qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
285,547 | [
"https://math.stackexchange.com/questions/285547",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/7994/"
] | It is very common to use the formula
$$x^{\frac{b}{c}} = (x^b)^\frac{1}{c}$$
to simplify the evaluation of a fractional exponent.
I want to know what circumstances allow us to do this step. For example, it does not work in this situation:
$$(-4)^{\frac{2}{4}} = ((-4)^2)^\frac{1}{4} = 16^\frac{1}{4} = 2$$
The correct... | By <em>definition</em> $x^{\alpha}$ is equal to $\textrm{exp}(\alpha \, \textrm{log} \, x)$. So <em>by definition</em> it is <em>not</em> defined if $x$ is not a in $\mathbb R^*_+$.
As a consequence, you cannot say that $\sqrt{-4} = 2i$ is the correct answer.
All this depends on a choice you make at first : the choice... | It holds always.
But De Moivre's Theorem says that $z^{\frac{1}{q}}$ is one of the values from the set $\{|z|^{\frac{1}{q}}\xi: \xi^q=1\}$, provided $q\in\mathbb{Z}^+$.
So, $16^\frac14\in\{2,-2,2i,-2i\}$
| https://math.stackexchange.com |
2,338,659 | [
"https://math.stackexchange.com/questions/2338659",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/259085/"
] | How can I show that if $A$ is (real) square matrix that has eigenvalues $\{\lambda_i\},$ then $-A$ has eigenvalues $\{-\lambda_i\},$ i.e., the same set, but negated?
I think it should be obvious, but it is eluding me for the moment.
Thanks.
| <strong>Hint:</strong> If $v$ is an eigenvector of $A$, it is also an eigenvector of $-A$.
| Hint: if $A v = \lambda v$, what is $-Av$?
| https://math.stackexchange.com |
348,598 | [
"https://softwareengineering.stackexchange.com/questions/348598",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/271890/"
] | <blockquote>
Member variables of a class are typically hidden from the outside word
(i.e., the other classes), with private access control modifier.
Access to the member variables are provided via public assessor
methods. This follows the principle of information hiding. That is,
objects communicate with each... | Because <strong>information hiding is not a security measure.</strong>
It's a human-oriented measure for <em>improving understanding</em>.
The point of making a field private is not to prevent it from being changed. If an attacker wants to change values, well, if they have access to your program's process, they can c... | I'd like to add this to the good answer of @KilianFoth
getter/setter methods as described in your quote <strong>violate</strong> <em>information hiding</em> principle.
In general we have two kinds of objects:
<ul>
<li>pure data containers (aka <em>Value Objects</em> or <em>Data Transfer Object</em>)
These object ... | https://softwareengineering.stackexchange.com |
281,831 | [
"https://electronics.stackexchange.com/questions/281831",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/122343/"
] | I have configured timer 4 for PWM with following code and connected LED to the configured pin. It is working.
<pre><code>TIM_TimeBaseInitTypeDef TIM_BaseStruct;
RCC_APB1PeriphClockCmd(RCC_APB1Periph_TIM4, ENABLE); // Enable bus clock
TIM_BaseStruct.TIM_Prescaler = 0; // Set prescaler (frequency divider)
TIM_Bas... | With help from people on STM32 forum, I found out I was missing the following additional code to make advanced timer work the same way as general-purpose timer:
<pre><code>TIM_BDTRInitTypeDef TIM_BDTRInitStruct;
TIM_BDTRStructInit(&TIM_BDTRInitStruct);
TIM_BDTRConfig(TIM1, &TIM_BDTRInitStruct);
TIM_CCPreloadCo... | This is an old question but I have a general comment about your code as it might cause bugs (I came across this bug just today, preventing me to use the PWM at all). I am posting it as an answer because I can't use comments yet with my new account.
When using init structs, it is best practise to call their correspondi... | https://electronics.stackexchange.com |
32,963 | [
"https://cstheory.stackexchange.com/questions/32963",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/12710/"
] | It is well known that many important graph parameters show (strong) concentration on random graphs, at least in some range of the edge probability. Some typical examples are the chromatic number, maximum clique, maximum independent set, maximum matching, domination number, number of copies of a fixed subgraph, diamete... | Many parameters of the largest connected component are not concentrated for <span class="math-container">$G(n,p)$</span> if <span class="math-container">$p=1/n$</span> and more generally if <span class="math-container">$p$</span> is in the critical window. Examples are the diameter and the size of the largest componen... | Failure to concentrate happens for some counting ($\#\mathsf{P}$) properties, and maybe for many of them.
A simple example is the number of spanning subgraphs ($2^m$). The number of edges of a random graph fluctuates by $\pm \Theta(n)$ so the number of spanning subgraphs fluctuates by a factor of $2^{\Theta(n)}$, well... | https://cstheory.stackexchange.com |
239,110 | [
"https://softwareengineering.stackexchange.com/questions/239110",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/143904/"
] | I have the concept of a <code>SlowLoading</code> thing:
<pre><code>public interface SlowLoading {
boolean hasLoaded();
}
</code></pre>
I also have a component <code>MyComponent</code>:
<pre><code>public interface myComponent{
void doSomething();
}
</code></pre>
My implementation covers both:
<pre><code>public ... | How about intercepting every Method of Container subclasses that return Objects?
The advantage of this approach is that your core interfaces don't need to now anything about the "SlowLoading" concept. One disadvantage on the other hand is that you may intercept more calls than necessary - which may or may not a proble... | i think this is not the best example for AOP.
It seems it would have to break encapsulation, possible workarounds may be:
A. Use 2 more interfaces that cover the 2 cases of SlowLoading (either wait or not-wait) and use one of these interfaces in the AOP cut
B. Not use AOP at all for this functionality and use 2 inte... | https://softwareengineering.stackexchange.com |
336,379 | [
"https://softwareengineering.stackexchange.com/questions/336379",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/162246/"
] | I have an application that lets users create their own character from clothing like hat, pants and facial features, like beard and eyes. I'm using a canvas to display the built up character. The order in which these items get drawn are important, ie. the body of the character should appear behind the pants.
My teacher... | Do you want to build your character in code or do you want to make it easy for a user of your software to build a character using an interface? These are vastly different use cases. Until you say different I'll presume you simply wish to build in code.
I'm not sure why you'd use both the composite and the decorator ... | <h1>First of all...</h1>
Patterns are not made up from you or told to you. They were identified by the perception of the problem domain.
If your teacher told you to use pattern X and Y then he made some assumptions you have to know as we have an arbitrary solution space for every problem. The point is: what is his id... | https://softwareengineering.stackexchange.com |
341,125 | [
"https://physics.stackexchange.com/questions/341125",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/140249/"
] | In the problem where a man is walking on a platform kept over ice why can't we use the relative velocity of the man with respect to the platform in the conservation of linear momentum.
For example, if a man (mass $m_1$) is walking with velocity $u$ and the recoil velocity of platform (mass $m_2$) is $v$, then on apply... | Conservation laws are strongly dependent on what reference frame you are working in. A reference frame consists of everything one single observer would measure. Any physical situation can always be described by one observer who considers himself stationary. When writing down conservation of linear momentum, you should ... | First thing: As Bart W pointed out, Conservation Laws are valid in an frame of reference. You can't mix two velocities measured in two different reference frames. Velocities have to be measured in one reference frame like in solution it is measured with respect to ground.
Second Thing: Suppose you are sitting in a fra... | https://physics.stackexchange.com |
350,121 | [
"https://physics.stackexchange.com/questions/350121",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/131602/"
] | I googled for the above question, and I got the answer to be $$[\Psi]~=~L^{-\frac{3}{2}}.$$
Can anyone give an easy explanation for this?
| The physical interpretation of the wavefunction is that <span class="math-container">$|\psi(\vec r)|^2dV$</span> gives the probability of finding the electron in a region of volume <span class="math-container">$dV$</span> around the position <span class="math-container">$\vec r$</span>. Probability is a dimensionless q... | The three-dimensional integral of the norm square of the wave function is a probability, so it should be dimensionless. Therefore $\text{length}^3[\psi]^2=1$, so $[\psi]=\text{length}^{-3/2}$.
| https://physics.stackexchange.com |
56,276 | [
"https://mathoverflow.net/questions/56276",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7666/"
] | Let $R$ be a valuation ring containing a field $k$, with residue field $F$ and quotient field $K$. Assume $F/k$ is separable. Is $K/k$ separable?
I have convinced myself that (for a positive answer) it is enough to treat the case of a rank one valuation ("height one" in Bourbaki's terminology), with $F=k$ and $K/k$ fi... | What about this: we have to prove that $K$ and every purely inseparable extension $l/k$ are linearly disjoint over $k$.
Let $x_1,\ldots ,x_r\in l$ be $k$-linearly independent elements and assume $0=a_1x_1+\ldots +a_rx_r$ for some elements $a_i\in K$. We can divide by the coefficient $a_j$ with the least value and thus... | <strike>Assume that $F=k$ and let $p=char k$.
If $K/k$ is inseparable then there exists $\alpha\in K$ such that min. poly of $\alpha$ over $k$ is equal $g(X^{p^n})$ with $g$ irreducible separable. Since $R$
is a valuation ring, either $\alpha$ or $\alpha^{-1}$ is in $R$. We may assume that $\alpha\in R$ by symmetry. ... | https://mathoverflow.net |
92,575 | [
"https://softwareengineering.stackexchange.com/questions/92575",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/30296/"
] | The big project I'm working on for a couple years now is a control (and everything) application of an advanced device, heart of its firmware.
The device is quite advanced, with more different functionalities than I could say from memory, and 98% of them are handled by this one huge executable. In one hand, the program... | Except for the tiny comment at the end (second, supervising CPU) you could be describing my company. Yup, we need Easter too.
Well, we're a bit further along. We did split the big executable and tried to use standard components for standard bits. Not exactly the big improvement you'd hope for. In fact, performance is ... | <blockquote>
The device is quite advanced, with more different functionalities than
I could say from memory, and 98% of them are handled by this one huge
executable. In one hand, the program is quite maintainable, well
modularized inside, properly documented, there's a reasonable
separation of functionalities... | https://softwareengineering.stackexchange.com |
267,374 | [
"https://softwareengineering.stackexchange.com/questions/267374",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/146579/"
] | I am curious why exception handling is a topic often ignored in Scala. Is it the goal of the language (or the style) to not rely on exception handling except for external input/code?
I was hoping the style guide had some discussion on exception checking/handling. Is there a good reference that I could consult to unde... | Good functional style does not need defensive coding nearly as much as the imperative style. <strong>try</strong> and <strong>catch</strong> is not the only control structure which is neglected in Scala (and other functional languages); <strong>for</strong> and <strong>while</strong> loops are endangered species and e... | Scala encourages the use of constructs like options and futures for error handling. First of all, lazy evaluation makes exceptions problematic, because there is a different stack when a function is executed than when it's queued to execute. Scala isn't lazy by default, but it can be lazy when you choose.
Also, option... | https://softwareengineering.stackexchange.com |
52,671 | [
"https://dba.stackexchange.com/questions/52671",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/24616/"
] | When there are nested impersonations (as in <code>exec as user = 'user1'; exec as user = 'user2'; exec as user = 'user1';</code>), is there a way to revert all of them without having to use the <code>revert</code> command multiple times (e.g. <code>revert all;</code>)?
Or at least, if one must use <code>revert</code> ... | You could capture the name of the current user at the start of your batch, then compare that to the then-current user at the point where you want to <code>REVERT</code> back to the original user.
For instance:
<pre><code>DECLARE @Name SYSNAME;
SET @Name = SUSER_NAME();
SELECT @Name;
EXEC AS USER = 'SomeUser';
EXEC AS... | You could assign the current context to a cookie then revert to that cookie when you desire to.
| https://dba.stackexchange.com |
92,527 | [
"https://mathoverflow.net/questions/92527",
"https://mathoverflow.net",
"https://mathoverflow.net/users/22485/"
] | Let $a$, $b$ be two coprime natural numbers. Let $A \subseteq \{0,1,\ldots, a-1\}$ and $B \subseteq \{0,1,\ldots,b-1\}$ be two nonempty sets, which we think of as sets of residues mod $a$ and $b$ respectively.
I would like to know if anyone has ever seen (or knows a proof for) the following result: that any interval o... | [<strong>Edited</strong> <em>again mostly to spell out why the $m_j \bmod a$ are distinct</em>.]
Yes, the desired result is true for all $k$. The following proof
is elementary but possibly more algebraic than expected (apparently
some kind of variant of the "polynomial method" in combinatorics, though
with no need f... | Nice question! Maybe Jacobsthal's function might interest you. If the $a_i$s are all distinct primes, and the $A_i$s are the non-zero residue classes modulo the $a_i$s, the best known bounds for Jacobsthal's function, due to Iwaniec and Vaughan, will definitely help your $k$-variate case. The relevant publications are:... | https://mathoverflow.net |
214,886 | [
"https://dba.stackexchange.com/questions/214886",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/150832/"
] | I am confused about what encoding and collation I should use so my queries returns the correct sort order.
Right now my encoding is <code>UTF-8 Unicode</code> and collation <code>utf8_unicode_ci</code> for both <code>firstname</code> and <code>lastname</code>.
And the sort order would be something like this:
<pre><c... | I can reproduce your issue. <strong>Don't use <code>mysql.server start</code> in macOS</strong>.
If you installed MariaDB with <code>homebrew</code>, use <code>brew services</code> to start and stop the database. It takes only a second and doesn't write strange error to stdout.
<pre><code>brew services stop mariadb
S... | I resolved the problem by changing .my.cnf from:
<pre><code>[client]
user=myname
password=mypwd
database=mydb
</code></pre>
to:
<pre><code>[client]
user=myname
password=mypwd
[mysql]
database=mydb
</code></pre>
| https://dba.stackexchange.com |
44,201 | [
"https://stats.stackexchange.com/questions/44201",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/13525/"
] | I am trying to understand the link between the moment-generating function and characteristic function. The moment-generating function is defined as:
$$
M_X(t) = E(\exp(tX)) = 1 + \frac{t E(X)}{1} + \frac{t^2 E(X^2)}{2!} + \dots + \frac{t^n E(X^n)}{n!}
$$
Using the series expansion of $\exp(tX) = \sum_0^{\infty} \frac{... | As mentioned in the comments, characteristic functions always exist, because they require integration of a function of modulus $1$. However, the moment generating function doesn't need to exist because in particular it requires the existence of moments of any order.
When we know that $E[e^{tX}]$ is integrable for all... | From Proakis, Digital communication 5th ed., the straightforward relationship is
<span class="math-container">$$
\varphi(\omega) = M(j\omega)
$$</span>
and
<span class="math-container">$$
M_x(t) = \varphi_x(-j t)
$$</span>
| https://stats.stackexchange.com |
52,596 | [
"https://dsp.stackexchange.com/questions/52596",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/36797/"
] | In OFDM system, I need to transmit a signal <span class="math-container">$x$</span> in SIMO channel <span class="math-container">$H$</span> with one <span class="math-container">$Tx$</span> antenna and 4 <span class="math-container">$Rx$</span> receiver's antennas. The initial equation for that convolution is <span cla... | I've said, in another comment, convolution using the function conv "i.e in MATLAB" and convolution using the Toeplitx matrix <strong>must</strong> give the same results. That's ok.
Now, according to your code, the received signal <span class="math-container">$r$</span> is the results of convolution between channel <s... | The received sample <span class="math-container">$i$</span> at receive antenna <span class="math-container">$j$</span> is given by
<span class="math-container">$$r_{ij}=\sum_{l=0}^Lh_{j,l}x_{i-l}+n_{ij}$$</span>
where <span class="math-container">$L$</span> is the channel memory, <span class="math-container">$\{h_{j,... | https://dsp.stackexchange.com |
535,534 | [
"https://electronics.stackexchange.com/questions/535534",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/266096/"
] | What I have is a 250W PC AT power supply. It has 12V 8A, 5V 30A. I don't need the 5V, so I was thinking maybe I can use a booster to kick the 5V up to 12V and add some amps to the 12V side.
So if my math is correct, 5V * 30A = 150W and 12V * 8A = 96W. If I can combine these into just 12V, I should get 20A and that's ... | The transformer and the internal circuitry design of the PSU will not allow you to simply get >8A from the 12V output.
<blockquote>
So if my math is correct, 5V * 30A = 150W and 12V * 8A = 96W. If I can combine these into just 12V, I should get 20A and that's way more than I need, I only need about 12~15.
</blockquo... | The power calculations are not enough. They seem to allow what you want but before thorough investigations you do not know if 12V output has the rest what's needed for 15A
<ul>
<li>transformer wire thickness</li>
<li>other wire thicknesses including the connector</li>
<li>rectifier rating</li>
<li>output filter</li>
</... | https://electronics.stackexchange.com |
690,165 | [
"https://physics.stackexchange.com/questions/690165",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/326073/"
] | Basically the question is: Does it take the same forces to move a mass up or down including acceleration and deceleration?
The Newton second law: <span class="math-container">$F=m*a$</span> tend to say yes. In reality this is far from the case. Is it only due to friction? Is it also due to the increase of potential ene... | The lever arm for the counter clockwise torque about the bottom hinge is the perpendicular distance between the line of action of the gravitational force and the bottom hinge. The clockwise torque about the bottom hinge is due to the horizontal reaction at the top hinge where the lever arm is the distance between the h... | In a statics problem (with no rotation) any point can be chosen a reference point for calculating torques. You normally choose a point which eliminates one of more torques. If your first choice eliminates one of the unknowns, you can do another calculation with a different reference point.
| https://physics.stackexchange.com |
651,859 | [
"https://physics.stackexchange.com/questions/651859",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/280217/"
] | I know that when AC is passed through the primary coil of a step-up transformer a higher emf is induced in the secondary coil (with more turns) of the transformer. Since energy is conserved, and P = VI, this would mean a drop in current. But I'm not able to visualize what is really happening to the electrons in the sec... | Consider this. You have two particles and you want to know what the probability is to find particle 1 at <span class="math-container">$r_1$</span> and at the same time particle 2 at <span class="math-container">$r_2$</span>. Both particles live in the same 3D space but each particle has its own set of three coordinates... | I'll assume your wavefunction, say <span class="math-container">$\Psi$</span>, is a function of the positions <span class="math-container">$\mathbf{x},\,\mathbf{y}$</span> of two particles. Then <span class="math-container">$|\Psi|^2$</span> is the PDF of their positions' joint position. So if <span class="math-contain... | https://physics.stackexchange.com |
71,051 | [
"https://physics.stackexchange.com/questions/71051",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/24882/"
] | Doesn't $E=mc^2$ mean that mass can be converted to energy? But from what I have studied in high school nuclear physics, it seems that the only "$E=mc^2$" we can get is from binding energy between nucleons. This may sound really stupid but is it possible to actually convert matter into energy using a machine on earth? ... | <blockquote>
Like get 1 kilogram of dirt and convert it to c2 joules? What would it take to make this happen?
</blockquote>
To make something close to this happen you would need one kilogram of antimatter dirt. Then all the quantum number additions would be satisfied and a lot of radiation would come out, but not co... | The laws of physics that makes it difficult to convert dirt into pure energy are the conservation of lepton and baryon number. Each proton or neutron has a baryon number of one and a lepton number of zero, while electrons have a lepton number of one and a baryon number of zero. To reduce matter to pure energy such as e... | https://physics.stackexchange.com |
153,485 | [
"https://math.stackexchange.com/questions/153485",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/4171/"
] | Consider a function $f(r,R)$ of two variables, and consider that $R = R_0 + x$ for some constant $R_0$.
I'm looking for a series expansion of
$$1 / |r - R_0 - x|$$
for small $x$. In other words, the expansion of $1/|r - R|$ around a specific $R_0$.
Here, $r$ is yet another variable and not just a parameter. So, if it... | I don't think that the question got a satisfactory answer yet (mostly because of the way in which it was worded).
The first important point is that a Taylor series cannot get around a singularity: it only represents the original function in some open set where the function is smooth. So the distributional derivatives... | I guess one reason for confusion is that you are trying to expand a multivariable function near a point without actually having fixed a point. You need to consider a pair $(R_0, r_0)$ and then proceed:
$$f(R_0+x,r_0+y)=f(R_0, r_0)+...$$
Certainly the function must possess derivatives of all orders in order to be expand... | https://math.stackexchange.com |
8,868 | [
"https://stats.stackexchange.com/questions/8868",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/3926/"
] | When doing time series research in R, I found that <code>arima</code> provides only the coefficient values and their standard errors of fitted model. However, I also want to get the p-value of the coefficients.
I did not find any function that provides the significance of coef.
So I wish to calculate it by myself, ... | The "t value" is the ratio of the coefficient to the standard error. The degrees of freedom (ndf) would be the number of observations minus the max order of difference in the model minus the number of estimated coefficients. The "F value " would be the square of the "t value" In order to exactly compute probability you... | Since <code>arima</code> uses maximum likelihood for estimation, the coefficients are assymptoticaly normal. Hence divide coefficients by their standard errors to get the z-statistics and then calculate p-values. Here is the example with in R with the first example from <code>arima</code> help page:
<pre><code>> a... | https://stats.stackexchange.com |
149,158 | [
"https://dba.stackexchange.com/questions/149158",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/105408/"
] | I have created three table using with the following code:
<pre><code>CREATE TABLE Invoices (
invoiceID nvarchar(5) NOT NULL PRIMARY KEY,
invoiceDate date,
);
CREATE TABLE ContainsItems (
invoiceID nvarchar(5) REFERENCES Invoices(invoiceID),
itemID nvarchar(5) REFERENCES Items(itemID),
itemQuanti... | <pre><code> SELECT *
FROM ContainsItems ci
INNER JOIN Items i ON ci.itemID = i.itemID
INNER JOIN Invoice iv ON ci.invoiceID = iv.invoiceID
WHERE ci.invoiceID = @yourInvoiceID
</code></pre>
| You are going to want to select from a <code>JOIN</code> statement. In this case, an <code>INNER JOIN</code>.
Try something like this:
<pre><code> SELECT i.itemName, i.pricePerUnit, c.itemQuantity
FROM Items AS i
INNER JOIN ContainsItems ON i.itemID = c.itemID
WHERE i.invoiceID = @yourInvoiceID
</code></pre>
H... | https://dba.stackexchange.com |
23,260 | [
"https://dsp.stackexchange.com/questions/23260",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/15744/"
] | I have been trying to achieve a Hamming window length of 23 using the equation.
I tried several coding, one of the is the one below:
<pre><code>M=23
w = .54 + .46*cos(pi*(-M:M-1)'/M)
plot(w)
</code></pre>
| If the length of the window should be $23$, $M$ must equal $(23-1)/2=11$:
<pre>
M = 11;
m = -M:M;
w = .54 + .46*cos(pi*m/M);
plot(m,w)
</pre>
| You need to do two things:
<ul>
<li>Evaluate the cosine only at 23 points, not at 46 like you're doing in your code above.</li>
<li>Generate a time vector to go with your window signal. This means you'll also need to specify your sampling frequency.</li>
</ul>
You can do it like this:
<pre><code>M = 23; % samples... | https://dsp.stackexchange.com |
143,076 | [
"https://mathoverflow.net/questions/143076",
"https://mathoverflow.net",
"https://mathoverflow.net/users/40447/"
] | Let $I$ be an ideal and $f$ be an element of $R = \mathbb{C}[x_1,\ldots,x_n]$, where $\mathbb{C}$ is an algebraically closed field of characteristic $0$. Does
$$
(I+H):f = (I:f)+H
$$
hold for a general hyperplane in $\operatorname{Spec}(R)$, i.e., for $H = \langle \text{general linear function} \rangle$?
| This is true for a general affine-linear form. First we assume $(I,f)\neq R$. The point is that $(I,f)$ has finitely many associated primes, so a general $H$ would be a non-zerodivisor on $R/(I,f)$.
For any ideal $I$ and any element $f$, there is an exact sequence:
$$0\to R/(I:f) \to R/I \to R/(I,f) \to 0$$
(The f... | A silly counter-example. Take $n:=2$, $I:=Rx_1$, $f:=x_2$. Let $l\notin Rx_1$ be a general linear form in $x_1,x_2$ and $H:=Rl$. Then $I+H=Rx_1+Rl=Rx_1+Rx_2$ and $(I:f)=(Rx_1:x_2)=Rx_1$. Hence, $(I+H):f=(Rx_1+Rx_2):x_2=R$, whereas $(I:f)+H=Rx_1+Rl=Rx_1+Rx_2$.
That was really silly counter-example, as promised. Thanks ... | https://mathoverflow.net |
182,869 | [
"https://mathoverflow.net/questions/182869",
"https://mathoverflow.net",
"https://mathoverflow.net/users/59227/"
] | Let $A$ be an object of a concrete category $C$ with a forgetful functor $F\rightarrow Set$ and let $S \subseteq F(A)$. Is there a general construction that gives us a subobject $\left<S\right>$ of $A$ in $C$?
$S$ should, for example, satisfy the universal property that if $B$ is a subobject of $A$ in $C$ such t... | In a category $Alg$ of algebraic structures, such as groups, the forgetful functor $U:Alg \to Set$ has a left adjoint $F$. Thus given a subset $S \subseteq U(A)$ we have the adjoint map $FS \to A$ and now the substructure $\langle S \rangle$ of $B$ generated by $S$ is obtained by factorising $FS \to A$ through its ima... | Let's denote the forgetful functor by $U : C \to \mathsf{Set}$. (Usually its left adjoint is denoted by $F$.)
If $C$ is well-powered, has intersections (which are special limits), and $U$ preserves monomorphisms and intersections (for example when $U$ preserves limits), we may define $\langle S \rangle = \bigcap_{i : ... | https://mathoverflow.net |
375,909 | [
"https://electronics.stackexchange.com/questions/375909",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/124842/"
] | <strong>If I have a setup where a N MOSFET drives a heavy inductive load (say, 25A peak), can I use the MOSFET's internal resistance to measure said current the same way I would use a shunt resistor?</strong>
The value of the equivalent series resistance when the MOSFET is active (i.e. Rds-on) is usually very low and... | The term, \$V_\text{BE}\$, means \$V_\text{B}-V_\text{E}\$. And the sign is always related to convention current directions and voltage polarities. So in the case of the NPN, where the base is "more positive" than the emitter when forward-biased, the NPN's \$V_\text{BE}\$ is positive. The PNP's case has \$V_\text{BE}\$... | It shoudl be IB=−(VTH−VBE)/RTH+(β+1)RE
This answer above stuffed my results up
| https://electronics.stackexchange.com |
2,063,496 | [
"https://math.stackexchange.com/questions/2063496",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/397927/"
] | I need to prove that for $(\mathbf G, \circ)$ a group, if for every $a\in\mathbf G$ $$a\circ a=e$$ where $e$ is identity element of that group, then the group is abelian group.$$\\$$My proof:
$$\text{We know that:}\\a\circ e=a=e\circ a\\b\circ e=b=e\circ b\\b\circ b=e=a\circ a\text{, so if}\\a\circ a=b\circ b\text{, th... | Your proof is correct as others pointed out (although the last line might require further clarification). Let me provide a shorter way though:
\begin{align}
a \circ b &= \underbrace{(b\circ b)}_{e} \circ (a \circ b) \circ \underbrace{(a\circ a)}_{e} \\
&= b\circ \underbrace{((b \circ a) \circ( b \circ a))}_{e}... | The proof is valid if you meant $a^2=e$ <strong>for all $a\in G$</strong> at the beginning. Here's a variant:
We can read $(ab)^2=e$ as $ab=(ab)^{-1}$. Thus from the general rule of computing product inverses
$$
ab=b^{-1}a^{-1}.
$$
But also $a^2=b^2=e$, so that $a^{-1}=a$ and $b^{-1}=b$. Plugging in the previous displ... | https://math.stackexchange.com |
110,968 | [
"https://dba.stackexchange.com/questions/110968",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/72772/"
] |
How to I combine the two rows below:
<pre><code>Date Id For_Id Type New_Value Old_Value
------------------------------------------------------------------
2015-08-13 6 327 DELETE NULL Value1
2015-08-13 6 327 INSERT Value2 NULL
</code></pre>
...... | If I'm understanding your needs correctly, this would probably work...
<pre><code>SELECT t1.Date, t1.Id, t1.For_Id, t1.New_Value, t2.Old_Value
FROM table t1 JOIN table t2
ON t1.Date = t2.Date
AND t1.Id = t2.Id
AND t1.For_Id = t2.For_Id
WHERE t1.New_Value IS NOT NULL
AND t2.Old_Value IS NOT NULL;
</code></pre>
| If there are multiple delete and inserts in the same day, then you would either need to sort by date and time or some other sort mechanism to determine the latest value in the table. Based on what you have posted, the same day edits won't have differentiating factors.
If your intention is to <strong>combine the rows i... | https://dba.stackexchange.com |
428,346 | [
"https://mathoverflow.net/questions/428346",
"https://mathoverflow.net",
"https://mathoverflow.net/users/141146/"
] | Consider a set <span class="math-container">$X\subseteq \mathbb{R}$</span> such that
<ol>
<li><span class="math-container">$X$</span> is <em>not</em> separable wrt its subspace topology</li>
<li>For all <span class="math-container">$r\in\mathbb{R}$</span> there exists a sequence <span class="math-container">$(x_n)_{n\i... | The existence of such a set follows from <span class="math-container">$``\mathbb{R}$</span> is a countable union of countable sets.<span class="math-container">$"$</span> Let <span class="math-container">$\mathbb{R} = \bigcup_{n<\omega} S_n,$</span> each <span class="math-container">$S_n$</span> countable. Let <span... | Here is another way to show the consistency of such a set by a direct symmetric extension approach:<br />
Let <span class="math-container">$\mathbb{P}$</span> be the forcing that add Cohen reals (by reals I mean elements of <span class="math-container">$\omega^\omega$</span>) indexed by <span class="math-container">$\o... | https://mathoverflow.net |
2,745,000 | [
"https://math.stackexchange.com/questions/2745000",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/487077/"
] | I am trying to solve this problem: <br>
The force acting on a moving object is proportional to its displacement. In the same time, the object experiences the force of air resistance proportional to its speed. Find displacement as a function of time.
My problem is that I have never solved differential equations - I am ... | Try to substitute $\exp(\lambda t)$ as well. The difference is that $\lambda$ will have a complex and a real part this time. (The real part will cause the loss of velocity).
So let's rename the variables as I've mentioned in the comments to get
$$\ddot x + 2\beta \dot x +\omega_0^2x=0$$
Now substitute $x=\exp(i \ome... | You can treat the differential operator as a variable:
(mD$^2$+bD+k)x=0
This may seem like an abuse of notation, but it works.
If you treat what's in the parentheses as a quadratic polynomial in D, and apply the quadratic formula to find roots $r_1$ and $r_2$, then you have $(D-r_1)(D-r_2)x=0$. You can then take x =... | https://math.stackexchange.com |
660,918 | [
"https://physics.stackexchange.com/questions/660918",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/98734/"
] | In the case of the double slit experiment, in the space between the slits and the detector, the free particle’s wave function <span class="math-container">$\psi$</span>consists of two interfering radial waves. How is that wave function mathematically represented in that space, in a manner that satisfies the free partic... | The eigenfunctions of the Free Schodinger equation in cylindical coordinates with
<span class="math-container">$E(k) = \hbar^2 k^2/2m$</span> and angular momentum <span class="math-container">$n\hbar$</span><br />
are
<span class="math-container">$$
\psi_{k,n}(r,\theta)= J_n(kr)e^{in\theta}
$$</span>
where
<span class=... | The solutions to the free Schrodinger's equation in polar coordinates are the same as the solutions in Cartesian coordinates -- arbitrary superpositions of plane waves. The radial wave centered at zero is one such superposition, which just happens have a nice (i.e. separable) formula in polar coordinates. So is a radia... | https://physics.stackexchange.com |
495,836 | [
"https://stats.stackexchange.com/questions/495836",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/289365/"
] | My data set has:
<ul>
<li>20 categorical nominal predictor variables, each variable has on
average 5 distinct possible values</li>
<li>1 dependent binary class variable to be predicted by the Naive Bayes classifier</li>
<li>8000 rows/observations</li>
</ul>
For one specific categorical nominal predictor variable about ... | Being able to Implement the code does not necessarily indicate that the strategy is ideal though! From what I understood your problem, there can be 2 different approaches. You will have to experiment with the performance of the model on the test dataset to choose the right one.
A. Replace the null values with the not n... | you can either use <strong>mode imputation</strong> method or <strong>KNN imputation method</strong> to handle missing data.
omitting NAs is not a good solution at all.
| https://stats.stackexchange.com |
502,761 | [
"https://electronics.stackexchange.com/questions/502761",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/253031/"
] | I'm creating a numitron clock with 4xIV-9 tubes (seven-segment filament displays) and have decided to illuminate them using shift registers controlled by an arduino. Each segment takes a voltage of 4-4.2V and around 17-20mA of current.
My voltage I have available is a 5V output voltage from an LM7805 voltage regulator... | Replace the 7805 with a 1Amp or more adjustable regulator and set it to 4.2 volts. Run both the arduino and everything from that instead of running it off the 5V. The Arduino will be fine with 4.2 volts without any issue, and it makes it easier since you dont have to worry about level translation for the input lines e... | Use an adjustable voltage regulator.
| https://electronics.stackexchange.com |
70,252 | [
"https://softwareengineering.stackexchange.com/questions/70252",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1785/"
] | Are adding gimmicks to a website ever a good idea? What I mean by gimmick is adding "cool" features that solve no real problem.
We are currently considering adding a "Magazine style" product viewing application to the site. You know like a flash based app that shows magazine pages that you can click and flip the pages... | <strong>It depends.</strong>
A little gimmickry can make things more appealing. Look at any fun game: there are often a ton of little gimmicks. And a little more appeal can make the difference between success and failure.
But there are three problems with the situation you describe:
<ol>
<li><strong>It sounds like t... | First, let's unpack 'adding "cool" features that solve no real problem'.
What is a "real" problem? I would define a real problem as one that, when solved, provides value to your customers or clients (or other stakeholders), i.e. "business value". By that definition, a "cool" feature can solve a "real" problem, althoug... | https://softwareengineering.stackexchange.com |
94,910 | [
"https://biology.stackexchange.com/questions/94910",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/61108/"
] | I have been wanting to supplement my heating system with some plants that produce heat! I have become aware that there are around 14 species which generate significant amounts of heat for example the eastern skunk cabbage.
However I have also read that many species which are thermogenic release odours such as the smell... | <em>Philodendron bipinnatifidum</em> is a thermogenic houseplant. It is somewhat toxic, so not pet- or small-child-friendly, but commonly grown as a houseplant. However, I do not know if the heat generated would be enough to significantly impact your house; my impression is that most thermogenic plants merely warm thei... | The heat the plant produces ultimately comes from the light it uses. Unless the plant produces heat just in the wanted time (winter?) from light absorbed another time; then you would be just as warm by letting the light directly warm your environment regardless of plants.
| https://biology.stackexchange.com |
486,989 | [
"https://physics.stackexchange.com/questions/486989",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/235028/"
] | We can explain ionic bond as the force between charged particles due to Coulomb electrostatic law. This got me wondering how is then covalent bond explained purely in terms of physics?
| Eventually, every kind of bond in condensed matter is reducible to electrostatics. Covalent bond, ionic bond, van der Waals forces, metallic interactions and even more sophisticated interactions like the phonon-mediated electron-electron attraction in a superconductor, are all reducible to purely electrostatic interact... | Covalent bonding is a quantum-mechanical phenomenon that can't be explained classically. The basic idea can be demonstrated in the case of a hydrogen molecule if you think of the electrons as two particles in a box. By joining the two hydrogen atoms together into a molecule, you make the "box" twice as long. Let's pret... | https://physics.stackexchange.com |
153,700 | [
"https://mathoverflow.net/questions/153700",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41654/"
] | 4 end points (a,b,c,d say) are chosen uniformly randomly and connected a to b and c to d by two geodesics on the 2-dim round sphere. Here uniformly is in the obvious sense of the volume form associated with the round metric. What is the probability the two curves cross?
| The probability is 1/8. With each (generic) pair of geodesic segments you can associate another 15 pairs which you get by replacing each of the 4 end points by its antipodal point. You can easily check that of these 16 pairs, exactly 2 intersect.
| If you extend to complete circular geodesics then the probability is 1. So it is just a matter of finding the probability that the point of intersection is in both segments chosen, which is an easier linear (not spherical) problem.
| https://mathoverflow.net |
241,089 | [
"https://softwareengineering.stackexchange.com/questions/241089",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/17904/"
] | I have seen in a couple of projects that developers prefer to keep essential user info in one table (email/login, password hash, screen name) and rest of the non essential user profile in another (creation date, country, etc). By non-essential I mean that this data is needed only occasionally. Obvious benefit is that i... | It depends on the size and requirements of your project.
I can see one way in which data about users can be divided into two sets, with different purposes and thus requirements:
<ul>
<li>Identity data: user name, password hash, email address, last login time, etc.</li>
<li>User profile data, which includes users pref... | There are, at least, three cases when having a person table for basic attributes and a second table for other attributes with a one-to-one relationship, is desirable:
<ul>
<li><strong>BLOB data</strong> like a picture. A separate table allows data to be stored separately for performance reasons, for example in a separ... | https://softwareengineering.stackexchange.com |
284,771 | [
"https://mathoverflow.net/questions/284771",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8628/"
] | Let $p$ be a prime number, $n$ be a positive integer, and let ${\mathbb Z}_p^{n\times n}$ denote the set of $n\times n$-matrices over ${\mathbb Z}/p{\mathbb Z}$.
Suppose we are given an integer $m>0$ and matrices ${\bf A}_1,\ldots, {\bf A}_m\in {\mathbb Z}_p^{n\times n}.$ I am looking at the following problem: if t... | Yes. If we conider the sequence $A_i^n$, because it is a sequence inside a finite set, it must eventually repeat. After it repeats, the sequence won't take any new values, so we can assume $n_i$ is less than this first repetition. This means that there are only finitely many possibilities, which of course reduces the p... | Even more is decidable: we may get a list of all possible spaces which are images of the operator $A_1^{n_1}\dots A_m^{n_m}$.
Induction in $m$. Base $m=1$. Consider the spaces $X_k=A^k(\mathbb{Z}_p^n)$. Two of them coincide, since they take only finitely many possible values (and we know an a priori estimate for this... | https://mathoverflow.net |
3,689 | [
"https://quant.stackexchange.com/questions/3689",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/1696/"
] | Can someone shed some light on optimal ways to execute medium sized orders ~2000 shares in the market?
Unfortunately the execution algo I have access to is very dumb. It follows the top-of-book price and hence I can see that the algo I am using is getting gamed by some predatory algo. For example, if the spread is 2 ... | If your original algo's goal was the follow the top-of-book quote, then it should have had some <em>minimums</em> before it would join a new quote. For example, the reference quote must have a minimum size shown and must be live for a minimum amount of time before you'll join.
Also, it helps to "stack the book" by bre... | If you want to be more aggressive without revealing your hand, place your orders as hidden orders inside the bid/ask. Algos on the other side will fish with small size orders to see what is hidden however. The fishing will not reveal the size of your order, but reveal that something is there. Can get some size done... | https://quant.stackexchange.com |
5,155 | [
"https://chemistry.stackexchange.com/questions/5155",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/842/"
] | If a reaction requires a "strong" acid - what does this mean? Does it mean any acid of a specific concentration or pH? Are only certain acids classed as "strong"? I have read on Wikipedia that it needs to ionise completely in an aqueous solution - in this case, is a strong acid (for example, HCl) still classed as a str... | The strength or weakness of an acid is independent of its concentration. A strong acid dissociates completely in solution, so $\ce{HCl}$ at any molarity would be considered strong, and $\ce{HCOOH}$ (for example) at any molarity would be weak. It is more enlightening to consider $K_a$ values, which are essentially the e... | What makes an acid strong is also dependent on the context. E.g. lactic acid is considered strong in body fluids because lactate is completely ionized in body pH 7.4.
| https://chemistry.stackexchange.com |
674,470 | [
"https://physics.stackexchange.com/questions/674470",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208473/"
] | I have heard that a single electron has been trapped for a long time in I guess some kind of magnetic trap. I also understand that an electron in orbit around a proton in hydrogen atom is not really in a smooth planetary orbit but it is more like it "probably" is some place around the proton. So my question i... | Yes, the energy of an electron for any atom is zero at <span class="math-container">$n \to \infty$</span>.
Where does <span class="math-container">$E =0$</span> exist in an atom classically? Well past the atomic radius wouldn't it?
Why would an electron hang out at <span class="math-container">$n \to \infty$</span>? On... | For any hydrogen orbital there is a finite chance to detect the electron far away from the nucleus. In principle therefore the energy does not go to zero as r goes to infinity. Of course, in practice these probabilities decay exponentially. For a nearly ionised case this decay is much slower. For the ionised case the e... | https://physics.stackexchange.com |
65,426 | [
"https://physics.stackexchange.com/questions/65426",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/24781/"
] | Wave function interpretation $y(x,t) = (0.35m)\sin(10\pi t-3\pi x + \frac\pi{4})$
I used to deal with function with one variable
And now theres are two, how can I interpret them?<br/>
Is $10\pi$ still equal to $\omega$ ?
how about $-3\pi x$ and $ \frac\pi{4}$?
I just want to know the form of the equation?
Just lik... | The general solution to the classical wave equation is
$$y(x,t)=f(\mathbf{k}\cdot\mathbf{x}-wt)$$ where $f$ is an arbitrary function. In this case, $f(x)=(0.35m)\sin(-x+\frac{pi}{4})$.
Basically, whatever multiplies $t$ is $-\omega$, and whatever multiplies (or is dotted into) $\mathbf{x}$ is $\mathbf{k}$. Anything ... | The wave equations are second order equations on time and space:
$$
\nabla^2u(\mathbf{x},t) = \frac{1}{v^2}\frac{\partial^2 u(\mathbf{x},t)}{\partial t^2}
$$
Where $v$ is the speed of the wave. If we plug in Dan's functions we have:
$$
\nabla^2 y(\mathbf{x},t) = \nabla^2 f(\mathbf{k}\cdot\mathbf{x}-wt) = (k_x^2 +... | https://physics.stackexchange.com |
350,487 | [
"https://stats.stackexchange.com/questions/350487",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/53566/"
] | I know what is Winsorization and why is it applied. My understanding was that it is applied only on the train data to reduce the effect of outliers.
But! Recently I came across a kernel where Min, Max (or 99th percentile values) from training data are stored and applied on the test data before applying the model. Is i... | So, after talking to some experts, it is common practice to apply Winsorization to test data as well.
Which means this the full process of building the model.
<ol>
<li>Split the data into train and test sets.</li>
<li>Apply Winsorization on train data (of course, when necessary!!) and save the values (i.e. 99th or 95... | They key here is to imagine that you are going to deploy your final model and use it: your training data represents the data you will have before you deploy your model and the test data represents the data you will obtain after you deploy your model.
So you will do exactly the same modifications to your test data as y... | https://stats.stackexchange.com |
334,306 | [
"https://softwareengineering.stackexchange.com/questions/334306",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/200283/"
] | Admittedly, this is a homework problem but I have tried to figure it out on my own. Just want to make sure I get it correct. So far, the only design pattern I believe to be correct would be the Adapter design pattern. I could implement an Adapter class to publicly inherit from class C and privately from class D and ins... | Your problem states that D shall not inherit from C and that it doesn't inherit C's variables. It furthermore states that is is an alternative implementation.
I therefore think the question is not about making D an adapter (e.g. <code>D*d=new adapter()</code>). You have to consider that C and D are given classes t... | First of all, inheritance is not an option, especially if the methods of the class C are not virtual to begin with. You can do something like this (the language used is C#, but the approach works in C++ too, obviously):
<pre><code>public class C
{
public void foo()
{
}
public void bar()
{
}
}
... | https://softwareengineering.stackexchange.com |
108,653 | [
"https://physics.stackexchange.com/questions/108653",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/44645/"
] | Why does increasing the width of a rubber band increase its elastic constant($k$)? And why are the two variables directly proportional? Explain it in terms of the structure of the band, if that is relevant.
| Let me first make a general remark about internal symmetry groups, unrelated to our problem of the correct symmetry group for QCD.
<blockquote>
<em>The symmetry must act on Hilbert space as a unitary operator for the
conservation of probability.</em>
</blockquote>
Now let us turn to the strong interaction. The m... | Proving, that <span class="math-container">$N_c=3$</span> is not enough to verify, that the transformations are governed by <span class="math-container">$SU(3)$</span>. Imagine a SU(2) color triplet <span class="math-container">$\phi \to \phi^\prime=W\phi$</span>.
A meson would be color neutral, because
<span class="m... | https://physics.stackexchange.com |
89,250 | [
"https://dba.stackexchange.com/questions/89250",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/56575/"
] | I'm trying to make a trigger that checks which staff member have the least amount of assigned tasks, before adding the task, and assign it to that member.
What I came up with was something like this:
<pre><code>CREATE TRIGGER trgInsteadOfInsert ON helpCase
INSTEAD OF Insert
AS
declare
@helpCaseId int,
@problemTypeI... | You have a derived table in the from clause without an alias.
This will give you the same error:
<pre><code>select *
from (
select *
from YourTable
);
</code></pre>
Add an alias to the derived table.
<pre><code>select *
from (
select *
from YourTable
) as T;
</code></pre>
Note: Your t... | As Mikael already replied 'Add an alias to the derived table.' or Use below optimized version of your script.
<pre><code>CREATE TRIGGER trgInsteadOfInsert ON helpCase
INSTEAD OF INSERT AS
BEGIN
Declare @staffId int
SELECT @staffId = MIN(staffId)
FROM helpCase
WHERE hel... | https://dba.stackexchange.com |
1,368,899 | [
"https://math.stackexchange.com/questions/1368899",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/255933/"
] | I am fairly new to statistics and just recently encountered queueing theory.
I have programmed a simulation for a $M/M/1$ queue in which I specify the inter-arrival times and service times. I input say, an exponential distribution with a mean of $1$ for both the inter-arrival and service time.
I also measure for the ... | $$\dfrac{9\alpha^2}{2\alpha^2}=\dfrac{a^2}{a-b}$$
$$\implies9b=9a-2a^2=-2\left(a-\dfrac94\right)^2+2\left(\dfrac94\right)^2\le2\left(\dfrac94\right)^2$$ as $a$ is real
| $3\alpha=\frac{-a}{a-b},
2\alpha^2=\frac{1}{a-b}$
divide
$\frac{3\alpha}{2\alpha^2}=-a$,
$a\alpha=\frac{-3}{2}...............(1)$,
As $\alpha$ is a root of $(a-b)x^2+ax+1=0$,
$(a-b)\alpha^2+a\alpha+1=0$
$(a-b)\frac{9}{4a^2}-\frac{3}{2}+1=0$
$2a^2-9a+9b=0$
this is quadratic in $a$ and as $a$ being real
$81-4(2)(9b)\ge0$... | https://math.stackexchange.com |
6,695 | [
"https://cs.stackexchange.com/questions/6695",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/2329/"
] | I'd really like your help with proving the following.
If $\mathrm{NTime}(n^{100}) \subseteq \mathrm{DTime}(n^{1000})$ then $\mathrm{P}=\mathrm{NP}$.
Here, $\mathrm{NTime}(n^{100})$ is the class of all languages which can be decided by nondeterministic Turing machine in polynomial time of $O(n^{100})$ and $\mathrm{DTi... | Here is the solution using padding. Suppose $L \in \mathrm{NTime}(n^{1000})$. Define a new language $L' = \{x0^{|x|^{10}-|x|} : x \in L\}$. Each $x \in L$ corresponds to some $y \in L'$ of length $|y| = |x| + (|x|^{10}-|x|) = |x|^{10}$. Therefore we can decide whether $y \in L'$ in non-deterministic time $|x|^{1000} = ... | Break the problem into two parts:
<ol>
<li>There is a $\mathsf{NP}$-complete language in $\mathsf{NTime}(n^{1000})$.</li>
<li>If an $\mathsf{NP}$-complete language is in $\mathsf{DTime}(n^{1000}) \subset \mathsf{P}$ then $\mathsf{P}=\mathsf{NP}$.</li>
</ol>
| https://cs.stackexchange.com |
20,936 | [
"https://mechanics.stackexchange.com/questions/20936",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4906/"
] | In the manual for my 2003 Opel Agila it says:
<blockquote>
Do not start by pushing or towing, Your vehicle is fitted with a catalytic converter, it must NOT be started by pushing or towing.
</blockquote>
Why & how would starting my car in this way damage the catalytic converter?
Is there a serious risk of dama... | unburnt fuel can damage the catalytic converter. By tow starting the car you could cause large amounts of unburnt fuel to be pushed through the engine and into the catalytic converter.
| This is counterintuitive: Lean mixtures at high exhaust flow rates can damage a catalyst. The most common condition for this is the engine running out of fuel. But push starting could put the catalyst in the same condition. How this works it that the lean mixture does not burn in the cylinder but does in the catalyst... | https://mechanics.stackexchange.com |
490,725 | [
"https://physics.stackexchange.com/questions/490725",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/236248/"
] | If we increase the distance between the collector plate and the emitter plate in the setup of the photoelectric experiment, then will there be any change in the stopping potential? (this thought comes into my mind as electric potential is defined as <span class="math-container">$V=E\cdot d$</span>)
Also by making such... | Note that in the ideal case if we fix the potential between the plates then the electric field, the gradient of the potential, is <span class="math-container">$E = V/d$</span> and the work done is <span class="math-container">$W = F\cdot d = q\cdot E \cdot d$</span> so the two <span class="math-container">$d$</span>s c... | I like to think of potential as the depth of a well. When calculating the energy required to get a ball out of the well, it doesn't matter what the shape of the walls are and how long the slope is. It only matters how deep the well is relative to the surrounding ground.
So no, the distance won't matter at least in th... | https://physics.stackexchange.com |
1,902,034 | [
"https://math.stackexchange.com/questions/1902034",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/76333/"
] | The orientation presheaf of a topological $n$-manifold $X$ is
$$U \mapsto H_n(X, X-U)$$
The manifold $X$ is orientable iff there exists a global section which is a generator of each stalk (I believe).
How is this related to the condition that the orientation presheaf be a sheaf? What does it mean morally for the ori... | Because of the excision theorem, you can check the sheaf property on a neighborhood of a point homeomorphic to $\mathbb R^n$, in which case it is trivial using the covering space of $R$-orientations of a topological manifold (where $R$ is a general commutative unital ring ; in our case, use $R = \mathbb Z$). A very det... | It is always a sheaf, as it is the sheaf of sections of a surjective map, the covering map from the canonical double cover.
| https://math.stackexchange.com |
344,371 | [
"https://softwareengineering.stackexchange.com/questions/344371",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/265853/"
] | I had to develop an application in Java for a school project, so I designed a UML class diagram oriented towards Java (including structures, attributes and types). For example:
<pre><code>-getLists() : List<String>
</code></pre>
So the question is: should I assume which language I'll be using when creating a UM... | A rule of thumb is that the UML model should be technology independent. Having said that I would add that sometimes you use some constructs which might be more related to a specific technology (like multiinheritance).
In your case instead of
<pre><code>-getLists() : List<String>
</code></pre>
use multiplicity:... | If you know the language that will be used, I don't think it can hurt to use the naming conventions, notation, and so on of the language. It will save time when it comes time to code, and it can help you work out the exact contracts of your interface.
| https://softwareengineering.stackexchange.com |
983,436 | [
"https://math.stackexchange.com/questions/983436",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/26728/"
] | I thought that direct sum means each component of $V = \oplus U_i$ can be decomposed into elements of $U_i$. But if $U_i$ is replaced by the whole space, doesn't it mean the everything else in the direct sum doesn't matter?
Concrete case.
$\Bbb R = \Bbb R \oplus \Bbb R$, is this not true? All spaces are vector space... | Yours is just a problem of definitions. Given two vector spaces $V$ and $W$ we have $$V+W=\{v+w|v\in V,w\in W\}$$
While the simbol $V\oplus W$ means that $V\cap W=\langle0\rangle$. So $$\mathbb{R}=\mathbb{R}+\mathbb{R}$$ and $$\mathbb{R}\neq\mathbb{R}\oplus\mathbb{R}$$ $$\mathbb{R}^2=\mathbb{R}\oplus\mathbb{R}$$.
| I think you are confusing direct sum $\oplus$ and just the usual sum $+$ of subspaces. $\mathbb{R}\oplus \mathbb{R}$ is not isomorphic to $\mathbb{R}$ because they have different dimensions ($2$ and $1$ respectively). At the same time, $\mathbb{R}=\mathbb{R}+\mathbb{R}$ if you view $\mathbb{R}$ as a subspace of itself.... | https://math.stackexchange.com |
71,741 | [
"https://dba.stackexchange.com/questions/71741",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/43925/"
] | I have the following object model:
<pre><code>class A {
List<Thing> orderedListOfThings;
}
interface Thing {
}
class X implements Thing {
int attr;
}
class Y implements Thing {
String value;
}
class Z implements Thing {
B b;
}
class B {
...
}
</code></pre>
The order of the list <code>or... | As others have mentioned, this can be done rather easily via a SubClass / Inheritance model. I would advocate something closer to what Pieter Geerkens suggested than what VDohnal suggested as I prefer not having lots of NULL fields per row, depending on the "type" that the row represents (i.e. the [Value] field has to... | This type of structure is termed a Sub-Type relationship and is usually built in an RDBMS thus (using SQL Server T_SQL syntax):
<pre><code>create type B as table (
StringValue varchar(max) not null,
IntValue int not null,
FloatValue float not null
);
create table ThingTypes... | https://dba.stackexchange.com |
9,648 | [
"https://dsp.stackexchange.com/questions/9648",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/4854/"
] | I want to simulate a multipath fading channel, different amplitude and delay is given. I want to use delay in padding style. I read that the different values for delay like [0 .6 3.1 ...] represent the delay between the first and last signal arrival? Giving the number of paths, How to simulate it?
regards
| @MohammedFatehy If you put up -exactly- what you currently know and have, we can help you more.
Generally speaking, let us say you have a signal x[n]. And lets say your sampling rate is 1 Hz. So you take one sample every second.
Now you want to construct a channel for multipath. Right off the bat, your multipath ch... | Create a copy of your signal vector for each path, add zeros to its beginning according to how much delay you have. Add noise to each of them, then add them all up.
| https://dsp.stackexchange.com |
321,398 | [
"https://softwareengineering.stackexchange.com/questions/321398",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/232219/"
] | Recently I have come across with another way of writing a function expression, like this: <code>setTimeout(() =>{/*code*/},1000);</code> as opposed to: <code>setTimeout(function(){/*code*/},1000);</code>
What is the benefit of using <code>() = ></code> rather than <code>function(){}</code>
Can I use it all the ... | <blockquote>
I've left them public for ease of unit testing
</blockquote>
Ease of <em>writing</em> those tests, maybe. But you are then tightly coupling that class to a bunch of tests that interact with its inner workings. This results in brittle tests: they will likely break as soon as you make changes to the code.... | I would normally expect you to exercise the private member functions via the public interface. In this instance I would write different tests to feed different file contexts in, with different data sets present in order to exercise those methods.
I don't think your tests should know about those private methods. I thi... | https://softwareengineering.stackexchange.com |
181,064 | [
"https://softwareengineering.stackexchange.com/questions/181064",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/17438/"
] | Michael Perry states in his Pluralsight course on Provable Code (transcript subscription only) that:
<blockquote>
[T]he burden of proof rests with the caller
</blockquote>
In a code contract, why must the burden of proof rest with the caller and not the method of the class that is being called? Is this a preferred ... | I'd say that "burden of proof" is the wrong way to think about it. A class with a calling contract <em>can and should</em> validate that the contract is kept by callers. But when it's not, all it can do is produce an error/exception.
The point of the contract is to state clearly what the calling code must do to prod... | That's because it's the caller the one that passes the parameters.
The caller can pass wrong parameters, hence it must check the exceptions thrown by the callee (or err codes).
| https://softwareengineering.stackexchange.com |
240,138 | [
"https://mathoverflow.net/questions/240138",
"https://mathoverflow.net",
"https://mathoverflow.net/users/74343/"
] | Fix a $(B,N)$ pair (Tits system) of a semisimple Lie group $G$. Let $u$ and $v$ be two Weyl group elements such that $l(uv)=l(u)+l(v)$. It is known that $BuvB=(BuB)(BvB)$ (see for example Humphreys's Linear Algebraic Groups Section 29.3 Lemma A). Let $x$ be an element of the Bruhat cell $BuvB$ and I would like to facto... | Many thanks to Paul Garrett's comment above. Inspired by his comment I come up with a proof of the following equivalent statement.
Proposition. <em>If $x\in BwB$ where $w=s_{i(1)}s_{i(2)}\dots s_{i(l)}$ is a reduced word for $w$, then there exist $x_k\in Bs_{i(k)}B$ such that $x=x_1x_2\dots x_l$; further if $x=x'_1x'_... | Here is a (probably equivalent) way to see this. I'll give an argument for $(BsB)(BwB)$, where $s$ is a simple reflection. You should be able to expand this argument to $(BvB)(BwB)$ as requested in the question. The expansion will use the fact that $\ell(vw) = \ell(v) + \ell(w)$ implies $\ell(s_t \cdots s_1 w) = t + \e... | https://mathoverflow.net |
119,531 | [
"https://physics.stackexchange.com/questions/119531",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I was wondering why freshwater freezes from up to bottom and not the other way around. The reason I question this is because in a Video I came across, I discovered water freezes from top but surely with the current knowledge I would say it should be opposite because we know cool air drifts down while hot air drifts up ... | The density of water rises from 0 to 4 degrees celsius. So you would have a gradient of water temperatures. On the bottom 4 degrees celsius and colder water above it. This is also the reason why fish survive in winter, they just dive to the bottom where the temperature stays warm longer. Also the density of ice is smal... | I think it depends from pressure,that at the bottom is higher. So we need to reach a temperature lower than at the top of the liquid. You know,higher the pressure of water,lower the equilibrium temperature liquid-solid. So while at the same temperature the freezing starts from top,the lower layers are "heated" from the... | https://physics.stackexchange.com |
533,203 | [
"https://electronics.stackexchange.com/questions/533203",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/30449/"
] | This may be a stupid question but I'm missing something fundamental about energy conservation of electrical machines - I am sure I have forgotten something from basic machine theory but I haven't found out what thus far:
Let L, R, E be the equivalent model of a DC brushed motor winding (inductance, resistor, back-EMF).... | <h2>This is for inductor stored energy</h2>
So, if you discharge a charged inductor onto a 1 Ω resistor, the instantaneous current will be the same as you connecting the inductor to a 1000 Ω resistor but, the whole show will be over much more quickly. In other words, with a 1 Ω resistor, it might take 1 second for the ... | Lets say the motor provides 64W steady state and we use a 4Ω resistor to dissipate the energy:
The voltage across the resistor will be P=I^2<em>R so sqrt(64W/4Ω)=4A and the voltage would be sqrt(P</em>R)=V with sqrt(64W*4Ω)= 16V
16V times 4A across the resistor is 64W dissipated across the resistor
Now we put another 4... | https://electronics.stackexchange.com |
381,530 | [
"https://physics.stackexchange.com/questions/381530",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/105136/"
] | Imagine you are about to start a car race. You are on the grid, waiting for the green light. What should you do in order to optimize your start?
Some people would say that a drift start would be the best. Namely, pressing the clutch and then pressing the throttle, to suddenly let go the former and let the wheels start... | I believe the second case should be better because the maximum value of static friction is more than the value of kinetic friction; because <span class="math-container">$\mu_{s} > \mu_{k}$</span> and normal reaction is same in both the cases (equal to weight of car).
The best possible case can be when the wheels ap... | The first option is better. Friction comes only if you need it, If I don't touch a mug, there will be no force of friction. Static friction does have a higher maximum but the force of friction that will push the car forward will be equal to the force of the car acting on the ground. Kinetic force is indeed less then th... | https://physics.stackexchange.com |
282,459 | [
"https://physics.stackexchange.com/questions/282459",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20281/"
] | This may be a basic question, but I have never understood it completely: why is an earthed conductor always at zero potential? I would say it is because theoretically one can suck up charge from the earth without doing work, hence it is at zero potential (all earth charge is at infinity), not sure if this makes sense.
| The electrical potential has a gauge freedom because we can arbitrarily set the zero anywhere we want. This is because we can only ever measure differences in the potential and not the absolute value of the potential.
Conductors that are earthed are all at the same potential (because they are earthed to the same plane... | "why is an earthed conductor always at zero potential"
Because that's the definition. But we could have chosen any other number too. Voltage is a relative measure between two values, not an absolute value.
Think about length. When I say "12 feet", what does that mean? It means 12 feet from one point to another. We si... | https://physics.stackexchange.com |
242,032 | [
"https://physics.stackexchange.com/questions/242032",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/85574/"
] | Is it possible to use Gauss's law of electromagnetism, (The net electric flux through any closed surface is equal to $1⁄\epsilon$ times the net electric charge enclosed within that surface.) to calculate the gravitational field at point by making certain changes, i.e, by replacing electric flux with gravitational flux,... | Yes, you can use Gauss's law for gravity.
$$\nabla\cdot\vec{g} = 4 \pi\, G\, \rho $$
or
$$ \oint \vec{g}\cdot\mathrm{d}\vec{a} = 4 \pi\, G\, M_\mathrm{enc} $$
where $\vec{g}$ is the gravitational field (equivalently, acceleration due to gravity), $\rho$ is mass density, and $M_\mathrm{enc}$ is the total mass enclos... | Gauss Law for Gravity basically says that the total gravitational flux emanating from a sphere enclosing the Earth is <span class="math-container">$4 \pi G M$</span>.
Now divide this by the total surface of the sphere <span class="math-container">$4 \pi R^2$</span> with <span class="math-container">$R$</span> the radiu... | https://physics.stackexchange.com |
104,508 | [
"https://math.stackexchange.com/questions/104508",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/11857/"
] | From Ireland's Number theory book, Ch.3 ex. 6.
Let and integer $n>0$ be given. A set of integers $a_{1},a_{2}, \cdots ,a_{\phi(n)}$ is called a reduced residue system modulo $n$ if they are pairwise incongruent mod n and $(a_{i},n)=1$ for all $i$. If additionally $(a,n)=1$, prove that $aa_{1},aa_{2}, \cdots ,aa_{\... | There are exactly $\phi(n)$ elements of $\mathbb{Z}/n\mathbb{Z}$ that lift up to integers coprime with $n$, so any reduced residue system corresponds to exactly the same set of representatives in the ring of integers. This means that the product $a_1\cdots a_{\phi(n)}$ is the same as $b_1\cdots b_{\phi(n)}$ modulo $n$ ... | HINT: If $a_{1}, a_{2}, \cdots , a_{\phi(n)}$ and $b_{1}, b_{2}, \cdots , b_{\phi(n)}$ are two reduced bases, what can you say about the products
$\displaystyle \prod_{i=1}^{\phi(n)} a_i
$
and
$\displaystyle \prod_{i=1}^{\phi(n)} b_i?
$
| https://math.stackexchange.com |
1,021,899 | [
"https://math.stackexchange.com/questions/1021899",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/192575/"
] | I have a homework question that I just could not figure out.
Suppose that $f:A \rightarrow \mathbb{R}$ is a uniformly continuous real-valued function on a subset $A$ of a metric space $X$. Show that there is a continuous real-valued function $g:\overline{A} \rightarrow \mathbb{R}$ defined on the closure $\overline{A}$... | I’ll get you started. If $x\in\operatorname{cl}A$, there is a sequence $\langle a_n:n\in\Bbb N\rangle$ in $A$ converging to $x$. This sequence is Cauchy, so its image under $f$ is Cauchy; and since $\Bbb R$ is complete in the usual metric, $\langle f(a_n):n\in\Bbb N\rangle$ converges to some real number, $r$. Clearly o... | Choose $a \in {\overline A}$. then there is a sequence $a_n$ in $A$ so that $a_n\to a$. Let $\epsilon > 0$. Since $f$ is uniformly continuous on $A$, there is a $\delta > 0$ so that $d(a,b) < \delta\implies d(f(a),f(b)) < \epsilon$. Since the sequence $a_n$ converges, it is Cauchy. Choose $N\in\mathbb{N... | https://math.stackexchange.com |
603,748 | [
"https://electronics.stackexchange.com/questions/603748",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/304847/"
] | I have a small brushless motor running at 3 V and a cardboard disc (about 5.5 cm radius, 3 mm thick) which can be attached and detached from the shaft of the motor. When the disc is not attached the current drawn is 0.015 A and 0.11 A when the disc is attached.
I agree that the angular velocity of the system is lower w... | When nothing is attached to the motor shaft, the measured power is entirely losses in the motor. One part of those losses is the power lost due to the resistance of the copper windings. That loss is called the copper loss or I squared R loss. There is also power lost in the iron due to hysteresis and eddy currents, but... | <blockquote>
I agree that the angular velocity of the system is lower with the disc attached because of the conservation of angular momentum.
</blockquote>
No. Conservation of angular momentum has nothing to do with it.
Mechanical power = torque * angular speed in rad/s
The 'torque' you are calculating by (presumably) ... | https://electronics.stackexchange.com |
268,202 | [
"https://security.stackexchange.com/questions/268202",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/288922/"
] | My WordPress website received a couple of fake subscriptions to the newsletter. I identified the logs, most of them with the same form as below:
<pre><code>xx.xx.xx.xx example.com - [04/Feb/2023:06:01:42 +0100] "POST / HTTP/1.1" 200 207 "https://example.com/" "curl/7.54.0"
</code></pre>
Is... | Do not trust the <code>User-Agent</code> header; the circumvention is as easy as the protection. Even with cURL it is possible to change the header with a single command line option.
<pre><code>curl -A "Mozilla/5.0 (...) ..."
curl --user-agent "Mozilla/5.0 (...) ..."
curl -H "User-Agent: Mozill... | The log record that you posted shows that these requests are being sent with <code>curl/7.54.0</code> as the user agent string in the headers of these requests.
In PHP, you can use the <code>$_SERVER['HTTP_USER_AGENT']</code> environment variable to access the user agent string sent by the client in the request headers... | https://security.stackexchange.com |
217,971 | [
"https://dba.stackexchange.com/questions/217971",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/147147/"
] | I've just installed a Percona instance of Mysql on an Amazon server and can not find the <code>my.cnf</code> file anywhere. I found <code>auto.cnf</code> in <code>/var/lib/mysql</code> but there is nothing in that file like what I have seen for my standard mysql installs.
I'm using:
<pre><code>mysql Ver 14.14 Distr... | No there is no global variable for the config file locations. <code>mysqld --help --verbose</code> is best to show which ones are used.
Take a look at the linux processlist to see how <code>mysqld</code> is executed by init/service/systemd, that might specify a file.
Otherwise you might be running on a default confi... | Another place to look:
<pre><code>ls -ld /etc/*/my.cnf
</code></pre>
It might be here:
<pre><code>/etc/mysql/percona-server.cnf
</code></pre>
which is a softlink:
<pre><code>/etc/mysql/my.cnf -> /etc/alternatives/my.cnf -> /etc/mysql/percona-server.cnf
</code></pre>
| https://dba.stackexchange.com |
17,026 | [
"https://security.stackexchange.com/questions/17026",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/11153/"
] | Why does military and government not use special operating systems? I mean, if they do not use generic operating system based on Windows, Linux and Mac and create their own operating system, they will be much secure.. Or am I mistaken?
| There are a number of reasons why building their "own OS" is not a viable option.
<strong>1. Research Cost</strong>
To built a new OS, from ground up without the use of any existing code would require significant research. Even today, there are only four or five popularly used kernels like Unix , Linux kernel, BSD, X... | GreenHills Software is a company that specializes on creating OSes for military embedded systems. Their INTEGRITY system uses a microkernel (less code with less bugs) that has been formally verified (even less bugs).
Such special-purpose domains, where only the most basic software components can be re-used, are probab... | https://security.stackexchange.com |
148,357 | [
"https://stats.stackexchange.com/questions/148357",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/69240/"
] | We have some power load functions that of course are driven heavily by a workday rhythm that we need to forecast, and after some light research into the topic, I see that using ARIMA would seemingly be the logical/usual way to go here. However a colleague suggested that an Random Forest could do just as well and would ... | It has been awhile, but this is still getting upvotes. So ...
In the event, I did use a Random Forest, and it worked really well. A boosted tree did a bit better that that even. Also since then I know of several other similar projects that took the same route with success and very little fuss. While ARIMA is surely a ... | I don't see the argument that Random Forest is less work than ARIMA. I would present RF is more work.
Here is the process for ARIMA:
1. Detrend / transform your data
2. Test for stationarity
3. Run autocorrelation plots
4. Set your parameters for your model
5. Run a grid search if you want
6. Look at RMSE
Here is the... | https://stats.stackexchange.com |
84,786 | [
"https://security.stackexchange.com/questions/84786",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/71291/"
] | I'm new here. Over the past couple of years I've had a growing interest in the security aspects of IT/CS. Recently, I've started setting up a lab for myself based on a kali/win7 dualboot and I've been following the instructions given via The Hacker Playbook in setting it up.
So far, I've got separate partitions fo... | You first want to set up a host OS (Windows or Kali, whichever you prefer to use when you're not hacking.) Inside that host OS, install a virtual machine platform (VMware, VirtualBox, whatever you choose.) Inside the virtual machine control panel, create a first VM and install Kali, (presuming you want to use Kali fo... | Running a kali VM provides some benefits:
<ol>
<li><em>Restoration</em> - It is easy to restore your machine when you mess it up. If you're playing around with security tools and/or malware, changes are good that, at some point, you will damage your operating system. Without a VM, you would have to reinstall everyth... | https://security.stackexchange.com |
241,046 | [
"https://electronics.stackexchange.com/questions/241046",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/103699/"
] | Just got a (220<-->12-0-12) transformer hooked up with a bridge rectifier and it measured 13 volts DC output from rectifier, but when I added a 1uF capacitor it just jumped up to 20 volts, and same reading(20 volts) from a 0.1uF capacitor, how is that even possible!?
Note: Nothing is connected in the circuit more t... | \$V_{rms}\$ vs. \$V_{peak}\$. The peak voltage is \$\sqrt{2}\approx 1.4\$ times larger than the average (RMS) voltage.
If you put a capacitor on a rectified AC waveform it will smooth out the supply. If there is no load, it will smooth it out to around the peak voltage of the supply.
A 220V AC supply is 220V RMS, whi... | The "220VAC" and "12VAC" are RMS ("average") values. That is normally how Alternating Current is measured and specified.
By adding rectification and capacitive filtering, you have converted the RMS AC voltage into "peak" DC voltage. This is completely normal and predictable.
For a bridge rectifier and "capacitor-in... | https://electronics.stackexchange.com |
225,705 | [
"https://softwareengineering.stackexchange.com/questions/225705",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/80352/"
] | I realize that there are already a couple of questions about this, but they mostly are about <em>if</em> you should bring code to the interview, which is not the case here.
I have a job interview (at a startup) coming up next week and they <em>requested</em> to bring some code to the interview. I have two smaller open... | Why don't you do both? Bring paper print-outs and bring an electronic device to showcase the rest?
If they have let you know how many people you are interviewing with, bring print-outs for each interviewer plus two or three spares. Extra interviewers get added on all the time and you want to be prepared for that.
I... | There are several goals to that:
<ol>
<li>To see that the person can code.
Don't be surprised: many programmers who come to an interview don't know how to write code. While it's indeed difficult to write code under pressure during an interview, some are also unable to write it outside an interview. If those copy-past... | https://softwareengineering.stackexchange.com |
4,096 | [
"https://dba.stackexchange.com/questions/4096",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/2498/"
] | I developed an application with MySQL 5.1 back-end four years ago. After that, I only gave remote support a couple of times, but that too for application crashes, and not for database. The database is still running well. The customer takes the backup on decided schedules. I want to optimize the database as I think in t... | It always pains me to suggest it but theres a reasonable case for making use of an XML column here.
Create appropriate tables to handle commonly used fields i.e. name, address, email, age, gender etc. I'd be tempted to store the custom fieldsets as an XML column. Once the number of subscribers they are emailing reach... | You can use what is called a <strong>SuperType / Subtype</strong> data structure. You have one SuperType table that contains information that is the same for all subscribers:
<pre><code><b>[SuperType]</b>
SubscriberId
FirstName
LastName
Email
</code></pre>
Create a SubType table for Ecommerce
<pre><code><b>[SubType ... | https://dba.stackexchange.com |
240,333 | [
"https://dba.stackexchange.com/questions/240333",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/182965/"
] | I have created a select statement that show all the topics that are assigned to a book. Now I am trying to create a Select statement that shows all the topics that are not assigned to the book. Book and topic have a many to many relationship.
Problem: I am getting the topics that are assigned to other books because te... | This sounds like a use-case for temporal tables. AFAIK PostgreSQL does not implement this natively. There are extensions for it. It can be written in user-code, usually with triggers.
The basic idea is that the data table has two date/time columns. These define the interval during which the value in a row is applicabl... | I would add a <code>boolean</code> column named <code>active</code> to the table the is <code>TRUE</code> initially and gets changed to <code>FALSE</code> when a row version is deleted or updated.
This will make your queries simpler, and you can use partial indexes to efficiently search only the active rows.
You coul... | https://dba.stackexchange.com |
255,259 | [
"https://mathoverflow.net/questions/255259",
"https://mathoverflow.net",
"https://mathoverflow.net/users/74307/"
] | More precisely, suppose we a given two metrics $g_0$ and $g_1$ on a manifold $M$. Let $\nabla_0$ and $\nabla_1$ be the corresponding Levi-Civita connections. Set $\nabla_t:=(1-t)\nabla_0+t\nabla_1$. Then $\nabla_t$ is a torsion free connection. Does there exist a continuous family of metrics $g_t$ such that $\nabla_t$ ... | Here's a more specific approach that explains why you shouldn't expect this: For simplicity, I'll work in the 2-dimensional case, where it's probably the clearest. Let
$$
\omega = \begin{pmatrix}\omega^1\\\omega^2\end{pmatrix}
$$
be a coframing on a surface $S$. A metric $g$ is then defined by a $2$-by-$2$ matrix $G... | The answer of Professor Bryant shows, that the space of Levi-Civita connections is not convex. On the other hand, there are natural convex subspaces, at least in dimension 2, namely the space of Levi-Civita connections for metrics of a fixed conformal class. To prove this, let us assume we are in the oriented case, so ... | https://mathoverflow.net |
718,881 | [
"https://math.stackexchange.com/questions/718881",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/134510/"
] | The problem asks me how to distribute n balls into h boxes where each must get at least 1 n and t boxes where each can be left empty
What I have, and where I seem to have stalled is how to incorporate the t boxes, the formula I have right now for h boxes is (n+h-1) choose h
Which I believe is the correct formula for ... | It is not quite clear what is intended, so we rephrase. There are $h+t$ (distinguishable) boxes $A_1$ to $A_h$ and $B_1$ to $B_t$. The $A_i$ must each have at least one ball, but some or all of the $B_j$ can be left empty.
Put a ball into each $A_i$. That leaves $n-h$ balls, to be distributed among $h+t$ boxes with no... | Hint: let there be $k$ balls in the $h$ boxes, where clearly $k \ge h$. How many ways to distribute them? You have that above. Now for each of those you distribute $n-k$ balls into $t$ boxes. Sum over $k$ from $h$ to $n$.
| https://math.stackexchange.com |
387,761 | [
"https://physics.stackexchange.com/questions/387761",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/167103/"
] | Suppose I am going in a direction with a velocity $v_1$ and my friend is going in a direction which makes an angle of $A$ with my direction with a velocity of $v_2$.
Then what will be my relative motion with respect to my friend or his relative motion with respect to me?
Every book I have read gave example where tw... | Let's say your velocity is <span class="math-container">$\vec{v}_1$</span> is
<span class="math-container">$$\vec{v}_1= v_{1x}\hat{i} + v_{1y}\hat{j}$$</span>
and your friends velocity <span class="math-container">$\vec{v}_2$</span> is
<span class="math-container">$$\vec{v}_2= v_{2x}\hat{i}+v_{2y}\hat{j}$$</span>
The... | You could always break the question into two perpendicular directions
Your velocity will be subtracted from horizontal velocity of your friend's. The vertical velocity will remain same. The resultant of the vertical and new horizontal velocity will give you the final answer of how you see your friend.
Velocity of f... | https://physics.stackexchange.com |
117,512 | [
"https://softwareengineering.stackexchange.com/questions/117512",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7503/"
] | I am creating a RESTful JSON API to access data from our website where the content is in German.
A handful of the fields will return formatted HTML while most are single lines of text although they are highly like to include special characters.
To make it easy to use I wanted consistency throughout. As the text in th... | Generally a web service should return raw data, and a consuming application that embeds the data in a web page would encode the data it embeds. That way other applications that might display the data in a Windows application or do some other processing on it don't have to deal with html.
If the purpose of a service is... | It seems this depends on the intent of the API. Is it to provide formatted HTML to clients, or to provide data which the clients can use however they see fit?
If the purpose really is to provide consumable HTML, I would say to do the encoding. If it is to provide access to data, then don't.
If you really want to... | https://softwareengineering.stackexchange.com |
3,603,721 | [
"https://math.stackexchange.com/questions/3603721",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/210193/"
] | To begin with I already know any set with the cofinite topology is compact, but I am looking for a proof specific to <span class="math-container">$\mathbb{R}_{\mathcal{FC}}$</span>. My attempt to a proof is right here:
Recall that any <span class="math-container">$A \subset \mathbb{R}_{\mathcal{FC}}$</span> is open if... | I don't trust this sentence.
<blockquote>
As a result every possible open cover must the union of infinite sets in which case a subcover could be expressed as a finite union of infinite sets, so <span class="math-container">$\Bbb{R}_\mathcal{FC}$</span> is compact.
</blockquote>
More convincing would be to pick any... | To see why your argument fails, consider the cocountable topology on <span class="math-container">$\mathbb R$</span> where a non-empty set is open iff its complement is <em>countable.</em>
Since every non-empty open set is the complement of a countable set, it is uncountable, and therefore infinite. As a result, again... | https://math.stackexchange.com |
20,673 | [
"https://dba.stackexchange.com/questions/20673",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/10044/"
] | I have a SQL Server table with about 2 million rows in, this table stores short textual documents. Here's my schema:
<pre><code>CREATE TABLE Documents (
documentId bigint IDENTITY NOT NULL,
content nvarchar(MAX) NOT NULL,
isIndexed bit NOT NULL
)
</code></pre>
I have a separate Lucene-based indexer proces... | The table (now) has the following non-clustered indexes:
<pre><code>IX_Indexed_ASC (Non-Unique) ( IsIndexed ASC, DocumentId ASC )
IX_Indexed_DESC (Non-Unique) ( IsIndexed DESC, DocumentId ASC )
IX_IsIndexed_Filtered (Non-Unique) ( DocumentId ASC WHERE IsIndexed = 0 )
IX_DocumentId_Indexed (Unique) ( DocumentId ASC, Is... | An index on the bit column isn't going to help at all because of selectivity. You should consider a filtered index:
<pre><code>CREATE INDEX unindexed ON dbo.Documents(documentId) WHERE IsIndexed = 0;
</code></pre>
You should also include an <code>ORDER BY documentId</code> in your <code>SELECT</code>.
Though you sho... | https://dba.stackexchange.com |
210,113 | [
"https://mathoverflow.net/questions/210113",
"https://mathoverflow.net",
"https://mathoverflow.net/users/75381/"
] | I can't find a way to prove that the following equation has only one solution :
$$
X = \frac{2^Q - 1}{2^{P+Q} - 3^P}
$$
with $X,P,Q$ integers $> 0$.
One trivial solution is $X = 1, P = 1, Q = 1$.
Does anyone has an idea ?
Best regards
| I'm more used to the formulation in the following form:
$$ X(2^{P+Q} - 3^P)=2^Q-1 \\
2^Q(2^Px -1) = 3^Px -1 $$
and then
$$ 2^Q = {3^P \cdot X - 1 \over 2^P \cdot X - 1} \tag 1
$$
and Ray Steiner has proved in 1976 in the context of the Collatz-problem (using Rhin's result given in the other answer), that there is only... | Unless $3^P$ is very close to $2^{P+Q}$, the right hand side will be smaller than 1. Hence the linear form $(P+Q)\log 2 - P\log 3$ is exceptionally small, and you should be able to obtain effective upper bounds for $P$ and $Q$ by Baker's method. Looking at the continuous fraction of $\frac{\log 2}{\log 3}$ you can prob... | https://mathoverflow.net |
233,019 | [
"https://stats.stackexchange.com/questions/233019",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/58675/"
] | We know that, formally, the assumptions of a test cannot be tested, because if we choose what test to use based on the results of the test, the resulting composite test has unknown properties (Type I and II error rates). I think this is one of the reasons why "Six Sigma" kind of approaches to statistics (use a decision... | What I have seen done most often (and would tend to do myself) is to look at several sets of historical data from the same area for the same variables and use that as a basis to decide what is appropriate. When doing that one of course should keep in mind that mild deviations from e.g. normality in the regression resid... | Personally, I like to run a parametric test and its non-parametric equivalent, and test the assumptions of each all at once. If the assumptions of the parametric test aren't massively violated or if I get similar results with the non-parametric text, I will use the parametric test. Even if the parametric assumptions ar... | https://stats.stackexchange.com |
440,493 | [
"https://softwareengineering.stackexchange.com/questions/440493",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/419134/"
] | Let's assume we have a method that we want to run as fast as possible and it needs to loop on a 2D array, naturally we would do a nested for loop as such:
<pre><code> int[][] arr = new int[3][3];
for(int i = 0; i < arr.length; i++) {
for(int j = 0; j < arr[i].length; j++) {
arr[i][j] = ... | Both are O(N) where N is the number of elements in the array. The second one is just more confusing and has bugs.
Assuming you fix the bugs, they're both the same loop. They'll compile into similar assembly code (or Java bytecode). The second one is just more confusing (and has bugs).
So there's no good reason to write... | It’s the number of operations that counts, not the number of loops. Your code is supposed to set all array elements. Therefore if your code is correct the number of operations is proportional to the total number of array elements, no matter how you do it.
| https://softwareengineering.stackexchange.com |
17,077 | [
"https://electronics.stackexchange.com/questions/17077",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4245/"
] | No, I'm not asking you about my whole design - just one little bit of it.
I have SMT devices, and I am currently pushing 8 pins on each side of some chips (SO24) straight through to the other side of the board with vias:
<img src="https://i.stack.imgur.com/RhAGd.png" alt="Vias close together">
Having so many vias so... | It won't harm the PCB at all. The material is so stiff that even a slot over the length of the vias won't weaken it noticeably.<br>
The image may be a bit misleading too. The via holes are actually indicated by the smallest gray circles, the darker gray is the annular copper. So the distance between the vias is greater... | The holes in a row will weaken the board a little bit, but probably not enough to be significant. Have you ever tried snapping 0.1" matrix protoboard by hand? It's quite resilient.
I do suggest you increase the copper clearance on the IC pads so that you don't get ground plane between them. That will make assembly... | https://electronics.stackexchange.com |
3,828,157 | [
"https://math.stackexchange.com/questions/3828157",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/813536/"
] | Let <span class="math-container">$m\geq 1$</span> and <span class="math-container">$G$</span> a group such that <span class="math-container">$x^my^m=(xy)^m.$</span> Show that <span class="math-container">$M=\{x^{m-1} : x\in G\}$</span> is a subroup of <span class="math-container">$G$</span>.
I prove that
<span class="... | Let <span class="math-container">$z,t\in M$</span>, then <span class="math-container">$z=x^{m-1}$</span> and <span class="math-container">$t=y^{m-1}$</span>, so <span class="math-container">$$zt=x^{m-1}y^{m-1}=x^{-1}x^my^my^{-1}=x^{-1}(xy)^my^{-1}=y(xy)^{m-1}y^{-1}=(yx)^{m-1}\in M$$</span>
| If <span class="math-container">$z,t\in M$</span>, you wish to show that <span class="math-container">$zt$</span> is of the form <span class="math-container">$a^{m-1},a\in G$</span>.
Note that since <span class="math-container">$z,t\in M$</span> then <span class="math-container">$z=x^{m-1},t=y^{m-1}$</span>. Then:
<spa... | https://math.stackexchange.com |
151,894 | [
"https://cs.stackexchange.com/questions/151894",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/141590/"
] | If
<pre class="lang-java prettyprint-override"><code>int a = 250;
int b = 3;
int c = (a + b/2)/b * b;
</code></pre>
Why doesn't <code>c</code> equal 251, but rather 249?<br />
How is it that <code>c</code> is smaller than <code>a</code> when we are adding?<br />
Doesn't the <code>divide by b</code> and <code>multipl... | Operations are executed in order of precedence. When two operations have the same preference, they are evaluated from left to right. In your specific case:
<ul>
<li><code>b/2</code> is evaluated first and it evaluates to <span class="math-container">$1$</span> (notice the integer division).</li>
<li><code>a+1</code> is... | Let's discuss your confusion with precedence and associativity.
Among all the operators Parentheses has highest precedence. That's why <span class="math-container">$()$</span> is evaluated first. And then inside <span class="math-container">$()$</span> we see two operators <span class="math-container">$+$</span> and <s... | https://cs.stackexchange.com |
1,889,720 | [
"https://math.stackexchange.com/questions/1889720",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/227967/"
] | <blockquote>
<strong>Question:</strong>
Show that $\mathbb{R}$ is a closed subset of $\mathbb{R}$.
</blockquote>
<hr>
$\mathbb{R}\setminus \mathbb{R}=\left \{ x \in \mathbb{R} \mid x\notin\mathbb{R} \right \}.$
I need to show that $\forall x \in \mathbb{R}\setminus \mathbb{R}, \exists \epsilon >0$ s.t $B_{\ep... | I think you may be unfamiliar with the concept of "vacuous truth." If you say "Every element of the empty set has property X," that statement is automatically true, since there is no element of the empty set! This is called a vacuously true statement. $\mathbb{R}$\ $\mathbb{R}= \emptyset$. Can you prove the theorem now... | A sentence beginning by $\forall x\in\emptyset$ is always true (because you can't find any counterexample!). Thus $\Bbb R\setminus\Bbb R=\emptyset$ is open in $\Bbb R$ and so $\Bbb R$ is closed in itself.
| https://math.stackexchange.com |
167,295 | [
"https://physics.stackexchange.com/questions/167295",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/74110/"
] | For my computing project, I am creating a projectile simulator but I cant seem to get my head round the air resistance. I tried by working out the horizontal and vertical velocity by solving it (vertically and horizontally giving me two equations):
<ul>
<li>$dv/dt = -cv^2$ (horizontal)</li>
<li>$dv/dt = -cv^2 - g $ (v... | So yeah, there are these things called <em>vectors</em> which represent arrows; they are made up of <em>components</em>. For example, we would not say "velocity (horizontal)" and "velocity (vertical)" but we would add labels $v_x, v_y$ where $x$ is usually a horizontal-label and $y$ is usually a vertical-label; then we... | You made a mistake in the direction of your drag force (vector). You calculated the magnitude of this force correctly, then applied that magnitude both along your horizontal and vertical basis vectors for a total of $\sqrt{2}$ of the desired drag force, and pointing in the wrong direction!
The missing direction is giv... | https://physics.stackexchange.com |
316,986 | [
"https://mathoverflow.net/questions/316986",
"https://mathoverflow.net",
"https://mathoverflow.net/users/56931/"
] | Let <span class="math-container">$D(0,1)$</span> be the Skorohod space with the Skorohod topology, i.e. the space of real-valued càdlàg-functions on <span class="math-container">$[0,1]$</span> with topology induced by the metric
<span class="math-container">$$d(f,g) = \inf_{\varphi \in \Lambda} \left\{ \lVert \varphi -... | I think the following works, but please check me.
Note first that cadlag functions are measurable and bounded, so <span class="math-container">$D(0,1) \subset L^2(0,1)$</span>.
Suppose <span class="math-container">$f_n \to f$</span> in the Skorokhod metric. Note that <span class="math-container">$f$</span> has at mo... | <span class="math-container">$\newcommand{\de}{\delta}
\newcommand{\vp}{\varepsilon}$</span>
Take any <span class="math-container">$x,y$</span> in <span class="math-container">$D:=D[0,1]$</span> with <span class="math-container">$d(x,y)\le\vp$</span> for some <span class="math-container">$\vp\in(0,1)$</span>, so that ... | https://mathoverflow.net |
507,853 | [
"https://physics.stackexchange.com/questions/507853",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/226188/"
] | Is it because the <s>inability to generate true random numbers </s> (I dont think so) in the host machine or something else?
My understanding is that the ability to emulate a quantum computer in a conventional one would eliminate the need for a real physical quantum computer if we can emulate Qbits and superposition .
... | It is possible to simulate quantum computers with classical computers. However, the time (and typically memory) needed for such a simulation will scale <strong><em>exponentially</em></strong> with the time a quantum computer needs. Thus, if a quantum computer needs <span class="math-container">$10$</span> times the co... | The uses for quantum computers has two major sections: quantum algorithms and quantum networking.
Quantum algorithms are algorithms for quantum computers which offer a significant speed improvement over classical versions. A famous example is Shor's algorithm which factors integers in polynomial time compared to the ... | https://physics.stackexchange.com |
183,955 | [
"https://math.stackexchange.com/questions/183955",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/34917/"
] | I am working with a text book problem, trying to find the solutions to $x^3 = 2x^2 - x$, but I keep ending up with a different result than the book gives. I'm thinking the problem lie in getting the wrong square root towards the end, seeing as the text book gives different results for $x_1$ and $x_2$, but I can't find ... | Note that by dividing by $x$, you are implicitly assuming that $x$ is not $0$. It turns out that this is a solution. You can check this directly.
You are right that $1$ is a double root of the equation. If you move everything to one side and factor, you find that
$$x^3-2x^2+x=x(x-1)(x-1)=0$$
which confirms our ans... | You can not just divide by $x$, since $x$ could be $0$.
You have $x^3=2x^2-x$, which is equivalent to:
$$0=x^3-2x^2+x=x(x^2-2x+1)=x(x-1)^2$$
Hence $x=0$ or $x=1$.
| https://math.stackexchange.com |
34,255 | [
"https://physics.stackexchange.com/questions/34255",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/11417/"
] | For example, if I were to supercool water would it's refractive index still be 1.33 or would it be 1.31, the same as water-based ice even though it's still in liquid form?
| The statement is not correct, as $Q'=Q+g(A)$ satisfies (for an arbitrary function $g$) the same commutation relation. Thus you need to pay attention to the additional conditions posited in the context of your source.
| If a group has an irreducible representation on some vector space, then Schur's lemma says the only operators on that vector space which commute with every element of the group are the scalar operators. From this, If A and B have the same commutation relations with every element of the group, then $A-B$ commutes with e... | https://physics.stackexchange.com |
581,525 | [
"https://physics.stackexchange.com/questions/581525",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/275257/"
] | Why is the velocity at the point of contact (between wheel and surface when the condition is rolling without slipping) with respect to the surface remains zero all the times although the center of wheel moves forward?
| <blockquote>
If switch is opened when capacitor is fully charged energy of LC
system remains same.
</blockquote>
If it's a series LC circuit, then the energy will be <span class="math-container">$E=\frac{CV^2}{2}$</span> all residing in the electric field of the capacitor. If it is a parallel LC circuit of an ideal ind... | When the capacitor has no charge, the energy is in the magnetic field of the inductor, which is associated with a current flow. If the switch is open, the current cannot flow. The magnetic field collapses, leaving no energy. (The collapse of the field will cause a large voltage spike, and probably an arc across the op... | https://physics.stackexchange.com |
2,895,174 | [
"https://math.stackexchange.com/questions/2895174",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/394526/"
] | Let $H$ be a Hilbert space with orthonormal basis $(e_n)_n$ and $(a_n)_n \in \ell^2(\mathbb{N})$, so $$\sum_{n=0}^{\infty} |a_n|^2 < \infty$$
Now, define the sequence $(\xi_n)_n$ in $H$ as $$\xi_n= \sum_{k=0}^{n} a_ke_k $$
I now have to proof that this sequence is convergent in $H$ or, if not, give a counterexampl... | I claim the sequence
$\xi_n = \displaystyle \sum_{k = 0}^n a_k e_k \tag 1$
is Cauchy in $H$; for, letting $\langle \cdot, \cdot \rangle$ be the inner product on $H$, and $\Vert \cdot \Vert$ the corresponding norm, so that
$\Vert x \Vert^2 = \langle x, x \rangle, \; \forall x \in H, \tag 2$
we compute, for $m > l... | I don't think the observation of $a_k\to 0$ as $k\to\infty$ is going to help you much.
It suffices to show that $(\xi_n)$ is a Cauchy sequence. Essentially you need to estimate
$$
\|\xi_p-\xi_q\|=\left\|\sum_{k=q+1}^p a_ke_k\right\|.\tag{1}
$$
But the orthonormal property tells you that
$$
\left\|\sum_{k=q+1}^p a_ke_... | https://math.stackexchange.com |
3,671,480 | [
"https://math.stackexchange.com/questions/3671480",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/238156/"
] | Let <span class="math-container">$R$</span> be a finitely generated <span class="math-container">$k$</span>-algebra where <span class="math-container">$k$</span> is a field.
Let <span class="math-container">$0 \neq f \in R$</span>. I was wondering if it is the case that there are only finitely many primes
containing <... | No, this is generally far from the case. Consider for example <span class="math-container">$x \in k[x,y]$</span>. Every ideal of the form <span class="math-container">$(x, g)$</span> for <span class="math-container">$g \in k[y]$</span> irreducible is maximal (the quotient <span class="math-container">$k[x,y]/(x,g) \sim... | Try looking at <span class="math-container">$k[x,y]/(x^2)$</span> where the image of <span class="math-container">$x$</span> is your nonzero element for an answer to your question.
| https://math.stackexchange.com |
254,202 | [
"https://electronics.stackexchange.com/questions/254202",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/120783/"
] | Components data sheet can be confusing sometimes
Can anyone explain to me the difference between these counters 74LS196 and 74LS197 ?
can they replace each other? can the 74LS197 perform better in the place of 74LS196 in case if they do replace each other?
Other thing, I found 74S196 !! so is the LS is different than ... | As the datasheet says, one (74LS196) is a divide by 10 counter the other one (74LS197) is a divde by 16 counter.
<blockquote>
The SN54/74LS196 decade counter is partitioned into divide-by-two and divide-by-five
sections which can be combined to count either in BCD (8, 4, 2, 1)
sequence
or in a bi-quinary mod... | The 74S196 is a decade counter made using Schottky bipolar transistor technology. The 74LS196 is the same thing, but Low Power Schottky.
For modern CMOS parts, look for 74HC196 or 74AC196 (or other assortments of letters in the middle).
| https://electronics.stackexchange.com |
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