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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|---|---|---|---|---|---|
109,662 | [
"https://cs.stackexchange.com/questions/109662",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/105614/"
] | Given two strings, A and B, of the same length <span class="math-container">$n$</span>, find whether it is possible to cut both strings at a common point such that the first part of A and the second part of B form a palindrome.
I've tried bruteforce, and this can be achieved in <span class="math-container">$O(n^2)$</s... | <strong><em>Some notations in Python convention</em></strong>
<ul>
<li><span class="math-container">$S[:i]$</span> means the first <span class="math-container">$i$</span> letter of string <span class="math-container">$S$</span>. </li>
<li><span class="math-container">$S[-i:]$</span> means the last <span class="math-co... | I'm assuming by cutting at a common point you mean that only one cut can be made at the same index in both Strings and the resulting string must be of the same length as the original length of Strings A and B, and that A <em>must</em> be the first string and B <em>must</em> be the second?
In this case, this algorithm ... | https://cs.stackexchange.com |
357,545 | [
"https://stats.stackexchange.com/questions/357545",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/214841/"
] | Lets consider the following approach:
(1) We estimate a simple linear regression model y = b0 + b1*x + error. The input data in our model estimation shall be:
y = 1 month stock returns (cross sectional) for month n
x = market cap for each stock (cross sectional) for month n
(2) We test if our coefficient b1 is statis... | To answer that, you need to ask yourself what a model is. For example, a simple univariate linear model <span class="math-container">$y = \beta_0 + \beta_1 x$</span>, where you have 2 parameters <span class="math-container">$\beta_0, \beta_1$</span> and input data <span class="math-container">$x$</span>. You can predic... | Remember that 'parameter' is different in statistics; instead of merely an argument to a function, a parameter is a value that describes a population.
| https://stats.stackexchange.com |
119,756 | [
"https://physics.stackexchange.com/questions/119756",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10456/"
] | How do I definitively show that there are only <strong>two</strong> propagating degrees of freedom in the Lorenz Gauge $\partial_\mu A^\mu=0$ in classical electrodynamics. I need an clear argument that
<ol>
<li>involves the equations of motion for just the potentials $A^0$ and $\mathbf{A}$, and <em>not</em> the elect... | <blockquote>
I would like to know how exactly the equations of motion in the Lorenz
gauge removes the second degree of freedom.
</blockquote>
In the Lorenz 'gauge', we have
$$\Box A^{\mu} = \mu_0j^{\mu}$$
If $A^{\mu}$ is a solution, then so is $A^{\mu} + N\epsilon^{\mu}e^{-ik\cdot x}$ if
$$\Box (N\epsilon^{\mu}... | The sourceless non-homogeoneous Maxwell equations are given by:
$$
0 = \partial_\mu F^{\mu \nu} = \partial^2 A^\nu - \partial_\mu \partial^\nu A^\mu
$$
After imposing the Lorentz gauge, this becomes:
$$
0 = \partial^2 A^\nu
$$
Clearly, this equation has the solution (remember that $p^\mu p_\mu = E^2 - \mathbf{p}^2=0$)... | https://physics.stackexchange.com |
70,547 | [
"https://mathoverflow.net/questions/70547",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7206/"
] | Haar measure is a measure on locally compact abelian groups which is invariants to translations. For example, the Lebesgue measure on the reals is such measure.
It can be shown without the use of the axiom of choice that the Haar measure exists and it is unique up to a scalar, that is if we want the measure of the uni... | If $(X,\mathcal{S})$ is standard Borel space and $\mu$ a continuous measure on $(X,\mathcal{S})$ then there is a Borel isomorphism $F:X\to [0,1]$ that sends $\mu$ to Lebesgue measure on $[0,1]$. (See Kechris 17.41.) Since the isomorphism preserves measure this shows that any measurable subset of $[0,1]$ has measurable... | Solovay's model will have all subsets measurable as long as the group is (locally compact) metrizable. For "big" groups (non-metrizable) the Haar measure is naturally defined on the Baire sets (the least sigma-algebra so that all continuous real-valued functions are measurable), and extension even to the Borel sets may... | https://mathoverflow.net |
22,274 | [
"https://robotics.stackexchange.com/questions/22274",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/28170/"
] | I am new to ROS development and Staubli robots. Though i have some prior knowledge on UR5e, I am finding it hard to understand the architecture of Staubli and its other programming interfaces (like staubli robotics suite) and more importantly, is there a way to send commands to the robot from remote system via TCP/IP??... | Even at zero speed, stepper motors have a max torque, called the holding torque. If your design needs even higher torque than that, you <em>could</em> use a bigger (heavier, more expensive) motor. Alternatively, use a ratio in the belt drive.
To be concrete: a 1:2 ratio will double the available torque, but at the expe... | As r-bryan answered they do increase the effective torque. However that also increases the effective resolution giving you better repeatability. As an example a direct drive motor that provided a 0.1 degree repeatability using a 4 to 1 ratio belt drive would give you a 0.025 degree resolution. The trade off is a lower ... | https://robotics.stackexchange.com |
264,701 | [
"https://mathoverflow.net/questions/264701",
"https://mathoverflow.net",
"https://mathoverflow.net/users/93538/"
] | <blockquote>
I am looking for some non-trivial examples of (smooth) 4-mflds $M,N$ such that $M$ and $N$ are STABLY diffeomorphic. I.e. $$M\sharp_n (S^2\times S^2) \cong N \sharp_r (S^2\times S^2)$$ for $r,n$ not necessarily the same
</blockquote>
By non trivial I mean that $M$ and $N$ are not diffeomorphic or that $... | The main examples of this go back to work of Moishezon and Mandelbaum in the late 1970s. For instance, if a simply-connected elliptic surface E(2n+1) is homotopy equivalent to the connected sum of $4n+1$ copies of $\mathbb{C}P^2$ blown up $20n +9$ times, but those manifolds are not diffeomorphic for $n>1$. This is a... | Since the examples given above are smooth, simply connected, and homotopy equivalent, they are also homeomorphic. You might like the following examples. Let <span class="math-container">$L$</span> and <span class="math-container">$L'$</span> be 3-dimensional lens spaces that are homotopy equivalent but not homeomorphi... | https://mathoverflow.net |
7,494 | [
"https://scicomp.stackexchange.com/questions/7494",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/4469/"
] | I am running a mesh independence study. I start with <b>Mesh 1</b> and proceed up to <b>Mesh 4</b>, each time doubling the number cells in the mesh. In parallel, I am comparing my computational results to experimental data. <b>M. 1</b> shows poor results. <b>M. 2</b> shows a significant improvement and a good match to ... | No. As the mesh size $h\rightarrow 0$, the solution on a given mesh converges to the solution of the differential equation (assuming a well-posed PDE and a suitable discretization). Consequently, if your discrete solution on M2 is closer to experimental results than that on M3 or M4, then there are only two possibiliti... | I claim that the independent mesh <em>is</em> the best one. Say the actual solution is $U$ and your solver delivers an $u_h$ depending on a mesh parameter $h$. Then you can do the estimate for the distance of $u_h$ to the actual solution
$$\|U-u_h \| \leq \|U-u_m \| + \|u_m - u_h\|,$$
where $u_m$ is the solution of the... | https://scicomp.stackexchange.com |
17,433 | [
"https://dba.stackexchange.com/questions/17433",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1350/"
] | This is a different question than the one with the almost-identical title.
Again, this is more curiosity about how Oracle Database works than anything I need to change (yes I know multiple extents are fine, I read Tom Kyte too).
I have a table with the following characteristics:
<pre><code>Initial Ext: 1.44GB
Next E... | The data you're getting from Toad appears to be incorrect or, at least, misleading. If you are using a locally managed tablespace with automatic extent allocation, Oracle will determine your initial and next extent sizes automatically. In 11.2, the first 16 extents are going to be 64k in size (for a total of 1 MB). ... | To give details for future reference, Toad appears to be getting its information as follows:
<pre><code>Size: dba_segments.bytes
Initial Ext: dba_segments.initial_extent
Next Ext: dba_segments.next_extent
Num Extents: dba_segments.extent
</code></pre>
This is not the 10% sampling I mentioned, but I have see... | https://dba.stackexchange.com |
273,047 | [
"https://dba.stackexchange.com/questions/273047",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | I want to setup mysql replication between two servers one of them is my localhost and the other is online server.
I have all availability to make any one of them the master.
But according to that my localhost server doesn't have a static IP, i need to know which server of the two (master & slave) is the one which r... | I finally found out how to display a <code>bytea</code> column as a text!
I can use the function <code>convert_from</code> like so:
<pre><code>SELECT event_type, convert_from(metadata, 'UTF8') as metadata
FROM public.events
ORDER BY created_at DESC
LIMIT 100
</code></pre>
Then I'll have the metadata column in a human-... | <blockquote>
How can I get rid of this encoded, so that I only see the original
value of the column, in the text format
</blockquote>
Bytes have 256 possible values, when there are only about 95 visualizable ASCII characters, (the range [32:126]), so the mapping between ASCII text and binary representation cannot be on... | https://dba.stackexchange.com |
681,364 | [
"https://physics.stackexchange.com/questions/681364",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/316017/"
] | In Dirac's state vector notation, the position representation is given by :<br />
<span class="math-container">$$ |\psi\rangle = \int d^3r\;\psi(\mathbf{r})|\mathbf{r}\rangle$$</span>
My questions:
<ol>
<li>Is the State Vector Different from the wave function?</li>
<li>Can there be an energy representation of the state... | Current is not a vector; it doesn't have a direction in the same way that a velocity has a direction.
There is a good analogy between electric current in a wire and the flux or rate of flow of water through a pipe. The idea here is that we put an imaginary surface right across the interior of the pipe. It can be on the... | It is! Sort of.
You are thinking just straight Coulombs which might make sense in a 1D-application or so, you can pretend that charges have no spatial extent and are just individual point particles and travel along well-defined paths... But when you start dealing with three dimensions you start wanting to smear out ind... | https://physics.stackexchange.com |
124,446 | [
"https://softwareengineering.stackexchange.com/questions/124446",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/34116/"
] | I have used an MDA (model driven architecture) tool in the past where we modeled via UML and this generated the business entities (our domain model) and the ORM (mapping etc) amongst other things.
A lot of the business code and services working on the domain were part of the model and our repositories were returning t... | <blockquote>
so it would have been impossible to switch out to another ORM (not
that we wanted to)).
</blockquote>
That seems wrong. A major advantage of the repository pattern is that you hide the data access logic and that it is easily exchangeable.
<blockquote>
So far it feels as though I put my business log... | <blockquote>
However, if I wanted to continue to use the MDA tool for the ORM part
of the application, the model created here would be very anemic (i.e
not contain any business logic).
</blockquote>
I don't know which MDA tool you're using, but the ones I've worked with always create partial classes so you're fr... | https://softwareengineering.stackexchange.com |
38,753 | [
"https://engineering.stackexchange.com/questions/38753",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/29462/"
] | I am an undergraduate student in Electrical and Computer engineering. In our 5th semester we have a obligatory "Introduction to control systems course". I was wondering if these bunch of math theories is applicable to other directions of my school rather than the obvious (in the next semester we choose majors... | Yes, the ACI Standard 318 does specify “Concrete protection for reinforcement” (cover) for various issues, including: 1) standard placement in “principle structural members”, 2) reinforcement in extremely corrosive atmospheres, 3) fire protection, 4) bars, inserts and plates intended for future expansion, 5) precast co... | By definition, embedded items that stick out of the concrete have to have a reduced concrete cover. Otherwise they wouldn't stick out of the concrete.
What you see specified in the ACI code is concrete cover over reinforcing steel that is serving some long-term purpose. The minimum concrete cover is specified to provid... | https://engineering.stackexchange.com |
350,449 | [
"https://softwareengineering.stackexchange.com/questions/350449",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/65549/"
] | Say I have an MVP app. Should the Presenter handle events raised by the view. For example, please see the code below:
<pre><code>public void TextBox_TypeValidationCompleted(object sender, TypeValidationEventArgs e)
{
//do something
}
</code></pre>
and the code below:
<pre><code>public vo... | In order to keep your code organized and maintainable, I would say it is better to handle the event in the Presenter. The purpose of the view is to display information to the user. The purpose of the presenter is to execute logic and work as a middle man between data and users.
| This should not be handled by the view, as the view is only responsible for defining the layout of the UI.
Also, you should go with 2, handling it in the presenter directly. The presenter should also, in my opinion be responsible for wiring up the event; the views knowledge of the presenter should be minimized.
<pre>... | https://softwareengineering.stackexchange.com |
210,136 | [
"https://dba.stackexchange.com/questions/210136",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/133617/"
] | I have a <code>SELECT</code> that is very slow when using <code><</code> operator I'm looking for fixes or workarounds to perform this operation:
<pre><code>EXPLAIN (ANALYZE)
SELECT *
FROM "users"
WHERE (engagement_level(social) < 1)
AND (social_peemv(social) < 33.333333333333336)
AND (array['Uni... | You have a classic column dependence problem. PostgreSQL thinks there will be 4035 rows that meet the WHERE clause based on estimates. If I take the actual selectivities you reported and multiply them (which is correct only if each one is independent of the others), I get 8032 rows. But the true value is 20. Appare... | In the fast query, you're returning 0 rows. That's easy. PostgreSQL sees <code>social_peemv(social)</code> and has a juicy statistics estimate for it and scans <code>idx_in_social_peemv</code>. It returns 0 rows and the query is done.
In the other one you're saying <code>< 33.333333333333336</code>. As this means n... | https://dba.stackexchange.com |
8,465 | [
"https://security.stackexchange.com/questions/8465",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/2666/"
] | While using a wireless network recently that implemented a captive gateway, I noticed that any third party DNS servers manually set would not allow the network to connect properly.
This would seem to have the advantage of being able to block sites via DNS and not have people bypass that block by using an alternative ... | What are your goals? I think your goal is to <em>block</em> sites by denying name resolution. If that is your goal, it won't work.
<ol>
<li>Using IP addresses will still get to the sites.</li>
<li>Using a local hosts file (/etc/hosts) avoids the DNS protocol while providing for a limited subset of name resolution.</... | You could block all DNS requests except those to and from the DNS servers specified in DHCP by blocking port 53 on external connections.
Further you could relate those requests to a particular IP and revoke the DHCP lease.
Of course, this wouldn't stop someone from using a HOSTS file. It also wouldn't stop someone if... | https://security.stackexchange.com |
724,930 | [
"https://physics.stackexchange.com/questions/724930",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/333740/"
] | For an inductor in a circuit without a power source, does the induced emf found by using the mutual inductance value include self inductance, or is the self induced emf considered separately?
From Faraday's law I know that the induced emf is found by considering the total flux, and that this is equal to the self induce... | The key realization is that the equality
<span class="math-container">$$
\int_\mathcal{V} \vec{\nabla} \cdot \vec{E} \, dV = \int_\mathcal{V} \frac{\rho}{\epsilon_0} \, dV
$$</span>
must hold for <em>all volumes</em> <span class="math-container">$\mathcal{V}$</span>. By this, I mean that it is true when we integrate b... | The integral equation
<span class="math-container">$$\iiint_V (\nabla\cdot \vec{E})\ dV =\frac{\iiint_V \rho\ dV}{ε_0}$$</span>
is true for <em>every</em> volume <span class="math-container">$V$</span> independent of its shape.
This can only be true if the integrand functions
on the left and right side
are equal at eve... | https://physics.stackexchange.com |
488,411 | [
"https://electronics.stackexchange.com/questions/488411",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/218450/"
] | A 10 kVA transformer, its iron loss is 120 W, the copper loss is 240 W (full loading), now when the load factor is 0.9 delay, what is the efficiency when the transformer is in half loading?
The answer said <span class="math-container">\$\eta=\frac{\frac{1}{2}*10K*0.9}{\frac{1}{2}*10K*0.9+120+\frac{1}{2}^2*240}\$</span... | Because <span class="math-container">\$P=I^2R\$</span> since Copper loss is resistive loss so it is proportional to current squared.
Half the loading means half the wattage which means half the current <strong>IF</strong> your voltage stays the same. After all, you changed the loading to reduce the wattage right? You ... | The <span class="math-container">\$I^2R\$</span> loss is <span class="math-container">\$240\ W\$</span> at defined at full load of <span class="math-container">\$10\ k\mathit{VA}\$</span>.
The <span class="math-container">\$I^2R\$</span> loss at half load of <span class="math-container">\$5\ k\mathit{VA}\$</span> is <... | https://electronics.stackexchange.com |
61,060 | [
"https://mechanics.stackexchange.com/questions/61060",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/40441/"
] | I understand that lower viscosity oils are way easier to pump and move around engine parts, also they form a thinner "film" on friction surfaces which could improve parts measurements precision etc.
Is it only due to increased piston rings leakage that we don't use extremely thin oils?
Are they more prone to failure i... | Thin oils tend to have a very poor shear stability, especially when they are hot. The function of the oil is to protect and lubricate the engine and ancillaries (i.e. turbo chargers). In certain applications it also makes up some (where an oil cooler is employed) or all (for aircooled engines such as the Beetle) of t... | Tribology is a huge topic...
But, the thinner the oil, then the more oil in terms of volume and/or the higher pressure is needed for a given tolerance between bearing and surface.
So many things are taken into account when specifying the oil for a particular use. Operating temperature, load on the bearings, relative ... | https://mechanics.stackexchange.com |
37,159 | [
"https://dba.stackexchange.com/questions/37159",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/7718/"
] | How can I determine or estimate the size of the SQL dump file prior to using something like mysqldump?
| Please run this query:
<pre><code>SELECT
Data_BB / POWER(1024,1) Data_KB,
Data_BB / POWER(1024,2) Data_MB,
Data_BB / POWER(1024,3) Data_GB
FROM (SELECT SUM(data_length) Data_BB FROM information_schema.tables
WHERE table_schema NOT IN ('information_schema','performance_schema','mysql')) A;
</code></pre>
Th... | Based on the other answer, if you want a one liner to determine the size in bytes to use in a shell script, you can use this:
<pre><code>mysqlSizeBytes="$(mysql --database=information_schema --skip-column-names --silent --execute "SELECT Data_BB FROM (SELECT SUM(data_length) Data_BB FROM information_schema.ta... | https://dba.stackexchange.com |
277,027 | [
"https://physics.stackexchange.com/questions/277027",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/31572/"
] | Let us consider two different quantum field theories in 4 dimensional Minkowski spacetime, call them theory A and theory B, with 8 supercharges.
(i.e. 4D $\mathcal{N}=2$ theories). Let $G_A$ be the flavor symmetry group of A, and $G_B$ the flavor symmetry group of B.
<ol>
<li>Is it true that if $G_A$ and $G_B$ are iso... | 1.) NO
2.) Consider the lagrangian theories with gauge group G= USP(2N), four fundamental hypers and one antisymmetric, all these models have flavor symmetry SU(2) x SO(8), but the higgs branch is different in each case and it is the N-instanton SO(8) moduli space. These are different Hyper-Kahler manifolds with dimen... | This is an interesting question. My first sense was to say this is negative. However, maybe the Higgs branch for symmetries for gauge symmetry if equal to that for the Higgs on the color symmetries of fermions of that force. This is maybe an interesting research topic. It may have been pursued, maybe within the context... | https://physics.stackexchange.com |
392,677 | [
"https://physics.stackexchange.com/questions/392677",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/178349/"
] | From what I understand from the textbook, a two-particle bosonic wave function is symmetric, because you can exchange the position of the two particles and have the same wave function. But I think exchanging the position has nothing to do with symmetry. Symmetry means $f(x)=f(-x)$, not exchanging position. So I am conf... | We the physicists use to speak in a very particular way, but we don't notice because we are used to it. Lazyness makes us ommit many surnames, but all symmetries need a surname. You can't say "a function is symmetrical", you should say "a function is symmetrical <strong>to the y-axis</strong>. You always have to specif... | Because bosons are not fermions they do not obey Pauli exclusion principle. Hence they can have same quantum states. Thus if you stack up 2 bosons you should expect that the wave functions should not be different otherwise they aren’t bosons. Hence this symmetry. If symmetry would not exist then these would be fermions... | https://physics.stackexchange.com |
341,043 | [
"https://stats.stackexchange.com/questions/341043",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/199063/"
] | No apologies: I have not attempted to research this (beyond reviewing the list of questions CV provided that may have answered this query). I taught this in class last week for diagnosing logistic multiple regression models, and I warned the students in advance that I did not know the origins of the name.
What is the... | The earliest <em>book</em> reference that I know of is
<blockquote>
Woodward, P. M. (1953). <em>Probability and information theory with applications to radar.</em> London: Pergamon Press.
</blockquote>
but the concept, which was developed during World War II for the analysis of radar receivers, might have been pub... | Earliest article I can find is from 1954:
<ul>
<li>Peterson, W., Birdsall, T., Fox, W. (1954). The theory of signal detectability, <em>Transactions of the IRE Professional Group on Information Theory</em>, 4, 4, pp. 171 - 212. </li>
</ul>
Abstract:
<blockquote>
An optimum observer required to give a yes or no ... | https://stats.stackexchange.com |
412,796 | [
"https://electronics.stackexchange.com/questions/412796",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/207624/"
] | This question is regarding a 3D printer, specifically its heat bed. The head bed is a PCB heater with a resistance of 0.9 Ohms, so it's drawing around 13 Amps when supplied with 12 Volts.
I recently switched from Bang-Bang to PID controlled bed heating. The stock firmware pulsed On/Off with about 5 seconds each cycle.... | <blockquote>
So I was wondering, do the faster cycles cause more stress on the components
</blockquote>
Probably not. In fact, switching faster may stress component less.
Rationale: when switching slow, components have time to heat up and cool down on each cycle, which causes thermal expansion and contraction cycle... | <blockquote>
Although the total amount of energy used for heating should be less now since the heating is more efficient and doesn't waste energy by cooling down, I am a bit concerned of the fast pulsing of the rather high amperage.
</blockquote>
It's probably about the same. The heater cools down and heats up for a... | https://electronics.stackexchange.com |
12,148 | [
"https://astronomy.stackexchange.com/questions/12148",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/9267/"
] | Nuclear fusion is the main way for stars to generate energy. But we know that nuclear fission and fusion are not controlled, then it causes chain reaction and sudden explosion. But why in the case of stars it does not happen? I mean, that nuclear fusion happen in stars but it take few billion years to complete the amou... | Because in most stars, the pressure where nuclear burning takes place is proportional to temperature. In order for the nuclear reaction rate to increase, the temperature and hence pressure must increase. This would cause the gas to push out the layers above it, then to expand and cool.
Conversely, if the nuclear react... | Adding to Rob explanation. Once that equilibrium stops the bang happens known as Supernova and for smaller stars(our Sun) they will swell in to Red Giants.
| https://astronomy.stackexchange.com |
289,096 | [
"https://electronics.stackexchange.com/questions/289096",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | <blockquote>
In an npn power transistor the collector current is 20mA. If 98 percent of
the electrons injected into base region reach collector then the base
current in mA is nearly ?
</blockquote>
Here, in this problem is it okay to take \$\beta=I_c/I_b=98/2=49\$ ?
| It sounds like they mean 98% of the emitter current, not the base current. That means you're given \$\alpha = 0.98\$. You can use that to calculate \$\beta\$ and find the base current.
| You don't need to know \$\beta\$ to answer the question. Just Kirchoff's Current Law.
| https://electronics.stackexchange.com |
480,890 | [
"https://electronics.stackexchange.com/questions/480890",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/242485/"
] | I’m looking to make my own kiln coils and I wanted to know
<ol>
<li>why are the coils coiled? </li>
<li>When the coils are stretched too far apart they run cold and when they are close together they run hot. What is the reason for this if resistance doesn’t change whether a wire is coiled or straight?</li>
</ol>
| <blockquote>
I wanted to know first off why the coils are coiled?
</blockquote>
Suppose the wire is 10 m long. If you don't coil it, some of the heat it produces is "here" and some of the heat is 10 m away. Coiling it means you can heat a small area instead a long skinny area 10 m long.
<blockquote>
when the coil... | In addition to the accepted answer, coils also offer physical advantages in taking up the change in length when heated without sagging. The wire becomes brittle after use so the spring in the coil makes it easier to reroute into the channel in the firebrick if a coil pops out (heat the wire up when you do this).
I thi... | https://electronics.stackexchange.com |
53,520 | [
"https://quant.stackexchange.com/questions/53520",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/42799/"
] | Look at this trade:
<pre><code>Sequence Side Quantity @ Price
1. Buy 10 @ 1,0 (with leverage of 50)
2. Sell 10 @ 1,2 (inherits the leverage of 50?)
</code></pre>
Imagine that this trade is a CFD or a forex with USDEUR. I use a leverage of 50 for buy. How should I include this leverage... | PnL = Profit - Funding Costs
PnL = (Exit - Entry) - (50 * Capital - Capital) * Funding Rate
% Gain = PnL / Capital
Capital is how much you are investing (inclusive of margin). Your funding costs is 49 * Capital as that is how much you are borrowing to get to 50x leverage.
| Yes, that is right.
You could also do:
Pnl = (Exit - Entry) * Leverage
To save yourself multiplying by leverage twice.
There are also costs associated with putting trades on/off so these should be taken into consideration.
| https://quant.stackexchange.com |
457,436 | [
"https://physics.stackexchange.com/questions/457436",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/200375/"
] | For a purely inductive and capacitive ac(sinusoidally varying) circuit, average power dissipated across a capacitor or an inductor is zero. Then does that mean RMS current is zero?
| The water is supercooled,that is below 0°C . So density of water is probably not the issue. The hydrostatic pressure is also unlikely to be significant for a small bottle. If there were nucleation sites, supercooling would not have been possible.
The key issue is the necessity to disturb the water by giving it a "bang... | Three possibilities:
<ol>
<li>The surface is free to flex, to ripple, and that can promote
crystal nucleation. A ripple reflecting at the container surface is
doubled in amplitude (by the reflection) locally.</li>
<li>There is contamination at the surface (floating specks?) that
is introduced when a shock is applied ... | https://physics.stackexchange.com |
127,124 | [
"https://electronics.stackexchange.com/questions/127124",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/17604/"
] | Imagine there is a machine that has shared memory for both data and instructions (which means a control hazard can occur between the <code>MEM</code> and <code>IF</code> stages). Can instructions such as <code>ADD</code> that do nothing during the <code>MEM</code> stage cause a control hazard with other instructions th... | Utilizing six motor drivers for six motors is nothing unusual. As long as your controller output pins have a fanout of greater than six, you will be fine. This means that one output pin can drive six or more input pins of other ICs. If the fanout is lower (unlikely in my opinion), just use a buffer IC (e.g. 7406) to in... | When running motors in parallel, you may have overcurrent problems that can damage your motors if you are pushing the limits of what your motors can do and then one of the connections for a single motor disconnects. This will put higher current on the other motors. Wiring in a series is safer in this case because all t... | https://electronics.stackexchange.com |
1,107,356 | [
"https://math.stackexchange.com/questions/1107356",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/102514/"
] | My actual aim is to verify that each of the conditions in Dini's theorem is essential or not.Theorem says that A sequence {$f_{n}$} of continuous functions defined on a <strong>compact</strong> set $E$ converges to $f$ point wise satisfying the following properties :
$f_{n}$ is monotonic
and $f$ is continuous.
The... | Let $f_n$ be a big "spike" with support in $[0, 2/n]$. To be precise:
For $n \geq 2$, let $f_n$ be the unique piecewise linear function on $[0,1]$ such that:
(a) $f_n = 0$ on $[2/n, 1]$,
(b) $f_n$ is linear on $[0,1/n]$ and $[1/n, 2/n]$,
(c) $f_n(0) = f_n(2/n) = 0$, and
(d) $f_n(1/n) = n$.
The $f_n$ converge ... | Answer based on hints given by Nate Eldredge. But this one I obtained from one more book.
$f_{n}(x)=n^{2}x$ if $ 0 \leq x \leq \frac{1}{n} $,
= $-n^{2}x+2n$ if $ \frac{1}{n} <x< \frac{2}{n}$
=$0$ if $\frac{2}{n} \leq x \leq 1$ .
Here we have to start with $n=2$.
Graph of this function will look lik... | https://math.stackexchange.com |
481,142 | [
"https://physics.stackexchange.com/questions/481142",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/232448/"
] | I try to understand quantum entanglement and especially what it’s called « Action at a distance »
from my understanding, if you have a pair of entangled photon, after measuring the polarization of one photon you will find a correlation between his polarisation and the polarisation of the other photon even if they are ... | Brandonn, welcome to SE! Here is an attempt at a not-too-technical answer:
One simple way to see the difference is that, although the magnets' orientations may indeed be aligned (or antialigned) after some interaction between them, this correlation is <em>specific to a particular axis of measurement</em>, namely, the ... | One can have an even simpler classical entanglement conceptual set up. Bob and Bill are twins working for the same company , one in London the other in Paris. If you see Bob in London you immediately know that Bill is in Paris.
The only difference with the classical entanglement examples lies in quantum mechanics, whi... | https://physics.stackexchange.com |
64,467 | [
"https://physics.stackexchange.com/questions/64467",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/22643/"
] | I understand einstein's train paradox. Where one man on a platform is passed by a man in a traincar, at the moment they meet a flash of light is given off in the middle of the train car. To the man on the platform the light hits the ends of the car at opposite moments in time. To the man in the train car they hit at th... | The observer on the train is the least well defined part of this thought experiment. The thing is, Lorentz transformations and such are only valid for relative velocities of <em>strictly less than</em> the speed of light. All sorts of things go to $0$ and/or $\infty$ if you start boosting at $c$, and so you <strong>can... | You're incorrectly assuming that there is a frame of reference (the train) that moves with speed <em>c</em> relative to another frame of reference (the station).
But, there <em>isn't</em> such a frame of reference.
Mathematically, there is no spacetime coordinate transformation from the station's frame of reference t... | https://physics.stackexchange.com |
462,227 | [
"https://electronics.stackexchange.com/questions/462227",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/228500/"
] | I have a motor with these specifications:
<ul>
<li>star 400 V</li>
<li>delta 230 V</li>
</ul>
The motor is of course 3-phase.
How can I connect the motor using a delta connection if I have only 400 V line-to-line voltage? Where can I get 230 V line-to-line? Will I damage the motor in a delta connection? Is a delta conf... | <blockquote>
Now the question is, how can I connect the motor to delta connection
if I have only 400V line to line voltage?
</blockquote>
If you have 400 V, use the star connection. There is no reason to use the delta connection and the motor will draw too much current and overheat if you apply 400 volts to a conn... | <blockquote>
Now the question is, how can I connect the motor to delta connection if I have only 400V line to line voltage?
</blockquote>
Wire the motor in star and connect it to your 400 V phase-to-phase supply.
<blockquote>
Where can I get 230 V line to line?
</blockquote>
You can't.
<blockquote>
Will I d... | https://electronics.stackexchange.com |
315,914 | [
"https://physics.stackexchange.com/questions/315914",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/97850/"
] | I have an inclined plane with angle $\alpha$ with a block on it and a friction coefficient of $\mu$. I want to find $\alpha$ for which its acceleration, $a$, is maximum. Intuitively, 90$^o$ makes sense (regardless of the value of $\mu$) and anything above it would have the same acceleration as 90$^o$ since the block wo... | As Sumant pointed out in a comment, this equation does have its maximum when the angle is 90 degrees.
At 90 degrees the friction term becomes 0 regardless of $\mu $. The sin term also becomes 1, giving you $mg =ma$. This is the same as saying it is in free fall, which is what would happen when the slope is perpendic... | I believe you should find the derivative for the $a $. When you differentiate a differentiable function, one local minima point of the derivative should point the worst or best value for the first equation. In other words the $a $ value which makes the derivative of the function $0$ is your answer i believe.
Derivatio... | https://physics.stackexchange.com |
182,070 | [
"https://softwareengineering.stackexchange.com/questions/182070",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/61852/"
] | Where I work, new applications that are being developed that will use their own relational database, must have their database-models (conceptual, then physical ) reviewed and aproved by DBAs.
Things looked after are normalization, antipatterns, table and column naming standards, etc.
Is this really a DBA's responsabi... | Depends on how database-savvy your developers are, but normally yes. DBAs are usually better at spotting potential performance issues, plus it gives them a heads-up in case they need to do anything special or unusual when creating the database (allocating space on multiple drives, setting up failover plans, allocating... | Yes, that practice seems pretty standard to me.
If you have DBAs (whose expertise should include database modeling, normalization, table-naming structure, etc.) I would expect you would want to use them...
Why would you have DBAs and not want their their expertise and input? It seems like it is the obvious choice.... | https://softwareengineering.stackexchange.com |
169,018 | [
"https://physics.stackexchange.com/questions/169018",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/74816/"
] | I am fifteen and an aspiring Mechanical Engineer.
I read about ion-propelled aircraft, and was fascinated. On NASA's YouTube channels they outlined Ion Thrusters as a potential way to reach greater distance in space.
The way I see it Ion-propelled air-crafts are devices that use electrons to create air currents that... | Ion propulsion rockets are just that, rockets. They're just a different kind of rocket that the typical chemical propulsion rocket. Chemical propulsion uses chemical reactions and thermodynamics to create a high velocity exhaust, and hence thrust. Ion propulsion works by ionizing a gas (typically a gas with a high mole... | Just a start... there are others on this site that know much more about these things (David Hammen, are you reading this?).
For any rocket to gain speed, it needs to expel some material - and the faster the material is expelled, the more speed the rocket gains. There is a "rocket equation" that shows the velocity you ... | https://physics.stackexchange.com |
105,444 | [
"https://softwareengineering.stackexchange.com/questions/105444",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3491/"
] | We've hit an application issue with an Oracle table Primary Key exceeding the limits used by a Java Integer (2 ^ 32) and one of the suggestions is to reset this to 1000 and let it start again.
OR change the code to use Java Long (2 ^ 64) instead.
This has a ripple effect since this key is used as ID by a lot of other ... | In my experience, non-technical people often think it's OK to recycle "keys" or "IDs" after a certain amount of time because "we'll know by the date which one it was". They don't understand the technical hurdles it can cause if you end up with a computer trying to figure out which one is which.
Having absolutely uniq... | Maybe I'm misunderstanding something. If you change the key to a long, why do you need to reset it to 1,000? Just keep going from 2^32 on.
Were these alternative solutions? Is this a class that holds objects that live for a very short time, so while it has very few rows at any particular time, it churns the primary ke... | https://softwareengineering.stackexchange.com |
148,894 | [
"https://electronics.stackexchange.com/questions/148894",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/19179/"
] | I have seen that the channel size is in bits (64b/128b) which I understand is the amount of data one channel can transfer at an edge. But I see that the atom size is in Bytes. So does an atom of transfer take multiple dram transactions?
| Atom is the smallest amount of data that can be transferred to/from the DRAM. It is very common for ram modules these days to have a burst length of 8 which means that every time data is requested from the module, instead of just transferring 64bits(which is the channel width) it transfers 64bitsx8 bursts of data. Thus... | Atom size is the smallest addressable unit for writes.
If your CPU has a "write byte" instruction, it needs to be able to change a single byte while leaving the other bytes in the same word unaffected. If the RAM provides an atom size of one byte or smaller, this is a single access, where the unmodified bytes are mask... | https://electronics.stackexchange.com |
426,785 | [
"https://electronics.stackexchange.com/questions/426785",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/199225/"
] | I am trying to design a battery powered remote controller that has the following components, TPS63802 (converter), AP9211 (battery charger/protection), Atmega328 (MCU), NRF24 (transceiver). The following circuit uses a push button to send a signal to the MCU to tell it to go to sleep or turn on. My questions is regardi... | The front page of the datasheet shows operation down to light load; 80% at 100 uA load. Although the 2 A output seems excessive for a remote, this device is a reasonable choice. If TI has one that has a lower maximum output current, you will gain a little more efficiency at low loads because the gate charge in the powe... | The TPS63802 can certainly regulate the output at very low output currents.
It has a mode select pin that allows you to select between forced PWM mode (where the frequency will be constant but the efficiency low at light load) and PFM mode where the frequency will depend on load current at light load, but efficiency... | https://electronics.stackexchange.com |
45,324 | [
"https://mathoverflow.net/questions/45324",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5259/"
] | Over rational curve we know that any vector bundle is decomposable to direct sum of line bundles.
In higher dimensions there are examples of indecomposable bundles.
some indecomposable vector bundles have might have proper sub-bundles (all bundles and sub bundles here are in holomorphic category and not topological)... | Over a curve any rank $2$ bundle has a rank $1$ subbundle: Choose a subbundle defined over a Zariski dense open set, and then extend it over the missing points by observing that locally the problem of making such an extension is the problem of extending a map into $\mathbb P^1$.
| If $E$ is an indecomposable vector bundle and $S\subset E$ is a subbundle, then the sequence
$$0\to S\to E\to Q\to 0$$
gives a non-trivial element in $Ext^1(Q,S) = H^1(Q^* \otimes S)$. So a concrete way to construct the bundles you want is to find bundles $Q$ and $S$ such that $H^1(Q^*\otimes S)$ is non-trivial. On a c... | https://mathoverflow.net |
3,708,238 | [
"https://math.stackexchange.com/questions/3708238",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/511545/"
] | <span class="math-container">\begin{align*}
\max 3x_1+x_2\\
x_1 - x_2 \leq -1\\
-x_1 - x_2 \leq -3 \\
2x_1 + x_2 \leq 4\\
x_1, x_2 \geq 0\\
\\
\\
\\
\\
x_3 = -1 - x_1 + x_2\\
x_4 = -3 + x_1 + x_2\\
x_5 = 4 - 2x_1 - x_2\\
z = 3x_1 + x_2\\
\\
\text{we add:}\,x_0\\
\\
\\
\\
x_3 = -1 +... | This isn't the way the simplex algorithm is usually presented, but it is certainly equivalent to the usual presentation. I'm going to use the standard terminology (pivots, phase I, basic feasible solution); if wherever you got this from doesn't use this, feel free to ask about it in comments.
This isn't a regular pivo... | For min z I got 5 where
x1=1, x2=2, and x5=2
I forgot what the relationship between min and max are when finding solution to LP... I know the question wants to max z but the first constraint is tricky because it wants a negative number
| https://math.stackexchange.com |
30,546 | [
"https://security.stackexchange.com/questions/30546",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/8640/"
] | On a bank website the other day, I noticed that they were giving out a phone number on a page that wasn't over https. This seemed really wrong to me, since it would allow somebody to change the phone number to the bank and get me to dial a fake number.
Now, I'm realizing that we're providing a TON of information here ... | My 2 cents, not really from an IT security standpoint:
Ideally you would be correlating and checking up on information found on this site. Generally, answers fall into two categories:
<ul>
<li>Summarizing or explaining relevant information.</li>
<li>Providing original thoughts or analysis.</li>
</ul>
The first one u... | Really, you can't. There is no authentication on the information. That said, the chances of a meaningful attack in that vector are probably fairly minimal in general, so the bank probably decided that it wasn't worth the cost of having SSL on the page (it does take more server resources to do HTTPS). The balancing p... | https://security.stackexchange.com |
2,196,582 | [
"https://math.stackexchange.com/questions/2196582",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/205082/"
] | When the definition of a vector space starts of, it says: A vector space $V$ over a field $F$.
I want to know what it means when it is said that: "over a field $F$".
I know what a field is but I just want to know what is meant by "over a field $F$"?
| It is a common but somewhat abbreviated phrasing that can be slightly confusing at first. What it means is just something like
<blockquote>
If $F$ is a field, then a "vector space over $F$" means a set $V$ together with operations ${+}:V\times V\to V$ and ${\cdot}:F\times V\to V$, such that ...
</blockquote>
Thus, ... | A vector field has scalar multiplication, "over a field $F$" means that the scalars originate from $F$, you can for example have scalars come from $\Bbb F_9$ and so on. It doesn't need to be real or complex but just a generic field.
| https://math.stackexchange.com |
146,810 | [
"https://softwareengineering.stackexchange.com/questions/146810",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/53085/"
] | I am practicing algorithm and data structures. Therefore, I keep profiling my programs. Here is an example output from gprof:
<pre><code>Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls ns/call ns/call name
29.76 2.58 ... | It's not good nor bad.
Imagine I tell you that I spend 45 minutes to travel from point A to point B. Is it fast? Is it slow? Does it mean I spend too much time? Or not? Until I say what is the point A, what is the point B, and what are my speed expectations, you can't tell anything.
Profiler results are similar. They... | In this case, what it's telling you is that (as it's currently written) your program is spending most of its time doing I/O. The top two functions both appear to be involved with simply reading data from a file.
The part that would (or at least might) be somewhat disturbing is <code>memcpy</code> being the third highe... | https://softwareengineering.stackexchange.com |
414,556 | [
"https://physics.stackexchange.com/questions/414556",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/198031/"
] | Consider the standard Dirac Lagrangian, $\mathcal{L}=\overline{\psi}\left(i\gamma^{\mu}\partial_{\mu}-m\right)\psi$,
and a transformed one differing by a total derivative
$$
\mathcal{L}'=\mathcal{L}-\frac{i}{2}\partial_{\mu}\left(\overline{\psi}\gamma^{\mu}\psi\right).
$$
The energy-momentum tensor computed from the... | Never mind the anticommuting nature of the Dirac fields: if you're stuck to this problem, you probably didn't get there anyways. Just define $T^{\mu\nu}$ as
$$
T^{\mu\nu}=\frac{\partial \mathcal{L}}{\partial (\partial_{\mu}\psi)}\ \partial^{\nu}\psi+\partial^{\nu}\bar{\psi}\ \frac{\partial \mathcal{L}}{\partial_{\mu}\... | The general <em>canonical</em> energy-momentum tensor is defined by these components :
$$\tag{1}
T^{\mu\nu}=\frac{\partial\mathcal{L}}{\partial (\partial_{\mu}\phi_i )}\partial^{\nu}\phi_i-\eta^{\mu\nu}\mathcal{L},
$$
where $\phi_i$ are <strong>all the independent components</strong> of the fields in the game. Since t... | https://physics.stackexchange.com |
310,458 | [
"https://softwareengineering.stackexchange.com/questions/310458",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/106313/"
] | I was reading about <em>casts</em> in c++ and got confused about how are the expressions actually evaluated. Consider the following code in which <code>var</code> is of type <code>int</code> and after the expression <code>var = (var*10)/10</code> the memory of <code>var</code> gets overflowed:
<pre><code>#include<i... | Yes and no. At least in a typical case, the compiler won't store the intermediate results back in the original memory location. It will, however, typically carry out the operation(s) on a register that's the same size, and each intermediate result will be written back to that register. So, for your case, the compiler m... | <blockquote>
Does the compiler evaluates the expression step by step such that the result of first operation[ (var*10) ] performed on the numeric value of var is stored in it's allocated memory then the value stored in that memory space is used for further operations to be performed.
</blockquote>
Yes.
<blockquote>... | https://softwareengineering.stackexchange.com |
318,736 | [
"https://mathoverflow.net/questions/318736",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3969/"
] | I am looking for ideals <span class="math-container">$I\subset \mathbb{F}_2[x,y]$</span> with the following properties:
<ol>
<li><span class="math-container">$I$</span> is generated by two homogeneous elements;</li>
<li><span class="math-container">$I$</span> is invariant under the <span class="math-container">$SL_2(\... | There are tons of examples. Put <span class="math-container">$u = x^2+xy+y^2$</span> and <span class="math-container">$v = xy(x+y)$</span>. Then <span class="math-container">$u$</span> and <span class="math-container">$v$</span> are <span class="math-container">$SL_2(\mathbb{F}_2)$</span> invariant. If <span class="mat... | One can see that <span class="math-container">$I=(f_1,\dots, f_s)$</span> is <span class="math-container">$G$</span>-invariant iff <span class="math-container">$\alpha\cdot f_i \in I$</span> for each <span class="math-container">$\alpha \in G$</span> and <span class="math-container">$i$</span>. From this one can prove ... | https://mathoverflow.net |
72,787 | [
"https://electronics.stackexchange.com/questions/72787",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | When you have some device, like a TV, why is there a necessary Voltage-or current for that matter. Whenever I see circuits, it always says to find the current from the voltage and resistance given, so presumably with <em>any</em> battery there should be a current. Why do some things require bigger current and bigger vo... | The reasons vary greatly, but I think a good way to summarize them is this: a device does more than simply passively draw current. Often times the actuators and transformers in a device rely on electrostatic phenomena, so in order for it to accomplish a task, a varying range of voltages is required for various devices.... | Mostly you need a certain amount of current to make it physically work. For example, if you need an electric motor to have a certain torque, you have to make a magnetic field of a certain strength, which requires a specific amount of electric current.
For logic gates on computer chips, a 1 is created by charging a ... | https://electronics.stackexchange.com |
33,895 | [
"https://cs.stackexchange.com/questions/33895",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/22825/"
] | In finding the values of x and y, if <code>(x567) + (2yx5) = (71yx)</code> ( all in base 8) I proceeded as under.
I assumed <code>x=abc</code> and <code>y=def</code> and followed.
<pre><code> (abc+010 def+101 110+abc 111+101)=(111 001 def abc) //adding ()+()=() and equating LHS=RHS.
abc=111-010=101 which is 5 in ... | Assuming a 32-bit architecture (with alignment), then instructions are words; that is, every instruction is composed of 4 bytes.
That implies that the bottom two bits of the address are byte offsets within the word; that is, the address 10001111 denotes 4th byte of the word at 10001100. When we're talking about instru... | The program counter indicates the memory address of the current instruction. Depending on the architecture of the CPU it may be incremented by a fixed or a variable amount in order to point to the address of the next instruction. "You" the author of the program running on the CPU do not need to increment the ... | https://cs.stackexchange.com |
115,595 | [
"https://cs.stackexchange.com/questions/115595",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/109442/"
] | Suppose I have an <span class="math-container">$N$</span> length integer array of pairs of the type <span class="math-container">$[value, key]$</span>. Now, I need to query for range sum. Query is of the type : <span class="math-container">$l, N, x$</span> meaning I have to sum up all the <span class="math-container">$... | Since there are no updates there is a rather simple solution. Store a map of key -> array of pairs, such that for every element in your original vector (value, key) at position pos, you store in the vector associated with given key in the map the pair (position, value). Keep every vector sorted by position.
For exampl... | Since you have specified that the array is unsorted, i am afraid you cant do a query in <span class="math-container">$O(logN)$</span>, assuming we are talking about time complexity and not space complexity (but i think this is the case since you have expressed the desire to make the query efficient because there can be... | https://cs.stackexchange.com |
145,306 | [
"https://electronics.stackexchange.com/questions/145306",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/62056/"
] | <img src="https://i.imgur.com/4cZx4Cg.png?1" alt="circuit diagram">
I can solve the circuit for given DC input voltage with transistors Ies and alfa values. It amplifies the input signal for like 13 times. (Not linearly). But i couldn't understand the purpose of this circuit. Could you help me with that? Thanks in adv... | This is a standard textbook building block- an antilog amplifier. You'd normally have a diode from the emitter to ground to prevent the input from going too far negative and possibly damaging the transistor (by reverse B-E breakdown).
How it works:-
The transistor base-collector voltage is maintained at 0V by the op... | It is an <strong>Antilog Amplifier</strong>.<br>
The output voltage will be proportional to the antilog of input voltage.
| https://electronics.stackexchange.com |
1,845,365 | [
"https://math.stackexchange.com/questions/1845365",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/135204/"
] | Let the degrees of the polynomials
$$P(z)=a_0+a_1 z+a_2 z^2+\cdots +a_n z^n \; (a_n \neq 0)$$
and
$$Q(z)=b_0+b_1 z+b_2 z^2+\cdots +b_m z^m \; (b_m\neq 0)$$
be such that $m \ge n+2.$ Show that if all of the zeros of $Q(z)$ are interior to a simple closed ontour $C$, then $\int_C \frac{P(z)}{Q(z)}dz=0.$
The soluti... | Since $b_m\neq 0$, the fraction $$\frac{a_0 z^{m-2}+a_1 z^{m-3}+a_2 z^{m-4}+\cdots +z_n z^{m-n-2}}{b_0 z^m+b_1 z^{m-1}+b_2 z^{m-2}+\cdots +b_m}$$ is defined and continuous at $z=0$ (the denominator does not vanish). This means that the singularity of $$g(z)=\frac{1}{z^2} \cdot \frac{P(1/z)}{Q(1/z)}$$ at $z=0$ is remov... | The denominator polynomial <span class="math-container">$\Delta(z)=b_0 z^m+b_1 z^{m-1}+b_2 z^{m-2}+\cdots +b_m$</span>
is continuous at the origin and non-zero there: <span class="math-container">$\Delta(0)=b_m\not=0.$</span>
Of course <span class="math-container">$\Delta(z)$</span> is entire, so combining the observat... | https://math.stackexchange.com |
12,031 | [
"https://electronics.stackexchange.com/questions/12031",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3593/"
] | I'm not an electrical engineer. I have an unusual need and would like suggestions as to how to proceed. I have an application that needs very high currents at very low voltages. I'm trying to heat a thin strip of aluminum to temperatures near 100C quickly and then control the temperature. My calculations suggest about ... | Power supplies from arc welding devices are quite capable of what you describe. You may also try a soldering gun (the kind with a transformer inside) replacing the tip with your stuff.
Just be aware that you need really really thick wires for 100A. The problem will be worse with high frequency AC because of the skin e... | How thick is that strip? Aluminium is very reactive and oxidizes instantly when exposed to air, leaving an insulating coating on the aluminium. The resistance of this coating may be much higher than the strip itself, so that the largest part of the power is actually used to heat the contacts, even melt them. Make sure ... | https://electronics.stackexchange.com |
48,547 | [
"https://electronics.stackexchange.com/questions/48547",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/17697/"
] | I've been told that there's a design rule of thumb that whenever you have a "bus" providing power and ground (for example, in an array of PWM outputs) that the ground connection is placed nearest the edge.
What is the reasoning behind this?
<img src="https://i.stack.imgur.com/FkxpF.png" alt="enter image description h... | Ground ring around the periphery as a sort of EMI shield is what I was taught, but I understand that in a quarter century, the validity of that purpose may have worn off.
Pure speculation alert: One possible benefit of keeping the neutral rail consistently at the outer periphery of a board is that accidental contact b... | I was always taught that it is because the ground rail of a circuit normally runs around the outskirts of a board to help preventing any external noise. This is especially important in amplification circuits for obvious reasons but I suspect nowdays with surface mount and multi layer boards its probably just an old hab... | https://electronics.stackexchange.com |
3,308,739 | [
"https://math.stackexchange.com/questions/3308739",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/676671/"
] | Can anyone help me explain why the second equal sign is true for the variance?
<span class="math-container">$$\sigma^{2} \equiv \lim _{N \rightarrow \infty}\left[\frac{1}{N} \sum\left(x_{i}-\mu\right)^{2}\right]=\lim _{N \rightarrow \infty}\left(\frac{1}{N} \sum x_{i}^{2}\right)-\mu^{2}$$</span>
<br>
<span class="ma... | We have <span class="math-container">\begin{align} &\lim_{N\to\infty}\big(\frac1N\sum_{i=1}^N(x_i - \mu)^2\big) = \lim_{N\to\infty}\big( \frac1N\sum_{i=1}^N (x_i^2-2\mu x_i + \mu^2)\big)=\\&=\lim_{N\to\infty} \big(\frac1N\sum_{i=1}^N x_i^2\big) - 2\mu \lim_{N\to\infty}\big(\frac1N\sum_{i=1}^N x_i\big) + \mu^2 \... | <span class="math-container">$$\frac{1}{N} \sum\left(x_{i}-\mu\right)^{2} - \left(\frac{1}{N} \sum x_{i}^{2}-\mu^{2}\right)= 2\mu^2 -2 \mu \frac{1}{N} \sum x_i = 2\mu\left(\mu - \frac{1}{N} \sum x_i\right)$$</span>
so your second equality is a consequence of <span class="math-container">$\lim\limits_{N \rightarrow \in... | https://math.stackexchange.com |
474,110 | [
"https://math.stackexchange.com/questions/474110",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/61073/"
] | Use the method of undetermined coefficients to solve the IVP
$y′′ + 4y′ + 4y = (3 + x)e^{−2x},\; y(0) = 2,\; y′(0) = 5$ .
My answer (partial)
$r^2 + 4r +4 = 0$
$ (r+ 2)^2 = 0$
$r = -2$
$y_h = (c_1 +xc_2) e^{-2x}$
$y_p =(xc_1 + x^2c_2)e^{-2x} $
Unable to reach final answer. Need help!
| Your homogeneous solution is correct, but your particular solution should at least use different constants. Because $(c_1+c_2 x) e^{-2 x}$ returns zero upon substitution into the differential equation (because it is the homogeneous solution), the particular solution should contain the next two higher powers, i.e.
$$... | Just noting additional point, following @Ron's answer. If you have: $$a_ny^{(n)}+\cdots+a_1y'+a_0y=Q(x)$$ and two following conditions are fulfilled:
<ol>
<li>The characteristics equation of the associated homogenous OE has an $r$ multiple roots.</li>
<li>$Q(x)$ contains a term such that, ignoring constants, is $x^t$... | https://math.stackexchange.com |
4,406 | [
"https://quant.stackexchange.com/questions/4406",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/3045/"
] | Let's assume I am classifying every trading day as a 1 or a 0. Exactly what I am classifying doesn't matter, but for the sake of this question let's say I am predicting direction of price change. So, for a particular stock like GOOG:
For day N:<br>
1: close day N+1 > close day N<br>
0: close day N+1 <= close day N ... | Ok so for completeness, assuming Black-Scholes and an example portfolio of 100 long <span class="math-container">$C_1$</span>, 100 long <span class="math-container">$C_2$</span> (both on the same underlying), and 10 long shares of the same underlying, <span class="math-container">$S$</span>.
<strong>Portfolio delta:</... | Delta is a derivative of the price with respect of the price of underlying, so for the unit stock position delta is 1 and gamma is obviously 0. As for theta, rho and vega of the stock position, they do not make sense, at least not in the Black-Scholes setting they don't. You would not be able to hedge say vega or theta... | https://quant.stackexchange.com |
428,400 | [
"https://physics.stackexchange.com/questions/428400",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/206186/"
] | I know from electrostatics that electric field inside a conductor is zero. I also know that there must be electric field inside a conductor carrying current in electric circuits. I am confused.
| In principle, heat transfer out of the pot must occur through the surface area of that pot. The shape that holds a given volume but has the least surface area is a sphere, so the spherical shape will have the least area available for heat transfer to the environment. However, I doubt that you want a spherical pot for... | there are two mechanisms of loosing heat here:
1. heat transfer from liquid (natural convection) through solid (conduction) and to the ambient air (natural convection)
<ol start="2">
<li>Phase change - liquid layer on free surface will evaporate and absorb heat from the liquid.</li>
</ol>
You can do the following to ... | https://physics.stackexchange.com |
39,099 | [
"https://biology.stackexchange.com/questions/39099",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/19049/"
] | Can anyone please explain a little about these two elements of genes? My main problem is with "which ‘switch on’ instructions".
<blockquote>
genes have structural elements (which code for a particular protein) and regulatory elements (which ‘switch on’ instructions)
</blockquote>
| The expression of protein coding genes happens by the process of transcription. So promoters facilitate access of the RNA polymerase complex to DNA to begin transcribing a locus on the genome. The promoter of a gene often contains sequences that bind proteins called transcription factors, which play a role in various p... | A structural element is that part of the gene that is giving the code to specify an amino acid that's going to be translated into a protein. A lot of the rest of the code may say "start reading here" "stop reading" "ribosome bind here" etc.
| https://biology.stackexchange.com |
1,125,192 | [
"https://math.stackexchange.com/questions/1125192",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/211541/"
] | I am attempting a proof but it is driving me insane as I cannot see what I should do.
Given that $a$ is coprime to be $b$ and that $a|c$ and $b|c$ prove $ab|c$.
I simply wrote down what I know and tried to see what I could but but it made no difference and I still don't see how to proceed.
$a$ is coprime to be $b$ ... | Using your notation,
$$\begin{align*}
1 & =ax+by\\
c&=cax+cby\\
c&=(bm)ax+(an)by\\
c&=(ab)(mx+ny)
\end{align*}$$
Therefore $ab\mid c$.
| Hint: Think about the problem in terms of prime factorizations.
| https://math.stackexchange.com |
2,359,142 | [
"https://math.stackexchange.com/questions/2359142",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/457181/"
] | Let $\Omega$ be uncountably infinite, and $\mathcal{A}=\sigma(\{\omega\}: \omega\in \Omega\setminus\{\omega_0\})$.
I'm supposed to give a characterisation of $\mathcal{A}$ and then prove that $(\Omega,\mathcal{A},\delta_{\omega_0})$ is complete.
My try
For the characterisation: $\mathcal{A}=\{A\subset \Omega\setm... | I'm not sure your definition of completeness is correct.
You need to show that if
<ul>
<li>$A \in \mathcal{A}$,</li>
<li>$\delta_{\omega_0}(A) = 0$,</li>
<li>$B \subseteq A$,</li>
</ul>
then $B \in \mathcal{A}$.
This is different than showing that any subset of $\Omega \setminus \{\omega_0\}$ is in $\mathcal{A}$ (in ... | Note that this question concerns Exercise 1.3.2 from <em>Probability Theory: A Comprehensive Course</em>, 3rd edition, by Achim Klenke. This is a long, detailed, hopefully correct answer to the exercise in question.
<strong>Discussion</strong>
There is a perhaps natural, although totally misguided, desire to characteri... | https://math.stackexchange.com |
28,830 | [
"https://cs.stackexchange.com/questions/28830",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/20496/"
] | There is a complete graph $G$ with $n$ vertices and each edge has a distinct weight.
Is there an efficient (not necessarily optimal) algorithm to select $k$ vertices from the graph $G$, such that the total cost of the min-spanning tree of the selected $k$ vertices will be highest?
In my case, $n$ is around 1000, and ... | Your problem is NP-complete, so you should not expect to find any efficient algorithm for it.
If we could solve your problem efficiently, we could solve the $k$-clique problem, too. Let $G$ be an unweighted, undirected graph; we are curious whether it has a $k$-clique. Translate it into an instance of your problem b... | A theoretically efficient algorithm can be obtained as follows for constant $k$. First, notice you can compute a maximum weight spanning tree by negating the edge weights and running Kruskal's algorithm. Then, observe there are $\Theta(n^k)$ ways to choose a set of $k$ vertices. We can step through each set, and comput... | https://cs.stackexchange.com |
366,349 | [
"https://softwareengineering.stackexchange.com/questions/366349",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/277611/"
] | I have an ASP.NET Core 1.1 application which uses dependency injection and is splitted in 3 layers (web, business logic and data access).
I'd like to access to some values of the configuration file in some methods of the business logic layer. Which way would be more correct to keep a clean architecture?
<ul>
<li>Pass... | In any situation where information needs injecting into part of an app, remember the "tell, don't ask" principle.
If you pass configuration into the business logic layer directly, then you are creating a coupling between the two. It becomes difficult to change the configuration without breaking the business logic laye... | You can declare the configuration per module and have it provided/injected on creation:
<pre><code>package: Accounts
+ AccountService
+ // internal classes
+ AccountConfig
package: Users
+ UserService
+ // internal classes
+ UserConfig
package: Config
+ IConfigProvider
+ XMLConfigProvider
+ ... | https://softwareengineering.stackexchange.com |
70,489 | [
"https://stats.stackexchange.com/questions/70489",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/22405/"
] | I know that you can have a construct as a dependent variable: MANOVA or MANCOVA. Is it possible for me to have a construct as an independent variable?
I have a construct that consists of 3 variables that I want to use as my independent variable and I have one variable that I want to use as a dependent variable.
| Multiple regression should work, assuming all your variables are numerical. One DV and 3 IVs. So the analysis would look at how each IV is related to the DV after removing the effects of the other IV's, and also how all three combined are related to the DV.
| The only problem that might arise is that, if you include the three variables as separate variables they might be collinear.
One way to escape this is to create an actual construct variable (that is, make it a single variable). How to do this depends on the nature of the three variables, but a common method is factor ... | https://stats.stackexchange.com |
401,877 | [
"https://physics.stackexchange.com/questions/401877",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/183768/"
] | I'm trying to understand the absorption spectrum in terms of what happens when an electron absorbs a photon. If we shine white light through a sample and use a prism to disperse the light, we would see black lines corresponding to the wavelengths absorbed by the electron. However, if the specific wavelength is absorbed... | You need to apply the derivative to both terms inside the braces. The differential operator does not commute with $x$.
$$x \frac{d}{dx} \neq \frac{d}{dx}x = \left(\frac{d}{dx}x\right)+x \frac{d}{dx} $$
This means that
$$-i \hbar \frac{d}{dx}(x^n\Psi) = -i\hbar nx^{n-1}\Psi -i\hbar x^n \left(\frac{d}{dx}\Psi\right)$... | Here is another hint to help you out. Write the commutator as
\begin{eqnarray*}
[p, x^n] &=& p x^{n-1} x - x^{n - 1} x p \\
&=& p x^{n-1} x - x^{n-1}([x, p] + p x) \\
&=& p x^{n-1} x - x^{n-1} p x - x^{n-1}[x, p] \\
&=& [p, x^{n - 1}] x - x^{n - 1}[x, p] \\
&=& [p, x^{n - 1}] x ... | https://physics.stackexchange.com |
121,823 | [
"https://electronics.stackexchange.com/questions/121823",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/27067/"
] | I've read that digital I/O pins should have a resistor in series in order to limit noise. Should one also use such approach when interfacing with the I/O pins of an arduino, or is that already done on the arduino board?
| What that snippet seems to be talking about is restricting the propagation of noise generated inside the microcontroller (or other similar clock-based chip) into external circuitry.
To that end the recommendation in that document is not just to add a series resistor, but to form a low pass filter close to the chip usi... | Probably not a good idea in most circumstances. Here are a couple of examples: -
<ol>
<li>Inputs - adding a resistor will slow down the propagation of the digital signal into the input due to the inherent input capacitance of the IO gate - a resistor could be used to "bodge" bad hardware design of course i.e. it slows... | https://electronics.stackexchange.com |
624,696 | [
"https://electronics.stackexchange.com/questions/624696",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1908/"
] | I'm building a filter from a kit with some given (microscopic pre-soldered SMT) capacitors and 2 toroids. It looks like the notch frequency is a bit too low with 10 wire turns around a T37-2 iron powder toroid and a bit too high with 9 turns. The windings have all been wound tightly and evenly spaced.
Is there some v... | You are lacking several terms, and so you aren't asking quite the right question, or providing sufficient information to base an answer on.
There are a few things that can be measured, which can be described that way.
The most likely are the apparent or real power in a given component.
Apparent power is given by, rough... | All the power that goes in will end up going somewhere; either it is reflected back from the input, passed through to the output, or lost as heat.
You have described S21 as nearly lossless. You can look at the squared magnitudes of S11 and S21, the return loss and insertion loss, and estimate a how much power would be ... | https://electronics.stackexchange.com |
17,296 | [
"https://dsp.stackexchange.com/questions/17296",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/10464/"
] | I am trying to make a panadapter for a software defined radio and I am a little bit stuck and hope someone can help me.
I have an I Q signal from my radio. (Actually I am using an IQ wav file from the internet recorded at 44800 2 channels 16bit).
If I use HDSDR the spectrum looks like this:
<img src="https://i.stack... | Just change the code to the following:
<pre><code>x = randn(1,1000);
h = [1 2 3 4 5];
y = conv(x,h);
plot((abs(fft(h,1024))).*(abs(fft(x,1024)))); % It's |H(w)||X(w)|
hold on
plot(abs(fft(y,1024)),'--r')
</code></pre>
By mistake you raised the DFT of an impulse response to the second power. You could see that magnitu... | I think you made a mistake between the power spectrum and the Fourier Transform.
This is the right form of the Convolution Theory (Nothing is squared):
$$ \lvert Y(\omega)\rvert = \lvert H(\omega) X(\omega)\rvert $$
Try this and it will work for you on MATLAB.
<h3>MATLAB Code</h3>
<pre><code>% Calculating the Magni... | https://dsp.stackexchange.com |
103,376 | [
"https://mathoverflow.net/questions/103376",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25386/"
] | I can't solve following exercise in a note about prime numbers. I need this for study about large gaps of consecutive prime numbers.
Prove that f $0<1-\delta<1$ then
$$\sum_{p\le y}\frac{1}{p^{1-\delta}}\le\frac{y^\delta}{\log(y^\delta)}+\log(1/\delta)+O\left(\frac{y^\delta}{\delta(\log y)^2}+1\right)$$.
In th... | I only get<br>
$$\sum_{p\le y}\frac{1}{p^{1-\delta}}\le \frac{y^{\delta}}{\log(y^\delta)}
+e^2\log(1/\delta)+O\Bigl(\frac{y^\delta}{\delta^2(\log y)^2}+1\Bigr).$$
The first sum is
$$\sum_{p\le e^{2/\delta}}\frac{1}{p^{1-\delta}}=
\sum_{p\le e^{2/\delta}}\frac{p^\delta}{p}\le e^2
\sum_{p\le e^{2/\delta}}\frac{1}{p}$$
a... | By juan's answer above, one only needs to show $\sum_{p \leq e^{\frac{2}{\delta}}} \frac{1}{p^{1-\delta}} \leq \log \frac{1}{\delta} + O(1) $. But by estimating $p^{\delta} = 1 + O( \delta \log p )$, this sum is
$$ \sum_{p \leq e^{\frac{2}{\delta}}} \frac{1}{p} + O( \delta \sum_{p \leq e^{\frac{2}{\delta}}} \frac{\log ... | https://mathoverflow.net |
41,436 | [
"https://electronics.stackexchange.com/questions/41436",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9741/"
] | In fiber optics, why would RZ-DPSK be more suited for long-haul transmissions over NRZ-DPSK? Is the tolerance to non-linearity due to the power intensity or something else?
| RZ-DPSK is derived from NRZ-DPSK via a pulse carver, so you can see that a carrier will be more available than from the constant envelope of the NRZ. In NRZ the carrier arises from the phase shift chirps and non-linearities in that process.
Looking at the spectrum of the RZ vs. NRZ you will see a higher carrier to si... | At higher bit rates and long haul links RZ is more prone to dispersion as compared to NRZ.
| https://electronics.stackexchange.com |
71,795 | [
"https://dsp.stackexchange.com/questions/71795",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/23196/"
] | Let's say I have a causal 3-tap FIR filter:
<span class="math-container">$$y[n] = ax[n] + bx[n-1] + cx[n-2]$$</span>
Assuming I have access to all the data prior to filtering and generate a similar non-causal filter:
<span class="math-container">$$y[n] = ax[n+1] + bx[n] + cx[n-1]$$</span>
Would this new filter have the... | In general if you have a causal odd length <span class="math-container">$N$</span> FIR filter <span class="math-container">$h[n]$</span>, defined for indices <span class="math-container">$n\in[0,N-1]$</span>, moving the center bin to index <span class="math-container">$n=0$</span> means shifting the impulse response to... | Correct. The magnitude response would be the same and the phase response would be summed with <span class="math-container">$\omega$</span> (omega).
| https://dsp.stackexchange.com |
458,758 | [
"https://physics.stackexchange.com/questions/458758",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/221808/"
] | I'm not homeless, I'm just frugal and trying to drive a lot less.. maybe I'm adventurous. :) Anyways, I've been working , eating and sleeping out of my new Black van. The van is brutally hot during the day even in the so called South Florida winter. It's okay though, cause I drive w the windows open and I don't really... | Classroom instruction in classical physics <em>does</em> address some of the items in your list. In particular the treatment of light passing through a polarizing medium is handled with two sub rules: (a) The emerging light takes on the polarization of the medium and (b) the intensity is reduced by the rule <span class... | I can't address the state of education at your institution, but the effect of measurement on the state of a system has been a central theme in physics for well over a century.
In classical physics, one defines the gravitational or electric field using an arbitrarily small "test particle". That is, one imagines that t... | https://physics.stackexchange.com |
82,976 | [
"https://softwareengineering.stackexchange.com/questions/82976",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3530/"
] | We are a group that started working on a fairly big website with an existing codebase. We have a test and a production server.
Our idea is to have a test repository with a number of devs having push access to; and a blessed repository that only a few can push to. The blessed repo is supposed to be always stable and r... | To put it simple:<br>
The push process in itself should be fully automatic. Whether you have some custom script, or you simply pull from the "blessed" repo to the production environment. That is up to you. You should just have something automated, because automated processes can be made reliable (as opposed to uploadin... | I learned a lot about deployment from looking at how Capistrano operates. I was working with RoR at the time, so it was a logical choice and although I never quite got it to behave for the project I was working on, the way it performs automated updates was very useful.
You may be in a situation where you can use it di... | https://softwareengineering.stackexchange.com |
357,722 | [
"https://physics.stackexchange.com/questions/357722",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/29532/"
] | I was told that a use of both alpha and beta decay is in radiometric dating.
Why is radiometric dating not also considered to be a use of gamma radiation?
| Radiometric dating tends to use a nucleus that changes into some other easily distinguishable nucleus. For example uranium decays to lead 206 and 207, which can be easily measured in a mass spectrometer. We measure both the uranium concentration and the lead concentration and infer the age from how much of the uranium ... | John's answer is only part of it. There are gamma emitters that aren't simply due to an excited nucleus. However, the ones that occur naturally are part of the uranium decay sequence. They are not at either end of the chain and thus measuring the quantity relative to their parents or daughters only tells you the rat... | https://physics.stackexchange.com |
364,485 | [
"https://softwareengineering.stackexchange.com/questions/364485",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | In C# we have <code>Extension methods</code>.
<blockquote>
Extension methods enable you to add methods to existing types without
creating a new derived type, recompiling, or otherwise modifying the
original type.
An extension method is a special kind of static method, but they are
called as if they were ... | You cited
<blockquote>
Extension methods enable you to add methods to existing types <strong>without creating a new derived type, recompiling, or otherwise modifying the original type.</strong>
</blockquote>
and that is when you should use them almost exclusively - where you have a case where it would strongly mak... | <blockquote>
Adding to this there is this common notional that static classes are not a good fit for test driven development.
</blockquote>
This only holds true if those static methods access or mutate external state. If,
<pre><code>Order.CleanAddress();
</code></pre>
only modifies <code>Order</code> and doesn't ... | https://softwareengineering.stackexchange.com |
2,021 | [
"https://iot.stackexchange.com/questions/2021",
"https://iot.stackexchange.com",
"https://iot.stackexchange.com/users/4034/"
] | I'd like my MQTT broker to be accessible from outside my home network, but I'm a bit reluctant to open a port in the firewall. And I'd like to avoid using my home IP.
It's pretty convenient to have an unencrypted open broker at home, but that doesn't work if I am going to expose it. What other options do I have?
| You basically have 3 options if you don't want to forward a port.
<ol>
<li>Use a broker in the cloud so client from home always connect out to it. Use TLS and authentication so others can't eavesdrop or inject unwanted messages</li>
<li>Use a cloud broker and set up a bridge between the internal broker and cloud broke... | Since the broker is a server, you MUST open at least one port for clients to connect.
So, your problem becomes a special case of exposing a service on the Internet.
This has been done via DMZ, either through proxy or other way to enforce stricter authentication than the default service. If your proxy lives on the clo... | https://iot.stackexchange.com |
636,563 | [
"https://electronics.stackexchange.com/questions/636563",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/188450/"
] | I have a <code>0-10v</code> tension from a potentiometer generated current (1), and I would like to use something like a relay to switch on/off a <code>16A 230v</code> current (2) if (1) is below say <code>0.1v</code> or some value <code>Vs</code> that I could tune (eg., <code>0.01v < Vs < 1.0v</code>).
How can I... | No, it's not common.
While I can't be 100% sure, I believe this is a font issue with whatever tool was used to render the figures for display in the web version of the article (the PDF version displays the pi correctly).
In the old days, people represented Greek letters in their technical documents by selecting the &qu... | No, I've never seen it before. Maybe my beard isn't grey enough to make a blanket statement for the community, but I stand behind it.
If you can track down a link or email of the datasheet maintainers I would suggest complaining, because the last thing I'd like to see is little 'p's popping up in all my circle and freq... | https://electronics.stackexchange.com |
6,790 | [
"https://electronics.stackexchange.com/questions/6790",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | Is it possible to control a bicolor LED with just one pin of a microcontroller?
Instinct says NO, because you can have one end grounded and the other going to the micro's pin, allowing you to turn it on or off but not change its color.
But maybe someone has a better idea?
| You can do this with a bi-color LED that has the two LEDs back-to-back if you connect one LED terminal to an intermediate voltage eg 2.5V on a 5V design and connect the other side to the MCU via a suitable resistor (I used 560R).
Then a low output gives one colour, high gives the other and tri-state leaves the LED of... | If you didn't need an off state, and your Voh was sufficiently large (edit: to overcome the forward bias voltage of the LED), you might be able to hook one end of the LED to a mid-rail voltage. Outputting a 1 gets one color, outputting a 0 gets the other color. To turn it off...ha, good luck. Maybe you could try put... | https://electronics.stackexchange.com |
1,137,752 | [
"https://math.stackexchange.com/questions/1137752",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/40209/"
] | Let $X$ be any infinite set.
Define,
$T_f$ = $\{\emptyset,X\}\cup$ $\{$$G\subset X$| $X-G$ is finite$\}$ which is the cofinite topology.
And,
$T_c$= $\{\emptyset,X\}\cup$ $\{$$G\subset X$| $X-G$ is countable$\}$ which is the cocountable topology.
I was wondering which one of these is finer than the other ? Any ide... | Suppose that $G \in T_f$. That means $X \setminus G$ is finite, so in particular $X \setminus G$ is countable. Thus $G \in T_c$.
This prove that $T_f \subset T_c$. This means $T_c$ is finer.
| every finite set is a countable set but not conversely. this mean that every Tf open set is Tc open but not conversely. therefore Tf is a subset of Tc hence Tc is finer than Tf
| https://math.stackexchange.com |
47,595 | [
"https://dsp.stackexchange.com/questions/47595",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/17077/"
] | I have been studying about moments and cumulants of a random variable. Even though the definitions of characteristic and moments generating function are very similar (only the sign in the exponential is changed) to Fourier and Laplace transforms, respectively.
$\Phi_x(\xi) = E [ e^{j \xi x(\zeta)} ] = \int_{-\infty}^{... | As you well said, these functions are useful just for their mathematical properties that allow to compute the <em>m</em>-th order moment of a random variable.
Additionally, <strong>they happen to match Fourier transform theorems</strong>. However, <strong>not in the sense of a time-domain signal</strong>, since the v... | Hi: Since the characteristic function of any random variable uniquely defines the distribution associated with the random variable ( that's a theorem but
I forget the name of it ), the cf can be used to identify the distribution of some function of a random variable. ( e.g sum of n exponentials
is chisquared(n) ). A... | https://dsp.stackexchange.com |
62,949 | [
"https://mathoverflow.net/questions/62949",
"https://mathoverflow.net",
"https://mathoverflow.net/users/934/"
] | Bochner's theorem states that a positive definite function is the Fourier transform of a finite Borel measure. As well, an easy converse of this is that a Fourier transform must be positive definite.
My question is: is there a high-brow explanation for why positive definiteness and Fourier transforms go hand-in-hand?... | Perhaps the phenomenon you are asking about is: why is the definition of a positive-definite function natural?
One answer is that positive-definite functions are exactly coefficients of group representations, in the following sense. If $\pi : \mathbb{R}\to U(H)$ is a unitary representation of $\mathbb{R}$ on some H... | What about the fact Fourier transform converts convolution into ordinary (pointwise) product, and therefore converts positive-definiteness into ordinary positivity?
| https://mathoverflow.net |
42,896 | [
"https://datascience.stackexchange.com/questions/42896",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/64603/"
] | I have a dataset with one of the (important) features being the geographic distances from NYC. Of course, some of the values are missing.... The goal is predicting whether people with certain attributes (proximity being one of them, and the typical age, sex, education, etc. being the others) will engage in an activity ... | I would say that for your goal, the time to NYC is better than the distance. Indeed, whether I'm 100km or 10km, if it takes me an hour to go to the city center, it's the same burden to me.
So I would advise you to use the time as a metric rather than the distance itself due to how logistics work.
Then for your missin... | I don't think time alone is what you are after, although it would certainly be useful.
It sounds to me like you would also want to consider the <strong><em>cost</em></strong> of transport.
Yes the drive and flight may take the same amount of time, but you could be looking at orders of magnitude difference in the tota... | https://datascience.stackexchange.com |
239,937 | [
"https://stats.stackexchange.com/questions/239937",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/134556/"
] | I'm learning about the Empirical Cumulative Distribution Function. But I still don't understand
<ol>
<li>Why is it called 'Empirical'?</li>
<li>Is there any difference between Empirical CDF and CDF?</li>
</ol>
| Let <span class="math-container">$X$</span> be a random variable.
<ul>
<li>The cumulative distribution function <span class="math-container">$F(x)$</span> gives the <span class="math-container">$P(X \leq x)$</span>.</li>
<li>An empirical cumulative distribution function function <span class="math-container">$G(x)$</sp... | <blockquote>
Is there any difference between Empirical CDF and CDF?
</blockquote>
Yes, they're different. An empirical cdf is a proper cdf, but empirical cdfs will always be discrete even when not drawn from a discrete distribution, while the cdf of a distribution can be other things besides discrete.
If you treat... | https://stats.stackexchange.com |
120,398 | [
"https://stats.stackexchange.com/questions/120398",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/58766/"
] | Let me give the details of my problem setting, we have a learning algorithm that can take a collection of algebra problems and automatically generate similar ones. Of course, an important question to ask is are the problems we generated indeed similar to the original ones. We invited 20 students to answer the 10 questi... | No, it doesn't establish similarity, and indeed, it doesn't come close to answering the right question.
i) Failure to reject the null doesn't imply it's true. It simply implies your sample was too small to detect the difference.
ii) You're not actually even interested in the truth of the null you're testing. I presum... | No. You cannot use a t-test to prove the null hypothesis. A $p > \alpha$ only means that you do not have sufficient evidence to reject the null hypothesis.
You could try reporting a simple correlation between the two tests.
| https://stats.stackexchange.com |
557,147 | [
"https://physics.stackexchange.com/questions/557147",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/214702/"
] | I am wondering if it is possible to differentiate between pure states and mixed ones in the laboratory?
For example consider a quantum system define relative to the orthonormal basis {<strong>up</strong>,<strong>down</strong>}. We can build a mixed state which is a combination of 2 or more pure states. Then we measured... | Yes, you can differentiate (assuming you have many many copies of the identically produced systems) between a pure state and a mixed state. As you notice, you cannot differentiate using a single operator as you can imagine a pure state having the same probability distribution over the spectrum of that operator. However... | Well, a pure state is an eigenstate of some operator. So if you can measure that observable you can readily distinguish between pure and mixed states.
For example with spin halves, there will be some polarisation angle along which the pure state is an eigenstate and you’ll always get the same outcome. But for a mixed s... | https://physics.stackexchange.com |
23,181 | [
"https://stats.stackexchange.com/questions/23181",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9177/"
] | How to get the marginal pdf of $p(y)$? Do you just integrate out $p({\sigma}^{2})$?
Say, the following joint distribution for $y \in {{R}^{d}}$ and ${{\sigma }^{2}}\in {{R}^{d}}$
IG: means inverse Gamma
$${{\sigma }^{2}}\sim IG(\alpha ,\beta )\propto {{({{\sigma }^{2}})}^{-(\alpha +1)}}{{e}^{-\beta /{{\sigma }^{2}}}}$... | What you get as your bottom line is of the form
$$
(\sigma^2) ^{-\alpha-1-nd/2}\exp\{-A\sigma^{-2}\}
$$
so the posterior distribution in $\sigma^{-2}$ is an inverse gamma distribution. (Note that
$$
\text{tr}((\sigma^2\Sigma)^{-1}S)=\sigma^{-2}\text{tr}(\Sigma^{-1}S)\,.)
$$
From this property, you can derive the ... | Note that the normalising constant for a IG variable is
$$\frac{b^a}{\Gamma(a)}$$
This is equal to the reciprical of the integral over $\sigma^{2}$ of the kernel of the pdf. hence we have
$$\int_0^{\infty}(\sigma^{2})^{-(a+1)}\exp\left(-\frac{b}{\sigma^2}\right)d\sigma^2=\frac{\Gamma(a)}{b^a}$$
Your integral is of... | https://stats.stackexchange.com |
29,565 | [
"https://dba.stackexchange.com/questions/29565",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/15790/"
] | We have a Facebook game that stores all persistent data in a MySQL database that is running on a large Amazon RDS instance. One of our tables is 2GB in size. If I run any queries on that table that take more than a couple of seconds, any SQL actions performed by our game will fail with the error:
HTTP/1.1 503 Service ... | I solved the problem by creating a read replica of the database. We can now run queries as complex and as long as we like, without taking the game down! :)
| What idexes do you have on this table? If the dbms engine is doing a full table scan, it will completely load a cpu and take a long time. If you have a 2 cpu system and all your data is in RAM, then you'll see 50% cpu usage.
Please create and index, such as
<pre><code>CREATE INDEX BlueBoxEngineDB.TransferIdx1
ON Blue... | https://dba.stackexchange.com |
66,239 | [
"https://security.stackexchange.com/questions/66239",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/52078/"
] | How can I prevent the installation of Chrome extensions on desktop?
| You can do this with a GPO. Go to Computer Configuration > Administrative Templates > Google > Google Chrome. Look for a folder named Allowed extensions. There configure a blacklist of <code>*</code>. This will prevent users from installing plugins.
| you can make it local by giving permission on extention folder in this path
<pre><code>C:\Users\*your user*\AppData\Local\Google\Chrome\User Data\Default\Extensions
</code></pre>
rightclick->security-> select user-> deny all
| https://security.stackexchange.com |
166,690 | [
"https://math.stackexchange.com/questions/166690",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/29209/"
] | I came across a question:
<blockquote>
If j is divisible by 12 and 10, is it divisible by 24 ?
</blockquote>
The example draws the following factor tree which I agree with
<img src="https://i.stack.imgur.com/uUlwq.png" alt="enter image description here">
But then it states that
<blockquote>
There are only two... | You are trying to compute the least common multiple of $12$ and $10$. The idea is that to compute the least common multiple, you prime factor each of the two numbers. Then in the lcm, the exponent of $p$ is the max of the exponent of $p$ in the two numbers. So if $p = 2$, $2^2$ appears in $12$ and $2^1$ appears in $10$... | Because, as they said, it may be redundant: it may be one of the two $2$’s already counted in the lefthand tree. Suppose, for instance, that $j=60$: then $j=2^2\cdot3\cdot5$ has only two factors of $2$, but it <strong>is</strong> divisible by both $12$ and $10$.
| https://math.stackexchange.com |
214,289 | [
"https://physics.stackexchange.com/questions/214289",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/60080/"
] | Consider the case in which there is initially $0$ electric or magnetic field anywhere in space, and then in a circular region of radius $R$ a constantly increasing magnetic field is introduced (at a rate of say $p$ Teslas per second).
<img src="https://i.imgur.com/jUunhVy.png" alt="here">
(ok the picture isn't much ... | The differential versions of Maxwell's equations would tell you something about the fields <em>at a point</em>.
For example, inside the circle, where $\partial \vec{B}/\partial t = p \hat{k}$, then Faraday's law
$$ \nabla \times \vec{E} = - \frac{\partial \vec{B}}{\partial t},$$
tells you what the "curl" of the E-fiel... | As I understand it, your system does have a great deal of symmetry. I'm assuming the problem is cylindrical, <em>i.e.</em> the picture you have drawing is valid at all values of $z$, if we make the $z$ co-ordinate out of the page. So, I'm assuming your problem definition is $\vec{H}(t) = k\,t\, \hat{z};\forall\,t>0;... | https://physics.stackexchange.com |
72,651 | [
"https://dsp.stackexchange.com/questions/72651",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/54772/"
] | I am having trouble finding the same answer as the solution manual for this sequence.
The problem asks to compute the DFT of
<span class="math-container">$$
x[n] = \begin{cases}
1 & \text{for even } n \in \{0\ldots N-1\}
\\ 0 & \text{for odd } n \in \{0\ldots N-1\}
\end{cases}
$$</sp... | Assuming <span class="math-container">$N$</span> even :
<span class="math-container">$$
\begin{align}
X[k] &= \sum_{n=0}^{N-1} x[n] ~ W_N^{kn} ~~~,~~~k=0,1,...,N-1\\ \\
&= \sum_{n=0}^{N/2-1} 1 ~ W_N^{k ~2n} \\ \\
&= \sum_{n=0}^{N/2-1} e^{-j 4\pi kn/N} \\ \\
& = \frac{ 1 - e^{-j \frac{4\pi k}{N}N/2 }}{ ... | Figured I'd post this since I wrote it anyway, just a confirmation of Fat32's answer.
Letting <span class="math-container">$N' = \frac{N}{2} - 1$</span> we have
<span class="math-container">$\sum_{0}^{\frac{N}{2} - 1} e^{\frac{-j2\pi k (2n)}{N}} = \sum_{0}^{N'} e^{\frac{-j2\pi k
n}{(N'+1)}}$</span>
Then plugging in ... | https://dsp.stackexchange.com |
54,674 | [
"https://physics.stackexchange.com/questions/54674",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/17338/"
] | I know I'm wrong but this is my line of thought: If electrons are indistinguishable, then why do we have an exclusion principle? If we have two electrons in an s orbital, the Pauli exclusion principle says that they can't have the same set of quantum numbers, but then what does that say about electrons being indistingu... | The indistinguishability of particles is expressed by imposing certain symmetry constrains on the state functions and on the observables. As you may know, there can be symmetric and antisymmetric state functions as you interchange two particle coordinates, and all the observables must be invariant under such operations... | If you can tell the particles apart (i.e. they have different mass, charge, etc.) then the state of the two-particle system is just a product of the individual states of the two particles a and b:
$$\psi(\mathbf{r}_1,\mathbf{r}_2)=\psi_a (\mathbf{r}_1) \psi_b (\mathbf{r}_2)$$
If the two particles are utterly identica... | https://physics.stackexchange.com |
123,732 | [
"https://electronics.stackexchange.com/questions/123732",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/50541/"
] | I couldn't find anything about this specific situation, but will it work, and are there any side effects that could damage it? Also, will it treat the USB as a computer?
| You are probably right, but it depends on how you define the transfer function. The sine part is right, while as you can see your \$H(s)\$ is not adimensional, it's something like \$s^2\$, that is pretty strange for a transfer function[^seconds].
You are safe assuming that's a slide mistake. For the future keep in min... | If the DC gain (= steady state gain) of your transfer function should be unity, then yes, there should be a wn^2 in the numerator of the TF. But there's nothing essentially wrong with the TF as it stands, it could legitimately have a DC gain of 1/wn^2 (but include the missing 's' in the denominator!).
| https://electronics.stackexchange.com |
8,042 | [
"https://mathoverflow.net/questions/8042",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1149/"
] | The title pretty much says it all: suppose $R$ is a commutative integral domain such that every countably generated ideal is principal. Must $R$ be a principal ideal domain?
More generally: for which pairs of cardinals $\alpha < \beta$ is it the case that: for any commutative domain, if every ideal with a generati... | No such ring exists.
Suppose otherwise. Let $I$ be a non-principal ideal, generated by a collection of elements $f_\alpha$ indexed by the set of ordinals $\alpha<\gamma$ for some $\gamma$. Consider the set $S$ of ordinals $\beta$ with the property that the ideal generated by $f_\alpha$ with $\alpha<\beta$ is... | The question is fully settled by Hugh Thomas' anwer, but let me mention this related interesting fact.
<b>Theorem.</b> There is a ring R and ideal I on R, such that every countable subset
of I is contained in a principal subideal of I, but I is
not principal.
Proof. Let I be the ideal of nonstationary subsets of
&om... | https://mathoverflow.net |
4,032,981 | [
"https://math.stackexchange.com/questions/4032981",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/840735/"
] | It's been quite long since high school and I forgot some stuff.
I'm trying to find the values for which <span class="math-container">$\frac{x}{1-x^2} > 0$</span>.
Now, obviously this occurs when <span class="math-container">$x < -1$</span> and <span class="math-container">$x>0$</span>, yet if you just solve th... | For rational functions (ratios of polynomials), sign changes can only occur where a factor of the numerator or denominator is zero. At such a point, the function itself will be either undefined (if the denominator vanishes) or zero (if the numerator vanishes).
So the best approach is to make a sign chart for each facto... | Two cases:
<ol>
<li><span class="math-container">$x>0$</span> and <span class="math-container">$1-x^2>0$</span>, which means <span class="math-container">$x>0$</span> and <span class="math-container">$x^2<1$</span>, i.e.,<span class="math-container">$0<x<1$</span>.
</li>
<li><span class="math-containe... | https://math.stackexchange.com |
260,598 | [
"https://softwareengineering.stackexchange.com/questions/260598",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/88091/"
] | I'm growing my understanding of event sourcing. My understanding is that it provides a means of recording events as they happen so that given a common beginning state and an audit log of recorded events, the events can be replayed to achieve the same final state.
I know that sometimes events are triggered by other ev... | The CLR standard does not require a stack or a heap, so lets get that out of the way first. But C# implemented on paper isn't very useful. I describe here the implementations we can run code with "in practice", like the Microsoft C# or Mono C#. Regardless, the method and local variables have a conceptual relationship w... | In general, program code exists in an area outside of what you mean when you say "stack" and "heap." While you mentioned C#, there are no language tags so I will describe how a typical modern desktop OS handles this at a low level.
When your program loads, there are two main areas of memory: code and data. The OS allo... | https://softwareengineering.stackexchange.com |
542,445 | [
"https://physics.stackexchange.com/questions/542445",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I've been reading in Khan academy about the formula for calculating magnetic field lines (Ampere's law). Some materials have the ability to concentrate magnetic fields, which is described by those materials having higher permeability. The permeability of vacuum is <span class="math-container">$4\pi *10^-7$</span> , whi... | The "ability to concentrate fields" is, at best, a very loose description of limited validity. Loose descriptions of limited validity always lead to paradoxes when taken too literally.
The magnetic permeability is a proportionality factor in the relationship between field and current. In free space, the relationship i... | The permeability of vacuum arises in classical field theory from the idea that space is not a nothing, but is a substantive something which supports the notion of a field. It appears differently in quantum electrodynamics, in which electromagnetic forces can be seen as arising from the exchange of photons between charg... | https://physics.stackexchange.com |
433,261 | [
"https://stats.stackexchange.com/questions/433261",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/260972/"
] | I'm currently working on a Bayesian network designed to find the probabilities for various lung diseases. In the network there are, among others, a normally distributed random variable (body temperature) causally dependent on a binary one.
In order to reach a diagnosis MCMC sampling is used (Metropolis in Gibbs). When... | The setting sounds to be one where the quantity to be simulated, <span class="math-container">$X$</span>, is discrete (e.g., integer), while an observable <span class="math-container">$Y$</span> indexed by <span class="math-container">$X$</span> is continuous. The posterior distribution of <span class="math-container">... | Proportionality is not fixing it, the point is different. Even if density and mass probability are two different things, and it's important to understand it when first approaching statistics, from a mathematical point of view they are actually very similar, so they are often expressed with the same symbol <span class="... | https://stats.stackexchange.com |
148,657 | [
"https://mathoverflow.net/questions/148657",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41303/"
] | Let $F$ be an infinite field and let $f \in F[x_{11},x_{12},...,x_{nn}]$ be an <strong>arbitrary</strong> polynomial in $n^2$ variables. Consider the function $\phi : M_n(F)\longrightarrow F$ defined by $\phi((a_{ij})) = f(a_{11},a_{12}, ..., a_{nn})$ and suppose that $\phi(I_n) = 1$ and $\phi(AB)= \phi(A)\phi(B)$, ... | The answer is yes. Classically, there is a group endomorphism
$g$ of $F^*$ such that $\phi(M)=g(\det M)$ for all non-singular $M$
(this is obvious if $|F|=2$, otherwise one uses the fact that $[GL_n(F),GL_n(F)]=SL_n(F)$).
Then, $g$ is a polynomial map from $F$ to itself that satisfies $g(XY)=g(X)g(Y)$. From there, it ... | Your condition implies that $\phi$ defines a homomorphism $GL_n(F)\rightarrow F^*$. Any such homomorphism annihilates the commutator subgroup $SL_n(F)$, hence factors as $GL_n(F) \,{\buildrel {\det}\over {\longrightarrow}}\,F^*\,{\buildrel {\lambda }\over {\longrightarrow}}\, F^*$, where $\lambda $ is a homomorphism. S... | https://mathoverflow.net |
121,218 | [
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] | I want to backup a SQL Server database by copying its files manually. Is copying the <code>database.MDF</code> and <code>database.LDF</code> files enough or should I also add more files?
It might be not the proper way for backing up a database, but in certain cases it might help for testing purposes for example.
Su... | <ol>
<li>Is there a reason for you to do this? Why don't you use:
<pre><code>backup database x to disk...?
</code></pre></li>
<li>Try at least to list all files of your database:
<pre><code>select
db_name(database_id) as Database_Name,
physical_name,
name,
state_desc
from sys.master_files
where
db_n... | Yes, it is possible for a normal database, if for any reason you do not want to use native backup. Just stop MS SQL Server Service before copy (and restore) files.
An example of when it will not work - if you use <strong>FILE-STREAM</strong>.
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