qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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|---|---|---|---|---|---|
335,941 | [
"https://stats.stackexchange.com/questions/335941",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/30217/"
] | My dataset contains a set of samples from a set of normal RVs. Each RV is normally distributed with equal variances and varying means. However, I have only two samples from each RV.
How to estimate the variance in this case?
| These data can be described by two variables: one, a categorical variable $x$, identifies each random variable. Another, $Y$, gives an observation in the sample. Thus, in a tabular rendering of your dataset you would see two columns--one for the sample and another for the result--and two rows for each sample.
Your m... | Recall (population) variance is a measure of variability around a (population) mean.
Your dataset contains several sets of two samples from each RV, for which you know the variances are equal.
We first must estimate the sample mean, and then use that mean to estimate the sample variance.
The problem is, we have to '... | https://stats.stackexchange.com |
157,732 | [
"https://mathoverflow.net/questions/157732",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41274/"
] | Meta-matematical formulas of the language of set-theory (which are not sets, but just sequences of signs) should not be confused with mathematical ones (i.e. formulas coded as sets, e.g. finite sequences of natural numbers or even just natural numbers, if we wish). For instance, for each meta-mathematical formula $\phi... | To answer Question 2, I think your intuition is right. Assume $N \prec H_\lambda$, where $\lambda$ is a regular cardinal bigger than $2^\mathbb{P}$, where $\mathbb{P} \in N$ is a partial order. (Maybe Shelah has a more subtle argument where we assume less about $\lambda$, not sure.) Then $H_\lambda$ is a model of $Z... | Although the common slogan about forcing is that the forcing relation is definable in the ground model, nevertheless the slogan must be qualified for precisely the issue in your question, and the answer to question 1 is that no, the forcing relation is <em>never</em> definable in full generality as a binary relation in... | https://mathoverflow.net |
567,970 | [
"https://stats.stackexchange.com/questions/567970",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/349777/"
] | I'm preparing a time series model with LSTM, I noticed that the time series data is not stationary so I used <code>diff(period=1)</code> in <code>pandas</code>. I fitted the LSTM model and it looks good. I invert the difference operation using original data. When we are forecasting in real time, how to invert the predi... | The inverse difference is the cumulative sum of the first value of the original series and the first differences:
<pre class="lang-r prettyprint-override"><code>y=rnorm(10) # original series
dy=diff(y) # first differences
invdy=cumsum(c(y[1],dy)) # inverse first differences
print(y-invdy) # discrepancy between t... | For Python implementation of Richard's answer:
<pre><code>x = [0,11,24,37,49,59]
print(x)
z = pm.utils.diff(x,lag=1,differences=1)
print(z)
z = np.insert(z,0,x[0])
print(z)
print(np.cumsum(z))
</code></pre>
| https://stats.stackexchange.com |
128,960 | [
"https://stats.stackexchange.com/questions/128960",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/63729/"
] | I am trying to understand a little better mixtures of Gaussians and their generative approach in general. For a mixture of Gaussians we start with this formula:
$$p(x)=\sum_{k=1}^{K}\pi_{k}\cdot N(x|\mu_{k},\Sigma_{k})\,,\quad \sum_{i=1}^K\pi_k=1\,,$$ where $\mu_{k}$ and $\Sigma_{k}$ are the means and covariances for e... | To answer your first question, you can think of the proportion $ \pi_k $ as the probability that an observation comes from population k (Gaussian with mean $ \mu_k $ and covariance $ \Sigma_k^2$).
For sampling, you first sample from a uniform to decide from which Gaussian you will sample each observation. For estimatio... | <blockquote>
Is it just the probability with which we choose one of the Gaussians in the above formula or far from it?
</blockquote>
Yes, pretty much.
<blockquote>
By generative we mean that we have a model that can generate data?
</blockquote>
Yes. In this case use the $\{\pi_j\}$ to randomly choose a $k$ the... | https://stats.stackexchange.com |
255,362 | [
"https://softwareengineering.stackexchange.com/questions/255362",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/29899/"
] | I've recently been investigating SpecFlow and can see the value of it for writing client/stateholder specs which can show a feature's progress however I'm nervous of introducing them to a client...
Imagine a feature:
<pre><code>Given I'm on the "MyAccount" page
And I enter "Liath" into the "Name" textbox
When I cl... | The scenario above could be one of many around the account update story.
<pre><code>In order to keep my account up to date,
As a registered user
I should be able to update my account
</code></pre>
So you would multiple scenarios covering each of the potential outcomes for a story. A story could also be one of many st... | You have to come to an agreement on what "done" means for everything you deliver. You can give them a signed letter of agreement, a light, or a smoke-signal and if they think it means something else, you have a problem. Being concerned with client misconceptions is universal in this business, so the only way to get ar... | https://softwareengineering.stackexchange.com |
853,892 | [
"https://math.stackexchange.com/questions/853892",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/86238/"
] | I got this problem in an exercise list:
Let $G(x)$ be the generating function of the numeric sequence $(C_n; n \geq 0)$ satisfying the recurrence equation:
$$C_n = \sum_{k=0}^{n-1}C_kC_{n-k-1}, C_0=C_1=1.$$
Show that $xG(x)^2 - G(x)+1=0$ and conclude that
$$G(x)=\frac{1-\sqrt{1-4x}}{2x}.$$
Then, show that
$$G(x)... | Let
\begin{align}
I = \int \frac{\sin(x+a)}{\cos^3(x)}\cdot \sqrt{\frac{\cos x+\sin x}{\cos x-\sin x}}dx
\end{align}
then
\begin{align}
I &= \int (\sin(x) \cos(a) + \cos(x) \sin(a))(\cos(x) + \sin(x)) \ \frac{dx}{\cos^{3}(x) \sqrt{\cos(2x)}} \\
&= \cos(a) \ \int \frac{\sin^{2}(x) \ dx}{\cos^{3}(x) \sqrt{\cos(2... | Assuming what you have done up till the last part is correct, these hints I think will help you go further:
<strong>(1)</strong> Multiplying and dividing by $\sqrt{1+t}$
<strong>(2)</strong> Knowing the derivative of $\sinh^{-1} (\sqrt{t-1}) $ and $\sqrt{t+1}\sqrt{t-1}$
<strong>(3)</strong> Using partial integratio... | https://math.stackexchange.com |
273,800 | [
"https://electronics.stackexchange.com/questions/273800",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/130194/"
] | I'm trying to configure my Nucleo Board with a STM32L073RZ in deepsleep mode to get the lowest power consumption.
To do that I use the mbed librairies with the deepsleep() function (This function use Stop mode with RTC). On the application note given by STMicroelectronics the consumption is around 1µA in Stop mode with... | In addition to dim's answer, which would indicate that you might try manually turning off peripherals before going into deep sleep (I don't know if this is handled by deep sleep all by itself) to see if this reduces your sleep current, you need to absolutely <em>pore through</em> the schematics for the Nucleo Board to ... | I think there may still be some peripherals using a bit of current. The datasheet specifies about 1µA in stop mode with RTC enabled, but it also specifies that ~1.2µA is consumed by the PVD/BOR peripheral and ~1.7µA consumed by the internal voltage reference (see datasheet Table 41: <em>Peripheral current consumption i... | https://electronics.stackexchange.com |
28,422 | [
"https://dba.stackexchange.com/questions/28422",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/5990/"
] | From MySQL manual, it says:
<blockquote>
BOOL, BOOLEAN
These types are synonyms for TINYINT(1). A value of zero is considered
false. Nonzero values are considered true:
</blockquote>
I created a BOOLEAN column with <code>0</code> as the default value. Then I update the value to <code>2</code>. Logically, I w... | Those two are really synonyms, so you can use them interchangeably. You won't see any difference between them.
If you want to allow 0 and 1 only, you can still use the <code>bit</code> type.
| If you are working with other people (or you want to remind yourself), you can use the data type <code>BOOLEAN</code> to suggest that the data is only intended to take on a value of 1 or 0.
| https://dba.stackexchange.com |
451,228 | [
"https://math.stackexchange.com/questions/451228",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/70311/"
] | Given any number $n$, what is the method of finding out how many possible ways (unique) are there in which you can partition it - with the condition that all the numbers in each 'part' must be greater than or equal to 5.
e.g. say $n = 17$
So, $17$ can be written as:
<ol>
<li>$17$</li>
<li>$5 + 12$ (since the least n... | Note that we need to list partitions in increasing order to avoid duplicates. It follows we need to know, in determinate instance of this proccess, the number $n$ to partition and a lower bound wich we start to partition this number. If you consider $f(n,m)$ means the number of ways to partition $n$ with numbers $\geqs... | The question was becoming really huge and I feared people would skim the text in it. So I am adding this here (the following is quite answer-ish too!)
<strong>An interesting insight</strong>:
While working out manually for numbers till 20, I found out quite an amazing fact (which seems to hold for all integers) about... | https://math.stackexchange.com |
19,219 | [
"https://math.stackexchange.com/questions/19219",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/2109/"
] | <strong>A box contain $A$ white and $B$ black balls and $C$ balls are drawn, then the expected value of the number of white balls drawn is ?</strong>
The answer is $\large \frac{ca}{a+b}$. How to approach this one?
| These calculations are often made clearer by using indicator random variables. For $1\leq i\leq C$, define $Z_i$ by setting $Z_i=1$ if the $i$th ball drawn is white and $Z_i=0$ otherwise. Then the total number of white balls is $\sum_{i=1}^C Z_i$ and by linearity of expectation we have
$$ E(\mbox{ white balls })=E\left... | For those interested, just to elucidate on the "non-smart" method of attacking this problem, the probability of drawing exactly $k$ white balls in $C$ draws is
$$ \frac{ {A \choose k}{B \choose C-k}} { {A+B \choose C} } $$
and so the expected number of white balls is given by
$$\sum_{k=0}^C \frac{ k {A \choose k}{B \c... | https://math.stackexchange.com |
67,903 | [
"https://mathoverflow.net/questions/67903",
"https://mathoverflow.net",
"https://mathoverflow.net/users/35428/"
] | Let $X$ be a complex manifold and $g$ a hermitian metric on $X$. Consider the Riemannian exponential $\exp_p: T_p X \to X$.<br>
If $\exp_p$ is holomorphic for every $p \in X$, then $(\exp_p)^{-1}$, suitably restricted, provide holomorphic normal coordinates near $p$, with respect to which the metric osculates to order ... | NB: I've had a little time to think about this and can now improve my answer, in particular, removing the real-analytic assumption, which, as I suspected, was not necessary. Here is the improved answer:
If the metric $g$ is Kähler, then having the exponential map from a point $p\in M$ be holomorphic makes it flat i... | I do not like complex numbers and can make a mistake easily...
Let $L_p$ be a complex line in a tangent space $T_pX$.
It is easy to see that $\exp_p$ gives an isometric embedding $L_p\hookrightarrow X$ which is also star-shaped with center at $p$; set $L=\exp_p(L_p)$
Take any other point $q\in L$, and let $L_q\subset... | https://mathoverflow.net |
2,730 | [
"https://bioinformatics.stackexchange.com/questions/2730",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/772/"
] | I have a expression data from a small cohort of samples taken at baseline and after 2 independent treatments. I can do differential expression contrasting T1 and T2 or I can contrast T1 vs baseline and T2 vs baseline and look at the differences. What is the difference between these two analyses? Are they both valid? If... | If you're interested in looking at the differences between two treatments then you'll end up wanting to do both a direct contrast as well as the individual comparisons to baseline.
The direct contrast will give you the genes actually differentially expressed between the two conditions. In practice, you may want to fil... | Depending upon the type of treatment used the set of DEGs will change.If the treatments have similar kind of effect you will get a small list (less variable genes will have higher p-val) using a cutoff of p<0.05. So, it's better to start with control vs treated comparisons then T1 vs T2.
Compare the lists form CTRL... | https://bioinformatics.stackexchange.com |
366,026 | [
"https://softwareengineering.stackexchange.com/questions/366026",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/296297/"
] | Should I leave the else clause in a case like this where the compiler marks the else as redundant code and the else makes the code appear more logical --> better readable?
<pre><code>if (aCondition){
doStuff();
return someMethodResult();
}
else {
doOtherStuff();
return someOtherMethodResult();
}
</code... | It depends on the semantics of <code>aCondition</code>.
My guiding line is that the standard / normal path of execution should stay on the top nesting level, and conditional paths should be found on deeper nesting levels.
If <code>aCondition</code> checks for some special case, the <code>return someMethodResult();</c... | As for redundant elses after returns: <strong>It depends</strong>. What looks "most familiar" is probably the most readable. Follow the style used in typical existing code in your language.
In typical C / Java code, many would leave off the redundant else. (I'd tend to leave it, YMMV)
But, in asynchronous / callba... | https://softwareengineering.stackexchange.com |
326,291 | [
"https://softwareengineering.stackexchange.com/questions/326291",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/211229/"
] | There are a lot of questions on here that deal with the mechanics of authentication and authorization of RESTful APIs but none of them appear to go in to details of how to implement secure services at the application level.
For example let's say that my webapp (I've got Java in mind but this applies to any backend re... | <strong>Please for the love of God do not create a <code>SecurityUtils</code> class!</strong>
Your class will become 10k lines of spaghetti code in a matter of months! You would need to have an <code>Action</code> type (create, read, update, destroy, list, etc.) passed into your <code>isUserAuthorized()</code> method,... | A more convenient solution is to use annotations to mark methods which require some form of authorization. This stands out from your business code and can be handled by Spring Security or custom AOP code. If you use these annotations on your business methods rather than endpoints, you can be sure to get an exception wh... | https://softwareengineering.stackexchange.com |
4,191,989 | [
"https://math.stackexchange.com/questions/4191989",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/333236/"
] | This is a question from an (old) exam at my university on Rings and Modules. It's not part of any ongoing assignment.
We are given a homomorphism <span class="math-container">$\phi: \mathbb{Z}[X,Y] \rightarrow \mathbb{Z}[T]$</span>, defined by <span class="math-container">$\phi(X) = T^2, \phi(Y) = T^5$</span>.
The firs... | Here is what I would consider the standard "more algebraic" approach:
<span class="math-container">$X^5-Y^2$</span> is clearly contained in the kernel of <span class="math-container">$\phi$</span>. That means that we can "insert" <span class="math-container">$\Bbb Z[X,Y]/\langle X^5-Y^2\rangle$</spa... | As noted in the comments, you want to find generators for the kernel. The most obvious generator is <span class="math-container">$X^5-Y^2.$</span> Do you need more?
Now note that:
<span class="math-container">$$X^{5n}\equiv Y^{2n}\pmod {X^5-Y^2}$$</span>
So:
<span class="math-container">$$X^{i-5n}Y^{j+2n}\equiv X^iY^{j... | https://math.stackexchange.com |
580,671 | [
"https://physics.stackexchange.com/questions/580671",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/275057/"
] | Lets say we have a frictionless and massless pulley with a massless string over it. There are two masses attached to it <span class="math-container">$m_1$</span> and <span class="math-container">$m_2$</span> where <span class="math-container">$m_2>m_1$</span>.
So <span class="math-container">$m_2$</span> would an ex... | Newton's second law is
<span class="math-container">$$ F=ma $$</span>
For a massless object with no force on it, this equation becomes
<span class="math-container">$$ 0=0*a $$</span>
which is clearly true for any value of <span class="math-container">$a$</span>, and so any value of acceleration is consistent with Newto... | Your problem arises from the negligence of the fact that when we say massless, frictionless, etc. then we are only talking about the limiting case of these quantities tending to zero and not the absolute zero.
This in the given scenario means that you can neglect the mass of the string. But that doesn't imply that the ... | https://physics.stackexchange.com |
299,383 | [
"https://physics.stackexchange.com/questions/299383",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/138782/"
] | In the section on the discontinuity of the electric field (<em>Griffiths Introduction to electrodynamics</em>), there is the following statement:
<blockquote>
Where there is no surface charge, the perpendicular component of the electric field (to the surface) is continuous, as for instance at the surface of a unifor... | Surface charge refers to a thin layer of charge at a surface. For example, an ideal charged conducting sphere would have a layer of charge on the surface whose thickness would be infinitesimal. It would be represented by a delta function.
In the case of an idealized non-conducting uniformly charged sphere whose boun... | Take a uniformly charged solid sphere of radius $R$ and total charge $Q$. Electric field $\mathbf E$ at a radial distance $r$ is radially directed as there is no other unique direction. So,
$$\mathbf E(\mathbf r)~=\begin{cases}\dfrac1{4\pi\varepsilon_0}\dfrac{Q}{r^2}~\hat{\mathbf r}~~~~r\geq R\\ \dfrac{1}{4\pi\varepsi... | https://physics.stackexchange.com |
435,458 | [
"https://softwareengineering.stackexchange.com/questions/435458",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/352797/"
] | Let's say I have a function in a class with the following signature:
<pre><code>int fun(int x, int y,std::function<int(int, int)> funArg)
</code></pre>
The output depends on the operations done in <code>funArg</code>.
My question is, how do you ensure that the code is tested in the right way? I can of course add ... | The testable part of <code>fun</code> is only the code around the call to <code>funArg</code>. So feed it with a trivial <code>funArg</code> parameter that doesn't have to do anything but return a value that causes <code>fun</code> to touch one of the possible code paths after calling <code>funArg</code>.
For example, ... | As others have pointed out, the <em>semantics</em> of the function parameter matter. The tests for <code>fun</code> and <code>funArg</code> are <em>two completely separate tests</em>, and are <em>different kinds</em> of tests at that.
<h2>Testing <code>funArg</code></h2>
Since <code>funArg</code> will ultimately be <em... | https://softwareengineering.stackexchange.com |
397,206 | [
"https://stats.stackexchange.com/questions/397206",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/145482/"
] | <strong>Problem</strong>
I am trying to test gender differences in the risk propensity of investors related to specific kind of stocks. More specifically, I want to the test the hypothesis predicting that female investors would be less risk averse than male investors.
<strong>Data</strong>
For each stock in my datase... | I would treat <code>riskiness</code> as a continuous outcome and see if there are differences in the average riskiness between males and females. Moreover, it seems that you have a crossed design. Hence, I would start with a model of the form (using function <code>lmer()</code> from the R package <strong>lme4</strong>)... | A popular way to regress proportions to variables is to use the logistic regression.
Before fitting a model, you can also go non parametric and just plot the proportion of investors against the quantiles of riskiness.
| https://stats.stackexchange.com |
72,928 | [
"https://electronics.stackexchange.com/questions/72928",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/24611/"
] | Find the RMS value of the periodic triangular current, if I_m=1A, T=1s.
<img src="https://i.stack.imgur.com/sR92n.png" alt="enter image description here">
Could you tell me step-by-step how to do this? It's not a homework, I just want to find out how to solve this problem.
| RMS means "root mean square", in the order root(mean(square(paramter)).
First, square the function. The find the mean: that requires analysis (calculus). To find the mean value of a function \$f(x)\$ on some interval \$[a, b]\$, you integrate the function on that integral: \$\displaystyle\int_a^bf(x)dx\$ and then di... | Now that you've clarified you want to find the RMS value, a concrete answer is possible. Note that by symmetry, each of the line segments of this triangle wave will have the same RMS value. Note also that the time scale is irrelevant.
So, the question really comes down to <i>"What is the RMS value of a linear ramp f... | https://electronics.stackexchange.com |
2,111,319 | [
"https://math.stackexchange.com/questions/2111319",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Regarding the integral $\int^\infty_0\frac{x^2+1-\cos x}{(x^2+1)x^p} dx$ where $p$ is a real number. When does it converge and why? I am guessing that the necessary and sufficient condition be $1<p\le 2$, is this correct? Thank you.
| I find that the easiest way to do these problems is to argue non-rigorously. All of the following $\approx$ signs can be made rigorous, but morally, this is the correct argument:
As $x \to \infty$, we see $x^2 + 1 - \cos(x) \approx x^2$ and $(x^2+1)x^p \approx x^{p+2}$. Thus $$\frac{x^2 + 1 - \cos(x)}{(x^{2}+1)x^p} \... | Let $f(x)=\cos x-x^2-1+x^p$ on $[0,\infty)$. $f'(x)>0$ for $1<p<3$ thus $f(x)>f(0)=0$ this means $x^p>x^2+1-\cos x$ or
$$\frac{x^2+1-\cos x}{x^p}<1$$
With the integral
$$\int^\infty_0\frac{x^2+1-\cos x}{(x^2+1)x^p} dx<\int^\infty_0\frac{1}{x^2+1} dx=\arctan x\Big|^\infty_0=\frac{\pi}{2}$$
so the i... | https://math.stackexchange.com |
1,241 | [
"https://stats.stackexchange.com/questions/1241",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/684/"
] | When would you tend to use ROC curves over some other tests to determine the predictive ability of some measurement on an outcome?
When dealing with discrete outcomes (alive/dead, present/absent), what makes ROC curves more or less powerful than something like a chi-square?
| The ROC function (it is not necessarily a curve) allows you to assess the discrimination ability provided by a a specific statistical model (comprised of a predictor variable or a set of them).
A main consideration of ROCs is that model predictions do not only stem from the model's ability to discriminate/make predic... | An ROC curve is used when the predictor is continuous and the outcome is discrete, so a chi-square test would not be applicable. In fact, ROC analysis is in some sense equivalent to the Mann-Whitney test: the area under the curve is P(X>Y) which is the quantity being tested by the M-W test. However Mann-Whitney analysi... | https://stats.stackexchange.com |
647,620 | [
"https://math.stackexchange.com/questions/647620",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/116377/"
] | Maclaurin Expansion of $\frac{x}{\sqrt{4-2x}}$ up to order 4.
I really don't know how to do this, I can't find a helpful Maclaurin Series in my formula book to help me.
I want to do $x(4-2x)^{-1/2}$ and use the formula for $(1+x)^p$, but I don't think that works.
Thanks in advance.
| The Maclaurin's series is given by
<span class="math-container">$f(z)=\sum_{n=0}^\infty a_n x^n$</span>
where <span class="math-container">$a_n=\left(\frac{f^n(0)}{n!}\right)$</span>
Here <span class="math-container">$f(x)=\frac{x}{\sqrt{4-2x}}$</span>
Differentiate successive & find values of <span class="ma... | You can write $x(4-2x)^{-1/2} = x 4^{-1/2} (1-(x/2))^{-1/2}$ and now use the formula for $(1+x)^p$. More details? See also the comment by IB Wiglin.
| https://math.stackexchange.com |
22,307 | [
"https://ai.stackexchange.com/questions/22307",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/35585/"
] | Feature scaling, in general, is an important stage in the data preprocessing pipeline.
Decision Tree and Random Forest algorithms, though, are scale-invariant - i.e. they work fine without feature scaling. Why is that?
| Scaling only makes sense when there is something that reacts to that scale. Decision Trees though, just make a cut at a certain number.
Imagine: For a feature that goes from 0 to 100 a cut at 50 may be improving performance. Scaling this down to 0 to 1 making the cut a 0.5 doesn't change a thing.
Now on the other hand ... | Feature scaling happens to be a problem when a model is characterized by having a distance metric (or another kind of numerical evaluation for that matter). Therefore models such as support vector machines, neural networks, distance based clustering methods (e.g. k means) and linear/logistic regression are prone to cha... | https://ai.stackexchange.com |
2,553,625 | [
"https://math.stackexchange.com/questions/2553625",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/500356/"
] | Let $\sum\limits_{n=1}^\infty a_k$ be a convergent series, then the following statement is true:
$$\lim\limits_{n\to\infty}\frac{1}{n}\sum\limits_{k=1}^n a_{k} = 0$$
Since $\frac{1}{n}$ is a null series and the partial sum will never get greater than $\sum\limits_{n=1}^\infty a_{n} = c$, the limit is obviously $0$.
... | The limit of the product of two converging sequences is the product of the limits of the sequences.
| In $\varepsilon$ form, given
$$S_n=\sum\limits_{k=1}^{n}a_k$$
$$\lim\limits_{n\rightarrow\infty}S_n=c$$
we have
$$\left| S_n - c \right|<\varepsilon$$
from some $n$ onwards. Then
$$\left| \frac{S_n}{n} - 0 \right|=\left| \frac{S_n}{n} -\frac{c}{n}+\frac{c}{n}- 0 \right|\leq\left| \frac{S_n}{n} -\frac{c}{n}\right|+\... | https://math.stackexchange.com |
249,245 | [
"https://math.stackexchange.com/questions/249245",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/51415/"
] | Examine that $W$ is a subspace of the vector space $M_{3x3}$
$W=({A:det(A) \ge} 0)$
I have two conditions:
1) $ \vec u + \vec v \in W $
2) $ \alpha \cdot \vec u \in W $
$ B,C \in W $
$det(B) + det(C) \ge 0 $
I don't know any properties of determine of matrix which could help with these.
| <strong>This claim is not true:</strong>
First, note that $A=diag(-2,-8,1),B=diag(3,3,3)\in W$ but $A+B\not\in W$.
Moreover, if $A\in W$ then $|-A|=(-1)^{3}|A|\leq0$ and so $-A\in W$
iff $|A|=0$ but there are matrices in $W$ with non-zero determinant
| $W=\{A\colon \det A\geq 0\}$ is not a subspace of the vector space $M_{3\times3}$ (I assume it is over the reals). Take for example
$$
I=\begin{bmatrix}
1 & 0& 0\\
0&1&0\\
0&0&1
\end{bmatrix}.
$$
Obviously $\det I=1$ and $I\in W$. Now take $(-1)I$ and observe that $\det (-1)I=(-1)^3\det I$.
| https://math.stackexchange.com |
51,178 | [
"https://astronomy.stackexchange.com/questions/51178",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/48274/"
] | Often you hear people say "time is The 4th dimension". What confuses me is that people talk about "The 4th" dimension as if it's a specific thing and I don't understand why.
What I mean by that, is that I can plot the position of a point in 3D space with the 4th dimension being just about anything. ... | This is because time is <em>the</em> fourth dimension in the theory of General Relativity which describes gravity.
It turns out that a good way to describe the paths that objects or light take when in a gravitational field is to describe a curved four-dimensional space with coordinates x,y,z,t. A particle in space beco... | Just my 2c worth, I think there's an easier explanation. Not that I don't love the physics and maths behind this question.
Just linguistically speaking, we want to describe an object's position that's "good enough" without lacking detail or being superfluous. Thinking back many years in a book by Rudy Rucke... | https://astronomy.stackexchange.com |
47,637 | [
"https://mathoverflow.net/questions/47637",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11156/"
] | I am trying to find an explicit way to view global holomorphic sections of $\Omega^{1} \otimes \mathcal{O} (2)$ over $\mathbb{CP}^{2}$. I guess what I mean by "explicit" would be a formulation over an affine open $U_i \subset \mathbb{CP}^{2}$. According to what I found in Okoneck, Schneider and Spindler, there is a 3-... | If $x,y,z$ are coordinates on $P^2$ then the 3 sections of $\Omega(2)$ are given by $xdy - ydx$, $ydz-zdy$, and $zdx-xdz$.
| Use the Euler sequence:
$0 \to \Omega^1_{\mathbb{P}^n_A/A} \to \mathcal{O}_{\mathbb{P}^n_A}(-1)^{\oplus n+1} \to \mathcal{O}_{\mathbb{P}^n_A} \to 0.$
Everything can be seen explicitly from here. Tensoring the sequence with $\mathcal{O}(2)$ gives an exact sequence, which is still exact if you take global sections beca... | https://mathoverflow.net |
403,894 | [
"https://physics.stackexchange.com/questions/403894",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/194113/"
] | I'm studying electrostatics, then I read the concept of electric potential and potential difference. They said "the electric potential at a point in the given electric field is defined as the work done in moving per unit positive charge from infinity to that point against electrostatic forces of attraction of t... | Even if the beam did not interact with anything, it would still have energy/momentum. According to GR, any energy/momentum distribution will curve spacetime around it. In principle, it should be possible to see the bending of the light of distant stars passing through the region as a small change in the apparent positi... | The simple answer would be No.
Without any interations with other objects and the most clear path in the whole universe it would be nearly impossible or maybe even impossible to detect as light doesn't scatter/lose energy when it is travelling through a vacuum.However it could be that I am wrong and if so ,then please... | https://physics.stackexchange.com |
105,303 | [
"https://security.stackexchange.com/questions/105303",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/6276/"
] | We are currently switching over to Exchange 2013 and we are thinking about outsourcing the spam and malware filtering to Microsofts Exchange Online Protection. Its implemented by changing the MX Record of our domain to the address of their datacenter.
This would be a very practical and also relativley cheap solution f... | There's nothing in ISO27001 that would specifically preclude what you describe.
At a high level provided you have conducted a risk assessment applicable to the use of the email proxying service and the 'output' is consistent with your risk acceptance criteria it will not be incompatible with ISO27001.
Thinking more a... | ISO 27001 does not provide guidelines nor requirements regarding the technical setup and technology behind your controls. So there is nothing against outsourcing your email filtering protection per se.
However, you will need to make sure that the same level of control applies to your new setup compared to the previou... | https://security.stackexchange.com |
15,324 | [
"https://physics.stackexchange.com/questions/15324",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5514/"
] | Is there the effect of sun rising and sun setting, in terms of Rayleigh scattering and visual spectrum and other factors completely similar and symmetric? I mean can one recognise them from a picture taken from the sky?
| The average air temperature is always lower at sunrise, which changes the atmospheric refraction infinitesimally. On the moon, you would only have the tiny difference from the doppler shift due to your motion relative to the sun, so that sunrise would be a teeny-weeny bit bluer than sunset.
| In most areas yes, there is more atmospheric pollution generated during the day so sunsets are slightly redder than sunrises.
But from purely orbital/geometric measurements, no they are identical.
| https://physics.stackexchange.com |
429,055 | [
"https://math.stackexchange.com/questions/429055",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/59909/"
] | This problem comes from exercise from my lecturer
Let $A$ be a square matrix such that $\mbox{rank}(A)=1$. Prove that $\det(A+I)=\mbox{trace}(A)+1$.
($I$ is the identy matrix)
I usually haven't any idea in solving linear algebra problem.
| Edited in response to julien's comment
Recall that:
1) the rank is greater than or equal to the number of non-zero eigenvalues
2) the determinant is equal to the product of all eigenvalues
3) the trace is equal to the sum of all eigenvalues
You should also be able to show that if $\lambda$ is an eigenvalue of $A$ ... | <strong>Hint:</strong> If the rank of the matrix is $1$, it means that all columns can be written as multiples of one of them (say, wlog, the first one); since the determinant is invariant by linear combination of the columns, you can write $\det(A+I)$ as $\det(A'+I)$, where $A'$ and $A$ have same rank, but only the fi... | https://math.stackexchange.com |
14,748 | [
"https://engineering.stackexchange.com/questions/14748",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/10361/"
] | If you wanted highest efficientcy and speed from an AC motor what would you do?
Could the rate of alternation of current be optimizes?
More windings?
Materials?
More lamination?
Other factors I haven't thought of?
| You really can't change the frequency of alternating current. This is fixed at 60 hertz (cycles/sec) for USA and 50 hertz most everywhere else. by laminating the permanent magnets you reduce losses to hall effect currents on the surface. Most commercial motors have already made the most efficient design possible. Yo... | A possible avenue you could look at is the motor controllers that match power to load.
| https://engineering.stackexchange.com |
352,139 | [
"https://softwareengineering.stackexchange.com/questions/352139",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/262132/"
] | I have an API endpoint that returns some statistics. Currently the response looks like:
Option 1:
<pre><code>{
"stats": [
{
"name": "some-stats-key1",
"value": 10
},
{
"name": "some-stats-key2",
... | I'd go for option 2. If the API consumer will convert <code>some-stats-key1</code> into something readable, that probably means he/she has a list of values he/she is interested in (say, <code>some-stats-key1</code> and <code>some-stats-key3</code>), and will iterate over that list. By choosing a JSON object, it will be... | When I get data from an API, I <em>always</em> check that everything is as I expect it. So my effort to process your data consists of the verification, and the actual processing.
In case 1 I have to check: a. There is an array. b. All items in the array are dictionaries. c. Every dictionary has a key "name". d. All v... | https://softwareengineering.stackexchange.com |
302,147 | [
"https://softwareengineering.stackexchange.com/questions/302147",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/203422/"
] | Currently we have one master branch for our PHP application in a shared repository. We have more than 500 clients who are subscribers of our software, most of whom have some customization for different purposes, each in a separate branch. The customization could be a different text field name, a totally new feature or ... | You are completely abusing branches! You should have the customisation powered by flexibility in your application, not flexibility in your version control (which, as you have discovered, is not intended/designed for this sort of use).
For example, make textfield labels come from a text file, not be hardcoded into your... | <strong>Having 500 clients is a nice problem, if you had spent the time up front to avoid this problem with branches, you may never have been able to remain trading for long enough to get any clients.</strong>
Firstly, I hope you charge your clients enough to cover <strong>ALL</strong> the costs of maintaining their c... | https://softwareengineering.stackexchange.com |
9,134 | [
"https://physics.stackexchange.com/questions/9134",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/3290/"
] | I'm wondering how would you move without gravity? You would still have air pressure at 1Atm.
Would you "swim" in the air or would you have do something else?
| The answer is: with great difficulty.
In a space ship there should be hand holds and footholds and a grid of ropes crisscrossing and you would move by pulling and pushing yourself: muscle power.
Air is too thin to get a reactive force to propel yourself effectively by swimming.
Once a motion is started, stopping wi... | <img src="https://i.stack.imgur.com/kN5yy.png" alt="enter image description here">
Well we could use arrangements springs and nets.
Example:
Suppose you want to get from A to B. There is spring at A (launcher spring) and there is another spring at C(deflector spring). There is a net at B to catch you. And the big bla... | https://physics.stackexchange.com |
12,427 | [
"https://engineering.stackexchange.com/questions/12427",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/7246/"
] | My workplace has a policy to provide standing desks upon request, but no policy to provide chairs of matching height. (I work for the government...) We can buy our own, or build our own. However they added a stipulation that the chairs must be bought or built with five or more wheels.
Since five is an awkward symme... | Assuming all the wheels are evenly spaced on the same circle, then more wheels is always more stable than less wheels. However, there is diminishing return as the number of wheels gets large.
The metric of stability is how far from the center of the circle the center of mass can be before the chair tips over. The ch... | I think the "health and safety" regulation about 5 wheels is a compromise between stability and cost.
If your weight is on the edge of the chair seat and the chair has only 3 wheels, it is much less stable if you are in line with one of the wheels than if you rotate through 60 degrees to be mid-way between two wheels.... | https://engineering.stackexchange.com |
82,125 | [
"https://mechanics.stackexchange.com/questions/82125",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/34191/"
] | I recently pulled the driveshaft off my 1986 Dodge B250 van, expecting to replace one or both universal joints. I was surprised to see they both have zerks, so can be serviced (sure wish I'd noticed sooner).
The rear U-joint moves freely in all directions and seems fine, the front joint only moves freely in one direct... | Well the play in both causes the timing to drift between the two banks when there are two distributors.
A single distributor with either one or two sets of points is easier to time - especially if you go for an optronic ignition upgrade.
| Solar Mikes correct +1 .The single distributer must be proportionaly larger in diameter to keep the plug to plug voltage clearances to avoid one cylinder arcing into the next .The total HT lead length will be longer with the single distributer .
| https://mechanics.stackexchange.com |
379,642 | [
"https://softwareengineering.stackexchange.com/questions/379642",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I am pretty new within our Scrum team. (Round about 4 months)
Whenever I suggest some paradigm like "DevOps" or technology like "Kubernetes" to solve issues I am criticised at least from a part of the team.
Arguments are "these are just buzz words".
Other times the team just does not react to my proposals.
I am reall... | You have to explain two things in order for a new technology / paradigm / language / methodology / whatever to have any chance of success in a team. First, you need to explain what is not working with the current approach. You then need to explain how your proposed technology would solve those problems, while not intro... | Some things like <code>DevOps</code> really are just buzz words, and even groups that don't do "DevOps", really do indeed do large chunks of it.
For example:
<ul>
<li>do you have a code repository? </li>
<li>Do you run unit tests before promoting code? </li>
<li>Are your deployments automated? </li>
</ul>
There are... | https://softwareengineering.stackexchange.com |
156,949 | [
"https://math.stackexchange.com/questions/156949",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/32100/"
] | How is uncountability characterized in second order logic?
Also, why is this characterization of uncountability "absolute" in the way that FOL's characterization of uncountability is not?
A <em>very</em> direct answer will be much appreciated.
Much thanks.
| The definition of uncountability is essentially the same as it is in first order logic: a set $X$ is uncountable if there is no surjective function $F$ from the natural numbers $\mathbb{N}$ onto $X$ (there are other ways of formulating uncountability, but they are equivalent to this definition).
Consequently in order ... | There are slightly faster ways to define countability and uncountability in second-order logic, using more knowledge of the ambient set theory to avoid having to refer to axioms of arithmetic. In particular we can use the fact that "countable" is the smallest infinite cardinality.
First, a set $X$ is infinite if the... | https://math.stackexchange.com |
558,961 | [
"https://physics.stackexchange.com/questions/558961",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/247720/"
] | When you take a small portion of an adhesive, it solidifies after some time while the other part in the container remains in liquid state. Why does this happen?
| The 'solution' makes essentially zero sense. Indeed, it's of the <em>not even wrong</em> variety.
(0) A resistor is only a 'fuse' in the sense that it will overheat and perhaps smoke before opening up if the power dissipated is well above the power rating for some time. But there's no mention of the power rating of thi... | The teacher is wrong. Not even wrong. In a very embarrassing way.
You should complain to his supervisor if he is not willing to accept his mistake.
| https://physics.stackexchange.com |
350,572 | [
"https://softwareengineering.stackexchange.com/questions/350572",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/142664/"
] | For each row entered, the user will have one piece of data in either grams, kilograms or pounds. I supply 3 fields and the user must enter in one. The app then calculates the other two values off the entered value.
I am wondering if it is best practice to store all 3 values in the database, or just store the single v... | For data this simple to calculate, it does not make sense to store denormalized data (all three).
Store only the grams and user in the database, then load the user and grams properties of this object with the stored data.
<pre><code>public class Weight
{
public string User {get;set;}
public double Grams {ge... | It depends!
If possible, I'd always try and store everything in the database in the same unit. Makes comparisons, searching and lots of other things much easier ("Find me all the widgets over 1kg").
However, I've also been in situations where it was important that the user always got back <em>exactly</em> the same da... | https://softwareengineering.stackexchange.com |
665,695 | [
"https://physics.stackexchange.com/questions/665695",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/78111/"
] | So, I've been trying to prove this with pure trigonometry just for fun, without using the fact that <span class="math-container">$R + T = 1$</span>, but no success. Here's my last try, using a combination of both facts that the angles are complementary and Snell's Law:
<span class="math-container">\begin{align*}
t_\pi ... | Sumit Gupta essentially answered the question. However, I think it's not wrong to elaborate a bit further. Your calculation is entirely correct. Indeed,
<span class="math-container">$$ t_p = \frac{n_i}{n_t}. $$</span>
How does that relate to the well-known fact <span class="math-container">$T_\pi = 1$</span> at Brewste... | <span class="math-container">$t$</span> is the transmission coefficient.<br />
<span class="math-container">$T$</span> is the Transmittance which is equal to 1 at brewsters angle since <span class="math-container">$R$</span>, Reflectance goes to zero.<br />
Also,<br />
<span class="math-container">$$T = n\frac{\cos\the... | https://physics.stackexchange.com |
259,775 | [
"https://electronics.stackexchange.com/questions/259775",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/117872/"
] | I'm not understanding why there's a small 9V battery while a giant car battery is only 12V. Is a car battery 12V b/c it's enough to supply the whole car while getting recharged for prolonged time or is there a different reason why a car battery is 12V?
| The board will not fry if all analogue input voltages are within the range 0.3v below ground to 0.3v above Vdd, regardless of the PGA setting.
If the measurement voltage is outside the maximum voltage range according to the PGA setting, the digital code will be clipped at the maximum (or minimum).
If the differential... | As long as you keep within the supply voltages (plus or minus a few hundred mV as specified in the datasheet) you will not damage the part. The reading may not be correct (it will probably saturate at full count in either direction) if the gain is too high.
You do, however, have to ensure that the input voltage to th... | https://electronics.stackexchange.com |
395,157 | [
"https://stats.stackexchange.com/questions/395157",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/196928/"
] | The question:
<span class="math-container">$X_n\stackrel{d}{\rightarrow}X$</span> and <span class="math-container">$Y_n\stackrel{d}{\rightarrow}Y \stackrel{?}{\implies} X_n+Y_n\stackrel{d}{\rightarrow}X+Y$</span>
I know that this does not hold in general; Slutsky's theorem only applies when one or both of the converg... | The percentages of families (15%, 45%, etc.) add to 100% so you
can take <span class="math-container">$r_0 = 0.15, r_1=.0.45, r_2 = 0.25, r_3 = 0.13, p_4 = 0.02$</span>
as approximate relative frequencies as the numbers of cars 0, 1, ..., 4
of cars per family. It is possible that a very small percentage of
families ha... | Elaborating on @Martijn Weterings' comment, you have what I believe is called right censored data - families with more than 4 cars get their actual number of cars censored at 4.
You can't directly calculate the mean number of cars without making some assumptions, some of which are discussed in Glass and Grey (citation... | https://stats.stackexchange.com |
72,785 | [
"https://dsp.stackexchange.com/questions/72785",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/55205/"
] | For the system described by the differential equation below find its inverse zero-state unit step response <span class="math-container">$$\dfrac{d^2y(t)}{dt^2}-2\dfrac{dy(t)}{dt}-8y(t)=\dfrac{d^2x(t)}{dt^2}-2\dfrac{dx(t)}{dt}-3x(t)$$</span>
so that the cascade system of its inverse system and this system is the identit... | A general approach would be to take the Laplace Transform of the equation and put it in form of a transfer function:
<span class="math-container">$$H(s) = \frac{Y(s)}{X(s)}$$</span>
And then invert that and solve for the unit step response from <span class="math-container">$1/H(s)$</span>
Note that the inverse Laplace ... | Dan's answer -- to compute <span class="math-container">$H(s)$</span> as normal, and then compute <span class="math-container">$1/H(s)$</span> -- is equivalent to your suggestion of swapping the <span class="math-container">$x$</span> and <span class="math-container">$y$</span> (or doing it in one step by solving for <... | https://dsp.stackexchange.com |
134,133 | [
"https://electronics.stackexchange.com/questions/134133",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/45767/"
] | I found in a book a scheme representing a terminal connection used in making an ammeter shunt (with the purpose of extending its measuring domain). <img src="https://i.stack.imgur.com/CEDSR.jpg" alt="enter image description here">
I can't understand what the drawing at b) represents. All those resistances want to mod... | Drawing b) represents a terminal cut in half. Let's say that the white rectangle where R3 and Rs are connected is a nut, then you have one ring terminal lug between R3 and R2, then another one between R2 and R1, and then you have the head of a screw at the other end of R1.
Here the contact between the screw and the nu... | Cool, First I have no idea. But b, would look like c if the top of R1 was connected around to the bottom where Rs is. Perhaps this was from an era when the temperature coefficients of resistors weren't so good, and this was a method to reduce it.
| https://electronics.stackexchange.com |
243,844 | [
"https://dba.stackexchange.com/questions/243844",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/186350/"
] | this is a programming challenge I've undertaken to learn some MySQL fundamentals and I can't figure out how to implement a one-to-many relationship in the manner I need. See the below code:
<pre><code>CREATE TABLE Product (
id INT(6) UNSIGNED AUTO_INCREMENT PRIMARY KEY,
name VARCHAR(30) NOT NULL,
price FLO... | <pre><code>CREATE TABLE Product (
id MEDIUMINT UNSIGNED AUTO_INCREMENT,
name VARCHAR(30) NOT NULL,
price DECIMAL(8,2) NOT NULL,
bundle_id SMALLINT UNSIGNED NOT NULL,
PRIMARY KEY(id),
INDEX(bundle_id),
INDEX(name)
)
CREATE TABLE Bundle (
id SMALLINT UNSIGNED AUTO_INCREMENT,
price D... | Setting the column "needed_for_bundle" as a Foreign Key that references the Primary Key of the table Bundle would mean that there's a one-to-many relationship between the two tables. Each product has to belong to one bundle, and one bundle can be composed of one or * product(s).
So first, needed_for_bundle should be t... | https://dba.stackexchange.com |
188,898 | [
"https://electronics.stackexchange.com/questions/188898",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/81163/"
] | What FD, FE and FF hex values of chars represent in UART communication? For some time my UART won't work, and always returning me those three?
| They often mean that communications do not work properly. The very first bit (the start bit) appears, but the data bits do not. Common reasons for that are:
<ul>
<li>Bad connection in ground or data line (high resistance or capacitance)</li>
<li>Sender's baudrate is way too high (sender sends at 57600, receiver listen... | Nothing, they're just bytes. Why your device produces them and how your terminal emulator interprets them is implementation-specific, but they don't mean anything in a general sense.
| https://electronics.stackexchange.com |
117,787 | [
"https://mathoverflow.net/questions/117787",
"https://mathoverflow.net",
"https://mathoverflow.net/users/29992/"
] | Hello,
Does anybody know a reference for the following result: $d\ge 5$ points of $\mathbb P^2$ fail to impose independent conditions on curves of degree $d-3$ if and only if at least $d-1$ of these points are collinear. As usual, "fail to impose independent conditions" means $h^0(\mathcal I_D(d-3))>h^0(\mathcal O_... | You mean "curves of degree $d-3$". A reference (for a more general result) is: D. Eisenbud, M. Green, and J. Harris, CayleyBacharach theorems and conjectures, Bull. Amer.
Math. Soc. 33 (1996), 295–324.
| You can refer to lemma of "Principles of Algebraic Geometry" of Griffiths and Harries of page 481-482, that is the case of d=6 in your question. Sorry for my poor english.
| https://mathoverflow.net |
169,639 | [
"https://electronics.stackexchange.com/questions/169639",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/76082/"
] | I have a Canon AC adapter, Model K30321, that I'd like to use in a project. I'm attempting to test the adapter for correct voltage output.
<strong>Adapter specs:</strong>
<pre><code>Input Voltage: 100 - 240VAC ~ 50/60Hz 60VA 0.65A
Output: 24V === 1A
Connector: 3 pin rectangle white flat 1 [ ■ ■ ■ ] 3
(from Left to ri... | Probably a control input to put the adapter into standby mode so the printer uses less total power when in standby.
You might be able to coerce the adapter into giving you 24V by grounding the CONT line (use a few K resistor in series, just in case).
| You need connect PIN1 (24V) and PIN2 (CONT), there is a MOSFET that enables voltage regulation, and as a result PIN1 will be 24V
| https://electronics.stackexchange.com |
283,575 | [
"https://softwareengineering.stackexchange.com/questions/283575",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/179634/"
] | I have worked for many software projects where I am developing software solution to the customer where I need to integrate with the customer back-end using web service provided by the customer in order to retrieve information, etc...
The problem is the customer might not deliver the required web service on time. Or mi... | The important thing is to develop an open, transparent and trusting relationship with the client. The customer needs to understand what your challenges - and cost - are to work in the manner you are being forced to work in. At the same time, you need to understand why is it that the client cannot deliver in a predict... | Well... this happens all the time, and going agile is not going to fix the issue, rather you could get the web service definitions / contracts finalized. At this point you could actually start to build your system with mocking of the client web service using some tool like SOAPUI.
Once the customer service is up and ... | https://softwareengineering.stackexchange.com |
619,016 | [
"https://math.stackexchange.com/questions/619016",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/114409/"
] | I understand that the definition of an open set in a Metric Space and this can transfer over if you're dealing with a Metric Topological Space. However, I'm not sure if there is a standard definition of an open set in a Topological Space. I have read that it may vary under constraints.
I found one definition on Wikipe... | The definition is equivalent to the usual definition in a topological space. When you have a metric space $(X,\rho)$, you can consider the topological space $(X,\tau_\rho)$ where the topology $\tau_\rho$ consists of all sets in $X$ that are unions of open balls $B(x,\varepsilon)$. Observe that
$(1)$ $X$ is a union of ... | In <em>General Topology</em> there is no definition of the open set. It is just an element of the topology.
If $(X,\tau)$ is a topological space, then $U\subset X$ is open iff $U\in\tau$.
| https://math.stackexchange.com |
382,484 | [
"https://math.stackexchange.com/questions/382484",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/49864/"
] | Show that all roots of $a+bz+cz^2+z^3=0$ lie inside the circle
$|z|=max{\{1,|a|+|b|+|c| \}}$
Now this problem is given in Beardon's Algebra and Geometry third chapter on complex numbers.
What might be relevant for this problem:
<ul>
<li>author previously discussed roots of unity;</li>
<li>a little (I mean abut a p... | Suppose $a + bz + cz^2 + z^3 = 0$ and $|z| > \max\{1,|a|+|b|+|c|\}$. Use the triangle inequality to show that
$$
|z^3| = |a + bz + cz^2| < (|a|+|b|+|c|)|z^2|,
$$
which contradicts the assumption on the size of $|z|$.
| I'd simply be looking at showing that the $z^3$ term was dominant, so there could be no roots beyond the bound. I don't think it is at all sophisticated.
| https://math.stackexchange.com |
138,697 | [
"https://softwareengineering.stackexchange.com/questions/138697",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/47546/"
] | As I learned some basic programming languages I came across tens of IDEs, and tens of compilers. Most people you ask will tell you "Go with that IDE or go with the best" etc, however they do not provide a proper statement as to why this is important. I understand a good IDE will provide you with functionalities to save... | <blockquote>
What difference does a good IDE to your programming skills or your programming time?
</blockquote>
Potentially a lot. If you get to know the features and capabilities very well, you can greatly improve your productivity. But if you ignore the advanced features and treat it like a pretty text editor, the... | It's fairly subjective to say how 'important' the decision is, but consider this:
You will be investing a huge amount of time inside the IDE/editor. Small slowdowns caused by IDE problems quickly become large slowdowns over time. Additionally, you should not feel like the IDE is ever working against you as that takes ... | https://softwareengineering.stackexchange.com |
612,608 | [
"https://physics.stackexchange.com/questions/612608",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/205303/"
] | "Two pendulums with the same mass and length <span class="math-container">$R$</span> are released from rest. The first pendulum is released from an angle of <span class="math-container">$\theta_1 = -2º$</span>, and the second pendulum is released from an angle <span class="math-container">$\theta_2 = +5º$</span>. ... | This is due to the symmetry of the situation. We can divide a pendulum swing into four parts:
<ol>
<li>Pendulum swings from the highest point on the left down to the bottom.</li>
<li>Pendulum swings from the bottom up to the highest point on the right.</li>
<li>Pendulum swings from the highest point on the right down t... | Jonathan's solution is the most elegant I think. Here's a more mathematical one, assuming you know what the equation of motion is for the pendulum.
The angle <span class="math-container">$\theta(t)$</span> evolves according to the equation:
<span class="math-container">\begin{equation}
\ddot\theta(t)=-\omega^2\theta(t)... | https://physics.stackexchange.com |
64,665 | [
"https://cs.stackexchange.com/questions/64665",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/59916/"
] | Is existence of registers in CPU an obligation, Or we just do it for performance?
Can we theoretically and practically have computer architectures that don't use registers?
If yes, please name computer architecture and computer models that doesn't have register.
Update: Do stack machines use register? If yes, is it p... | Theoretically, the answer to your question is a resounding "yes". A Turing Machine, the very first definition of computability in terms of machine models, has no registers. Neither do stack machines (operations always act on the top elements of the stack). Register machines, of course, do.
Practically, the answer is "... | Every CPU has, at the very least, some internal registers: a <em>program counter</em>, a register storing <em>flags</em>, and in some architectures, an <em>accumulator</em> (though the latter isn't strictly required).
As you mention, registers are important for speed reasons. CPUs are designed with efficiency in mind.... | https://cs.stackexchange.com |
52,299 | [
"https://physics.stackexchange.com/questions/52299",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7433/"
] | While analysing a problem in quantum Mechanics, I realized that I don't fully understand the physical meanings of certain integrals. I have been interpreting:
<ul>
<li>$\int \phi^\dagger \hat A \psi \:\mathrm dx$ as "(square root of) probability that a particle with state $|\psi\rangle$ will collapse to a state $|\p... | I'll start with the second one. $\int\phi^\ast\psi\,\mathrm{d}x$ is, as Chris says in the comments, the scalar (or dot) product of $\phi$ and $\psi$. In the Dirac notation, it is written as $\langle\phi|\psi\rangle$ and it gives the overlap of the two wavefunctions. In other words, it gives the probability amplitude (i... | Think about vectors in $\mathbb{R}^2$. The inner product over this space gives you a notion of an angle and orthogonality. For example $\hat x \cdot \hat y= 0$ means they are completely orthogonal and you cannot express one in terms of the other.
This is the same interpretation for $\langle f | g\rangle = \displaysty... | https://physics.stackexchange.com |
574,689 | [
"https://physics.stackexchange.com/questions/574689",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/245142/"
] | I was following sidney coleman videos and lecture notes where he claimed that unique ground state requires spinless harmonic oscillator while spin introduces degeneracy in the ground state corresponding to the various values of the z component of the spin.
Can anyone explain how the degeneracy appear for ground state f... | Degeneracy occurs when a system has more than one <em>state</em> for a particular energy level. Considering the three dimensional harmonic oscillator, the energy is given by
<span class="math-container">$$E_n = (n_x + n_y + n_z) \,\hbar \omega + \frac{3}{2},$$</span>
where <span class="math-container">$n_x, n_y$</span>... | The 1D harmonic oscillator Hamilton is given by <span class="math-container">$$H=\left(n+\frac{1}{2}\right)\hbar\omega$$</span>
where <span class="math-container">$\omega$</span> is the frequency and <span class="math-container">$n$</span> is a natural number.
As you can see the Hamiltonian is independent of spin <span... | https://physics.stackexchange.com |
207,680 | [
"https://physics.stackexchange.com/questions/207680",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/89867/"
] | My question is, we can calculate distance of free falling objects with the equation of $d = \frac{1}{2}gt^2$ where $d$ is distance in meter, $t$ is time in seconds, but I wonder how we achieved this equation. I know that the object's velocity isn't constant, the object is accelerating. So we can't calculate it via $x =... | The answer by ryanp16 gives a great derivation of the equation you're asking about using calculus, and in fact, that is the approach that I would have taken had I not seen his answer. However, if you're not familiar with calculus, there's a second, algebraic approach that you can use to arrive at the same conclusion. ... | Acceleration $a$ is defined as the rate of change of velocity $v$ with respect to time $t$, or
$a=\frac{dv}{dt}$. For constant acceleration we can integrate both sides with respect to $t$ to obtain $v=u+at$ where $u$ is the velocity at our initial time $t=0$.
Since velocity $v$ is defined as the rate of change of dis... | https://physics.stackexchange.com |
239,420 | [
"https://stats.stackexchange.com/questions/239420",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/128502/"
] | In a town with 5000 adults , a sample of $100$ is asked about their opinion on a proposed municipal project , $60$ are found to favor it and $40$ oppose it. If in fact the adults of the town were equally divided on the proposal , what would be the probability of obtaining a majority of $60$ or more favoring it in a sam... | While @Time Lee is technically correct that it is a hypergeometric distribution, you're gonna end up in a whole world of pain if you try to do it that way. The population and number of people who favor it are both large enough that a Binomial distribution will suffice as an approximation.
As @whuber noted in the comme... | The distribution discussed here is the hypergeometric distribution, with N=5000, K=2500, n=100, and k=60. To solve for the probability of the 60 or more, the true CDF of this function is not very easy to use, however you can use the inverse method which is easier to use. I did the work for P(X=60), and P(X=60)=.0105. Y... | https://stats.stackexchange.com |
2,056,828 | [
"https://math.stackexchange.com/questions/2056828",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/173057/"
] | In a non-trivial optimization problem, we have among others two variables $x_1$ and $x_2$ both of them are ranged, i.e. $x_1,x_2\in[L,U]$. It is requested that if one of them is positive then the other must be negative. That is:
$$
(x_1>0 \Rightarrow x_2<0) \land (x_1<0\Rightarrow x_2>0)
$$
The question: is... | Regarding the notation, $\Bbb Z [\Bbb i]$ is $\{a + b\Bbb i \mid a, b \in \Bbb Z\}$, i.e. exactly what you incorrectly call $\Bbb Z (\Bbb i)$.
Regarding the problem itself, since you want to use the fundamental isomorphism theorem, I suggest the following approach: find the quotient ring $\Bbb Z [\Bbb i] / (1 + \Bbb i... | From the question <em>What does $\mathbb{Z}[i]$ means?</em> the answer can be <em>They're the Gaussian integers</em>, that are the elements of the form $a+bi$ with $a,b$ integers. They're interesting for a lot of things, for example in geometry and if you notice, all the prime numbers of structure $4k+1$ in $\mathbb{Z}... | https://math.stackexchange.com |
354,158 | [
"https://physics.stackexchange.com/questions/354158",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75502/"
] | 2 bundles of electrons, bundle 1(even indexed electrons) bundle 2(odd indexed electrons) not important how I label them.
Bundle 1 remains on Earth doing double slit while bundle 2 is doing double slit on a relativistic missile traveling at 0.99c towards voyager 1.
We shall agreed that both must shows interference pat... | Entanglement is a property of wave functions of more than one particle, it really does not care whether one part of your system is stationary and the other part is moving relativistically. From your description, it is not clear that anything interesting will happen because you did not say whether the first bundle of el... | Don't forget that if you are dealing with subatomic particles you have to consider the Heisenberg uncertainty principle as well.
I think that entanglement and the twins paradox are two separate entities formed by two separate branches of physics.
| https://physics.stackexchange.com |
41,041 | [
"https://mechanics.stackexchange.com/questions/41041",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/2078/"
] | I recently purchased a used 2002 Toyota Sienna XLE that had brake issues. I replaced the master cylinder, put in new pads, pins, rubber boots, and checked the rear drum brakes, which had almost no wear on them. I did clean them with brake cleaner anyway. I then followed the test in my Haynes Manual to check the brak... | Different vehicles have different pedal feels. There's not much to be done to adjust it. You may want to bleed the brakes again, just to make sure there isn't any air trapped in the system.
| I'm leaving the accepted answer as it was correct. However, in my case after the brakes were bleed a second time they finally got all the air out.
In conjunction with this though was the drum brakes. They had almost all the pad showing, but when I backed them off to remove the drums, I didn't tighten them back all ... | https://mechanics.stackexchange.com |
133,793 | [
"https://dba.stackexchange.com/questions/133793",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/45976/"
] | Hi I have a J2EE Server(clustered) that executes requests from multiple users.
I would like that each request of a given user will be handled like so:
<pre><code>{
acquireLockForUser(userId); // i.e. insert a lock row for a dedicated table
doSomeStuffInDbForUser(user);
releaseLock(userId); // i.e. delete a loc... | This is a parsing error, not a runtime error. You can avoid this by removing the <code>GO</code> commands (these can't exist inside an <code>IF</code> block anyway) and using dynamic SQL.
Why <code>IF DB_ID()</code> instead of just putting the <code>DROP</code> inside <code>TRY/CATCH</code> (or letting it error)?
Yo... | Below should work
<pre><code>If exists (select 1 from master.sys.databases where name ='db you want to check')
Begin
Alter database db-name set restricted user with rollback immediate ;
Drop database db-name;
End
Else
Print 'db does not exist '
</code></pre>
Note: If you offline the database and drop ... | https://dba.stackexchange.com |
2,085,744 | [
"https://math.stackexchange.com/questions/2085744",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/378988/"
] | So this is another practice problem I have for discrete math, this time involving compound propositions, with the book my campus uses is <em>Discrete Mathematics with Applications, 7th Edition</em> by Ken Rosen. The problem goes "Let p and q be two given propositions. Use equivalence laws shown in Table 6 and example ... | $p\wedge(p\rightarrow q)\equiv p\wedge(\neg p \vee q) \equiv (p \wedge \neg p) \vee (p\wedge q) \equiv (p \wedge q)$
Hence,$\neg\left(p\wedge(p\rightarrow q)\right)\equiv \neg(p \wedge q)$
| $\neg[p\land (p\rightarrow q)]\equiv \neg[p\land (\neg p\vee q)] \ \ $(by the definition of $p\rightarrow q$)$\ \ \equiv [\neg p \vee\neg(\neg p\vee q)] \ \ $(DeMorgan's Law) $\ \ \equiv [\neg p\vee (p\land \neg q)]\equiv (\neg p\vee p)\land (\neg p\vee \neg q))\equiv \neg(p\land q)$ (by the distributivity property.)... | https://math.stackexchange.com |
59,254 | [
"https://softwareengineering.stackexchange.com/questions/59254",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/16175/"
] | Do you do any performance testing in any repeatable and automated way? Do you trigger it as a part of CI builds? What tools do you use? How do you spot changes in trends?
I'm looking for how-tos and description of working set-ups for end-to-end automated performance testing approaches.
| Repeatable - yes. Automated - not fully. We have automated the generation of test data for our performance tests, and the test driver. The tests themselves are triggered by hand whenever necessary. Such as before releases, or platform changes (right now we are migrating our legacy project from Java 5 to 6, and we are a... | We are just getting started with load and performance testing. Right now, we're doing simple tests: Run operation X for Y iterations, possibly with some level of randomness to inputs or things that could happen during operation (e.g., close the connection occasionally and make the program recover). Then automaticall... | https://softwareengineering.stackexchange.com |
443,186 | [
"https://electronics.stackexchange.com/questions/443186",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/141377/"
] | I don't understand why CPU manufacturers make multi-core chips. Scaling of multiple cores is horrible, this is highly application specific, and I am sure you can point out certain program or code that runs great on many cores, but most of the time the scaling is garbage. It's a waste of silicon die space and a waste of... | The problem lies with the assumption that CPU manufacturers can just add more transistors to make a single CPU core more powerful without consequence.
To make a CPU do more, you have to plan what doing more entails. There are really three options:
<ol>
<li><strong>Make the core run at a higher clock frequency.</strong>... | <h2>Data dependency</h2>
It's fairly easy to add more instructions per clock by making a chip "wider" - this has been the "SIMD" approach. The problem is that this doesn't help most use cases.
There are roughly two types of workload, independent and dependent. An example of an independent workload might be "given two... | https://electronics.stackexchange.com |
4,477,215 | [
"https://math.stackexchange.com/questions/4477215",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I want to calculate the Galois Group of <span class="math-container">$p= (x^2-5)(x^2-7) \in \mathbb{Q} $</span>. Because I saw a solution to this problem in a German textbook and think it is incorrect.
So: <span class="math-container">$p$</span> is irred. over <span class="math-container">$\mathbb{Q}$</span>, and <span... | Dealing with the confusion about the discriminant only as the others have handled the main question.
<hr />
The group <span class="math-container">$S_4$</span> of permutations of <span class="math-container">$1,2,3,4$</span> contains several copies of <span class="math-container">$V_4$</span>. The subgroup <span class=... | You have factored <span class="math-container">$p$</span>, so it is apparently false that <span class="math-container">$p$</span> is irreducible over <span class="math-container">$\mathbb Q$</span>. But your computation of <span class="math-container">$|\text{Gal}(p)|=4$</span> is more or less correct, except <span cla... | https://math.stackexchange.com |
1,462,566 | [
"https://math.stackexchange.com/questions/1462566",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Regarding the function $f(x) = x\sqrt{3-x^2}$, I can determine that there are local min/max at +/-$\sqrt{\frac{3}{2}}$. I assumed these would also be the global max and min after looking at the graphed function. However, when I try to confirm my results via Wolfram Alpha, I am told that no global max or min exists. I c... | It is divergent. When $R>1$, $a_n\not\to0$. This is also true for $R=\infty$.
| If $\lim_{n\to\infty}\frac{a_{n+1}}{a_n}=\infty$, then you can find $\bar{n}$ such that, for all $n\ge\bar{n}$, $\frac{a_{n+1}}{a_n}\ge2$. Therefore $a_{\bar{n}+k}\ge2^ka_{\bar{n}}$ and the series diverges by comparison with a clearly divergent series.
| https://math.stackexchange.com |
548,492 | [
"https://physics.stackexchange.com/questions/548492",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/262229/"
] | Can you assume that an object moving counterclockwise has positive angular velocity and any torque that is pushing the object counterclockwise is positive? And vice versa for clockwise?
| It depends, but it is the common assumption that we follow for vector quantities like Angular velocity, angular momentum, torque for the purpose of analysis of rotation i.e. static or dynamic equilibrium.
Suppose that a body is subjected to two forces which try to rotate it in opposite directions then we have to follo... | The direction and magnitude of angular velocity is governed by this equation
<span class="math-container">$$\vec{v}=\vec{\omega}×\vec{r}$$</span>
Angular velocity and torque are related to each other by this equation
<span class="math-container">$$\vec{T}=I\frac{d\vec{\omega}}{dt}$$</span>
| https://physics.stackexchange.com |
51,386 | [
"https://mathoverflow.net/questions/51386",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1930/"
] | I wonder what the prerequisites for learning the representation theory of reductive groups over a p-adic field are? Can someone recommend me any book or article for learning this theory if I wanna clearly know what this theory is about and what kind of applications this theory has?
I just know some fundamental concep... | Hello, I think a good first step is to learn the theory of admissible representations of p-adic groups and for this Godement's notes on Jacquet-Langlands theory and then Casselman's unpublished book on p-adic groups (available from his website) are good starting points. A good way to read Casselman's notes is to rewrit... | When I learned this material, 10 or so years ago, I read Cartier's article in <em>Corvalis</em> (linked to by Thomas in the comments above),
and then Casselman's notes (mentioned by Ramin). My experience has been that all of this material is a little dry and difficult to learn (due to lack of apparent motivation) if i... | https://mathoverflow.net |
129,183 | [
"https://stats.stackexchange.com/questions/129183",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/31466/"
] | Why in "Method of Moments", we equate sample moments to population moments for finding point estimator?
Where is the logic behind this?
| A sample consisting of $n$ realizations from identically and independently distributed random variables is ergodic. In a such a case, "sample moments" are <em>consistent</em> estimators of theoretical moments of the common distribution, if the theoretical moments exist and are finite.
This means that
$$\hat \mu_k(n... | Econometricians call this "the analogy principle". You compute the population mean as the expected value with respect to the population distribution; you compute the estimator as the expected value with respect to the sample distribution, and it turns out to be the sample mean. You have a unified expression
$$
T(F) = \... | https://stats.stackexchange.com |
190,707 | [
"https://security.stackexchange.com/questions/190707",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/175909/"
] | I am filling out a form to set up a recurring payment with a local government building. The form requests that I put my credit card number, expiration date, and CVV number, which I'm a little hesitant to do.
How I can minimize my risk of the information being stolen/misused?
<hr>
My plan:
<ul>
<li>I was given the o... | Privacy.com allows you to generate virtual card numbers which are per-merchant and can have limitations put upon them (e.g., $15/month). They use your checking account as a backend to cover the payments.
That's a more generic equivalent to Virtual Card Numbers, which some specific cards provide as a feature (e.g., ... | They shouldn’t be asking you to write down your CVV number at all. Payment Card Industry security standards prohibit merchants from storing that information, and on paper counts. If they can’t process your card electronically so that the CVV is only ever held in memory then they shouldn’t be using the CVV at all, and a... | https://security.stackexchange.com |
368,111 | [
"https://math.stackexchange.com/questions/368111",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/73041/"
] | Consider (1) $a_{n+2} = 2a_{n+1} - a_n + 4n3^n$ with $a_0 = a_1 = 1$.
Using generating functions and setting $A(x) = \sum a_nx^n$ we obtain
$$\begin{align*}&\quad\sum a_{n+2}x^{n+2} = \sum2a_{n+1}x^{n+2} - \sum a_nx^{n+2} + \sum 4n3^nx^{n+2}\\ &\implies [A(x) - a_0 - a_1x] = 2x[A(x)-a_0] - x^2A(x) + \sum_n 4n... | Everything is OK except $\sum_n 4n3^n x^{n+2}$. Let $B(x)=\sum_{n=1}^\infty 4n3^n x^{n+2}$. Then
$$ \frac{1}{12x^3}B(x)=\sum_{n=1}^\infty n (3x)^{n-1}. $$
Using the fact that $\sum_{n=1}^\infty nx^{n-1}=\frac{1}{(1-x)^2}$ for $|x|<1$, we have
$$\frac{1}{12x^3}B(x)=\frac{1}{(1-3x)^2}$$
or
$$B(x)=\frac{12x^3}{(1-3x)^2... | In this case an easy way to derive a closed form solution is to rewrite the sequence as
$$a_{n+2}-a_{n+1} = a_{n+1} - a_n + 4n3^n$$
Then you can define $b_n = a_{n+1}-a_n$ and you'll get
$$b_{n+1} = b_n + 4n3^n$$
for which it is easy to give a closed-form solution. You can then obtain $a_n$ by summing over $b_n$:
... | https://math.stackexchange.com |
149,760 | [
"https://security.stackexchange.com/questions/149760",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/137705/"
] | I'm new to shellcoding.
I have written assembly code :
<pre><code>section .text
global _start
_start:
jmp end
start:
;open file
pop ebx ; get address of filename
xor eax,eax
mov [ebx+3], al
mov al,5
xor ecx,ecx
mov edx,777
int 80h
;exit
xor eax,eax
mov al,1
mov ebx,1
int 80h
end:
cal... | I got the solution. Actually by mistake I compiled the shellcode testing program as 64bit executable and that's why the shellcode was being executed as 64bit and in 64bit mode the syscall no 5 is for "fstat" and that's what strace tool was showing.
| I'm editing this answer to clean up the confusion about <code>-e open</code>. <code>-e</code> only does filtering and will not add extra info to the strace log. The only case when <code>strace</code> is not logging <code>open</code> syscalls is when a forked subprocess is invoking them and the <code>-f</code> parameter... | https://security.stackexchange.com |
316,771 | [
"https://electronics.stackexchange.com/questions/316771",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/94946/"
] | I'm into a preliminary design of a eletrical vehicle that uses BLDC permanent magnet motors for motion (3 phases 36V 300W hub motors in wheel). For safety compliance this vehicle needs to provide a breaking mechanism that stops the vechicle when there's a power failure. My first choiche will be using reverse-action bra... | This type of system is fairly common but you must remember that this is a reactive system. It will not HOLD the vehicle but rather, will retard it's speed.
That is, the amount of brake force generated will depend on the speed of the vehicle. When stopped, there is ZERO brake force.
A vehicle parked on a steep slope w... | This is dynamic braking. In 0 speed does nothing, on lower speed stops the motion. But on high speed that will heat and destroy the motor. At very least you need a power resistor to waste regenerated energy on it. Pain in your neck, bht like Transistor said, vehicle should keep moving, but not under power.
| https://electronics.stackexchange.com |
700,352 | [
"https://physics.stackexchange.com/questions/700352",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/101428/"
] | So normally, taking <span class="math-container">$c = 1$</span> and <span class="math-container">${8\pi G = 1}$</span>, and assuming the cosmological constant is negligible, the Einstein field equations read:
<span class="math-container">$$R_{\mu \nu} - \frac{1}2Rg_{\mu\nu} = T_{\mu \nu}.$$</span>
However, there also e... | those are the Helix equations
<span class="math-container">$$x=b\cos(\varphi)\\
y=b\sin(\varphi)\\
z=a\varphi$$</span>
the generalized coordinate is <span class="math-container">$~\varphi~$</span> thus
you need two constraint equations
<span class="math-container">$$x^2+y^2=b^2\tag 1$$</span>
<span class="math-containe... | You can think of this problem in the following way.
We are talking about a particle in <span class="math-container">$\mathbb{R}^3$</span>. The space it exists in has a dimension of <strong>3</strong>.
But the particle rides on a path (helix) that only takes <strong>1</strong> quantity to fully describe its position.
Th... | https://physics.stackexchange.com |
332,711 | [
"https://softwareengineering.stackexchange.com/questions/332711",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8518/"
] | What is complexity related to number of operations/interactions between objects within a system? as that number increases the programmer capability of understanding and maintaining the system degrade.
| <em>High coupling</em> may be the closest term. People may argue that having a lot of systems does not necessarily imply high coupling. Hopefully, the systems are well-architected with clearly-defined interfaces and separate concerns. But the OP states that <em>all</em> these systems can interact with <em>every other</... | It's object abstraction, but usually referred to as abstraction. The principle is that most people can only comprehend 7 +/-2 given objects in short term memory; therefore layers of abstraction through the system should strive to stay within this level.
<em>High Coupling</em> or intracomponent linkage as mentioned by... | https://softwareengineering.stackexchange.com |
3,111,056 | [
"https://math.stackexchange.com/questions/3111056",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
For subsets <span class="math-container">$A, B \subseteq \mathbb{R}^{n}$</span>, is it true that <span class="math-container">$A
\subseteq B \implies \partial A \subseteq \partial B$</span>?
</blockquote>
I believe the answer is no. But, I cannot come up with a counterexample. I need the boundary of <s... | <blockquote>
I believe the answer is no.
</blockquote>
That is correct. The boundaries can even be disjoint.
<blockquote>
I was thinking like two concentric circles with different radii won't have intersecting boundaries.
</blockquote>
Correct again, assuming that with “circles” you mean <span class="math-contai... | Take <span class="math-container">$B=\mathbb R^{n}$</span>. then <span class="math-container">$\partial B=\emptyset$</span>. Can you think of some subset whose boundary is not empty?.
| https://math.stackexchange.com |
478,734 | [
"https://physics.stackexchange.com/questions/478734",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/206319/"
] | I'm studying about curved spaces and I read that a manifold is flat if there a coordinate system such that the metric tensor is constant everywhere.
Then I also read that when the space-time tensor is the Minkowski tensor that is constant everywhere, so why is space-time curved?
| Space-time can be curved, does not mean that it is always curved. By substituting Minkowski metric in general relativity one will arrive at the equations of special theory of relativity. That is why it is called <em>special</em> theory of relativity. When there is no space-time curvature we are dealing with special rel... | The metric tensor is defined by the matrix <span class="math-container">$e_i.e_j$</span>. Where <span class="math-container">$e_i$</span> and <span class="math-container">$e_j$</span> are the basis vector at a point. For a curved space these basis vector differs at each point. In special relativity we consider a small ... | https://physics.stackexchange.com |
3,348,200 | [
"https://math.stackexchange.com/questions/3348200",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/425089/"
] | <blockquote>
If you have <span class="math-container">$m$</span> and <span class="math-container">$n$</span> number of distinct items, and you get to choose <span class="math-container">$p$</span> and <span class="math-container">$q$</span> things respectively out of them, then the number of ways you can permute <spa... | You made your very first mistake in the first line. The statements <span class="math-container">$x=y$</span> and <span class="math-container">$\sqrt{x^2}=\sqrt{y^2}$</span> are not equivalent as claimed, since the latter means <span class="math-container">$|x|=|y|.$</span> Thus, if you take <span class="math-container"... | <blockquote>
<span class="math-container">$$x=y\iff -x=y\lor x=-y\tag{1}$$</span>
</blockquote>
Doesn't makes sense since <span class="math-container">$-x=y\iff x=-y$</span>, that is, they're equivalent. This reduces <span class="math-container">$(1)$</span> to <span class="math-container">$$x=y\iff -x=y\tag{2}$$</s... | https://math.stackexchange.com |
17,190 | [
"https://electronics.stackexchange.com/questions/17190",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3552/"
] | AFAIK each of the world leading cordless power tools manufacturers produces several "product lines" of cordless power tools with different voltages. For example, Bosch currently produces tools with Li-Ion batteries with 10,7V, 14,4V, 18V and 36V output and the higher the voltage the more powerful a tool is.
Now those ... | Matt already explained that using a higher voltage you'll have a <strong>lower current for the same power rating</strong>. This means <strong>thinner and less heavy wires</strong>, which means savings (copper is expensive). You may have to pay attention to <strong>better insulation</strong>, but that doesn't outweigh t... | For exactly the same reason the power companies transmit power around the country at many hundreds of thousands of volts instead of just doing it all at 110/230v.
A higher voltage means a lower current for the same amount of power.
A lower current means smaller components and thinner wires, thus making it cheaper and... | https://electronics.stackexchange.com |
3,336,409 | [
"https://math.stackexchange.com/questions/3336409",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/579944/"
] | <blockquote>
Find minimum of function <span class="math-container">$f(x) = \frac{\left| x-12\right|
}{5}+\frac{\sqrt{x^2+25}}{3}$</span>
</blockquote>
I tried compute min using by definition of abs function.
I consider two cases:
<ol>
<li>when <span class="math-container">$x > 12$</span> we have:
<span class="m... | We can use C-S and the triangle inequality:
<span class="math-container">$$\frac{|x-12|}{5}+\frac{\sqrt{x^2+25}}{3}=\frac{|x-12|}{5}+\frac{\sqrt{(3^2+4^2)(x^2+5^2)}}{15}\geq$$</span>
<span class="math-container">$$\geq \frac{|x-12|}{5}+\frac{|3x+20|}{15}=\left|\frac{12}{5}-\frac{x}{5}\right|+\left|\frac{4}{3}+\frac{x}... | Your reasoning is spot on!
Indeed, since both terms are never negative, it is certain that there is a minimum. But you have exhibited the only possibility. It follows that that is indeed the minimum value of the function.
| https://math.stackexchange.com |
54,045 | [
"https://mathoverflow.net/questions/54045",
"https://mathoverflow.net",
"https://mathoverflow.net/users/12676/"
] | There seems to be a wide variance in what faculty members view as their responsibilities as a student’s adviser. I understand that some advisers go above and beyond what's expected and we can't hold everyone to their standards. I also understand that there is no one right method and two advisers with very different met... | Claim 1: If $x\in H_2X$ is a homology class, then there exists a 2-dimensional CW complex $K$ and a map $f:K\to X$, such that $x$ is in the image of $f_*:H_2K\to H_2X$.
Claim 2: If $X$ is simply connected with $\pi_2X=0$, then every map $K\to X$ from a 2-dimensional CW complex is null homotopic.
Claim 1 can be prov... | You can build a weak homotopy equivalence $K \to X$ from a CW complex with $2$-skeleton
$K_2 = *$. Then cellular homology gives the result, provided your homology
respects weak equivalence.
| https://mathoverflow.net |
51,525 | [
"https://mathoverflow.net/questions/51525",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10820/"
] | hello, I need a book where i can find the proof for the classification of 1-dimensional topological manifolds.
(i already have Milnor's for the classification of 1-dimensional smooth manifolds)
thank you
| If I remember well, Introduction to topological manifolds (Lee) proves the classification theorem for 1-dim manifolds.
| Fuks, D. B.; Rokhlin, V. A. Beginner's course in topology. Geometric chapters. Springer Series in Soviet Mathematics. Springer-Verlag, Berlin-New York, 1984.
For dim 1 and dim 2 manifolds.
| https://mathoverflow.net |
62,441 | [
"https://dba.stackexchange.com/questions/62441",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/36604/"
] | I'm working on a school project and I need some help.
I want to create three tables which should contain these fields:
<strong>User</strong>
UserID (AI, PK),
UserEmail,
UserPassword
<strong>WorkGroupMember</strong>
GroupID(PK, FK WorkGroup)
UserID (PK, FK User)
<strong>WorkGroup</strong>
GroupID (AI, PK),
GroupFac... | First you should clarify the relationships between your entities by asking these questions:
<ul>
<li>Can a facilitator of a group be a user that is not a member of that group?<br>
Or a facilitator must always be a member of that group?</li>
<li>Do groups always have a facilitator? (your design indicates: yes)</li>
<li... | An alternative might be to have a field in <code>WorkGroupMember</code> called <code>IsGroupFacilitator</code> (or something else suitably descriptive of its function) which defaults to whatever you decide should mean no (perhaps 0 if it is a numeric type) but can be set to a non-zero value (1 is considered the traditi... | https://dba.stackexchange.com |
134,911 | [
"https://dba.stackexchange.com/questions/134911",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/73087/"
] | I try to find companies whose fare has minimum fare of destination which more than one companies use that destination. My command;
<pre><code>SQL> select tickets.bus_id bus, tickets.fare fare, route.destination dest
from tickets left join route on route.route_id=tickets.route_id;
BUS FARE DEST
--... | You want to aggregate an aggregate, so the easiest way to see this is to group twice, I believe. You may also want to rename the subquery table aliases I've used here to make them more meaningful.
<pre><code>SELECT sub2_.bus, MIN(sub2_.fare), MIN(sub2_.dest)
FROM (SELECT sub1_.bus, MIN(sub1_.fare) AS fare, sub1_.des... | I think you have to include the column bus in the group by
| https://dba.stackexchange.com |
69,451 | [
"https://biology.stackexchange.com/questions/69451",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/-1/"
] | First off, I don't know if this is the correct site to post this question as it could possibly fit into others? If so, please flag it to be moved as I would appreciate that very much.
Now, if my body was at a temperature of 30 degrees (celcius), I would feel somewhat warm. However if I then dipped my hand into a bowl ... | Your sensation of heat is dependent on the <strong>change in temperature</strong> of your skin, which is roughly proportional to the difference in temperature between skin and material.
However, temperature difference is much less important than the <strong>transfer of heat</strong> between your skin and an object, wh... | My first suggestion would be to try this yourself as an experiment, including the variations you mentioned. In each situation, take a guess at what the temperature of the water is, then write it down, then take a measurement with a thermometer to compare your perception versus the real temperature. Then try comparing i... | https://biology.stackexchange.com |
248,731 | [
"https://math.stackexchange.com/questions/248731",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/51389/"
] | We have the Cartesian product $B \times B$ and there we have the addition
$$(f,g)+(h,k)=(f+h,g+k)$$
and the multiplication
$$(f,g) \cdot (h,k)=(f\cdot h+g\cdot k,f\cdot k+g\cdot h).$$
I want to find the identity element of the group related to the addition. So I must have something like $(f,g)+e=(f,g)$. What do I do no... | The σ-algebra generated by a collection of sets is the smallest σ-algebra containing all the given sets.
The σ-algebra generated by a collection $\mathcal F$ of functions is the smallest σ-algebra so that all those functions are measurable with respect to that σ-algebra. Equivalently, it is the σ-algebra generated by ... | Yes, it is the same:
A sigma algebra generated by a collection of random variables (say, real-valued) is the smallest sigma algebra that makes these random variables measurable: that means that it is the sigma algebra generated by the pre-images of any interval of the real line (with rational boundary points, if you pr... | https://math.stackexchange.com |
33,850 | [
"https://dba.stackexchange.com/questions/33850",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/18316/"
] | I am working on various query optimization techniques. I reduced the query execution time from 1 minute to 12 seconds just by adding a Non-Clustered-Index on a table including one column (which is used in multiple where conditions) but DBA is very picky about adding indexes.
I would like to know if it makes any differ... | Synopsis on the approach of adding NCI dynamically on a high traffic table :
The time involved in creation of NCI on a temp table was much more than reading it. So, overall it took much more time to execute the query.
NCI on actual table is much much faster.
Finally, decided to optimize the query a little bit and creat... | Temporary tables comply to the same rules as permanent tables when it comes down to indexing. The only difference is in the storage location, which is Tempdb for temporary tables.<BR> However, if you are adding an index to a table that is heavily written, you have to take into account the write vs. read tradeoff.<BR>
... | https://dba.stackexchange.com |
186,644 | [
"https://softwareengineering.stackexchange.com/questions/186644",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/48898/"
] | I'm developing a suite of software tools that I need help with which is why I want to release my software open-source. People should be able to use and modify my code as they please while contributing to my project. Ultimately, the tools that I develop will require a paid commercial license, but may be free to those fo... | Licensing some part of the code under open-source license means that this part will be always open-source. Then you can't control how the people will use it. If you choose copyleft license, you only can be sure that no one will be allowed to use this code for closed source projects.
If you choose some permissive licen... | <strong>Disclaimer: talk to an attorney. I am not an attorney.</strong>
You are contemplating the need to be able to dual-license your software someday down the road. The authority to licence something is derived (directly or indirectly) through owning the copyright to the materials.
Therefore, you <strong>NEED</st... | https://softwareengineering.stackexchange.com |
57,329 | [
"https://chemistry.stackexchange.com/questions/57329",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/32081/"
] | I would like to know how adsorption works particularly between a gas and a solid. I know that there is an attraction of intermolecular forces between the gas molecules and the solid surface molecules. But how can this attraction suck all the gas molecules onto the solid surface? I thought the intermolecular forces cann... | The different occupations you suggest correspond to different spin states. Therefore, they are quite simple to distinguish.
On the other hand, the ground states are often degenerate (in the terms of 5 equivalent d orbitals available). Therefore the lowest (and sufficient) level of theory is the CAS-SCF with inclusion o... | To have such detailed information you need to use a highly correlated method (CI) adding spin-orbit coupling. Dirac should do the job.
Of course you cannot "force" the electrons on orbitals, but check the different spin states.
| https://chemistry.stackexchange.com |
644,897 | [
"https://electronics.stackexchange.com/questions/644897",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/327542/"
] | I'm not getting a clear answer to this from my reading or reviewing previous questions here. Is there a difference in the power supply requirements if LED strips are wired in parallel vs serial? Most of the examples use/imply serial wiring.
Specifically if I have a strip that is rated;
24VDC
1m = 6.8 watts
3m = 19.8 ... | Most LED strips are constructed so that you can cut them at periodic intervals so you can customize the length. What this means is that the LEDs are arranged in a parallel-series configuration. For instance, you might have a 24V strip that can be cut at every 12 LEDs. So if you have a strip of 48 LEDs it is electricall... | If the strips are wired in parallel you will require the same voltage as for one strip, but the supply must be able to supply the sum of the currents for each strip (for 2 strips, twice the current for one strip).
Wiring the strips in series (positive of the supply to positive of one strip, negative of that strip to p... | https://electronics.stackexchange.com |
69,130 | [
"https://stats.stackexchange.com/questions/69130",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/29876/"
] | Using Amelia in R, I obtained multiple imputed datasets. After that, I performed a repeated measures test in SPSS. Now, I want to pool test results. I know that I can use Rubin's rules (implemented through any multiple imputation package in R) to pool means and standard errors, but how do I pool p-values? Is it possibl... | No: KL divergence is only defined on distributions over a common space. It asks about the probability density of a point $x$ under two different distributions, $p(x)$ and $q(x)$. If $p$ is a distribution on $\mathbb{R}^3$ and $q$ a distribution on $\mathbb{Z}$, then $q(x)$ doesn't make sense for points $p \in \mathbb{R... | Yes, the KL divergence between continuous and discrete random variables is well defined. If $P$ and $Q$ are distributions on some space $\mathbb{X}$, then both $P$ and $Q$ have densities $f$, $g$ with respect to $\mu = P+Q$ and
$$
D_{KL}(P,Q) = \int_{\mathbb{X}} f \log\frac{f}{g}d\mu.
$$
For example, if $\mathbb{X} = ... | https://stats.stackexchange.com |
38,937 | [
"https://security.stackexchange.com/questions/38937",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/28273/"
] | I want to design a system that hinges on ECDSA. All messages are signed using the algorithm, and this is used to prevent spoofing.
However, if a user were to somehow lose control of their key, they would be forced to create a new key to sign their messages.
Is there any mechanism that can be implemented to transition... | Yes, but there are potentially far reaching consequences. I'm going to answer your question more generally.
The simple answer is to revoke the signing key. As easy as that answer is for a user key, there are still issues. For example, is everyone who might rely on that signature subscribed to and updating based on ... | Both PGP and the global SSL PKI solve this problem in roughly the same way. You create a super "trusted" key with a long expiration which you guard with religious fervor; key stays encrypted, tucked away in a holy temple, only ever glimpsed by duly anointed CSOs, that sort of thing. It's the one you trust. You do not u... | https://security.stackexchange.com |
115,449 | [
"https://mathoverflow.net/questions/115449",
"https://mathoverflow.net",
"https://mathoverflow.net/users/29663/"
] | Excercise 2.2.1 in Weibel ("An Introduction to Homological Algebra") states that an object $P$ in the category of chain complexes over an abelian category is projective if and only it is a
split exact complex of projectives.
I was able to solve the only-if-part but I have touble with the if-part and would be glad if... | The trick with Weibel's hint is to decompose $P$ as direct sum of complexes of type
$$\cdots \to 0 \to P_1 \xrightarrow{\cong} P_0 \to 0 \to \cdots$$
Since $P$ is split exact, we can write $P_n=P_n^{'}\oplus P_n^{''}$ where $P_n^{'}=\text{ker}(d_n)$ and $d_n^{''} =d_n|P_n^{''}:P_n^{''} \to \text{im}(d_n)=P_{n-1}^{'}$... | As another solution I want to offer a closed formula for the sought-after morphism $g=(g_i):P \to X$:
Since $P$ is split exact, it's contractible, i.e. there are maps $s_i : P_i \to P_{i+1}$ with $s_{i-1}d_i^P + s_i d_{i+1}^P=id_{P_i}$. Moreover, since each $P_i$ is projective we can choose $h_i: P_i \to X_i$ such th... | https://mathoverflow.net |
409,122 | [
"https://mathoverflow.net/questions/409122",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3441/"
] | Let <span class="math-container">$m, n\in \mathbb{N}$</span> and <span class="math-container">$|x| < 1$</span>. I look for hints to derive an analytic formula for
<span class="math-container">$$f_{m,n}(x) = \sum_{k \in \mathbb{N}} {n + k \choose k} {m + k \choose k} x^{k}. $$</span>
| This is Gauss' hypergeometric function
<span class="math-container">$F(n+1,m+1,1;x)$</span>. You can then apply the huge theory of hypergeometric functions to derive further expressions. For instance, Euler's transformation formula gives the alternative expression
<span class="math-container">$$\frac 1{(1-x)^{m+n+1}}\,... | With proofs abound, I would like to record yet another instance of application due to the Wilf-Zeilberger techniques. The aim is to prove the identity shown above (from GH from MO, Hjalmar Rosengren):
<span class="math-container">$$\sum_r\binom{m+n+k-r}{k-r}\binom{m}r\binom{n}r\binom{m+k}k^{-1}\binom{n+k}k^{-1}=1.$$</s... | https://mathoverflow.net |
141,870 | [
"https://chemistry.stackexchange.com/questions/141870",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/63035/"
] | We learned in school that state change is a matter of molecules moving faster and faster. And we learned "heat em up, speed em up, spread em out". Why then can some liquids have higher temperatures than some gases?
| <strong>Interactions between molecules determine whether something is a gas, solid or liquid not just temperature</strong>
You have missed an important component of why some things are gases and others are liquids. While, in general, the hotter things are the more the molecules are spread out and the faster they will m... | Of course heating a gas increases the speed of the molecules. But the speed and the existence of the gas molecules do not depend exclusively on the temperature. The mass and the interatomic forces have a greater importance.
First, light molecules are easier to put in the gas state than heavy molecules. That is why :
<u... | https://chemistry.stackexchange.com |
29,001 | [
"https://softwareengineering.stackexchange.com/questions/29001",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/11062/"
] | I'm developing an application for Android/Java. This application is a kind of password manager, so I'm storing encrypted passwords under the hood of a master password. There are a number of encryption algorythms DES/AES/BlowFish/TwoFish and so on. My intention is to develop application which is free of commercial copyr... | As stated before, algorithms are not copyrighted, only individual implementations. Algorithms can be patented, however. You should read the licensing information for your platform to ensure that you are in the purview of their license grants. Presuming that you are, in effect, dynamically linking to an encryption li... | IMO, algorithms are not copyrighted, libraries are. But if you are using something that comes by default from JAVA, then there will not be any copyrighted issues.
| https://softwareengineering.stackexchange.com |
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