qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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|---|---|---|---|---|---|
1,121,283 | [
"https://math.stackexchange.com/questions/1121283",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/44940/"
] | I'm not sure how to show this
$$\mathbb{Z}_3[X]/(x^3 -x +1)\cong\mathbb{Z}_3[X]/(x^3 -x^2+x +1).$$
Any help or hint would be helpful.
| Since the two polynomials are irreducible (no roots, small degree) you simply need to invoke the uniqueness of finite fields of a given order: Finite field extensions are uniquely characterized by their order. Since both of them are finite fields of order $3^3=27$ they are isomorphic, and in fact are exactly the set o... | First, observe that each of the polynomials $x^3-x+1$ and $x^3-x^2+x+1$ are irreducible over $\mathbb Z_3$. To prove this, we use the following fact.
<strong>If $\deg p\leq 3$ and $p$ has no roots, then $p$ is irreducible</strong>
<strong>Proof:</strong>
If $p$ was reducible, there would be non-constant polynomials ... | https://math.stackexchange.com |
158,847 | [
"https://softwareengineering.stackexchange.com/questions/158847",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/32262/"
] | I work in a small team of developers who all collaborate on several Zend PHP projects. We are using Mercurial with a collection of upstream repositories, as well as Jenkins for centralized testing and health reports. We want to implement a shared library of common classes, but are struggling with finding a workflow t... | The SRP states, in no uncertain terms, that a class should only ever have one reason to change.
Deconstructing the "report" class in the question, it has three methods:
<ul>
<li><code>printReport</code></li>
<li><code>getReportData</code></li>
<li><code>formatReport</code></li>
</ul>
Ignoring the redundant <code>Rep... | The way I check for the SRP is to check every method (responsibility) of a class and ask the following question:
<em>"Will I ever need to change the way I implement this function?"</em>
If I find a function that I'll need to implement in different ways (depending on some kind of configuration or condition) then I kno... | https://softwareengineering.stackexchange.com |
122,084 | [
"https://softwareengineering.stackexchange.com/questions/122084",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/330318/"
] | DR-DOS, Plan, BSD, Sun Solaris, HP/UX, OpenServer.....and so on.
Why high-tech OSs (like UNIX family) are mostly command based (rather than GUI based)?
| <ol>
<li>GUI is more difficult to build than CLI (command line interface).</li>
<li>CLI is easier to agree on standards, as it's much simpler.</li>
<li>GUI requires a graphical subsystem (more hardware and software components on servers which don't need it at all).</li>
<li>CLI is easier to automate (scripts), simplifi... | Try explaining in an email, or by phone, how to interact with a GUI.
Try explaining in an email, or by phone, how to interact with a command line. It is considerably easier: you could copy & paste the command inside the email.
(Variant, try to explain by email or by phone how to lace your tie or your boots)
Our ... | https://softwareengineering.stackexchange.com |
176,173 | [
"https://electronics.stackexchange.com/questions/176173",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/53300/"
] | I believe the title says everything about the question. My issue has to to do with the following: Consider a two-port given by:
$$V_1 = Z_{11}I_1 + Z_{12}I_2$$
$$V_2 = Z_{21}I_1 + Z_{22}I_2$$
Cleary by the equations above, one would expect that the measurement of the \$Z_{ij}\$ parameters to be performed while keepin... | The two test configurations tell you two different things.
If you short the input, you're testing the output impedance of the circuit as it is normally used. This is because you typically drive the circuit with a (relatively) low impedance source.
If you open the input, you get the \$Z_{22}\$ as defined in circuit th... | If you want to solve for any of the Z parameters it is clear that you must assume Iac=0, which means Idc=const.
However, remember that there are other sets of parameters for describing the BJT:
<ul>
<li>Y-parameters are all "short-circuit"-parameters (Vac=0, Vdc=const)</li>
<li>h-parameters are "short-circuit-paramet... | https://electronics.stackexchange.com |
223,657 | [
"https://dba.stackexchange.com/questions/223657",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/82383/"
] | I have installed Oracle Driver ( 12.1.0 ) and I have VS 2017 Data Tools SSIS . The connection to Oracle Service from local machine via ODBC 64 bit on my machine is working.
Connection to Oracle Server from SSMS 17 via Linked Server is not working
I get 'Architecture Mismatch' error when I create a Oracle OLDEB conne... | Visual Studio and SSDT are 32bit programs, so they can't use the 64bit OleDB provider. You can run your SSIS package in 64bit mode, but the designers don't work unless you also have the 32bit OleDB provider, and are running visual studio using a Path that allows it to load the 32bit OCI.DLL.
| On a windows 2016 server I was forced to use oracle 12C drivers. I installed 32 and 64 bit and can connect and execute sql via sql developer, sqlserver 2016 linked server but not from visual studio 2017 SSIS in debug mode although the connection tests OK.
| https://dba.stackexchange.com |
31,289 | [
"https://scicomp.stackexchange.com/questions/31289",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/30287/"
] | When solving a system of ODEs, as part of a preconditioner, I get the system
<span class="math-container">$(A + D(t))x = b(t)$</span>
where <span class="math-container">$A$</span> is a sparse matrix and <span class="math-container">$D(t)$</span> is diagonal. I'm currently solving this by taking the LU-decomposition o... | I do not believe that a direct solve is possible in your situation, there are simply <em>too</em> many applications with <em>too</em> many users which would benefit <em>too</em> much if it was possible. In particular, the problem of computing, say, the transfer function <span class="math-container">$T(s) = C(A - sI)^{-... | No (unless <span class="math-container">$D$</span> has few nonzeros). Variants of this question get asked a lot here, and the answer is invariably the same.
| https://scicomp.stackexchange.com |
128,418 | [
"https://physics.stackexchange.com/questions/128418",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/15631/"
] | Here is the problem I am working on
<blockquote>
For what temperatures are the atoms in an ideal gas at pressure P quantum mechanical ? Hint: use the ideal gas law P V = N kT to deduce the interatomic spacing (the answer is $T < (1/k)(h^2/3m)^{3/5} P^{2/5})$. Obviously we want m to be as small as possible and P a... | The idea of the question is to find the temperature at which the average interparticle spacing is equal to the average de Broglie wavelength. Both of these are averages because the atoms of the ideal gas are not evenly spaced and the velocity (and therefore de Broglie wavelength) of the ideal gas atoms follows the Maxw... | "The size of a single gas particle" is a bad term for what you calculate. A better term would be:
"The volume one of the gas particles would occupy, if the total volume were distributed equally among all gas particles"
And this translates loosely to
"The volume, in which you find one gas particle on average"
If you ... | https://physics.stackexchange.com |
293,525 | [
"https://softwareengineering.stackexchange.com/questions/293525",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/139925/"
] | I decided to write a singly-linked list, and had the plan going in to make the internal linked node structure immutable.
I ran into a snag though. Say I have the following linked nodes (from previous <code>add</code> operations):
<pre><code>1 -> 2 -> 3 -> 4
</code></pre>
and say I want to append a <code>5</... | With lists in functional languages, you nearly always work with a head and tail, the first element and the remainder of the list. Prepending is much more common because, as you surmised, appending requires copying the entire list (or other lazy data structures that don't precisely resemble a linked list).
In imperati... | You are correct, appending requires copying the whole list if you are unwilling to mutate any nodes in-place. For we need to set the <code>next</code> pointer of the (now) second-to-last node, which in an immutable setting creates a new node, and then we need to set the <code>next</code> pointer of the third-to-last no... | https://softwareengineering.stackexchange.com |
126,383 | [
"https://mathoverflow.net/questions/126383",
"https://mathoverflow.net",
"https://mathoverflow.net/users/27566/"
] | Consider the hyperplane $H=\{f\in L^\infty: \int f = 0\}$ of $L^\infty = L^\infty[0,1]$. My question is:
<strong>1. What is the Banach-Mazur distance between $H$ and $L^\infty$? Are there "natural" isomorphisms between these two spaces?</strong>
Since $L^\infty$ is 1-injective, we have the lower bound
$$
inf\{\|P\|... | IIRC, if $K$ is a compact Hausdorff space that has no isolated points, then every projection from $C(K)$ onto a hyperplane has norm at least two. Maybe Dan Amir proved this? Anyway, in your situation the proof goes like this. A projection $P$ from $L^\infty$ onto $H$ has the form $Pf = f -(\int f) g$, where $\int g ... | For a pointed metric space $(M,d,0)$, we denote by $Lip_0(M)$ the Banach space of all real-valued Lipschitz functions $f$ defined on $M$ and such that $f(0)=0$. Recall that $Lip_0 [0,1] = L^\infty$ (see, for example, N. Weaver's book Lipschitz Algebras). It's not hard to see that the hyperplane $H$ defined above is iso... | https://mathoverflow.net |
72,325 | [
"https://cs.stackexchange.com/questions/72325",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/68808/"
] | I came across the following equality of regular expressions $$(r|s)^* = (r^*.s^*)^*\,,$$ where $r$ and $s$ are two regular expressions and $.$ denotes concatenation, but I don't know how could I prove it.
<strong>My try:</strong>
I call $L(r)$ the language defined by the regular expression $r$. And I want to use the ... | In one direction,
$$
L((r^*s^*)^*) \subseteq L(((r|s)^*(r|s)^*)^*) = L(((r|s)^*)^*) = L((r|s)^*).
$$
In the other direction, $L(r) \subseteq L(r^*s^*)$ and $L(s) \subseteq L(r^*s^*)$ imply that $L(r|s) \subseteq L(r^*s^*)$, and so
$$
L((r|s)^*) \subseteq L((r^*s^*)^*).
$$
| Your mistake is in the step
$$
L(r|s)^i = L(r)^i \cup L(s)^i.
$$
Consider for example $r=a$ and $s=b$. Then $L(r|s)^i$ consists of all words (over $\{a,b\}$) of length $i$, whereas the righthand side is $\{a^i,b^i\}$.
| https://cs.stackexchange.com |
124,073 | [
"https://cs.stackexchange.com/questions/124073",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/112585/"
] | We know that the lower bound is the minimum amount of work needed to solve a problem. So for a given problem say x it has the best algorithm ( the most efficient algorithm to solve this problem ) say algorithm y, then the lower bound efficiency calculated from this algorithm y is the least time this problem x can be ... | When analyzing algorithms it makes little sense to consider the best-case scenario as it is very often trivial and not very informative.
You can convince yourself that almost every algorithm can be adapted to have a best-case complexity of <span class="math-container">$O(n)$</span>, where <span class="math-container">... | "lower bound" can be applied for each scenario and individually not meaningful! (lower bound of what?) As we analyzed the worst-case scenario most of the time as time complexity of an algorithm, hence, "lower bound" is applied for the worst-case scenario (not the best case).
In other words, as the time complexity is e... | https://cs.stackexchange.com |
431,987 | [
"https://physics.stackexchange.com/questions/431987",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/194370/"
] | In the interaction:
<span class="math-container">$$\rm \nu_\mu + e\to\nu_e+\mu$$</span>
the <span class="math-container">$\nu_\mu$</span> energy threshold to produce the process is <span class="math-container">$m_\mu^2c^2/2m_e$</span>, which gives a <span class="math-container">$\sim10~\rm GeV$</span> threshold.
Fo... | Quick note: I'm suppressing factors of <span class="math-container">$c$</span> here. Anywhere you see a <span class="math-container">$p$</span> imagine it's really <span class="math-container">$pc$</span> and anywhere you see an <span class="math-container">$m$</span> it should be <span class="math-container">$mc^2$</s... | I am not sure what "physical reason" is meant to help you intuit the different relativistic kinematics involved.
You are getting the threshold by calculating the invariant mass in the lab frame on the left hand side and in the cm frame on the right hand side of the reaction, assuming the product are produced at rest,... | https://physics.stackexchange.com |
55,789 | [
"https://security.stackexchange.com/questions/55789",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/35588/"
] | I'm working on a website that allows a current user to invite another individual to be friends by typing in the non-user's email address. The non-user would then receive a custom registration url by email which would, when used, automatically connect the two users, giving each access to the other's private information.... | For this your main concern is making sure that the information is only accessible to the intended recipient; which sounds a lot like what public cryptography / PGP tries to achieve.
Unless you want to see if the target non-user has a PGP key published, or if you can get his certificate to encrypt the email with his ... | I don't think you can. You know nothing about the intended recepient, so whomever
receives and uses the link is as likely as anyone else to be the right guy. A common
half-measure is to make the link valid only for a short time.
| https://security.stackexchange.com |
38,960 | [
"https://chemistry.stackexchange.com/questions/38960",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/30140/"
] | <blockquote>
We have the following reaction:
<span class="math-container">$$\ce{A + B<=>2C +D}$$</span>
The initial concentration of <span class="math-container">$\ce{A}$</span> and <span class="math-container">$\ce{B}$</span> are <span class="math-container">$\pu{1M}$</span> each. <span class="math-container">$K... | No need for the cubic equation. Just firstly assume that <span class="math-container">$\ce{A}$</span> and <span class="math-container">$\ce{B}$</span> reacted completely, then <span class="math-container">$\ce{[C]}=\pu{2M}$</span>, <span class="math-container">$\ce{[D]}=\pu{1M}$</span>, and from <span class="math-conta... | This problem can be solved iteratively, if you are looking to increase precision. A first iteration ("zeroth order solution") was presented in another answer, where it was first assumed that approximately all reagent is converted to product before using the result to back-compute the residual (very small) con... | https://chemistry.stackexchange.com |
24,623 | [
"https://engineering.stackexchange.com/questions/24623",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/14940/"
] | My professor, when discussing about Random Walk model during diffusion in metals said that "Vacancies are equilibrium defects but dislocations are not". I could not understand why. Why is it so?
| Imagine you have two boxes separated by a removable partition. Each box is filled with a different pure monatomic gas. When you remove the partition, the gases mix. Their equilibrium state tends toward an equitable mixture at every point in time. The likelihood of the gases spontaneously separating is essentially zero ... | Nature will always try to minimize the number of dislocations and grain-boundaries, whereas in the case of vacancies, there is an optimum number that will lead to the lowest Gibbs energy.
| https://engineering.stackexchange.com |
386,702 | [
"https://softwareengineering.stackexchange.com/questions/386702",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/269955/"
] | I recently started working at a place with some much older developers (around 50+ years old). They have worked on critical applications dealing with aviation where the system could not go down. As a result the older programmer tends to code this way.
He tends to put a boolean in the objects to indicate if an exception... | The problem with this approach is that while exceptions never get thrown (and thus, the application never crashes due to uncaught exceptions), the results returned are not necessarily correct, and the user may never know that there is a problem with the data (or what that problem is and how to correct it).
In order fo... | <blockquote>
Is this a good way of handling exceptions?
</blockquote>
No, I think this is pretty bad practice. Throwing an exception vs. returning a value is a fundamental change in the API, changing the method's signature, and making the method behave quite differently from an interface perspective.
In gener... | https://softwareengineering.stackexchange.com |
243,219 | [
"https://stats.stackexchange.com/questions/243219",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/109372/"
] | <blockquote>
Assume that $\Omega=[0,2]$ and $\mathbb{P}$ is probability on $\Omega$. Find the distribution function of the random variable defined as $$X(\omega) = \begin{cases} \omega, & 0 \le \omega < 1 \\ \omega-1, & 1 \le \omega \le 2 \end{cases}$$
</blockquote>
If $X$ is a continuous random variable,... | <strong>In general, finding a CDF requires solving inequalities.</strong>
Recall the definition: the distribution function (CDF) of any random variable <span class="math-container">$X$</span> is defined to be the function that sends real numbers <span class="math-container">$x$</span> into the probability that <span cl... | In general, if $X$ is a random variable, and $F(t)$ is its cumulative distribution function, then we can say the following about $F(t)$:
<strong>(i)</strong> $F(t)$ is defined for all real numbers $t$.
<strong>(ii)</strong> $0 \leq F(t) \leq 1 $
<strong>(iii)</strong> $F(t)$ is a (weakly)-<em>increasing</em> functi... | https://stats.stackexchange.com |
294,104 | [
"https://softwareengineering.stackexchange.com/questions/294104",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/192524/"
] | I have a class called MyClass and a method called Get that looks something like this:
<pre class="lang-cs prettyprint-override"><code>public class MyClass{
string ClassVariable1 {get; set;}
string ClassVariable2 {get; set;}
string ClassVariable3 {get; set;}
public MyClass Get()
{
..se... | I don't know if it is "wrong," but it certainly doesn't look "right" to me. I don't know why you are doing what you are doing. It looks like you are creating instances, but it's unclear if these are new instances or copies.
If you are creating new instances, the usual way to do that is to use a static factory method.... | It's not uncommon to have methods that return the type of the class--how else would a clone function work?
However, that's not what you are doing here. You have a class that returns a list of itself. I do not believe this function belongs in your Facebook class.
| https://softwareengineering.stackexchange.com |
311,202 | [
"https://stats.stackexchange.com/questions/311202",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/183141/"
] | I am conducting a classification problem. Usually AUC is used to check the effectiveness of a model when performing logistic regression model. However, if I fit the same data set by using Random forest and logistic regression models, which measures should be used to check the accuracy of the two models? Are there any m... | Since the assertion in the quotation is a <em>collection</em> of statements about rescaling the columns of <span class="math-container">$X$</span>, you might as well prove them all at once. Indeed, it takes no more work to prove a generalization of the assertion:
<blockquote>
When <span class="math-container">$X$</spa... | Define the least squares estimator $\hat\beta = \arg\min_{\beta\in\mathbb{R}^p} \|y - X \beta\|_2^2$, where the design matrix $X \in \mathbb{R}^{n \times p}$ is full rank. Assuming that the scaling matrix $S \in \mathbb{R}^{p \times p}$ is invertible.
Define this new scaled estimator $\tilde\alpha = \arg\min_{\alpha\... | https://stats.stackexchange.com |
339,987 | [
"https://softwareengineering.stackexchange.com/questions/339987",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/201289/"
] | I'm using swagger to prototype a RESTful API and I got to a situation where one property is part of a resource but not always should be filled.
Let's say my resource is <code>stores</code>.
Basic endpoints would be:
<code>GET: /stores</code> - returns a list of <code>store</code>
<code>GET: /stores/{storeId}</code>... | <blockquote>
GET: /stores - returns a list of store
GET: /stores/{storeId} - returns a single store
</blockquote>
These are two different resources (a store, and a list of stores), so it is fine that they have different data.
The resource representing a list of stores can contain just enough information for th... | If you have a many/many relationship (ie. a picture can go with mutiple stores) I would go with
<pre><code>Store {
id: integer,
name: string,
pictureIds: array[]
}
</code></pre>
and a separate endpoint
<pre><code>POST: /getPictures pictureIds: array[]
</code></pre>
If its a one store per picture relationship ... | https://softwareengineering.stackexchange.com |
15,416 | [
"https://ai.stackexchange.com/questions/15416",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/28605/"
] | I often read <em>"the performance of the system is satisfactory"</em> or <em>" when your model is satisfactory"</em>.
But what does it mean in the context of Machine Learning?
Are there any clear and/or generic criteria for Machine Learning model to be satisfactory for commercial use?
Is decision what model to ch... | The answer is "when it works well enough to perform the task that you have set it".
It is a good idea to set your performance criteria in advance so that you can clearly identify the goal that you are trying to achieve and also so that you will know if the model is likely to be successful or not.
| From what I have observed, the ability to scale an ML model is key.
Real time inference must be quick, and cause no delays from the provider side. Being able to deploy the model also carries enormous weight - that is, how easy would it be to build the data pipelines and how easy would it be to integrate it in a web ap... | https://ai.stackexchange.com |
689,947 | [
"https://physics.stackexchange.com/questions/689947",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/325870/"
] | This question might be nonsensical and, if it is, please leave a reply so I know and can remove it.
I'm currently learning about basic thermodynamics and was thinking, if there is some "average" or median movement pattern or velocity which a system of molecules reach after some time has gone.
Is there some &q... | <blockquote>
Every book says that friction is independent of surface area in
contact. It is pretty obvious that equation for our friction doesn't
have any "area term" in it.
</blockquote>
The "area term" is built into the value of the normal (perpendicular) force, <span class="math-container">$N$</s... | The reason is that the weight of the cube is now spread over a larger area of contact, so each part of every plate is now pressed more lightly in contact with the surface.
| https://physics.stackexchange.com |
187,300 | [
"https://security.stackexchange.com/questions/187300",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/179796/"
] | I was thinking about alternatives to hashes for storing passwords, and I was wondering if there was any huge security flaw with one I came up with.
If, when the user creates their account, their password is used as a key to encrypt itself and stored that way, you could validate logins by decrypting the stored password... | <blockquote>
Is there any inherent theoretical problem with this idea, assuming the encryption is immune to such things as collisions and related-key attacks?
</blockquote>
Yes, there is a problem with this idea even given your assumptions.
Just use bcrypt for god's sake!
Some problems: The way you have stated you... | You still have to make it computationally expensive like it would be in a slow hash algo like BCrypt or SCrypt. You can use a KDF with a fine tuned quantity of iterations to achieve the level of expense that your users will tolerate without noticing a performance lag.
Keep in mind that whatever is encrypted by the use... | https://security.stackexchange.com |
151,617 | [
"https://mathoverflow.net/questions/151617",
"https://mathoverflow.net",
"https://mathoverflow.net/users/44073/"
] | How does one prove that the space $B(\mathbb H)$ of bounded operators on a infinite dimensional (separable) Hilbert space is <strong>not</strong> reflexive?
I guess this should go along the lines of the non-reflexivity of $l_\infty$, but I was unable to find this written down somewhere.
| It seems to be a good idea to extend my comment to an answer.
First of all, pick any orthonormal basis of $\mathbb{H}$ so that $B(\mathbb{H})$ can be identified with $B(\ell_2)$. The subspace of diagonal operators is clearly isometric to $\ell_{\infty}$. It is a general truth that if $Y$ is a closed subspace of a refl... | The predual of $B(H)$ are the trace class operators. It is a general result that if $X$ is not isomorphic to $X^{**}$ via the canonical embedding, so is $X^{*}$ not isomorphic to $X^{***}$ via the canonical embedding. The last fact is an exercise in Simon-Reed Mathematical Prinicple of Physics Vol 1.
| https://mathoverflow.net |
163,763 | [
"https://electronics.stackexchange.com/questions/163763",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43434/"
] | I did a real mistake when un-soldering this PCB :
<img src="https://i.stack.imgur.com/QFZWS.jpg" alt="enter image description here">
The metal part of the PCB was accidentally removed. Now it is impossible to solder anything at this place again: the solder material (what's the name again in english?) doesn't "glue" t... | Gently scrape a little of the soldermask (the green semitransparent paint) off the end of the track which leads to the pad you've lifted.<br>
You should see bright shiny copper underneath where you've scraped. Make sure its reasonably clean, but don't be to hard on it or you'll destroy that too ...<br>
Then push your w... | The picture is very unclear. As far as I understand, you mean to say that the copper track is removed from the PCB, probably due to overheating. If that's the case, the solder will not be able to stick to PCB as it only sticks to the copper layer. There are some ways to "FIX" ( make it run) depending on what you are tr... | https://electronics.stackexchange.com |
11,990 | [
"https://stats.stackexchange.com/questions/11990",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1586/"
] | I'm analyzing pairwise correlations of time series between two different types of microarrays done for several samples as biological replicates.
So, I have M1 number of variables on type 1 array, M2 number of variable on type 2 array, N samples and T time points. For each sample, I calculate M1 x M2 correlation coeff... | OK, I have been fighting with a similar problem as well. Here are a few conclusions I have arrived at.
You see, for me the main problem is that if you consider rigorous correction for multiple testing or false discovery rate control, you need to worry about the fact that all these correlations that you test are not in... | I don't actually know the answer to this question, but I wonder if some sort of bootstrap approach would be the most tractable. So: for each combination of variables on Type 1 and Type 2 arrays, randomly select biological replicates, and measure correlation over time. Do this many times (hundreds to thousands should be... | https://stats.stackexchange.com |
69,423 | [
"https://softwareengineering.stackexchange.com/questions/69423",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23334/"
] | I like the way planning poker works at the beginning of any project, letting you compare and discuss details of each story with one another.
One of the issues I've noticed with this is that through time and as you gain more experience with the problem domain, you tend to vote less points for each story, i. e., a story... | I don't think that's a big problem.
There are two obvious things that could be causing that. One is that you're experiencing some mild point deflation. The other is that your team is actually getting faster. (I hope it's the latter!)
Either way, it shouldn't be a big deal. The two main uses of velocity are figuring o... | Fundamentally, this isn't really a big problem, as most of these things will come out in the wash. By and large, explicit manipulation of the output of estimations is going to be a negative for the process. Story points estimation works best when teams keep their eyes on the ball - you're estimating relative complexi... | https://softwareengineering.stackexchange.com |
177,133 | [
"https://softwareengineering.stackexchange.com/questions/177133",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/36622/"
] | I got into an interesting internet argument about getter and setter methods and encapsulation. Someone said that all they should do is an assignment (setters) or a variable access (getters) to keep them "pure" and ensure encapsulation.
<ul>
<li>Am I right that this would completely defeat the purpose of having getters... | I remember having a similar argument with my lecturer when learning C++ at university. I just couldn't see the point of using getters and setters when I could make a variable public. I understand better now with years of experience and I've learned a better reason than simply saying "to maintain encapsulation".
By de... | If the getter/setter simply mirrors the value then there is no point in having them, or in making the value private. There is nothing wrong with making some member variables public if you have a good reason. If you are writing a 3d point class then having .x, .y ,.z public makes perfect sense.
As Ralph Waldo Emerson ... | https://softwareengineering.stackexchange.com |
28,880 | [
"https://dba.stackexchange.com/questions/28880",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/15388/"
] | This is a simplified example of a design issue that I am facing: I have 3 tables: <code>Car</code>, <code>Ship</code> and <code>Bicycle</code>. I need to add an "activity logging" table that records user actions such as deletion and user comments etc. I was thinking of creating just one table. Rather than 3 tables. Th... | I work with a database that has this solution that I outline below. I don't like it because the base table has an entry for each type and it ends up being a huge table that is slow to query.
--base table
<pre><code>CREATE TABLE APPLICATION_LOGGING
(
ID NUMBER(9) NOT NULL, --primar... | Arguments can be made either way depending on whether you want to handle populating these tables using triggers or the application(s).
I think this depends on what exactly you want to store in these logging tables, if you're logging anything specific to your 3 "data" tables then you'd be better off with 3 logging tabl... | https://dba.stackexchange.com |
6,806 | [
"https://stats.stackexchange.com/questions/6806",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/18462/"
] | I have a dataframe df as shown below
<pre><code> name position
1 HLA 1:1-15
2 HLA 1:2-16
3 HLA 1:3-17
</code></pre>
I would like to split the position column into two more columns based on the ":" character such that i get
<pre><code>name seq position
1 HL... | <pre><code>df_split<- strsplit(as.character(df$position), split=":")
df <- transform(df, seq_name= sapply(df_split, "[[", 1),pos2= sapply(df_split, "[[", 2))
>
> df
name position pos seq_name pos2
1 HLA 1:1-15 1:1-15 1 1-15
2 HLA 1:2-16 1:2-16 1 2-16
3 HLA 1:3-17 1:3-17 1... | The "trick" is to use <code>do.call</code>.
<pre><code>> a <- data.frame(x = c("1:1-15", "1:2-16", "1:3-17"))
> a
x
1 1:1-15
2 1:2-16
3 1:3-17
> a$x <- as.character(a$x)
> a.split <- strsplit(a$x, split = ":")
> tmp <-do.call(rbind, a.split)
> data.frame(a, tmp)
x X1 X2
1 ... | https://stats.stackexchange.com |
525,830 | [
"https://physics.stackexchange.com/questions/525830",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/245323/"
] | I have heard that it's possible for a permanent magnet to become too hot to function, especially if it reaches melting temperature however I cannot find much on the affect of cooling a magnet especially to temperatures around absolute zero.
| In the case of permanent magnets, there are two effects of temperature on the strength of the magnet:
<ul>
<li>saturation magnetization</li>
<li>coercivity</li>
</ul>
Both of these will be larger at low temperature, a stronger magnet.
A ferromagnetic material will order below its Curie temperature, often because of ... | Permanent magnets (ferromagnetic materials) arise from an emergent property of their structure. The exact physics of what makes certain elements magnetic is largely based on quantum mechanics and requires half-filled atomic orbitals etc. etc. etc.
The important thing to take away from this is that if an element has th... | https://physics.stackexchange.com |
816 | [
"https://mechanics.stackexchange.com/questions/816",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/374/"
] | When I drove a manual transmission, I got in the habit of shifting to neutral on long, shallow grades to save fuel. Now I'm driving an automatic (specifically, a recent Corolla) and still doing it.
But someone told me recently that being in neutral while moving can cause an automatic transmission to overheat, since th... | I don't think it will make a difference on gas mileage either way. Anytime the engine is running the front pump on the transmission is being turned by the torque converter and is lubricating the transmission which is also circulating fluid through the transmission cooler.
I don't see how it could cause premature failu... | Auto transmissions are designed to operate similarly to manual transmissions.
If you are coasting with an automatic transmission, all you are doing is the same as when you coast with a manual transmission.
It cannot damage the box if the engine is running and your transmission pump is working.
But the downside is: do ... | https://mechanics.stackexchange.com |
459,451 | [
"https://electronics.stackexchange.com/questions/459451",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/125622/"
] | Im trying to load 2 values in assembly under the tm4c1294ntpcd (Cortex M4) then add it with the next code
<pre><code> .global main
.text
main
BL LRut
LRut
LDR r5,=2172428;
LDR r6,=0x7CD32A58;
ADD r0,r5,r6;
STR r0,[r1];
END
</code></pre>
But it keeps saying errors... | It depends if the radiated light is diffused over the same area.
50Cd/m^2 = 50 nits would be a dim desktop monitor or a bright mobile.
Adding 10 in the same area with diffusion makes that 10x brighter.
But if not diffused each source would not appear to be brighter by neighbouring LEDs but the flux of radiated light... | You're comparing apples and oranges when you refer to 'brightness' and 'luminance'.<br>
'Brightness' is 'how bright is the light when I look at it', while 'luminance' is 'how will lit is the surface the light is shining on'.
Luminance is additive - if you shine more lights on the same surface, the surface gets more... | https://electronics.stackexchange.com |
195,168 | [
"https://softwareengineering.stackexchange.com/questions/195168",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/30343/"
] | I am creating a stored procedure that is logging some data. The data ultimately needs to end up in 2 tables. The incoming data is coming from a JSON string containing 15 parameters, and the data is then logged to the database using the stored procedure I'm writing. I would like to send the data into 1 stored procedure ... | I prefer to keep plenty (not <em>all</em>, but plenty) of the logic in the database for just a ton of reasons (and without getting into the whole "who needs stored procedures nowadays" argument).
Do this in your stored procedure.
These look like simple computations. Also use a transaction in your sproc to manage the... | I prefer to keep as much of the logic <em>outside</em> the database as possible. So that if the way calculations are done gets changes, I only need to update the code in the program and not mess around with the stored procedures.
I'm not sure how complex these calculations are, but if they do become a bottleneck you c... | https://softwareengineering.stackexchange.com |
2,595,913 | [
"https://math.stackexchange.com/questions/2595913",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/404078/"
] | Consider the system:
$$\begin{alignat}{2}
x_{1}' &=&~ -ax_2 &+ x_{1}\left(1-x_{1}^2-x_{2}^2\right),\\
x_{2}' &=& ax_1 &+ x_{2}\left(1-x_{1}^2-x_{2}^2\right)-b,
\end{alignat}
$$ where $a,b$ are real numbers. The task is to show that there is a disk which eventually contains every orbit ... | And now you can use AM-GM: $$1=\frac{(x+y)^2}{4}\geq\frac{(2\sqrt{xy})^2}{4}= xy.$$
I think the following way a bit of better.
By C-S we obtain:
$$\frac{x^2}{1+y}+\frac{y^2}{1+x}\geq\frac{(x+y)^2}{2+x+y}=1.$$
We can use also the Tangent Line method.
Indeed,
$$\sum_{cyc}\frac{x^2}{1+y}-1=\sum_{cyc}\left(\frac{x^2}{3-... | We have
$$ \frac{x^2}{1+y}+\frac{y^2}{1+x}= \frac{x^2}{3-x}+\frac{y^2}{3-y}.$$
Put $f(x)=\frac{x^2}{3-x}.$ Since
$$
f''(x)=\frac{18}{3-x} >0,
$$
$f(x)$ is convex function for $x<3.$
Then by Jensen inequality
$$
\frac{x^2}{3-x}+\frac{y^2}{3-y}=f(x)+f(y) \geq 2 f(\frac{x+y}{2})=2 f(1)=2 \cdot \frac{1}{2}=1.
$$
| https://math.stackexchange.com |
34,202 | [
"https://security.stackexchange.com/questions/34202",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/24668/"
] | On a Linux-based server, I follow basic practices as below:
<ol>
<li>Make the admin account password long and complicated enough (i.e. theoretically speaking, password cannot be cracked within reasonable time).</li>
<li>Monitor <em>all</em> incoming network traffic to the administrative files.</li>
<li>To extend the l... | Not making sure all security updates are applied? Remember, as the defender, you must win <em>100% of the time</em>. A hacker only needs to win once.
The steps you listed are also a lot easier said than done (except the password thing... and yet people still choose horrible passwords!).
2) Also, what's a "credible so... | If I might mangle Schneier's law:
<blockquote>
Anyone, from the most clueless amateur to the best systems administrator, can create a security system that he himself can't crack.
</blockquote>
| https://security.stackexchange.com |
126,241 | [
"https://chemistry.stackexchange.com/questions/126241",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/81005/"
] | <img src="https://i.stack.imgur.com/AjyFH.jpg" alt="enter image description here">
I am confused between option (2) and (4). Both lone pairs of nitrogen are localized, so next, I looked at the hybridization of <span class="math-container">$\ce{N}$</span> in each compound. As in (2), the <span class="math-container">$\... | A good way to compare basicity of basic compounds is to draw their corresponding conjugate acids and compare their stability. As you might figured out from drawing resonance forms of compound (2)'s conjugate acid (its protonated form ), the positive charge is going to be shared by the 3 nitrogens in the compound. On th... | See the stability of conjugate acid is very important. In case of secondary amine the basicity is appreciable but in guanidine system the conjugate acid is remarkably stable due to stabilizing conjugation that is occurring there.<img src="https://i.stack.imgur.com/Q63mi.jpg" alt="enter image description here">
| https://chemistry.stackexchange.com |
45,777 | [
"https://quant.stackexchange.com/questions/45777",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/41165/"
] | I'm trying to find a way to compute an optimized basket of n currency pairs based on 2 properties.
Let's say i have 50 pairs * 2 (long/short) = 100 possible items.
A basket has 2 properties to optimize: correlation and property X.
I want to have an optimized basket with configurable:
- maximum correlation between all ... | Firstly, I think you need to quantify a single score function - e.g. a combination of the correlation and X, that way you can rank solution A with some correlation and X value vs some solution B with a different correlation and X.
There may be more direct ways of finding baskets with particular properties; for exampl... | Still failing to see what you actually doing let me describe an optimisation process in general for a minimisation problem:
<blockquote>
For a starting point <span class="math-container">$x$</span> and function value <span class="math-container">$f(x)$</span>, find a search direction <span class="math-container">$p$... | https://quant.stackexchange.com |
459,357 | [
"https://physics.stackexchange.com/questions/459357",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/222092/"
] | If we consider an electrical field, or a gravitational field, and two points in this field, is the difference of potential between this two points depending of a frame of reference ?
It seems to me that in a uniform gravitational field (<span class="math-container">$\cong$</span> at the surface of Earth), the differen... | In ordinary Newtonian physics, when one changes reference frame, the gravitational potential energy does not change. On the other hand, the total energy of a particle is <em>not</em> the same in two different frames of reference. The kinetic energy does change, when one goes from one frame to another, so the total ener... | I may have misunderstood your question to be about relativity. I am leaving the original answer up below <strong>this one</strong>:<br>
The gravitational potential energy does not depend on reference frame in classical physics, as you note it only depends on h which does not change between reference frames. You can not... | https://physics.stackexchange.com |
488,128 | [
"https://physics.stackexchange.com/questions/488128",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/210696/"
] | The fully symmetric spin-up proton spin-flavour wave function in the constituent quark model is usually presented as follows:
<span class="math-container">$$\begin{align}
\frac{1}{\sqrt{18}} ~ (
&2 |u\uparrow ~ u\uparrow ~ d\downarrow \rangle
- |u\uparrow ~ u\downarrow ~ d\uparrow \rangle
- |u\downarrow ~ u\upar... | I'm not an expert in this, and this isn't explicitly group-theoretical, but here's my understanding of it:
If you set <span class="math-container">$a = -b = 1$</span> in the ansatz you've provided, you get something that factors out nicely:
<span class="math-container">\begin{align}
(
&\> |u\uparrow ~ u\uparr... | Michael Seifert's answer is exactly what I needed. An additional piece of information is also helpful: most configurations of <span class="math-container">$a$</span> and <span class="math-container">$b$</span> will not be eigenvectors of total square spin and isospin, <span class="math-container">$\hat{S}^2$</span> and... | https://physics.stackexchange.com |
130,455 | [
"https://dba.stackexchange.com/questions/130455",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/67793/"
] | I have a SSIS package which has the following:
<ol>
<li>Data Flow Task
<ul>
<li>OLE DB Source (select * from table1 where DateCol <= ISNULL(@DateVar,DateCol ))</li>
<li>OLE DB Destination</li>
</ul></li>
<li>DateVar variable</li>
</ol>
And I need to have a possibility to set value for DateVar or leave it empty or... | Heh... It was really easy.
All what I need is change query to:
select * from table1 where DateCol <= @DateVar OR @DateVar = ''
| You may be interested in a standard approach to solve this problem. It is something called <strong>short circuit</strong>. To illustrate it, here's the code:
<pre><code>DECLARE @chooseDate datetime2
--SET @chooseDate = '1966-04-08'
SET @chooseDate = NULL
SELECT *
FROM DimCustomer
WHERE @chooseDate IS NULL OR BirthDate... | https://dba.stackexchange.com |
146,908 | [
"https://mathoverflow.net/questions/146908",
"https://mathoverflow.net",
"https://mathoverflow.net/users/38200/"
] | Is there a model of set theory in which:
<ol>
<li>Every projectively definable family of sets of reals has an OD or projectively definable member;</li>
<li>Every OD or projectively definable set of reals has the property of Baire.</li>
</ol>
PS: By a projectively definable family of sets of reals I mean:
There exist... | Let me ignore the OD issue for a moment, and just prove that there is always a projectively definable family of sets of reals, with no projective member. Indeed, there is such a family consisting of a single set.
Namely, let $S$ be the full satisfaction relation on the reals for projective truth. Thus, $S$ consists o... | Probably "model of set theory" was intended to mean "model of $\mathsf{ZFC}$" but I thought it might be worth mentioning that if we consider models of $\mathsf{ZF}$ then the answer is yes—provided that for (1) we are satisfied with a member that is $\text{OD}_a$ for some real $a$ instead of a $\text{OD}$ member, ... | https://mathoverflow.net |
13,156 | [
"https://dsp.stackexchange.com/questions/13156",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/5665/"
] | When you plucked on a string, the string is vibrate and except the fundamental frequency,
there are an integer multiple of the fundamental frequency, which are the harmonics.
I know that the HPS algorithm is a tool to find the fundamental frequency, but
I don't understand the downsample part. How can I know how man... | OK Lets go!
I consider HPS a very simple algorithm, this image representation show exactly how HPS work !
<img src="https://i.stack.imgur.com/Ccs0H.jpg" alt="enter image description here">
Yeah is highly recommended apply a hann window for every framed data !
What do you need to do is apply one window function ove... | i might suggest looking up the good ol' Average Magnitude Difference Function (AMDF) or Average Squared Difference Function (ASDF) or Autocorrelation as means of determining the period which is the reciprocal of the fundamental frequency.
| https://dsp.stackexchange.com |
4,125,863 | [
"https://math.stackexchange.com/questions/4125863",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | When counting FLOPS, one must often compute
certain sums.
Prove the exact formula
<span class="math-container">$$\sum_{k=1}^nk^3=\frac{n^2(n+1)^2}{4}$$</span>
I have used the approximation <span class="math-container">$\sum_{k=1}^{n}f(k)\approx\int_{1}^{n}f(k)dk$</span> to find that
<span class="math-container">$$\sum... | First note that
<span class="math-container">$$
\frac{n^2(n+1)^2}{4} + (n+1)^3 = \frac{[n^2 + 4(n+1)](n+1)^2}{4} = \frac{(n+2)^2(n+1)^2}{4}
$$</span>
Then proceed by induction.
| If you are not a fan of induction, you can solve problems like these using something that's similar to the derivative for sums. If you have seen derivatives before, you may know the power rule, which shows that <span class="math-container">$\frac{d}{dx} x^n = \lim_ {h \to 0}\frac{(x+h)^n-x^n}{h} = nx^{n-1}$</span>. The... | https://math.stackexchange.com |
290,220 | [
"https://mathoverflow.net/questions/290220",
"https://mathoverflow.net",
"https://mathoverflow.net/users/61426/"
] | Define $A=(a_n)$ and $B=(b_n)$ as follows: $a_0=1$, $a_1=2$, $b_0=3$, $b_1=4$, and $$a_n=a_0b_{n-1}+a_1b_{n-2}$$ for $n \geq 2$, where $A$ and $B$ are increasing and every positive integer occurs exactly once in $A$ or $B.$ Can someone prove that $\lim_{n \to \infty} a_n/n = 4$?
Here are first terms and some eviden... | <em>[edit 12/01/2018: a remark]</em>.
The sequence $a_n-4n$ being unbounded also rules out any polynomial recurrence of the form
$$a_{n+r+1}=P(a_{n+1},\dots,a_{n+r})$$
for $P\in\mathbb{C}[x_1,\dots,x_{r}]$.
Otherwise $b_n:=a_{n+1}- a_{n}$ would also satisfy a polynomial recurrence
$$ b_{n+s+1}=Q(b_{n+1},\dots,b_{n+s... | Let $\alpha_*$, $\alpha^*$ denote the lower, respectively upper asymptotic density of the set $A$, and $\beta_*$, $\beta^*$ the lower and upper asymptotic density of the set $B$. Note that $$\limsup_{n\to\infty} {a(n)\over n}=1/\alpha_*\ ,\qquad\liminf_{n\to\infty} {a(n)\over n}=1/\alpha^*$$
$$\limsup_{n\to\infty} {b... | https://mathoverflow.net |
150,262 | [
"https://cs.stackexchange.com/questions/150262",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/149442/"
] | I am reading Introduction to the Theory of Computation by Michael Sipser and I am in chapter 5. It says here that the Post Correspondence Problem is undecidable, but thinking about it, given a collection, if someone permutes using the algorithm:
<pre><code>try every single permutation of the collection:
if it is a ... | Suppose that such a set <span class="math-container">$S$</span> existed. Consider the following program, which accepts an input <span class="math-container">$x$</span>:
<ul>
<li>Check whether <span class="math-container">$x \in S$</span>. If not, return TRUE.</li>
<li>Run <span class="math-container">$x$</span> on <spa... | I think there might be two questions in this.
<ol>
<li>Do all Turing complete programming languages have to contain infinite loops?
Yes. Turing complete <=> Simulate any Turing machines. As there are Turing machines with infinite loops your statement has to be true.
</li>
<li>How to (dis)prove your Conjuncture. O... | https://cs.stackexchange.com |
372,487 | [
"https://softwareengineering.stackexchange.com/questions/372487",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/260437/"
] | I know there has been 1 million and 1 discussions about Singletons on SO and here and I have had to clean up my fair share of terrible singletons in our code base; one of the reasons I am gun-shy here. But I am running into a situation where I feel like a Singleton is a reasonable solution and wanted to see what others... | The worst singleton problem after shared mutable state is a reference, which cannot be parametrized.
Use of stateless singleton is equivalent to use of ad-hoc instantiated class. Both are perfectly valid, if decoupling is deemed unnecessary. If decoupling is necessary, both would work fine, being injected in top leve... | My design for an alternative to singleton: static construction
<pre><code>public static void main() {
KbTypeMapper singleKbTypeMapper = new SpecificKbTypeMapper();
SomeClass x = new SomeClass(singleKbTypeMapper);
SomeOtherClass y = new SomeOtherClass(x, singleKbTypeMapper);
y.doSomethingFun():
}
</cod... | https://softwareengineering.stackexchange.com |
23,909 | [
"https://stats.stackexchange.com/questions/23909",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9524/"
] | Notes for my intro to probability class give a theorem which states the following:
<pre><code>P(A) = P(A ^ B) + P(A ^ ~B)
</code></pre>
What would the proof for this look like given the basic probability axioms?
Here's a list of axioms I start off with:
<pre><code>0 <= P(A) <= 1
P(True) = 1
P(False) = 0
P(A v... | From the set-theoretic equations
$$\eqalign {
A &= A \cap 1 \\
&=A \cap (B \cup \sim B) \\
&=(A \cap B) \cup (A \cap \sim B) \\
}$$
and
$$\eqalign {
(A \cap B) \cap(A \cap \sim B) &= (A \cap A) \cap (B \cap \sim B) = A \cap \varnothing = \varnothing
}$$
we apply the penultimate ... | First prove that $A=(A\cap B)\cup(A\cap B^c)$.
You may just draw a Venn diagram or do it formally, which means that you have to prove that $A\subset (A\cap B)\cup(A\cap B^c)$ and $(A\cap B)\cup(A\cap B^c)\subset A$.
<img src="https://i.stack.imgur.com/Vbv2n.png" alt="Venn diagram">
For example, to prove the first i... | https://stats.stackexchange.com |
283,260 | [
"https://electronics.stackexchange.com/questions/283260",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/137466/"
] | I am trying to use a DMA in circular mode to transfer data from an ADC to an array that will hold the data. I need to concurrently use the incoming data (in this case, I am using AT commands to send the data over Wi-Fi with the esp8266 module)
I am wondering what the software flow would look like.
Here are some quest... | <blockquote>
How will the DMAC know when to wrap around when it reaches the end of
the array? -- i.e. how can I ensure that the DMA won't transfer data
past the last array index? (Is this size limit defined by the
DMA_BufferSize?)
</blockquote>
Yes, it will either stop at the limit you set, or if you enable <s... | It appears that the STM32 DMA supports Double-Buffering operation (I'm no STM32 pro so I cannot tell you what the related API calls are). This is what you're actually looking for. This is how you handle it:
<ol>
<li>You configure size and memory location for two buffers. Usually those two are equally sized</li>
<li>Yo... | https://electronics.stackexchange.com |
450,402 | [
"https://physics.stackexchange.com/questions/450402",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/190849/"
] | The common way of finding the work done on some object is by applying the equation: force*displacement.
However, suppose we apply a force of F newtons on an object of mass M for a duration of T seconds. We can then express the work done in terms of T and F, by expressing the change in velocity in terms F and T and the... | Suppose you know that a constant force <span class="math-container">$F$</span> is applied for a distance <span class="math-container">$d$</span> then you know the work done is equal to <span class="math-container">$Fd$</span> - no further information is needed.
But suppose I tell you that a force <span class="math-con... | The <span class="math-container">${\bf F} \cdot {\bf l }$</span> definition can be recast in the form of <span class="math-container">${\bf F} \cdot {\bf v } dt$</span> just parametrizing the work differential form with time. But this rewriting is a mathematically equivalent way of expressing the same thing.
The key ... | https://physics.stackexchange.com |
128,704 | [
"https://physics.stackexchange.com/questions/128704",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/56326/"
] | I apologize if this question is trivial, but I am new to physics and am struggling with some of the basic concepts.
Working in $\mathbb{R}^2$ with standard coordinates $(x,y)$, suppose we have a particle of mass $m$ moving on a curve $(x(t),y(t))\in\mathbb{R}^2$. It's tangent vector (velocity vector) is $$x^\prime(t)\... | <blockquote>
"but how can you have a "basis" that changes at every point?"
</blockquote>
This is really the root of your problem. Mathematically (and physically) speaking, such a basis works fine. You just have a (hopefully temporary) conceptual problem.
Maybe try thinking of it this way: How does $\hat{x}$ know to... | In case anyone is interested I'll post here what I learnt. If anyone has any corrections or comments please let me know.
The thing that I was missing was that the metric makes the kinetic energy well defined, i.e. independent of coordinates. Working in $\mathbb{R}^2$ with standard coordinates $(x^1,x^2)$ we have the i... | https://physics.stackexchange.com |
3,535,654 | [
"https://math.stackexchange.com/questions/3535654",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/748063/"
] | <blockquote>
Prove the following inequality: <span class="math-container">$$ \int_{0}^{\frac{\pi}{2}}\frac{\sin
x}{\sqrt{9-\sin^{4}x}}\ \mathrm dx\geq\frac{1}{3}. $$</span>
</blockquote>
I am thinking of replacing the equation with <span class="math-container">$\int_{0}^{\frac{\pi }{2}}\frac{\sin x}{9-\sin^{4} x }... | <span class="math-container">\begin{align*}\int_{0}^{\pi/2} \frac{\sin{x}}{\sqrt{9-\sin^4{x}}}dx &\geq \int_{0}^{\pi/2}\frac{\sin{x}}{\sqrt{9}}dx\\& = \frac{1}{3}\int_{0}^{\pi/2} \sin{x}dx \\&=\frac{1}{3}[-\cos{\pi/2}-(-\cos{0})]\\&=\frac{1}{3}[0+1]\\&=\frac{1}{3}
\end{align*}</span>
The inequality... | The given inequality can be deduced from AM-GM. Indeed<span class="math-container">$$\begin{eqnarray*} I=\int_{0}^{\pi/2}\frac{\sin x}{\sqrt{9-\sin^4 x}}\,dx &=& \int_{0}^{1}\frac{z\,dz}{\sqrt{(9-z^4)(1-z^2)}}\\ &=& \frac{1}{2}\int_{0}^{1}\frac{du}{\sqrt{(3-u)(3+u)(1-u)}}=\int_{0}^{1}\frac{dv}{\sqrt{(2+... | https://math.stackexchange.com |
85,767 | [
"https://security.stackexchange.com/questions/85767",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/72250/"
] | I am writing a bachelor thesis and I am having a hard time figuring out the difference between phishing and DNS spoofing. From what I understand, DNS spoofing is a way to achieve a succesfull phishing of somebody's user name and passwords (or other credentials).
Do I understand it correctly ?
| Phishing is mostly a social attack, i.e. you might setup up a site which looks like a trusted one (i.e. copy of Paypal), give it a hostname which might fool the user (e.g. https-paypal.encrypted.whatever) so that the URL and links look trustable, put it together with some story ("detected hacking attempt, needs verific... | Phishing is a way of getting credentials by manipulating the victim in some way to give his credentials. An example will be a fake login page.
DNS spoofing is a method to alter the DNS information and bringing victim to your personalized server or not letting him access the website completely. It's one application is ... | https://security.stackexchange.com |
845,462 | [
"https://math.stackexchange.com/questions/845462",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/149933/"
] | I am having problems understanding how to extract this information into a formula.
<code>The sum of two nonnegative numbers is 1. Express the sum of the square of one and twice the square of the other as a function of one of the numbers.</code>
(<strong>note</strong>, i do have have the answer to the question, my q... | I will go through it very slowly so that you have lots of examples of how do things like this. Please don't be insulted; it just pays to be careful because this is a very detail-oriented task. First give the things you want to find names: they're natural numbers so I'll call one $n$, and one $k$.
Then look at the info... | Let the two numbers be $x$ and $y$. Then $x+y=1$. We need to express $g(x,y)=x^2+2y^2$ as a function of one of the numbers. If you want it to be a function of $x$ then, substitute $y=1-x$ in $g(x.y)$ will lead $g(x,1-x)=x^2+2(1-x)^2$. Call $f(x)=g(x,1-x)$. Then $f(x) = x^2+2(1-x)^2$.
If you want it to be a function o... | https://math.stackexchange.com |
19,942 | [
"https://mathoverflow.net/questions/19942",
"https://mathoverflow.net",
"https://mathoverflow.net/users/737/"
] | I have a n-by-k matrix A and a n-by-n matrix B, where B is positive definite. I can form the matrix $M = A^t B A$. Playing around, I always found $rk(M) = rk(A)$ but I can't prove this.
| $A^T BAx = 0 \implies (Ax)^TB(Ax)=0 \implies Ax=0$ by positve definiteness of $B$. So $ker(M)=ker(A)$ and hence $rk(M)=rk(A)$.
| This is rather tangential, but I can't help mentioning that this is related to the fact that in a hilbert space, for a (compact) linear operator one has: $Ker A^* \perp Im A$.
| https://mathoverflow.net |
51,216 | [
"https://quant.stackexchange.com/questions/51216",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/41681/"
] | Suppose I buy a call and then sell a call one dollar in strike higher. Suppose I get into this position for 10 cents lower than it is theoretically worth. (I.e if this spread is worth 0.50 I just bought it for 0.40). Then I delta hedge the spread to expiry. What will be my PnL? What will be my average PnL?
| If the actual dynamics are those of Black Scholes and if the vol used in the delta hedge is the actual vol, then the P&L will be 10 cents i.e. not random
and not dependent on the path.
| When you compare the market price to the theoretical price, your difference is model dependent.
Let's say you are using Black Scholes and you're using some other vol that you think is more appropriate (you're not using the IV because that would give you the market price)
Under the Black Scholes assumptions of continu... | https://quant.stackexchange.com |
10,011 | [
"https://robotics.stackexchange.com/questions/10011",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/11489/"
] | With the problem of stabilising an inverted pendulum on a cart, it's clear that the cart needs to move toward the side the pendulum leans. But for a given angle $\theta$, how much should the cart move, and how fast? Is there a theory determining the distance and speed of the cart or is it just trial and error? I've see... | There are lots of ways to solve this problem, which falls into the category of Control Engineering. There are two standard approaches:
Classical Control: The control command has to be proportional to a linear combination of the error, the rate of change of the error, and the integral over time of the error, a.k.a. ... | The theory that describes what you are looking for is call Control Theory. Search for the <em>Nonlinear Systems</em> textbook by Hassan Khalil for an excellent overview of the material--the inverted pendulum problem is addressed explicitly.
To theoretically stabilize the inverted pendulum on the cart, a model of the d... | https://robotics.stackexchange.com |
333,639 | [
"https://physics.stackexchange.com/questions/333639",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21146/"
] | In his QFT book, Matthew Schwartz first talks about tree level as follows:
<blockquote>
We will begin by going through carefully some of the predictions that the theory gets right without infinities. These are called the tree-level processes, which means they are leading order in an expansion in $\hbar$.
</blockquot... | Suppose you want to compute a correlation say in Euclidean signature
$$
\frac{1}{Z}\int D\phi\ \prod_i \phi(x_i)\ \exp\left(-\frac{1}{\hbar}S(\phi)\right)
$$
with
$$
S(\phi)=\frac{1}{2}(\phi,A\phi)+g\int dx\ \phi(x)^4
$$
where $(\phi,A\phi)=\int\ dx\ dy\ \phi(x)A(x,y)\phi(y)$ for some "matrix" or rather kernel $A$.
One... | In principle in QFT you want to calculate the interaction picture unitary time evolution operator. Then you can use the operator to evolve quantum states just like you would in normal quantum mechanics. So, for example, suppose you set up your particle accelerator to generate a certain state $|i\rangle$ at a time $t_0$... | https://physics.stackexchange.com |
133,942 | [
"https://security.stackexchange.com/questions/133942",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/105924/"
] | If I have a form that accepts inputs through the GET method, and can be generated vulnerabilities as XSS.
<strong>Using the POST method is possible to prevent vulnerabilities that can be generated through URL's?</strong>
For example, the following code is vulnerable to XSS, if the url is:
<code>example.com/?nickna... | No, using POST is no defense against XSS at all.
Sure, an attacker cannot simply send you a link that contains the payload, but they can send you a link to a webpage which contains HTML/JavaScript that submits the payload.
Example:
<pre><code><form method="post" action="http://yourserver.com/yourscript.php" id="... | Using POST offers the following advantages over GET:
<strong>Avoid the browser's URL history</strong>. Any sensitive data in the form is not passed in the URL, which means that data in the form are not visible in the browser history and cannot be shoulder surfed once submitted. (Note: the form body is sometimes store... | https://security.stackexchange.com |
15,666 | [
"https://physics.stackexchange.com/questions/15666",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5172/"
] | What is the current "consensus" on Max Tegmark's Mathematical Universe Hypothesis (MUH) which claims every concievable mathematical structure exists, including infinite different Universes etc.
I realize it's more metaphysics than physics and that it is not falsifiable, yet a lot of people seem to be taking a liking t... | The problem with such ideas is that they are empty words. In order to say what "exist" means, you need to specify an outcome of a physical measurement which confirms the existence. For example, the Elitzur Vaidman bomb-tester is a way of giving a logical positivist meaning to the existence of counterfactual worlds with... | The MUH is related to but separate from Multiverse theories. Multiverse theories are becoming quite respectable because of the String Landscape, eternal inflation, anthropic coincidences, Everett manyworlds, all of which point towards multiverses. MUH is more controversial, however given a broad-enough definition of "m... | https://physics.stackexchange.com |
58,388 | [
"https://softwareengineering.stackexchange.com/questions/58388",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/20212/"
] | It's been only several years since I migrated from Visual Source Safe to SVN. And SVN for me is still kinda "WOW! I can do so many things! SVN is so cool!"
But many people around me keep saying "SVN? Really? Meh..."
And there's so many of them that I'm worried. Should I move my team to Git / Mercurial or some other f... | It entirely depends on usage.
If you have one team of people in a room and they do most of their work there, if you have a build and deploy process you already like, and if you are not looking to share your code with people widely (as you would with an open source project), then you shouldn't sweat it.
I switched ma... | I believe one should never make decisions out of ignorance. If you don't know what you're missing, you should try git out long enough until you do, then you can make an informed decision. The jump to distributed control can't really be comprehended without trying it out, and letting go of some old habits while you do... | https://softwareengineering.stackexchange.com |
166,954 | [
"https://physics.stackexchange.com/questions/166954",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/46227/"
] | I have encountered something that is very confusing. My problem is this. I am assuming two infinite cubical Gaussian surfaces sharing a common side. One of the cubes contains a charge $q_1$ at a finite distance from the common surface and the second cube contains a charge $q_2$ at a finite distance from the common sur... | You have two distinct errors. One is claiming that because the electric field goes to zero at infinity so does the flux. The flux is the integral of the electric field over the surface. The electric field goes down as $\frac 1{r^2}$, but the area goes up as $r^2$, s the flux constant. Ask Gauss about this. The sec... | Your problem is the assumption "both the charges contribute flux to their respective Gaussian surfaces only at the common surface."
When you take your surface out to infinity you are also increasing its area, so even though the electric field goes to zero, the integral of the electric field over your surface will be n... | https://physics.stackexchange.com |
1,889,537 | [
"https://math.stackexchange.com/questions/1889537",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/258516/"
] | Let <span class="math-container">$b_1,b_2,\dots,b_n$</span> denote non-zero real numbers satisfying <span class="math-container">$\sum_{i=1}^n {b_i}=0$</span>. Prove that there exists a permutation <span class="math-container">$ a_1,a_2,\dots,a_n$</span> of these numbers such that <span class="math-container">$a_1a_2+a... | What do you get when you sum over all possible permutations?
You get <span class="math-container">$$2n(n-2)!\sum\limits_{1\leq i<j\leq n}a_ia_j=2n(n-2)!\dfrac{(a_1+a_2+\dots+a_n)^2-\sum\limits_{i=1}^na_i^2}{2}=-n(n-2)!\sum\limits_{i=1}^na_i^2.$$</span>
Since this sum is negative at least one sumand is negative.
| We consider a random permutation of $b_1,b_2,b_3,\cdots,b_n$
like $a_1,a_2,\cdots,a_{n} $ and define $X_i=a_ia_{i+1},X_{n}=a_{n}a_1$.
$$E[X_i]=\sum_{(v,w)}{b_vb_w}\times P(a_{i}={b_v},a_{i+1}={b_w})$$
$$=\sum_{(v,w)}{b_vb_w\times{\frac{(n-2)!}{n!}}} \ \ \ \ \ \ \ \ \ \ $$
Now consider $X=\sum_{i=1}^{n}{X_{i}}$ the... | https://math.stackexchange.com |
102,348 | [
"https://math.stackexchange.com/questions/102348",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/23645/"
] | Of course, if you plug the cube root of 9 into a calculator, you get an endless stream of digits. However, how does one prove this on paper?
| Suppose that $9^{1/3}=m/n$ with $m$, $n$ integers with ${\rm GCD}(m,n)=1$.
This may be assumed because if $d$ is an integer divisor of both $m$ and $n$, then $m/n=(m/d)/(n/d)$.
Then
$$
9n^3=m^3
$$
so that $3$ divides $m^3$, hence $m$ since $3$ is prime. Thus $3^3=27$ divides both sides of the equality so that $3$ di... | By the rational root test, if
$$P(x) = a_nx^n+\cdots +a_0$$
is a polynomial with integer coefficients, and $\frac{u}{v}$ is a rational number with $\gcd(u,v)=1$ such that $P(\frac{u}{v})=0$, then $u$ divides $a_0$ and $v$ divides $a_1$.
(This holds in any GCD-domain, even if there is no unique factorization into prim... | https://math.stackexchange.com |
118,243 | [
"https://stats.stackexchange.com/questions/118243",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/56043/"
] | Let independent random variable $Y_1,...,Y_n$ have respective distributions $N(0,\sigma^2x_i^2)$, where $i=1,2,...,n$ are known constants such that $x_i\neq 0$ for all $i=1,2,...,n$. Find the maximum likelihood estimator of $\hat{\sigma}^2$, of the unknown parameter $\sigma^2$.
My attempt:
The likelihood function is ... | I think you miss square of $y_i$ in the likelihood. Then the Likelihood is $\Pi_{i=1}^n\frac{1}{\sqrt{2\pi x_i^2 \sigma^2}}e^{-\frac{y_i^2}{2x_i^2 \sigma^2}}=e^{-\sum_{i=1}^n\frac{y_i^2}{2x_i^2 \sigma^2}} \Pi_{i=1}^n\frac{1}{\sqrt{2\pi x_i^2 \sigma^2}}$. Taking log-likelihood and differentiating w.r.t. $\sigma$, you ge... | <ol>
<li>the density function $f_i$ of $Y_i \sim \mathcal{N}(0, \sigma^2 x_i^2)$ is
$$
f_i (y_i) = \frac{1}{\sqrt{2 \pi \sigma^2 x_i^2}} \mathrm{exp}\left\{ - \frac{1}{2} \frac{(y_i - 0)^2}{\sigma^2 x_i^2} \right\}$$</li>
<li>e.g. $x_1 = -1$ and $x_2 = \dots = x_n = 1$, so
$$\prod_{i=1}^n \frac{1}{\sqrt{x_i^2}} = \frac... | https://stats.stackexchange.com |
134,798 | [
"https://cs.stackexchange.com/questions/134798",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/118707/"
] | Given a directed graph <span class="math-container">$G=(V, E)$</span>, two nodes <span class="math-container">$s, t \in V$</span> and a subset of nodes <span class="math-container">$U \subseteq V$</span>.
Provide an algorithm that determines if there is a shortest path from <span class="math-container">$s$</span> to <s... | <span class="math-container">$d_{t}(s)$</span> denote the shortest path length from <span class="math-container">$s$</span> to <span class="math-container">$v$</span> in <span class="math-container">$G$</span>.
<span class="math-container">$d_{t}(v)$</span> denote the shortest path length from <span class="math-contain... | The purpose of the BFS in the transposed graph is to eliminate edges that are part of shortest paths to <em>some</em> vertex, but not to <span class="math-container">$t$</span>. These "useless" edges could otherwise lead to false positives in the traceback phase that builds <span class="math-container">$c(\cd... | https://cs.stackexchange.com |
56,927 | [
"https://physics.stackexchange.com/questions/56927",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/22011/"
] | Because the indefinite integral of the electric field results in a negative value? (As the function is proportional to $r^{-2}$?
I've got to be missing something... Help please!! Thanks!
Also, I took the integral from infinity to the radius of the charged sphere and got
$$V = \int_\infty^R{\frac{q*dr}{4*\pi*\epsilon... | $V_f - V_i = \int_i^f \vec{E} \cdot d \vec{r}$. The dot product has a sign depending on the relative orientation between the electric field $\vec{E}$ and infinitesimal displacement $d \vec{r}$. Also note that as you move radially inwards from infinity to some point, the displacement $d \vec{r} = \vec{r_f} - \vec{r_i}$ ... | You are missing the minus sign itself!<br>
The electric potential at the surface of the sphere is the work done by you on unit positive charge moving it against the forces of the field to bring that charge from place with zero potential (this place is $R\rightarrow\infty$) to the surface of the sphere.<br>
Work done by... | https://physics.stackexchange.com |
93,029 | [
"https://security.stackexchange.com/questions/93029",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/40087/"
] | The way I see it: there are two ways to encrypt data for a web app.
1) Store a single encryption key on the server, and use it to encrypt / decrypt data at runtime. The obvious issue here is that if a hacker does gain access to your server, it's only a matter of time until they find the encryption key and then all hop... | It depends on from which threats are you going to protect.
Encrypting data on database level is great protection, when you have so many IT employees, that you're able to divite them into teams responsible for each layer.
For example, banks and credit cards acquirers use PCI DSS security standard, which require such p... | Nothing is futile, and there are no silver bullets. Everything depends.
There was a sidebar about using disk encryption. That is protecting against a different attack surface, so lets ignore it.
The question asks if it makes sense to encrypt data that is in a database, under the assumption that it needs to be plain... | https://security.stackexchange.com |
155,878 | [
"https://physics.stackexchange.com/questions/155878",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/68717/"
] | I'm working through an introductory electrodynamics text (Griffiths), and I encountered a pair of questions asking me to show that:
<ol>
<li>the divergence transforms as a scalar under rotations</li>
<li>the gradient transforms as a vector under rotations</li>
</ol>
I can see how to show these things mathematical... | There are a number of ways of mathematically formalizing the notions "transforming as a vector" or "transforming as a scalar" depending on the context, but in the context you're considering, I'd recommend the following:
Consider a finite number of types of objects $o_1, \dots, o_n$, each of which lives in some set $O_... | I think you have the right idea, but I'll try to write it in a more elucidating notation.
The first thing to make clear is that for this discussion we are only ever working at a single point. We only care about transforming the coordinates that describe the domain to the extent this induces changes in the associated <... | https://physics.stackexchange.com |
443,615 | [
"https://electronics.stackexchange.com/questions/443615",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/224265/"
] | Ive got about 36 batteries that all stay between 2.8v and 3.6v, and I want to be able to accurately monitor the voltage(and therefor the state of charge) of all of them using an Arduino Nano, the two ways I can think of is use some analog multiplexers to get the 36 different batteries down to the 6 analog pins on the A... | Mean and RMS are two different measurements which both have a use. It's not that mean current is somehow "wrong" and RMS current is "right". The kind of measurement you need will depend on what you plan to do with the value.
RMS is useful for <em>power</em> measurements assuming a constant load resistance, because pow... | For a DC supply of near constant voltage, it is the average current taken by the load multiplied by that constant DC voltage that yields true power consumption. Any AC content in the current does not contribute to average power consumption on a stable DC supply. Why: because a sine wave multiplied by a DC value is stil... | https://electronics.stackexchange.com |
638,194 | [
"https://physics.stackexchange.com/questions/638194",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/299900/"
] | I'm starting my studies now, and wondering why a lot of things that at the beginning I don't know if the motivation is based on the intuition of concrete thinking or the logic of abstract thinking, and this is the case with the definition of vectors. I understood that the vectors are composed by direction and magnitude... | A vector is not a line. Nor is it "something that has magnitude and direction".
A vector is instead <strong>a type of mathematical object</strong> that can be <strong>used to represent</strong> things with magnitude and direction, or even just direction. That is, vectors come <em>first</em>, "magnitude a... | A vector is NOT a line. It has a magnitude, which is conveniently represented on paper as a line of a given length, but such a representation is purely for the convenience of the person who is working a particular physics problem. A vector also has a direction, which must be specified relative to some reference point... | https://physics.stackexchange.com |
436,634 | [
"https://physics.stackexchange.com/questions/436634",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20134/"
] | I am very much familiar with Atomic spectroscopy, not much with nuclear spectroscopy.
In atoms (electronic cloud), we have electromagnetic interaction that plays the leading role, whose exchange boson is the photon, and that's why we have photon spectroscopy.
Now, we have the nucleus, where allegedly strong force pla... | 1) In QCD without the electro-weak interaction every nucleus has many excited states (states with energies above the ground state energy) that are absolutely stable. This is because both the total baryon number and the total charge (the number of protons and the number of neutrons) are conserved, and because angular mo... | In both atomic and nuclear spectroscopy, we can gain information about the spacing of the energy levels inside an object by exciting the object and then looking at the energy emitted when it transitions back to the ground state. In atoms, this energy is in the form of photons in the infrared/visible/UV range. In nuclea... | https://physics.stackexchange.com |
72,856 | [
"https://math.stackexchange.com/questions/72856",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/15618/"
] | Let <span class="math-container">$F$</span> be a finite field.
How do I prove that the order of <span class="math-container">$F$</span> is always of order <span class="math-container">$p^n$</span> where <span class="math-container">$p$</span> is prime?
| <ol>
<li>Prove that the smallest multiple $m$ of 1 that gives zero has to be a prime. (Otherwise there are divisors of $m$ which are then divisors of zero.)</li>
<li>Prove that a field is a vector space over a subfield.</li>
<li>Count the elements of the field if the dimension of this vector space is $n$.</li>
</ol>
| Let <span class="math-container">$p$</span> be the characteristic of a finite field <span class="math-container">$F$</span>.<span class="math-container">${}^{\text{Note 1}}$</span> Then since <span class="math-container">$1$</span> has order <span class="math-container">$p$</span> in <span class="math-container">$(F,+)... | https://math.stackexchange.com |
115,950 | [
"https://electronics.stackexchange.com/questions/115950",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/45891/"
] | This is the circuit: <img src="https://i.stack.imgur.com/hVk5Y.png" alt="http://i.stack.imgur.com/hVk5Y.png">
I've simulated it and got a current of 30.76mA at the voltage source (5V).
With this I've calculated the total resistance to be 162.5 Ohm.
Each resistors is 100 Ohms big.
But why is this the case?
My first (a... | The trick here is to simplify.
Starting from the furthest point away from the power source, combine the resistors in pairs and replace those pairs with a single resistor. Keep going until you have only one resistor.
\$R_3\$ and \$R_6\$ add together to form a single resistor. That new resistor (we'll call it \$R_{36... | You're right about the eqivalent resistance being 162.5 Ohms, but there is little we can do to verify this through a direct approach without knowing the values of each resistor in your schematic.
All I can help you with is to say that you would go about this by simply using the relationships between series/parallel r... | https://electronics.stackexchange.com |
50,960 | [
"https://security.stackexchange.com/questions/50960",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/15194/"
] | I'm responsible to create new accounts for some services on my job. Some of these service do not allow password change by the user, so in the case the user wants to change its password, he would need to tell me it or I should change it and tell him. In any case, the password has to be send.
So far I've been using emai... | Email is insecure. Emails can be lost, misdirected, eavesdropped and faked. Sending a password by email is a big vulnerability.
"We" do it nonetheless because in some situations alternatives are just worse for usability reasons. And we apply mitigation measures:
<ul>
<li>The password is temporary and does not allow a... | Obviously it is not ideal that users cannot change their passwords. But I take it that you have no capability to modify these applications; you need to operate what you have as securely as you can.
I do recommend you flag issues like this to your management, partly in the hope they will get the developers to make chan... | https://security.stackexchange.com |
15,433 | [
"https://mechanics.stackexchange.com/questions/15433",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/9431/"
] | Last week end, I rented a car, fairly new car (probably 1 year old).
On the way to give it back, 20 minutes before arriving, the gearbox just broke. I couldn't accelerate etc.
During the week end, I did maybe 300 km, and although my driving is not the best, I highly doubt I'm the only responsible for that gearbox iss... | As far as I know rental companies have insurance that covers this sort of thing. This may be a good time to contact a lawyer.
You can't break a gearbox by doing the wrong thing in traffic. You would destroy the clutch first. The only ways to destroy a gearbox is by running it without oil (not your responsibility becau... | Not knowing what type of car it is, how many miles were on the car, or even whether it's a manual or automatic (assuming automatic), this is all I have for you ...
To easy your mind a little, any single 300km stint is not going to cause a transmission to go bad. The problem is, the transmission chose <strong><em>your<... | https://mechanics.stackexchange.com |
111,678 | [
"https://math.stackexchange.com/questions/111678",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/25404/"
] | Is
$$\bigcup_{p<\infty}\ell_p=c_0 ?$$
At least one inclusion obvious: every $p$-summable sequence converges to zero.
| Consider
$$
x(n)=\frac{1}{\log(n+1)}
$$
It is easy to check that $x\in c_0\setminus \left(\bigcup_{1\leq p<\infty}\ell_p\right)$. Indeed
$$
\lim\limits_{n\to \infty} x(n) = \lim\limits_{n\to \infty}\frac{1}{\log (n+1)}=0
$$
so $x\in c_0$. Now for fixed $p\in [1,+\infty)$ there exist $N\in \mathbb{N}$ such that f... | Prove: If $V$ is a separable Banach space, then $V$ cannot be written as a countable union of proper linear subspaces.
Because of inclusions among the $\ell_p$ spaces, your union is, in fact, equal to a countable union.
| https://math.stackexchange.com |
51,226 | [
"https://physics.stackexchange.com/questions/51226",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/19854/"
] | Say I have a hollow cylinder and I wanted to strap it down to the bed of a truck. I would tension the strap on one end, and it would exert a force on the cylinder. My intuition tells me that the strap would crush the hollow cylinder down toward the truck bed, but when I think about it, there are inward forces perpendic... | You have successfully discovered that the kinetic energy depends on the reference frame.
That is actually true. What is amazing, however, is that while the value of the energy is frame DEpendent, once you've chosen a reference frame, the law of conservation of energy itself is <b>NOT</b> reference frame-dependent -- e... | As you say, energy is <em>not</em> invariant under reference frame change.
Imagine a moving ball. It has kinetic energy, but if I move in its reference frame, it doesn't. It's as simple as this.
There's no need to make up for the missing energy.
| https://physics.stackexchange.com |
436,881 | [
"https://math.stackexchange.com/questions/436881",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/85147/"
] | <img src="https://i.stack.imgur.com/YU3nI.jpg" alt="enter image description here">
i want to find $$\frac{1}{2\pi i}\int _\gamma \frac{1}{z}dz$$
well $0$'s winding number is $2$, so $\frac{1}{2\pi i}\int _\gamma \frac{1}{z}dz=2$
but when I explicity calculate the integral I get
$$\frac{1}{2\pi i}\int _\gamma \frac{... | The imaginary part of logarithm increases as you go around the origin.<br>
It is the angle between z and the positive real axis.<br>
As you go around from 3 to -1 to $\sqrt{2}$, that angle increases from 0 to $\pi$ to $2\pi$. So the imaginary part of $\log(\sqrt{2})$ is $2\pi$.<br>
$\log x$ has lots of complex values,... | An exaggerated idea to try to understand a little more that branch cut thingy of the logarithmic function: let us try to divide the given path in several semicircles, say
$$\begin{align*}\gamma_1&:=\{z\in\Bbb C\;;\;|z-1|=2\;,\;\;\text{Im}\,(z)\ge 0\}\\
\gamma_2:&=\left\{z\in\Bbb C\;;\;\left|z-\frac{\sqrt2 -1}2... | https://math.stackexchange.com |
2,742,453 | [
"https://math.stackexchange.com/questions/2742453",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/552861/"
] | I know lambert function is available to solve function like $xln(x)$, I wonder if there is a similar way I can solve function $b - x log_2(1+\frac{a}{x})=0$.
| An example to broaden your thinking:
$$f(x)=\begin {cases}\frac 12 & x \in \Bbb Z\\
x-\lfloor x \rfloor & x \not \in \Bbb Z \end {cases}$$
This is bounded between $0$ and $1$ but achieves neither. It is not continuous, but we were not asked for that. It is a fine function, delivering a single output for every... | $f\colon \mathbb{R}\to \mathbb{R}$ means "to", not "onto", so $f(x)=\arctan x$ is a good example.
| https://math.stackexchange.com |
63 | [
"https://dba.stackexchange.com/questions/63",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/39/"
] | In MySQL, is it better to always allow nulls unless you know a field is required, or always use <code>Not Null</code> unless you know a field will contain nulls? Or doesn't it matter?
I know in some DBMSs they say to use <code>Not Null</code> as much as possible because allowing nulls requires an extra bit (or byte?)... | In most DBs a <code>NOT NULL</code> column will be more efficient in terms of stored data for the reason you state, and also more efficient to query and index - so unless you want to allow NULLs in a column you should explicitly disallow them.
There will be a slight performance implication, as the extra <code>NOT NULL... | You should let your schema design and application requirements guide this decision. The performance differences are probably not noticeable either way in most cases.
| https://dba.stackexchange.com |
2,788,059 | [
"https://math.stackexchange.com/questions/2788059",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/451403/"
] | Two soldiers A and B shoot a bullet towards a target. If the probability that
$A$ shot the target is $0.4$ and $B$ shot the target is $0.7$ Find the probability of:
a. Only one shot the target
b. At most one of them shot the target
My solution:
a. $P(A \cup B) - P(A \cap B)$
since A and B are independent, then
$... | For a) you could use the law of total probability: set $A$: only one hits, this becomes:
$$
P(A) = P(A|S_1)P(S_1) + P(A|S_2)P(S_2)
$$
You are given marginal probabilities. For the conditional, it means: $P(A|S_1)$: probability the first one hits AND the second misses (and vice versa), so $P(A|S_1) = 0.4 \times 0.3$ and... | Your first answer is indeed correct. Perhaps a quicker way to do it would be to say $$\underbrace{P(A')}_{A\text{ does not hit}}=0.6; \underbrace{P(B')}_{B\text{ does not hit}}=0.3$$
then Probability of only one hitting is:
$$P(B)P(A')+P(A)P(B')=0.54$$
<hr>
For the second, add $P(A')P(B')$ for when neither of them hi... | https://math.stackexchange.com |
566,457 | [
"https://physics.stackexchange.com/questions/566457",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/41677/"
] | <strong>My Background:</strong>
In high school, I completed AP Physics C Mechanics and Electricity and Magnetism. In my first year of undergrad, I completed a course on Newtonian Mechanics and a course on Special Relativity and Electromagnetism which both approximately followed the sections on those topics in the Feynm... | Most of what you said is right.
<blockquote>
If the energy-momentum tensor is known, the Einstein field equations can be used to solve for the metric tensor
</blockquote>
This is wrong. For example, suppose the energy-momentum tensor is zero. There are still many possible metrics, including Minkowski space, versions of... | <blockquote>
If the energy-momentum tensor is known, the Einstein field equations
can be used to solve for the metric tensor (i.e. the Schwarzschild
metric is the solution for the metric tensor if the energy-momentum
tensor is that of a spherical star or black hole).
</blockquote>
The metric tensor depends also on the ... | https://physics.stackexchange.com |
86,561 | [
"https://dsp.stackexchange.com/questions/86561",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/61292/"
] | For example if I have the following transfer function:
<span class="math-container">$$H(s) = \frac{1}{\cosh(\sqrt{s/10})}$$</span>
Can I do the bode plot it in matlab or do I need to rationalize it beforehand?
| If that's a problem for you, I recommend taking a basic Matlab class first.
<pre><code>%% plot a transfer function
% frequency axis
omega = logspace(-2,2,1000)';
% calculate the trasnfer function
H = 1./cosh(sqrt(1i*omega/10));
% and plot it
clf;
subplot(2,1,1);
semilogx(omega,10*log10(H.*conj(H)));
grid on;
ylabel('L... | Matlab's <code>bode</code> function is just a wrapper for calculating a system response and then graphing it.
So, just do that by hand.
| https://dsp.stackexchange.com |
59,741 | [
"https://cs.stackexchange.com/questions/59741",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/44791/"
] | I have a set of points (tiny triangles) $K=\{1,2,\ldots, k\}$ and a set points (tiny circles) $N=\{1,2,\ldots, n\}$ and a matrix of positive real values $\mathbf{D}=\left[d_{ij}\right]$ for all $i\in K$ and for all $j\in N$. The entry of the matrix $d_{ij}$ can be viewed as the Euclidean distance between triangle $i$ a... | There are lots of community detection algorithms that need the number of communities as input. For example, Bigclam [1], a matrix factorization approach, needs the number of communities as input. Another example is the seed expansion [2] method that needs the number of communities as input. I'm sure there are many algo... | A very simple algorithm is as follows:
<pre><code>while #components < n
delete the lightest edge in the graph
</code></pre>
But perhaps you want to define more precisely what you want from your algorithm, e.g. which measure you want to maximize. Most community detection algorithms have some tuneable parameters.... | https://cs.stackexchange.com |
228,762 | [
"https://mathoverflow.net/questions/228762",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Let $a_n\in \mathbf{N}$ be an infinite sequence such that $\forall i\neq j, a_i\neq a_j$.
I have the following theorem:
<blockquote>
For $0<c<\frac{3}{2}$, there are infinitely many $k$ for which $[a_k,a_{k+1}]>ck$, where $[\cdots]$ denotes least common multiple.
</blockquote>
<strong>Idea of proof</stron... | In fact there are sequences $\{a_k\}$ of pairwise distinct positive integers
such that $[a_k, a_{k+1}] \ll k^{1+\epsilon}$ for all $\epsilon > 0$.
We first exhibit a sequence with
$[a_k, a_{k+1}] \ll k^{3/2} \log^3 k$ for all $k>1$, which already disproves
the conjecture that $[a_k, a_{k+1}] \gg k^2$ infinitely ... | Here is a counterexample for the exponent 2. But I think it should be wrong also for some smaller exponents.
We construct $(a_k)$ by blocks. The $n$th block consists of all the numbers of the form $(2n-1)2^t$, where $t$ is an integer satisfying $0\leq t\leq 10+\log_2 n$. The values of $t$ inside the block are ordered ... | https://mathoverflow.net |
2,423,737 | [
"https://math.stackexchange.com/questions/2423737",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/28816/"
] | In general, if $t \in \mathbb{N}$, when is it true that
$$\sqrt{2^{2t}} = 2^t = 2t?$$
I know of course that it is true when $t - 1 = \log_{2}(t)$. Are there other (<em>more arithmetic</em>) conditions, for which the equation $2^t = 2t$ holds, for $t \in \mathbb{N}$?
It appears to be true when $t = 2^s$, for some $s ... | The first equality is true: $\sqrt{2^{2t}}=\sqrt{2^{t+t}}=\sqrt{2^t\cdot2^t}=2^t$.
The second holds only for $t=1$ and $t=2$. Indeed, define for $t\in\Bbb R$ $$f(t)=\cfrac{2^{t}}{2t}$$ and $$g(t)=\ln f(t)=t\ln 2-\ln 2-\ln t$$
Now,
$$g'(t)=\ln2-\frac1t$$
We see that $g'$ vanishes only at one point, namely $t=1/\ln 2$.... | Proposition:
$2^t \gt 2t$ for $t \gt 2,$ $ t \in \mathbb{N}.$
Proof by induction:
0)True for $t=3.$
1) Assume true for $t.$
2) Step: Show for $t+1.$
$2×2^t = 2^{t+1} \gt $
$2×2t =4t \gt 2(t+1)$.
| https://math.stackexchange.com |
79,930 | [
"https://cs.stackexchange.com/questions/79930",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/63873/"
] | In books, I have read that FCFS suffers from convoy effect. I think that even SJF and priority(both preemptive and non preemptive) can suffer from convoy effect.
In SJF, if a process with large burst time arrives first then no other process can preempt it causing convoy effect.
In preemptive and non preemptive priori... | This seems like a rather difficult question. Here is one approach.
Every 3CNF on $n$ variables can be encoded as a binary string of length $8n^3$ (how?). Consider the following two languages:
$$
\begin{align*}
L_1 &= \bigcup_{n=1}^\infty \{ xy0^{8n^3} : |x|=n, |y|=8n^3, \text{$x$ is an assignment satisfying the 3C... | I have other idea, I am not sure if it is correct:<br>
Let $k$ will be number of clauses and $n=5$ number of variables.
I reduce $3-$SAT problem, for each clause $c_i=(x_1, x_3, \neg x_5)$ I create language $$L_i= \{1\{0,1\}\{0,1\}\{0,1\}\{0,1\},\{0,1\}\{0,1\}1\{0,1\}\{0,1\}, \{0,1\}\{0,1\}\{0,1\}\{0,1\}0 \}$$<br>
So $... | https://cs.stackexchange.com |
2,615,396 | [
"https://math.stackexchange.com/questions/2615396",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/523523/"
] | The question is find the vector equation for the line passing through two points P1 = (6,2,4) and P2 = (12,0,3)
But the formatting of the answer is throwing me off. Should I just find the difference between these two points?
The answer format is as follows:
[x,y,z] = [0,0,0] + t[0,0,0]
| The equation of the line in <span class="math-container">$\mathbb{R}^n$</span> can be represented as <span class="math-container">$\vec{x} = \vec{u} + t \vec{v}$</span>, where <span class="math-container">$\vec{u}, \vec{v} \in \mathbb{R}^n$</span> are some constants and <span class="math-container">$\vec{x} = (x_1, x_2... | You just apply the formula:
<span class="math-container">$$M=P_1+t \,\overrightarrow{P_1P_2}\quad (t\in\mathbf R),$$</span>
where the coordinates of <span class="math-container">$\overrightarrow{P_1P_2}$</span> are very simply the difference of the coordinates of <span class="math-container">$P_2$</span> and <span clas... | https://math.stackexchange.com |
102,810 | [
"https://mathoverflow.net/questions/102810",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15424/"
] | I don't known the correct credit for the following: every non-empty $\Pi^1_1$ set of reals contains some $X \in L_{\alpha}$ for some $X$-recursive $\alpha$. (Addison-Kondo?)
So, my question is: what is the least $\beta$, s.t. $\mathcal{P}(\omega) \cap L_\beta$ is a basis for all non-empty $\Pi^1_1$ sets?
| I can't access the full paper at the moment, but I'm pretty sure this is exactly the question addressed in the paper "A Note on the Kondo-Addison Theorem" by D. Guaspari
| The least such ordinal is the least ordinal which cannot be a $\Delta^1_2$-well-ordering over natural numbers.
Let $$\delta^1_2=\mbox{ supremum of the }\Delta^1_2 \mbox{
wellorderings of } \omega,$$ and $$\delta=\min\{\alpha\mid
L\setminus L_{\alpha}\mbox{ contains no }\Pi^1_1 \mbox{
singleton}\}.$$
We claim that $\... | https://mathoverflow.net |
90,903 | [
"https://softwareengineering.stackexchange.com/questions/90903",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/5024/"
] | As most projects use a C++ API, they deal with constraints of the API and constraints of the project itself.
I'm a beginner at programming, I don't like to use OOP at all because nobody clearly managed to explain to me WHY it's is so important to restricting yourself with private scope to prevent others programmers to... | Have you ever heard the saying <strong>"No man is an island"</strong>?
For most programmers this is true. Hardly anyone writes code that is "just an app". On many non-trivial apps one programmer writes the UI which needs to be easily modified by a designer. It also must allow for clear data binding to the business log... | <blockquote>
Any fool can write code that a computer can understand. Good
programmers write code that humans can
understand. ~Martin Fowler
</blockquote>
That, in a nutshell, is why you want to care about beautiful code.
You don't write code for the computer. The computer only understands binary code anyway ... | https://softwareengineering.stackexchange.com |
20,452 | [
"https://stats.stackexchange.com/questions/20452",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/8289/"
] | My primary question is how to interpret the output (coefficients, F, P) when conducting a Type I (sequential) ANOVA?
My specific research problem is a bit more complex, so I will break my example into parts. First, if I am interested in the effect of spider density (X1) on say plant growth (Y1) and I planted seedling... | What you are calling type II SS, I would call type III SS. Lets imagine that there are just two factors A and B (and we'll throw in the A*B interaction later to distinguish type II SS). Further, lets imagine that there are different $n$s in the four cells (e.g., $n_{11}$=11, $n_{12}$=9, $n_{21}$=9, and $n_{22}$=11). ... | For illustration I assume a two dimensional ANOVA model specified by <code>y ~ A * B</code>
<h2>Type I ANOVA</h2>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th>Line term in ANOVA table</th>
<th>Hypothesis from model</th>
<th>Hypothesis to model</th>
</tr>
</thead>
<tbody>
<tr>
<td>A</td>
<td>... | https://stats.stackexchange.com |
598,137 | [
"https://electronics.stackexchange.com/questions/598137",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/296197/"
] | Why is it, when I'm powering a circuit via a lab bench power supply set to limit 2 mA and the current drawn from the circuit reaches the limit, the supply voltage drops?
| That is called Constant Current Constant Voltage (CC/CV). The power supply has to lower the voltage to keep the current at the limit, when the current limit is reached. If the voltage were to keep rising then the current limit you set would be violated.
Imagine if you had a simple resistive load. If the voltage goes up... | First, any two-terminal device can control its current <em>or</em> its voltage <em>or</em> some combination of the two. You can't control both independently without controlling the two-terminal device to which it's connected.
Second, most lab supplies are constant-voltage/constant current supplies. They're designed t... | https://electronics.stackexchange.com |
20,020 | [
"https://dba.stackexchange.com/questions/20020",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1642/"
] | If I want to run a query that will only execute on the master mysql server and not the slave. assuming we have an environment with replication through query logs. Could I and how?
The idea is to have some records that are archived on the slave. Lets say the master is a production website and only requires data that ha... | <h1><em><strong>There is a much, much simpler way</strong></em></h1>
A Replication Slave relies on the Master's binary logs so as to ship SQL from them into the Slave's local relay logs. Just <em>tell the Master not to record the SQL</em>
<pre><code>SQLSTMT="SET SQL_LOG_BIN=0;"
SQLSTMT="${SQLSTMT} DELETE... | The only way is for you to have another table with the same data and <strong>exclude</strong> that from replication in <code>my.cnf</code>.
MySQL's replication is going to copy and execute every statement you perform on the relevant tables and/or databases. So when you execute something on the master, the slave will a... | https://dba.stackexchange.com |
308,006 | [
"https://physics.stackexchange.com/questions/308006",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/96114/"
] | [I've seen several related questions but I ask for a confirmation here.]
I have a set of point charges to model atoms, say:
$q_1$ at $(x_1,y_1,z_1)$
$q_2$ at $(x_2,y_2,z_2)$
...
$q_n$ at $(x_n,y_n,z_n)$
Is the electric field at a given point $\vec{r}_j$ simply:
$$\vec{E}_{j} = k\sum_{i=1}^n \frac{q_i}{\vec{r}_{i... | Almost correct; the problem is that electric fields are vectors (replacing your $1/r_{ij}^2$ with $1/r_{ij}$ you'd get a valid expression for the electric potential, which is a scalar).
Instead the electric field at a point $\vec r$ is:$$\vec E(\vec r) = \sum_{i=1}^n\frac{q_i (\vec r - \vec r_i)}{4\pi\epsilon_0|\vec r... | The expression fails if $\vec r_j$ is a point where there is a charge, i.e. if $\vec r_i-\vec r_j=0$. Basically, the field becomes technically infinite there. In some cases, it is possible to find a workaround using Gauss' law to find the field of charge distributions where there is charge, but for a discrete distrib... | https://physics.stackexchange.com |
3,723,883 | [
"https://math.stackexchange.com/questions/3723883",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/800869/"
] | If you are trying to prove <span class="math-container">$x \to y \ \ \text{or} \ \ z$</span>, how do you prove by contradiction? Do you split into two cases, or do you assume both are false?
| Determining for any statement if there is a proof with <span class="math-container">$n$</span> symbols or less is an <span class="math-container">$NP$</span> problem (i.e. the proof can be checked in polynomial time with respect to the length of the proof and the statement), that's probably the sense in which they mean... | The "P versus NP" problem is a single yes-no question: is <span class="math-container">$NP = P$</span>? The correct answer is either "yes" or "no", we just don't know which. But the complexity of the answer is <span class="math-container">$1$</span>.
| https://math.stackexchange.com |
65,336 | [
"https://dba.stackexchange.com/questions/65336",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/38561/"
] | I am trying to design a database relational model for an assignment. First, I design the ER diagram, and then the relational model with tables (schemas).
Here's my question: Is it possible for an entity to have only one attribute?
To put a bit more to this: is it possible or logical to come to a relation with a single... | Yes, but.
If an entity only has one attribute, then that attribute must serve as an identifier for the entity. Typically, if only one attribute is found for an entity in the given data stream, then another attribute is "invented" for purposes of identifying. It's often called "id", it's often an integer, and it's of... | Walter Mitty's answer is good, but I'd like to add something.
If the column contains unique values, the surrogate key (the <code>id</code> column) can be added only for performance reasons. But this makes little sense if the other column is small (integer, date...) and the DBMS does not organise tables by primary key ... | https://dba.stackexchange.com |
615,278 | [
"https://electronics.stackexchange.com/questions/615278",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/194626/"
] | I want to make a retro computer around a 6809E and a CPLD. It occurs to me that the physical layout/design of this board would be nearly identical for all the 40 pin, 8 bit CPUs except for power and ground. I want to use a Lattice ispMACH 4000ZE for the CPLD (3.3V I/O, 5V tolerant) and primarily I'm interested in the Z... | <ol>
<li>A PMOS/NMOS pair for every pin, to connect it to VCC/GND. Those typically are best obtained as H-bridges that integrate mosfets and interface to logic level control inputs.
</li>
<li>Two rotary decimal switches (like DIP switches but look like potentiometers) for each VCC and GND pin selection.
</li>
<li>8 BCD... | The common solution in such cases (ICs with different voltages) is to use level translators. An example would be the 74LV8T245 for an 8-bit bus. You generally don't want to change the ground reference of a design, unless you absolutely have to.
| https://electronics.stackexchange.com |
328,513 | [
"https://physics.stackexchange.com/questions/328513",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/134670/"
] | In any situation, while applying torque upon any rigid body, can the reference point/axis be any arbitrary point/axis?
I mean, is it necessary for the reference axis to be taken only through the centre of mass?
Also should the reference axis be stationary? That is, can we take a moving or accelerating axis as referen... | The restrictions on the useful set of refernce points that we can use for rotation dynamics comes from the following algebra.
Let
$$
{\bf L}_{\bf R}= \sum ({\bf r}_i-{\bf R}(t))\times m_i\dot {\bf r}_i
$$
be the total angular momentum of the collection of mass $m_i$ particles about the point ${\bf R}(t)$.
Then
... | It is not exactly necessary to take the reference axis to pass through CM. This is done to lower the mathematical complications. But if we take some other point all the data has to referred with respect to that point.
<ul>
<li>the torque is to be taken $wrt$ that reference axis.</li>
<li>also important to consider th... | https://physics.stackexchange.com |
67,756 | [
"https://mathoverflow.net/questions/67756",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15770/"
] | Let G be a group and g and h be elements in G. If g commutes with all conjugates of g and h commutes with all conjugates of h, can one conclude that gh commutes with all conjugates of gh?
Thanks!!
| No; the smallest counterexamples are given by the groups SmallGroup(54,5) and SmallGroup(54,6) (in GAP's SmallGroups library); these are groups of the form
$$G_1 = ((3 \times 3) : 3) : 2 \text{ and } G_2 = (9 : 3) : 2.$$
In both cases, there are 15 elements with the given property (i.e. that they commute with all their... | You have that the normal subgroups $U, V$ generated by $g$ and by $h$ are Abelian. This only implies that $UV$ is normal and solvable of class 2. Take the group of unitriangular 3 by 3 matrices $H_3$ over
${\mathbb Z}_p$.
It has two normal Abelian subgroups $U,V$ containing the center (= the derived subgroup) genera... | https://mathoverflow.net |
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