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[ "https://cstheory.stackexchange.com/questions/1410", "https://cstheory.stackexchange.com", "https://cstheory.stackexchange.com/users/-1/" ]
I don't quite understand why almost all SAT solvers use CNF instead of DNF. It seems to me that solving SAT is easier using DNF. After all, you just have to scan through the set of implicants and check whether one of them contains not both a variable and its negation. For CNF, there's no simple procedure like this.
The textbook reduction from SAT to 3SAT, due to Karp, transforms an arbitrary boolean formula $\Phi$ into an “equivalent” CNF boolean formula $\Phi'$ <strong>of polynomial size</strong>, such that $\Phi$ is satisfiable if and only if $\Phi'$ is satisfiable. (Strictly speaking, these two formulas are not equivalent, be...
Most of the important things were said but I would like to stress a few points. <ol> <li>satisfiability of a DNF formula is P</li> <li>satisfiability of a CNF formula is NP</li> <li>testing if a CNF formula is a tautology is P</li> <li>testing if a DNF formula is a tautology is coNP</li> <li>negating DNF yields CNF an...
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176,636
[ "https://mathoverflow.net/questions/176636", "https://mathoverflow.net", "https://mathoverflow.net/users/56228/" ]
can anyone help me with the following statement (it is part of a bigger proof where it is not explained). Let $B$ be a finite type commutative $A$-algebra (where $A$ is a commutative ring), and consider the kernel $I$ of the diagonal homomorphism $B\otimes_A B\to B$ (defined by $b\otimes b'\mapsto bb'$). Then $I$ is ...
Let $I'\subset B\otimes_A B$ be the ideal generated by the elements $b_i\otimes 1-1\otimes b_i$, and define $$ R=\{b\in B:b\otimes 1-1\otimes b\in I'\}. $$ It’s not hard to check that $R$ is an $A$-subalgebra of $B$, so that $R=B$ (because the generators $b_i$ are in $R$ by construction). Now $b\otimes 1-1\otimes b\in ...
It's a (pretty easy) standard exercise in algebra to show $I=(b\otimes 1 - 1 \otimes b\mid b \in B)$. Let $a\in A, b,c \in B$. Then $$ab\otimes 1 - 1 \otimes ab = (a\otimes 1)(b\otimes 1 - 1\otimes b)$$ $$bc\otimes 1 - 1 \otimes bc = (b\otimes 1)(c\otimes 1 - 1 \otimes c) + (b \otimes 1 - 1 \otimes b)(1 \otimes c)$$...
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89,708
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Here is a classic problem: <blockquote> <em>A 60kg boy and a 40kg girl are sitting in front of each other on skateboards on a frictionless horizontal surface. The boy pushes the girl and the girl gains a velocity of 0.3m/s during the 0.5s the boys hand was in contact with her. What is the boy's resulting velocity?</...
In both of your solutions, you attempted to use Newton's 3rd law: $$\vec{F}_{1\rightarrow2}=-\vec{F}_{2\rightarrow1}.\tag{Newton's 3rd law}$$ You did this correctly in your first method ("Newton's law method") but incorrectly in your second method ("Kinetic energy method"). In your first method, you explicitly set the...
Equal and opposite forces do not imply equal energies. Conservation of momentum is what is important here. You'll notice that the two children end up with equal and opposite momenta when all is said and done. But energy is not being conserved because this is an inelastic collision (i.e. work is being done). Moreover, e...
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71,656
[ "https://electronics.stackexchange.com/questions/71656", "https://electronics.stackexchange.com", "https://electronics.stackexchange.com/users/22885/" ]
What I understood at least at a basic level the operation boost converter, the inductor supplies output current when the switch is OFF. <img src="https://i.stack.imgur.com/pSjkn.png" alt="enter image description here"> <img src="https://i.stack.imgur.com/tc3PR.png" alt="Switch is OFF"> <br> When the switch is ON the th...
<blockquote> What actually is the output current of a boost converter? </blockquote> Hopefully the diagrams below will explain the output current and the difference between continuous and discontinuous operation. <img src="https://i.stack.imgur.com/x2jme.jpg" alt="enter image description here"> Look at the blue tr...
As your current graphs show, the inductor current is not constant, so the concept of 'the inductor current' being a single (time-independent) value is not valid. What is valid though, is that the inductor current has no sudden changes (the first derivative is always finite). This is a fundamental property of an induct...
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251,993
[ "https://softwareengineering.stackexchange.com/questions/251993", "https://softwareengineering.stackexchange.com", "https://softwareengineering.stackexchange.com/users/17948/" ]
I'm learning about unit tests, and have a doubt for a test i want to do, to implement an "AND" logic gate <pre><code>A B A^B 0 0 0 0 1 0 1 0 0 1 1 1 </code></pre> how can i test for a method that works like AND gate?, is this what a mock object is? or stub? Thanks, Please provide pseudo code,
<ul> <li>It's a good practice.</li> <li>You are following the scientific method.</li> <li>If you change several things before any testing, then the testing of each will be more difficult, and perhaps not reliable, since preconditions will be more difficult to prepare and the different changes can interact with each oth...
Making lots of little changes and testing each one is not a bad thing. It allows you to see the effect of each change, and then when one change causes a problem, it's much easier to know <em>which</em> change caused issues - the most recent one! If you have a task list with 10 items, and you do all of them at once and...
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75,875
[ "https://mathoverflow.net/questions/75875", "https://mathoverflow.net", "https://mathoverflow.net/users/4037/" ]
I am asking in the sense of isometry groups of a manifold. SU(3) is the group of isometries of CP2, and SO(5) is the group of isometries of the 4-sphere. Now, it happens that both manifolds are related by Arnold-Kuiper-Massey theorem: $\mathbb{CP}^2/conj \approx S^4$; one is a branched covering of the other, the quotie...
Why would you think that they are related? The map $\mathbb{CP}^2/\text{conjugation} \to S^4$ is only $SO(3)$-equivariant, where $SO(3) \subset SU(3)$ consists of the real matrices and $SO(3) \subset SO(5)$ is the maximal subgroup acting irreducibly on the 5-dimensional vector representation of $SO(5)$. Not sure if t...
$SU(3)$ has center of order 3 and $SO(5)$ has center reduced to the identity. In fact they are not even locally isomorphic: $SU(3)$ is of Cartan type $A_2$ and $SO(5)$ is of type $B_2$.
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33,805
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What the question says. For example, if I knew the specific heat capacities of lithium and oxygen, could I work out the specific heat capacity of lithium oxide with no further information?
There is not much connection between the heat-capacity of a compound and the heat-capacity of the elements it is made of. Heat capacity is primarily coming from the low frequency vibrations of the lattice (if it is solid), and vibration+rotation+translation if it is liquid or gas. These have no connection with the prop...
Yes, one can calculate the specific heat capacity of the compound from its constituent elements that is just some of its constituent element's specific heat capacity. As it is known that specific heats of elements remain unchanged when they enter into compounds. However, the density/volume/mass may change and so the he...
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2,854,177
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I'm currently studying taking the second derivative of equations and I have been told the symbol used to represent second derivative is <blockquote> $$\frac{d^2y}{dx^2}$$ </blockquote> I was just wondering, why this symbol is chosen? Why is it not $$\frac{dy^2}{dx^2}$$ or $$\frac{d^2y}{d^2x}$$
The first derivation is $$\dfrac{dy}{dx}$$ taking other derivation respect to $x$ has the representation $\dfrac{d}{dx}$, then for second derivative we write $$\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right)=\dfrac{d^2y}{dx^2}$$ means in non-standard symbol $$\color{blue}{\dfrac{d\times d~y}{(dx)^2}}$$
Differentiation by $x$ takes $y$ to $$\frac{dy}{dx}$$ or if you like, to $$\frac{d}{dx}y.$$ One would write, say $$\frac{d}{dx}\cos x=-\sin x$$ etc. So the derivative of $dy/dx$ is then $$\frac{d}{dx}\frac{dy}{dx}$$ which one naturally abbreviates as $$\frac{d^2y}{dx^2}.$$
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1,925,478
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I did the right implication: $U_{y},V_{y}$ open disjoint sets such that $x \in U_{y}, y \in V_{y}$ Then $\cup_{y \in G} V_{y}$ is open such that $y$ is in and $x$ not. Then $\cup_{y \in G} V_{y} = G - \{x\}$ is open, therefore $\{e\}$ is closed. But how to do the left? I know that for every neighborhood $L$ of $e$ t...
HINT: Assume that $\{e\}$ is closed. Let $\mathscr{U}$ be the family of all open nbhds of $e$. <ul> <li>Show that $\bigcap\mathscr{U}=\{e\}$. (This is in fact equivalent to the assertion that $\{e\}$ is closed.)</li> <li>Show that if $\bigcap_{U\in\mathscr{U}}\operatorname{cl}U=\{e\}$, then $G$ is Hausdorff.</li> </ul...
Hints: (1) A topological space $\;X\;$ is Hausdorff iff the diagonal $\;\Delta:=\{ (x,x)\;/\;x\in X\}\;$ is closed in $\;X\times X\;$ (with the product topology) . (2) Now look at the continuous (why?) map $$F:X\times X\to X\;,\;\;f(x,y):=xy^{-1}\;,\;\;\text{and check}\;\;F^{-1}(\{e\})$$
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63,065
[ "https://stats.stackexchange.com/questions/63065", "https://stats.stackexchange.com", "https://stats.stackexchange.com/users/26579/" ]
Say I have a database with <code>10000</code> protein sequences of the same species in it. I was to study if mutations at positions <code>i</code> and <code>j</code> are correlated. I can decompose each sequence into strings of binary variables <pre><code>11 - i is mutated, j is mutated 10 - i is mutated, j is not mut...
In the Bayesian model you are subtracting something (mean_factor_b1, etc.) from each of the predictor variables. But you are not doing the same thing in the call to <code>lm</code>. Assuming that "mean_factor_b1" is the mean of the "b1" variable, etc. this means that the intercept in the Bayesian model represents t...
I believe Greg Snow's answer is the probable cause, and have given it a +1. But, there are two other considerations: <ol> <li>Did the BUGS calculations properly converge? It may not have. Did you do any convergence diagnostics/plots? Did you try different initial values?</li> <li>Note that the <code>lm</code> regress...
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366,613
[ "https://electronics.stackexchange.com/questions/366613", "https://electronics.stackexchange.com", "https://electronics.stackexchange.com/users/113720/" ]
Does anybody know how to enter curved text in Altium PCB editor? For instance, you have an arc and you want to put some string to follow the curve of the arc. I couldn't find that option anywhere and also I didn't find anything on the internet.
You can create it with some appropriate tool such as Adobe Illustrator or Inkscape (open-source) and then import it as you would a logo. (There's probably also some way to do it with scripting, but I guess it would be more difficult to learn that than use a tool designed for graphic editing).
If it is only a short piece of text you can create several individual pieces of text to spell your word and then and them individually.
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356,709
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I am very puzzled with the obsession that many people seem to have with using Microsoft frameworks. I have seen several tutorials and projects (both open and closed source) that seem to utilize all of the additional .NET framework libraries and code when they are not really needed. To be clear, I am not talking about c...
When you start a project and have a particular need, you have a choice: <ul> <li>Either you implement your own solution from scratch,</li> <li>Or you use an existent library or framework.</li> </ul> When implementing your own solution, you introduce several risks: <ul> <li>The needs may evolve, requiring you to cons...
Yes, most places I've worked at use some of those libraries. It is tempting to see them as bloat, I for one dislike Entity Framework and tend to 'hand crank' my repositories. But, in fact the Microsoft libraries are very well written and are often complicated because they handle stuff you haven't thought of, or don't...
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482,158
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As I know, high speed transceivers always use a 0.1uF or 0.01uF capacitor for AC-coupling. <pre><code>Tx---&gt;capacity-------------------&gt;Rx | end resistor </code></pre> Capacitor and end resistor are a high-pass filter. If end resistor is 50 ohm. I calculate bandwidth with <span...
It's a <em>HIGH</em>-pass filter, not a low-pass filter. That cutoff frequency you calculated is the LOWEST that can get through, not the highest. Frequencies lower than that are blocked, and frequencies higher than that are passed.
A binary data signal isn't a single frequency. If it's truly random, it will have frequency content from near DC all the way up to about half the data rate (i.e. a 1 Gbps signal has content from DC to ~500 MHz). Using a smaller capacitor value would block some of the low-frequency content of the signal, resulting in ...
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111,096
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Clearly AJAX improves the user interface but does this also decrease server load? You would think it does because the entire page will not have to be served up each time, but maybe there are other variables I'm not considering.
It depends on what you're doing and how you're doing it. <ul> <li>If you're replacing full page loads with AJAX requests (i.e. only doing AJAX calls when a user clicks on what would have been a full page load) then AJAX will decrease server load because you're (presumably) doing less processing and returning less data...
There are other factors you are not considering -- in most cases, AJAX will increase server load. In a typical, non-ajax scenario, a user loads one big page every few seconds or few minutes. Yes, that single page is a bit more work for the server, but it has plenty of time between requests to recover and serve other re...
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192,752
[ "https://dba.stackexchange.com/questions/192752", "https://dba.stackexchange.com", "https://dba.stackexchange.com/users/140256/" ]
We have a simple postgres database: <pre><code>book: id: primary key, integer title: varchar borrowed: boolean borrowed_by_user_id: foreign key user.id user: id: primary key, integer name: varchar blocked: boolean </code></pre> And now I would like to "borrow a book" <code>b</code> to a user <code>u</c...
I finally managed to daisy-chain. <ol> <li>Since the binlogs were removed, I copied <code>rsync</code> them each 30 seconds</li> <li>Dump Slave A to Slave B</li> <li>Stop MySQL server <code>service mysql stop</code></li> <li>Copy back the deleted binlogs on Slave A in the MySQL data folder</li> <li>Add the binlogs fil...
Master -> A -> B <code>binlog</code> on A needs to be turned on. B must use the binlogs from A, not from the Master. So... <ol> <li>Turn on binlogging on A.</li> <li>Stop replication from Master -> A.</li> <li>Dump A</li> <li>Load dump onto B</li> <li><code>CHANGE MASTER</code> to point B to A.</li> <li>Start repli...
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107,803
[ "https://mathoverflow.net/questions/107803", "https://mathoverflow.net", "https://mathoverflow.net/users/24796/" ]
I have a simple terminology request: recall that given sets $A$ and $B$, a <em>relation</em> $R$ from $A$ to $B$ is any subset of the product $A \times B$. Thus, one may view a relation as a function $A \times B \to \lbrace 0,1 \rbrace$ where $(a,b)$ maps to $1$ if and only if it lies in $R$. What I'm looking for is t...
This is called an <em>$L$-valued relation</em>, when $L$ is the target of the function, which can be viewed as the collection of possible truth values. Thus, a $2$-valued relation is just an ordinary relation of classical logic, where every instance has truth value either true or false. But for any Boolean algebra $\...
I'm not sure if there is a name for situations like $\mathbb{R}^{+}$, but if your ordered space is a Heyting algebra, then it's still just called a relation. The notion of a relation makes sense in any category with finite products, even when the objects don't have an underlying set structure. A relation from $A$ t...
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437,936
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I am working on a problem with lots of if-then-else calculations. I am trying to compartmentalize the logic to make it more maintainable and less error prone. But, as I try options, I don't see what the best practice should be. By way of example, suppose I am building an order fulfillment system. One thing that must...
It helps to define the concepts of the problem you are dealing with. My understanding is that you have a <em>tax policy</em> that is specific to each <em>state</em> and depends on attributes of a <em>customer</em> in order to calculate the tax of an <em>item</em>. The tax policies seem to be quite simple, if we take th...
This is essence of programming - the multitudes of if-else - the nestings - and ofcourse the loops. You have to iterate over each customer, so there is a loop at top. May be your code need to handle only one customer so you can may be omit this level. Then you have to go through each order of the (current) customer. Th...
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305,404
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Sometimes the user starts an extended technical operation that takes a while to execute. In these cases, it's usually nice to display some kind of progress bar, along with information about which task is being executed right now. In order to avoid close-coupling the UI and the logic layers, it's usually best to have ...
<blockquote> Pass a mutable object to the back-end, and have the back-end make changes to it on progress. The object notifies the front-end when a change occurs. </blockquote> It's difficult to balance efficiency if the backend notifies in this respect. Without care you might find that incrementing your progress...
This is the difference between a <em>push</em> and <em>pull</em> notification mechanism. The mutable object (the <em>pull</em>) will need to be repeatably polled by the UI and synchronized if you expect the back-end task to be executed in a background/worker thread. The callback (the <em>push</em>) will only create ...
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93,687
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I currently have a master postgresql 9.4 server containing many databases on Ubuntu 14.04. I tried to use Barman to setup backup, but would like to set up streaming replica so that when the master goes down, I can promote the standby replica to be the new master. I looked in to repmgr, but this will only produce a rea...
As soon as your recovery thread is interrupted, making it impossible to recover from an earlier backup to the current time, the remedy is to take a backup before something more serious happens. Next investigate how the archives became corrupted and solve that. Backups are of no importance, important is the ability to...
As soon as your instance is down ; start recovery to its latest current time by getting SCN from control file and try to get any of old archive log and start recovery with reset log option. After starting instance try to investigate the basic reason of corruption and malfunctioning of system.
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8,737
[ "https://quantumcomputing.stackexchange.com/questions/8737", "https://quantumcomputing.stackexchange.com", "https://quantumcomputing.stackexchange.com/users/9006/" ]
I tried to measure quantum state with a quantum state tomography. However, I encountered a situation when two different quantum states had the same density matrix. In particular, these states were <span class="math-container">$\frac{1}{\sqrt{2}}|0\rangle + \frac{1+i}{2}|1\rangle$</span> and <span class="math-container"...
There isn't. A density matrix encodes all the knowledge available about a state, therefore if two states are described by the same density matrix, they are indistinguishable. Ket vectors differing by only a global phase have always the same density matrix, and represent the same physical state.
The question presupposes a misconception that the vector form of a state <span class="math-container">$|\psi\rangle$</span> exists independently of its density operator form <span class="math-container">$|\psi\rangle\langle\psi|$</span>, which is often described as secondary. In reality, the density operator of a stat...
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348,920
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C# 7 has a nice new language feature: The De<strong>con</strong>structor. It is possible to use it for value tuples for instance. However, I can also create my own deconstructors for my own classes. Why would I do that? My classes have properties. So individual items can be accessed anyway.
Deconstruction offers considerable brevity and clarity over the traditional alternative, and provides support for a fully functional-style of programming. Consider this simple, one-line deconstructor example from Microsoft: <pre><code>var (first, middle, last) = LookupName(id1); </code></pre> To do the same thing i...
"Use cases" is a slightly strange verbiage for the question. This doesn't really allow you to do anything you couldn't before. It's simply neater in some cases. The only major thing I can think of is that it gives you some limited compile-time checking. For example, suppose you have a <code>UsAddress</code> class. You...
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101,998
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I need some help with my SQL 2005 server. I am trying to setup log shipping, I've successfully done so for all user-databases, except one. From the looks of it, it once had log shipping configured until the secondary server was decommissioned before log shipping could be deleted. The old DBA deleted the old jobs. So...
After further investigation, I found the answer. I ran <pre><code>Exec sp_delete_log_shipping_primary_secondary @Primary_database = N'DATABASE_NAME' ,@secondary_server = N'SECONDARY_SERVER_NAME' ,@secondary_database = N'SECONDARY_DATABASE_NAME' </code></pre> To delete all reference to that server. followed by <pre...
If something is still setup on the secondary server you need to run <code>sp_delete_log_shipping_secondary_database</code> there. You can clear the log shipping configuration on the primary by executing <code>sp_delete_log_shipping_primary_secondary</code> <pre><code>USE master; GO EXEC master.dbo.sp_delete_log_shi...
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751,190
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It may sound like an old problem but I don't find a good reference. Gases are physically soluble in water. Given a water column without any salts solved in it. Air with a given concentration <span class="math-container">$c_0$</span> (maybe as mol <span class="math-container">$\text{CO}_2$</span> per litre or whatever u...
regarding the first statement, &quot;magnitude&quot; is the &quot;quantity&quot; of something and vectors with opposite sign can have same &quot;quantity&quot; since it's not depended on direction of vector, for example, if you and your friend are playing tug of war and none of you is being displaced from your initial ...
<em>If a vector pointing upward has a positive magnitude, a vector pointing down has a negative magnitude.</em><br /> Magnitude is always positive.<br /> One way of thinking of this is to think of the length (magnitude) of a vector and note that length (magnitude) can only be positive.<br /> A correct statement would b...
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29,806
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Every once in a while I have to set up an account on a site that, while apparently at least not storing my password in plaintext, still force me to choose from a limited set of security questions that can be used for password recovery purposes. Since the questions are usually moronically easy to answer by some googling...
"Security questions" are just an alternative password which is not used often, but which, presumably, will <em>not</em> be forgotten by the user. Since it <em>is</em> a password-equivalent information, treat it as such: use true, high-entropy passwords as answers to security questions. Of course, since you will not ent...
My current "solution" is entering an arbitrary long senseless sentence that I don't even intend to remember and instead store that and my password in (separate) KeePass files, and maybe complaining to the webmaster about this. That way it's unlikely someone else can answer the "secure" question without any less effort ...
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1,720
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I have a 2002 Ford Focus. Whenever the car is idling the heat gauge goes up at an alarming rate and goes the farthest into the red that it can if left alone. Now if I rev the engine a little the temperature goes down (no matter the gear), I took it to a couple of mechanics and they couldn't figure it out. What could...
Usually coolant temperature problems as you described (without leaks) are caused by any of the following or a combination thereof: <ul> <li>Partially blocked or missing ducting to the radiator so either not enough air reaches the radiator or it goes past the radiator instead of through it. This should be relatively ea...
Another thing to check is the condition of the radiator - if it is missing a lot of fins or full of gunk, it won't cool as efficiently. If your heater isn't working either then you definitely have a cooling system issue - I would replace the thermostat as a matter of course, and give the whole cooling system a good f...
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15,597
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Just experienced this, I saw lightning outside my window (not hitting our building or anywhere close to it), and immediately after the smoke detector went off for a short while. Can anyone explain what caused this?
Lightning is a nasty thing. Powerful. Very high current at very short rise time. This causes an strong EMP (ElectroMagnetic Pulse) which will be picked up by anything conducting. A 1m free-hanging wire may create a voltage peak between its ends. Even short connections may see spikes. Decoupling doesn't always work as t...
Just to add what the other folks have said... The fire alarms in my house are all inter-connected. When one goes off, they all go off. There are wires inside the walls/ceilings that connect them all. Those same wires, because they are long and unshielded, are excellent antennas and would easily pick up the EMI from...
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315,093
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I am going through Casella's statistical inference in one-semester standard statistic course and have mathematical background from Sheldon Axler's linear algebra done right and Louis Brand's advanced calculus. I wish to self-study these topics: <ul> <li>Lindeberg condition</li> <li>Analysis of variance</li> <li>Akaike...
<strong>Negative numbers</strong><br> When you subtract the mean, all differences will be centered around zero. So if you present your data in a barplot, the bars may suddenly be negative. However, how you apply standardization can have quite a different effect. <strong>Scale</strong><br> When you divide by the standa...
The problem probably arises, because you compare two different kinds of data. In your first bar plot, all measurements of both subjects are displayed together and undistinguishable. Frans Rodenberg has commented on that in the first comment. In the next bar graph, one part of the data has been treated differently than...
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I need to create a log table to stores the connections to out network (last 3 years, after that the log will go into backup). The hardware/software used is proprietary, and for accounting it just call our custom script with some arguments like this: <ul> <li>when a user connects (<code>our_script START user mac ip</...
You need to do log backups at least daily (we do them every 15 mintues). Read in books online about how to backup the log (not the daatbase, the log, these are two separate types of backups) and you should find directions for how to truncate the log without backing it up which you will likely need since you have let it...
This may be caused by <ol> <li>open transaction that you can see it by <code>@@TRANCOUNT</code> or <code>DBCC OPENTRAN</code>. </li> <li>you have many <code>CRUD</code> operation in your database so you database log grows too much.</li> </ol> If you don't need your log file you can detach your database and then rena...
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Whenever I find myself writing the same logic more than once, I usually stick it in a function so there is only one place in my application I have to maintain that logic. A side effect is that I sometimes end up with one or two line functions such as: <pre><code>function conditionMet(){ return x == condition; } </c...
Hehe, oh Mr Brown, if only I could persuade all the developers I meet to keep their functions as small as this, believe me, the software world would be a better place! 1) Your code readability increases ten fold. 2) So easy to figure out the process of your code because of the readability. 3) DRY - Don't Repeat Your...
Can a function be too short? In general no. In fact the only way to ensure that: <ol> <li>You have found all the classes in your design </li> <li>Your functions are doing only one thing. </li> </ol> Is to keep your functions as small as possible. Or, in other words, extract functions from your functions until y...
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I understand gray coding contributes to BER of QPSK, yet really don't understand why it brings improvement to SER. According to the relationship of SER and BER, it should be improved. Actually, when mapping the symbol to constellation points, the minimum distance between two different points remains the same, and that ...
Well, when <span class="math-container">$m=k$</span> the integral is: <span class="math-container">$$ \int_0^T e^{j(m-k)\Omega_0t} dt = \int_0^T e^{j \cdot 0 \cdot\Omega_0t} dt = \int_0^T dt = T $$</span> So as Juancho says in the comments, it's the same signal and so can't be orthogonal to itself.
The text is a bit cumbersome, in that it states "things" before defining them. And the zero-signal (or vector) is considered orthogonal to every other vector. This is why the sentence "If <span class="math-container">$I=0$</span> for..." seems unnecessarily complicated to me. And the <span class="math-container">$m$</s...
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Let $A$ be an invertible matrix. If $v$ is an eigenvector of $A$, show it is also an eigenvector of $A^k$ for all integers $k$. What are the corresponding eigenvalues?
Hint: go directly from the definitions.
By definition, $v \neq 0$ is an eigenvector of $A$ with eigenvalue $c$ if and only if then $Av = c v$. Proceed by induction to show $A^k v = c^k v$ for any $k$. If $k = 2$, then $A^2 v = A(Av) = A(cv) = c(Av) = c^2 v$. Suppose $A^{k} v = c^k v$. Then $$A^{k+1} v = A(A^{k}v) = A(c^{k}v) = c^{k} Av = c^{k+1}v.$$ Therefor...
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In the example below how do I get the rows where the swap id is the maximum value in relation to the reservationId? I am currently joining multiple tables to get customer, reservation, room etc information. But I don't want rows with a <em>swapnumber</em> of 1 if a value is higher then that. <pre><code> DECLARE...
You can use window functions: <pre><code>select id, reservationID swapNumber, oldRoom, newRoom from ( select id, reservationID swapNumber, oldRoom, newRoom , row_number() over (partition by reservationId order by swapNumber desc) as rn from @RoomExchange ) as T where rn =...
I know, it's an old question, but another solution would be FIRST_VALUE: <pre><code>SELECT DISTINCT re.reservationID, FIRST_VALUE(re.id) OVER (PARTITION BY re.reservationID ORDER BY re.swapNumber DESC ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW) id, FIRST_VALUE(re.newRoom) OVER (PA...
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I've been volunteered to sit down and talk about the life and work of a Developer with a 15 year old work experience student next week. The catches are that <ul> <li>I've got just half an hour, and</li> <li>I'll be just one of the people talking to her - other people in different roles in the business will also be ru...
I interact with high schoolers a lot, so I answer this question quite often. Keep in mind that 15 year olds are much easier to explain programming to than 50 year olds -- so you need not dumb things down or use far-fetched analogies. I usually start off with examples of what programs are: <ul> <li>Apps like iTunes, P...
I explained it to my five year old with the following: Me: "You know how, in stories, people say magic words, and change things in the world?"<br> Her: "Yeaaa?"<br> Me: "That's what computer programming is."<br> Her(quietly): "Wow." 15-30 minutes isn't enough to explain anything real, and explaining the underlying c...
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A tiny symmetry transformation may change the Lagrangian <span class="math-container">$L$</span> by a total time derivative of some function <span class="math-container">$f$</span>. This is a basic fact used in the proof of Noether's theorem. How can we see the effect of this total derivative term in the Hamiltonian f...
I suppose I figured out the "answer" to my very vague question, although the other answers here are also helpful. The "Hamiltonian Lagrangian" is <span class="math-container">$$ L = p_i \dot q_i - H. $$</span> Say we have a conserved charge <span class="math-container">$Q$</span>, that is <span class="math-container">...
The reason we don't talk about "changing the Hamiltonian by a total derivative" is because symmetries and conservation laws are usually handled differently in the Hamiltonian picture. In Hamiltonian mechanics, any function <span class="math-container">$f$</span> on phase space generates a flow on phase space, i.e. a ...
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Not sure if this is the correct place to put this question. Suppose you put a chicken breast in the oven and somehow managed to get it to levitate, i.e. it wasn't in contact with anything. Would the chicken still cook? Or is part of the reason why chicken breasts cook because they're typically placed on something me...
<h1>Yes, there is one universal electromagnetic field</h1> Clear answer: yes, there is only one electromagnetic field for the whole universe. Ontological answer: You can go to any spot in the universe and take a measurement. Even if you were to find a large chunk of space with "0" as your result (and for this part of...
You can define a "wind field" for the Earth by putting a weather vane at every point. You've probably seen drawings of these wind fields in weather reports; you can even define 'wind field lines' in analogy with electric and magnetic field lines. Then a completely analogous question is, "is there just one wind field on...
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1,000,340
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Let $A$ be an infinite set that includes rational numbers and is bounded. Let $B$ be a set of rational numbers $x$ s.t. the intersection $A\cap[x,\infty)$ is empty or includes finite number of subsets. <ol> <li>prove that $\inf B$ exists.</li> <li>prove or disprove $\inf B=\min B$</li> <li>prove or disprove that $\in...
Look at the structure of this $x(x+1)=0$. This will always have the solutions $x=0$ and $x=-1=n-1$ and if $n$ is prime that will be all. But if neither factor is zero, the ring will have zero divisors in it, and you are looking at two consecutive zero divisors, one even and one odd. So the first thing to test is $2 \...
If $n$ is not the power of a prime there are solutions distinct from $0$ and $-1$. Indeed, in this case you can write $n=ab$ where $a$ and $b$ are coprime. Bezout's identity gives: $$ax+by=1$$ That means that there are two consecutive integers, one of them is a multiple of $a$ and the other a multiple of $b$. This gi...
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Civic vti em1 I was checking my oil level and it kept showing below minimum, empty or just at minimum. At one point I added a quarter of a litre and the oil level when a a third above the minimum mark. However I remember checking the next day and it was slightly above the maximum mark. Having read some questions ...
<blockquote> I take it one should not check it when running or too soon after running and if it shows empty or below minimum in these cases, one should not worry? </blockquote> As far as engine oil goes, there are very few cars which you should check the engine oil while running. To check the oil, do the following...
To read the oil level: (general method: use the manufacturers method if available) 1) stop engine &amp; wait 10 minutes. 2) remove dipstick, wipe clean and refit. 3) remove dipstick and then read level. 4) adjust oil level appropriately - the “usual” volume between min and max mark is 1 litre. Some find that a tra...
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As in the title, how to convert <span class="math-container">$\rm cm^{-1}$</span> to <span class="math-container">$\rm eV/Å^2$</span>? Å stands for angstrom.
You are correct. <span class="math-container">$W=mgh$</span> is also correct, but it brushes something under the rug. It ignores the force required to accelerate an object from rest, and it ignores the opposite force that slows the object to a stop. In between speeding up and slowing down the velocity is constant wh...
For a very small change in the kinetic energy of the body, the total work done (by you and by gravity) is zero, by the definition of work in classical mechanics (change in kinetic energy due to the net force acting over a distance). The work done by gravity is typically considered as the negative of the change in grav...
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Do I get 12V on OBDII pin 16 without ignition ON?
Not a good idea - leave the OBD connectors for OBD. Instead, a simpler solution is to look for an add-a-circuit device in your local car spares store. Plug it into a known 12V supply in the cars cabin fusebox, and run the power lead to the dashcam. This is a much quicker solution than trying to find switched 12V in t...
Yes you get constant voltage from pin16 on a OBD2 even with out ignition on. It is a direct fused line in most cases and a lot of the times it is also the same fused line as the main cigarette lighter plug (many people use to plug in accessories).
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Assume I was in a falling box that falls at exactly 50 mph. I drop a penny and this penny is travelling toward the floor of this box at 20 mph. Because the speed of the box is greater than the speed of the penny, what would happen to the penny?
Remember that if you drop something, it doesn't fall at a constant speed, but picks up speed as it falls. This is due to the acceleration of gravity. If the box is not accelerating, but has a constant velocity, the penny will fall exactly as it would if the box was on the ground. (From a physics standpoint, the box be...
If the speed of the falling box was only a constant 50 mph then it would obviously not be free falling. Inside the box if you let a penny freefall then after 2 1/2 seconds it would be moving faster than 50 mph and constantly gaining speed. In reality if both the box and the penny were freefalling then they would move a...
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I'm having trouble using the pumping lemma to prove this language $L := \{a^n\mid\exists k \geq 0\ n = k^3\}$ is not regular. <ol> <li>Assume $L$ is regular. Thus there is a DFA $M$ for it.</li> <li>Choose $m$ as the number of states in a DFA $M$.</li> <li>Choose $w = a^m$ such that $|w| \geq m$.</li> <li>Decompose $w...
Your use of the ratio test is fine--clearly, it won't converge outside of $[-1,1]$, and you are correct in asserting that it doesn't converge for $x=-1$ and $x=1$. You probably still have to prove that it converges for $x\in (-1,1)$, but you can use the comparison test against the series $a_n = x^n$ for that.
Split this up into three parts: 1). $x\in (-1,1)$ 2). $x\notin (-1,1)$ 3). $x=1$ or $x=-1$. 1). In this case your general term is $\leq $ $x^n$. On comparison with the geometric series, your series then converges. 2) and 3). In these cases, the series diverges, because the general term does not go to zero as $n\...
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I'm wondering whether it is possible to Partition the closed interval $[0,1]$ into closed, countably infinite sets. The only observations I could make were as follows: <ol> <li>When we remove the endpoints, we effectively end up with $\mathbb R$, and can consider the image of $$\mathscr S :=\{r+\mathbb N\mid r\in [0,...
Yes. You can build such a partition by transfinite recursion. Specifically, we construct a sequence of disjoint closed countably infinite subsets $A_\alpha\subset[0,1]$ where $\alpha$ ranges over the ordinals. Having constructed $A_\beta$ for all $\beta&lt;\alpha$, let $S=[0,1]\setminus\bigcup_{\beta&lt;\alpha}A_\be...
It may be worth pointing out that a partition of $[0,1]$ into countably infinite closed sets can be constructed effectively, without using transfinite induction or the axiom of choice. Let $C$ be the Cantor set. It is well known that we can define a bijection $h:(\frac13,\frac23)\to C.$ If $(a,b)$ is a connected comp...
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I already derived a QM expectation value for ordinary momentum which is: <span class="math-container">$$ \langle p \rangle= \int\limits_{-\infty}^{\infty} \overline{\Psi} \left(- i\hbar\frac{d}{dx}\right) \Psi \, d x $$</span> And I can read clearly that operator for momentum equals <span class="math-container">$\wid...
Well, $\widehat{p^2} = \hat{p}^2= \hat{p} \hat{p}$. So, in the position basis it is $-\hbar^2 \frac{d^2}{dx^2}$, and $\langle p^2 \rangle = \int_{-\infty}^\infty \bar{\Psi}\left(-\hbar^2 \frac{d^2}{dx^2} \right)\Psi dx$. Note: $\hat{p}$ is technically not equal to $-i\hbar d/dx$, but rather in the position basis $\la...
The expectation value for some operator $A$ is given by $$\langle A\rangle = \int \Psi^*A\Psi.$$ If we set $A=p$ then we get the expression you've written above. Now just set $A = p^2$ to get what you want.
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In my analyses I had a clear hypothesis about a relationship Y ~ X1. In order to show that this is specific, I ran a control analyses with Y ~ X2. I showed that the relationship with X1 was significant, and the one with X2 not (we did this for several specific predictions). The reason that I should not correct for mul...
This isn't the right way to do things. There is no reason to look at the relationship between Y and X2 in order to say something about the relationship between Y and X1. You haven't given a lot of detail on exactly what you did, but this can't be right in any situation that I can see. Perhaps you are conflating signif...
X2 not significant and X1 significant does say nothing very strong at all about X1 being a better predictor than X2. This type of comparing significance is not the right way of going at this. It is not even worth discussing type I error control in this context. Depending on your question and context analyses adjusting ...
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I was studying for my freshman chemistry course, and ran into a mind-boggling contradiction. We know, at equilibrium, entropy is at a maximum: <span class="math-container">$$\left(\frac{\partial S}{\partial V}\right)_U=0$$</span> From the first law <span class="math-container">$$dU=TdS-pdV$$</span> which leads to ...
The problem begins with your first statement: <span class="math-container">$$\left(\frac{\partial S}{\partial V}\right)_U=0$$</span> Because in fact: <span class="math-container">$$\left(\frac{\partial S}{\partial V}\right)_U=\frac{p}{T},$$</span> which is clearly non-zero (except in limit of zero pressure or infin...
<span class="math-container">$\require{begingroup} \begingroup \newcommand{\pd}[3]{\left(\frac{\partial #1}{\partial #2}\right)_{\!#3}}$</span> If you write <span class="math-container">$$dS=\pd SVT dV + \pd STV dT$$</span> then <span class="math-container">$$\pd SVU=\pd SVT + \pd STV \pd TVU \tag{1}$$</span> N...
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4,385,908
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For an ideal <span class="math-container">$I$</span> in <span class="math-container">$A = \mathbb{C}[x, y, z]$</span> set <span class="math-container">$$Z_{xy}(I) = \{(a, b) \in \mathbb{C}^2: f(a, b, z) = 0\text{ for all }f \in I\}.$$</span> Let <span class="math-container">$$J = \{f(x, y): f(a, b) = 0\text{ for all }(...
(1) <span class="math-container">$X_n$</span> needs to be <span class="math-container">$\mathcal F_n$</span>-measurable, meaning only that it must be constant on <span class="math-container">$\{n,n+1,\ldots\}$</span>. (2) you need to have <span class="math-container">$E[X_n\cdot 1_B]=E[Y\cdot 1_B]$</span> for each <spa...
Conditional expectation is defined with the property such that for any <span class="math-container">$A \in \mathcal{F}_n$</span>, <span class="math-container">$\int_A X_n \, dP = \int_A Y \, dP$</span>. Consider sets of the form <span class="math-container">$A = \{k \} \in \mathcal{F}_n$</span> which exist for <span cl...
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I was waiting on a red light the other day and was wondering. If I'm in my car, not moving and I see a car that's going to hit me from behind. Would I (my body) be safer if I put on the break or if I put the car in neutral? I assume there's no car in front of me and there's no posibility to be hit by an other car. ...
I agree with RedGrittyBrick's answer i.e. that you should apply the brakes, but it's interesting to see why. The easy situation to analyse is when you don't apply the brakes so (ignoring rolling friction and air resistance) you have a collision between free bodies. Suppose the other car hits you at a velocity of $v$, ...
The amount of harm to you depends on how fast your car seat is accellerated into your skull and spine. If your car were an immovable rigid steel block fixed to the ground, you would feel almost nothing and be completely safe. The easier it is for the colliding vehicle to accelerate your car into you, the more force wi...
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I have two variables for some districts in the UK: <ol> <li>Number of crimes per habitant</li> <li>Median yearly income</li> </ol> Here's what it looks like: <img src="https://i.stack.imgur.com/dDKM9.png" alt="Plot of number of crimes per habitant in function of the median yearly income"> I would like to determine i...
I think you need to consider two issues when interpreting correlations. 1) the p-value tells you the probability of observing an effect of this magnitude due to chance alone. In your case, the probability that a correlation of this magnitude occurring solely by chance is 17.2%. This is what it is. Statistical conve...
So you don't want to add any other variables in your model (average age, level of education, ethnicity, etc.)? It may be useful to visualize these two variables on a geographical map. You may see some patterns from there (including correlation, which may be slightly "shifted in space").
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I recently jumped onto the hypetrain for an unnamed email service and am currently on my way to update all my accounts on various websites to get most of my (future) data off Google's Gmail. During this adventure I came across a couple user-flows of changing your e-mail address which I would like to share (amounts like...
The problem I see with confirming the old email address is that sometimes people change address because they cannot access the old one anymore. For example, the old address might have expired (and maybe even reassigned to someone else!). Or they might just have forgotten the password to the old address, and have no alt...
If you consider email as a form of verification of account identify then ideally you should be looking to confirm any changes via an alternative form, for example sms, other email account, soft token, physical letter etc. In many cases email is the primary id for your account and depending on how secure the account is ...
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Imagine the following scenarios: A. We have a spaceship at <code>x</code> distance from a star. It faces directly away from the star, and fires its engines such that it remains at exactly the same distance from the star until it runs out of fuel. At this point, it falls into the star. B. We have a spaceship at <cod...
I am confused (and I think you may be confused) about whether you are asking about energy or momentum. However the <em>momentum</em> aspects are simple. Let's assume: <ul> <li>all the fuel ejected by the spacecraft hits the star;</li> <li>the spacecraft and star are initially momentarily at rest in some inertial fra...
If I understand your question right, we don't need a star or spaceship, we just need a gravitational field. Let's imagine we're on the surface of the Earth and we have a VTOL (vertical take off and landing) aircraft. It could hover or it could take off. The question then asks how it's possible that the two "final" stat...
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I have read that both of them are conventionally the same. But there must be a few differences which differentiates the two terms. Anyone please explain.
Finally I have found the answer. If we are able to steal someone's(Say user John) cookies and gain access to their sessions, we are able to do this only if the user (John) is logged in to his account from somewhere else. It is actually called session fixation. But once if he has logged out, the value of cookie for that...
I think session recreation or session replay means recreating the user's activity for a given session. Typically as a form of troubleshooting and/or analysis. Something bad happened with user <strong>__. Based on logged activity they did <em>_</em></strong> things before they encountered the issue. I could then attempt...
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It is Exercise 1.6.1 in Jürgen Neukirch's number theory textbook(P38). I think the number $n$ here means $[K:\mathbb{Q}]$, the degree of field extention for algebraic number field K. I can image how simple this question is, but I was still floored by it. Any help would be appreciated.
In order to end this question, I demonstrate an example of cyclotomic field $K=\mathbb{Q}(\zeta_5)$, which is not so simple as a PID (equal as UFD in Dedekind domains) (Since it's well-known that $\mathbb{Q}(\sqrt{5})\subset\mathbb{Q}(\zeta_5)$, and $2^2=(\sqrt{5}+1)(\sqrt{5}-1)$ in $\mathbb{Q}(\sqrt{5})$). Here cons...
No, $[K:\Bbb{Q}]$ has nothing to do with it. You could rephrase the exercise as <blockquote> Given a fixed positive integer $n$, how many ideals are there with norm $n$? </blockquote> <strong>Hint:</strong> You know that $\mathfrak{N}$ is multiplicative, i.e. that $\mathfrak{N}(\mathfrak{a}\mathfrak{b}) = \mathfrak...
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I want to test the hypothesis that correlation coefficient between X and Y is 0 with a bootstrap, however I don't know which is a correct way to construct bootstrap samples. I have several ideas, which may be wrong: 1) randomly permute Y among X's as in permutation test, but sample Y with replacement 2) permute Y am...
Just sample pairs (X,Y) with replacement. You should not be permuting anything.
If you sample pairs of (X,Y) with replacement, then you are bootstrapping and it will give you the variance (or other measure of spread) of the correlation. You can use this to test your hypothesis. If you permute either, then you are doing a permutation test and it will tell you how a correlation as large as the one ...
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169,398
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I have an ESC and a brushless DC motor. I am interfacing the ESC to the motor. But I am not getting what I want, so my question is, can I directly connect the motor to the battery without taking the ESC into account?
No, you can't. A brushless DC motor is very similar to a three phase AC induction motor. You need to use a brushless DC motor controller (ESC) designed to generate the rotating field. A DC motor with brushes can indeed be run directly off of a battery (if it has a Permanent magnet field), as the rotating armature ha...
No you cannot run a brushless DC motor straight off a battery. Brushless DC motors are not really DC motors. The reason they are called DC motors is that their performance characteristics resemble a brushed DC motor (fairly linear speed/torque curve, fairly linear torque/Amp, etc.). A permanent magnet DC motor ca...
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Typically, I recommend against using join hints for all the standard reasons. Recently, however, I have found a pattern where I almost always find a forced loop join to perform better. In fact, I am beginning to use and recommend it so much that I wanted to get a second opinion to make sure I am not missing something...
<blockquote> <em>SampleTable is contained on 4714 pages, taking about 36MB. Case 1 scans them all which is why we get 4714 reads. Further, it must perform 1 million hashes, which are CPU intensive, and which ultimately drives the time up proportionally. It is all this hashing which seems to drive the time up in case ...
50,000 rows joined against a million-row table seems to be a lot for any table without an index. It's hard to tell you exactly what to do in this case, since it is so isolated from the problem that you're actually trying to solve. I certainly hope that it's not a general pattern within your code where you're joining ...
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If $m \in \mathbb{N}$ is a natural number, prove that $$ m! \leq \prod\limits_{\begin{align}k = &amp;m+2 \\ k \text{ not }&amp; \text{prime.} \end{align}}^{2m+1}k.$$
Note that the binomial coefficient $\binom{2m+1}m$ is an integer, and $$\binom{2m+1}m=\frac{(2m+1)!}{m!(m+1)!}=\frac 1{m!}\prod_{k=m+2}^{2m+1}k$$ Here comes the number-theory part: we know $m!(m+1)!$ divides $(2m+1)!$, and since no primes $p&gt;m+1$ is divisible by the donominator $m!(m+1)!$, we see that $m!(m+1)!$ di...
There has been an edit to the question that makes this answer hard to understand. The original version of the question asked: $$ \frac{\displaystyle\prod_{k=m+2\\k\text{ not prime}}^{2m+1}k}{m!}\geq 1. $$ Sketch: <ul> <li>Assume that $p$ is a prime such that $p\leq m$.</li> <li>The number of times that $p$ divides $...
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The term $((\bigvee_{i=1}^{n} p_i) \wedge (\bigwedge_{i=1}^{n} (p_i \to p)) \to p$ should be proven through induction. I'm relatively new to it, but I started with: <strong>basis</strong>: $p(1): (p_1 \wedge (p_1 \to p)) \to p$ is true (modus ponens) <strong>induction step</strong>: $((p_1 \vee p_2 \vee ... p_n) \wed...
Your "induction step" is not stated correctly. The correct assumption on the induction step is $$\Bigl( \bigl(p_1\lor\cdots\lor p_n\bigr) \land \bigl( (p_1\to p)\land (p_2\to p)\land\cdots\land (p_n\to p)\bigr)\Bigr) \to p.$$ From this, you want to show that $$\Bigl( \bigl(p_1\lor\cdots\lor p_n\lor p_{n+1}\bigr) \lan...
First understand why the statement holds: $$((\bigvee_{i=1}^{n} p_i) \wedge (\bigwedge_{i=1}^{n} (p_i \to p)) \to p$$ A concrete example, $$((A \lor B \lor C) \land ((A \to p) \land (B \to p) \land (C \to p)))\to p$$ In the hypothesis at least one of $A,B,C$ is true, suppose that $B$ is true.. then we could simplif...
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164,040
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I have the following query: <pre><code>SELECT SUM(cast(Amount as decimal(10,2))) as result FROM tblserviceinvoice </code></pre> and values of <code>amount</code> (which is <code>varchar</code>) are: <pre><code> 2.00 276,00 528.00 759.00 759.00 233.00 7,956.00 5,328.00 </code></pre> But as I...
The issue in the above query is only due to these value (7,956.00 and 5,328.00 ) when casting in implemented on these values the value returned as 7.00 and 5.00 due to which the query gives the result as 2569.00. Just remove these commas from these numbers and the query will execute properly SELECT SUM(REPLACE(Amount...
You could strip the commas from the number strings before converting them to numbers: <pre><code>SELECT SUM(CONVERT(REPLACE(amt_tran,&quot;,&quot;,&quot;&quot;),DECIMAL(9,2))) as result FROM tblserviceinvoice </code></pre>
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I use streaming replication and PITR (WAL files) in my cluster, currently I have different versions of <code>postgresql.conf</code> for the master and the standby server. The only difference in the files is the archive command, that points to a different directory. for example, on master I have: <pre><code>archive_c...
In theory this should work. After all, the files should be identical. In practice I think it is scary and I wouldn't do it. I would worry about file locking contention, and also the fact that if I am archiving twice to two locations I get a full backup of the WAL's esp, if I send to different file servers. If one g...
Indeed, the standby does not archive wal segments, but you should always test for the existence of the segment about to be written and skip the write if it exists already.
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I have a method that does something like this <pre><code>public void addFunds(Account account, int price) { int credits = account.getCredits() account.setCredits(credits + price) saveOrUpdate(account) } </code></pre> the method <code>saveOrUpdate</code> is already tested, so my question is: should I test the...
<strong>TL;DR</strong> "Dogmatically" speaking: <strong>Yes.</strong> <em>Practically</em> speaking: <strong>It's up to you and your team.</strong> If I were on your team, I'd strongly argue that the tests are <em>valuable</em>, since they help to define and enforce the method's complete contract, including its behav...
IMHO you are asking the wrong question. The fact <code>saveOrUpdate</code> is tested obviously does not guarantee the calculation logic in <code>addFunds</code> to be correct. So it is pretty clear the logic has to be tested somehow. So the question you need to ask here is, how to accomplish this? <ol> <li>Does one n...
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So, $A$ is a $n \times n$ matrix with integer entries. The question is to prove that $A^{-1}$ has all integer entries if and only if ${\rm det}\ (A) =\pm 1$ . I know that $A^{-1}= {\rm adj}(A)/{\rm det}(A)$ but I have no idea where to go from there for the forward direction. Any help here would be greatly appreciate...
The direction you've done is correct to a t and is exactly how I'd do it. As for the other direction, you might be tempted to try to reverse your argument but that definitely isn't going to go your way. Here's a hint: suppose that $A^{-1}$ has integer entries, then we know that $$\det(A^{-1}A) = \det(I) = 1$$ but we ...
You did one direction well. Here the other direction: If <span class="math-container">$A$</span> only contains integers then <span class="math-container">$\det(A)$</span> is an integer (computing a determinant only uses <span class="math-container">$+$</span> and <span class="math-container">$\cdot$</span>). Assume <sp...
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I have 2003 Kia Sedona 2.5 liter AT in good condition. I've replaced some of the old parts with new ones. Both highway and city fuel consumption is bad compared to other cars with same engine displacement. I'm wondering what makes the fuel economy so bad? Is it caused by dirty injectors? Bad ignition timing? Wrongly ...
There are many factors which could influence your fuel consumption, namely, the design of the car itself - not much you can do about it. Are you getting what the EPA label said you would be getting? Also, here are some things that will improve your fuel economy: <ul> <li>Use full synthetic oil and change at regular ...
You haven't mentioned how many miles per gallon you are getting but several things come to mind. How are you calculating milage? Fill the tank until the pump shuts off. Drive until 1/4 or less remains. Refill at the same station using the same pump if possible. Refill until the pump shuts off.Divide mileage by gallons ...
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191,458
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Let $Y(3)$ be the fine moduli space (say, over $\mathbb{C}$) representing elliptic curves equipped with a full level 3 structure. Abstractly, there are 24 such structures for any elliptic curve, but thanks to every elliptic curve having $[-1]$ as an automorphism, there are generically only 12 equivalence classes. Thus,...
If the map from $M_{1, 1}$ to the $j$-line can be said to have a degree, that degree should be $\frac{1}{2}$, which makes everything work out. The reason is that its fibers are generically not a finite set but a finite groupoid, namely $\text{pt}/\mathbb{Z}_2$ (corresponding to the $-1$ automorphism), which has groupoi...
This is to record User74230's answer to your question. The map $j:M_{1,1}→\mathbb A^1$ is indeed proper and etale but not representable, just like the map to the coarse moduli space from any separated DM stack (of finite type over a noetherian ring) when the stack isn't an algebraic space. (The map $Y(n) \to M_{1,1}$...
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Assume we have an infinite time series $v_1,v_2,\dots,v_i,\dots,v_j,\dots,v_y,\dots,v_z,\dots$ and use Gaussian process for prediction. At time $i-1$, we want to use the previous observed data to predict the values for $\bar{v_i}$ to $\bar{v_j}$. If these values are predicted, they cannot not be observed. We can cont...
<strong>Predictions are not data</strong> - they are <em>functions</em> of the observed data. As such, they add no information to your knowledge of the process beyond what is already in the observed data. If you make a prediction based on some observed values, and then observe the predicted value, the new information...
Have you searched for censored time series? Note that if the process is not observed for some reason, it is possible that the latent variable didn't cross a certain threshold to become observable. Hence, missing values indicate such a fact, and the likelihood estimation process can further benefit from such. Indeed, ...
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Consider the Klein-Gordon equation of the form <span class="math-container">$$\square_g \psi - m^2 \psi - \xi R \psi \enspace = \enspace 0 \quad .$$</span> This equation describes the relativistic propagation of a scalar field with mass <span class="math-container">$m$</span> on a curved spacetime with metric <span cla...
Let <span class="math-container">$A^\mu=(1,100)$</span> and let <span class="math-container">$B^\mu=(0,-99)$</span> which are both spacelike then <span class="math-container">$A^\mu+B^\mu=(1,1)$</span> which is null. The issue is your conditions for being spacelike are wrong.
<span class="math-container">$a&lt;b$</span> is not the right condition to make <span class="math-container">$A=(a,b)$</span> spacelike. Instead, we should have <span class="math-container">$\eta(A,A) = a^2-b^2 &lt;0$</span>, which neither implies nor is implied by <span class="math-container">$a&lt;b$</span>. <blockq...
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I was reading over Sakurai's <em>Modern Quantum Mechanics</em> textbook and had the following question. He introduces the spinor representation where a spin state can be represented as <span class="math-container">$$\chi = c_{+}\chi_{+} + c_{-}\chi_{-},$$</span> where <span class="math-container">$\chi_{+}=(1,0)^{T}$</...
There are only two numbers needed to specify a spin-<span class="math-container">$\frac{1}{2}$</span> state. Each of the coefficients in the general spinor <span class="math-container">$$\chi=\left[\begin{array}{c} c_{+} \\ c_{-} \end{array}\right]$$</span> is a complex number, giving four real parameters. However, o...
Quantum state or <em>state-vector</em>? The spin vector requires three numbers: two polar angles <span class="math-container">$\theta,\phi$</span> parametrizing the direction of the spin and an overall-phase. The quantum <em>state</em> does not depend on the overall phase, as states are specified by <em>rays</em> in...
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192,793
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I am making a obstacle avoiding robot and wanted to power it with mobile phone batteries. But wondering how to solder wires on battery correctly for no inconvenience. <em>p.s.</em> I am a new arduino enthusiast.
<strong>Step one is trying to avoid wanting to solder to any kind of pre-fab battery, as you don't know 100% for sure what's in them in ways of protection.</strong> <strong>Step two is really thinking hard if you can't stick to step one.</strong> <em><strong>Step three would be: Very, very carefully.</strong></em> <str...
Don't. The battery manufacturers specifically tell you not to do this, as the batteries are quite heat-sensitive. If you manage to set one on fire, you can't extinguish it either: it reacts explosively with water, so you have to bury it in sand or powder. The correct solution is to get spring-loaded contacts or "pogo...
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107,584
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I'm a teen who has been programming for about 3 years, I can do some basic Software and so, but I feel I can't do all by myself. What can I do to find people interested in Programming ? None of my friends does, I only have a Cousin which is studying Software Engineering, but he is in another country. I live in Spain,...
You can contribute to open source and you will find people from all over the world , you can look at their code and learn. Some open source groups are very elitist some friendly. Choose your pick. Good for you on starting early :)
If you're talking about actually meeting up with real people you might find this difficult as a teenager. The easiest places to meet like-minded people when it comes to programming are probably at college/university and/or when you get a job as a programmer. Perhaps there are evening computing classes you can attend ...
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124,253
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I searched for the answer for this question on Wikipedia and Stackexchange a lot but couldn't find same question or a required answer in some other similar question. I understand that the function of the salt bridge is to complete the circuit and maintain electrical neutrality in both the half cells of a galvanic cell...
Consider a salt bridge as a part of the cell electrolyte, that is not allowed to mix with the rest of electrolyte. For a particular ion, there are 2 cases: <ol> <li>The ion <strong>is shared</strong> with the electrolyte part, from which the ion migrates toward the bridge. Then the ion gets depleted from electrolyte ...
Salt Bridge is like a source which provides cations to the the half cell where the negative ions are more than the positive ones in the electrolyte . Similarly it gives anions to the half cell where positive ions are more than the negative ones in the electrolyte. It basically ensures continuity of the flow of elect...
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167,280
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I've been working in Ruby for the last couple weeks, and I've come to the subject of procs, lambdas and blocks. After reading a fair share of examples from a variety of sources, I don't how they're much different from small, specialized functions. It's entirely possible that the examples I've read aren't showing the ...
First of all, what do you mean by "functions"? Proc and lambda <em>are</em> "functions" -- and they evaluate to a function object, which could be assigned to a variable or used in any other expression. There is no other way to define a non-method "function" in Ruby. <code>def</code>, by contrast, defines a <em>method<...
Good question! I'm curious on the answers. One difference I know: You get no error with this call: <pre><code>zero_proc.call() </code></pre> But you get a <code>wrong number of arguments (0 for 1) (ArgumentError)</code>-error with the following calls: <pre><code>puts zero_function() puts zero_lambda.call() </code>...
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I had a discussion with one of my teachers the other day. We debated the impact that simpler <strong>scripting languages</strong> (like Python or Ruby) have on junior programmers. He argued that scripting languages engender sloppy coding techniques because beginners don't understand what is going on "under the hood...
I disagree. First, scripting languages are at a higher level of abstraction, and there is nothing wrong with this. At the beginning one is just trying to learn the principles. Actually I would say that choosing a lower level language may encourage bad coding, since one has to deal with some details before being able to...
It doesn't matter where you start. It matters where you go <em>after</em> you start. BASIC may not be the most elegant language on the planet, but it encompasses the fundamentals of procedural programming, and that's enough to get started. I started with BASIC. I didn't <strong>stay</strong> there.
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PCI-DSS states the following: <blockquote> 3.5 Protect any keys used to secure cardholder data against disclosure and misuse </blockquote> I have a service which stores a salted bcrypt hash of the user's PAN. Assuming the bcrypt algorithm is adjusted for significant slowness, how does the 3.5 requirement apply to t...
In my opinion, you don't. The salt cannot be used directly to get the clear PAN back, so it is not subject to requirement 3.5.
Requirement 3.5 does not apply to hashing initialization vectors. It applies to encryption keys (such as RSA or AES keys).
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I have a model with a negative binomial distribution using the <code>glm.nb</code> function from R: <pre><code>Call: MASS::glm.nb(formula = Counts ~ Gender + offset(log(Offset_Days)), data = r_dataset, init.theta = 1.023811633, link = log) Deviance Residuals: Min 1Q Median 3Q Max -0.5973...
Two ways I see. <h2>Marginal Effects</h2> You're basically asking about a contrast. The <code>{marginaleffects}</code> library handles this elegantly. <pre><code>library(tidyverse) library(rsample) library(marginaleffects) y &lt;- c(7, 5, 4, 7, 5, 2, 11, 5, 5, 4, 2, 3, 4, 3, 5, 9, 6, 7, 10, 6, 12, 6, 3, 5, 3, ...
<ol> <li>Draw, with replacement, a random sample from your observations. The size of the sample should be the same as that of your observations. </li> <li>For this random sample, fit the model as you have above. </li> <li>For the fitted model in step 2, compute the difference in rates. Call this a bootstrap replication...
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428,303
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<blockquote> <strong>Problem</strong>: Find number of solutions of <span class="math-container">$|2x^2-5x+3|+x-1=0$</span> <strong>Solution</strong>: Case 1: When <span class="math-container">$2x^2-5x+3 \geq 0$</span> Then we get, <span class="math-container">$2x^2-5x+3+x-1=0$</span> x=1,1 Case 2: When <span class="mat...
Nope, if you have $|f(x)| + g(x) = 0$ $(1)$ you solve it as follows: <ol> <li>assume that $f(x)\geq 0$, find solutions of $f+g = 0$ - say $x_1$. Check whether $f(x_1)\geq 0$. If it holds, then $x_1$ solves $(1)$ as well. If it does not hold, it's not a solution of the original equation.</li> <li>assume $f(x)&lt;0$, fi...
$$|2x^2-5x+3|+x-1= \begin{cases} 2x^2-5x+3+x-1 &amp; x\ge\frac32 \quad \text{and} \quad x\le1 \\ -(2x^2-5x+3)+x-1 &amp; 1\lt x\lt\frac32\\ \end{cases}\Rightarrow\begin{cases} 2x^2-4x+2 &amp; x\ge\frac32 \quad \text{and} \quad x\le1 \\ -2x^2+6x-4 &amp; 1\lt x\lt\frac32\\ \end{cases}$$ <img src="https://i.stack.imgu...
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116,214
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If we have a circuit in dynamic logic: <img src="https://i.stack.imgur.com/YxIf3m.png" alt="image"> What should the size of the charge transistors (Qe and Qp) be? I know that increasing the size improves the speed but also increases the dissipation, and that it doesn't affect the functionality. If the highest transi...
In normal static CMOS logic, you need to maintain equal rise &amp; fall times because there is both PDN &amp; PUN networks. But in this footed Dynamic logic, you have only PDN network. So during precharge period (\$\Phi=0\$), PDN network is idle and charging through PMOS can occur more slowly than static CMOS logic. Th...
For CMOS logic, you may want to look for the topic of "logical effort." This describes, in detail, some formulas to compute the sizing off pmos vs nmos to balance out rise and fall times. A rule of thumb is Lp = 2 * Ln, where Lp is the pmos gate length and Ln is the nmos gate length. You should be able to characteriz...
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38,183
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When someone mentions tuning the car for low end torque, do they mean changing something mechanical (gear ratios/final drive) or something that has to do with the ECU ? if so what is done exactly to tune for low, high or mid end torque? I don't think changing the fuel ratio or something similar gives such effect, so wh...
If the powertrain is identical, there's not much the ECU can do. The word <code>tuning</code> is thrown around a lot and means different things to different people. ECU tuning is one thing, and basically you can set the ECU to run the engine more aggressively (for power and torque) or more conservatively (for fuel ec...
normally it would just be changing gear ratios/final drive just like you said, you could also do different tires/tire sizes as well, the person could go as far as changing the transmission if they really wanted. so yes, typically it would be something mechanical. (gear ratios I would say)
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54,726
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Suppose I have the following OIS Swap rates: 1 year OIS Swap: 0.36% 2 year OIS Swap: 0.37% 3 year OIS Swap: 0.38% 4 year OIS Swap: 0.40% From these, how do I get the OIS Discounting factors for these respective years? Could someone please explain with a proper formula that can be applied for this?
The discount factor is just 1 divided by the interest rate, if you want a quick proxy and don't want to Bootstrap the OIS Swap curve. 1y Swap rate = 0.38% =&gt; the effective interest rate is 1.0038. Therefore the discount factor is: <span class="math-container">$$DF(1y) = \frac{1}{1.0038}=0.99621$$</span>. For the sec...
It depends on the discounting index of your OIS swaps : we recently switch from the standard OIS discounting for standard swaps to SOFR discounting. As the basis between OIS and SOFR is small, the effective impact is minimal. The methodology is the following : DF(1y) = 1/(1+0.0036) = 0.996413 DF(2y) = DF(1y)*DF(1y1y) D...
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I'm reading Einstein Gravity in a Nutshell (by Zee) and here he defines a vector as an object which is invariant under coordinate representation; concretely, if in one coordinate representation, $V$, $p_V=(p^1,p^2)$ then when we transform it via a rotation $p_W = R(\theta)p_V$ then we do not violate any physical laws....
Let's do this systematically: (I must admit that the part of your question with &quot;prove that <span class="math-container">$p'$</span> is not a vector if <span class="math-container">$p$</span> is&quot; did not really make sense to me, so I decided to show you how vectors in GR are really defined and how transformat...
I just wanted to comment on what I think the question from Zee's book is getting at. I don't think that this question from Zee is a particularly good question, and I think ACuriousMind's answer is excellent and gets at the real points that you should be trying to learn. So this is being written purely for the sake of t...
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During hot and humid weather, we sweat incessantly due to high humidity. But when we sit under a fan, we feel cold and comfortable. Why do we feel cold and chilled? Why don’t we feel the humidity?
When you switch on the fan, the air of the fan removes or evacuates the water vapour from the nearby areas.So.the place [not large although] becomes void of water vapour...And so when you sit there with sweat, your sweat is absorbed by the apparently dry air of that place.During evaporation, the sweat absorbs the laten...
The moving air produced by the fan causes forced evaporation of the sweat secreted by the sweat glands. It takes energy (heat) to change sweat (liquid water) into water vapor and that heat energy is taken from the body thus cooling the body down which makes one feel more comfortable. This is one of Nature’s way of r...
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245,381
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I am about to make a forensic image (using dc3dd from OSFClone) of two laptops and in this specific case I'd like to startup using an bootable USB stick with OSFClone and image the disk to an external disk. The laptops (HP ProBooks) in this case uses Bitlocker and has (according to the vendor specifications) an TPM 2.0...
OK, first things first: if you're trying to make a forensic image of a disk, and you're doing <em><strong>ANYTHING AT ALL</strong></em> that involves booting the machine it's in before you initiate the image, stop and ask yourself why you aren't just removing the disk and cloning it using dedicated hardware. Or at leas...
I've managed to do make an forensic physical image of both systems using OFSClone with Secure Boot disabled. The machine configuration was slightly different so both machine’s required slightly different steps to disable Secure Boot although the BIOS looked identical. <ol> <li>For one machine I went into bios by pressi...
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12,132
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I have a database that is in Single User Mode. When I run this: <pre><code>exec sp_dboption 'MyDb', 'single user', 'FALSE' </code></pre> It fails, telling me that there is still a user connected. But when I run both of these: <pre><code>exec sp_who2 select d.name, d.dbid, spid, login_time, nt_domain, nt_username...
You can use nested <code>EXEC</code> calls. The database context changed by the <code>USE</code> persists to the child batch. <pre><code>DECLARE @DB SYSNAME SET @DB = 'tempdb' DECLARE @CreateViewStatement NVARCHAR(MAX) SET @CreateViewStatement = ' USE '+ QUOTENAME(@DB) +'; EXEC('' CREATE VI...
One way I have handled when run into this case is placing GO after use statement. <pre><code>set @CreateViewStatement = ' USE ['+ @DB +']; GO CREATE VIEW [dbo].[MyTable] AS SELECT ........something' exec (@CreateViewStatement) </code></pre>
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Basically I want to classify a rather rare status (about 2% of the 2000) with some predictors. I have used logistic regression, neural network, and Support Vector Machines to do it. All the predictors in the logistic regression are statistically significant. And to avoid overfitting, I have self-implemented a 10-fold...
The SVM is designed to determine the optimal decision boundary for only one ratio of false-positive and false-negative misclassification costs, so it is not really a fair comparison to change the threshold to adjust the sensitivity. A better approach would be to tune the regularisation parameters (C or nu) for each cl...
you can use the matlab codes for svm and compare your answers with that I think different packages give different answers and it sounds matlab is satisfactory. Here are codes for 10 fold cross validation in matlab: load fisheriris %# load iris dataset groups = ismember(species,'setosa'); ...
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The permanent $P(M)$ of a matrix $M$ of size $n$ is defined to be: $$ P(M) := \sum_{\sigma \in S_n}\prod_{i=1}^n M_{i\sigma(i)} $$ If you have a matrix of the form $$ M_{ij} := A_i + B_j $$ where $A$ and $B$ are indexed sets of numbers and if $x_k(S)$ is the sum of all products of $k$ elements taken from the set $...
The permanent of the biadjacency matrix of a bipartite graph counts the number of perfect matchings of that graph. By the biadjacency matrix, I mean the matrix with rows indexed by one of the independent sets and the columns indexed by the other. An entry is 1 if the vertex represented by the row and the vertex represe...
A large class of matrices for which the permanent can be efficiently computed has been constructed by Klaus Meer: <em>An extended tree-width notion for directed graphs related to the computation of permanents:</em> <A HREF="https://mit.spbau.ru/csr2011/sites/default/files/talks/CSR2011_June16_15_45_Meer.pdf" rel="nofo...
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Ok, sort of as a follow up to my previous question, let's recall the de Rham-Weil theorem: Let $F$ be a sheaf on a topological space $X$ and let $\mathcal{L}^{\bullet}$ be an acyclic resolution of $F$. Then $H^{q}(X,\mathcal{F}) \cong H^{q}(\mathcal{L}^{\bullet}({X}))$. Now let's say I want to compute the cohomology o...
In brief: For your first question, no. Let $X_\bullet$ be any semi-simplicial space and $Y_\bullet$ have a point in degree zero and be empty in every other degree. Then $\vert X_\bullet \times Y_\bullet \vert = X_0$, which will not usually be equivalent to $\vert X_\bullet \vert$. For your second question, yes. This ...
[ I now realize that the OP is asking about functors in the image of the forgetful functor from simplicial spaces to semisimplicial spaces, though I focus my answer mainly on a general semisimplicial space. I'll keep the answer up anyway in case it's helpful. To clarify, by a simplicial blah, I'm as usual talking abou...
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238,978
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The harmonic numbers are given by $$H_n=\sum_{k=1}^n\frac{1}{k}.$$ Numerical calculation suggests $$ \sum_{k=1}^{n}(-1)^k{n\choose k}{n+k\choose k}\sum_{i=1}^{k}\frac{1}{n+i}=(-1)^nH_n. $$ I can not give a proof of this identity. How to prove it? Hints, references or proof are all welcome.
First we prove the formula $$\sum_{k=0}^n (-1)^k\binom{n}{k}\binom {x+k}{k} = (-1)^n\binom xn,\tag{1}$$ which is special case of Vandermonde's theorem: $$\begin{aligned} \sum_{k=0}^n (-1)^k\binom{n}{k}\binom {x+k}{k} &amp;= \sum_{k=0}^n \binom n{n-k} \binom{-x-1}{k}\\ &amp;= \binom{n-x-1}{n} = (-1)^n\binom xn. \en...
Here is a proof. At first, use $(-1)^k\binom{n+k}k=\binom{-n-1}k$. Then $$F(y):=\sum_k (-1)^k\binom{n}k\binom{n+k}ky^k=[x^n] (1+x)^n(1+xy)^{-n-1}.$$ Next, for any polynomial $F(y)=\sum c_ky^k$ we have $$ \sum c_k\sum_{i=1}^k\frac1{n+i}=\int_0^1 y^n\frac{F(y)-F(1)}{y-1}dy. $$ Integration over $[0,1]$ and taking the co...
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I'm assuming that after a while, many developers come to know/love a particular VCS. What happens if you find yourself on a team using an incompatible system - do you learn the new system and adapt your workflow to the team's, or do you keep your old system, and try to get both working in tandem? It strikes me that thi...
The short answer is, it depends on the version control systems in question, your role in the team you're working on, and the policy of the company. Some companies have very strict policies about what you can use, and you'll probably be stuck with whatever version control software is the company standard. At other shops...
It is certainly possible to use the new generation of DVCS alongside any other source control system. I do this with Git when I have to. When working with Subversion, Git has built-in client support which works really well. I have occasion to use Git alongside other source control systems. You can create a Git reposi...
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I was doing some testing on a server to see if it was vulnerable to a 0-day local exploit (the exploit was for gaining root privileges using a bug in the Linux kernel). There was no real information yet on how to know if your vulnerable or not except by running the exploit. Which I did and ended up getting a heap of tr...
I would consider 2 possible approaches - I note that you are trying to verify an exploit for escalation of privilege exploiting a bug in the kernel. For the sake of the experiment, I would ignore user space software even though this is probably a bad idea. Approach #1 assuming that you may need access to data on the ...
Find what the exploit takes advantage of. Is it your Linux kernel (version)? Then all systems with that version number may be effected. Assuming you have a vulnerability, you should know what it attacks. If for some reason you don't know what the exploit does don't test it on production servers. If the exploit is ...
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I have a list of numbers I need to group by similarity (differences being 1 between each). For example, in a list of [198, 202, 207, 218, 219, 220], 190 would be put into a list, 202 would be put into another list, 207, into a list, and 218 219 220 into another list.
Although some clustering algorithms will do this, <strong>there's a simpler way</strong>: sort the input, create a binary vector indicating whether each neighboring pair is <em>dissimilar</em> or not, prefix that with a <code>1</code> for the initial value of the input, and compute its cumulative sum. This creates a n...
This can be accomplished with hierarchical clustering using the <code>hclust</code> function in R. Here's some example code. The <code>cutree</code> function allows you to specify the distance (height) at which the tree should be cut and returns the cluster for each data point. <pre><code>numbers_to_cluster &lt;- c(0:...
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Absorption spectra are a result of light of a certain wavelength exciting an atom from a lower energy level to a higher one and at the same time being absorbed. However, the atom should eventually go back down to its lower energy state, and at the same time emit a photon of same frequency it absorbed earlier. Overall, ...
When the energy level drops and the photon is re-emitted, it is scattered or re-emitted in a random direction, so less of that frequency reaches your telescope/spectroscope. It is sort of analogous to the "why is the sky blue" question. What you are looking at is direct line photons(line of sight), so photons passing t...
A similar explanation, is that the intensity at any given frequency is the optical depth weighted average of the plank (black body) function. As the light ray goes deeper (maybe comes from deeper down is more intuitive) for each delta in optical depth the local temperature determines the ratio of emission to absorption...
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96,852
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Should I develop on the latest and greatest 1.7 version of Joomla or stick with the well documented version of 1.5? I'm new to Joomla (and webDev in general), so I bumble around, search online, and ask those wiser then myself. The problem is that the answers are for version 1.5, and don't apply to 1.7, so I'm flounder...
If there is no compelling reason to use the latest major release (i.e. a must have feature, a must have with no work around bug fix) it is more economical to stick to a well proven version that been around for a while. My rule of thumb is double the effort required when using a Beta version of software. Some software i...
<ul> <li>At work, develop with well documented versions of anything. This will let you focus on domain issues. You will also get faster and better results.</li> <li>At home, fight against the latest and greatest. This will let you gain non-working but very valuable experience with new tools. You will also get deeper in...
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I am working on a project of an online service provider. I have tables for admin, agent, customer and tables for data storage like city, services, category, sub-category, gender. I have created classes for the <code>admin</code>, <code>customer</code> and <code>agent</code>. But should I create classes for <code>cit...
Put them in their own class (city, services, category, sub-category, gender). Why wouldn't you? Is there a concern that you'll have too many classes that interact with the data storage? If you want to expand on any of these entities, there would be no reason to change the: customer, agent or admin classes. That doesn...
Yes, its normally good to have a one to one mapping between classes and tables. The type of objects you mention are regarded as 'entity objects' in that they represent a 'real' thing, many of which exist, each with differing, but not necessarily different, data. eg you have many customers in your database and when yo...
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Given a tree $T=(X,E)$, is it guaranteed for any orientation of the edges $E$, there exist a strict total order preserves it? For instance, let $X=\{x_1,x_2,..x_n\}$ and $E=(x_i,x_{i+1})$ the result is a tree $T$. Let $G$ be directed graph of $T$ (add directions into the set of edges in $T$). is it always the case wh...
When $N=\frac pq$, with $p,q\in\mathbb N$, $q\neq 0$ and $\gcd(p,q)=1$, he must have played as least $q$ games.<br> <strong>Prove:</strong><br> It is possible when $q$ games have been played: If he won (scored $1$) $p$ times and lost $q-p$ times (score $0$), the average score is $$\frac{p\cdot 1+(p-q)\cdot 0}q=\frac pq...
Just write $N$ as $\frac{p}{q}$ with $\mathrm{gcd}(p,q) = 1$. Basic number theory then gives $q$ as a solution to your question.
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Let $\{\lambda_n\}$ be the sequence given by $H_n - \ln n$. We claim that $\lambda_n$ is irrational for every integer $n&gt;1$ and justify this by the following argument: Assume that $\lambda_k$ is rational for some integer $k&gt;1$ such that $H_k - \ln k = p/q$ where $p$ and $q$ are integers. Rearranging the above w...
You are implicitly claiming that the set of irrational numbers is closed in $\mathbb R$, which it is not. Indeed its closure is $\mathbb R$ (it is a dense subset), i.e. every real number is the limit of a sequence of irrational numbers.
You can have a rational limit of a sequence of all irrational numbers. Consider for example $\sqrt{2{\sqrt{2{\sqrt{2\ldots}}}}} = 2$
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So I was verifying wether <span class="math-container">$\partial_\mu \partial^\mu$</span> is a scalar. To do this I used the chain rule: <span class="math-container">$$\frac{\partial }{\partial x^\mu} = \frac{\partial \tilde x^\nu }{\partial x^\mu}\frac{\partial }{\partial \tilde x^\nu}, \qquad \frac{\partial }{\parti...
<span class="math-container">$\partial^\mu$</span> is not <span class="math-container">$\partial/\partial x_\lambda$</span>. There is no such thing as <span class="math-container">$x_\lambda$</span>. Instead <span class="math-container">$\partial^\mu \equiv g^{\mu\nu}\partial_\nu$</span>. In curvilinear coordintes <s...
Your identity is false. Here is a simple counter example in 2D switching between cartesian and polar coordinates: <span class="math-container">$(x^1,x^2)=(x,y)$</span> and <span class="math-container">$(\tilde{x}^1,\tilde{x}^2)=(r,\theta)$</span>. A simple calculation yields <span class="math-container">$$ \frac{\part...
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Is the non-principal ultraproduct of finite fields $\prod_p \mathbb{F}_p/\sim$ a nonstandard model of the rationals $\mathbb{Q}$? EDIT: Can we realize $\mathbb{Q}^*$ as an ultraproduct?
It is easy to see that at least one of $-1,2,-2$ is a square in that field: the set of primes where neither $-1$ nor $2$ is a quadratic residue is contained in the set of primes where $-2$ is a quadratic residue.
A (non principal) ultraproduct of finite fields of unbounded cardinalities is a pseudo-finite field : <ul> <li>It is perfect (if its characteristic is a prime number $p$, then any element is a $p$th power) ;</li> <li>For any positive integer $n$, it has exactly one extension of degree $n$ (equivalently, its Galois g...
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Currently i have requirement saying user from an UI creates there own forms which has types textbox,choicegroup etc.. Does anyone have a any idea on how to architect the database to store all data? If user want to link form1 to form2 etc.. how will these data links stored in database? For example, parent1 has child1...
<strong>This abstract of table can help u, which I am using in my project.</strong> <strong>Parent</strong> : Equipment <strong>Child</strong> : Component <strong>Sub Child</strong> : Sub Component Table 1 <strong>Columns</strong><br /> id(PK) | Parent_Equipment_Id | Componentid | component Order Table 2 <strong>Colu...
Parent-child relationships are usually implemented in databases by having a <code>parent_id</code> column. So, each child has a direct reference to its parent, and all the children of parent A can be found by performing a <code>SELECT ... WHERE parent_id = A</code>. This has the disadvantage of not encoding the ord...
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I'm working on a greenfields project with two other developers. We're all contractors, and myself and one other just started working on the project while the orginal one has been doing most of the basic framework coding. In the past month, my fellow programmer and I have been just frustrated by the design descisions do...
I would spend some time with the people that did the job and ask enough questions to understand why. <blockquote> Seek First to Understand, then to be understood. </blockquote> If you come into their thing too quickly, they will feel attacked and they will try to protect themselves and their comfortable status quo....
I myself am not afraid of offending, but sometimes asking simple questions helps. In this particular case, "What if the user right clicks and chooses open in new tab?" might be effective, and "What if the user is fond of the back button?" definitely will be.
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I have a shopping cart with a checkout page. On the checkout page is a payment button which takes them to a stripe payment form. I've read some books on building eCommerce shopping carts in which the order is created when the user clicks the payment button and the order id is passed to the payment gateway. In this sc...
<h2>Yes, create it!</h2> You <strong>absolutely</strong> must create the Order (or some other kind of record) before taking payment, not afterward. I have never seen an e-commerce system not do this. Here are just a few reasons why, off the top of my head. <strong>Very bad edge cases.</strong> The payment could go thro...
one way of approaching this problem is to consider the various states of an order as separate entities. so, you might have (in a simple example) something like <code>OrderUnpaid</code>, <code>OrderPaid</code>, <code>OrderPaymentFailed</code>, <code>OrderCancelled</code>, <code>OrderApproved</code>, <code>OrderUnfulfill...
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239,971
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If I use a transformer to step the voltage down from 220V to around ~30V and I expect the 30V end to draw up to ~30A, what kind of current magnitude will I have to plan for or expect to see on the 220V side? I am very noob. Please feel free to help make this question better/clearer or give suggestions.
For a ideal transformer, current scales inversely proportional to voltage. Put another way, current x voltage is constant. That's because current x voltage is power, and for a ideal transformer, power in and power out are the same. Of course no transformer is ideal. There will always be some loss, so power in will ...
Power in has to equal power out. V1*I1 = V2*I2 Solving the equation (30*30)/220 = 4 amps. This is theoretical. In reality there will be losses. Provision for 5 to 6 amps to have enough overhead at the output.
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As we know, tiles can make it quicker to update large portions of the display at once, as compared with a bitmap. To put, say a letter, on the screen, the Commodore 64 typically does two writes (the screencode and the attribute), but the ZX Spectrum typically does 9 (eight bytes which make up an 8x8 bitmap, plus 1 for ...
The Vulkan specification is very clear on this: <blockquote> A native window <strong>cannot</strong> be associated with more than one non-retired swapchain at a time. </blockquote> You can create a new swapchain for a surface, but only by passing the old swapchain as the <code>oldSwapchain</code> parameter, which w...
Dear ImGui doesn't attempt to create a swapchain for your main window. The <strong>example</strong> code (main.cpp) in the Vulkan back-end calls a helper <code>ImGui_ImplVulkanH_CreateWindowSwapChain()</code> which calls <code>vkCreateSwapchainKHR()</code>... well, because it is an example app.. you should probably no...
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