qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
2,624,320 | [
"https://math.stackexchange.com/questions/2624320",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/183917/"
] | Let $$x_{n} = (n)^{\frac{1}{n}} - 1.$$
Use the fact that $$(1+x_{n})^n = n$$
To show that $$(x_{n})^2 \leq \frac{2}{n}$$
Hint: Use Binomial Theorem and trow away most terms
Attempt:
I've tried all sorts of manipulations, but I stil feel I am at ground zero.
I first expanded $$(x^{2}_{n}) = n^{\frac{2}{n}} - 2n^... | <blockquote>
Use the fact that $(1+x_{n})^n = n \;\;\ldots\;\;$ Hint: Use Binomial Theorem and trow away most terms
</blockquote>
Using the given hint, and discarding all (positive) terms except the first and third ones:
$$\require{cancel}
\begin{align}
1+ \binom{n}{1}x_n+\binom{n}{2}x_n^2+ \ldots = n \;\;&\imp... | Use $(1+x_n)^n=\sum_{i=0}^n{n \choose i}( x_n)^{n-i}$ by the binomial theorem
So $1+nx_n+\frac {n(n-1)}2(x_n)^2+...=n \implies \frac {n(n-1)}2(x_n)^2\le n-1 \implies (x_n)^2\le \frac2n$
| https://math.stackexchange.com |
387,084 | [
"https://physics.stackexchange.com/questions/387084",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/184239/"
] | I was looking at a question on aviation.stackexchange and an interesting answer I found included that even today, we have no physical way to get around the fact that drag of a body is roughly the square of velocity. Theoretically is there any way to get around this?
| It comes from the Navier-Stokes equation.
More specifically, it's the <em>ram pressure</em> term which goes as <span class="math-container">$ -\nabla (\frac{1}{2}\rho u^2)$</span>. This gives a force per unit mass, since the LHS o the N-S equation is usually <span class="math-container">$\rho \frac{\partial \mathbf{u}... | Inviscid drag due to lift (induced drag) of a wing or similar lifting body follows a different trend. It is roughly proportional to the inverse of the velocity squared, so it actually decreases with speed.
The total drag of the wing includes both viscous and inviscid components. The inviscid component dominates at ver... | https://physics.stackexchange.com |
604,043 | [
"https://electronics.stackexchange.com/questions/604043",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/290579/"
] | I have 2 exact electronic circuits, with one malfunctioning while the other is functioning. The total current consumed by the malfunctioning circuit is 0.48 A, while the functioning PCB has 0.271 A.
<strong>My question is</strong>, how can I know which parts in the PCB is eating up this current difference?
What I tried... | The difference in power consumption is about a watt (assuming 5V power). That's enough to get a reasonable size component noticeably warm (or perhaps remove a bit of skin if it's a small part such as an SOT-23 or SOIC-8). So look for charring or smell with the power off. If <strong>safe</strong> and feasible you might ... | I do not know how you are measuring "resistance," but if doing so with a multimeter (while circuit powered off), then you cannot measure the resistance of an IC (or rather, it has nothing to do with how it behaves once powered.)
In your place, I would look for any hot components in your bad circuit. Be carefu... | https://electronics.stackexchange.com |
59,284 | [
"https://security.stackexchange.com/questions/59284",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/47745/"
] | I see a lot of materials in Internet about this technique. I'm not really interested in malwares, but I'm curious when you change bytes to an exe with other bytes, wouldn't this corrupt the exe? I can give example videos if somebody didn't understand my question.
| You'll want to load into tool such as OllyDbg and you'll have instructions and you can modify them to do the same sort of job as alternative instructions then save them to executable so byte signature against your file would be bypassed.
You can rewrite code to do same job. Let's make a really basic scenario.
Imagine ... | It <em>could</em> easily corrupt an exe but there is a lot of data in an exe that isn't actually executable. Also much that may be rarely executed and so might be changed without discovery for a long time.
There are tools that can help with this kind of exercise without changing the actual code. They look for the "res... | https://security.stackexchange.com |
279,528 | [
"https://physics.stackexchange.com/questions/279528",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/84039/"
] | I am trying two days now to simplify the numerator of the electron vertex correction in the one-loop contribution. My problem is to prove that
$$\bar{u}(p')\left[-\frac{1}{2}\gamma^\mu l^2+(-y \gamma ^{\nu} q_{\nu}+z\gamma ^{\nu} p_{\nu})\gamma^{\mu}((1-y) \gamma ^{\nu} q_{\nu}+z\gamma ^{\nu} p_{\nu})+m^2\gamma^{\mu}-2... | I cannot tell you where your calculation went wrong, but Peskin and Schroeder are correct. Here is a step-by-step derivation. Forgive me for not including any English, the steps should be self-evident (but see the bottom).
We start with
$$\bar{u}(p')\left\{-\frac{1}{2}\gamma^\mu\ell^2+(-yq\!\!\!/+zp\!\!\!/)\gamma^\mu\... | I would like to share my idea:
<ol>
<li>at first, only <span class="math-container">$(-y{\not q}+z{\not p}) \gamma^\mu ((1-y) {\not q}+z{\not p})$</span> need special concern. We rewrite terms before <span class="math-container">$\gamma^\mu$</span> in <span class="math-container">${\not p'}$</span> and <span class="mat... | https://physics.stackexchange.com |
55,467 | [
"https://dba.stackexchange.com/questions/55467",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/32024/"
] | For some reason, the query state hangs on "Sending Data" (using show processlist;) and I have no idea why.
This is the table creating script:
<pre><code>CREATE TABLE IF NOT EXISTS `esp_game` (
`gameID` int(10) unsigned NOT NULL,
`gameType` tinyint(3) unsigned NOT NULL,
`mapID` tinyint(3) unsigned NOT NULL,
`cr... | First, look at the EXPLAIN plan again.
The first line says that the Query Optimizer will do the following:
<ul>
<li>Full table scan of at least 7,706,280 rows without using any keys (thus the root cause of the <code>Sending data</code> query state)</li>
<li>Each row in passes through from <code>esp_game</code> will d... | I had a similar issue on queries that had previously worked fine and found damage to the underlying filesystem. If you are having this issue it's wise to ensure that the issue is not external to the db engine itself.
| https://dba.stackexchange.com |
1,028,360 | [
"https://math.stackexchange.com/questions/1028360",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/168977/"
] | Determine (with justification) whether the series:
$$\sum_{n = 2}^{\infty} \frac 1{n\sqrt{(n^2-1)}}$$
Since this will be positive at all times I thought it was a good candiate for the Limit Comparison Test. So I let the origional function be my $a_n$, and I chose my $b_n$ as $\frac 1{n^2}$. And I know that will go t... | <strong>hint:</strong>
$$
\sqrt{n^2 - 1} = \sqrt{(n+1)(n-1)} \ge n-1
$$
so:
$$
\frac 1{n\sqrt{n^2 - 1} }\le \frac 1{n(n-1)} = \frac 1{n-1} - \frac 1n
$$
and $$
\sum_{k=2}^N \frac 1{n-1} - \frac 1n
= 1 - \frac1N\to 1
$$is convergent.
| Hint: Use the limit comparison test, with $\sum 1/n^2$ to compare against like you suspected, which gives a convergent series (which can be shown by the Cauchy condensation test). Then all you have to show is that $\lim_{n \to \infty} n/\sqrt{n^2+1} = 1$.
| https://math.stackexchange.com |
124,821 | [
"https://softwareengineering.stackexchange.com/questions/124821",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23991/"
] | In researching unit testing best practices to help put together guidelines for my organization, I've run into the question of whether it is better or useful to separate test fixtures (test classes) or to keep all tests for a single class in one file.
Fwiw, I am referring to "unit tests" in the pure sense that they are... | I wish I could remember/find the link where the technique I've chosen to adopt was first demonstrated. Essentially I create a single, abstract class for each class under test that contains nested test fixtures (classes) for each member being tested. This provides the separation originally desired but keeps all of the... | Can't really see any compelling reason why you would split a test for a single class into multiple test-classes. Since the driving idea should be to maintain cohesion on a class-level, you should strive for it on a test-level as well. Just some random reasons:
<ol>
<li>No need to duplicate (and maintain multiple versi... | https://softwareengineering.stackexchange.com |
392,753 | [
"https://mathoverflow.net/questions/392753",
"https://mathoverflow.net",
"https://mathoverflow.net/users/17064/"
] | In all that follows, let <span class="math-container">$k$</span> be a field and <span class="math-container">$G$</span> be a finite group.
It is well-known that the order of <span class="math-container">$G$</span> is invertible in <span class="math-container">$k$</span> iff the group ring <span class="math-container">$... | Here is another proof that the global dimension is infinite that is specific to groups and explicitly identifies a module of infinite projective dimension. Let <span class="math-container">$G$</span> be a finite group and suppose that the characteristic <span class="math-container">$p$</span> of <span class="math-co... | If <span class="math-container">$kG$</span> is not semisimple, it is a non-semisimple Frobenius algebra and has infinite global dimension always in that case, see for example the books of Lam on rings and modules where the global dimension of a Frobenius algebra is determined.
So yes, finite global dimension is equival... | https://mathoverflow.net |
124,124 | [
"https://electronics.stackexchange.com/questions/124124",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/45446/"
] | Using a mobile device so I can't upload a picture. I need to find Z_total in a circuit. I will simplify the circuit description so that its easily pictured.
The simple circuit contains The 5<20 phasor current source ("<" representing angle here). The source is in series with a 10ohm resistor and an induct... | When there is an inductor impedance and a resistor impedance in series the total value of the impedance is: -
\$Z_{total} = \sqrt{R^2 + X_L^2}\$
Where, in your example R = 10 ohms and XL is 30 ohms (reactive) making the total impedance 31.623 ohms
| $$X_L = 2 \pi F L = 30 \Omega $$
This is the equivalent impedence of the inductor. Use that to compute the total equivalent impedence of the circuit, as described in an earlier response.
| https://electronics.stackexchange.com |
365,486 | [
"https://softwareengineering.stackexchange.com/questions/365486",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/260537/"
] | I'm a CS student and in order to practice my coding skills I'm trying to implement an e-book reader and I want some advice from more experienced programmers. I'm using C++\QML but I'll try to keep my problem non-specific to any technology.
<h1>Small preface</h1>
Once the book opened I keep it in memory. I also genera... | It's definitely a good idea to separate out the laying out of the pages from the rendering. Putting them on different threads is a good idea as well. I don't think the solution is to do speculative layout at different sizes, though. I think you'll end up doing a lot of unnecessary work. I also don't like the idea of fo... | I take it that the re-calculation you mention is the text re-flow calculation, as you keep the font size same, but change the page area ?
<ol>
<li>You need to optimize the page rendering/rasterization logic for speed.</li>
<li>Adjacent pages can be kept in a lower quality/resolution.</li>
<li>Each page can have its o... | https://softwareengineering.stackexchange.com |
209,272 | [
"https://softwareengineering.stackexchange.com/questions/209272",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/44497/"
] | <h1>The way it was</h1>
For years, I have organized my software solutions as such:
<ul>
<li>Data Access Layer (DAL) to abstract the business of accessing data</li>
<li>Business Logic Layer (BLL) to apply business rules to data sets, handle authentication, etc.</li>
<li>Utilities (Util) which is just a library of common... | Not sure if this is the answer you're looking for.. but here goes.
We do it to keep things separated/organised. Yes, EF/NHibernate are data access.. but we limit its use to its own assembly with a generic repository setup. This assembly also contains all of our NHibernate mappings, Session factory, code for handling m... | I view the EF and DAL as separate components in an Enterprise system. The Data Access Layer is an abstraction that other services use to perform data persistence and management. Typically Entity Frameworks build a nice API around querying, updating, deleting and inserting however at the core they still require a direct... | https://softwareengineering.stackexchange.com |
186,873 | [
"https://math.stackexchange.com/questions/186873",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/25805/"
] | On evaluating quadratic equations, It always equals zero:
$$ax^2+bx+c=0$$
Why zero? Is it possible to use other number for another purpose?
| The value of c is a simple number with no variable. So you can move any value on the right side over to the left and it will just become part of c. Example:
$$x^2+x-6=6$$
$$x^2+x-12=0$$
Therefore, we can set the right hand side equal to any number we want. We usually set it equal to zero because this helps to solve... | Absolutely! But think about what you end up with. Consider the quadratic equation
$x^2 + 2x + 3 = 2 \, . $
If we now subtract 2 from both sides we get $x^2 + 2x + 1 = 0.$ Meaning that these two equations are just two ways of expressing the same thing. So, to save you the trouble of substracting 2 from both sides, you... | https://math.stackexchange.com |
83,392 | [
"https://mathoverflow.net/questions/83392",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19905/"
] | If $C$ is a smooth elliptic curve and $f: C \to \mathbb P^n$, then
$H^1(C,f^*T_{\mathbb P^n}) = 0.$ How do I prove this? The implication is that map
from $C$ to $\mathbb P^n$ is unobstructed.
| I am a beginner but here is my attempt:
the Euler sequence on $\mathbb{P}^n$ pulls back to $0 \to O_C \to O_C(1)^{n+1} \to f^*T_{\mathbb{P}^n} \to 0$ and so from the associated long exact sequence we want to show $H^1(O_C(1))=0$ (as $H^2(O_C)=0$ since $\dim C = 1 <2$). Let $D$ be an effective divisor on $C$ so tha... | In general, for any <em>non-constant</em> morphism $f:C \to \mathbb P^n$, from a $1$-dimensional Cohen-Macaulay (for instance reduced) curve $C$, one has that $$H^1(C,f^*T_{\mathbb P^n}\otimes \omega_C)=0.$$
Indeed, (as already pointed out by Al e) considering the pull-back of the Euler sequence
$$0 \to f^*\mathscr O_... | https://mathoverflow.net |
374,949 | [
"https://mathoverflow.net/questions/374949",
"https://mathoverflow.net",
"https://mathoverflow.net/users/137336/"
] | Let be <span class="math-container">$a,b> 0$</span> and <span class="math-container">$\gamma \in (0,1) $</span>. Set <span class="math-container">$x_n = (\gamma \sqrt[n]{a} + (1-\gamma)\sqrt[n]{b} )^n$</span> for each <span class="math-container">$n\in\mathbb{N}$</span>.
My question is if this sequence <span class="... | No, take <span class="math-container">$E:=\mathbb{R}$</span>, <span class="math-container">$x_0:=1$</span> and <span class="math-container">$T$</span> any continuous bounded function with <span class="math-container">$T(1)=-1$</span>, <span class="math-container">$T(-1)=1$</span>, <span class="math-container">$T(0)=2$<... | While attempting to answer this question, I recalled that the term “bounded” can be pretty confusing in normed vector spaces if not clarified; in general they all take the form <span class="math-container">$$\|Tx\|\le L\|x\|+M\,,$$</span> where <span class="math-container">$L,M$</span> are some nonnegative real numbers... | https://mathoverflow.net |
93,683 | [
"https://dba.stackexchange.com/questions/93683",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/59965/"
] | All recently generated archive logs were corrupted but datafiles are fine.What if recently generated archives corrupted and the archives backup is not available, so what would be the strategy to resolve the issue and is there any possible way to rectify the archive log corruption.
| As soon as your recovery thread is interrupted, making it impossible to recover from an earlier backup to the current time, the remedy is to take a backup before something more serious happens.
Next investigate how the archives became corrupted and solve that.
Backups are of no importance, important is the ability to... | As soon as your instance is down ; start recovery to its latest current time by getting SCN from control file and try to get any of old archive log and start recovery with reset log option.
After starting instance try to investigate the basic reason of corruption and malfunctioning of system.
| https://dba.stackexchange.com |
208,817 | [
"https://mathoverflow.net/questions/208817",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6094/"
] | Let $P$ be an opaque convex polyhedron containing the origin in $\mathbb{R}^3$,
and let $S$ be an origin-centered sphere strictly containing $P$: $S \supset P$.
For a point $x$ on $S$, let $\sigma(x)$ be the area of the shadow
of $P$ cast from a light at $x$ onto the plane tangent to $S$ at $-x$:
<hr />
&... | Let me try to give a computation free (sketch of) proof that the shadow area is not $C^1$. The basic idea is the same as in the answer of Willie Wong: a problem happen when a corner shows up.
Consider a position $x_0$ where some corner $c$ of the polytope is projected right on a facet of the shadow. Then move $x_0$ al... | Just doing this very quickly, so maybe computational errors:
In the case $d = 2$, take $P$ as an equilateral triangle centered at the origin inscribed in the unit circle, and $S$ the circle of radius 2, the problem is equivalent to computing the order of tangency of the two functions $$f_1(\theta) = \frac{\sin\theta}... | https://mathoverflow.net |
56,049 | [
"https://datascience.stackexchange.com/questions/56049",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/78082/"
] | Is the Cross Entropy Loss (CEL) important at all, because at Backpropagation (BP) only the Softmax (SM) probability and the one hot vector are relevant?
When applying BP, the derivative of CEL is the difference between the output probability (SM) and the one hot encoded vector. For me the CEL output, which is very sop... | From ISLR:
<blockquote>
... we consider all predictors <span class="math-container">$X_1$</span>, . . . , <span class="math-container">$X_p$</span>, and all
possible values of the cutpoint s for each of the predictors, and then
choose the predictor and cutpoint such that the resulting tree has the
lowest RSS .... | The gini coefficient computed for each node is the one computed for all observations assigned to that node. So in the root node you have 2 ones and 3 zeros which leads to 0.49 as expected. To select the best split you compute the gini coefficients for both left and right nodes of instances and select the one which has ... | https://datascience.stackexchange.com |
3,456,906 | [
"https://math.stackexchange.com/questions/3456906",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/653945/"
] | <span class="math-container">$\int_E (\sum_{i = 1}^{n}x_i)^p d\lambda_n$</span>, where <span class="math-container">$E = \{x_i\in \mathbb{R}, x_i\ge 0, \sum_{i = 1}^nx_i \le 1\}$</span>
What is the best way to find this integral? I've tried to count it as
<span class="math-container">$\int_0^1dx_1\int_0^{1-x1}dx_2\c... | <span class="math-container">$$y=ax^3+bx^2\tag1$$</span>
<span class="math-container">$$y'=3ax^2+2bx\tag2$$</span>
<span class="math-container">$$y''=6ax+2b\tag3$$</span>
From <span class="math-container">$(3)$</span>, <span class="math-container">$~xy''=6ax^2+2bx=2y'-2bx\tag4$</span>
From <span class="math-container"... | <strong>HINT:</strong>
Second and third equations form a pair of linear equations in two variables <span class="math-container">$a$</span> and <span class="math-container">$b$</span>. Solve for them and plug in first equation.
| https://math.stackexchange.com |
38,166 | [
"https://mechanics.stackexchange.com/questions/38166",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/23331/"
] | I want to purchase a VW Ameo Highline. It comes with stock tyres (185/60 R15), and alloy rims. The spare wheel, however, is a standard steel rim (non-alloy) with 175/70 R14 tyres. The dealer explained this to me as an international norm, that a spare wheel is to be sparingly used.
It made sense to me but I had never ... | <blockquote>
Do all cars that come factory fitted with alloys follow this rule?
</blockquote>
No, there are three basic options that I see all the time.
<ol>
<li>An Emergency wheel - Will get you to the next tire shop or gas station. Has a speed limit of 55/mph and is smaller than normal. Also has a limited range. ... | Because you rarely use it, reducing its size and weight is an effective method for cutting down costs. It also saves space and makes packaging easier for the engineers. The cost aspect is also the reason for the spare being being a steel one instead of the more expensive alloy.
| https://mechanics.stackexchange.com |
107,072 | [
"https://electronics.stackexchange.com/questions/107072",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/40535/"
] | I have a thick film circuit from a calculator that I want to use. How can I attach external connections to the sheet? I tried simply using the circuit as a contact in between a battery positive and an led with the negative attached to see if it would carry signal and it doesn't.
<img src="https://i.stack.imgur.com/pw8... | Those are carbon traces, so can't be soldered to.
Note the fingers at center top. Those are meant to go into a connector that will mechanically clamp the conductive part against metal contacts in the connector. They could also be meant for a "zebra stripe" connector, or something that is screwed down on the PCB that... | I've never tried it, but conductive glue (AKA wire glue) <em>might</em> enable you to make a connection to wires if you can't obtain a suitable connector.
This probably wouldn't be reliable without some mechanical arrangement to hold the wires with strain relief.
It's also fairly non-reversible.
| https://electronics.stackexchange.com |
104,622 | [
"https://stats.stackexchange.com/questions/104622",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/32470/"
] | I am just wondering what we can infer from a graph with x-axis as the actual and y axis as the predicted data?
<img src="https://i.stack.imgur.com/dwlOW.png" alt="signups">
| Scatter plots of Actual vs Predicted are one of the richest form of data visualization. You can tell pretty much everything from it. Ideally, all your points should be close to a regressed diagonal line. So, if the Actual is 5, your predicted should be reasonably close to 5 to. If the Actual is 30, your predicted s... | In the linear regression, you want the predicted values to be close to the actual values. So to have a good fit, that plot should resemble a straight line at 45 degrees. However, here the predicted values are larger than the actual values over the range of 10-20. This means that you are over-estimating. Therefore, the ... | https://stats.stackexchange.com |
430,583 | [
"https://softwareengineering.stackexchange.com/questions/430583",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/63946/"
] | In the Book "Implementing Domain-Driven Design" the author suggests to implement a repository method to provide the next application-generated (not database-generated) ID. Like so:
<pre><code>class MyRepo {
public MyId nextId() {
return new MyId(UUID.fromRandom());
}
}
</code></pre>
That would lead to... | The advantages that I can see:
<ol>
<li>Easier testing; injecting the ID as a dependency allows you to create the entity in a known state, which would help value-based assertions (<code>Assert.assertSame()</code>);</li>
<li>Injecting the ID allows the repository to recreate an entity from storage (i.e. <code>repository... | One scenario that comes to mind, while trying to wrap my own head around the whole DDD approach, is if you're implementing event sourcing system and say you have events "aggregate TypeA created with id ", "aggregate TypeB created with id ". Then you have some other event that assigns TypeB's id to T... | https://softwareengineering.stackexchange.com |
293,552 | [
"https://softwareengineering.stackexchange.com/questions/293552",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/44370/"
] | I have a simple object like this
<pre>
public class Book
{
public List Chapters { get; private set; }
public TableOfContent BookTOC { get; set; }
public string Identifier { get; private set; }
public string Title { get; private set; }
public string Publisher { get; set; }
... | OK I think some of the other answers touch on this, but I will spell it out.
Constructors are not part of the Interface so you can have different ones for each repo.
<pre><code>public BookRepoXml(string xmlStringContainingAllBookData) //or a filename to the bookxml?
{
this.cachedChapters = this.ParseXmlIntoChapte... | I would decouple the three responsibilities for a repository (load book from XML, load book from a database, cache book) into three different implementations:
<pre><code>public interface BookRepository {
Book getBookFromId(string id);
}
public sealed class XmlBookRepository : BookRepository {
private readonly... | https://softwareengineering.stackexchange.com |
468,051 | [
"https://stats.stackexchange.com/questions/468051",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/286068/"
] | <strong>Questions:</strong>
I want to know if this problem can/should be solved using machine learning? If I can and I should, what resources or next steps should I take ? Which approach seems to fit ?
<strong>Problem:</strong>
There are 500,000 buildings, and at any given moment there could be anywhere from 0 to 10... | Think about a vector <span class="math-container">$a$</span> specifying a linear combination of the <span class="math-container">$\hat\beta$</span>s -- a direction in <span class="math-container">$\hat\beta$</span> space.
One natural way to extend the one-dimensional comparison based on variances is to say the linear ... | This condition is a natural extension of the scalar variance inequality. The condition that <span class="math-container">$\mathbb{V}(\tilde{\boldsymbol{\alpha}})-\mathbb{V}(\hat{\boldsymbol{\alpha}})$</span> is positive definite is equivalent to saying that <em>any linear combination</em> of the elements of <span clas... | https://stats.stackexchange.com |
148,631 | [
"https://softwareengineering.stackexchange.com/questions/148631",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/11950/"
] | I have been learning C for a while but still get confused about designing large programs within C (a large application such as the Linux kernel).
Moving from Java where you have classes it's difficult to understand how to design a large application in C.
What advice/links can people advise from moving from a high lev... | In general, the lower level the language, the more rigorous you have to be about style. Many of the same style rules to any language are important. Keep functions short. Keep like methods together. Generalize repeated code. Also, lower level code demands more comments as the code is itself less readable.
In most ... | You wind up implementing objects more directly, without the syntactic sugar. Essentially, structs with function pointers.
You mention the Linux Kernel; you might consider reading its source looking for that pattern.
| https://softwareengineering.stackexchange.com |
258 | [
"https://physics.stackexchange.com/questions/258",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/71/"
] | Dominoes, when placed upright, remain that way. Sometimes, even if you tip them a little bit, they will go back to their upright position.
However, if you tip them too far, they will fall over.
After trying this with many different sized/shaped dominoes and some textbooks, I've noticed that this angle of "maximum ti... | To make it fall you need a torque. This torque is provided by the weight force acting on the center of mass of the object and by the offset between the center of mass and the edge of the object.
Imagine your domino standing upright then tilt it. You are moving the center of mass. When the center of mass (blue) is on t... | The direction that the domino falls is determined by the location its center of mass. It falls to the left or right depending on whether the center of mass is to the left or right of the bottom-most edge. If the center of mass is precisely above the edge, then it balances on that edge in an unstable equilibrium.
| https://physics.stackexchange.com |
314,793 | [
"https://physics.stackexchange.com/questions/314793",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/146729/"
] | Please tell me the reason in reference of thermodynamics that why pressure in a car tyre increases during driving.
| when we drive , the frictional force between the tires and the road increases the temperature of the air inside the tire.
According to Gay-Lussac's Law,
p ∝ T ; [When volume is constant]
so the increase in temperature also increases tire pressure.
| The tyre does heat up, <strong>but not because of friction:</strong> the tyre does not slide along the road and the friction between tyre and road therefore does no work.
What does happen is that the tyre is not perfectly circular. It is squashed by the weight of the vehicle. As the vehicle moves, the part of the tyre... | https://physics.stackexchange.com |
38,009 | [
"https://physics.stackexchange.com/questions/38009",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/12377/"
] | <img src="https://i.stack.imgur.com/axNCt.gif" alt="Pion Plus Decay">
Since the charged pions decay into two particles, a muon and a muon neutrino Fractional electric Charge disappeared, why?
The decay proceeds by the weak interaction <span class="math-container">$W^{+}$</span> and can be visualized in terms of Feynm... | As you say, there exists a Feynman diagram <img src="https://i.stack.imgur.com/y1BVL.jpg" alt="Feynman diagram">
for the process, and the real question is: "what happens with the quarks"
The up and antidown quarks manage to "annihilate" into a virtual W+ which decays into the mu+ and nu_mu.
Simple. All annihilat... | Because negative pion is not known hero of strong and weak interaction.
Brefly - in 1932-1934 James Chadwick which knew no negative particle except for electron, told to physical community that neutron cannot be composite particle consisting of proton and electron. From this obvios fact he made speculative statment tha... | https://physics.stackexchange.com |
52,163 | [
"https://electronics.stackexchange.com/questions/52163",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11271/"
] | Ive been reading Sedra/Smith's Micro Electronic Circuits book, and it has a lot of info which I like, however I dont know how much of it is actually practial and useful, for instance it talks about Ebers-Moll equations and models, which I know are useful to understand how transistors work and how the practical equation... | IMHO it's very useful to know all this stuff, even if you don't use it from day to day, as it deals with the fundamentals of what makes everything else you use IC-wise work.<br>
Whether it will be of "practical use" depends on your field, nowadays especially there is much less discrete design, but if you are designing ... | All The Time -> you need to take these factors into account to ensure low distortion, gain drop off, operational mode etc. The difference that you are noticing is that simply, most advanced designs cannot be done using discretes, and discreet transistors have enough mismatch issues as it is that you don't need to worr... | https://electronics.stackexchange.com |
133,392 | [
"https://stats.stackexchange.com/questions/133392",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/66567/"
] | I have two processes, lets call them A and B. I want to infer whether their population means are equal for their experimental outcomes. Both of these processes generate 1s and 0s only. That is, the outcome is binary.
My situation is similar to using two different processes to flip a coin a few times. The idea is to c... | Based on your comments, I think I have an answer for you. It seems like for the processes you currently have, you have binary outcomes, but that there will be other processes which will not. You would like to use a t.test to analyze the results.
The issue that you're having is that the t.test is not designed for use o... | A t-test is appropriate for continuous data that is normally distributed. If you have binary data, you need to do a proportion test or binomial test.
You point out in the comments that you don't know if the data are always binary or continuous. In R it is not complicated to write a code to automatically determine whi... | https://stats.stackexchange.com |
116,839 | [
"https://cs.stackexchange.com/questions/116839",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/1342/"
] | In the partition problem, the task is to partition <span class="math-container">$n$</span> given integers into two subsets <span class="math-container">$A$</span> and <span class="math-container">$B$</span> with equal sum. This problem is known to be NP-hard, but it becomes easy if the "equal sum" requirement is replac... | There is an <span class="math-container">$O(n \log n)$</span> algorithm for this problem.
To formalize, lets say that the task is to partition <span class="math-container">$n$</span> given integers into two partitions <span class="math-container">$A$</span> and <span class="math-container">$B$</span> that have sizes <... | W.l.o.g. assume the integers are ordered such that <span class="math-container">$x_1 \geq \cdots \geq x_n$</span>.
@Laakeri presented an algorithm for finding a partition <span class="math-container">$(A,B)$</span> that satisfies:
<ul>
<li><span class="math-container">$\sum_B + x_1 \geq \sum_A \geq \sum_B - x_1$</sp... | https://cs.stackexchange.com |
401,290 | [
"https://electronics.stackexchange.com/questions/401290",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/201256/"
] | Voltage drop across a component describes the reduction of energy when current moves through passive elements, is this the same as voltage across?
What about for capacitors, technically current does not actually travel through the dielectric, can this term still be used for capacitors?
| <blockquote>
Voltage drop across a component describes the reduction of energy when
current moves through passive elements, is this the same as voltage
across?
</blockquote>
Voltage drop and Voltage across the component mean the same thing, assuming the same component and the voltage across that component.
<blo... | Yes, they're the same, although I think that most people would want to reserve the phrase "voltage drop" for the voltage developed by running current through a dissipative element such as a resistor, relay, or diode junction.
As a counter-example, referring to a "-9V drop across the battery" would be somewhere between... | https://electronics.stackexchange.com |
179,617 | [
"https://mathoverflow.net/questions/179617",
"https://mathoverflow.net",
"https://mathoverflow.net/users/57582/"
] | Let $E/\mathbb{Q}$ be an elliptic curve and suppose that the trace of Frobenius values are such that $a_{p}(E) \equiv 0 \pmod{2}$ for all odd primes avoiding the conductor. Is it the case that $E$ contains a nontrivial rational two torsion point? Why?
| Yes. Let $P(x) \in {\mathbb Q}[X]$ be the cubic whose roots are
the $x$-coordinates of the $2$-torsion points. The hypothesis says that
$P$ has a root mod $p$ for all but finitely many primes $p$.
If $P$ were irreducible then its Galois group would contain a $3$-cycle,
and then there would be infinitely many $p$ suc... | Alternative method without using the cubic equation (of course not fundamentally different): the Galois representation $\rho: G_{\mathbb Q} \rightarrow GL_2(\mathbb Z/2 \mathbb Z)$ on the points of $2$-torsion of $E$ satisfies tr $\rho(Frob_p)=0$ for every odd prime $p$ by hypothesis, hence tr $\rho=0$ by Chebotarev. (... | https://mathoverflow.net |
169,109 | [
"https://electronics.stackexchange.com/questions/169109",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/23256/"
] | I have a 20A ESC, I have connected it to the brushless dc motor as shown in picture. When i apply a 1ms + signal with rate of 50hz it produces beeps but doesn do any thing. i have connected the wire to mc as; the red one to +5 black to gnd, and white to MC for apply pulse. where am i doing it wrong.<img src="https://i.... | It's hard to tell from the spacing but that hole is likely there so you can screw the regulator to the board, or more likely mechanically attach a heatsink.
You can see an example:
<img src="https://i.stack.imgur.com/j4Dx3.jpg" alt="enter image description here">
If there was copper you'd run the risk of connecting ... | That is the normal mounting hole for a TO-220 package when mounted "lying down" on the board. If you are using a small heatsink, it would be placed between the regulator and board, and held in place, and in good contact with the regulator, by a screw through that hole.
| https://electronics.stackexchange.com |
118,586 | [
"https://softwareengineering.stackexchange.com/questions/118586",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/34364/"
] | <em>Note: I am surprised that this hasn't been asked before, and if it has I could not find it in a search.</em>
I've been on tons of websites, I've read tons of articles, and I have heard tons of explanations. Most of them were good, but they were all either to broad or too complicated or just plain bad. So my questi... | A compiler is a program that translates the source code for another program from a programing language into executable code.
The source code is typically in a high-level programming language (e. g. Pascal, C, C++, Java, Perl, C#, etc.). The executable code may be a sequence of machine instructions that can be execute... | A compiler is a computer program (or set of instructions) that transforms source code written in a programming language (the source language) into another computer language (the target language, often having a binary form known as object code). The most common reason for wanting to transform source code is to create an... | https://softwareengineering.stackexchange.com |
1,559,741 | [
"https://math.stackexchange.com/questions/1559741",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/31458/"
] | Find the number of ways in distributing <span class="math-container">$8$</span> distinct balls into <span class="math-container">$6$</span> distinct boxes such that there is at least <span class="math-container">$1$</span> ball in each box.
We are well acquainted with the traditional Inclusion-Exclusion principle in s... | $K[X;Y], \enspace K$ a field, is not a P.I.D. and the ideal $(X,Y)$ is prime, not principal.
In $\mathbf Z[X]$, the ideal $(2,X)$ is also prime, not principal.
| Hint: consider $\langle 2,x\rangle$ in $\Bbb Z[x]$.
| https://math.stackexchange.com |
14,196 | [
"https://electronics.stackexchange.com/questions/14196",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1623/"
] | I've read a lot about people cleaning keyboards in the dishwasher. But how does the water damage electronics? Does it cause shorts on the ICs on the internal circuitry or physically get in the IC(which I can't see happening). So what actually happens?
| Many electronic assembly lines have a water cleaning machine in them. Basically it runs the PCB through it on a conveyor belt while spraying it with water. One smaller contract manufacturer I visited actually used standard dishwashers to clean PCB's (but had a closed water system, so no bad stuff made it into the sew... | If the device is off and you are just using plain water it's not going to harm the device as long as you dry it off again before turning it on. Dishwashers work quite well for this, but you shouldn't put much soap into it (too much and the residue could stick to the PCB and cause problems.
If you run electronic equip... | https://electronics.stackexchange.com |
4,637,486 | [
"https://math.stackexchange.com/questions/4637486",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1138065/"
] | What is the quantile, p, from the density <span class="math-container">$e^{-x}(1+e^{-x})^{-2}$</span>?
I believe I am on the right path to the solution, but I am stuck part way through.
I figure that the CDF is almost certainly <span class="math-container">$(1+e^{-x})^{-1}$</span>.
So to start, then we must have <span ... | By setting <span class="math-container">$a = (1-p)/p$</span> in the general formula <span class="math-container">$\ln(a^{-1})=-\ln(a)$</span>, you have
<span class="math-container">$$x = -\ln((1-p)/p) = \ln\left(\left(\frac{1-p}p\right)^{-1}\right) = \ln\left(\frac{p}{1-p}\right)$$</span>
| First you have to define your pdf completely, that is
<span class="math-container">$$f(x)=e^{-x}(1+e^{-x})^{-2}$$</span>
for <span class="math-container">$-\infty < x <\infty $</span>. You have to find <span class="math-container">$a$</span> such that
<span class="math-container">$$\int_{-\infty}^{a} e^{-x}(1+e^{... | https://math.stackexchange.com |
318,028 | [
"https://dba.stackexchange.com/questions/318028",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/164093/"
] | Tools such as MySQLTuner add up globally allocated memory and add it to the product of max connections and per connection memory requirement. I formulated the following query to better estimate how much max memory would be required, if 100% of the max_connections are used.
Can someone verify whether it looks correct an... | That's a good stab at a better formula. But I still believe that it is not possible to get a "correct" upper bound.
<ul>
<li>max_connections, table_open_cache, max_allowed_packet, etc, are rarely hit. (That is, your formula will still be an over-estimate of the max.)</li>
<li>Some of the per-query buffers a... | This is really not a useful figure to calculate even if you could get a more accurate estimate, because the theoretical "max memory usage" never happens.
In every production MySQL Server I've analyzed (I've visited dozens of companies as a consultant, and supported thousands of MySQL Server instances as a DBA... | https://dba.stackexchange.com |
40,172 | [
"https://softwareengineering.stackexchange.com/questions/40172",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1728/"
] | I often encounter this when I am helping out someone who is new to programming and learning it for the first time. I'm talking about really new newbies, still learning about OOness, constructing objects, method calls and stuff like that. Usually, they have the keyboard and I am just offering guidance.
On the one hand,... | I think making use of the IDE helps in the learning process. Methods, properties, parameters, overloads and the like are discoverable. With the overwhelmingly huge libraries, Intellisense helps trickle down JIT knowledge. In today's coding environment, it is impossible to learn everything up front, and JIT learning i... | Understanding the concepts and memorising dozens of hundreds of stupid library classes and methods are two completely different things. Intellisense helps to kick all that useless knowledge off from your mind completely, and the earlier you do it, the better. Leave more space for the useful concepts, don't waste your l... | https://softwareengineering.stackexchange.com |
278,706 | [
"https://mathoverflow.net/questions/278706",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | For $k>1$ ($k=2$ in particular for reason) and $\lim\limits_{n \to \infty}\frac{a_{n+1}}{a_{n}}=1$ (it is $a_{n} > 0$ as well, but that is not crucial) we compare these two series:
$\sum\limits_{n=1}^{+\infty}(-1)^n ((\frac{a_{n+1}}{a_{n}})^k-1)$
$\sum\limits_{n=1}^{+\infty}(-1)^n (\frac{a_{n+1}}{a_{n}}-1)$
Ca... | No, one can create sequences in which the first sequence converges but the second does not (or vice versa).
For sake of argument take $k=2$. To begin with let us ignore the requirement that the $a_n$ be natural numbers. Let $\varepsilon_m>0$ be a sequence of numbers tending very slowly to zero (e.g. $\varepsilon_... | This is false, and the reason for this is fairly general, so in fact pretty much any such statement has to be false. Let's write $b_n=\frac{a_{n+1}}{a_n}-1$, so $b_n\to 0$, and we're now asking if the convergence of $\sum (-1)^n b_n(2+b_n)$ implies that of $\sum (-1)^n b_n$.
This will not be the case if the convergenc... | https://mathoverflow.net |
647 | [
"https://dba.stackexchange.com/questions/647",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/492/"
] | I am looking at rolling out a CMS system that will require the creation of around 10,000 tables within the primary MySQL database of the system.
The database will be the data store for several hundred small website front ends that might draw a modest load of around 150k unique viewers per month, but this might have to... | This is no different than the average shared web hosting company. Hundreds to a thousand or more small sites sharing single database server. The high number of tables won't affect anything. I have a database server with over 40,000 actively used tables.
So don't use that as a basis in your hardware planning at all. Ge... | welcome to the dba.StackExchange.com website, and it looks like you've got quite a pickle. So before I answer the question that you posed, I'll mention some details to (hopefully) get you off to a good start:
<h2>10,000 tables in a database are always wrong.</h2>
I take that back. If you had all of the Microsoft or I... | https://dba.stackexchange.com |
377 | [
"https://mechanics.stackexchange.com/questions/377",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/116/"
] | My e46 M3 is making the tell-tale whining and groaning of a power steering pump that is either out of PS oil, or gasping it's last breath. The oil level is fine, so I immediately jumped to the conclusion that the pump is bad. The thing that gives me pause is that the noise goes away after a few minutes, which seems od... | My power-steering pump failed about 2 months after the noise you described. I'm in an E46 3 Series. The noise would be louder when turning at a slower speed than it would at a higher speed. Dealer labour and part came to $1600 CAD, warranty saved me there.
| A lot of BMWs have a noise, but it might be a pump going bad. If I remember right, the lines are right under the reservoir. Check them for softness, and if they are soft/chewy I guess you can replace them. If it's a pump, run until it pops, as they are like $400. As far as the lines from the rack, those are hard lines,... | https://mechanics.stackexchange.com |
13,605 | [
"https://dsp.stackexchange.com/questions/13605",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/7277/"
] | <ul>
<li>How come FIR filters are always stable?</li>
<li>Since they contain poles, shouldn't they be more affected by stability issues than others?</li>
</ul>
| FIR filters contain only zeros and no poles. If a filter contains poles, it is IIR. IIR filters are indeed afflicted with stability issues and must be handled with care.
EDIT:
After some further thought and some scribbling and google-ing, I think that I have an answer to this question of FIR poles that hopefully wi... | FIR filters contain as many poles as they have zeros. but all of the poles are located at the origin, $z=0$.
because all of the poles are located inside the unit circle, the FIR filter is ostensibly stable.
this is probably not the FIR filter the OP is thinking about, but there is a class of FIR filters called Trunc... | https://dsp.stackexchange.com |
528,583 | [
"https://physics.stackexchange.com/questions/528583",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/251344/"
] | Consider a scalar field <span class="math-container">$\phi$</span> as a function of spacetime coordinates <span class="math-container">$x^\mu$</span>. The four-gradient of <span class="math-container">$\phi$</span> is given by
<span class="math-container">\begin{equation}
\frac{\partial \phi}{\partial x^\mu} = \left( \... | The <span class="math-container">$4$</span>-gradient is a <span class="math-container">$4$</span>- vector.
Formally, when <span class="math-container">$x^\mu\to x'^\mu=\Lambda^\mu{}_\nu x^\nu$</span>
<span class="math-container">$$
\begin{align*}
\partial'_\mu
&=\frac{\partial}{\partial x'^\mu}\\
&=\frac{\par... | The four gradient is a four vector but it transforms covariantly, rather than contravariantly. This makes it a "covector".
It also has a contravariant form, obtained by multiplying it by the metric, which transforms like 4 four position or four momentum.
| https://physics.stackexchange.com |
88,500 | [
"https://softwareengineering.stackexchange.com/questions/88500",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/29832/"
] | I would like to switch from a 5 day week to a 4 day, but maintain a 40 hour working week.
Would the 10 hour days affect your ability to be productive? I hate our public transit system so if I could reduce my transportation by 20% I would be happy.<br>
If other developers who work 10 hours shifts could be clear as the ... | The literature on the subject points to the harm that long days (e.g., death marches) do.
It is
<ol>
<li>Impossible for humans to work productively for extended periods of time<sup>1</sup>,</li>
<li>Unrealistic to expect people to work more than 2-6 hours in an 8-hour day<sup>2</sup>, and</li>
<li>Detrimental to ov... | I work a 10-hour day about once a week, and use the hours on other days. Some days I'm on a roll and don't want to stop, and others I would just be going through the motions during the last hour or so. This lets me use both circumstances most productively.
| https://softwareengineering.stackexchange.com |
6,505 | [
"https://stats.stackexchange.com/questions/6505",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/588/"
] | Suppose I am going to do a univariate logistic regression on several independent variables, like this:
<pre><code>mod.a <- glm(x ~ a, data=z, family=binominal("logistic"))
mod.b <- glm(x ~ b, data=z, family=binominal("logistic"))
</code></pre>
I did a model comparison (likelihood ratio test) to see if the model... | Basically, yes, provided you use the correct difference in log-likelihood:
<pre><code>> library(epicalc)
> model0 <- glm(case ~ induced + spontaneous, family=binomial, data=infert)
> model1 <- glm(case ~ induced, family=binomial, data=infert)
> lrtest (model0, model1)
Likelihood ratio test for MLE me... | An alternative is the <code>lmtest</code> package, which has an <code>lrtest()</code> function which accepts a single model. Here is the example from <code>?lrtest</code> in the <code>lmtest</code> package, which is for an LM but there are methods that work with GLMs:
<pre><code>> require(lmtest)
Loading required p... | https://stats.stackexchange.com |
2,739,150 | [
"https://math.stackexchange.com/questions/2739150",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/531324/"
] | <blockquote>
Let $V$ and $W$ be vector spaces on a field $K$. Prove, constructing an explicit isomorphism, that $(V \oplus W) ^*$ is isomorphic to $V^* \oplus W^*$.
</blockquote>
I need just one hint, please. How might one define an isomorphism?
| Let $\varphi:V^{\ast}\oplus W^{\ast}\rightarrow(V\oplus W)^{\ast}$ be defined as $\varphi(v^{\ast},w^{\ast})(v+w)=v^{\ast}(v)+w^{\ast}(w)$, $\varphi$ is an isomorphism.
Let $\eta:(V\oplus W)^{\ast}\rightarrow V^{\ast}\oplus W^{\ast}$ be defined as $\eta(\omega^{\ast})_{1}(v)=\omega^{\ast}(v)$ and $\eta(\omega^{\ast})_... | Hint: take an element of $V^*\oplus W^*$, and think how you could make it a functional acting on $V\oplus W$.
Or, taking the opposite approach, take a functional from $(V\oplus W)^*$, and think how you can obtain a functional on $V$ and another one on $W$.
| https://math.stackexchange.com |
15,053 | [
"https://mechanics.stackexchange.com/questions/15053",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/9133/"
] | Is it safe to use impact wrench when you try to loosen the crankshaft pulley retaining bolt?
Many suggest just that without any concern for possibility of causing the damage to engine mounts, maybe crankshaft bearings, seals etc..
I think Honda produced that 50 mm hex tool for reason. To hold crankshaft safely and prot... | I wouldn't hesitate using an impact to <em>loosen</em> the crankshaft pulley retaining bolt. The reason for this is because even though there is an impact involved, it is a <em>rotary</em> impact. The crank itself would incur no damage, nor would the bearings. The bearings take a worse beating during normal operation t... | @paulster2 is agreed with. However in real life it is sometimes necessary to find compromises. Packing a cylinder with rope, putting a lock on the flywheel, and other crankshaft holding techniques may be necessary. In some cases, mechanics will simply eyeball the torque needed with an impact tool, or with an impact ... | https://mechanics.stackexchange.com |
74,059 | [
"https://mechanics.stackexchange.com/questions/74059",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/22096/"
] | I'm a bit worried about my front brake calipers on my MX5 MK1. I was replacing the front brake pads, and I had to push the caliper piston back in order to fit with the new pads. I used a C clamp to gently push the piston back, but after a few mm going back, it started leaking fluid.
Additionally, when I removed one of... | If your caliper has any brake fluid coming out of it, it's time to rebuild/replace the caliper. There should be absolutely no fluid loss anywhere in your braking system. If it is leaking at the caliper, not only is the caliper failing, but if the brake fluid gets on the rotor/pads, it won't provide much in the way of s... | The brake calipers is a simple hydraulic pistons system, with the rubber rings. Replace the rubber seals it will do your job. Also check for any leaks from bleeder screws.
| https://mechanics.stackexchange.com |
393,589 | [
"https://softwareengineering.stackexchange.com/questions/393589",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/280793/"
] | In JavaScript (ES6), I can have optional function parameter with default value. So to add a new behavior to the existing code base, I could either introduce new method(s) or extend the existing method with an optional parameter.
Consider the following example:
Existing method:
<pre><code>doSomething(param) {
// ... | I'd choose option 2 for the following reasons:
<ul>
<li>A separately named method reveals the intention better than a boolean parameter that you need to look up to understand what it does.</li>
<li>Since you're not modifying any existing behaviour but simply doing something extra at the end, there isn't a good reason ... | There is no right answer to this. In a general sense, you actually have three options:
<ol>
<li>Add an optional parameter,</li>
<li>Add a second function with a different name,</li>
<li>Add a second function with the same name, ie overload the function.</li>
</ol>
I don't think JavaScript supports the third option, ... | https://softwareengineering.stackexchange.com |
848 | [
"https://mechanics.stackexchange.com/questions/848",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/433/"
] | Quite often I encounter a vehicle that has exhaust with rather sharp smell similar to perfume. As far as I know this is attributed to the engine malfunctioning - normally working engine will exhaust gases without sharp smells.
What exactly causes the gasoline engine to produce exhaust with sharp perfume-like smell?
| Most of the perfumes I know have a lot of carbon content (Alcohol based). So if I am to take a quick guess, this might be unburnt fuel being pumped out in gaseous form, a precursor to blackening of your tail pipes.
Or your vehicle might just be wooing the beetle behind - who knows? :)
| If it's a sweet smell it might be antifreeze, although you'd usually get white smoke as well.
| https://mechanics.stackexchange.com |
65,490 | [
"https://quant.stackexchange.com/questions/65490",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/-1/"
] | I was reading about exotic options and I came across something new. <strong>One touch down no touch up option</strong> and the other one I saw was <strong>One touch up no touch down option</strong>.
I would like to understand how it works. Does it payout when the barrier is touched or on the expiration date of the opti... | Commonly, the definition of <strong>credit risk</strong> is the risk that, over a given time horizon, at a certain confidence level, names in our credit portfolio deteriorate or even default, leading to a (present value) loss. Commonly, this risk is not marked-to-market (most of our credit is not tradeable) and the ris... | Credit spread risk is a risk-neutral probability of default. That is, it includes the expected loss plus a systemic risk premium if one ignores factors like liquidity, counterparty risk, and tax effects. Other posts in this page show how one can calculate a risk-neutral probability of default given CDS spreads.
CDS Spr... | https://quant.stackexchange.com |
414,703 | [
"https://softwareengineering.stackexchange.com/questions/414703",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/372752/"
] | A company wants to build an online recruitment system. The logged-in person can add the recruitment application, and attach his CV and some documents.
He will wait for the application to be reviewed by the HR, perhaps for a few days.
The company requests to continue the recruitment process or informs that the applicati... | <blockquote>
Are the "waiting application to be reviewed" and the "company’s response" considered within the flow of events for the "add employment application" use case?
</blockquote>
That depends on the level of abstraction and the viewpoint you have in that use case.
If the use case is ... | The use-case <code>Add employment application</code> seems to correspond to a rather precise and elementary goal: once it’s added, it’s done. Nothing suggest that there could me more behind it.
If it would be <code>Apply for employment</code>, it would suggest that there is a bigger picture: the application process is... | https://softwareengineering.stackexchange.com |
305,597 | [
"https://softwareengineering.stackexchange.com/questions/305597",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/203026/"
] | I'm thinking that I could simplify my life by making an exception handling class that I can just ship all exceptions to and it will handle appropriately.
Ideally:
<pre><code>def dostuff():
try:
dothis()
except Exception e:
Handler.handle(e)
</code></pre>
To avoid
<pre><code>def dostuff():
try:
dot... |
My conjecture is that if you feel a need for such a helper, you're probably catching too many exceptions in the first place. What useful action can you take on an exception? You either know the cause of the error from the context (that is, you <em>expect</em> the exception) and can provide a reasonable fall-back stra... | What you lose is context. You're passing the exception object <code>e</code>, but <code>Handle.handle</code> has no idea whether (say) <code>IndexError</code> happened at an input sanitiser, in which case it might trigger some kind of defensive mechanism; or whether it happened deep in an algorithm after sanitisation, ... | https://softwareengineering.stackexchange.com |
42,928 | [
"https://mechanics.stackexchange.com/questions/42928",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/21638/"
] | This question is about a 2014 Renault engine fitted in our family car, we've owned it since new and I've done all the maintenance to the book. We chose the petrol engine over the diesel because we knew we would use it in the city and only do less than 5000 miles per year with it.
It has 13,000 miles currently and has ... | One cause can be head gasket failure as you say, but another cause is continuous short trips where the engine does not get properly hot - the 8 mile city trips can be an example of the type of use to cause condensation in the engine leading to the mayonnaise you have found.
Solution give it a good run where the engine... | It sounds like it isn't being driven enough and there is condensation in the crankcase that isn't being burned off. You should probably follow the recommendations for harsh driving conditions
| https://mechanics.stackexchange.com |
99,111 | [
"https://mathoverflow.net/questions/99111",
"https://mathoverflow.net",
"https://mathoverflow.net/users/36572/"
] | I have a question about some defitions :
Orbifold, Alexandrov space, limit of manifolds in Gromov-Hausdorff distance sense.
Consider following example.
Let $r> 0$
$L_c = \{ (x cos \theta, x sin \theta, cx) | 0 \leq x$ and $0 \leq \theta < 2\pi \}$
$S$ : $(z-\sqrt{2} r)^2 + x^2 + y^2 = r^2$
$T$ : $ ... | <strong>Q1.</strong> Note that one oriented orthonormal frame bundle $FO$ over a smooth orbifold $O$ is a smooth manifold.
This frame bundle admits a one-parameter family of metrics which collapse to the original manifold and its curvature can be made bounded from below.
<em>Proof.</em> Equip $FO$ with $SO(n)$-invaria... | By Perelman's Stability Theorem, if a (compact) limit of $n$-dimensional Alexandrov spaces of curvature $\ge k$ has the same dimension, then the convergent spaces are eventually homeomorphic to the limit space. So in this context a limit of manifolds is always a topological manifold.
And there exist non-manifold examp... | https://mathoverflow.net |
80,660 | [
"https://physics.stackexchange.com/questions/80660",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/30998/"
] | I got this question in a assignment and haven't been able to figure out how to get to the correct result.
<blockquote>
<em>A force of 6 newtons and a force of 10 newtons can be combine to form
a resultant of what magnitude?</em>
<em>Ans ( 8 newtons )</em>
</blockquote>
I though this would simply be the sum o... | Since you are only asked about the magnitude of the resultant, the directions of the vectors are only relative. So we can locate the first vector anywhere we want. So:
Draw a line 10 units long along the x-axis, starting at the origin.
Using the endpoint of this line, at $(10,0)$, as the center, draw a circle of rad... | Forces are vectors, which have magnitude and direction. Is the direction of the vectors known? If yes, then you need to resolve the forces into components along a common coordinate system, and add the components. In the end, the resultant components will give you the resultant magnitude also.
| https://physics.stackexchange.com |
705,571 | [
"https://physics.stackexchange.com/questions/705571",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/243062/"
] | In the notes I'm using for General Relativity, the author begins their proof of the Ricci identity <em>with</em> torsion by writing
<span class="math-container">$$\nabla_{[\mu}\nabla_{\nu]}Z^{\sigma}=\partial_{[\mu}(\nabla_{\nu]}Z^{\sigma})+\Gamma^{\sigma}_{[\mu|\lambda|}\nabla_{\nu]}Z^{\lambda}-\Gamma^{\rho}_{[\mu\nu]... | Hint: You can, in a first step, expand the outer derivative (write <span class="math-container">$D_\nu Z^\sigma=A_\mu^\sigma$</span> if you wish). You will get a partial derivative acting on <span class="math-container">$A_\mu^\sigma$</span> and two terms with Christoffel symbols.
Can you take it from here?
| We have
<span class="math-container">$$\nabla_\mu \nabla_\nu Z^\sigma=\partial_\mu(\nabla_\nu Z^\sigma)+\Gamma_{\lambda\mu}^\sigma \nabla_\nu Z^\lambda - \Gamma_{\nu\mu}^\rho \nabla_\rho Z^\sigma$$</span>
as <span class="math-container">$\nabla_\mu$</span> is acting on the <span class="math-container">$(1,1)$</span> te... | https://physics.stackexchange.com |
10,598 | [
"https://cs.stackexchange.com/questions/10598",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/2042/"
] | Suppose, I have an array of length 100.
I have 0s at some positions and 1s at some other positions.
What is the <strong><em>fastest method</em></strong> by which I can separate the <strong>0s</strong> and <strong>1s</strong>, so that we get all the 0s at the beginning and all the 1s at the remaining positions / vice-ve... | Here is another version of Yuval's algorithm that uses two loops only.
<pre><code>int number_of_ones = 0;
for(int i = 0; i < 100; ++ i)
{ number_of_ones += A[i];
A[i] = 0;
}
for(i = 100 - number_of_ones; i < 100; ++ i)
{ A[i] = 1;
}
</code></pre>
| <pre><code>i=0, j=size(ar)-1;
while(true)
increase i to position of first 1;
decrease j to position of first 0;
if(i>=j) break;
ar[i]=0, ar[j]=1;
</code></pre>
| https://cs.stackexchange.com |
262,541 | [
"https://dba.stackexchange.com/questions/262541",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/71848/"
] | So the way I have been backing up Postgres is with:
<pre><code>pg_dumpall -U eox-dev -h localhost --clean --file=/home/backups/postgres.sql
</code></pre>
I want to make sure I have a production ready backup that has functions, relationships, triggers, in addition to tables and data.
I'm trying to restore it now in a... | If you want to restore individual databases, you should probably be using <code>pg_dump</code>, not <code>pg_dumpall</code>. And if you don't intend to restore over the top of an existing populated database, you shouldn't be using <code>--clean</code>.
Backing up your entire cluster and migrating/cloning one database... | I don't think that pg_dump or pg_dumpall or pg_restore can change the database name to be restored. However after restoring the database (with the same name) you can rename it with:
<pre><code>alter database old rename to new;
</code></pre>
| https://dba.stackexchange.com |
131,584 | [
"https://security.stackexchange.com/questions/131584",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/44058/"
] | The MVC Framework Symfony uses the following method in its creation of a remember me cookie:
<pre><code>/**
* Generates a hash for the cookie to ensure it is not being tempered with.
*
* @param string $class
* @param string $username The username
* @param int $expires The Unix timestamp when the cookie expire... | This mechanism is so that when the user changes their password, all "remember-me" sessions are invalidated.
The two key features of this mechanism in regards to security is:
<ul>
<li>That the password cannot be determined from the hash in the cookie, if the attacker manages to gain access to the cookie somehow.</li>
... | <blockquote>
...
Now here is my issue with this: Why put the password in the cookie? Though it is the hashed, salted password (with another salt, unique for each user), isn't that an unnecessary risk?
</blockquote>
Risk assessment is on a case-by-case bases, so we can not say if its acceptable or not without fur... | https://security.stackexchange.com |
146,024 | [
"https://math.stackexchange.com/questions/146024",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/31167/"
] | I don't know if $f$ is continuous. I believe that isn't necessarly continuous but I don't know some example. If it is continuous I don't know how to prove.
| For example take any $f$ and $g=0$.<br>
For a less trivial example: take $f(x)=\left\{ \begin{array}{cc} 1 & x\in\mathbb{Q}\\ -1 & x\notin\mathbb{Q} \end{array}\right.$.<br>
Take $g(x)=[x]$. Then $f(x),g(x)$ are both not continuous, while $f(g(x))=1$ is. (Of course you can take a constant function $g$ - in that... | If $g$ is a constant function, $f \circ g$ can be continuous while $f$ isn't necessarily so.
| https://math.stackexchange.com |
511,082 | [
"https://electronics.stackexchange.com/questions/511082",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/225766/"
] | I was working on a project converting 220V AC to 5V DC and I accidentally touched the underside of the transformer which gave me a big shock and I was wondering if it's a good idea to ground my self like with a wrist band or something like that to the ground too if this happens again, I protect my heart, etc.
Is this s... | Grounding won't protect you against shocks when touching live wires!
Quite the opposite, the better you are grounded, the higher the resulting current through your body will be.
| Grounding oneself, while working on live electrical equipment, would be an open invitation to disaster.
Insulating oneself from ground would be the only way to ensure total safety.
That's why rubber mats are provided on the door side of control panels. Electrical maintenance personnel are also provided with rubber shoe... | https://electronics.stackexchange.com |
125,122 | [
"https://stats.stackexchange.com/questions/125122",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/61306/"
] | I had been studying statistics, I have a doubt that I couldn't find the answer of. Its related to estimating population parameters using statistic.
Suppose we have a population size of 10000, we want to estimate mean for it since it is too costly to collect data for all the observations. As far as I know standard proce... | "As far as I know standard process is to arrive on a sample size, say, 100 find the mean for this sample, iterate these steps over some time and then arrive at population mean and its standard deviation assuming normal distribution."
I think this is your fundamental misunderstanding. It is standard to take a single sa... | See, the very word <strong>estimation</strong> implies that you are not necessarily getting the exact value, but reasonably close enough.
In sampling theory, the sample mean is an unbiased estimate of the population mean. Therefore, if you have a set of <strong>randomly selected</strong> 100 data points, you can be ... | https://stats.stackexchange.com |
89,822 | [
"https://physics.stackexchange.com/questions/89822",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/32284/"
] | I am trying to solve the following.
<blockquote>
An object of mass $m$ slides on a horizontal surface with initial velocity $v_0$. If the kinetic friction between the object and mass is given by $\mu$, find the following.<br>
a) the time $t$ necessary to stop the object from moving.<br>
b) the distance $d$ that ... | You should realize that the first equation you write gives you the value of $a$.
In these kinds of problems, you are always given some force, and you are expected to apply Newton's laws to the problem. Therefore
$F_{\mu} = -mg\mu \underbrace{=}_{\text{$2^{nd}$ Law}} ma \quad \quad \to \quad \quad a = -g\mu$
Now you ... | Remember the law $F=ma$; you already know the force from friction $F_{\mu}= -mg\mu$. Hence you can get $a=-g \mu$, and one of your unknowns is gone.
| https://physics.stackexchange.com |
50,313 | [
"https://dba.stackexchange.com/questions/50313",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/28559/"
] | I want to return column names into a table. But I also want to avoid redundancies like 'id' and 'id'.
I did:
<pre><code>INSERT INTO columns(name)
SELECT COLUMN_NAME FROM INFORMATION_SCHEMA.COLUMNS
WHERE table_name='contacts' or table_name='companies';
</code></pre>
But as expected I get <code>id</code> from the f... | You first try was very close. Just prepend the table_name and a dot:
<pre><code>INSERT INTO columns(name)
SELECT CONCAT(TABLE_NAME,'.',COLUMN_NAME) FROM INFORMATION_SCHEMA.COLUMNS
WHERE table_name='contacts' or table_name='companies';
</code></pre>
Give it a Try !!!
| You can use <code>GROUP BY</code>:
<pre><code>SELECT COLUMN_NAME FROM INFORMATION_SCHEMA.COLUMNS WHERE TABLE_NAME = 'contacts' OR TABLE_NAME = 'companies' GROUP BY COLUMN_NAME;
INSERT INTO columns (name) SELECT COLUMN_NAME FROM INFORMATION_SCHEMA.COLUMNS WHERE TABLE_NAME='contacts' or TABLE_NAME='companies' GROUP BY... | https://dba.stackexchange.com |
575,270 | [
"https://math.stackexchange.com/questions/575270",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/92654/"
] | Show that if $f_n \to f$ uniformly on $[a,b]$ and $f_n$ is integrable for each n then <strong>$\int_{a}^{x}f_n(t)dt\to \int_{a}^{x}f(t)dt$</strong> uniformly in $x$ on [a,b].
I know how to prove the question <strong>$\int_{a}^{b}f_n(x)dx\to \int_{a}^{b}f(x)dx$</strong> uniformly in $x$ on [a,b]. <img src="https://i.st... | Nearly so. Did you understand the proof you have pasted above?
$$
\left|\int_a^x (f_n(t) - f(t))\,dx\right| \leq \int_a^x |f_n(t) - f(t)| \,dt \leq \int_a^b \epsilon/(b-a) \,dt < \epsilon,$$
for all $n$ sufficiently large. The last inequality follows from the fact that $|f_n(t) - f(t)|$ is nonnegative.
(I've left... | "I know how to prove the question <strong>$\int_{a}^{b}f_n(x)dx\to \int_{a}^{b}f(x)dx$</strong> uniformly in $x$ on $[a,b]$."<br>
This is a sequence of numbers so we can not talk about uniform continuity.
I think you can use the same method, just use that $x-a\le b-a$.
| https://math.stackexchange.com |
226,536 | [
"https://electronics.stackexchange.com/questions/226536",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/98056/"
] | Im working on a uC that has interrupts configured for various FIFO's present in the uC. Each FIFO is connected to a common bus and can receive data independently(at any point of time). Now, everytime a FIFO receives 8 bytes of data a single ISR is called and in the ISR I have to identify which FIFO caused the interrupt... | Your question isn't limited to FIFOs or any particular interrupt-causing hardware.
Clear interrupt conditions as soon as you know you will handle that condition.
In the case of vectored interrupts, this is very early in the interrupt routine because you know the interrupt cause just from being there. You might do ... | It is better to clear the interrupt flag ("reset the interrupt") at the beginning of the ISR because you will not loose another interrupt if it happens while the first invocation is still running.
Quick example: you receive data using some peripheral, the ISR takes some time to process it, if you receive a second byte... | https://electronics.stackexchange.com |
637,669 | [
"https://physics.stackexchange.com/questions/637669",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/299934/"
] | <em>A half pipe of a skateboard park consists of a concrete trough with a semicircular section of radius 5m, I hold a frictionless skateboard on the side of the trough, pointing down toward the bottom and release it; how long will it take to come to back to the point of release?</em>
I got this from an example in the b... | <ol>
<li>The state of the Universe is governed by a function.
</li>
<li>Neural networks approximate functions -- it is what they are designed to do. Period.
</li>
<li>Therefore, the Universe is an approximation of some ideal and unattainable function ... wait, what? Why? Why bother? Why do we need an approximation when... | There's less to pop physics than meets the eye. The full technical content of the argument is:
<ol>
<li>Physical theories are described by sets of complicated differential equation.</li>
<li>Training a neural network can be described as a set of complicated differential equation.</li>
<li>Since you can get any differen... | https://physics.stackexchange.com |
369,518 | [
"https://physics.stackexchange.com/questions/369518",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/174025/"
] | I realize this seems like a pretty simple issue of drawing a free body diagram, but I just can't seem to figure it out.
If a bike leans, then it must have had a torque that made it lean. I considered the centripetal force, in this case friction, as a possible source for this torque, but that would create torque in th... | Two things that need to be considered. Often it is not the cyclists weight that causes the lean in. Subconsciously, as people learn to ride a bike, they do something called counter-steering.
So for example coming in to turn right, a cyclist will quickly turn the handlebars left to lean the bike to the right due to cen... | The bike would lean in the other direction, due to centripetal force, without a cyclist. A cyclist leans the bike on purpose into the turn, to counteract said centripetal force.
The torque involved is the cyclist's weight as they lean into the turn.
| https://physics.stackexchange.com |
51,887 | [
"https://mathoverflow.net/questions/51887",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1837/"
] | Are there constructive examples of doubly stochastic matrices (whose rows and columns all sum up to $1$ and contain only non-negative entries) that are not diagonalizable?
| Sure. For example:
$$A = \begin{pmatrix}
5/12 & 5/12 & 1/6 \\
1/4 & 1/4 & 1/2 \\
1/3 & 1/3 & 1/3
\end{pmatrix}$$
Note that
$$A \begin{pmatrix} 0 \\ 1 \\ -1 \end{pmatrix} = \begin{pmatrix} 1/4 \\ -1/4 \\ 0 \end{pmatrix} \ \mbox{and} \ A^2 \begin{pmatrix} 0 \\ 1 \\ -1 \end{pmatrix} = 0.$$
Thi... | In complement to David's answer, the eigenvalue $\lambda=1$ of a doubly stochastic matrix $A$ is always semi-simple. The matrix is permutationally similar to a block upper-triangular matrix $B$ whose diagonal blocks are irreducible. Because $B$ is doubly stochastic too, the sum of the entries in the upper-triangular b... | https://mathoverflow.net |
25,447 | [
"https://mechanics.stackexchange.com/questions/25447",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/14697/"
] | I have a 2005 Corolla CE with manual transmission. About one month ago the car would not start, and the battery was discharged to about 8.5V. Car had been not running for a couple of days but nothing was left on.
Since the battery was under warranty, I replaced it. Charging system is OK (about 14V, and this problem ... | I've seen where mis-adjusted trunk light switches cause the light to stay on with the trunk closed and then the battery drains. If you have fold-down rear seats this is easy to check. Otherwise you may need to enlist a small fearless helper or a video camera. Or just remove the bulb and see if the problem goes away.... | Checking the Key Off amperage draw is the standard test for this symptom. An ammeter that is very accurate in the Milliamp range is needed. Low quality meters are readily available and can quickly lead one to a false conclusion.
The test: Remove ignition key, wrap in aluminum foil if Smart Key, Wait at least five mi... | https://mechanics.stackexchange.com |
384,682 | [
"https://math.stackexchange.com/questions/384682",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/69780/"
] | Let $V_1$ and $V_2$ be two subspaces of a vector space of finite-dimension, such that $$\mbox{dim}(V_1+V_2)\ =\ \mbox{dim}(V_1\cap V_2) + 1,$$
show that $V_1 \subseteq V_2$ or $V_2 \subseteq V_1$.
Please help me with this problem. Thanks in advance.
| Note that
$$\dim(V_1\cap V_2)\le\dim V_1\le\dim(V_1+V_2)=1+\dim(V_1\cap V_2).$$
It follows that either
$$\dim V_1=\dim(V_1\cap V_2) \Rightarrow V_1\subseteq V_2,$$
or
$$\dim V_1=\dim(V_1+V_2)\Rightarrow V_2\subseteq V_1.$$
| $\mbox{dim}(V_1+V_2)\ =\ \mbox{dim}(V_1\cap V_2) + 1,$ means that base of $(V_1+V_2)$ has only one element more than $(V_1\cap V_2)$ then this one extra base must be belong to $V_1$ or $V_2$ so
$V_1$ is subspace of $V_2$
or $V_2$ is subspace of $V_1$
| https://math.stackexchange.com |
263,004 | [
"https://physics.stackexchange.com/questions/263004",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/90543/"
] | What is the meaning of system rigidity in mechanics? I can't understand how to classify the system as rigid or not, and what is the effect of rigidity on the whole system.
If you know anything about system rigidity... Please let me know
| In the materials science context, rigid means hard, resisting deformation. It is the opposite of elastic.
If two material bodies are forced sideways against each other and one or both are elastic like rubber, it/they will deform, allowing them to squeeze past each other without much damage being done.
However, if ... | It simply means that the object is so stiff that it can only move by proper Euclidean isometries. At any time, the whole body can only be a combination of rotations and translations of itself at any other time. In particular:
<em>This means that the distance between every pair of points within the body stays the same ... | https://physics.stackexchange.com |
14,741 | [
"https://electronics.stackexchange.com/questions/14741",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4435/"
] | I'm having trouble in explaining kirchoff's laws to my cousin who is studying in first year Engineering.
Can somebody explain me in simple plain english.
Thank you very much in advance :)
| <strong>Kirchhoff's current law</strong> (KCL): the sum of the currents in a node is zero.
<img src="https://i.stack.imgur.com/Aaen4.png" alt="KCL">
Say you have 5 wires coming together in a node as shown, and \$I_1\$, \$I_3\$ and \$I_4\$ supply current to the node. This current has to go somewhere, and will go fro... | Kirchoff's law: What goes in must come out.
| https://electronics.stackexchange.com |
694,557 | [
"https://physics.stackexchange.com/questions/694557",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/316673/"
] | In <em>Shankar's Quantum Mechanics book</em> p-64 the last equation reads:
<span class="math-container">$$ \delta'(x'-x) = -\delta'(x-x'); $$</span>
I am confused because if I think of it using the gaussian approximation then since: <br />
<span class="math-container">$$ g(x' -x) = \frac{1}{\Delta^2 \sqrt{\pi}} \exp\le... | If it is not clear from the context that all index are summation ones, we can raise some of them to make it explicit. It is possible to choose them freely because the metric is the identity:
<span class="math-container">$$ \nabla \cdot (A \times B) = [\epsilon^i{_{jk}} A^j B^k]_{,i} \\
= \epsilon^i{_{jk}} A^j{_{,i}}... | Sure! However when you mix up contravariant and covariant indices on the orientation tensor <span class="math-container">$\epsilon$</span>, you can get very confused very quickly on its antisymmetry properties.
A more elegant convention:
<span class="math-container">$$\begin{align}
\mathbf u&=\nabla\times\mathbf v\... | https://physics.stackexchange.com |
2,619,238 | [
"https://math.stackexchange.com/questions/2619238",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/307383/"
] | $P,Q,R,S$ are four coplanar points on the sides $AB,BC,CD,DA$ of a skew quadrilateral. The product $\frac{AP}{PB}.\frac{BQ}{QC}.\frac{CR}{RD}.\frac{DS}{SA}$ equals?
<strong>My attempt:</strong>
<blockquote>
I was not able to even start the problem, because I have never worked
on a skew quadrilateral. Any hints w... | You're on exactly the right track.
Select a basis $(w_1,\dots,w_9)$ of $\Bbb R^9$. Define $\phi_{i,j} \in V$ by
$$
\phi_{ij}(v_k) = \begin{cases}
w_j & k = i \\
0 & k \neq i
\end{cases}
$$
Verify that $\{\phi_{i,j}: 5 \leq i \leq 11, 1 \leq j \leq 9\}$ forms a basis of $V$.
| Yes; a linear map in $\mathcal L\bigl(\mathbf R^{11},\mathbf R^9\bigr)$ is determined by the images of the vectors of a basis of $\mathbf R^{11}$, i.e. by the column vectors of a $9\times 11$-matrix relative to this basis. The condition of vanishing on the first $4$ vectors of the basis means it depends on the $9\tim... | https://math.stackexchange.com |
581,228 | [
"https://physics.stackexchange.com/questions/581228",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/275215/"
] | I get that <span class="math-container">$S_z$</span> operator has spin <span class="math-container">$\frac{h}{2\pi}$</span> ,<span class="math-container">$\frac{-h}{2\pi}$</span> because the spin angular momentum along the <span class="math-container">$z$</span> direction is the latter. But why should this be the same ... | Invariance of the physical systems under rotation allows the operators <span class="math-container">$S_z$</span> and <span class="math-container">$S_x$</span> be rotationally equivalent means they can be used one another under a rotation operation. The roots of the rotational invariance can be shown by Noether's theore... | Qualitatively, the reason is simple. You distinguish between <span class="math-container">$S_z$</span> and <span class="math-container">$S_x$</span> because of axis orientation, but in case you rotate your axis, <span class="math-container">$S_z$</span> becomes your <span class="math-container">$S_x$</span> and vice-ve... | https://physics.stackexchange.com |
40,957 | [
"https://scicomp.stackexchange.com/questions/40957",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/34261/"
] | I am used to solving elliptic PDEs of even order. I was wondering what would one do for odd order PDEs. Notably the discretisations of those results in unsymmetric matrices. I tried solving the following simple problem:
<span class="math-container">$$\frac{d^3u}{dx^3}(x) = 0,\, x\in \Omega \quad u(x) = f(x), \, x \in \... | The matrix for <span class="math-container">$d/dx$</span> is skew-symmetric for a suitable discretization scheme, and the same is true for its odd powers.
Moreover, the operator <span class="math-container">$i d/dx$</span> is hermitian, and again, by using a skew-symmetric discretization, all its powers are hermitian a... | As mentioned in my comments to davidhigh's answer, using the discretisation in my question results in a skew-symmetric matrix which when modified to add Dirichlet conditions becomes singular. To better understand the problem I looked at discretisations of:
<span class="math-container">$$\frac{du}{dx} = 0$$</span>
and t... | https://scicomp.stackexchange.com |
144,581 | [
"https://chemistry.stackexchange.com/questions/144581",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/103022/"
] | I need to measure out 70 ml of liquid.
I have a 10 ml measuring cylinder with a maximum uncertainty of 0.1 ml and a 100 ml measuring cylinder with a maximum uncertainty of 1 ml.
I've calculated that using the 10 ml cylinder 7 times would give a 0.7 maximum uncertainty, or a 0.7/70=1% percentage uncertainty. Meanwhile, ... | You have three types of errors:
<ol>
<li>The errors in the accuracy of your measurement. Assuming you are reading the water levels consistently (at eye level at the bottom of the meniscus), these should be random.
To add random, uncorrelated errors, the standard method is to sum their squares and take the square root.... | Keep in mind that a graduated cylinder is never meant for accurate volume transfer. You would probably use a Class-A 100 mL buret to transfer 70 mL to a vessel if accuracy were that critical say, 70.0 mL was desired. All these general chemistry rules of thumbs are not useful for real analytical work. Experimental numb... | https://chemistry.stackexchange.com |
18,074 | [
"https://engineering.stackexchange.com/questions/18074",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/13727/"
] | I would like to learn to weld (stick welding) for my own purposes (mostly for small repairs and building simple metal constructions). So far I'm trying to educate myself by reading and watching instructional videos, but so far I haven't found an answer to one question which is bothering me (I know it may sound stupid):... | No. Current will always take the path of least resistance. The path of least resistance is through the ground clamp that you secure to the workpiece, or another conductor that the workpiece is touching. If this ground clamp becomes disconnected, you can't weld (or start to), because the circuit would be broken.
If yo... | As long as the equipment isn't faulty and you don't do anything really silly you are very unlikely to get electrocuted from stick welding simply because the voltages involved are not large enough.
Indeed in most welding processes it is fairly normal to be touching the work at some point during welding, albeit you are... | https://engineering.stackexchange.com |
278,672 | [
"https://softwareengineering.stackexchange.com/questions/278672",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/90356/"
] | I'm working on a personal project that uses a few different libraries, such as GLFW, glm and Bullet. How are different naming conventions usually dealt with in this context?
Working with C++ I always used the same convention the standard library uses (all lowercase, underline as word separator, not ::getSize(), just :... | Accept and use each library's preferred naming preferences.
To do anything else would add a layer of abstraction between the true names and the ones you've picked to enforce your preferred style. That makes it somewhat of a nightmare to look up anything (including the library documentation for a method or function)... | What's worse than dealing with this is dealing with projects that have dealt with it in a cute way.
If I know something is supposed to be in a namespace, then at least I know that. I know it in all projects whenever I work with it. It might work great for you but anyone else who has used that library will be unnecessa... | https://softwareengineering.stackexchange.com |
141,969 | [
"https://electronics.stackexchange.com/questions/141969",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | We worked two years on and off on this project at my friend's place. Finally we finish, I take it home. There's a power supply unit but it can't be connected directly to mains, it expects some lower AC voltage. There's a bridge rectifier and a cap directly after the input. I had an 18V AC adapter and connected it. I kn... | I don't think the electrolyte is particularly nasty stuff. Electrolytics have been in use for about 80 years now (and failing!) and I've not heard of any major health scares, so I'd suggest you're OK with basic precautions - use rubber gloves getting it off, and wash those PCBs with flux cleaner to be on the safe side.... | After you clean the PCB using Brian's instructions, replace the cap with a 25v rating (not 16v). Also, use a 12v AC source (not 18vAC). If the PCB does not works fine, then replace the bridge rectifier, also. Most likely the other parts were not damaged, but if they were, replace them as needed.
| https://electronics.stackexchange.com |
21,051 | [
"https://quant.stackexchange.com/questions/21051",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/17286/"
] | I am estimating <strong>GARCH model</strong> for volatility calculation and as a <strong>data input I have used log first difference data</strong> (ln(a)-ln(b)). <strong>Usually I would check for autocorrelation in residuals</strong>(to check the model), but since my input was already in the form of first difference, <... | You should check for autocorrelation. However, its presence does not necessarily mean your model will produce inaccurate figures. The ARCH family of models were developed to help analyze the volatility of a time-series. This data is assumed to display a degree of heteroskedasticity. Using the GARCH model, small amounts... | To add to @Brumder's answer, people typically take a two-step approach when concerned about both Garch and autocorrelation: first fit some sort of ARMA(p,q) model, and then second use maximum likelihood on the residuals of the first step to estimate the Garch parameters.
| https://quant.stackexchange.com |
45,566 | [
"https://datascience.stackexchange.com/questions/45566",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/61756/"
] | I'm not sure if this exists. Is there such a situation where weights in gradient descent fail to work or break up? If so, how and when?
| I dont think its necessarily related to the type of algorithm performing the regression(XGBoost here) - but to inherent nature of regression algorithms.<br>
Many loss function are aimed to reduce distance between <span class="math-container">$y$</span> and <span class="math-container">$\hat{y}$</span>.<br>
That can lea... | Maybe you can try using multiple XgBoost models instead of 1 and take an average (or weighted average) of their predictions.
| https://datascience.stackexchange.com |
236,598 | [
"https://softwareengineering.stackexchange.com/questions/236598",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/123065/"
] | I'm building websites in ASP.NET MVC and I quickly figured out that my models are getting harder to organise as they grow.
What I normally do is create one model to add and edit data. But in my add view I have 2 extra properties. So I'm re-using the same model with 2 extra properties but I don't use these my edit view... | I don't see a compelling argument here for non-line comments, and personally I cannot remember the last time I've used one.
<ol>
<li>Comments in and of themselves are decreasing in frequency, and should be focused on explaining <em>why</em> code is doing stuff. That is done using line comments.</li>
<li>Leaving commen... | I going to go further than "Yes, they should be in" and say they're a basic requirement for any modern language and something I would just expect to work, at least 2 levels, preferably // and /* */ since that's what most developers are used to.
While I agree with @Telastyn that:
<blockquote>
Leaving commented code ... | https://softwareengineering.stackexchange.com |
64,340 | [
"https://mathoverflow.net/questions/64340",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11016/"
] | The smallest two perfect numbers $n=6$ and $m=28$ satisfy
$$
\frac{m}{n+1} = 2^k
$$
with $k=2.$
Question: Are there more pairs of perfect numbers $n,m$ with $n < m$
and such that
$$
\frac{m}{n+1} = 2^k
$$
for some positive integer $k>0.$
Observe that the perfect number $n$ , the smallest of $n,m$
may be als... | If $m$ is odd, it's clearly impossible.
If $m$ is even and $n$ is odd, I don't know.
So suppose $m$, $n$ both even. Then $m=2^{r-1}p$ where $p=2^r-1$ is prime, and $n=2^{s-1}q$ where $q=2^s-1$ is prime, and $s\lt r$.
The equation becomes $$2^k(n+1)=2^k(2^{s-1}q+1)=2^{k+s-1}q+2^k=2^{r-1}p$$ Now $2^k$ divides the s... | [After typing out this attempt at a "partial" answer, I realized that the details have already been worked out by Luis, Gerhard and Todd. I am posting it as an answer for anybody else who might be interested in how the final result is obtained. - Arnie]
Suppose $m$ is even and $n$ is odd.
Then if $m$ and $n$ are per... | https://mathoverflow.net |
2,630 | [
"https://physics.stackexchange.com/questions/2630",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1129/"
] | So, I remember in college physics the prof using liquid nitrogen in a demonstration. When he was done, he threw the container of LN at the front row, and of course it evaporated (or whatever) before it got to the students.
I am watching a cooking show now and they are using LN -- if they touched that, what would happ... | Liquid nitrogen boils when it comes in contact with skin, so small amounts of spatter are no danger at all-- the droplets just bounce off. I regularly pour a liter or so (a bit at a time) out on a lab table when I do liquid nitrogen demos, with no problems or safety gear.
The biggest risk from the low temperature is g... | Liquid nitrogen will not moisten human skin, so short contact with small amount of it should not be too harmful -- it would just float on a evaporated portion of itself like water over very hot pan; yet of course putting a hand into a container with it is not a good idea.
From what I have heard, the biggest problem is... | https://physics.stackexchange.com |
664,621 | [
"https://physics.stackexchange.com/questions/664621",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/247323/"
] | Suppose that a man departs from Earth to reach a planet that is ninety-nine light-years away with 0.9802 light speed, c. According to special relativity, it takes him 40 years (measured by his own clock) to reach the planet and then return to Earth. But for the Earth's clock, 202 years have passed. When he reaches the ... | When I face west, Los Angeles is 3000 miles in front of me (in my frame, of course). When I turn my body 90 degrees and face north, Los Angeles is 3000 miles to my left (in my new frame). Do you want to say that Los Angeles moved several thousand miles in the instant that I changed frames?
When I am at the end of m... | It is a consequence of the relativity of simultaneity. When two observers move relative to each other, their time axes diverge and their respective planes of simultaneity become tilted relative to each other, the degree of tilt depending upon their relative speed of motion. When your imagined traveller hops from the ou... | https://physics.stackexchange.com |
260,985 | [
"https://dba.stackexchange.com/questions/260985",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/180495/"
] | Warning up front: unfortunately I'm limited to using SQL*Plus on remote site, with no other tools available. This is Oracle 12c (12.2.0.1.0) Standard Edition running on Windows Server 2012R2.
Over the weekend there was an outage where Oracle stopped responding for approx 15 minutes. Looking at application logs and Or... | You can inspect V$SQL for statements that don't use binds, eg.
<pre><code>select substr(sql_text,1,80), count(*)
from v$sql
group by substr(sql_text,1,80)
order by count(*) desc
</code></pre>
Then inspect the full text of the statements that come on top, see where they differ.
| someone has access to the alert log. Try to get access. Maybe they can send it to you. Do you have full rights on that database? If so try to figure out what directory has the alert log. For example "show parameter diag" Take that directory add the following %DIAG%\rdbms\\\trace and create a directory object for that p... | https://dba.stackexchange.com |
44,497 | [
"https://dsp.stackexchange.com/questions/44497",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/30679/"
] | Currently, I am trying to work with the Dataset UrbanSound8K to try some Audio classification. And I got stuck in the preprocessing step already.
Since the audios are of different lengths, like 4 seconds or 0.3 seconds, I found it impossible to directly pass into the whitening algorithms like PCA even after Feature Ex... | I suggest that you compare things that are similar and don't compare things that are not. You could proceed with a preliminary classification of "short", "medium", and "long" and do a second set of classifications afterward. Within the duration classes, perform as much stretching and padding you need.
Another po... | If the signals were of the same duration but obtained using different sampling rates, so that they have different sample lengths, you can <strong>resample</strong> the <strong>shorter</strong> sequence with a higher sampling rate to match that of the longer sequence.
| https://dsp.stackexchange.com |
7,631 | [
"https://quant.stackexchange.com/questions/7631",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/5025/"
] | Which of the following statements is correct?
a. If a bond’s yield to maturity exceeds its coupon rate, the bond’s current yield must also exceed its coupon rate.
b. If a bond’s yield to maturity exceeds its coupon rate, the bond’s price must be less than its maturity value.
The correct answer is b. I would like to ... | <strong>(a) is false</strong>
Consider a zero coupon bond. Yield to maturity clearly exceeds the coupon rate, but
$$
Y_\text{current} = 0 = \text{Coupon}
$$
while the question asks about a strict inequality.
| No you're right. If YTM > coupon rate, then the bond is selling below par and therefore current yield > coupon rate.
| https://quant.stackexchange.com |
475,952 | [
"https://physics.stackexchange.com/questions/475952",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | <img src="https://i.stack.imgur.com/53NED.jpg" alt="enter image description here">
So the suggested solution is A. But here's what I don't get, when the F is doubled, how is it possible that the acceleration(A) tripled?
If the answer is m.a should the question be "a person needs to push the car by a force of 4F to g... | Newton 2nd law says that <strong>total force</strong> (or <strong>the sum of all forces</strong>) causes acceleration:
<span class="math-container">$$\sum F=ma$$</span>
Imagine having a resistive force of <span class="math-container">$1 \;\mathrm N$</span> while applying <span class="math-container">$2\;\mathrm N$</s... | There is a constant resistive force so you could just solve the simultaneous equation <span class="math-container">$F - R = ma$</span> and <span class="math-container">$2F - R = 3ma$</span> to get R, which is the resistive force.
| https://physics.stackexchange.com |
4,289,215 | [
"https://math.stackexchange.com/questions/4289215",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/721971/"
] | I proved this statement via contradiction. Assume there is some <span class="math-container">$a\in \mathbb{R}$</span> such that <span class="math-container">$\big\{\frac{1}{n}\big\}_{n=1}^{\infty}\longrightarrow a$</span> with respect the metric <span class="math-container">$d$</span> defined in the title. This guarant... | It looks fine. I would do it as follows: if <span class="math-container">$\left(\frac1n\right)_{n\in\Bbb N}$</span> converges to <span class="math-container">$a$</span>, I would take <span class="math-container">$N\in\Bbb N$</span> such that <span class="math-container">$n\geqslant N\implies d\left(\frac1n,a\right)<... | Notice that you are working with the discrete metrics. You can generalize the result in a general topological space:
<blockquote>
If <span class="math-container">$X$</span> is a disrete topological space and <span class="math-container">$\{ x_n\}$</span> is a sequence in <span class="math-container">$X$</span> such tha... | https://math.stackexchange.com |
4,714 | [
"https://bioinformatics.stackexchange.com/questions/4714",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/2687/"
] | Suppose we have a fasta file like
<pre><code>>Seq1
GTTGAGAGGTGTATGGACACGAAAAACGAAACTGTATCCCGTGTTTAGCAAAGAAATCAT
>Seq1
AAAAACGAAACTGTATCCCGTGTTT
>Seq2
CGTGTTTAGCAAAGAAAT
</code></pre>
I want to produce
<pre><code>>Seq1
GTTGAGAGGTGTATGGACACGAAAAACGAAACTGTATCCCGTGTTTAGCAAAGAAATCATAAAAACGAAACTGTATCCCGTGTTT
&... | Certainly this python script is not the most elegant solution but it will give you the desired result:
<pre><code>import sys
seqs = {}
with open(sys.argv[1], "r") as fh:
curr = ""
for line in fh:
if line.startswith(">"):
curr = line
if curr not in seqs:
seqs[... | This is a scenario where awk excels and yields a much simpler solution than the other examples here (though the logic is essentially equivalent to terdon’s Perl solution):
<pre class="lang-bash prettyprint-override"><code>awk '
/>/ { id = $0 }
!/>/ { seq[id] = seq[id] $0 }
END { for (id in seq) pri... | https://bioinformatics.stackexchange.com |
2,355,620 | [
"https://math.stackexchange.com/questions/2355620",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/115082/"
] | Im given the problem:
<ol start="9">
<li>Determine whether the points lie on a straight line.</li>
</ol>
(b) K(0,3,-4), L(1,2,-2), M(3,0,1)
I take the distance between KL, LM, and KM and every single time KL + LM = KM.
2.5 + 4.1 = 6.6
I use the distance formula and get for KL square root( (1-0)^2 + (1-0)^2 + (1-0... | If you’d used enough decimal places, then you wouldn’t have run into this (at least, not for this problem). If you take $\sqrt6\approx2.44949$, $\sqrt{17}\approx4.12311$ and $\sqrt{43}\approx6.55744$, then you have $$2.44949+4.12311=6.5726\ne6.55744$$ As JMoravitz comments, this is a good reminder to work with exact va... | If 3 points $K,L,M$ lie on the same straight line, then $K - L$ and $K-M$ would be the multiples of the same vector. Note that
$$
K-L = (0,3,-4)-(1,2,-2) = (-1, 1, -2)
$$
and
$$
K-M = (0,3,-4)-(3,0,1) = (-3, 3, -5)
$$
and clearly, those 2 vectors are not scales of each other, so the 3 points are not collinear.
| https://math.stackexchange.com |
1,555,414 | [
"https://math.stackexchange.com/questions/1555414",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/284574/"
] | I was assigned this problem for homework but don't know if I'm tackling it properly..
Find a basis for the orthogonal complement of the column
space of the following matrix
$
M=
\begin{bmatrix}
1 & 1 \\
1 & -1 \\
1 & 1 \\
1 & -1 \\
\end{bmatrix}
$
I'm guessing I need to find $\vec... | $$M^Tx=0 \\ \iff \begin{bmatrix}
1 & 0 & 1 & 0 \\
0 & 1 & 0 & 1 \\
\end{bmatrix}\begin{bmatrix}x_1 \\ x_2 \\ x_3 \\ x_4\end{bmatrix} = \begin{bmatrix}0 \\ 0\end{bmatrix} \\ \iff \begin{cases}x_1 + x_3 = 0 \\ x_2 + x_4 = 0\end{cases}$$
Let $x_3=s$ and $x_4=t$ where $s,t\in\Bbb R$, then $$... | In general, you can use the fact that the kernel of $M^*$ annihilates the image of $M$. If $M$ is relative to the standard basis, then $M^*=M^T$, so all you need to do is find the kernel (nullspace) of $M^T$, which is equivalent to solving the system of linear equations in Bye_World’s answer.
| https://math.stackexchange.com |
158,904 | [
"https://electronics.stackexchange.com/questions/158904",
"https://electronics.stackexchange.com",
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] | If my source is 9 or 12v should I first us a linear regulator to step it down to 5v and from the 5v use another linear regulator to step it down to 3.3v? The 3.3v will be going to a micro-controller while the 5v will drive some 5v sensors/relays.
Current is under 500mA total, probably closer to 300. The power source f... | If those sensors/relays are external to your device, there's a fair chance that the 5V supply can get shorted and shut down. If you wish your microcontroller to work through such an event, it'd be necessary to have a separate buck converter for both 5V and 3.3V - if you care about power efficiency. If you don't mind so... | A linear regulator will dissipate power but if the current in the load is small this power loss may be acceptable. If this power loss is not acceptable then use two switching regulators.
Generally having a linear regulator fed from a higher voltage linear regulator is OK but the higher voltage regulator may overheat i... | https://electronics.stackexchange.com |
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