounded smooth function for instance).
The question I have is whether it follows that ... | As Mateusz remarked, $V$ must be assumed to have a meromorphic extension to $\mathbb C$, and $V = \lambda + \psi''/\psi$. Now if $\psi$ has a pole or zero at $z=p$, so that $\psi(z) \sim c (z-p)^d$ as $z \to p$ (with $d \ne 0$), then
$V(z) \sim d (d-1) (z-p)^{-2}$. Thus the only poles that $V$ may have are
poles of ... | As Robert Israel mentioned, it is necessary that $V$ is meromorphic, with all poles of order two. This is far from sufficient. If $V$ has no poles then every solution is entire. In general, solutions undergo transformations when one
performs analytic continuation around the poles of $V$, the so-called monodromy
transfo... | https://mathoverflow.net |
172,638 | [
"https://stats.stackexchange.com/questions/172638",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/86794/"
] | I am working on a logistic regression model that attempts to predict failure events in a population of devices using the previous 10 days of data (60 features from sensor data). The failure event is rare; I would expect to find approximately 20-30 on a given day, and the total population size is > 10,000.
Here is wher... | What you do is 'over sample' on the 'failures' and as you conclude, this biases your estimates. When you do not draw a random sample, but a sample based on the values of the binary outcome, then you are doing a so-called 'choice based sampling'.
The correction of King and Zeng is one option, another option is to us... | This approach definitely does corrupt the model. The output of logistic regression is meant to convey the probability of an event given some configuration of independent variables. Explicitly removing large amounts of data <em>because of the value of the dependent variable</em> will definitely harm this aspect of the... | https://stats.stackexchange.com |
7,013 | [
"https://quant.stackexchange.com/questions/7013",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/2257/"
] | Should I include or not the days a strategy has no open positions (thus no returns) in the Sharpe ratio calculation?
| No, don't include them. Otherwise you'll just wind-up with zero-value returns (or worse, forward-filled returns), which will make your Sharpe ratio reflect a performance that didn't actually occur.
| If you really think about the actual meaning of Sharpe ratios then you should come to the right conclusion yourself:
<ul>
<li>It is a measure of excess risk-adjusted return (whether realized or unrealized) </li>
</ul>
In that you obviously only want to calculate actual returns. You do not have any actual returns on d... | https://quant.stackexchange.com |
122,848 | [
"https://security.stackexchange.com/questions/122848",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/110194/"
] | Does correcting a misspelled username and prompting the user with a valid username introduce a security risk?
I recently tried logging into facebook and misspelled my email. They prompted me with the message below.
<blockquote>
Log in as {username}
{email}@gmail.com · Not You?
Please Confirm Password It ... | As you said, you saw this on facebook - so I tried these steps:
<ul>
<li>Login with lukas@gmail.com and real password -> works</li>
<li>Login with lukas@gmail.cmo and real password -> works, too (!)</li>
<li>Login with luksa@gmail.com and real password -> also works</li>
<li>Login with luksa@mail.com and real password... | Allowing username or email iteration may be a security problem for most sites, but not for Facebook. For sites as large as Facebook, finding emails that have accounts is easy because the sites have so many users. This holds for other huge user databases like Google and Microsoft. These companies just have to be secure ... | https://security.stackexchange.com |
4,039,684 | [
"https://math.stackexchange.com/questions/4039684",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/521252/"
] | <blockquote>
Prove that <span class="math-container">$h(u)=\frac{2}{u^2}(u-\log(1+u))$</span> is decreasing on <span class="math-container">$(-1,\infty)- \{0\}$</span>
</blockquote>
This function appears on the proof of Stirling's formula in Principles of Mathematical Analysis, by Walter Rudin.
The classic way to appro... | Another approach is to notice that <span class="math-container">\begin{align*}
\log (1 + u) = \int_0^u {\frac{{dt}}{{1 + t}}} & = u - \int_0^u {\frac{t}{{1 + t}}dt} = u - u^2 \int_0^1 {\frac{s}{{1 + su}}ds} \\ & =u - u^2 \int_0^1 \int_u^{ + \infty } {\frac{{s^2 }}{{(1 + st)^2 }}dt} ds
\end{align*}</span>
for ... | To show <span class="math-container">$g(u)\ge 0$</span> it suffices to show <span class="math-container">$$k(u)=u(1+u)-2\log (1+u)\cdot (1+u)+u\le 0\tag 1$$</span> for all <span class="math-container">$u\in(-1,0]$</span>
and <span class="math-container">$$k(u)=u(1+u)-2\log (1+u)\cdot (1+u)+u\ge 0\tag 2$$</span> for all... | https://math.stackexchange.com |
1,880,231 | [
"https://math.stackexchange.com/questions/1880231",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/64460/"
] | When working with real numbers, should we interpret it as
$$\left( (-1)^{2} \right) ^{\frac 12}=1$$
or rather as
$$\left( (-1)^{{\frac 12}} \right) ^2= \text {not real/undefined}$$
or rather as $$(-1)^{\ 1} = -1$$
What about when we work with complex numbers?
<strong>EDIT:</strong>
The reason why I called the s... | It depends on what the person who wrote down $(-1)^{\frac22}$ <em>meant</em> by writing that.
The notation $A^B$ has a well-defined meaning that everybody agree on in the following cases
<ul>
<li>$B$ is a natural number.</li>
<li>$B$ is a (possibly negative) integer, and $A\ne 0$.</li>
<li>$B$ is real and $A$ is posi... | The rule
$$a^{m/n} = (a^m)^{1/n} = (a^{1/n})^m$$
typically comes with the restriction that $a \ge 0$ if $n$ is even, so that rule can't really be applied to $(-1)^{2/2}$. I think the right way would be to simplify the exponent as much as possible first, then evaluate:
$$(-1)^{2/2} = (-1)^1 = -1$$
The question about c... | https://math.stackexchange.com |
561,422 | [
"https://physics.stackexchange.com/questions/561422",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/268336/"
] | Suppose we have two different objects, one denser than the other. In short, what I mean is that one object is bigger than the other but they have the same mass. Now why does it take different efforts in raising those two objects to a same height from the same level even though the force required to lift the two object... | If the two objects have the same mass, the work done in raising both by a set distance is the same.
However, if a human is the thing doing the lifting, biomechanical efficiency needs to be taken into account. For example, larger objects may require more awkward grips or be held further away from the body, resulting in ... | Maybe because those same objects are in different places.
If one of them is on earth and the other one on the ISS (International Space Station), lifting them both for the same height will take different efforts.
| https://physics.stackexchange.com |
2,578,773 | [
"https://math.stackexchange.com/questions/2578773",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Centralizer
<strong>Given :</strong> $G, H \le \text{Sym}(\Omega)$ and $G$ normalises $H$ means $\{g \in G \mid gH = Hg\}$
<strong>Find :</strong> $C_H(G) = \{g \in G \mid hg = gh, \forall h \in H \}$
I am not getting the difference $C_H(G)$ and normaliser of $H$, which is already given. What I am missing here?
| $gH=Hg$ only means that $gh=h'g$ for some $h,h'\in H$, not necessarily with $h=h'$. Take $G=S_3$ and a subgroup $H$ to see this in an explicit example.
| That' very simple: $G$ normalises $H$ if for all $g\in G$,and every $h\in H$, there is an $h'\in H$ such that
$$gh=h'g.$$
For the centraliser, $h'=h$ for any $h\in H$.
In other words, $G$ normalises $H$ if you have a homomorphism
\begin{align}
G&\longrightarrow \operatorname{Aut} H\\
g&\longmapsto(h\mapsto ghg... | https://math.stackexchange.com |
19,565 | [
"https://quant.stackexchange.com/questions/19565",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/6804/"
] | Strategies published in journal papers like SMB, HML, UMD have annualized sharpe ratios around 0.5. These long-short portfolios are formed with monthly rebalance. People who backtest some daily rebalancing strategies usually claim annualized sharpe ratio that is above imaginable like above 3. How is this frequency of t... | It is true that strategies with higher trading frequencies have Sharpe ratios that appear implausibly high by the standards of Fama-French factors. The strong law of large numbers really helps them, as they realize profits repeatedly while not increasing the standard deviation very quickly.
The real barriers to entry... | One very basic reason why one can't compare Sharpe ratios with different rebalancing (trading?) timeframes is in the way they calculate SR: the numerator is proportional to $N$ while denominator is proportional to $\sqrt(N)$. By increasing the frequency over which returns are averaged and annual volatility is calculate... | https://quant.stackexchange.com |
350,061 | [
"https://physics.stackexchange.com/questions/350061",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/40371/"
] | I'm reading a book about single particle detection and particle detectors in general. All detectors in the book rely on some energy transfer from the particle to the detector in form of ionisation, activation, photo effect, etc.
I'm wondering if it is possible to detect incident particles of any form with a detector, w... | We can use a qubit as a particle detector that doesn't change the particle's energy. This can be implemented as follows. We start out with a qubit initialized in the state $\left|0\right>$ and we apply the Hadamard gate $U$ that acts as follows:
$$
\begin{split}
U\left|0\right> &= \frac{1}{\sqrt{2}}\left[\le... | All detection requires a signal, which in turn requires energy. You can't detect without taking energy from the signal!
| https://physics.stackexchange.com |
550,982 | [
"https://physics.stackexchange.com/questions/550982",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/204087/"
] | A metal rod is bolted down on one end. The other end has a rocket firmly attached, pointing perpendicularly to the rod. Before the rocket is turned on, the system is at rest. Thus net force <span class="math-container">$= 0$</span>.
When the rocket is turned on, the only new force is thrust, which acts to the right (o... | Your question is a good one. It is based on your intuition that for parallel rays, flat beamsplitter, flat mirror, and perfect alignment; the split rays will travel exactly the same distances. Your intuition is right.
In a Michaelson interferometer with that description, you <em>don't</em> see fringes: instead you s... | I am not an expert on this subject. However, I'm sure that we are not allowed to use simple geometrical optic. Instead, we have to use <strong>Rayleigh-Sommerfeld's diffraction formula</strong> to obtain the image at the detector. This formula reads,
<span class="math-container">\begin{align}
U(x_i,y_i,z_i) &\propt... | https://physics.stackexchange.com |
611,147 | [
"https://physics.stackexchange.com/questions/611147",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | Can someone explain why, in the conical pendulum, the weight vector is perpendicular to the displacement of the object being moved by the tension force in the system? I understand that the tension force does no work on the object because it makes a 90-degree angle to the displacement. But it is yet unclear to me why th... | No, <span class="math-container">$\langle x|$</span> is not <strong><span class="math-container">$L^2$</span> continuous</strong> so that the Riesz theorem does not apply. Actually it is not even a functional on that space since the vectors are equivalence classes up to zero Lebesgue measure sets and <span class="math-... | Well, while "<span class="math-container">$\langle x|$</span> is a continuous linear functional" is a true statement, you have to know some subtleties why you cannot draw a conclusion about it from the Riesz (or Fischer-Riesz) representation theorem. The latter is valid for a Hilbert space with a unique scala... | https://physics.stackexchange.com |
329,967 | [
"https://math.stackexchange.com/questions/329967",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/9791/"
] | Let $K[t]$ be the algebra of all polynomials in $t$. What are maximal ideals of $K[t]$? I know that $\langle t \rangle = \{tf \mid f \in K[t]\}$ is a maximal ideal. Are there other maximal ideals? Thank you very much.
| If $\,K\,$ is a field then $\,K[t]\,$ is an euclidean domain and as such also a PID (and even a UFD), so an ideal there is maximal iff it is prime iff it is generated by an irreducible polynomial of positive degree.
If $\,K\,$ is <em>not</em> a field things may be far away from being so pretty and simple...
| If $K$ is algebraically closed then all the maximal ideals are of the form $\langle t - a\rangle$ where $a \in K$. If $K$ is not algebraically closed there can be others, for example $\langle t^2 + 1\rangle$ is a maximal ideal in $\mathbb R[t]$.
| https://math.stackexchange.com |
967,810 | [
"https://math.stackexchange.com/questions/967810",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/173459/"
] | I want to count how many values of x in range [A,B] give remainder of 1 when divided by N.
Is there any formula I can apply?
| When you say, "which then becomes", presumably you're taking the limit as $x \to y$. Taking the limit (and treating the absolute value carefully) gives
$$\left\vert \frac{df}{dx}\right\vert \leq 0,$$
and in particular equality holds. So, if $f$ is defined on all of $[0, 1]$, it constant on that interval, and so
$$f(1) ... | $$|f(x)-f(y)|\leq (x-y)^2\Rightarrow -(x-y)^2\leq (f(x)-f(y))\leq (x-y)^2$$
Substitute $y=0$ to get
$$-x^2\leq f(x)\leq x^2$$
at $x=1$ you have the range for possible values of $f(1)$ as
$$-1\leq f(1)\leq 1$$
| https://math.stackexchange.com |
433,510 | [
"https://electronics.stackexchange.com/questions/433510",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/218685/"
] | <strong>Intro</strong>:
I feel like there is one more thing that I really need to get a grasp of.
Let’s say I have a circuit with a 5V battery and a LED that has a 3V forward voltage. Then before the LED is a resistor with say 100 ohms, the resistor should drop all of the voltage, should it not?
<strong>Math</strong... | Your first equation assumes that the full voltage is across the resistor. Then your second equation finds out that the full voltage is across the resistor.
What's really going on is that within a pretty broad range of currents, the voltage drop across your LED is roughly 3V. So you assume that 3V drop. Then you fin... | If you put 0 V across an LED, then 0 amps will flow through it. If it's in series with the resistor, though, it must have the same current as the resistor. The current can't be both 50 mA and 0 at the same time. So this is obviously not the right answer.
Like any diode, for a wide range of currents, the voltage will ... | https://electronics.stackexchange.com |
196,384 | [
"https://softwareengineering.stackexchange.com/questions/196384",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/54480/"
] | I'm writing an application that deals with the network and the hard drive. For the network portion, the application measures in bits per second, while the disk portion measures in bytes per second. This becomes an issue as they both are abbreviated <code>b/s</code> or <code>bps</code> everywhere I've seen. How could I ... | <blockquote>
How do I tell a user that one means bits per second while the other
means bytes per second and how would I style the lettering
</blockquote>
Seems like this is one of those things that you get to decide as the designer of the program. There are lots of options, including but not limited to:
<ul>
<li>... | The abbreviations for bits and bytes are differentiated by their case: lower case (<code>b</code>) means bits and upper case (<code>B</code>) means bytes.
| https://softwareengineering.stackexchange.com |
62,916 | [
"https://mathoverflow.net/questions/62916",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14660/"
] | Hi everyone!
I am currently studying the basic theory of measurable actions and need the following result, which I am not able to prove myself. It is stated without a proof, so probably it should not be hard, but I am lost...
<blockquote>
Question: Suppose $T$ is an invertible
measure-preserving map of standard ... | If $X$ is a standard probability space then we may assume it to be the disjoint union of an interval with Lebesgue measure and a countable set of atoms. If $p$ is an atom, then by assumption, $T(p) = p$, since $p$ has positive measure. So none of the atoms can be "bad" points. So we may assume that there are no atoms, ... | <strong>not an answer to the revised question</strong><br>
But Das Curious asks for the counterexample (to the <strong>original question</strong>) when the countability assumption is omitted. Here it is.
Let $X = [0,1)^{[0,1]}$, that is: the set of all functions $x \colon [0,1] \to [0,1)$. Let $\lambda$ be Lebesgue ... | https://mathoverflow.net |
18,876 | [
"https://mathoverflow.net/questions/18876",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4782/"
] | There is the invariant Maurer–Cartan 1-form on a compact semi-simple Lie group G. So if we pull it back using a map from X to G then we get a G-connection on X. The question is, can all G-connections on X ( here just regarded as elements in ${\Omega}^1(X, \mathfrak{g})$, i.e. we are using the trivial G-bundle over X ) ... | José Figueroa-O'Farrill has already pointed out one necessary condition, namely that your connection must be flat. The remaining condition is that the monodromy should be trivial. In what follows $X$ is any connected smooth manifold, not necessarily a surface, and $G$ is any Lie group.
Let's first consider the analogo... | The answer is most certainly negative, since the structure equation for the Maurer-Cartan form will tell you that the pullback connection is flat.
In fact, I don't really recognise the initial construction that you mention. The connection one-form on the total space of a principal $G$-bundle on $X$ restricts on each ... | https://mathoverflow.net |
366,369 | [
"https://softwareengineering.stackexchange.com/questions/366369",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/22027/"
] | From a REST API, we write to the database. We want to store who was the person that triggered this change. We have this information at the controller layer. The saving happens at the repository layer (We use spring boot, and have a service layer in between for business logic).
How can I stop leaking the auditing infor... | Personally I do the following:
<ol>
<li>User logs into app (or not) - an auth token (generated/stored on the server) is (also) stored locally if they log in successfully</li>
<li>Any feature that requires a login (token) checks local storage first; if there is no token, prompt to login - if there is a token attempt th... | Where you have an Access and Refresh token, usually the refresh token will have a long expiry period.
You need only ask the user to login when that refresh token expires. Which can be days or even months.
I would suggest that you check the expiry date when the user launches the app and ask them to re-login if the to... | https://softwareengineering.stackexchange.com |
80,406 | [
"https://physics.stackexchange.com/questions/80406",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/30457/"
] | I've always assumed that the strong resistance of air is the reason there is no flow of electrons between the terminals of a battery until a wire is connect. However, in a vacuum there is no resistive substance to impede the flow of electrons.
Does this mean that in a vacuum an average AA battery will spontaneously ha... | In a vacuum, the dc resistance to the flow of current is infinite. There is nothing contained within the vacuum that can conduct electricity.
| Vacuum tubes can conduct hundreds of amps of electricity quite readily. The effect depends on heating the negative terminal so that electrons can leave the metal surface which otherwise keeps them in the surface owing to a phenomenon called work function.
| https://physics.stackexchange.com |
186,975 | [
"https://mathoverflow.net/questions/186975",
"https://mathoverflow.net",
"https://mathoverflow.net/users/40793/"
] | Do we have $Cap_{N}(S(0,r))=P_{x}(T_{S(0,r)}<\infty)$ for $x\in [B(0,r)]^{c}$, where $B(0,r)$ is a ball centered at the origin ?
I know for $x=0$, they are both equal to 1. How can I go about proving or disproving the above equality?
Thanks
| Consider the map $\varphi:S\to R$ given by
$$\varphi(x) = \frac{4x}{4-x},$$
and similarly for $y$, $z$, and $w$. One needs to check that this is well-defined;
indeed, $\varphi$ maps $xyz+xyw+xzw+yzw+xyzw$ to
$$\frac{4^4(xyz+xyw+xzw+yzw)}{(4-x)(4-y)(4-z)(4-w)}.$$
Since $\varphi$ obviously induces an isomorphism on the... | This is a bit too long for a comment.
Let me denote by $L_k=\sum_i x_i^{k+1}\frac{\partial\phantom{x_i}}{\partial x_i}$ the operators via which vector fields on a line act on polynomials in several variables (via the diagonal embedding). I noticed that if you take polynomials in $n$ variables, then the elementary sym... | https://mathoverflow.net |
12,641 | [
"https://physics.stackexchange.com/questions/12641",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4643/"
] | Most audio signal are described by a curve having two parameters: The amplitude and the frequency (amount of time from positive to negative amplitude value).
What I want to understand is how the sound level and absolute pitch are encoded to these two values. How would amplitude and frequency change if I'd change volum... | By definition an orbit occurs when gravity balances with the "centrifugal" force. It is essentially a <strong>free fall</strong> situation.
So the answer is the same reason why you don't get stuck to the ceiling of a free falling elevator. Both the spacecraft and the occupants are moving <strong>in-sync</strong>.
| Actually, the astronaut would only float completely free in the middle of the space station. Elsewhere, he will stick slightly to whatever side is closer to the Earth than is the middle, or farther from the Earth than is the middle. The reason is the tidal force from the Earth, which will be very small but probably det... | https://physics.stackexchange.com |
2,961,088 | [
"https://math.stackexchange.com/questions/2961088",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/535397/"
] | I need to show that this is an algebraic number by showing that it is a solution to:
<span class="math-container">$x^{6} - 9x^{4} - 4x^{3} + 27x^{2} + 36x -23 = 0.$</span>
I'm really struggling with this one, I tried squaring and cubing <span class="math-container">$\sqrt{2} + \sqrt[3]{2}$</span>, but I only end up wi... | <span class="math-container">$$(x-\sqrt2)^3=2$$</span>
<span class="math-container">$$\iff x^3-2+3x\cdot2=(3x^2+2)\sqrt2$$</span>
Square both sides
| The minimal polynomial of <span class="math-container">$\alpha=\sqrt{2}$</span> is <span class="math-container">$a^2-2$</span> and the minimal polynomial of <span class="math-container">$\beta=\sqrt[3]{2}$</span> is <span class="math-container">$b^3-2$</span>. <br>
<span class="math-container">$\{1,a,b,b^2,ab,ab^2\}$</... | https://math.stackexchange.com |
110,225 | [
"https://stats.stackexchange.com/questions/110225",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/40215/"
] | How can I perform a two sample test of means with unequal variances for a very large sample in R?
In case of large samples the statistic will asymptotically follow a normal distribution.
Which R function will help me to do this?
| While you can compute the z-statistic, actually an ordinary Welch t-test will do that just fine - in R that's <code>t.test</code> with all its default options.
The form of test statistic is the same in both cases. The only difference is in which table is used, and if the size of the smaller group is large enough, the ... | A few points in addition to what @Glen_b makes.
1) The default in t.test is var.equal = FALSE which means it assumes the samples have different variances.
2) I think it is a useful exercise to just skim over the proof of this result in the case of the z-test (involves Slutsky's theorem and the CLT) which you will f... | https://stats.stackexchange.com |
154,351 | [
"https://electronics.stackexchange.com/questions/154351",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/66814/"
] | everyone!
I would like to know if I can avoid to use current limiting resistors by pushing my power supply to its limits (it already sounds not like a good idea... btw...).
Say I have a 3.3V power supply with 200mA current limit.
Question 1: is it safe to suppose that connecting 10 LED in parallel with no resistors... | <ol>
<li>No, it is not safe to assume that the current will be divided equally between LEDs in parallel, as there will invariably be differences between the LED dies. They might be closer if from the same batch, but <strong>it is still a bad idea</strong>. What would be closer to working would be connecting them in s... | If ten <em>identical</em> 20 mA LEDs are connected in parallel and all held at the <em>same</em> temperature then you'll have the same current through each and the total current will be 200 mA. This could work for small 5 mm devices at low current, less than 3 mA per LED, say, since everything will be close to ambient ... | https://electronics.stackexchange.com |
117,646 | [
"https://electronics.stackexchange.com/questions/117646",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43414/"
] | Whenever I look for parts in my local electronics store, I come across parts(e.g a speaker), that have just a power rating stated(e.g 2W).
While I know how to calculate power,voltage, resistance etc, how exactly do I figure out the exact current and voltage for the given part?
For example, if the part has a power rat... | If you have only the power rating, you are stuck.
If you have the resistance in ohms as well, you have enough information via either of the equations:
$$P = \frac{V^2}{R}$$
or
$$P = I^2 R$$
So given a 2 Watt 8 ohm speaker,
$$V^2 = P \cdot R = 16$$
so V=4 volts, and I = V/R = 0.5 amps
Now for a speaker you ... | If it's a speaker, and for some reason the ohms are not marked on it, check it with an ohmmeter (bring your own or borrow one from the sales dudes).
Generally the DC resistance will be a bit less than 4 ohms or 8 ohms, so if it measures around 6-7 ohms it's probably an "8\$\Omega\$" speaker.
If it's a random compon... | https://electronics.stackexchange.com |
28,101 | [
"https://stats.stackexchange.com/questions/28101",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2860/"
] | I am interested in finding the relation between two (possibly multi dimensional) time series $x_{1:T}$ and $y_{1:T}$. I wonder how I can do that with a linear dynamical system/Kalman filter.
My approach would be sth like estimating the parameters $\theta$ with EM for the joint probability $p(x_{1:T}, y_{1:T}, h_{1:T})... | Since I believe to have found the solution myself, I am gonna post it here.
We are being given a hidden Markov model (as in HMM or LDS) with estimated transition and emission probabilities $p(h_t|h_{t-1})$ and $p(v_t|h_{t})$. In our case, $v_t$ is a concatenation of unobserved variables $u_t$ and observed ones $o_t$. ... | You should look at Shumway and Stoffer, Time Series Analysis and Its Applications, Chapter 6. And the code on their website.http://www.stat.pitt.edu/stoffer/tsa2/chap6.htm
| https://stats.stackexchange.com |
55,242 | [
"https://physics.stackexchange.com/questions/55242",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10362/"
] | In the pilot's introductory book "Stick and Rudder" it claims that a nose-up glide is possible. It doesn't state how, why or when. It implies it's possible to do and maintain a constant forward velocity.
Is this possible? I really don't see how, unless the aircraft has what I assume would be an extremely unusual desig... | The essence of a glide is that the aircraft is descending.
Just like a car rolling down a moderate grade, it is trading potential energy to replenish the kinetic energy lost to drag.
Whether the nose points up or down only relates to the angle of attack, which only relates to speed.
An aircraft traveling at slow speed... | Your misconception is that the net force on the wing (lift + drag) acts "upward, and slightly behind the normal of the <strong>chord</strong>".
Actually, it acts "upward, and slightly behind the normal of the <strong>direction of air flow</strong>".
When descending in a glide with a high angle of at... | https://physics.stackexchange.com |
33,954 | [
"https://dsp.stackexchange.com/questions/33954",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/23499/"
] | I was posed the following homework problem:
<blockquote>
<strong>2.10</strong> The following input-output pairs have been observed during the operation of a time-invariant system:
\begin{align}
x_1(n)&=\{\underset{\uparrow}{1}, 0, 2\}\overset{\mathcal T}{\longleftrightarrow} y_1(n)=\{\underset{\uparrow}{0}, 1,... | If you assume that the system is time invariant, then a shift to the right of $x_2$, say $$x^s_2 = \{\underset{\uparrow}{0}, 0,0, 3\}$$ should give you the shifted version of $y_2(n)$, in other words: $$y^s_2(n)=\{\underset{\uparrow}{0}, 0, 1, 0, 2\}\,.$$ But $x^s_2 = 3 x_3$ (a linear factor), and $y^s_2$ is not a mu... | This looks like a very contrived question, but the idea is simple: if the system were linear, then, since $x_2[n]=3x_3[n+1]$, then $y_2[n]$ should be $3y_3[n+1]$. The impulse response can be obtained by time-shifting $x_3$ so that the $1$ is at $n=0$, and then time-shift $y_3$ the same amount.
| https://dsp.stackexchange.com |
18,619 | [
"https://engineering.stackexchange.com/questions/18619",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/14321/"
] | <h2>The Problem</h2>
I'm proposing a 2D problem in the x-y plane. Say there is a free-floating disk of radius R and mass Md (no velocity), at which a projectile is shot. The projectile (velocity Vp, mass Mp) has a velocity which is parallel to the x axis. If taking the disk's center for the origin, the projectile conta... | When it comes to solving any collision problem, it is always important to apply <em>conservation of linear momentum</em> and <em>conservation of angular momentum</em>. This gives us the first two equations.
<strong>Conservation of linear momentum</strong>
For two rigid bodies 1 and 2, the conservation of linear momen... | Suggested approach and a bit of reasoning.
There are multiple ways to view the final situation. You can look at it at the instant of contact and realize that the final velocity of the projectile is Vd + Wd * y. This works, but isn't fun. A better way is to think of the final <em>average</em> velocity of the projectile... | https://engineering.stackexchange.com |
464,035 | [
"https://electronics.stackexchange.com/questions/464035",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/142039/"
] | I am using the ball and beam control system from Acrome robotics and I would like to identify the transfer function of the RC servo motor which translates motion to the system. First of all, I have asked the company for information about the model of the motor used but I have not received an answer. Is there any way to... | Most hobby servos have a rotation angle of 90° when the pulse width is varied from 1 to 2ms. The standard frame rate is 50Hz (20ms PWM period). Digital servos can often handle frame rates up to ~250Hz, but analog servos tend to misbehave (or even burn out) above 60Hz.
There is no standard rotation direction - som... | Stimulate pulse width, measure arm position, then do a literature search on "system identification".
You <em>really</em> want to make sure you're in the linear range of operation, though -- servos have top speeds, and if you hit that top speed in operation, then the servo will no longer behave in a linear manner, and ... | https://electronics.stackexchange.com |
304,964 | [
"https://physics.stackexchange.com/questions/304964",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/141863/"
] | Why is there still a non zero centripetal acceleration for a particle at equilibrium in uniform circular motion if equilibrium implies total Force = 0?
| A particle in uniform circular motion is not in equilibrium by definition. As you noted there is a non zero centripetal force. For a object to be in equilibrium, the sum of the forces acting on it must be zero (that is the definition of equilibrium).
| Centripetal force can be cancelled by centrifuge force so net acceleration may be zero and body can be in equilibrium
| https://physics.stackexchange.com |
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