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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|---|---|---|---|---|---|
164,137 | [
"https://mathoverflow.net/questions/164137",
"https://mathoverflow.net",
"https://mathoverflow.net/users/46638/"
] | Let $G$ be a group. Consider an arbitrary equation given by $w(\vec{g})=e$, where $w: G^n \to G$ takes an $n$-tuple $(g_1,...,g_n)$ to some expression involving products of the $g_i$, their inverses and other elements of $G$.
Are there any good methods to determine whether such equation has a solution $\vec{g} \in G^n... | If you are interested in finite simple groups, there is a whole raft of literature considering the related question of which words maps $w: G^n\to G$ are <strong>surjective</strong>. The answer is often yes, so this gives a strong affirmative answer to your question in this case.
In general you should search the liter... | This may be largely irrelevant to what you're interested in, but in case it helps:
Philip Hall, On a theorem of Frobenius, Proceedings of the London Mathematical Society, (2) 40 (1936), 468-501.
| https://mathoverflow.net |
544,360 | [
"https://physics.stackexchange.com/questions/544360",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/260929/"
] | The problem is
A 2.00-kg textbook rests on a frictionless, hori-
zontal surface. A cord attached to the book passes over a pulley
whose diameter is 0.150 m, to a hanging book with mass 3.00 kg.
The system is released from rest, and the books are observed to
move 1.20 m in 0.800 s. (a) What is the tension in each p... | We need to first look at why the case you've mentioned is any different from the case where tensions are equal. A rotating pulley has mass and friction. The mass does the obvious, it gives the pulley a moment of inertia.
However, let's look at why we need friction. When the rope wants to move on the pulley, the fricti... | For this problem I would assume static friction between the cord and the pulley, and no friction at the axle of the pulley. Two different tensions result in a net torque on the pulley, giving it an angular acceleration. Use a kinematics equation to get the linear acceleration. Then write force equations for each boo... | https://physics.stackexchange.com |
62,277 | [
"https://physics.stackexchange.com/questions/62277",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4156/"
] | Having a brick lying on a table, I can exert horizontal force equal to $\mu m g$ to a middle of it's side, and it will start moving (assume $\mu$ is the friction coefficient). However, can I make the brick moving with less horizontal force? May be, applying it not to a middle of a side can help? I have no idea of how t... | Suppose that you exert the force with angle $\theta$ (with respect to ground). Then you will have:
$$\mu(mg-F\sin(\theta))=F\cos(\theta)\text{, so }F=\frac{{\mu}mg}{\cos(\theta)+{\mu}\sin(\theta)}.$$
Now, if you minimize this function with respect to $\theta$ you will find that
$$\tan(\theta)=\mu.$$
Replacing this $... | This may be a bit of an eye-rolly answer, but since you specifically state that all you care about is minimizing the horizontal force:
All you need to do is lower the normal force since the horizontal force you need to apply to get the brick moving needs to overcome the force of friction. Since friction, in the stati... | https://physics.stackexchange.com |
14,559 | [
"https://mechanics.stackexchange.com/questions/14559",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4922/"
] | I recently bought an "old" 1996 Dodge Dakota. When I turn left in a tight circle, I hear a pop or a click on the front-right side of the vehicle. I was told by the previous owner that it's the CV joint. Sure enough, I was under the car yesterday replacing the idler arm and saw grease sprayed all over the place around t... | The ball bearings are involved, but the noise isn't because they are dropping. What happens is when the boot splits, the grease starts oozing out (less lubricant) and dirt gets in causing wear. One of the jobs of grease is to take up excess slack in the joint (not that there is much in the first place when it's not wor... | The balls do not "click from side to side". As the balls shrink due to wear they are no longer thick enough to prevent the bearing spacer from hitting the joint housing as it passes by the housing. a joint with proper specs will not click at all, even when dry.
| https://mechanics.stackexchange.com |
582,980 | [
"https://physics.stackexchange.com/questions/582980",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/275963/"
] | I tried to imagine what would happen to a theoretical astronaut in the following thought experiment. The astronaut floats in space with the velocity of zero. He/she has a 10kg object and a wall 2 meters away (it floats in one place too). The wall and the object both have a(n) elasticity (coefficient of restitution) of ... | There are no external forces acting on the total system of astronaut, ball and wall. So if the centre of mass of the system is initially at rest (e.g in a reference frame in which the astronaut and the wall are both initially at rest) then it will remain at rest.
So after the astronaut has thrown the ball, it has bounc... | As @gandalf61 noted that there is no external force the center of the mass stays still till the object and the astronaut hits to the wall. Then because the collisions are not fully elastic there will be some loss in energy and also momentum (between astronout and the object). Considering the amount of defect center of ... | https://physics.stackexchange.com |
575,297 | [
"https://physics.stackexchange.com/questions/575297",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/244756/"
] | When we apply a voltage across a metallic conductor, the current starts to flow almost instantaneously. But when a temperature difference is established across the same conductor, the flow of heat is much slower. It takes larger time for the heat to reach from one end to the other than the current. Why is this so?
| The current flows almost instantaneously because it is driven by an electric field which appears across the conductor almost instantaneously (near the speed of light). All electrons in the conductor are set into motion by a chain reaction. Collectively they all move through the conductor at what is called the drift ve... | Let me first point out that heat is not carried by electrons. In fact, the temperature of the electron gas is much higher than that of the metal itself (thousands of Kelvins), but it makes a small fraction of the total thermal energy.
Electric current is a response to the electric field, which propagates with the speed... | https://physics.stackexchange.com |
427,774 | [
"https://electronics.stackexchange.com/questions/427774",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/148503/"
] | I am currently making a build-in PSU for my own audio-effect-rack-thing.
The internal PSU consists of two print-transformers(THT), one for 6VAC and the second one for 9VAC. These are also pretty low power ones (max 1A on the output).
I want to put the PSU circuit on a perfboard, since this is a simple design. I am al... | First of all, having the PCB properly manufactured would include solder resist all over the back side. Nowadays you can get reasonably good PCBs for a few dollars, if at all possible avoid the perfoboard and use a "real" PCB. If that is not possible, painting or conformal coating is the way to go. Make sure to use prop... | Your enclosure is not big enough.
However, most power supplies in metal enclosure have the enclosure grounded, provide enough distance to the board, and add a insulating material sheet as additional precaution.
Beware that sharp pins or soldering residue may not cut into this sheet, care must be taken when choosing t... | https://electronics.stackexchange.com |
86,594 | [
"https://electronics.stackexchange.com/questions/86594",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/30922/"
] | <img src="https://i.stack.imgur.com/JsbGL.png" alt="enter image description here" />
In the picture above I am trying to implement a steerable antenna, by means of the phase shifter chips U1, U2, and U3. Each is capable of varying the phase of the input by a maximum of 100 degrees (output depends on the bias). My goal ... | There are a couple of issues with your implementation:
1) 1.4 dB of loss is about 28% power loss -1.4 =10*log10(P1/P0), so by cascading you end up losing quite a bit to a point of not being able to steer
2) matching: when you are splitting a 50 Ohm line into 2 50 ohm lines, the line in effect sees a 50||50 or 25 Ohms... | Your LED would have to receive a power of 1.8V x (say) 5mA to illuminate - that is a power of 9mW. Your transmit antennas will have to be close to the receiving antenna for it to illuminate the LED and this means you are likely to be in the near field of your transmit antenna(s).
I'm half thinking that this rules out ... | https://electronics.stackexchange.com |
45,826 | [
"https://cs.stackexchange.com/questions/45826",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/37986/"
] | A lot of "famous" undecidable problems are nonetheless at least semidecidable, with their complement being undecidable. One example above all can be the halting problem and its complement.
However, can anybody give me an example in which both a problem and its complement are undecidable and not semidecidable? I though... | Consider the following language:
$$L_2 = \{(M_1,x_1,M_2,x_2) : \text{$M_1$ halts on input $x_1$ and $M_2$ doesn't halt on input $x_2$}\}.$$
$L_2$ is undecidable and not semi-decidable, and same is true of its complement. Why? The intuition is "$M_2$ doesn't halt on input $x_2$" isn't semi-decidable, so $L_2$ is not... | Note that the overwhelming majority of problems fit the criterion you're looking for: both the problem and its complement are not semi-decidable. This is because there are only countably many semi-decidable problems but there are uncountably many problems.
For an example, let $H$ be the halting problem for Turing mach... | https://cs.stackexchange.com |
1,793,414 | [
"https://math.stackexchange.com/questions/1793414",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/342906/"
] | Let $T$ be a linear map which is represented by the following matrix in the standard basis.
$$\begin{pmatrix}-1 & 0 & 1 \\ 1 & 2 & 3 \\ 2 & 3 & 4 \end{pmatrix}$$
I'm trying to find the kernel of the map $T$.
First I added row $3$ to row $1$ which gave me $$\begin{pmatrix} 0 & 0 & 1 \... | Because you are adding column 3 to column 1, which is incorrect. You can only do ROW reductions.
<br/>First switch row 2 to row 1 and switch row 3 to row 2, you get $\begin{pmatrix}1&2&3\\2&3&4\\-1&0&1\end{pmatrix}$
<br/>Then add row 1 to row 3, and add (-2)row 1 to row 2, you get $\begin{pmatri... | I would start with:
$A\mathbf x = 0$
$\mathbf x = \begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$
From the first row we an tell that $x_1 = x_3$
Arbitrarily, set them both equal to 1.
Multiply the next row, $4 + 2x_2 = 0, x_2 = 2$
And, check it with the 3rd row.
| https://math.stackexchange.com |
416,297 | [
"https://physics.stackexchange.com/questions/416297",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/197523/"
] | if you have 2 bodies (A,B), with Temperature of B>A, can you have heat transfer from A to B through radiation?
In particular if A reflects the wavelengths that B is emitting the radiation at would this be possible?
And if so is this process independent of the temperature of B (since A is reflective) or does A radiate... | <blockquote>
if you have 2 bodies (A,B), with Temperature of B>A, can you have heat
transfer from A to B through radiation?
</blockquote>
Yes, for instance, if radiation from A is focused on B, while radiation from B is directed elsewhere. The relevant statement of the second law of thermodynamics says:
<em>Heat ... | Yes, some times it is possible
This is happening in refrigerator.
In this case some energy must be supplied to complete this transaction
| https://physics.stackexchange.com |
310,828 | [
"https://physics.stackexchange.com/questions/310828",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/116557/"
] | I was wondering on which property does a material's tendency to fold depends upon.
When we push a metal plate, it seems to move forward. However a rug would start to fold and form crests. A piece of paper moves forward but folds very easily when an obstacle is present in its path.
<br> This tendency to fold seems to be... | Yes. It's compressive failure. There are three main strengths considered in evaluating material strength; tensile (stretching), compressive (opposite of stretching), and shear (cutting).
What you are calling "folding" is usually called "buckling" or the sudden sideways deflection of a structure.
Think of your paper a... | Elasticity has a lot to do with it.
Some materials respond with bigger displacements when stressed than others. In the case of a rug, it's a lot easier to make a rug bend than a piece of metal, because the rug is more elastic (that also has to do with it being a lot of thin fibres while metal would be a thick sheet... | https://physics.stackexchange.com |
109,581 | [
"https://cs.stackexchange.com/questions/109581",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/89097/"
] | Can anyone please help me out with my query: can disconnected graphs have minimum spanning trees?
| All you're looking for is some mapping between the elements of <span class="math-container">$P$</span> and their indexes, that can be found in <span class="math-container">$O(1)$</span> for each element of <span class="math-container">$P$</span>. Suppose given <span class="math-container">$p_i \in P$</span>, you can us... | Hint, try to determine which element of <span class="math-container">$R$</span> should be mapped to 0.
Then try to determine which element of <span class="math-container">$R$</span> should be mapped to 1. You will get the idea.
<hr>
Here is the pseudocode.
Input: array <span class="math-container">$P[0], P[1], \cd... | https://cs.stackexchange.com |
2,110,754 | [
"https://math.stackexchange.com/questions/2110754",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/408919/"
] | Show that for $k = 0, 1, 2, \ldots , n$, and for $n = 1, 2, 3, \ldots$ we have: $$ {n \choose k} = {{n-1} \choose {k-1}} + {{n-1} \choose k}$$
I know that there are a lot of solutions for the Newton's equal but I'm really sure what to answer.
| $\newcommand{\bbx}[1]{\,\bbox[8px,border:1px groove navy]{\displaystyle{#1}}\,}
\newcommand{\braces}[1]{\left\lbrace\,{#1}\,\right\rbrace}
\newcommand{\bracks}[1]{\left\lbrack\,{#1}\,\right\rbrack}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\ds}[1]{\displaystyle{#1}}
\newcommand{\expo}[1]{\,\mathrm{e}^{#1}\,}
\newc... | $$LHS={n\choose k}=\frac{n!}{(n-k)!k!}$$
$$RHS={n-1\choose k-1}+{n-1\choose k}=\frac{(n-1)!}{(n-k)!(k-1)!}+\frac{(n-1)!}{(n-k-1)!k!}=\frac{(n-1)!}{(n-k-1)!(k-1)!}\left[\frac{1}{n-k}+\frac1k\right]=\frac{(n-1)!}{(n-k-1)!(k-1)!}\left[\frac{n}{(n-k)k}\right]=\frac{n!}{(n-k)!k!}=LHS$$
| https://math.stackexchange.com |
1,466 | [
"https://dba.stackexchange.com/questions/1466",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/91/"
] | So, I'm about to write a quite simple web application, I am currently working actively on the database schema, and I need help to avoid major drawbacks. I've been programming (php) for a few years now, but never had any theoretical education, so I'm totally ignorant about database best practices, and would really like ... | Seriously look at third normal form. I would use surrogate keys with the natural keys implemented as unique keys. You will likely find that author belongs in its own authors table. You may find you have a few tables which are quite similar such as user_content_faves, user_author_faves, user_author_shares. This is no... | Creating generic tables with e.g. discriminator columns like you seem to suggest is a possible, but somewhat tedious practice when using an RDBMS - although some ORM frameworks have pretty good support for it. However, it will definitely cause a performance hit. It sounds like you are looking for a hierarchical model r... | https://dba.stackexchange.com |
114,939 | [
"https://electronics.stackexchange.com/questions/114939",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/18049/"
] | I wanted to switch a 60Vdc line to ON/OFF using a 60Vdc controlling signal for some kind of a feedback system (yes both are 60Vdc). Presently I have two options visible:
<ol>
<li>Solid State 60Vdc input relay</li>
<li>A dc/dc buck converter that changes my controlling signal to 12Vdc and then I use a normal 12Vdc ... | If you use a solid state relay you can just step down the voltage with a couple of resistor since the input current might be low enough. Just read the spec of your favorite SSR and size the resistors accordingly. If the maximum input current is \$I_{max}\$ and the minimum on voltage <em>on the input</em> is \$V_{IH}\$ ... | If the relay coil doesn't take much power you can use dropper resistors to power it. You already have "isolation" because of the relay coil-contact separation so the expense of a DC-DC converter is possibly too much. This assumes that most DC-DC converters are "isolating".
If the power lost in the coil dropper resisto... | https://electronics.stackexchange.com |
372,087 | [
"https://softwareengineering.stackexchange.com/questions/372087",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/287608/"
] | I have a validation method like this
<pre><code>def validate(a, b, c, d, e, f): Boolean = {
val rs1 = check1(a, b)
val rs2 = check2(c, d)
val rs3 = check3(e, f)
rs1 && rs2 && rs3
}
</code></pre>
I have tests for all of the smaller methods <code>check1</code>, <code>check2</code>, and <code>ch... | Test things that could go wrong. So maybe, writing tests for this method would not have much value. It is very simple code, and unlikely to be incorrect. The most likely source of errors is that you are passing the wrong arguments to the check() functions. If you are using a statically typed language, that risk is alre... | <blockquote>
I have tests for all of the smaller methods <code>check1</code>, <code>check2</code>, and <code>check3</code>...
</blockquote>
That is the cause of your current problems. <code>check1</code> etc are implementation details of <code>validate</code>, so should only be tested via testing <code>validate</cod... | https://softwareengineering.stackexchange.com |
430,043 | [
"https://physics.stackexchange.com/questions/430043",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/207305/"
] | I have a controversial case. I have a rod, which is fixed from one end (constraint). From another end, I apply a compressive force, by pressing the rod down. So in a way I have a constraint, but at the same time an external force. How do I model it? Do I give a boundary condition (displacement = 0) from both ends, or j... | Possibly you are making the mistake of thinking of the universe as expanding from some central explosion? That is not so. All parts of the universe were part of the big bang.
The "oldest" light we can see was emitted about 13.7 billion light years ago, approximately 400,000 years after the big bang. That light has tra... | After the Big Bang the universe was full of hot plasma, which both absorbed and emitted photons. The result was that the oldest photons we can see come from the end of that era (a few hundred thousand years after the big bang); they make up the cosmic microwave background today.
The age of the universe is calculated ... | https://physics.stackexchange.com |
430,293 | [
"https://softwareengineering.stackexchange.com/questions/430293",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/357086/"
] | Say I have the following data-structure describing a given widget sold by my company, which contains fields of purely atomic information (i.e. data that cannot be otherwise derived from other available fields).
<pre><code>my-widget = { "widget-id": 1, "amount-sold": 100, "profit-per-sale":... | The answer depends largely on the mutability of the structure. If the values used to create the calculation can change, then storing the computed result can be a source of bugs. That is, you must ensure that it is recalculated when the inputs to the calculation are updated. This is achievable but adds risk. I woul... | The collection of techniques/tools called <strong>Optics</strong> holds the true, and most elegant, answer here. You can have your datastructures of completely pure and atomic information, and make access to frequently calculated information as easy as normally querying any field, by making a Lens or similar entity for... | https://softwareengineering.stackexchange.com |
170,590 | [
"https://physics.stackexchange.com/questions/170590",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/72125/"
] | Fierz-Pauli action can be written as
$$
\tag{1} S = \int d^Dx \; \frac{1}{2} h_{\mu \nu} \mathcal{O}^{\mu \nu, \alpha \beta}h_{\alpha \beta}
$$
where the operator
$$
\tag{2} \mathcal{O}^{\mu \nu} {}_{\alpha \beta} = \left( \eta^{( \mu}{}_{\alpha}\eta^{\nu )}{}_{\beta} - \eta^{\mu \nu} \eta_{\alpha \beta}\right) \le... | You are basically asking how to compute $$e^{i\gamma B \hat{S}_z t/\hbar} |+\rangle.$$
Now, $e^{i\gamma B \hat{S}_z t/\hbar} =\sum_{n=0}^{n=\infty} \frac{\left(i\gamma B \hat{S}_z t/\hbar\right)^n}{n!},$ so you can approximate it quite well by
$$\sum_{n=0}^{n=N} \frac{\left(i\gamma B \hat{S}_z t/\hbar\right)^n}{n!}.$... | <blockquote>
but I'm stuck to carry the computation forward: what does
$e^{i\hat{S}_zt}$ do to an eigenvector like $|+\rangle$? I'm stuck
because the exponential contains an operator, and I want to get an
expression without operator.
</blockquote>
Luckily, you only have to act the operator on its own eigenvect... | https://physics.stackexchange.com |
194,149 | [
"https://stats.stackexchange.com/questions/194149",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/103116/"
] | I am trying to find a way to classify and segment a large set of time series that each individually describe a dynamical system. I wanted to know if the following idea for doing so is a feasible method. If I used a dynamic time warping based clustering method to segment the set of time series into separate clusters, wo... | <blockquote>
If I used a dynamic time warping based clustering method to segment the set of time series into separate clusters, would those clusters tend to be the same in a topological sense? (i.e. they each describe dynamical systems that have the same number of attractors with the same stability types?)
</blockquo... | (Writing in the answers section since I cannot comment yet)
A couple of points and sanity checks:
<ul>
<li>Are you dealing with linear dynamical systems? Even the simplest non-linear ones, such as the Duffing oscillator, can exhibit extreme sensitivity to initial conditions and a time-series analysis involving initial... | https://stats.stackexchange.com |
72,361 | [
"https://mathoverflow.net/questions/72361",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1898/"
] | Let $M_n$ be the $n\times n$ matrix
$$
(M_n)_{ij}=\begin{cases}1 & i\leq j,\\\\ 0 &i>j.\end{cases}
$$
Is there around an explicit expression or at least an asymptotic for $\left\Vert M_n \right\Vert$? The norm is the usual Euclidean induced norm $\left\Vert M \right\Vert=\rho(M^TM)^{1/2}$.
I apologize if th... | The eigenvalues of $M^{\rm T}M$ are $1 / (4 \phantom. \cos^2\frac{k\pi}{2n+1})$ for $k=1,2,\ldots,n$. The largest of these arises for $k=n$ and equals $1/(4\phantom.\sin^2\frac{\pi}{4n+2})$. Hence $\|M\| = 1 / (2 \phantom.\sin\frac{\pi}{4n+2})$, which is asymptotic to $2n/\pi$. This is easier to see if we work not w... | [This may be largely an alternate version of Noam's answer, but the extra context could be
interesting.]
Let $N$ be the $m\times m$ matrix with $N_{i,i+1}=1$ for $i=1,\ldots,m-1$
and all other entries zero. Then the matrix
$$
A = \begin{pmatrix}0&I+N\\\\ (I+N)^T&0 \end{pmatrix}
$$
is the adjacency matrix ... | https://mathoverflow.net |
312,563 | [
"https://softwareengineering.stackexchange.com/questions/312563",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/220219/"
] | I am solving an algorithm question and my analysis is that it would run on O(2^sqrt(n)). How big is that? Does it equate to O(2^n)? Is it still non-polynomial time?
| This is an interesting question. Fortunately, once you know how to solve it, it is not particularly hard.
For functions <i>f</i>: <b>N</b> → <b>R</b><sup>+</sup> and <i>g</i>: <b>N</b> → <b>R</b><sup>+</sup>, we have <i>f</i> ∈ <b>O</b>(<i>g</i>) if and only if lim sup<sub><i>n</i>→&... | How big is that? Well, O (2 ^ sqrt (n)) is exactly how big it is :-(
To get an idea what it means, imagine your algorithm wouldn't be just O (2 ^ sqrt (n)), but that it actually takes precisely 2 ^ sqrt (n) nanoseconds on your computer:
n = 100: 2^10 = 1024 nanoseconds. No time at all.
n = 1000: 2^31.xxx = 2 billio... | https://softwareengineering.stackexchange.com |
115,599 | [
"https://softwareengineering.stackexchange.com/questions/115599",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/39161/"
] | I am fairly new to PHP and OOP. Having said that, I wanted to know how independent functions should be within a class. I know that each function should be responsible for doing just one thing. However, as you can see in my class below, I occasionally find myself creating functions that build upon one another in a "c... | What you have looks fine.
You have several actions <code>setEmailAddresses</code>, <code>getEmailAddresses</code> each of which comprise of a series of steps. Some of these steps are common across multiple actions so it makes perfect sense to factor them out into their own methods.
The remaining part of the action co... | To answer your question, no, it's not at all bad practice to divide the internals of a class across multiple methods as you've done here. As the other answers and comments have said, it's actually good practice.
You're on the right track, but I did see a couple of things that I think need attention. From the example y... | https://softwareengineering.stackexchange.com |
86,326 | [
"https://dsp.stackexchange.com/questions/86326",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/45510/"
] | My question is:
Which type of diversity technique is used by the rake receivers?
In Bahai, et. al. "<em>Multi-Carrier Digital Communications Theory and Applications of OFDM,</em>"
Second Edition, 2004, on page 27, it is said that RAKE, OFDM, and Equalization, are all using frequency diversity, but here and th... | I just received this email from one of the greatest in wireless communications: Dr. Fuyun Ling.
He said:
"I think the confusion point is what is the definition of the (optimal) frequency or time diversity. I don't think there is such a rigorous definition. If we define the optimal frequency/time diversities as a... | Personally, I think it's more natural to describe the RAKE receiver as a time-diversity system.
However, in a wireless system multipath is only resolvable if the bandwidth is large, so RAKE receivers are only useful for wideband signals. So, in a sense, the RAKE receiver depends on the fact that the channel exhibits fr... | https://dsp.stackexchange.com |
234,785 | [
"https://dba.stackexchange.com/questions/234785",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/111981/"
] | I wrote a query that finds me records in <code>discovery</code> table that contain a needle from <code>whitelisted</code> (LIKE %needle%) and don't have a record in <code>logs</code> table (and some other easy to understand filtering):
<pre class="lang-sql prettyprint-override"><code>SELECT * FROM (
SELECT discove... | If your database supports it, you can use a table level CHECK constraint to compare two columns to make sure that they're equal. You could have a single CHECK constraint that confirms the <code>course_id</code> and <code>sem_id</code> pointing to each parent are the same.
Alternatively, you could just have one <code>... | I think your issue is a modeling one, as you skipped a few relations along the way. You can enforce your data consistency exclusively with the schema, no need for code enforcement with triggers or otherwise.
Also, why use surrogate keys for such a model? Try using the natural keys which in your case are short, stable,... | https://dba.stackexchange.com |
140,930 | [
"https://security.stackexchange.com/questions/140930",
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"https://security.stackexchange.com/users/96659/"
] | Are CRL lookups performed when receiving a S/MIME signed e-mail or onyl when it's encrypted ?
| It is difficult to provide a single complete answer because there are too many variables and what may work for one model/brand may not work for another. The term 'Smart TV' is also poorly defined and not all of them 'call home' - many don't even have a built in webcam or microphone.
The first question you need to ask... | My suggestion would be to get a large computer monitor instead; you'll often get a higher resolution that way, it will be good for gaming, and it (likely) won't be able to access the internet on its own.
| https://security.stackexchange.com |
252,287 | [
"https://security.stackexchange.com/questions/252287",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/261186/"
] | I have numeric IDs that I would like to use in filenames. So for example with IDs 1, 2, 3 we would have 1.jpg, 2.jpg, and 3.jpg
Now the problem is that clearly a user could just guess 4.jpg and view something they shouldn't be able to find.
Previously we have used UUIDs for this purpose but in this particular case I th... | No security concern
For hmac it’s all about keeping the key secret - downsides are difficulty in rotating the key (in this use case). If you need the url to be a permanent link then you can’t rotate the key. If the key is compromised you can’t rotate without revoking all the old urls.
But how will you know what file th... | Security concerns? It depends on the goals of your system and on the threats you consider.
For instance, if you you want to provide links only to the users who paid for them, then users can share the links. You have no way to know if particular request comes from the user that has paid for the link.
Also if users store... | https://security.stackexchange.com |
2,104,937 | [
"https://math.stackexchange.com/questions/2104937",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/407271/"
] | How would i prove a conditional in this form:
$ A \rightarrow (B \vee C)$
through 'algebraic' manipulations i come up with the equivalence
$ A \rightarrow (B \vee C)$ $\Leftrightarrow$ $( A \wedge ¬B \rightarrow C)\wedge (A \wedge ¬C \rightarrow B)$
So, to prove $ A \rightarrow (B \vee C)$ one must prove $ A \wedg... | For the homogeneous, and trying solutions of the form $y=t^k,$ we get $y'=kt^{k-1}$ and $y''=k(k-1)t^{k-2}.$ So, $$t^2k(k-1)t^{k-2}-2tkt^{k-1}+2t^k=0$$
$$\Rightarrow k(k-1)-2k+2=0.$$ Now, find $k.$
| Outline: This is an Euler equation. Try the a solution of the form $y = t^r$ in the homogeneous equation. After you plug it in, you can cancel all $t$'s and you have a quadratic in $r$. The two solutions for $r$ give you two solutions for the homogeneous equation. Then use variation of parameters to find a particu... | https://math.stackexchange.com |
601,689 | [
"https://physics.stackexchange.com/questions/601689",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/266050/"
] | This question was inspired from the fact whether a moving body can become a blackhole in a frame of reference. On looking it up here, I found the answer was that its not possible since it violates priciple of relativity as you can be in a frame where the black hole was never formed and was ordinary matter.
So, I conclu... | This is not uncommon idea from beginners: if relativistic mass increases without bound, then at some speed, a blackhole should be formed.
Let's say we're talking about a uniform density prolate spheroid with major axis <span class="math-container">$a$</span> and minor axis <span class="math-container">$b$</span>. Also,... | (i)Why does that violate the principle of relativity? Which law is violated?
(2) On what can observers actually agree and what decides that (i.e what quantities are invariant and what decides that)?
I try to answer both of the questions at once. The observers will always agree on <span class="math-container">$ds^2$</sp... | https://physics.stackexchange.com |
19,787 | [
"https://electronics.stackexchange.com/questions/19787",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5817/"
] | A flip flop is a sequential circuit and it stores a 1-bit value,
but it is designed using only basic, universal gates and a feedback circuit. How then is it able to store or handle a 1-bit value?
I thought that it is due to clock usage but I don't know the exact reason.<br>
Is my assumption is correct or not?
| The easiest flip-flop to understand is the SR (Set-Reset) flip-flop:
<img src="https://i.stack.imgur.com/SXfyD.png" alt="SR flip-flop">
Normally both inputs are high. When you pull the \$/S\$ input low, output \$Q\$ will go high regardless of the other input. Since the other NAND gate sees now a high level on both ... | For those who are not engineering students (curiosity-seekers) I will try to get a metaphor in your mind: think of the set-reset flip-flop picture as a water park with water streams instead of electricity. The water flows in a circle, like a slide with some turns. In this (simple) metaphor, there are two possible flows... | https://electronics.stackexchange.com |
3,287,925 | [
"https://math.stackexchange.com/questions/3287925",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/685160/"
] | I want to solve this inequality <span class="math-container">$\left| x-3\right|\le 4$</span>, and I know that it's solved like this: <span class="math-container">$$\because-4 \le x-3 \le 4 \iff-1 \le x\le 7 \\ \therefore S.S=\left[-1, 7\right]$$</span>, but I want to know why I solve it like that, I have tried to say: ... | What you are trying to do can be interpreted like this.
<span class="math-container">$|x-3| \le 4$</span> has two possible cases:
<ul>
<li><span class="math-container">$x-3 \ge 0$</span>, then <span class="math-container">$|x-3| = x-3$</span> and the inequality yields <span class="math-container">$x-3 \le 4 \iff x \l... | You have to work with the definition of the absolute value for <span class="math-container">$x \in \mathbb{R}$</span> being <span class="math-container">$\vert x \vert = x$</span>, for <span class="math-container">$x \geq 0$</span> and <span class="math-container">$\vert x \vert = -x$</span> for <span class="math-conta... | https://math.stackexchange.com |
16,939 | [
"https://stats.stackexchange.com/questions/16939",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6072/"
] | Can someone please offer a nice succinct explanation why it is not a good idea to teach students that a p-value is the prob(their findings are due to [random] chance). My understanding is that a p-value is the prob(getting more extreme data | null hypothesis is true).
My real interest is <strong>what is the harm</st... | I have a different interpretation of the meaning of the wrong statement than @Karl does. I think that it is a statement about the data, rather than about the null. I understand it as asking for the probability of getting your estimate due to chance. I don't know what that means---it's not a well-specified claim.
But ... | I've seen this interpretation a lot (perhaps more often than the correct one). I interpret "their findings are due to [random] chance" as "$\text{H}_0$ is true", and so really what they are saying is $\Pr(\text{H}_0)$ [which actually should be $\Pr(\text{H}_0 | \text{data})$; say, "given what we have seen (the data), ... | https://stats.stackexchange.com |
283,710 | [
"https://math.stackexchange.com/questions/283710",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/50005/"
] | I need help with this exercise:
Given the PDE $$u_t=-10u_{xx}\tag{1},$$ with periodic boundary conditions in $[-1,1]$: $$u(-1,t)=u(1,t), \qquad u_x(-1,t)=u_x(1,t).$$
A) Obtain the solution $u(x,t)$ if $u(x,0)=u_0(x)=\sin(\frac{\pi}{10}x)$
B) If we consider as initial data $u_0(x)=x^2$ defined also in $[-1,1]$, does ... | First of all, periodic boundary conditions look like a <em>pair</em> of boundary conditions, e.g. like $$u(-1,t)=u(1,t), \quad u_x(-1,t)=u_x(1,t).$$
Start by separating variables, finding the eigenvalues $\lambda_n$, eigenfunctions $X_n(x)$, and temporal solutions $T_n(t)$.
Superimpose those to get something of the f... | I doubt that whether you can really solve it even for A).
Let $u(x,t)=X(x)T(t)$ ,
Then $X(x)T'(t)=-10X''(x)T(t)$
$\dfrac{T'(t)}{10T(t)}=-\dfrac{X''(x)}{X(x)}=n^2\pi^2$
$\begin{cases}\dfrac{T'(t)}{T(t)}=10n^2\pi^2\\X''(x)+n^2\pi^2X(x)=0\end{cases}$
$\begin{cases}T(t)=c_3(n)e^{10n^2\pi^2t}\\X(x)=\begin{cases}c_1(n)\... | https://math.stackexchange.com |
22,678 | [
"https://mathoverflow.net/questions/22678",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5072/"
] | In a ring <strong>R</strong> (nonempty class of sets closed under difference and finite union), any sequence (here means a function on natural numbers $\mathbb N$) {$E_i$} in <strong>R</strong> can be disjointlized to a disjoint sequence {$F_i$} such that $\bigcup E_i=\bigcup F_i$ by traditional induction using the equ... | Let's take the usual ring of finite unions $E$ of half-open rectangles $[a,b)\times [c,d)$ on the plane. The closed half-plane $x+y\ge 0$ is a union of continuum of such rectangles (all possible rectangles contained in that closed half-plane) but, since each $E$ contained in this half-plane can intersect the boundary l... | "Disjointlization" ... the world would be a better place without this word!
| https://mathoverflow.net |
3,862,127 | [
"https://math.stackexchange.com/questions/3862127",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/771930/"
] | I tried this: <span class="math-container">$a_n=\frac{\ln(n^2+n+2)}{\ln(n^2+n+1)}=\frac{\ln(n^2+2n-n+2)}{\ln(n^2+n+1)}=\frac{\ln(n(n-1)(n+2))}{\ln(n^2+n+1)}$</span> and I did calculations, but I don't get a good result!
| Geometrically & binomially expand ...
<span class="math-container">\begin{eqnarray*}
\left(1+\frac{x}{j}\right)^{-1}\left(1+\frac{1}{j}\right)^{x}= \left(1-\frac{x}{j}+\frac{x^2}{j^2}+ O(\frac{1}{j^{3}}) \right)\left(1+\frac{x}{j}+\frac{x(x-1)}{2} \frac{1}{j^2} +O(\frac{1}{j^{3}}) \right)
\end{eqnarray*}</span>
| okay so if we have some <span class="math-container">$x\in\mathbb{C}$</span> then it is fair to write it as <span class="math-container">$x=a+bj$</span>
now:
<span class="math-container">$$\frac1j=\frac1j \frac jj=-j$$</span> and so:
<span class="math-container">$$\frac xj=-j(a+bj)=-aj+b$$</span>
see if you can do anyt... | https://math.stackexchange.com |
386,843 | [
"https://stats.stackexchange.com/questions/386843",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/113793/"
] | Generate 1000 sets of numbers from the Cauchy distribution. Do this for set size 2, 5, 10 and 20. Compute the median of each set. Find the distribution of the medians, for each set size.
How do I create the set size of 2,5,10, and 20?
| The idea is to simulate 1000 random variables time the set size.
The following code will give you a matrix of 1000 row and a number of column corresponding to the set size.
<pre><code>set_number <- 1000
set_size <- 2
location <- 0
scale <- 1
mat <- matrix(data = rcauchy(set_number*set_size, location, s... | Thank you for your question!
The question is basically asking to run 1000 iterations of Cauchy distribution generated numbers for sets of sizes of 2 variables, 5 variables, 10 variables, and 20 variables.
The solution below demonstrates how to solve the step with 2 variables.
<strong>Step 1:</strong> Create an empty ... | https://stats.stackexchange.com |
405,888 | [
"https://electronics.stackexchange.com/questions/405888",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/35737/"
] | Referring to just what the I2C lines draw, am I wrong thinking that the higher the clock frequency the shorter the time there will be (the same amount of) current flowing through the pullups and thus lower power consumed?
<hr>
<strong>side qeustion</strong>
I don't think I am going to reach 100 kHz, that's way over ... | Higher clock frequency usually require lower pull-up value, thus increasing the current.
Increasing the clock frequency from 100kHz to 400kHz usually requires the pull-up to be reduced with a factor of 4-5.
Since the power is inverse proportional to the resistance the power consumed will be almost the same.
| Your thinking is correct, as long as you can achieve a higher speed with the same pull up resistors.
| https://electronics.stackexchange.com |
431,844 | [
"https://electronics.stackexchange.com/questions/431844",
"https://electronics.stackexchange.com",
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] | Measuring ripple of 28V/12V power supply module across +/- output pins. Does the probe tip have to be placed at +pin and probe gnd to -pin, or it can be reversed?
Having inverted readings when polarity is inverted is fine, but is there a possibility to damage the module or the scope?
| Most outlets aren't polarized. Even in places where the outlets are polarized, mistakes happen.
There's a straight connection between the outlet and the ground of the USB port. All there is in between the two is a diode.
If that wire is connected to neutral in the outlet, then nothing bad will happen if you touch t... | The impedance of that capacitor at 50Hz is about 3200 Ohms. Which means a current of 75mA if I have done the maths correctly. The problem is that the voltage at the user end will rise until it either gets to 240VAC or it drives that 75mA through whatever - including you. Which is quite possibly fatal. There is nothing ... | https://electronics.stackexchange.com |
606,024 | [
"https://physics.stackexchange.com/questions/606024",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/281673/"
] | so there is an exercise where you need to find out what the maximum compression is of two blocks hitting eachother, what the velocities are after the collision and if the collision is elastique. I've tried and tried but didn't seem to get anywhere. Maybe I'm just making a stupid
reasoning error. Hopefully one of you co... | I am just going to explain the process going on.
As they collide the spring will compress first till both the blocks reach same velocity; as now they move with same velocity the spring does not compress further and max compression is reached. Now due to <span class="math-container">$F_{spring}$</span> the blocks will s... | In addition to the prior answer: an ideal spring is always elastic, as it has zero mass and zero damping. The spring can only store energy, temporarily. It cannot dissipate it, or keep it stored (as potential/kinetic energy oscillations after the collision, as <span class="math-container">$m=0$</span>).
A spring with d... | https://physics.stackexchange.com |
104,153 | [
"https://electronics.stackexchange.com/questions/104153",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/38125/"
] | I am trying to make a copper pipe which is placed in a natural park capacitive. It is placed in the soil meaning that it is already grounded. I am using a basic arduino and their capacitive sensing library to quickly experiment with, but the issue I am having is that the arduino itself needs to be grounded in order to ... | Your basic problem is that you have a relatively small resistance accross your capacitor. This resstance is dominating when you try to measure the capacitance.
You are trying to measure something that doesn't make much sense. You have to decide what exactly you are really trying to measure. If you want to measure c... | You have answered your own question.
You have grounded the capacitive sense object (pipe) and thus the value of the reading will be near zero or at least not have much of a change range.
In order to sense people approaching the pipe you need to have it isolated from the ground.
| https://electronics.stackexchange.com |
357,622 | [
"https://stats.stackexchange.com/questions/357622",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/209784/"
] | Let $X_1, X_2$ be independent, exponentially distributed random variables with mean 2. So $X_1+X_2=Z$ is gamma distributed with $\alpha=2$ and $\beta=1/2$.
I am trying to solve the probability that $X_1>3$ given that $X_1 +X_2>3$. This should be fairly straightforward, yet my answer differs from the book's answ... | \begin{equation}
\begin{aligned}
P(X_1 > 3 \mid X_1 + X_2 > 3)
& = \frac{P(X_1 + X_2 > 3 \mid X_1 > 3)P(X_1 > 3)}{P(X_1 + X_2 > 3)} \\
& = \frac{P(X_1 > 3)}{P(X_1 + X_2 > 3)} \text{ since $ X_2 > 0 $ with prob. 1} \\
& = \frac{e^{-1.5}}{P(X_1 + X_2 > 3)} \text{ using Exp($\frac... | Z denotes the point in time when the second Poisson event occurred. Z>3 means that the second Poisson event occurred after time 3, and therefore it is equivalent to Q<2 (Q being the number of Poisson events up to time 3) and not to Q>=2 as you calculated. If you divide 0.223 by 1-0.442=0.558, you will get the correc... | https://stats.stackexchange.com |
13,133 | [
"https://mathoverflow.net/questions/13133",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2348/"
] | Is it possible that $\mathbb{P}^n$ is an algebraic vector bundle over some algebraic variety? This is an interesting question that my friend asked in a student seminar. I believe that the answer is NOT. Because the only global sections of $\mathcal{O}_{\mathbb{P}^n}$ are constants. However as a total space of vector bu... | Stephen Griffeth's argument works over any field. The total space of a vector bundle is never proper (follows by, e.g., valuative criterion for properness). On the other hand, $P^n$ is always proper.
Here is an argument that the total space of a vector bundle is not proper: A fiber of a vector bundle is isomorphic to ... | That's right. I think the one sentence rephrasing of Kevin's argument would be <em>proper morphisms are stable under pullback</em> (this is obvious by the very definition of properness which is stated through the pullbacks).
Of course a variety is proper if and only if the structure map to the point scheme (spec k) is... | https://mathoverflow.net |
135,616 | [
"https://stats.stackexchange.com/questions/135616",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/67773/"
] | I have a few questions about unrestricted error correction models.
The UECM for a model where $Y$ is the dependent variable and $x$ is the sole independent variable is given by
$$
\Delta Y_{t}=\alpha_{0}+\sum_{n=1}^{N}\beta_1\Delta y_{t-i}+\sum_{n=1}^{N}\beta_2\Delta x_{t-i}+\gamma_{1}y_{t-1}+\gamma_{2}x_{t-1}.
$$
Her... | <ol>
<li>In the long run the first differences are taken as zero and the long-run equation reduces to </li>
</ol>
$\gamma_1y+\gamma_2x$=0 which is the long run relationship between the variables. The $\gamma$'s define this long run relationship. The $\beta$'determine the short run adjustment to this equilibrium.
2.Se... | On question 1:
In this setting we assume that <span class="math-container">$Y$</span> and <span class="math-container">$x$</span> are not stationary. If they were stationary there'd be little sense in talking about a long-run relationship -- <span class="math-container">$E[Y_t]$</span> would be some <span class="math-c... | https://stats.stackexchange.com |
484,431 | [
"https://physics.stackexchange.com/questions/484431",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/180710/"
] | Premise: The speed of light is set <span class="math-container">$c = 1$</span>.
Let's consider an electron in an external electromagnetic field. Its four-momentum will be
<span class="math-container">$$p^{\mu} = (E, \bar p) = (\gamma m_e, \gamma m_e \bar v),$$</span>
where <span class="math-container">$m_e$</span> is ... | The charge of <span class="math-container">$1C$</span> was derived from the definition of Ampere. If you look at the SI units, you'll check that, surprisingly, intensity of current is a basic unit, whereas charge is a derived quantity. This is a bit weird, because charge is seen as "more fundamental" than current, curr... | I edited the question to be of the right form. The ampere is now defined by fixing the numerical value of the elementary charge (the charge of an electron or proton) in the International System of Units to be exactly equal to <span class="math-container">$1.602176634\times10^{-19}$</span> coulombs.
So why not a nice r... | https://physics.stackexchange.com |
25,211 | [
"https://mathoverflow.net/questions/25211",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5534/"
] | Let's say I have a multiset of complex numbers $\lbrace a_1,\cdots,a_n\rbrace$ (so some of the elements may be repeated) and I would like to construct an entire function $p(z)$ with those numbers as zeroes. However, I also have a multiset of complex numbers $B = \lbrace b_1,\cdots,b_n \rbrace$ such that I wish $p(b_i) ... | If I read you right,
you want an entire function that takes the values $0$ and $1$ at only
finitely many (specified) points. This implies that the function must be a polynomial,
by Picard's great theorem, since there will be deleted neighbourhoods of
infinity where the function misses two values.
| In your statement, you do not say explicitly, whether $p$ is aloowed to have other zeros, except
those in the set $A$.
If you want to construct an entire function with zeros and ones exactly prescribed, this is clearly
impossible when your sets $A$ and $B$ are both finite. For the reason explained by Robin Chapman.
... | https://mathoverflow.net |
48,346 | [
"https://datascience.stackexchange.com/questions/48346",
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] | number of features: 12 , -15 < each feature < 15
number of targets: 6 , 0 < each target < 360
number of examples: 262144
my normalization: I normalized the features so that they are between 0 and 1. I normalized the targets so that they are between 1 and 10.
This is the model that I am using:
<pre><co... | Accuracy is a metric for classification, not regression.
<span class="math-container">$$Accuracy = \frac{\text{Correct classification}}{\text{Number of classifications}}$$</span>
So when you use accuracy for regression only the values where <code>actual_label == predicted_label</code> are evaluated as true are count... | You don't have to normalize regression targets but in a different case you might have wanted to scale them so that the loss of one output doesn't dominate over the loss for other outputs.
The very important thing here is that you are predicting angles which are periodically bounded but you have them as continuous valu... | https://datascience.stackexchange.com |
2,896 | [
"https://dsp.stackexchange.com/questions/2896",
"https://dsp.stackexchange.com",
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] | I am implementing a Flanger using a fractional delay line. I am modulating the length of the delay line using a sin function. The delay line already uses linear interpolation to compute the delay output for the fractional sample.
When the delay length is decreasing (and pitch is increasing), the modulated length sou... | It's a bug.
M_PI*config->count++
You are processing 2 channels, but incrementing your modulation in the inner loop. So at the end of processing 1 channel, you <em>continue</em> to increment the modulation as you process the second channel.
<pre><code>c1 [ 1,2,3,4] [9,10,11,12]...
c2 [5,6,7,8]
</cod... | Some artifacts are always going to be present whenever you deviate from strict LTI (linear time invariant) systems. With time varying systems you will see FM sideband energy dispersions, which present as non removable aliasing noise. This is sadly the case even assuming bug free code, band limited interpolation and a m... | https://dsp.stackexchange.com |
78,392 | [
"https://dba.stackexchange.com/questions/78392",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/47231/"
] | I want to clone oracle databases on the same machine and
I need to change user etc. from e.g. PROD to DEV.
For that I use expdp/impdp, but this tends to be slow with increasing database size.
I need to do this on linux and windows machines.
Is using expdp/impdp the fastest way to do this?
Or should I use a completly ... | The user must be a member of <code>dbcreator</code> server role for user to have enough permissions to create a database.
You can execute the following statement to make a user member of <code>dbcreator</code> server role.
<pre><code>EXEC master..sp_addsrvrolemember @loginame = N'Shubhankar', @rolename = N'dbcreator'
G... | All the above points are clear but there is one which is missing. I struggled to find the solution to this problem and finally got it after long research.
To get permission to create database in your local account follow the below given steps.
Step 1: Disconnect from your local account.
Step 2: Again Connect to Ser... | https://dba.stackexchange.com |
15,186 | [
"https://chemistry.stackexchange.com/questions/15186",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/5084/"
] | I understand that in general, when in acidic media, the nucleophile tends to attack the more substituted side of the epoxide due to electronic reasons. And when in basic media, the nucleophile attacks the less substituted side of the epoxide due to steric reasons.
What if the hydride anion attacks an epoxide? I'd ima... | <blockquote>
in acidic media, the nucleophile tends to attack the more substituted side of the epoxide due to electronic reasons
</blockquote>
This is an $\ce{S_{N}1}$ like reaction. First we would protonate the epoxide oxygen. If we examine the case of an unsymmetrical epoxide and draw the resonance structures for... | There's much detail to it beyond the scope and nit necessary but the final result is:
<ol>
<li>Bases (or ions with negative charge) attack the sterically unhindered positions</li>
<li>Acid catalyzed ring opening happens from the position best to stabalize positive charge even though it doesn't form</li>
</ol>
| https://chemistry.stackexchange.com |
26,886 | [
"https://stats.stackexchange.com/questions/26886",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/8288/"
] | <img src="https://i.stack.imgur.com/nXT1s.png" alt="enter image description here">
I have one question about this. I know that if we have $\mathrm{X}_1,\mathrm{X}_2,\ldots,\mathrm{X}_n$ independent and normally distributed random variables, then the sum $\mathrm{X}_1+\mathrm{X}_2+\ldots+\mathrm{X}_n$ has the normal di... | Let $X,Y$ be random variables with variances $\sigma^{2}_{x}$ and $\sigma^{2}_{y}$, respectively. It is a fact that ${\rm var}(Z) = {\rm cov}(Z,Z)$ for any random variable $Z$. This can be checked using the definition of covariance and variance. So, the variance of $X-Y$ is
$$ {\rm cov}(X-Y,X-Y) = {\rm cov}(X,X)+{\rm... | If $X$ and $Y$ are independent random variables, then so are $X$ and $Z$ independent random variables where $Z = -Y$. Now,
$$\text{var}(Z) = \text{var}(-Y) = (-1)^2\text{var}(Y) = \text{var}(Y)$$
and so
$$\text{var}(X-Y) = \text{var}(X + (-Y)) = \text{var}(X+Z) = \text{var}(X) + \text{var}(Z) = \text{var}(X) + \text... | https://stats.stackexchange.com |
282,406 | [
"https://physics.stackexchange.com/questions/282406",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/131141/"
] | Will divergence get vanished in vector fields? What is vanishing divergence in a vector field?
| To put it simply, a divergence of 0 means that there is no 'source' of vector field in the infinitesimal volume that is considered. This is because divergence is a measure of flux entering and leaving. If there is no vector field 'source' (or drain), then what goes in <em>must</em> come out.
If we take region of space... | The statement vanishing divergence of a vector field simply means
$$ \nabla\cdot\mathbf{E}=0 . $$
Here $\nabla=\hat{x}\partial_x+\hat{y}\partial_y+\hat{z}\partial_z$. In this case the electric field is the vector field under consideration. This situation applies in electromagnetism when there are no charges. On the oth... | https://physics.stackexchange.com |
145,972 | [
"https://cs.stackexchange.com/questions/145972",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/113043/"
] | Given an array of N non-negative integers, and a number K, we need to find two non-overlapping contiguous subarrays that have a total sum of K. Our algorithm is supposed to find the minimum total length of the two subarrays that have total sum K.
Also, after I checked the biggest test cases that we got, N doesn't go ab... | Our professor gave us this solution, which has <span class="math-container">$O(N^2 + K)$</span> time complexity, and <span class="math-container">$O(N+K)$</span> space complexity (since for the biggest test cases <span class="math-container">$K$</span> is about <span class="math-container">$N^{1.5}$</span>, it is as go... | <strong>The following algorithm works but does not achieve the required time complexity of <span class="math-container">$O(n^2 \log n)$</span>, since I misread the time constraint as just being subcubic.</strong>
Let <span class="math-container">$a_i$</span> be the <span class="math-container">$i$</span>-th element in ... | https://cs.stackexchange.com |
493,990 | [
"https://stats.stackexchange.com/questions/493990",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/270128/"
] | I am reading about L2 Regularization. As far as I know we add a thing to the loss function that:
<span class="math-container">$$J(w) = LOSS + \lambda w^T w$$</span>
In the book Deep Learning by Goodfellow et al., they stated "minimizing J(w) results in a choice of weights that make a tradeoff between fitting the t... | <span class="math-container">$w^t w$</span> term can be written as:
<span class="math-container">$$
w^t w = \sum_j w_{j}^2
$$</span>
This becomes smaller when <span class="math-container">$w_j$</span> is closer to zero.
That is why the weight tend to be close to zero due to the regularization term.
| The <span class="math-container">$w^Tw$</span> is a quadratic function with minimum at <span class="math-container">$0$</span>. If the <span class="math-container">$w$</span> is "big" (in term of its distance from origin), the <span class="math-container">$\lambda w^Tw$</span> term grows and make loss bigger.... | https://stats.stackexchange.com |
333,795 | [
"https://physics.stackexchange.com/questions/333795",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/84626/"
] | This is the question from Goldstein's Classical Mechanics, 2nd edition. Chapter 3 problem 1.
<blockquote>
A particle of mass $m$ is constrained to move under gravity without friction on the inside of a paraboloid of revolution whose axis is vertical. Find the one-dimensional problem equivalent to its motion. What... | This is an overview of what I would do.
<ol>
<li>Write down the Lagrangian of a particle under the gravitational potential in cilindrical coordinates. Use the paraboloid equation $z = r^2 c$ to constraint it on the surface of the paraboloid.</li>
<li>Find the EOM for $r$ and $\theta$. If you set in them $r = R_0$, whe... | You forgot the fact that the $\theta$ motion will no longer be uniform once the particle is no longer in circular motion: angular momentum is conserved in this situation, which implies that if $r$ changes then $\dot{\theta}$ must change as well. So you have to look for a solution of the equations that takes both of t... | https://physics.stackexchange.com |
332,017 | [
"https://softwareengineering.stackexchange.com/questions/332017",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/123106/"
] | I have a global position keeper of screen items so items don't need store their own positions.
<pre><code>class Screen_Position_Keeper:
# functions to add stuff
def get_px_row( self, item ):
try:
return self.item_to_row[ item ]
except KeyError:
raise KeyError( 'You nev... | The answer to your question is you want meaningful exceptions.
In most contexts, this involves an exception that adds <em>actionable</em> information in one of two ways:
<ul>
<li>Useful typing to the developer who might be catching the exception</li>
<li>Useful error information to the user (and/or to the developer w... | An error I encountered late last week wasn't due to a python script, but the same principle applies. I had the "privilege" of having to use an old version of subversion on a project. I mistakenly mistyped
<pre><code>prompt: svn co https://some.site.com/some/path
</code></pre>
The system's response was
<pre><code>svn... | https://softwareengineering.stackexchange.com |
11,723 | [
"https://scicomp.stackexchange.com/questions/11723",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/8299/"
] | I have to solve the problem
$$\min_x 1^Tx+\frac{\lambda}{2}\|\Omega\mu-x\|_2^2+\frac{\beta}{2}\|x-\bar{\gamma}\|_2^2\quad\text{w.r.t.}\quad Px-c=0,\ \ x\geq0$$
and in order to do that with Matlab I am currently using <code>fmincon</code> like that:
<pre><code>FMinValue = @(x) sum(x) + lambda * sum((Omega*... | The problem is (likely) that your gradient and Hessian are incorrect:
$$\nabla \left(\frac\lambda 2 \|\Omega\mu-x\|_2^2 \right)= \lambda(\Omega\mu-x)(-1) = \lambda(x-\Omega\mu)$$
and hence the corresponding part of the Hessian is
$$\nabla^2 \left(\frac\lambda 2 \|\Omega\mu-x\|_2^2 \right) = \lambda I.$$
| One way you could overcome this situation is to correct the Hessian of your objective function, which should be $(\lambda + \beta)I$, and then see if you still have scaling issues.
| https://scicomp.stackexchange.com |
138,659 | [
"https://dba.stackexchange.com/questions/138659",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/90804/"
] | I have done a SQL database mirroring setup. There is a Sql job which takes continues full database backup daily. Should I stop this job ?
| No, you still need to take backups including FULLs and LOGs (DIFFs work too, just depends on your set up).
Make sure you are taking LOG backups as well, or your log file will get full and things go breaky.
All mirroring does, depending on what mode (async or sync), is keep data in sync between your primary and secon... | Ideally the mirror db instance acts as the backup for the principal. So you already have a hot standby for the data in your principal in the form of the mirror dbs
You cannot take backups of the Mirror databases as they are in restoring mode..obvious..ain't it?
As of Principal, you can take continue to take your full... | https://dba.stackexchange.com |
307,639 | [
"https://softwareengineering.stackexchange.com/questions/307639",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/184058/"
] | I often hear things like:
<ul>
<li>Mapping the classes</li>
<li>Mapping the objects from the database</li>
<li>Mapping the objects</li>
<li>Mapping the elements of a list</li>
<li>A mapper</li>
</ul>
What does a mapper and the act of mapping something actually mean?
| The programming uses of the verb "map" and the noun "mapper" are largely unrelated to their common uses in English, so this is a very understandable question.
The programming use is also very broad, so let's start with the most concrete and well-defined meaning of "map". Namely, the higher-order <code>map</code> funct... | It's a mathematical concept.
www.thefreedictionary.com
<blockquote>
<pre><code>2. Mathematics The correspondence of elements in one set
to elements in the same set or another set.
</code></pre>
</blockquote>
It's to establish a correspondence between two distinct data models.
<ul>
<li>For example, you can say thay ... | https://softwareengineering.stackexchange.com |
256,969 | [
"https://softwareengineering.stackexchange.com/questions/256969",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/149944/"
] | I've learned from a textbook how to implement binary search trees recursively in Java, and am working on implementing them nonrecursively. I've found a simple and elegant way to implement an insert method in C/C++ by traversing the tree using a pointer of type Node**, but can't find an elegant way to do this in Java.
... | Part of the problem is that you're not following good OO principles.
In this case, the one that's probably most applicable is "<strong>Tell, don't ask</strong>": If you want a <code>Node</code> to add a child, you should <em>tell</em> it to add a child, you shouldn't <em>ask</em> it to expose all the relevant informat... | You can avoid the repetition by creating the new child <code>Node</code>s earlier and defaulting them to empty, rather than using <code>null</code> to represent an empty <code>Node</code>. The body of your <code>while</code> loop might look something like:
<pre><code>Node child = node.right;
if (k < node.key)
... | https://softwareengineering.stackexchange.com |
133,651 | [
"https://dba.stackexchange.com/questions/133651",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/90750/"
] | I'm trying to migrate a MySQL database to SQL Server using the <strong>SQL Server Migration Assistant for MySQL</strong>. Converting the schema and synchronizing with SQL Server works fine.
However, after clicking the Migrate Data button, SSMA crashes after a few seconds (<em>SSMA has stopped working</em>). What might... | On some certain conditions, SSMA seems to cause problems when using it on a multi-core machine.
I opened the Task Manager and set SSMA's processor affinity to Core 0 only. This fixed the crash and I was able to migrate the whole database.
| One more thing that helped me in addition to setting affinity to <code>Core 0</code> only:
SSMA stopped crashing after I set Parallel Data Migration Thread Count to 1.
You can find it in <code>Tools > Project settings > Genaral > Migration (in the left pane) > Parallel Data Migration</code>. Set <code>Par... | https://dba.stackexchange.com |
268,719 | [
"https://physics.stackexchange.com/questions/268719",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/263243/"
] | I have studied the quantum harmonic oscillator and solved the Schrodinger equation to find the eigen-energies given by
$$ E_n = \left(n+\frac{1}{2}\right)\hbar \omega. $$
Which means the energy levels are separated by
$$ \Delta E = \hbar \omega = hf $$
I have also studied blackbody radiation and one of the assump... | It's not a coincidence! You can see the reason even in classical mechanics: if you take a charge and shake it sinusoidally at frequency $\omega_q$, it makes light with equal frequency $\omega_{\gamma} = \omega_q$.
If you quantize light wave emission into individual photons, so that $E = \hbar \omega_{\gamma}$, the sp... | A photon is produced by a transition between two levels and by definition of "photon" its energy is $h\nu$, where $\nu$ is the frequency of the classical electromagnetic wave that will emerge from a great number of the same energy photons. So it is a matter of coincidence only because Maxwell's equations have sinusoida... | https://physics.stackexchange.com |
73,075 | [
"https://physics.stackexchange.com/questions/73075",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23752/"
] | I am going over Coulomb's law and there is something that is a bit
confusing for me:
According to Coulomb's law, if I have a charge $q_{1}$ at a point
$\vec{r_{1}}$ and a charge $q_{2}$ at a point $\vec{r_{2}}$ then
the force that the first charge applies to the second charge is given
by
$$
F_{1,2}=\frac{Kq_{1}q_{2}}... | The mistake you made is in the way you stated Coloumb's law.
It's either
$$ \vec{F} = K \frac{q_1 q_2}{r^\color{red}3} \color{red}{\vec{r}} $$ <strong>OR</strong> $$ \vec{F} = K \frac{q_1 q_2}{r^\color{red}2} \color{red}{\hat{r}} $$
but definitely <strong>NOT</strong>
$$ \vec{F} = K \frac{q_1 q_2}{r^\color{red}3} \... | The notion behind probing the variance of one physical quantity with respect to another is simple.
<blockquote>
Simplify your equation, before you conclude.
</blockquote>
So when you write the vector equation like this :
$$
\overrightarrow{F} = K \frac{q_{1} q_{2}}{r^{3}} \overrightarrow{r}
$$
You are actually ... | https://physics.stackexchange.com |
530,324 | [
"https://physics.stackexchange.com/questions/530324",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/65074/"
] | In my QFT course, we are looking at writing the most general lorentz invariant, renormalizable lagrangians with hermitian interactions.
However I have never seen the interaction in the title mentioned, where <span class="math-container">$\phi$</span> is a complex scalar field. To me it seems this would fulfill all the... | it is odd under <span class="math-container">$\phi \to -\phi$</span> and therefore the energy will be unbounded from below, which is a requirement
Edit following discussion in comments:
We demand that our theories will have an energy spectrum bounded from below. Taking the proposed term to be the only term in the pote... | It seems like it's allowed to me. But this term precludes a straightforward coupling to a <span class="math-container">$U(1)$</span> gauge field, and we usually want to do that: under <span class="math-container">$\phi\to \exp(i\alpha)\phi$</span>, this term is not invariant.
| https://physics.stackexchange.com |
68,196 | [
"https://electronics.stackexchange.com/questions/68196",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/22587/"
] | I connected an LED in series with the capacitor (any type of capacitor. I used one of 10 μF) and connected them with the 9V DC battery. I connected the positive pin of the capacitor directly to the positive side of the battery and attached the positive pin of the LED with the negative pin of the capacitor (as the LED a... | Short answer: Current stops when the capacitor gets charged up to the battery voltage.
When current flows through the circuit, the bulb lights up. In this case you can consider the bulb as a 'current detector'. Current in this case is flow of charge, and the charge carriers are electrons. They are pushed around bec... | If you had two batteries; one charging the other, the current stops when the more discharged battery reaches the same level of charge as the other battery.
The capacitor isn't a battery but it behaves like one in this circuit - it progessively becomes charged with an increasing voltage which progressively opposes the... | https://electronics.stackexchange.com |
15,452 | [
"https://physics.stackexchange.com/questions/15452",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5567/"
] | If centripetal acceleration is towards the center, then why - when you spin a bucket of water (a classic demonstration) - does the water not get pushed out but rather stays in the bucket without spilling?
| Nothing gets <em>"pushed away"</em>. Instead, if it was left to itself everything would fly off in a straight line (Newton's law, right?).
This is easy to see if you are, say, hovering over the playground in a helicopter watching children fly off the merry-go-'round.
I did a sketch. The dark haired kid is holding on... | For the same reason you are "pushed" backward when your car accelerates in the forward direction.
Let us analyze the situation from an external inertial observer's point of view. The centripetal force acts on the <em>bucket</em> towards the center, but the water due to its inertia "tries" to maintain its state of moti... | https://physics.stackexchange.com |
567,724 | [
"https://stats.stackexchange.com/questions/567724",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/10416/"
] | I have a model with several parameters. I apply Bayesian inference with a uniform prior for all of the parameters. After the process is finished, I realize that I need one of those parameters <span class="math-container">$x$</span> parametrized as its logarithm:
<span class="math-container">$$y = log(x/a)$$</span>
wher... | For the first equation, it's the result of zero gradient;
<span class="math-container">$$
\begin{aligned}
S &= \sum_{j=1}^p (y_j-\beta_j)^2 +\lambda\sum_{j=1}^p\beta_j^2\\
\end{aligned}
$$</span>
at extrema,
<span class="math-container">$$
\begin{aligned}
\frac{\partial S}{\partial \beta_j} &=0\\
-2(y_j -\beta_... | The main technique has two steps: 1) take derivative w.r.t <span class="math-container">$\beta_j$</span> and 2) set it to <span class="math-container">$0$</span>. I will outline the steps to help go from 6.12 to 6.14 and leave the other one.
Step 1):
Combining the summation and opening the quadratic expression of 6.12 ... | https://stats.stackexchange.com |
236,410 | [
"https://math.stackexchange.com/questions/236410",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/10394/"
] | <blockquote>
On a plane we have finite amount of points. Any three of them are not collinear. Show that there exist circle (formed with three or more points) that doesn't contain other points in it.
</blockquote>
Source: a national mathematics magazine.
My approach:
Assume we have some circle created from 3 or m... | Your argument is wrong. You assume that if $D$ is inside the circle circumscribing $ABC$ then one of the circles circumscribing $ABD$, $BCD$, or $ACD$ is inside the original circle. That is far from obvious, and actually false.
And, as noted by Henning in comments, it is absolutely false. When $D$ is in the interior o... | Let $S$ be the given finite set. The convex hull of $S$ is a convex polygon $P$ whose vertices are elements of $S$. Take any two subsequent vertices $p$, $q$ of $P$. The line $g:=p\vee q$ is a supporting line of $S$, i.e., on one side $G^+$ of $g$ there are no points of $S$. Let $h$ be the median line of $p$ and $q$, a... | https://math.stackexchange.com |
12,312 | [
"https://electronics.stackexchange.com/questions/12312",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2968/"
] | I'm looking at a datasheet for a digital circuit and it specifies that the typical input hysteresis is 100 mV. What does this mean exactly?
| Let's say you detect a low-to-high transition at 2.5 V. A 100 mV hysteresis would mean that the low-to-high transition is detected at 2.55 V and the high-to-low transition is detected at 2.45 V, a 100 mV difference.<br>
Hysteresis is used to prevent several quickly successive changes if the input signal would contain s... | The other two answers give an example of what hysteresis means in a particular case where there is a discrete trigger, but hysteresis has a more general meaning in the continuous domain, which is the following:
A system is said to exhibit hysteresis when measurements taken in one "direction" are not necessarily equal ... | https://electronics.stackexchange.com |
18,747 | [
"https://mathoverflow.net/questions/18747",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4721/"
] | Well, I don't have any notion of <em>arithmetic geometry</em>, but I would like to understand what arithmetic geometers mean when they say "integer point of a variety/scheme $X$" (like e.g. in "integer points of an elliptic curve").
Is an integer point just defined as a morphism from $Spec\mathbb{Z}$ into $X$?
Suppos... | To make sense of the notion of integer points, your scheme should be defined over $\mathbb{Z}$. What do we mean by that? Of course we should not ask for a structure map tp $Spec(\mathbb{Z})$, since every scheme has one such map. The right notion is the following.
Let $X$ be a scheme over $\mathbb{C}$; so by definition... | <blockquote>
Is an integer point just defined as a morphism from Spec ℤ to <em>X</em>?
</blockquote>
Yes, but in order for there to be any, your scheme has to be genuinely "over ℤ", that is, equipped with a <em>surjective</em> map to Spec ℤ. To see what a difference this makes, consider affine spa... | https://mathoverflow.net |
366,938 | [
"https://softwareengineering.stackexchange.com/questions/366938",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/297670/"
] | I employ a lot of meta-programming to avoid repetitive tasks and build safer-to-use abstractions.
I recently moved to a new job where I am working in a larger team and this worries some of my colleagues, because they do not comprehend it.
I always try to leverage the full potential of the language, but some (not all)... | Metaprogramming is OK. What you are trying to do is not OK.
I use metaprogramming all the time in my job. It's a powerful tool which can be used to do a lot of things in a more readable and maintainable way. It's also one of the harder to comprehend styles of programming out there, so it really needs to earn its ke... | First and foremost, this is the team's issue, and you have to solve it with the team. If you have backup from the team for programming using certain elements and constructs, do it; if not, discuss it with them and if you cannot convince them and make a strong case why "your approach" is clearly better, you will be bett... | https://softwareengineering.stackexchange.com |
599,579 | [
"https://physics.stackexchange.com/questions/599579",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/281942/"
] | I have a very silly doubt, and it's bothering me. Magnetic Force because of a line current is:
<span class="math-container">$$\mathbf{F_{mag}} = I\int\mathrm{d}\mathbf{l\times B}$$</span>
However, in a constant magnetic field, for closed circular loops, force is zero as limits of integration goes from <span class="math... | It depends which integral you calculate, the line integral of a scalar field or the line integral of a vector field. In books usually <span class="math-container">$ds$</span> means scalar field and <span class="math-container">$d\textbf{s}$</span> means vector field. I will give you example for both for a circular loop... | I think you have mis-interpreted what is meant by <span class="math-container">$d\overrightarrow l$</span> and <span class="math-container">$dl$</span><br>
What we use in calculating <span class="math-container">$F_{mag}$</span> is <span class="math-container">$I \int{d\overrightarrow l \times \overrightarrow B}$</span... | https://physics.stackexchange.com |
4,139,047 | [
"https://math.stackexchange.com/questions/4139047",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/872788/"
] | a) Show that <span class="math-container">$UA = AV$</span>.
b) Show that <span class="math-container">$VA^2 = A^2V$</span>.
c) Show that <span class="math-container">$VA = AV$</span>.
d) Show that <span class="math-container">$U = V$</span>.
I did a, b and d, but I'm having trouble with c. I would appreciate some he... | I presume that this is home-work and that you are supposed to use elementary arguments, so here is a hint for proceeding:
Let <span class="math-container">$x$</span> be any eigenvector of <span class="math-container">$A^2$</span>, i.e. <span class="math-container">$A^2x=\lambda^2 x$</span> for some <span class="math-c... | For part c, start with part b.
<span class="math-container">$$
VA^2 = A^2V \implies VA^2V^* = A^2.
$$</span>
Now, by the uniqueness of the positive (semi-) definite square root, we have
<span class="math-container">$$
VAV^* = A \implies VA = AV.
$$</span>
| https://math.stackexchange.com |
211,757 | [
"https://dba.stackexchange.com/questions/211757",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/115397/"
] | MSSQL database has previously been archived on another database. Approximately 70m rows (includes sales information.)
Now, I am asked to move this archived data to live database. Because, customer can't see order history older the 3 years.
Is it reasonable to do this? I think it will be slow. Are there other solution... | If I were to implement the migration, I would ensure to have a good planned indexing.
First of all, move the historical data into history tables, having the same structure as the current working tables, then create indexes for big groups: For example, including a YEAR column and making sure this one is a mandatory filt... | If there's no duplicate data to worry about, adding another 50 GB of data to a 250 GB database is not going to matter much, especially since the business requirements need the archived data in the live database.
Make sure you have good covering indexes. Perhaps you can import the historic data into a separate filegrou... | https://dba.stackexchange.com |
1,294,778 | [
"https://math.stackexchange.com/questions/1294778",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/187799/"
] | What is the $$\lim_{n\rightarrow \infty }\left(1+\frac{1}{n}\right)^{n^n}$$
I know that the $\lim_{n\rightarrow \infty }\left(1+\frac{1}{n}\right)^{n}=e$, so I wanted to find the limit by the same way by taking $\log$ two times but I found the solution became not easy. Any help
| <strong>Hint</strong>:Observe that: $$\left(1+\dfrac{1}{n}\right)^{n^n}> \left(\left(1+\dfrac{1}{n}\right)^n\right)^n> 2^n$$ for sufficiently large $n$.
| Here is the solution, maybe, you are looking for:
Let $L=\lim_{n\rightarrow \infty }\left( 1+\frac{1}{n}\right) ^{n^{n}},$ then
\begin{eqnarray*}
\log L &=&\log \lim_{n\rightarrow \infty }\left( 1+\frac{1}{n}\right)
^{n^{n}} \\
&=&\lim_{n\rightarrow \infty }\log \left( 1+\frac{1}{n}\right) ^{n^{n}} \\... | https://math.stackexchange.com |
45,296 | [
"https://dba.stackexchange.com/questions/45296",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/18592/"
] | I have a table where the RowNumber is of essence.
It has a range of clients, and a running total for that client - which resets every time the Client changes.
e.g.
<pre><code>client rownr amount runtotal
Company A 1 1.00 1.00
Company A 2 1.00 2.00 1+1 = 2
Company A 3 5.00 7.00 2+5 = 7
Compan... | How about:
<pre><code>SELECT c.client, c.rownr, c.amount
, runtotal = SUM(e.amount)
FROM #Checks c
JOIN #Checks e ON e.RowNr <= c.RowNr AND e.Client = c.Client -- row from c (note <= not <) and all earlier rows
LEFT OUTER JOIN -- rows between with different cli
#Checks d ON d.RowNr < c.RowN... | This should do what you want:
<pre><code>WITH CTE AS
(
SELECT *,
RN = ROW_NUMBER() OVER(PARTITION BY Client ORDER BY RowNr)
FROM #Checks
), CTE2 AS
(
SELECT *,
RN2 = RowNr - RN
FROM CTE
)
SELECT A.Client, A.RowNr, A.Amount, B.RunTotal
FROM CTE2 A
CROSS APPLY (SELECT SUM(Am... | https://dba.stackexchange.com |
384,061 | [
"https://physics.stackexchange.com/questions/384061",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/183633/"
] | I'm confused between fermions and electrons. For example say I have a system comprises of three electrons and there are three single particle energy level accessible to each of three electrons.
What will be the possible configuration for electrons and in this example, what will be the possible configuration for fermion... | I think, the short answer is: Electrons are one possible type of fermions. So, each electron is a fermion but not each fermion is an electron. Therefore electrons as all the other fermions behave in the same way when it comes to quantum number configurations.
To give more background: Fermions are arbitrary particles w... | Electrons are one kind of fermion. The ways electrons fill energy levels follow from energy minimisation subject to the exclusion principle. The only options the exclusion principle rules out are those in which two fermions of the same type share a state. For example, an electron can share its state with a muon, which ... | https://physics.stackexchange.com |
1,788,513 | [
"https://math.stackexchange.com/questions/1788513",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/333900/"
] | Show that $7^{\sqrt {5}}>5^{\sqrt {7}}.$
I am stuck in this problem.
Any help in solving this problem will be appreciated.
| $7^{\sqrt {5}}>5^{\sqrt {7}}$
$\Leftrightarrow 7>5^{\sqrt{7/5}}$
$5^{\sqrt{7/5}}=5^{\sqrt{1.4}} <5^{\sqrt{1.44}}=5^{1.2}=5^{6/5}=\sqrt[5]{5^6}=\sqrt[5]{15625}<\sqrt[5]{16807}=\sqrt[5]{7^5}=7$
So, the claim is proved.
| Showing that$$7^{\sqrt {5}}>5^{\sqrt {7}}$$ is te same as showing that $$7^{\frac{1}{\sqrt{7}}}>5^{\frac{1}{\sqrt{5}}}$$ So, now, consider the function $$f(x)=x^{\frac{1}{\sqrt{x}}}$$ After simplification, its derivative writes $$f'x)=-\frac{1}{2} x^{(\frac{1}{\sqrt{x}}-\frac{3}{2})} (\log (x)-2)$$ which cancels ... | https://math.stackexchange.com |
178,049 | [
"https://softwareengineering.stackexchange.com/questions/178049",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/34069/"
] | Applying styles to the body tag will be applied to the whole page, so
<pre><code>body { font-family: Verdana }
</code></pre>
will be applied to the whole page. This could also be done with
<pre><code>* {font-family: Verdana}
</code></pre>
which would apply to all elements and so would seem to have the same effect... | Functional differences between these two choices of CSS selector...(my take)
<strong>body</strong>
<ul>
<li>Applies style properties to body element.</li>
<li>Elements within body may inherit the property values. Some properties default to 'inherit'.</li>
<li>Style declarations that match an element within body can o... | Try something like this
<pre><code>body { font-family: Verdana }
table { font-family: Arial }
</code></pre>
against
<pre><code>* { font-family: Verdana }
table { font-family: Arial }
</code></pre>
And see which styles are applied to the cells of the table.
There is a difference between "applied to the whole docum... | https://softwareengineering.stackexchange.com |
35,198 | [
"https://mathoverflow.net/questions/35198",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4362/"
] | Let us define the nth smooth homotopy group of a smooth manifold $M$ to be the group $\pi_n^\infty(S^k)$ of smooth maps $S^n \to S^k$ modulo smooth homotopy. Of course, some care must be taken to define the product, but I don't think this is a serious issue. The key is to construct a smooth map $S^n \to S^n \lor S^n$... | Yes, the map you mention is an isomorphism. I think the main reason people rarely address your specific question in literature is that the technique of the proof is more important than the theorem. All the main tools are written up in ready-to-use form in Hirsch's Differential Topology textbook.
There are two step... | Dear Paul, as Ryan says the smooth and continuous homotopy groups of a manifold coincide.
This is stated as Corollary 17.8.1 in Bott and Tu's book <em>Differential Forms in Algebraic Topology</em> (Springer Graduate Texts in Mathematics, #82).The Corollary is to the preceding Proposition 17.8, which says that a contin... | https://mathoverflow.net |
253,679 | [
"https://math.stackexchange.com/questions/253679",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/47988/"
] | <blockquote>
Prove that for all $x\in \mathbb{Z}$ the sequence $(1+\frac{x}{n})^n$ is converging and it's limit is $e^x$.
</blockquote>
I'm not even sure how to start this one. How can I even open $(1+\frac{x}{n})$ to something I can work with? I do know $\lim(1+\frac{1}{n})^n=e$, but not sure how to get from one to... | HINT: Write
$$\left(1+\frac{x}n\right)^n=\left(\left(1+\frac{x}n\right)^{n/x}\right)^x?$$
and substitute $u=\dfrac{x}n$.
| You should know (sometimes by definition) that $(1+\frac1n)^n\to e$.
Consider the case $x\ne0$ (with $x=0$ being trivial).Then clearly $(1+\frac1n)^{nx}\to e^x$.
This already shows $(1+\frac xn)^{n}\to e^x$ at least for the subsequence of naturals $n$ where $n$ is a multiple of $x$.
For the general case, investigate th... | https://math.stackexchange.com |
302,530 | [
"https://softwareengineering.stackexchange.com/questions/302530",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/203997/"
] | I'm new to Ruby and I was surprised when I found out that all objects are true apart from nil and false. Even 0 is true.
A nice thing about that property of the language is that you can write:
<pre><code>if !variable
# do stuff when variable is nil
end
</code></pre>
My colleagues, who are more seasoned Ruby develo... | Write what you mean. Mean what you write.
Lets take a different test. <code>.vowel?</code>
<pre><code>if char == 'a'
# do stuff
end
</code></pre>
vs
<pre><code>if char.vowel?
# do stuff
end
</code></pre>
Now, its obvious that these do not do the same thing. But if you're only expecting <code>char</code> t... | Not only is <code>if variable.nil?</code> read more like natural language, it also guards against a programmer accidentally assigning it a <code>false</code> value and falling into your <code>if</code> statement, since Ruby is a loosely typed language.
| https://softwareengineering.stackexchange.com |
116,391 | [
"https://electronics.stackexchange.com/questions/116391",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16307/"
] | A data acquisition channel is fed by a signal which first passes through a clamping circuit as I draw below. Here in the figure Output goes into the data acquisition board after a 8V clamp circuit:
<img src="https://i.stack.imgur.com/unNSb.jpg" alt="enter image description here">
When I opened the clamp box I saw 2 re... | In case input probe is connected to a point with a higher voltage than zenner's, it will draw a lot of current from that point if it is not limited by R1. Without R1, taking a measurement could break the circuit which is tested, the probe, or even the acquisition board, in case of a high voltage.
R2 may be there to pr... | R1 limits the current into the zener to protect the zener from abnormal input voltages. R2 limits the current into whatever circuit follows.
| https://electronics.stackexchange.com |
45,608 | [
"https://dba.stackexchange.com/questions/45608",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/820/"
] | When I query the configuration of the default trace, it shows enabled:
<pre><code>exec sp_configure 'default trace enabled';
-->
name minimum maximum config_value run_value
default trace enabled 0 1 1 1
</code></pre>
But when I query <code>sys.traces</code>... | I would say there is a strong correlation between your out of space event and the missing trace. Note that the <code>sp_configure</code> option merely tells you that the default trace is enabled, but that does not mean that it is running or that it even exists. Note that <code>sys.traces</code> is not a table but a vie... | I had the same issue after the drive filled up. The default trace was enabled but not running. Disabling it and re-enabling it worked immediately without stopping services.
| https://dba.stackexchange.com |
2,704,275 | [
"https://math.stackexchange.com/questions/2704275",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/544785/"
] | How are you supposed to simplify a natural log over another natural log?
Ex.
$$\frac{\ln(64)}{\ln(4)}.$$
| $\def\d{\mathrm{d}}\def\peq{\mathrel{\phantom{=}}{} }$As is pointed out by @AndreaL, conditional probability should be used to calculate to desired probability.
Suppose the elder son eats an angle of $X_1$ and the younger son eats an angle of $X_2$. Translating to probabilistic notation, there is $X_1 \sim U(0, 2π)$ a... | Let $x$ be the fraction of pie that the first son eats, and $y$ be the fraction of the remaining pie that the second one eats.
$x$ and $y$ are both taken uniformly in $[0;1]$.
Let $\theta_1 = x$ and $\theta_2 = y(1-x)$ be the fraction of the pie eaten by son 1 and 2 respectively.
You want to find out the expected va... | https://math.stackexchange.com |
1,113,228 | [
"https://math.stackexchange.com/questions/1113228",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/168232/"
] | Let $X$ be continuous uniform over $[0,2]$ and $Y$ be continuous uniform over $[3,4]$. Find and sketch the PDF of $Z = X + Y$, using convolutions.
<hr>
So I have:
$$f(x) = 1/2, 0 \leq x \leq 2 $$
$$f(y) = 1, \leq y \leq 4 $$
And my bounds of integration are between $[3,6]$(?)
I know I have to use the convolution fo... | Suppose for the moment that we're working with uniform discrete random variables, $U\sim \mathcal{U}\{0..2\}$ and $V\sim\mathcal{U}\{3..4\}$
The probability mass of $W=U+V$ is calculated by summing the the joint probability mass $p_{\small U,V}(u,w-u)$ over all supported values of $u$:
$$\begin{align}
p_{\small W}(w)... | $$f_{Z}\left(z\right)=\int f_{Y}\left(z-x\right)f_{X}\left(x\right)dx=\int_{z-4}^{z-3}f_{X}\left(x\right)dx$$
Now realize for what values $f_{X}\left(x\right)$ is zero or is not zero and in
that light (by calculating this integral) discern the cases:
<ul>
<li>$z-3<0$</li>
<li>$z-4<0\le z-3$</li>
<li>$0\le z-4&l... | https://math.stackexchange.com |
609,018 | [
"https://physics.stackexchange.com/questions/609018",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/279086/"
] | I was solving this rocket propulsion's classic mechanics exercise: M is the instantaneous rocket's mass, and v its velocity. The exhaust gases are ejected with speed relative to the speed of the rocket (there's the weight and friction forces acting on the rocket, but that's not relevant for now). So with <span class=... | The notation <span class="math-container">$M(dt)$</span> or <span class="math-container">$v(dt)$</span> is not acceptable. Typical notations are like:
At the time <span class="math-container">$t$</span>:
<ul>
<li>mass of rocket <span class="math-container">$M(t)$</span></li>
<li>velocity of rocket <span class="math-co... | <span class="math-container">$d M$</span> would be equal to <span class="math-container">$M(t+dt) - M(t)$</span>, as an infinitesimal <span class="math-container">$M$</span> is the change in <span class="math-container">$M$</span> after an infinitesimal time <span class="math-container">$dt$</span>.
| https://physics.stackexchange.com |
1,506,249 | [
"https://math.stackexchange.com/questions/1506249",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/285595/"
] | So I got this assignment. And I was wondering how is it possible to get a limit from a constantly changing formula.
$$\lim_{x\to+\infty}\frac{\sin(x)}{x}$$
Can I only look in the domain $]0,2\pi[$?
| A possible approach is to take help of the following:
<ol>
<li>$$\lim_{x\to+\infty}\frac{1}{x}=0$$</li>
<li>$$-1\le\sin x\le1$$</li>
</ol>
| No, you cannot only analyze the problem within $]0, 2\pi[$, although $\sin$ is periodic.
Yes, the limit exists and $=0$. We have $x > 0$ only if
$$
\bigg| \frac{\sin x}{x} \bigg| \leq \frac{1}{x};
$$
given any $\varepsilon > 0$,
we have $1/x < \varepsilon$ if $x > 1/\varepsilon$;
hence we have proved this... | https://math.stackexchange.com |
269,582 | [
"https://mathoverflow.net/questions/269582",
"https://mathoverflow.net",
"https://mathoverflow.net/users/955/"
] | This is a theoretical question about poker-type games. I'm not going to specify the rules. You can consider No Limit Texas Hold'em or some simple theoretical model, where each player holds a number from the $(0,1)$ interval. We only consider playing heads-up, i.e., when two players play.
Playing against Darth Vader is... | Here is an answer to the updated question:
Suppose that there are two betting rounds. Darth Vader has three types of hands. Type 1 wins with probability 1. Type 2 is a draw that hits (becomes a winning hand) with probability $1/10$ between the betting rounds. You can't see whether type 2 hands hit. Vader has Type 1 $1... | <h2>Getting all-in while behind</h2>
It is not just when you are ahead that you might want to get all-in against someone who has an information advantage. Suppose the pot is $1$ and the effective stack depth is $1$, and there are two streets of NL-betting with the chance round between the betting rounds. Suppose Darth... | https://mathoverflow.net |
561,020 | [
"https://math.stackexchange.com/questions/561020",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/14366/"
] | Consider propositional logic with primitive connectives $\{{\to},{\land},{\lor},{\bot}\}$. We view $\neg \varphi$ as an abbreviation of $\varphi\to\bot$ and $\varphi\leftrightarrow\psi$ as an abbreviation of $(\varphi\to\psi)\land(\psi\to\varphi)$, etc.
The <em>classical sequent calculus</em> LK has rules such as
$$\... | This rings a bell. And ah yes, on p. 48 of Sara Negri and Jan van Plato's admirable book <em>Structural Proof Theory</em> (CUP, 2001), they write
<blockquote>
It is not the [general] feature of having a multiset as a succedent that leads
to classical logic, but the unrestricted $R\!\supset$ rule,
</blockquote>
wh... | Peter Smith found a nice reference which more or less settles the question. Here are some concluding remarks that won't fit as comments:
Knowing that it's true gave me the courage to try proving it, which turned out to be easier than expected. In fact, each of the classical rules <em>except</em> ${\to}R$ (but includin... | https://math.stackexchange.com |
69,658 | [
"https://softwareengineering.stackexchange.com/questions/69658",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/18020/"
] | This is for ordered collections e.g. java.util.List. Why did the language designers not include a last method? The only reasons I can think of are:
<ul>
<li>ambiguity when the collection is empty (return null or throw exception)</li>
<li>API bloat</li>
</ul>
Any other reasons?
| API bloat is probably the answer. From my experience the only time I've needed this functionality a Queue or Stack was the correct data structure for the job having the appropriate method.
| a <code>last()</code> method is just as easy as <code>list.get(list.size()-1)</code>, just like there is no <code>first()</code> method or <code>fifth()</code> method. It isn't that hard to synthesize and is a specialization. You can also <code>reverse()</code> the list and <code>list.get(0)</code> which will give the ... | https://softwareengineering.stackexchange.com |
1,853,069 | [
"https://math.stackexchange.com/questions/1853069",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/321264/"
] | <blockquote>
Let <span class="math-container">$f:\mathbb{R}\to\mathbb{R}$</span> be a continuous function such that <span class="math-container">$f(x+1)=f(x) \quad \forall x\in\mathbb{R}$</span>.
Define <span class="math-container">$g(t)=\displaystyle\int_0^tf(x)\,dx$</span>, <span class="math-container">$t\in\mathbb{R... | <blockquote>
As the period of $f$ is $1$, we can say that $\displaystyle\int_0^tf(x)\,dx=t\displaystyle\int_0^1f(x)\,dx$
</blockquote>
Is false.
For example, take $f(x)=\sin(2\pi x)$. Then
$$t\cdot\int_0^1 f(x)dx=0=t\cdot 0 = 0$$
while $$\int_0^t f(x)dx$$
is <em>not</em> $0$ for all values of $t$.
<hr>
To solv... | $\newcommand{\angles}[1]{\left\langle\,{#1}\,\right\rangle}
\newcommand{\braces}[1]{\left\lbrace\,{#1}\,\right\rbrace}
\newcommand{\bracks}[1]{\left\lbrack\,{#1}\,\right\rbrack}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\ds}[1]{\displaystyle{#1}}
\newcommand{\expo}[1]{\,\mathrm{e}^{#1}\,}
\newcommand{\half}{{1 \ov... | https://math.stackexchange.com |
645,950 | [
"https://physics.stackexchange.com/questions/645950",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/304605/"
] | I learned the total angular momentum is conserved in a two-body system. But as far as I saw the descriptions of two-body problem on several textbooks, none of those mention the angular momentum of each body. My question is: is the angular momentum of each body a conserved quantity?
| The question requires an additional specification to allow a non-ambiguous answer, i.e., what is the reference frame used for describing the two-body problem. Indeed, if one would use the non-inertial reference frame centered on one of the two bodies, the angular momentum of that body would be trivially conserved (it r... | No, the angular momentum of a closed system will always be conserved, but if you consider only one body within that system then its angular momentum will
change based on its interactions with other bodies in the system just like linear momentum.
Physics problems usually require a lot of simplification of the system whi... | https://physics.stackexchange.com |
34,354 | [
"https://softwareengineering.stackexchange.com/questions/34354",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8054/"
] | I started working at my current job about 8 months ago, and its been one of the best experiences I've had as a young programmer. It's a small company, and both my co-developers are brilliant guys.
One of the practices that they both have been encouraging is lots of code-reuse. Our code base is mainly C#, and we're usi... | I think the answer is at least in part in communication. If all developers communicate well about what they're working on, others can suggest which methods may be already implemented and immediately reusable. Similarly, if you develop something that fits in well in the common libraries, let others know that it's there.... | <blockquote>
how the current structure of the folder can be made more conducive for finding those libraries again.
</blockquote>
There are limits. Years ago (decades really) I read a nice paper by some folks at the old AT&T (before they were broken up and reassembled) that described profound limitations in unde... | https://softwareengineering.stackexchange.com |
627,898 | [
"https://physics.stackexchange.com/questions/627898",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/295572/"
] | I have seen similar questions in the forum but they fail to be very specific .
I would ask the question from the viewpoint of Problem Solving. Let me put this question from a textbook :
<blockquote>
A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be?
</... | You just answered your question yourself: if the supply is voltage-limited, the first answer is correct. <strong>Under the assumption of constant voltage</strong>, what the expression <span class="math-container">$P = I^2 R$</span> <em>really</em> means is <span class="math-container">$$P = I(R)^2 R.$$</span> That is, ... | It's not a contradiction! You're just considering two different cases, since it makes a huge different wether you have fixed current or fixed voltage. Now the thing is that if you have fixed voltage, you'd have to reinterpret the current intensity in the second answer as <span class="math-container">$V=I\cdot R \Righta... | https://physics.stackexchange.com |
1,710,533 | [
"https://math.stackexchange.com/questions/1710533",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/150294/"
] | The problem I have is this: There are N colors. A list of size $i$ is created by choosing $i$ distinct colors randomly from the total $N$ possible colors. A second list of size $j$ is created in a similar manner, choosing $j$ distinct colors out of the $N$ possible colors. What are the expected number of common colors ... | The function $$f(x)=\int_{-2}^x\sqrt{3w^4-1}\,dw$$ is a curve in the plane. The formula for arc-length of a curve is $$L=\int_a^b\sqrt{(f'(x))^2+1}\,dx.$$ The fundamental theorem of calculus tells us that $$f'(x)=\sqrt{2x^4-1}.$$ Therefore, you need to solve the integral $$L=\int_{-2}^{-1}\sqrt{(\sqrt{3x^4-1})^2+1}\,dx... | Use the formula for the arc length:
$$\int_{-2}^{-1}\sqrt{1+\frac{\partial}{\partial x}\left[\int_{-2}^{x}\sqrt{3w^4-1}\space\text{d}w\right]^2}\space\text{d}x=$$
<hr>
Using the fundamental theorem of calculus:
$$\frac{\partial}{\partial x}\left[\int_{-2}^{x}\sqrt{3w^4-1}\space\text{d}w\right]=\frac{\sqrt{-\left(3x... | https://math.stackexchange.com |
100,310 | [
"https://datascience.stackexchange.com/questions/100310",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/76137/"
] | I'm working on my custom Named Entity Recognition model that I'm making in Python's Keras lib.
I have read that I should enumerate all words that are appearing, so that I get vectorized sequences. I have done that like this:
<pre><code>word2idx = {w: i + 1 for i, w in enumerate(words)}
label2idx = {t: i for i, t in enu... | EDA(Exploratory Data Analysis) as suggested by the name is an initial analysis of the data. Understanding the distributions, getting an idea of the kind of values and their range. It's getting a feel of the data before further analysis and understanding the nature of it.
This would ideally give you an idea of the kind ... | I assume you are talking about a Machine Learning application. I like to think about the distinction in terms of at what point a model is being trained:
EDA - no model trained yet, just exploring the data to see if there are potential problems in the dataset (outliers, mislabeled data, unwanted correlations between var... | https://datascience.stackexchange.com |
583,181 | [
"https://physics.stackexchange.com/questions/583181",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/271193/"
] | I was running some calculations of ideal gas molecules in a box for <span class="math-container">$O_2$</span> molecules at <span class="math-container">$T=300K$</span> and <span class="math-container">$V = 100 cc$</span>, and I saw that <span class="math-container">$v = 445 m/s$</span>.
My question is, why don't we hea... | A sonic boom is produced when an macroscopic object moves through a gas faster than the speed of sound in that gas. It is due to a shock wave, which is an abrupt change in pressure in the gas. This is a behaviour of the gas in bulk.
The thermal motions of gas molecules do not create sonic booms because (a) they are in ... | Macroscopic bodies like planes are moving through air. But what are molecules moving through? The answer is empty space, because that's what separates molecules. So the means by which macroscopic bodies cause a sonic boom (formation of a shock wave in air) is missing in the case of molecules.
The existence of so much e... | https://physics.stackexchange.com |
55,943 | [
"https://electronics.stackexchange.com/questions/55943",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/17608/"
] | Consider the following circuit:
<img src="https://i.stack.imgur.com/MPxSL.png" alt="schematic">
This is a simple first-order low-pass RC filter. The cutoff frequency is:
\$ f_c = \dfrac{1}{2 \pi (1k\Omega) (1\mu F)} \approx 159 Hz \$
The reactance of C1 at \$f_c\$ is:
\$ X_{C1} = \dfrac{1}{2 \pi (159 Hz) (1uF)} = ... | Unfortunately, you cannot simply replace reactances by resistances because you are then ignoring the phase shift. In your first example, the cutoff frequency of a low-pass filter is defined as the frequency for which the output voltage is 3 dB down (0.707) from its maximum, not half. So replacing the capacitive react... | It fundamentally misses the energy storage aspect of the components, which will manifest itself a a phase delay or resonances depending upon the order of the system.
But you know that already. So I will extend the thoughts to two further areas.
Case 1): Thought experiment: in the case where you are measuring the ti... | https://electronics.stackexchange.com |
101,479 | [
"https://security.stackexchange.com/questions/101479",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/81526/"
] | I understand how DoS/DDoS attacks work on servers. If I have not been misled, it is possible to DoS/DDoS a system that does not act as a server, but is still connected to the internet. How is this possible, as normal computers don't take data requests?
| You can saturate a computer's incoming network connection by just flooding it with packets. Even if every incoming packet bounces off the firewall or off a closed port (no process listening on that protocol+port on that interface), the bits are still being sent; legitimate traffic will need to compete for time on the w... | Interesting point is that (D)DoS attacks simply mean (Distributed) Denial of Service attacks. They refer to the effect, not the cause. What you are doing is stopping a device from functioning in it's intended fashion.
For servers, this is often done by tying up resources to the point where other things either can't r... | https://security.stackexchange.com |
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