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104,995
[ "https://dba.stackexchange.com/questions/104995", "https://dba.stackexchange.com", "https://dba.stackexchange.com/users/41539/" ]
We have a monitoring tool that can check if Microsoft SQL Server jobs have run successfully. What I want to do is create a user that has as little permission as possible but it must be able to watch the history log to see if the job completed. What role should I assign the user? Edit: The servers are Microsoft SQL ...
You can do that this way: <pre><code>-- write everything from your buffers to the disc! CHECKPOINT; GO -- Clean all buffers and caches DBCC DROPCLEANBUFFERS; DBCC FREEPROCCACHE; DBCC FREESYSTEMCACHE('ALL'); DBCC FREESESSIONCACHE; GO -- Now shrink the file to your desired size DBCC SHRINKFILE (TEMPDEV, 40960); -- Mak...
You can just go with below step only <pre><code>USE tempdb; GO; dbcc freeproccache; DBCC SHRINKFILE (tempdb_file_name, memory_in_MB); GO; </code></pre>
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97,017
[ "https://mathoverflow.net/questions/97017", "https://mathoverflow.net", "https://mathoverflow.net/users/19544/" ]
Is a family of bounded bi-harmonic functions defined in the unit disk an equicontinuous family of functions on compacts? A bi-harmonic function $u$ is a solution of the equation $\Delta^2 u =0$.
Consider the infinite word $W=xx_1xx_2xx_3x....$. Let $R=R(W)$ be the ring which consists of all integral linear combinations of finite subwords of $W$. The product of two subwords $u,v$ is either the concatenation $uv$ if $uv$ is a subword of $W$ or $0$ otherwise. It is clearly an associative ring. The element $x$ i...
However Roman may still have a point: the strong nilpotents depend on the naively strong nilpotents in the sense that if there are no naively strong nilpotents, then there are no strong nilpotents. Proof: If there are no (non-zero) naively strong nilpotents, then there are no nilpotent ideals. Hence for any $x\ne0$, o...
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45,130
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According to my solution, $$y(n) = x(n^2) \tag{1}$$ for $y(n,k)$ i.e output for delayed input $x(n-k)$ $$x_2(n) = x(n-k)$$ so $$y_2(n) = x_2(n) = x\big((n-k)^2\big)$$ and for delayed output signal $y_1(n)$, replace $n$ by $n-k$ in equation (1), so we get, $$y_1(n) = x\big((n-k)^2\big)$$ and therefore system is t...
The system is obviously <strong>time-varying</strong>. You make the usual mistake when showing the response to the delayed input <span class="math-container">$x_2[n] = x[n-k]$</span>; the correct one as shown below. Writing the output <span class="math-container">$y[n]$</span> in the formal manner: <span class="math-co...
@Fat32 followed a generic approach. It can be completed with something more ad-hoc, depending on the specific problem at hand. Here, the $n^2$ indices entail that $y$ will be limited to values of $x$ with positive (and square) indices. Now, we suspect a counter-example will do the job, by chosing some with given valu...
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20,232
[ "https://electronics.stackexchange.com/questions/20232", "https://electronics.stackexchange.com", "https://electronics.stackexchange.com/users/1912/" ]
Are there removable/soluble potting compounds that are moisture-proof yet removable without damaging electronic components? I've been able to plunge-mill potted devices to get near enough to components or test points to take measurements. A potting compound that is soluble in some sort of solvent would make failure ana...
The ability of a material to mechanically protect components, keep water out, and withstand environmental conditions is in direct opposition to being able to easily remove it. Ultimately every compound is soluble in something (water, alcohol, acetone, benzene, piranha bath, aqua regia, HF...), but the problem is that c...
May I suggest a conformal coat instead. For conformal coat, there are three main types. 1. Silicone conformal coat keeps contaminants off the circuit board whilst letting water through, effectively filtering the water. Pure water is a poor conductor so it will not affect the performance of the circuit. This can be remo...
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638,314
[ "https://physics.stackexchange.com/questions/638314", "https://physics.stackexchange.com", "https://physics.stackexchange.com/users/96769/" ]
We are taught 2/4 second rule when we learn to drive. But shouldn't it become even more than 2/4 seconds when driving on a decline in the mountains? Now, I think we can agree that indeed a declining road would make the stopping distance longer, and inclining road - shorter. But by how much? Is there a formula where we ...
Force of friction is directly proportional to the normal force of the road on the car. So the stopping force decreases according to: <span class="math-container">$F_f = \mu N = \mu mg\cos(\theta)$</span> Where <span class="math-container">$\mu$</span> is the coefficient of friction and <span class="math-container">$m$<...
The &quot;2 second rule&quot; is mainly about your reaction time when the vehicle in front brakes, and that doesn't depend on the slope of the road. The reduction in braking efficiency affects both vehicles in the same way (assuming they are have similar designs of course) so the increase in stopping distance is the sa...
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4,604
[ "https://mechanics.stackexchange.com/questions/4604", "https://mechanics.stackexchange.com", "https://mechanics.stackexchange.com/users/2356/" ]
My windshield washer pump in my Toyota Yaris Verso has stopped working. The fuse seems to be fine, so either it's due to a loose connection, or the pump is broken. What is the likely cause, and how can I access the pump?
The pump is usually mounted to the bottom of the tank. Common causes of failure: <ul> <li>Disconnected or clogged hose with the engine off can you hear the motor running under the hood? If so could be a clogged or disconnected hose.</li> <li>Wax or other debris in the jets, if the jets are located on the hood they c...
I've had a faulty windshield washer pump motor changed in my Yaris once. This one is not so easy to access. The mechanic replaced it via front right wheel area after removing front guard. He said this way is better other wise he'll have to remove front bumper, headlight then washer water tank to get to motor. Hope this...
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118,393
[ "https://chemistry.stackexchange.com/questions/118393", "https://chemistry.stackexchange.com", "https://chemistry.stackexchange.com/users/78533/" ]
Is it correct to say that "Increasing the temperature will always increase the rate of any chemical reaction"? Many articles on the internet and textbooks say yes but what about biochemical reactions that take place in our body? To my knowledge at higher temperatures some enzymes (which are catalysts in chemical rea...
Well mostly it does but there can be exceptions. Eg Consider the reaction <span class="math-container">$$\ce{2NO + O_2 -&gt; 2NO_2}$$</span> It has a negative temperature dependence. The rate decrease in increasing the temperature. There is a simple reason to why this happens. We have a RDS with an intermediate spec...
It is correct to say: "If nothing else changes, an increase in temperature will increase the rate of an elementary step of a chemical reaction". All kinds of things could go wrong. If the temperature is so high that your reaction vessel melts, spilling a liquid reactant and removing it from a solid reactant, the rate ...
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99,166
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I would like for every string that has a letter on the end make it a negative value. <pre><code>&lt;field&gt; = '00000000014545p';--Varchar(15) &lt;field&gt; = '00000000012645x';--Varchar(15) &lt;field&gt; = '00000000012345p';--Varchar(15) &lt;field&gt; = '000000004512345';--Varchar(15) SELECT SUM(CAST(&lt;field...
You should really consider fixing this data before it gets into your tables, because working around bad data is cumbersome. <pre><code>DECLARE @x TABLE(col VARCHAR(15)); INSERT @x(col) VALUES ('00000000014545p'),('00000000012645n'), ('00000000012345p'),('000000004512345'); ;WITH x AS ( SELECT col, switch = CASE W...
After finding out exactly what the data was I had to modify the code given from Aaron Bertrand to handle "over punch dibol ascii" <pre><code>DECLARE @x TABLE(col VARCHAR(15)); INSERT @x(col) VALUES ('00000000014545p'),('00000000012645v'), ('00000000012345w'),('00000000012845x'), ('000000004123450'),('000000004512345'...
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141,698
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Our project uses a user-specific configuration file. This file is currently not in version control, since it is different for each user. The problem is, whenever a developer adds a new module that requires configuration, or changes the name of an existing modules, the other developers get errors because their private c...
Though you already got some good answers here, most of them miss the root cause of your problem: your user config files seem to contain more than just user-specific information, they also contain (perhaps redundant) information which is under version control somewhere else, probably in different files, like module nam...
It's a reasonable solution. You need a way of specifying the initial value(s) of any new configuration element(s). These have to be stored somewhere and a global, read-only, configuration file is the obvious choice. Then when each user changes their personal configuration you write these changes to their local copy. ...
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31,519
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I'm trying to wrap my head around causality in LTI-systems. Considering continuous time only, I'm happy with the fact that the system is causal iff the impulse response function $h(t)=0$ for $t&lt;0$. What I don't understand is how this is embodied in an LTI differential equation. Specifically, what makes the positive...
It's important to realize that generally the differential equation (DE) alone doesn't tell us anything about causality. You claim that the system given in your question is causal. However, an anti-causal system with impulse response $h(t)=-u(-t)$ (where $u(t)$ is the step function) also satisfies the very same DE! So t...
A differential equation <strong>alone</strong> cannot tell whether the system being modeled is causal or anti-causal. Causality is an <strong>external constraint</strong> put on the system, which will guide you through the solution process. i.e. if you somehow (by other means) know that a <strong>system</strong> is cau...
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4,202,377
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I have this simple code: <pre><code>D = np.random.rand(X.shape) # Create array of given shape with [0,1] bound random floats D = ( D &lt; k ) # Get boolean values from evaluation against [0,1] bound constant k </code></pre> I would like to write this with the corresponding mathematical notations. I believe a random nu...
For the first matrix, something like this: Let <span class="math-container">$D$</span> be a matrix of the same dimensions as <span class="math-container">$X$</span> (or more likely, if <span class="math-container">$X$</span> is already known to be <span class="math-container">$m\times n$</span>, &quot;Let <span class="...
<span class="math-container">$$\{ A \}\ {\rm s.t.}\ A \in {\bf M}^{n \times m}, m_{ij} = \sim {\cal B}[\theta]$$</span> The set of matrices <span class="math-container">$A$</span> in the set of <span class="math-container">$n \times m$</span> matrices in which every component is chosen from the Bernoulli distribution w...
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468,949
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So I am given this integral <span class="math-container">$$\mathrm{I}=\int_{38}^{\infty} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=\int_{38}^{\infty} \mathrm{e}^{-\mathrm{x}} \mathrm{x}^{2} \mathrm{dx}$$</span> and i am also given this p.d.f <span class="math-container">$$g(x)=e^{-(x-38)}, \quad x \geq 38$$</span>...
Importance sampling approximates the integral <span class="math-container">$\mathbb E_{\pi(x)}[h(x)]$</span>, so <span class="math-container">$\pi(x)$</span> is the original distribution. It makes sense if the original problem is to calculate an expected value of a function wrt distribution, <span class="math-container...
There may be confusion between <em>inverse (cdf) sampling</em> which means simulating from a distribution with cdf G by taking the quantile transform of a uniform <span class="math-container">$$X=G^{-1}(U)\qquad U\sim\mathcal U(0,1)$$</span> and <em>importance sampling</em> which means replacing the expression of an ex...
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79,924
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What is the most suitable optimization algorithm for optimizing maximum likelihood estimator? In excel I used GRG non linear optimization algorithm, is that good enough? I want to write my own code to understand optimization better so I want to choose most suitable non linear constrained optimization algo for MLE. C...
Although this is obviously related to my previous answer, I think it's different enough to be considered separately. Given a point in an $n$-dimensional cloud of iid standard normals, shrink it radially a chosen proportion of the way to the corresponding fractile of a uniform distribution in the unit-radius $n$-ball. ...
For a cloud of i.i.d. standard normals, try shrinking the points toward the origin logarithmically. That is, multiply the coordinates of each point by $\log(1+\alpha\, d)/(\alpha\, d)$, where $d$ is the distance of the point from the origin, and $\alpha$ controls the amount of shrinkage, with larger values shrinking mo...
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317,558
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I would like to have a good feature selection method for a continuous response variable, over around 100 predictors. I would like to keep my model type as linear multiple regression model, rather than tree-based model. My current method: I could calculate the (linear) correlation between each of my predictor and resp...
Firstly, a method that first looks at univariate correlations for pre-identifying things that should go into a final model, will tend to do badly for a number of reasons: ignoring model uncertainy (single selected model), using statistical significance/strength of correlation as a criterion to select (if it is about pr...
There are also variable selection methods (e.g. forward or backward) with the AIC or BIC. Be aware, that interpretation of p-values after variable selection is not any more completely correct. Search "post-selection inference" for more informations about this.
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42,066
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I've been doing thermodynamic chemistry, and recently focusing on Gibbs Free Energy. Whilst doing calculations using, $$\Delta G = \Delta H - T \Delta S$$ I have been given a table of values for $\Delta H$ and $\Delta S$, and a temperature to work with. I was wondering , as the unit for entropy is $\mathrm{J/K}$ or $\m...
The most common way of measuring $\Delta S^\circ$ for a chemical reaction is probably by making a van't Hoff plot. You measure the equilibrium constant $K$ at different temperatures and plot $\ln K$ vs $T^{-1}$. The $y$-intercept = $R\Delta S^\circ$ and the slope = $-R\Delta H^\circ$. Another option is to measure $\D...
The entropy change between two thermodynamic equilibrium states of a system can definitely be directly measured experimentally. To do so, one needs to devise (dream up) a reversible path between the initial and final states. Any convenient reversible path will do, since the integral of dq/T is the same for all revers...
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11,693
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I have been working on a trained data for Word2vec algorithm. Since we need words to stay as original we don't make them lowercase at the preprocessing phase. Thus there are words with different variations (e.g "Earth" and "earth"). The only way I can think of is to take average of vectors for "Earth" and "earth" to c...
Just averaging them might not be good because that would assume that they they have the same weight, and that is probably not the case if the capitalized and uncapitilized version appear with very different frequencies in your training data. An incremental improvement would be to average them proportionally to their ...
The words "Earth" and "earth" may have the same meaning, but according to word2vec algorithm, it derives the semantic information from the position of the words. Thus commonly, "Earth" will appear most often at the start of the sentence being a subject and "earth" will appear mostly in the object form at the end. So,...
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17,444
[ "https://quantumcomputing.stackexchange.com/questions/17444", "https://quantumcomputing.stackexchange.com", "https://quantumcomputing.stackexchange.com/users/15823/" ]
I am in a study group learning about quantum computing using O'Reilly - Programming Quantum Computing. I'm a developer, not a physicist. :) I feel like my question is rudimentary but I can't seem to find an answer here or anywhere else. I'm confused on the Swap test; why it works and why doesn't it affect the qubits be...
From a programmer's perspective, you have actually asked a pretty nuanced question. You seem to have all the building blocks so I'll try and share how I think about this. Quantum gates are sometimes named similary to classical computing operations. This is usually done when the quantum gate acts like the classical ope...
Deciding which qubit is a source and which is a target and changes depends on a basis. In a basis-independent sense, the qubits get entangled, and it affects both sides. In a swap test you apply Hadamard gate to the control qubit which can be interpreted as a change of basis, and subsequent CSWAP gate changes the contr...
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2,610,547
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How could one find the complex or imaginary roots of any equations like $$x+\sqrt[3]{x}-2=0$$ One of its roots is $1$, but what is/are the other/s?
Let $\sqrt[3]{x}=t$. Hence, we have: $$t^3+t-2=0$$ or: $$t^3-t^2+t^2-t+2t-2=0$$ or: $$(t-1)(t^2+t+2)=0,$$ which gives: $$\sqrt[3]{x}=-\frac{1}{2}\pm\frac{\sqrt7}{2}i$$ or: $x=1$.
One can make the substitution $t^3=x$ so that the equation becomes a cubic in $t$: $$t^3+t-2=0$$ As you say, $x=1\iff t=1$ is a solution, so we can divide the polynomial in $t$ by $t-1$ to obtain a quadratic (I leave the long division or factoring to you). Then the resulting quadratic can be solved by the quadratic for...
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613,047
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PCB tracks carry electric signals and these produce magnetic and electrical fields around them. Due to these fields, the PCB tracks have inductive and capacative cross talk with nearby PCB tracks. I sometimes see design where signal tracks are crossing others on an immediately higher or lower layer. In my understanding...
<blockquote> When is it acceptable to have signal tracks crossing each other in the way I have described? </blockquote> Signal tracks are just pieces of metal, when you have two bits of metal with distance between them they function as capacitors. When you bring them closer together or have more area between them, it c...
Our standard stackup for multilayer (12, 14 or greater layer count) boards usually have two routing layers adjacent to each other, with a ground or power plane on either side of them. This organization is repeated throughout the stackup. One layer of those pairs is primarily for routing signals in the X direction, and...
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3,561
[ "https://security.stackexchange.com/questions/3561", "https://security.stackexchange.com", "https://security.stackexchange.com/users/-1/" ]
This is going to branch into a bunch of separate questions.....here is some background for the question: The Rijndael algorithm was crowned the new AES by Uncle Sam for sensitive, but unclassified info (128-256 key+block sizes through 10-14 rounds) . The Kerckhoff school of thought is "Let the algorithm be known, just...
There are several ways to secure the systems you are questioning in a spectrum from just physical/logical isolation to multilevel security. Your set up is simply isolated networks with plain commercial systems as the user interface. The key in your secure facility is physical separation and some logical controls of n...
According to Wikipedia, the NSA has approved AES for "Top Secret" information. You seem to think there is a single "crypto" thingy in the computer. It doesn't work that way. Each software application contains it's own crypto software. Some may choose to use the AES crypto in an OS API, or a hardware module (rare), or ...
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72,495
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In what situation should I use a Private Set on a property versus making it a ReadOnly property? Take into consideration the two very simplistic examples below. First example: <pre><code>Public Class Person Private _name As String Public Property Name As String Get Return _name ...
There are a couple reasons to use <code>private set</code>. 1) If you are not using a backing field at all and want a read-only automatic property: <pre><code>public string Name { get; private set; } public void WorkOnName() { TextInfo txtInfo = Thread.CurrentThread.CurrentCulture.TextInfo; Name = txtInfo...
Use <strong>private set</strong> when you want <strong>setter can't be accessed from outside</strong>. Use <strong>readonly</strong> when you want to <strong>set the property only once</strong>. In the constructor or variable initializer. <strong>TEST THIS:</strong> <pre><code>void Main() { Configuration config ...
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2,703,948
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There is a differential equation given: $$x' = t^3 - x^3$$ This equation's solution can't be extended to the right.<br> We are to prove that with the given initial condition: $$x(t_0) = x_0$$ contains the interval $[t_0, \infty)$.<br> What's more the proof should be completed without solving the equation.<br> I tried t...
Max vol is $x^2h$ not $xh$, hence $20^2\cdot 10=4000$, not $20\cdot 10$ (which is, by the way, 200, not 300).
<em>Oh, no, I forgot how to use derivatives!</em> Maybe I can solve this anyway, let's see.<br> $$ 1200=x^2+4xh=x^2+2xh+2xh\stackrel{\text{AM-GM}}{\geq} 3\sqrt[3]{x^2\cdot 2xh\cdot 2xh} =3\cdot4^{1/3} V^{2/3}$$ so $V\leq 4000$ and equality is attained iff $x^2=2xh$, i.e. iff $x=2h$, i.e. iff $(x,h)=(20,10)$.<br> <em>Ph...
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16,266
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I would like to develop a neural network to measure the distance between two opposite sides of an object in an image (in a similar way that the fractional caliper tool measures an object). So, given an image of an object, the neural network should produce the depth or height of the object. Which computer vision techniq...
<blockquote> For example, from among house size, lot size, age of house and asking price, what formula best predicts selling price? </blockquote> There is no general formula for this. Search for neural network regression and you can get started. The AI technique or any prediction algorithm in general will learn a fu...
You are mixing up lots of things here. Specifically, you seem to be lacking a basic understanding of artificial neural networks and what they can do (e.g. what type of articifial neural networks are linear classifiers/regressors and which can model non-linear relationships). Therefore, I'd take a step back and start ...
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510,704
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I'm approaching the potential of electrostatic field and before that, following my class' program, we prove that electrostatic field is conservative and therefore define the electrostatic potential energy due to a point charge <span class="math-container">$q$</span>: given a point at a distance <span class="math-contai...
Your two equations are the same for a system of point particles. I will show how. First, let's consider a point charge <span class="math-container">$q_i$</span> at the origin. The field <span class="math-container">$\mathbf E(\mathbf r)$</span> produced by this charge is given by <span class="math-container">$$\mathbf...
Potential energy is defined for a system i.e two or more charges. Since electric field is conservative, the work done by it is the change in the potential energy of the system. Using work energy theorem, work done by field is the negative of the work done by external force. Since work done by a conservative field is th...
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143,332
[ "https://mathoverflow.net/questions/143332", "https://mathoverflow.net", "https://mathoverflow.net/users/-1/" ]
Fix a positive integer $k$. Let $$ f(n):= \frac{k!\binom{n}{k}}{n^k} $$ Then $\lim_{n\to \infty} f(n) = 1$. Hence $f(n) \ge 1-\epsilon$ for large $n$. Define $n_0(\epsilon)$ as the least positive integer such that $n\ge n_0$ implies $f(n)\ge 1 -\epsilon$. Is there an asymptotic for $n_0(\epsilon)$ as $\epsilon\to 0$? ...
The approximation coming from the normal approximation of the binomial distribution is $$ k = \sqrt{-2n\ln(1-\epsilon)}.$$ To get more terms write $\Delta=-\ln(1-\epsilon)$, then by expanding $-\ln(1-i/n)$ as a Taylor series in $i$ and summing over $i=0\ldots k-1$, you get a series $$ \Delta = 1/2\,{\frac {k\, ( k-1 ...
Too long to fit in a comment and render all the math correctly... but why can't we just expand out $f_k(n)$ to $$ f_k(n) = \frac{n!}{n^k(n-k)!} = \prod_{j=1}^{k}\left(1-\frac{j-1}{n}\right) $$ Since the terms in this product expansion are indexed in decreasing order, for any $k$ we immediately have, for instance: $$ \...
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258,170
[ "https://mathoverflow.net/questions/258170", "https://mathoverflow.net", "https://mathoverflow.net/users/36904/" ]
The <em>diameter</em> of a bounded set is the supremum of the distances between any two points of the set, and the <em>circumradius</em> is the infimum of the radii of balls containing the set. Obviously, the diameter is never greater than twice the circumradius. A hyperplane passing through the center of the unit cub...
Answer to (a): We consider first $n$ odd and the hypercube $[-1,1]^n$. Let $(a_1,\dots,a_n)\in \mathbb{R}^{n}$ be a normal to the hyperplane. W.L.O.G we can assume that $0\leq a_1 \dots \leq a_n=1$. Consider the edge $(1,-1,\dots,1,-1,x), x\in [-1,1]$. The hyperplane will cut this edge at $x=\frac{a_1-a_2+\dots+a_{n-2}...
This seems to be just a rephrasing of Markus's answer, with some more details on the circumradius. The minimal diameter is $d=\sqrt{n-3/4}$, the minimal circumradius is half the minimal diameter. An example is indeed provided by the hyperplane parallel to some $(n-1)$-dimensional face. Consider any edge $ab$ which is...
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468,673
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A question I found in a book recently concerned two worms climbing up one side of a wall and back down the other side, such that the worms were each half across the wall (I.e. the lengths on either side of the wall were equal for each worm). To calculate the amount of work done against gravity, it is suggested that thi...
If you climb up and back down the same distance, the net work you have done against gravity is zero. Climbing up involves you doing positive work; climbing down involves you doing negative work. You don’t have to come back down the same way you went up. Over any closed loop, the net work you will do is zero.
<blockquote> does this imply that negative work can be done against gravity? </blockquote> This isn't a very well-worded questions. Forces do work. This work is independent of what other forces may be acting on the object<span class="math-container">$^*$</span>. So you should just ask "can this force do negative wor...
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33,476
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Sometimes, given an object A in an Abelian category, the Yoneda product on Ext(A, A) is graded-commutative, for example in cases where it coincides with the cup-product in singular cohomology. Are there any nice theorems about when the Yoneda product is graded-commutative in general? Thanks in advance.
I move this to a more proper answer to discuss some subtle points of the question. The Eckman-Hilton argument (or more concrete calculations) shows, as Chris points out, that $\mathrm{Ext}(A,A)$ is commutative when $A$ is the unit for a monoidal category. The subtleties appear when we consider for instance the ring $R=...
Another starting point is to think of ${\rm Ext}(A,A)$ as the derived endomorphism ring of the object $A$ and recall Schur's lemma. If $A$ is a finitely-generated simple module over a ring $R$, then ${\rm Hom}_R(A,A)$ is a division algebra. For example, if $R$ is a $k$-algebra over an algebraically closed field $k$, ...
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188,622
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I am preparing a program in VHDL and I got stuck in type-conversion. I tryed google-search and also here at stack exchange, but I am quite confused since one answer contradicts other and neither one I can get to work. But finally to the question of mine: I have to display ordinary digital clocks. I have got from my pro...
First delete the non-standard <code>std_logic_arith</code> and <code>std_logic_unsigned</code> libraries, leaving std_logic and numeric_std. As well as being non-standard, they cause problems through a VHDL rule that - if two definitions of a type (or procedure or operator or whatever) are visible - like <code>unsig...
Using the information you have given, I assume you are using incorrect type conversion functions.<br> Assuming <code>min</code> and <code>d4</code> are <code>std_logic_vector</code>s the line to calculate <code>d4</code> should look like: <pre><code>d4 &lt;= std_logic_vector(to_unsigned(to_integer(unsigned(min)) - 5...
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2,307,770
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Suppose that $(C_n)$ is a sequence of connected subsets of $X$ such that $C_n\cap C_{n+1}\neq\emptyset$ for each $n\in\mathbb{N}.$ It is required to prove that $\bigcup C_n$ is connected. The following is my attempt. Let $P(n)$ be the statement $\bigcup_{k=1}^n C_k$ is connected. Obviously $P(1)$ is true. Now let $n\i...
The first part with induction is fine. I wouldn't do it differently. The last part can be done differently as well: define $D_n=\cup_{i=1}^n C_i$. All $D_n$ are connected by the first part, and they all intersect in the non-empty $D_1 = C_1$, so their union $\cup_n D_n = \cup_n C_n$ is also connected.. This way both ...
Looks good to me. Note that as an alternative to the second paragraph, you could instead invoke the fact that a union of connected subsets that intersect nontrivially is connected (if you've already seen/proven this). That is, if $(U_\alpha)$ is a collection of connected subsets and $\bigcap_\alpha U_\alpha \neq \empty...
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84,682
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We have financial some data (500-1000 samples), which is not normally distributed (well known fact from the literature). I have some ideas to do parametric transformations of this data (using some other data) to produce "adjusted" series. My goal is to find a transformation that makes the series normally distributed (w...
The Anderson-Darling test is considered one of the best tests for normality, I think.
Sort all your data points in increasing value. If you have $n$ point (1 to $n$), transform point $i$ into $\mathcal{N}^{-1}\left( \frac{i-1/2}{n} \right)$. It does exactly what you want but it's dumb because it's not going to have a lot of predictive power. One of the main source of non-normality in financial time se...
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125,189
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Basically what I know is that 8086 can address up to 1 MB of locations which are divided in 4 segments(code, data, extra and stack) 64 KB each. But 64 KB * 4 is 256 KB, which doesn't add up to 1 MB(1024 KB). So what about the rest of space.
The four segments you mentioned are not static - these are in fact registers that can point to any 64kb zone in the 1MB memory. By changing the value of these registers we can point to other fragments of the memory. The exact computation of the effective address is performed using 2 registers: a segment register (CS,D...
The leftmost four bits of a segment register are used to extend 16-bit memory addresses, yielding 20-bit addresses. <span class="math-container">$2^{20}$</span> bytes is 1 MB.
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I am trying to derive a probability function and here are the assumptions. <ol> <li>Let <span class="math-container">$S = \{x_{(1)},x_{(2)},...,x_{(7)}\}$</span> be a set of distinct values that are ordered.</li> <li>Let <span class="math-container">$S*=\{x_1^*,x_2^*,...,x_7^*\}$</span> be a replication of <span class=...
There are <span class="math-container">$7^7=823543$</span> equally likely possibilities for the resampling with replacement. This is a tractable number and it is possible just to count how many give which order statistic as the median: <pre><code> x_(1) x_(2) x_(3) x_(4) x_(5) x_(6) x_(7) 8359 80809 196519 25...
Let <span class="math-container">$F(k,n,p)$</span> denote the binomial CDF. To keep things general, let's use <span class="math-container">$n$</span> as the (odd) number of elements instead of <span class="math-container">$7$</span>. Then, <span class="math-container">$$ p(i)=F((n - 1) / 2, n, 1 - i / n) - \sum_{j &lt;...
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207,934
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I'm reading about the twin paradox in special relativity - if there are two identical twins, one of whom who sets off in a high speed rocket to a planet, and then heads back, will find the twin who remained on Earth to have aged comparatively more due to time dilation. However, from the perspective of the travelling tw...
<blockquote> And therefore he would be able to return to Earth without having changed inertial reference frame, and then we would actually have a paradox? </blockquote> No paradox. The equations of general relativity can be solved with a universe hat wraps around, even if it is flat. What happens is that you see tw...
You and your twin both start out on the equator at 0 degrees longitude, and you both set your car odometers to zero. You drive five degrees to the east. Your twin drives 355 degrees to the west. Even though you both started and ended at the same place, your odometers show different readings. Would you count that ...
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3,250,889
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I am asked to prove this: <blockquote> Let <span class="math-container">$f$</span> be an entire function such that <span class="math-container">$f(1)=2f(0)$</span>. Prove that <span class="math-container">$\forall\epsilon&gt;0, \exists z\in\mathbb{C}$</span> such that <span class="math-container">$|f(z)|&lt;\epsilon...
<strong>Hint</strong> Assume by contradiction that this is not true. Show that <span class="math-container">$g(z)=\frac{1}{f(z)}$</span> is entire and bounded.
I was just giving my answer a final polish edit when N.S. posted; our proofs are essentially the same, though I have fleshed out a few details. Perhaps someone will find it useful. If <span class="math-container">$\forall \epsilon &gt; 0 \exists z \in \Bbb C, \; \vert f(z) \vert &lt; \epsilon \tag 1$</span> is <stro...
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492,130
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Since the voltage in a coil is proportional to the number of turns, the ratio of voltages is equal to the ratio of turns. So if you need a big increase in voltage, what stops you from having one turn on the primary (instead of a bunch) and then many more on the secondary. Or is this actually a thing? We wouldn't need...
Imagine that the secondary isn't connected to anything and isn't pulling any power. What keeps the primary current from being infinite? It's just a wire, connected across a voltage source, right? The answer is the inductance of the primary: It impedes the AC current from the AC voltage source. Even when the curren...
The transformer with too small inductance can not work normally, the primary is basically equal to shortcut circuit if the number of turns is too small.
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I'm well aware that the default answer to this textbook default question is "it doesn't work", but still, I believe it does. To cool the insides of the fridge, the compressor must do work, and since the efficiency isn't 100% you are constantly warming the whole room to cool it's insides, the winning move here is simpl...
No, you are making the fridge do extra work, so more energy is coming in (through the plug) as the pump continues to run since it's not reaching it's cold point. A normal operating fridge does not manifest cold air; it just pumps all the heat out of the inside of the fridge. The action of pumping the heat out also ...
NO. What allows a fridge maintain cool inside is the fact that the walls of the CLOSE fridge prevents heat from outside (the room heat) flows to the inside of the fridge WHILE the rate the fridge's compressor is drawing heat out (from the back or lower grills of the fridge). But if you open the door, the same amount o...
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128,706
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The following question comes from <em>General Chemistry: Principles and Modern Applications, 11th ed.</em> by Pettruci. <blockquote> <strong>Exercise 15-33.</strong> A mixture consisting of 0.150 mol H<sub>2</sub> and 0.150 mol I<sub>2</sub> is brought to equilibrium at 445 °C, in a 3.25 L flask. What are the equili...
<blockquote> In other words, is there a scenario where I could end up with two possible [solutions]? </blockquote> No, there is always a single solution. The reaction quotient Q assumes values from zero (no products) to infinity (no reactants). It varies monotonically with the extent of reaction (the x in the ICE ta...
An ICE table is moderately complicated, so it ends up seeming a bit mysterious when you get two solutions. But it's really not that mysterious at all. In fact, this sort of thing is pretty common, since it happens anytime you have two variables related to each other through a square. Let's use a very simple example ...
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52,413
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Usually, blurring filters have the sum of all the values in the filter matrix equal to <span class="math-container">$1$</span>. Why is it so?
The fft returns complex values, to get the amplitude you need to take the abs( ). The real and imaginary portion tell you about the signals phase. Remember the fft is changing the basis by projecting your signal onto a complex sinusoid: <span class="math-container">$$e^{i \omega t} = \cos(\omega t) + i \sin(\omega t)$$...
The Fourier Transform is complex valued, it can be represented either as "real part and imaginary part" or as "amplitude and phase". Normally you need two graphs to show the entire picture of a Fourier Transform The link you post just shows the real part and in this particular example, the imaginary part happens to be...
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2,229,916
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I am trying to show that the function $f:\mathbb{R}^2\to\mathbb{R}$ by the formula $$f(\mathbf{x}) = \dfrac{x_1x_2^2}{x_1^4+x_2^2} \textrm{ if }\mathbf{x} \neq \mathbf{0}$$ $$f(\mathbf{0}) = 0$$ has a limit of $0$ as $\mathbf{x}\to\mathbf{0}$. My book says I have to start by letting $\epsilon&gt;0$ and find $\delt...
Mario's answer is good, but it is also good to practice $\varepsilon-\delta$ proofs. Let $x:=x_1$ and $y:=x_2$ for easy typing. Fix an arbitrary $\varepsilon&gt;0$. First notice that for any $(x,y)\neq (0,0)$ \begin{align*} |f(x,y)-0|&amp; = \left| \frac{xy^2}{x^4+y^2}\right | \\ &amp; \leq \frac{|x|y^2}{y^2}~\text{not...
If the value you get is independent from the x1 and y1 coordinates then it exists, no need to use the epsilon delta definition: I am gonna assume x1=x and x2=y Since x and y are in the (x,y) plane, I can write x and y using polar coordinates: $$ x=rcos(\theta) $$ $$ y=rsin(\theta) $$ the limit will become: $$ \lim...
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13,314
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There is a table in our database <pre><code>tblCustomText( ParentID int NOT NULL, CustomFieldID int NOT NULL, Value char(50) NOT NULL, Log_CreateDate datetime NOT NULL ) </code></pre> (ParentID+CustomFieldID) is unique. Read operations are like: SELECT Value WHERE ParenID=@p1 AND CustomFieldID = @p2 (someti...
Seems like the following would be sufficient: <pre><code>CREATE TABLE dbo.tblCustomText ( ParentID int NOT NULL, CustomFieldID int NOT NULL, Value char(50) NOT NULL, Log_CreateDate datetime NOT NULL, PRIMARY KEY CLUSTERED (ParentID, CustomFieldID) ); </code></pre> You may also find later that you are query...
Since ParentID + CustomFieldID are unique AND NOT NULL, I would suggest you make a clustered primary key on the combination of those two fields.
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I'm conducting a project where I determine which factors (3 in total) contribute to the accuracy in which one would hit a dartboard. Each factor has two levels, low and high. For example, one of the factors is distance and the lowest distance (closest to the dart board) is 2 meters while the highest distance is 4 meter...
I would go for the distance and then use a linear model to describe this score. The other option would be a logistic regression approach, but if you have mostly "failures" as you point out in the comments, this will not be very informative. The only drawback with the distance is that it is not well behaved in terms of...
I agree that distance is your best option. The use of a cutoff throws away information about the accuracy. So accuracy change with distance from the target is better assessed with a continuously changing measure. If the shooter is unbiased (i.e. his aim is on center and the hits scatter around the center then if the...
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59,619
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I've read that too much engine oil can damage your engine, however I've also seen mechanics suggest you should just let excess engine oil burn off with driving so it's 'nothing to worry about'. These seem a contradiction of statements. When do you know whether to let it burn off and whether to drain it? I'm assuming ...
The problem is, if your engine is running correctly, <em>it won't burn it off</em>. While engines will use a little bit of oil, most of that oil is replaced by unburnt hydrocarbons introduced through blowby. Due to this, oil levels most often stay right about where they should be throughout the life expectancy of oil. ...
Engineers decide how much oil a given engine requires. If you add too much it can cause engine damage. One of the issues with an overfull crankcase is the crankshaft may dip into the oil in the oil pan. This can result in the oil being whipped into a foam. The foam by nature contains air bubbles. The air bubbles are co...
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117,400
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There are a lot of mobile apps nowadays with payment gateways support. However, unlike desktop browsers, these mobile apps do not show us an 'Address bar' by which we can identify a HTTPS connection. How can I make sure I am making a payment on a mobile app with a HTTPS connection?
As @StefHeylen says, you can't, generally. And as @d1str0 says, Burp is one way to see if the traffic is encrypted, if you can proxy the app through it. It's actually worse than that though - mobile apps don't always only make a single connection to a server. It's not uncommon for them to use HTTP for some parts, and ...
Unfortunately, unless you sniff and inspect your own traffic, you can not... My advice is not to use built-in browsers that do not indicate the protocol being used to handle sensitive information
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36,660
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Subsurface oceans in satellites are pretty common: Europa, Enceladus, Ganymede, Callisto, maybe Pluto... This is due to tidal heating of their host planet, Jupiter and Saturn, which heats up the inner ice of those satellites. However, planets don't exhibit this inner ice layer, so they don't usually have subsurface oce...
The terrestrial planets are Mercury, Venus, Earth and Mars. Mercury and Venus are too hot for liquid water to exist at any level, Mars has lost nearly all its water and Earth has a surface ocean, not a subsurface one. The inner planets lost most of their volatiles (including water) as they formed, the water on Earth w...
Some hypothesize that the Earth did have a subsurface ocean during the Cryogenian period, which lasted from 720 to 635 million years ago. The Cryogenian saw the two greatest known ice ages in the Earth's history, the Sturtian and Marinoan glaciations. There is some evidence that the Earth was completely covered with ic...
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2,954,533
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Let <span class="math-container">$e_n = (0,0,\dots,1,0,0,\dots)$</span>,(i.e. the n-th component is 1). Show that <span class="math-container">$e_n\rightharpoonup 0$</span> in <span class="math-container">$\sigma(\ell^{\infty},(\ell^{\infty})')$</span>. I'm having trouble because the dual of <span class="math-container...
You're right that you can't use the direct argument for <span class="math-container">$1 \le p &lt; \infty$</span>. Have you tried contradiction? This gives you an <span class="math-container">$x' \in (\ell^\infty)'$</span> and <span class="math-container">$\varepsilon &gt; 0$</span> with <span class="math-container">$|...
Well, in some sense, <span class="math-container">$l_1$</span> is 'enough' of a dual for the purposes of this problem! Suppose <span class="math-container">$f$</span> is a linear functional, let <span class="math-container">$g_k = f(e_k)$</span>. Choose <span class="math-container">$x_k$</span> such that <span class=...
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I'm working on a project where exist one method with title <pre><code>string ValidateNewPasswordExpireCurrentPasswordAndCreateNewPassword(...) </code></pre> I'm sure the method name must be changed. But can't found good and descriptive alternative. Also I can't separate method in multiple methods, like ValidateNewPa...
I expect this method to call three other methods: <pre><code>public string ValidateNewPasswordExpireCurrentPasswordAndCreateNewPassword(string password) { AccountManager.ValidatePassword(password); AccountManager.ExpirePasswordForAccount(this.CurrentAccount); AccountManager.AssignPasswordToAccount(this.Cur...
<pre><code>string ChangePassword(...) { if(ValidateNewPassword(...)) { ExpireCurrentPassword(); CreateNewPassword(); return ... //Method signature is string? } else { //Handle invalid password } } </code></pre> Much cleaner IMO!
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The residual in estimation is the difference between the measurement and the previous estimate. My question is when I plot this quantity, what is ,if any, information I can extract or infer from this quantity? No beneficial information I can see from the figure. Any suggestions?
If your estimate is based on a linear time invariant model then you could use the following measures for the quality of your estimate: cross-correlation between the estimate and residual, and the autocorrelation of the residual. Namely the cross-correlation should be close to zero at all time, otherwise there would sti...
Your residual tells you if your model ,is a good fit to the data. It should meet the orthogonality criteria as described in @fiboranic’s answer if your model is linear and noise is Gaussian. In Kalman Filter Tracking, the Interacting Multiple Model Technique (IMM) the residuals are the innovations sequence and they ar...
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567,465
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Is there a way to algebraically see why when I take the second derivative of a potential energy in a point where it is minimal (force is zero), I generally get the frequency (squared) of the oscillations around this point?
In a harmonic oscillator, <span class="math-container">$$F=-kx$$</span> where <span class="math-container">$k$</span> is a constant and <span class="math-container">$x$</span> is the displacement from the mean position. Thus, <span class="math-container">$$\frac{\mathrm dF}{\mathrm dx}=-k\tag{1}$$</span> about the equi...
The other answers have begun by assuming a force linear in displacement. Let us take a step back and see why harmonic oscillators are popular in physics. Consider perturbing a system slightly off a stable equilibrium. This means that it is perturbed from a minima (by a small amount <span class="math-container">$\epsilo...
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Sorry for a rather rookie question. I am very new to vehicle maintenance, and trying to do my own oil change. Recently I bought a used Volkswagen T5 Transporter 2.0 TDI DSG. And I've been looking at videos about oil change. <strong><em>My question is:</em></strong> Is the DSG transmission fluid the same as engine o...
<blockquote> Is the DSG transmission fluid the same as engine oil? </blockquote> No, it's a specific fluid (DSG's aren't conventional torque-converter automatics and you shouldn't use Automatic Transmission Fluid in them). You can buy a kit for a DSG fluid change which should come with the requisite DSG oil (6 litr...
Gearbox fluid and engine oil are different things. If you are a beginner you should probably think twice about changing your gearbox oil, especially since you probably don't need to - it's something with a long life. The filler cap is removed to let you fill the engine oil reservoir, when it's in place it prevents th...
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3,295,946
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This is a problem from Spivak's Calculus 4th ed., Chapter 1, Problem 16(b). <blockquote> Using the fact that <span class="math-container">$x^2 + 2xy + y^2 = (x + y)^2 &gt; 0$</span>, show that <span class="math-container">$4x^2 + 6xy + 4y^2 &gt;0$</span> unless <span class="math-container">$x$</span> and <span c...
It is almost correct. The only flaw lies in the fact that you should assume only that <span class="math-container">$x\neq0$</span> <em>or</em> <span class="math-container">$y\neq0$</span>. Therefore, you cannot say that both numbers <span class="math-container">$x^2$</span> and <span class="math-container">$y^2$</span>...
More generally, since <span class="math-container">$\begin{array}\\ ax^2+2bxy+ay^2 &amp;=a(x^2+y^2)+b(x^2+2xy+y^2)-b(x^2+y^2)\\ &amp;=(a-b)(x^2+y^2)+b(x+y)^2\\ \end{array} $</span> if <span class="math-container">$a &gt; b$</span> then <span class="math-container">$ax^2+2bxy+ay^2 \ge 0$</span> with equality if and on...
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My 2001 Honda Civic needs a new muffler every two (2) years or so, because the inlet pipe corrodes just after the union. Is this a common problem, or would installing a better quality muffler prevent this? Aren't most exhaust system components stainless steel, how is it that it corrodes so quickly?
Sounds like the power window motors are dying. It's actually a fairly rare situation though, usually switches fail first. Might be worth pulling the switches and checking/cleaning them just to make sure you're not actually having some sort of weird intermittent switch connection that's making the motor appear to be w...
Sounds like the both front window run channels are dirty and dry may want to try cleaning and run some silicone spray down rubber run channels
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225,201
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<strong>Need of SSC:</strong> Spread spectrum clocking (SSC) is a special way to reduce the radiated emissions of digital clock signals. These levels or energy is radiated and therefore this is where a potential EMI issue arises. <strong>Doubt:</strong> Assume that SSC clock has range from -5300 to 300 ppm, assuming...
Most of radiated energy in EMI/RFI comes from the edges or clock transitions. How SSC works is by dithering these edges to reduce the reinforcement of the transmitted frequencies. Essentially you are broadening out the peak transmission energy. You are not really changing the energy as the integrated energy (integrat...
According to me, <blockquote> If core clock (generated SSC) is given to whole system blocks then does it affect Fmax of designed system? (Frequency of operation may varies!!), every thing including SerDes have same source of frequency. </blockquote> Option is better, because we know SSC, so we have to design our s...
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29,408
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I have two random variables: $x = N(0, \sigma^2)$ and $y =U[0, b]$. I need to compute $E(x/(1+y))$. How does one go about doing this? They are independent so the joint pdf is just the product of the two pdfs but can the integral be computed in closed form or is this something that should just be done numerically?
From your description (and comments) you're trying to calculate $E \left( \frac{X}{1+Y} \right)$ where $X \sim N(0,\sigma^2)$ and $Y \sim {\rm Uniform}(0,b)$. By independence, $$E \left( \frac{X}{1+Y} \right) = E(X) \cdot E \left( \frac{1}{1+Y} \right)$$ We know $E(X) = 0$, therefore $$E \left( \frac{X}{1+Y} \righ...
Since it's not homework, then the expectation is zero by symmetry. How could there be an argument suggesting the answer is $k&gt;0$ without a similar argument suggesting $-k$?
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127,064
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I want to be able to control a heating element's (which runs on 230V mains) power level, and I'm thinking of running it using a solid state relay and PWM. However, I'm unsure of the implications of doing this. <ol> <li>Current draw - The heating element is 2000W, so ~9 amps. Will the switching this amount of current a...
Turning it on and off using a zero-crossing SSR and a timebase of 10 or 30 seconds will not cause significant EMI (because it's switching at the zero crossings). It may cause objectionable light flickering if the lights are on the same circuit, in the same way that laser printers and copiers sometimes cause flickering...
Heating elements are designed to handle the mechanical stresses from thermal cycling. Turning them on and off many times doesn't usually cause problems. One thing to consider is the time constant from applying power to a heating element to the temperature changing in whatever is being heated. Most likely this is muc...
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96,362
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What do we really mean when we say that the neutron and proton wavefunctions together form an $\rm SU(2)$ isospin doublet? What is the significance of this? What does this transformation really doing to the wavefunctions (or fields)?
Two particles forming an $SU(2)$ doublet means that they transform into each other under an $SU(2) $ transformation. For example a proton and neutron (which form such a doublet) transform as, \begin{equation} \left( \begin{array}{c} p \\ n \end{array} \right) \xrightarrow{SU(2)} \exp \left( - \frac{ i }{ 2} \theta_...
I don't know what background you bring to the question. So at the risk of sounding patronizing, let me give a down-to-earth answer. I wonder if this helps. <hr> Think of rotations on the (Real) 2-dimensional plane $\mathbb{R}^2$. You can rotate the X-axis into the Y-axis, and the Y-axis into the negative X-axis. Thi...
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486,089
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Many applications of image classification involves convolutional neural network, where the image is treated directly as a 2D (or 3D, if multiple images) matrix. I wonder if images can be classified (and with reasonably good performance) with a MLP or softmax regression or even SVMs by vectorizing them, meaning to stack...
Standard <em>error</em> decreases as the sample size increases. Standard deviation is a related concept but perhaps not related enough to warrant such similar terminology that confuses everyone who is starting to learn statistics. A sampling distribution is the distribution of values you would get if you repeatedly sam...
Standard deviation <em>does not</em> decrease with sample size. The bigger your sample is, the closer the standard deviation should be to the standard deviation of the population. What follows, with larger sample size the spread of the standard deviations estimated on larger vs smaller samples would decrease, because b...
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490,994
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Let's supposed a box is sliding on a friction-less surface, so it has some KE at this point, and let's imagine an external force is being applied on the opposite direction of the displacement of the box, the work of the external force is negative, so it will start reducing the KE of the box, and eventually it will sto...
I think what he means is with reference to his equation (5.1) <span class="math-container">$$\psi = \sum_n c_n \psi_n. $$</span> These <span class="math-container">$\psi_n$</span> states are in a superposition and this superposition is not the same as saying the system has some probability of being in one state or the...
If I interpret what the author had in mind correctly, he would like to distinguish between the uncertainty (and related probability distribution) inherent to quantum mechanics, and the incomplete statistical description given by a density matrix. In fact, a (non-pure) density matrix describes a (quantum) system on whi...
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14,693
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Suppose we have two matrices $A$ and $B$ (we can assume they're symmetric; if absolutely necessary I think they may be positive definite). Then, is there any technique for solving $$(A\circ B)x=b,$$ where $\circ$ denotes the Hadamard (elementwise) product? I am seeking a direct solver if possible rather than iterat...
Ultimately, it depends on the sparsity of $A$ and $B$ and the symmetry of the resulting hadamard product. The hadamard product will aggregate the sparsity structure of $A$ and $B$. So if one or the other is sparse, the product is also sparse (and may be more so if $A$ and $B$ have difference sparsity structures). So...
The nonzero elements of the product are exactly those locations that are nonzero in <em>both</em> matrices. In other words, the sparsity pattern of the product is a <em>subset</em> of the sparsity patterns of the two matrices, and a cheap way to form the product is to take the sparser of the two matrices and for each o...
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27,083
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Since they exist for several fields with varying degrees of usefulness, I'm curious as to the reputation of headhunters/recruiters that focus solely on IT professionals (e.g. programmers, software engineers, CIOs, etc) when it comes to finding a new job. Are they actually useful or is it fairly hit or miss? Does the ...
I think they can be helpful, but you have to be aware that their job isn't to find a good place for you, it's to sell you on a place that hired them to find people. I haven't dealt with many recruiters in my career (yet?) but the ones I did come across were fairly non-technical and were just parroting vague job descri...
<strong>Some agents are brilliant, others not so</strong> As a contractor in the UK, I deal with many agents (headhunters) on a regular basis. Almost invariably they do not have strong technical skills and it doesn't really matter. <em>Their business is to get their candidate to be accepted by their client</em>. If th...
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4,253,910
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Let <span class="math-container">$M\in \text{SO}(3,\mathbb{R})$</span>, prove that <span class="math-container">$\det(M-I_3)=0$</span>. My attempt: <span class="math-container">$$ \begin{align} \det(M-I_3)&amp;=\det(M-M^TM)\\&amp;=\det((I_3-M^T)M)\\&amp;=\underbrace{\det(M)}_{=1}\det(I_3-M^T) \end{align} $$</span> He...
Your answer is certainly the most direct proof, assuming you know <span class="math-container">$M\in SO(3,\mathbb R)$</span> if and only if <span class="math-container">$M^TM=I_3$</span> and <span class="math-container">$\det M=1.$</span> We could, instead, go back to another definition of orthogonal matrix: <blockquot...
This argument checks out. For an alternative approach, start with the fact that <span class="math-container">$M$</span> corresponds to a specific rotation of 3D space. Thinking geometrically, it is clear that this rotation will have a unique axis of rotation (itself a 1D subspace of <span class="math-container">$\mathb...
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77,383
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I asked myself the following question when I was student just for curiosity. I asked a bit around (my professor, some researchers that I know), but nobody was able to give me an answer. So maybe it is just that nobody thought enough about that, or maybe it is not a stupid question. <strong>Question:</strong> Do there ...
The duals of $C[0,1]$ and of $C[0,1]\oplus_\infty c_0(\Bbb{R})$ are isometrically isomorphic.
The James Tree space $JT$ and $JT \oplus_2 \ell_2(2^{\aleph_0})$ have isomorphic duals.
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237,931
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Edward Frenkel said that "we can see Langlands program as a generalization of Shimura-Taniyama-Weil conjecture in the case of elliptic curves" I hope I'm not distorting his phrase, can someone explain what that means. Lets say that I'm little bit familiar with the ingredients used in both conjectures, Galois represen...
Clearly you can find an unbounded definable curve $C\subset X$. Any set in $\mathbb{R}_{an, exp}$ admits a <em>finite</em> stratification by real analytic submanifolds. Pick one such stratification of $C$. One of the strata of this stratification is an unbounded real analytic curve contained in $C$ and, a fortio...
This holds in any o-minimal structure. First perform an inversion $i\colon x\mapsto x/\|x\|^2$ so that the origin becomes a limit point of $i(X)$. Then apply the <em>Curve selection lemma</em>: for every definable set $A$ in an o-minimal structure, and any limit point $a\in \overline A$, there exists a definable map $...
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21,446
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I have a question about Newton's law. The question says <blockquote> block A(mass 2.25kg) rests on a tabletop. It is connected by a horizontal cord passing over a light, friction less pulley to hanging block B(mass 1.30kg). The coefficient of kinetic friction between block A and the tabletop is 0.450. After the blo...
The short answer is, it doesn't really mean much of anything, because it's not meaningful to compare the Gibbs free energy of two systems unless they're at the same temperature. To show you why, I'll quickly run you through the derivation of the Gibbs free energy and point out where the constant temperature assumption...
The absolute value of the Gibbs free energy decreases as the spontaneous process happens. The negative value represents the spontaneity of expansion. The more negative (smaller) the G, the more work you can obtain from the system. So as work is done on the surroundings, G becomes closer to zero, and in this case increa...
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102,260
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Assuming that f(n) >= n. If possible, I'd like a proof in terms of Turing machines. I understand the reason why with machines that run on binary, because each "tape cell" is a bit with either 0 or 1, but in Turing machines a tape cell could hold any number of symbols. I'm having trouble why the base is '2' and not som...
<blockquote> why the base is '2' and not something like 'b' where 'b' is the number of types of symbols of the Turing machine tape? </blockquote> Because it does not matter in the sense that <span class="math-container">$2^{O(f(n))} = b^{O(f(n))}$</span> for any positive <span class="math-container">$b &gt; 1$</span...
Because an exponential function to any base can be expressed in terms of any exponential function of another base, in a way which also happens to make this possible. Namely, for any real number <span class="math-container">$a &gt; 0$</span>, <span class="math-container">$a^x = 2^{\lg(a)\ x}$</span>. Thus if you have <s...
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4,600
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As I understand it, greenhouse gases absorb infrared radiation from the sun. Much of that radiation would otherwise continue and be absorbed on the planet surface in the ocean or on land. If CO<sub>2</sub> increases are causing the oceans to warm, does that happen mainly by convection? It's counter intuitive to me t...
<blockquote> If CO2 increases are causing the oceans to warm, does that happen mainly by convection, then? It's counter intuitive to me to think about air convection having that much effect on ocean temperatures. Why wouldn't greenhouse gases' soaking up of infrared instead cool the oceans, that would otherwi...
No, greenhouse gases do not absorb infrared radiation from the sun... the Earth is really the source of infrared. The amount of infrared energy from the sun that reaches Earth is insignificant. Visible light from the sun heats the Earth, NOT infrared light. The visible light passes through the atmosphere and is abso...
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114
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I know that minimal light pollution is a must for stargazing, and a place which is away from civilization is better. Does altitude of a place matter for light pollution? Does it affect the quality of star gazing?
A good question, and in the early 2000s John Bortle published a categorization of a variety of conditions, with descriptions for each category. It is the commonly used scale to describe to others the sort of conditions at a location. Probably one of the more significant factors provided by a dark sky site is: how fai...
Yes, altitude does play a role. The higher you go, less photons from civilization will reach you, as most of it will be scattered by dust in the air. Also, as to answer "what qualifies as a good place", as if you are asking for a criterion, a popular one is : "If you can see all the stars of Little Dipper, well that'...
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108,992
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When a current carrying wire attracts(or repels) another wire, the wire moves under the action of a force. Also, it is obvious that the work done is due to force of "magnetic field" on "moving electrons". Now, from the equation $$\overrightarrow F=q[\overrightarrow v,\overrightarrow B] $$, where $[\overrightarrow a,\o...
<blockquote> Also, it is obvious that the work done is due to force of "magnetic field" on "moving electrons". </blockquote> This part is problematic, as you probably already know (you've put the quotes). There is macroscopic magnetic force on wire 1 due to wire 2 given by $\int \mathbf j_1 \times \mathbf B_2 \,d^3\...
The work done will be the change in electric potential . If we assume current density to be constant and electric current to be constant(DC current) then we can equate this wire to a linearly charged wires(Static field). The amount of charge per unit length is always constant since outgoing electrons are replaced by in...
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One of the following is a subspace of <span class="math-container">$P_{2}$</span>. A. <span class="math-container">$W= \{ax^2+bx+c\mid a+b+c=1\}$</span> B. <span class="math-container">$W= \{ax^2+bx+c\mid a+b+c=0\}$</span> C. <span class="math-container">$W= \{ax^2+bx+c\mid a \geq 0\}$</span> D. <span class="math-conta...
<blockquote> How does having 'a' greater than or equal zero differ from having 'b' and 'c' greater than or equal zero? Can someone please explain how it works? </blockquote> So, for example, consider the polynomials <span class="math-container">$$ p_1(x) = 2x^2 + 3x + 4,\\ p_2(x) = -3x^2 + 4x + 5,\\ p_3(x) = 0x^2 - 5x ...
<strong>Hint to answer the title question:</strong> A subspace must be closed under multiplication by a scalar such as <span class="math-container">$−1$</span>.
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To put this question in precise language, let $X$ be an affine scheme, and $Y$ be an arbitrary scheme, and $f : X \rightarrow Y$ a morphism from $X$ to $Y$. Does it follow that $f$ is an affine morphism of schemes? While all cases are interesting, a counterexample that has both $X$ and $Y$ noetherian would be nice.
No, here is an example of a morphism $f:X\to Y$ which is not affine although $X$ is affine. Take $X=\mathbb A^2_k$, the affine plane over the field $k$ and for $Y$ the notorious plane with origin doubled: $Y=Y_1\cup Y_2$ with $Y_i\simeq \mathbb A^2_k$ open in $Y$ and $Y\setminus Y_i= \lbrace O_i\rbrace$, a closed ...
Though it is not true in general, it is true whenever $Y$ is separated. The map $f$ from $X$ to $Y$ factors as a composition $$ X \stackrel{f'}{\rightarrow} X \times Y \stackrel{f''}{\rightarrow} Y$$ The map $f''$ is a pullback of the projection map from $X$ to a point (or Spec $\mathbb{Z}$, or whatever base you are wo...
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14,361
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Does anyone know of a chip which can extract the colour burst from a PAL or NTSC video signal? Then, I would need to start an oscillator of the right frequency (4.43361875 MHz for PAL, and 3.579545 MHz for NTSC) and keep it oscillating once this frequency is established. If the signal is PAL, I would also need to phase...
I would guess you're trying to upgrade your video overlay projects for color? A tough job. One difficulty you're apt to encounter is that while a 100ns jitter on a luminance signal is annoying but tolerable, and 50ns would be barely noticeable, even a 25ns jitter on your chroma signal will be clearly visible (it's ab...
I know this is a year old but I came across someone with a similar issue who solved it differently. He was doing capture of NTSC colour images. He threw out the notion of genlocking to the NTSC colour burst at all. He used a synchronous detector to sample the color burst at the beginning of each line at the chroma fre...
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4,079,072
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<strong>The Question</strong> <span class="math-container">$$\int \csc\left(x-\frac{\pi}{3}\right)\csc\left(x-\frac{\pi}{6}\right) dx $$</span> <strong>What I Tried-</strong> <br/> I tried dividing both numerator and denominator by <span class="math-container">$\sin \pi/6$</span> but couldn't get too far, what I got af...
Hint <span class="math-container">$$\csc(x-\pi/3)\csc(x-\pi/6)$$</span> <span class="math-container">$$=\dfrac1{\sin(\pi/3-\pi/6)}\cdot\dfrac{\sin(x-\pi/6-(x-\pi/3))}{\sin(x-\pi/3)\sin(x-\pi/6)}$$</span>
<span class="math-container">$$\csc \left(x-\frac{\pi }{3}\right)\csc \left(x-\frac{\pi }{6}\right)= \csc \left(\frac{\pi }{6}-x\right) \sec \left(x+\frac{\pi }{6}\right)=\frac{4}{\sqrt{3}-2 \sin (2x) }$$</span> Now, let <span class="math-container">$x=\tan^{-1}(t)$</span> and tou face <span class="math-container">$$I=...
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37,619
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So we're looking at the possibility of porting our software to support multiple languages and one of the areas we're going to have to deal with is error messages and other notifications. These obviously have to be reported to the users in their own language. Our team (largely) only speak English and even if we were a...
In applications I have done that needed to be multi-lingual we use a table type approach to hold each language set of strings. Access to the table is via an enumeration. This plus error codes that are universal would allow the end user to see your error message while retaining a code value to help the development tea...
If you have the translations in your database, then you have the ability to translate them back to English. After a while you will be fluent in globalized error messages :) <blockquote> My suggestion is to not worry about that and focus on being user friendly. </blockquote> Please keep in mind that non english spea...
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237,684
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Generally we equate change in potential energy to change in kinetic energy but in case of a charged particle like electron this is inconsistent. Consider a case: An electron(of charge e)from rest is accelerated in potential difference V then the final kinetic energy is given by KE=eV But we know that accelerating ...
Speed of sound in air is the speed with which a pressure wave propagates. If you look at the wave itself, without considering its source, you have all the information you need to determine the speed of propagation - since it's only the local conditions (things like the density, and the local rate of change of pressure)...
When you are quoted a value for the speed of sound it is implicit that it is the speed of sound relative to the medium which in air is about 330 m/s. The significant difference with electromagnetic waves is the necessity for a medium for a sound wave to exist.<br> It means that if there is a wind of speed 30 m/s (rela...
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137,512
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I have following table of number ranges <pre><code>Create table Ranges { Id int identity(1,1) primary key, RangeFrom int not null, RangeTo int not null } Insert into Ranges(RangeFrom, RangeTo) VALUES (1,4) Insert into Ranges(RangeFrom, RangeTo) VALUES (5,9) Insert into Ranges(RangeFrom, RangeTo) VALUES (10,14) ...
You could use an insert trigger to check the inserted values against the table data, and fail if the range already exists. But since you are using a Stored Proc, you can check in the proc. Something like this: <pre><code>CREATE PROCEDURE blah (@rangeFrom int, @rangeTo int) AS BEGIN IF EXISTS( SELECT 1 FROM Ranges W...
<pre><code>select count(*) from ( select RangeTo, LEAD(RangeFrom, 1, 0) OVER (ORDER BY RangeTo) AS LeadRangFrom from table ) ss where @RangeFrom &gt; RangeTo and ( @RangeTo &lt; LeadRangFrom or LeadRangFrom is null) </code></pre> If count(*) is one then you can insert<br> Is ...
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76,730
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What is the physical significance of molecular partition function? I reason, that the molecular partition function \begin{align} q &amp;= \sum_i \exp(-\beta\varepsilon_i),&amp; \beta &amp;= \frac{1}{k_\mathrm{B}T} \end{align} is found in the expression for the populations of each configuration, derived from the Bol...
The partition function $q=\sum_i\exp(-E_i/k_BT)$ in your question can be regarded as the <em>effective</em> number of levels accessible to the molecule at a given temperature. It also means that in the equilibrium distribution the partition functions tells us how the systems are partitioned or divided up among the diff...
In the simplest terms and most convenient definitions, it represents the total amount of states that the energy can be in. The probability expression you wrote emphasizes this. A probability is a part over a whole. So in the case of Boltzmann's distribution, it is one state over the sum of all the states.
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231,865
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I have an inexpensive 2 inch diameter speaker. The back is stamped with “8 ohm, 0.5 W”. The measured DC resistance is 7.2 ohms. Does the stamped “8 ohm” refer to the total impedance at some standard sine wave frequency, e.g., 1 kHz? If so, does that mean that when driven at 1 kHz that the total impedance may be exp...
<blockquote> Does the stamped “8 ohm” refer to the total impedance at some standard sine wave frequency, e.g., 1 kHz? </blockquote> Only approximately. It's a "nominal" value, but the actual value can vary over a rather large range. <blockquote> If so, does that mean that when driven at 1 kHz that the total imped...
Just using this as an opportunity to reflect on why those impedances might be "nominal". The speaker is an electro-mechanical-acoustical device and as such all those characteristics are seen across the two terminals on the back of the speaker. Electrically there is the obvious resistance of the coils, the magnetic ma...
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26,419
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In a lecture, we were given the following example to explain the operational significance of the trace distance. Suppose that Alice prepares one of two (known) states <span class="math-container">$\rho_0$</span> or <span class="math-container">$\rho_1$</span> with equal probability, and then passes the state to Bob. Bo...
If <span class="math-container">$f(x) = a^x \pmod{N}$</span> passes through <span class="math-container">$-1$</span>, that value of <span class="math-container">$a$</span> won't work. For example, <span class="math-container">$a=2$</span> fails for <span class="math-container">$N=33$</span> because <span class="math-co...
What you <em>should</em> have seen in texts is the statement that you have to pick <span class="math-container">$a$</span> at random from the numbers that are coprime to <span class="math-container">$N$</span>. There are then certain claims about the order, <span class="math-container">$r$</span> that you get: <ul> <li...
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107,509
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Usually in a LSTM network, we have certain parameters that need to be set before the model can begin training. I am specifically talking about <strong>vocabulary size</strong>, <strong>padding length</strong> and <strong>embedding dimension</strong>. Below is a simple LSTM network where I have randomly chosen the 3 par...
Vocabulary size, padding length and embedding dimension are like hyperparameters which needs to chosen wisely to get good performance from model Vocabulary Size : The set of unique words used in the text corpus is referred to as the vocabulary. When processing raw text for NLP, everything is done around the vocabulary....
Ideally padding should not be done for whole data but for batches. Padding comes from the need to encode sequence data into contiguous batches: in order to make all sequences in a batch fit a given standard length, it is necessary to pad or truncate some sequences. Usually people do post padding i.e. introduce zero af...
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89,514
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I am trying to determine a set of differential equation which can describe the motion of a mechanical system as below. Here, at the bottom we have a plate, and a box on top of it. Inside the box, there is a ball supported by 2 springs. Then we try to oscillate the bottom plate. If needed, the assumptions are as below...
Here are the steps you can take. <ol> <li><strong>Degrees of Freedom</strong>. There are 3 degrees of freedom, one for the base plate, one for the box and one for the mass. Hence there are 3 variables that you need to track, as well as their derivatives. I will name them $x_0=\gamma(t)$ for the plate, $x_1$ for the bo...
The behavior of the system (not surprisingly)depends on the initial conditions. (For the sake of argument, we can assume the box starts stationary with respect to the table and $\gamma(0)=0$) I am assuming the problem is $1d$; this way we will end up with two coupled equations of motion. Let's show the box's coordinat...
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40,471
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While looking at the database structure of an application I am using I recognized that it uses 3 different databases on the same SQL Server instance for different things. The first one contains the main data that changes rarely. The second one contains event logs with high traffic and volume and the last one is an ar...
Ask the developers/architects who designed the solution. Only they can really tell. I can think of several reasons: <ol> <li>It could be that the databased was added at different times. First the main database, then they decided they needed a database for the events and last a place to store old data. Depending on env...
You've got two different questions in here that I'll answer separately. <strong>Q: Can the performance of one table suffer from other large tables in the same database?</strong> Yes, during insert/updates/deletes. SQL Server only has one log file per database. When you insert/update/delete, your transaction doesn't c...
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378,055
[ "https://mathoverflow.net/questions/378055", "https://mathoverflow.net", "https://mathoverflow.net/users/66131/" ]
Consider the following identity <span class="math-container">$$\sum_{n=0}^{R-t}\binom{n+\ell}n\binom{R-\ell-n}{R-t-n}=\binom{R+1}{t+1}.\tag1$$</span> It is relatively easy to give an algebraic or mechanical proof of (1). But, I like to ask: <blockquote> <strong>QUESTION.</strong> is there a combinatorial reason why the...
<em>(I am late to post a very similar answer to the already given one, yet I'd like to post it as well, since it differs in some detail)</em> Changing the summation index to <span class="math-container">$m=n+\ell$</span>, the identity writes <span class="math-container">$$\sum_{m=\ell}^{R-t+\ell } {m\choose \ell}{R-m...
Well, here's a combinatorial proof of the identity anyway (but not a direct proof of independence of <span class="math-container">$\ell$</span>). Write <span class="math-container">$N = R - t$</span>. Then the identity is <span class="math-container">$$\sum_{n=0}^N \binom{n + \ell}{n} \binom{R - n-\ell}{N - n} = \binom...
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179,907
[ "https://softwareengineering.stackexchange.com/questions/179907", "https://softwareengineering.stackexchange.com", "https://softwareengineering.stackexchange.com/users/74449/" ]
I'm building a blogging site for learning, with a PHP/MySQl back-end. All of the user input is handled with forms sent in POST requests. Will using JSON somehow make it cleaner, or easier to maintain or add features? Or am I just adding an interchange format for no reason? So essentially, what functionality would be ...
JSON has a few advantages: <ul> <li>It's a structured format, which can be validated and parsed with existing, mature tools.</li> <li>It can speak easily to JavaScript, which makes it very useful for AJAX communication.</li> <li>It's extremely simple and lightweight. Anything you'd want to use XML data interchange fo...
For what you describe - it sounds like a blogging platform where everything is submitted via forms - no, you dont need to convert it all to JSON. PHP handles forms seamlessly for you. There's no reason to introduce a new piece of complication in that situation. Again, <em>in your specific circumstance</em>, JSON mig...
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2,683,645
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I was doing an exercice and there is a sentence in the correction i didn't quite understand. I had three balanced dices and I had to find the probability that the sum gave an even result. When I check my answer they just give a weird explanation : let $(i,j,k)$ be result of my 3 dices in $\{1,2,3,4,5,6\}$ and an applic...
It's one-to-one, each triple $(7-i,7-j,7-k)$ corresponds to a single input $(i,j,k)$. There's no way to have $(7-i_1,7-j_1,7-k_1)=(7-i_2,7-j_2,7-k_2)$ unles $(i_1,j_1,k_1) = (i_2,j_2,k_2)$. Furthermore, it is surjective (onto) since we have when $(7-1,7-1,7-1,)=(6,6,6)$ all the way to $(7-6,7-6,7-6)=(1,1,1)$, i.e. all ...
If $i+j+k$ is even $(7-i)+(7-j)+(7-k)$ is odd.
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422,185
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My company has its own proprietary software that I have both built and maintained over the last 5 years I am about to release a big change for all of my software to use OAuth2 instead of handling emails and passwords ourselves. Prior to this release because I managed 100% of the dataflow, I had a feature for the admins...
There is no standard which is used by every company: some rely on impersonation; others avoid it at all costs. Impersonation was useful fifteen years ago, where there weren't many convenient tools for screen sharing. Today, not only there are plenty of tools for that, but most users are familiar with at least one of th...
Whether you own the company or not, I think the only clean way is the ability to change someone’s password, in a way that is clearly and undeletably logged. If you can log in as an arbitrary user without a trace, then any user can deny any wrongdoing because you could have done it without leaving evidence. And then the...
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119,037
[ "https://mathoverflow.net/questions/119037", "https://mathoverflow.net", "https://mathoverflow.net/users/30685/" ]
Is the statement below false? "The metaplectic group Mp2(R) is not a matrix group: it has no faithful finite-dimensional representations." <hr> Possible "counterexample": Sp(2n,R) is a subgroup of O(4n,C) (or O(2n,2n) if you prefer). So the Clifford algebraic Pin group will contain a double cover. The double cover w...
Keep in mind that any finite-dimensional representation of a Lie group determines a finite-dimensional representation of its Lie algebra, and for a connected Lie group the induced Lie algebra representation determines the Lie group representation. However, every finite-dimensional representation of $\operatorname{Lie}...
The answer of Theo seems to be right. Nevertheless, it is not explained that "the Mp(2,R)-representation that gave rise to V factors through SL(2,C) and on the other hand Mp(2,R) -> SL(2,C) factors through SL(2,R)". This cannot be true in general. E.g. in the case of SO(n) and Spin(n), i.e., when SL(2,R) is replaced by...
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698,080
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How do I find the unit of a log-normal probability density function?
The units of a probability density function (PDF) for a quantity <span class="math-container">$x$</span>, are the inverse of the units of <span class="math-container">$x$</span>. For example, if <span class="math-container">$x$</span> has units of length, then the PDF <span class="math-container">$P(x)$</span> has unit...
Consider any <em>continuous</em> random variable <span class="math-container">$V$</span> with the probability density function <span class="math-container">$p_V$</span>. For <span class="math-container">$v$</span> any specific value of <span class="math-container">$V$</span>, <span class="math-container">$p_{V}(v)$</sp...
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115,440
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I have a problem. I have a NLP classification problem. There are different methods to decompose sentences into tokens, for example in whole words or in characters. Then there are different tokenizers like: <ul> <li>TF-IDF</li> <li>Binary</li> <li>Frequency</li> <li>Count</li> </ul> My question now aims, why should one ...
<ul> <li>It's rare to represent sentences as sequences of characters, since most NLP tasks are related to the the <strong>semantics</strong> of the sentence, which is expressed by the sequence of words. A notable exception: stylometry tasks, i.e. tasks where the style of the text/author matters more than the topic/mean...
The reason to explore different tokenization and vectorization methods is that those modeling choices might impact classification performance. The best practice is to train with different values for those hyperparameters and see which combination has the highest evaluation metric performance on a hold-out dataset.
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295,100
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I have an architecture problem/doubt and I'd like some insight on this. <strong>Context :</strong> We're in a mobile app that solely relies on webservice calls to be used. There can only be one user logged in at any given time and all calls require a user. We're talking about (for the sake of examples and clarity) me...
Unless <code>User</code> must have a <code>Service</code> to do user things, do not make the user pretend to be the application context/ overall state. "Convenience" and "LOC per class" are not design principles. Focus your classes sharply. Fanatically adhere to single responsibility principle. <blockquote> the ...
Each service should be self-contained. Most devs know that when something is <strong>"set in stone"</strong>, it will change on you when you least expect it, forcing you to re-architect your solution. You should always design your solutions to be correct from a technological stance even if it makes things a little mo...
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121,993
[ "https://mathoverflow.net/questions/121993", "https://mathoverflow.net", "https://mathoverflow.net/users/31491/" ]
Let $\mathcal{F}$ and $\mathcal{G}$ be abelian categories. It is well-known that if a functor $\phi : \mathcal{F} \rightarrow \mathcal{G}$ has a right-adjoint (so $\phi$ is itself a left-adjoint to some other functor), then $\phi$ is right exact. Similarly, if $\phi$ has a left-adjoint (so $\phi$ is itself a right-ad...
I would disagree that the hypotheses of the adjoint functor theorem are much stronger than exactness. Left exactness is equivalent to preserving all finite limits, and the hypotheses of the adjoint functor theorem are existence of all limits, preserving all limits, and a smallness condition that usually is easy to ver...
There are important functors like this associated with coalgebras or corings. E.g., let $C$ be a coassociative coalgebra with counit over a field and $N$ be a right $C$-comodule. Then the cotensor product with $N$ over $C$ is a covariant left exact functor $N\square_C{-}\colon C{-}comod \to k{-}vect$ from the categor...
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40,823
[ "https://chemistry.stackexchange.com/questions/40823", "https://chemistry.stackexchange.com", "https://chemistry.stackexchange.com/users/22769/" ]
The production of ethanol by fermentation is exothermic. My textbook says that the yeast stops working if the mixture gets too warm. Why would the mixture get warm if the reaction is exothermic?
In thermodynamics, we like to divide any situation into two parts, the system and the surroundings. In general the system is the part of the universe that is being studied while the surroundings is everything else that interacts with the system. Between the boundary of the system and the surroundings, energy and heat c...
An exothermic reaction is a reaction whereby energy is released, typically in the form of heat. As fermentation is an exothermic reaction, it releases heat to the surroundings, i.e. the mixture warms up. Hope that helps!
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19,338
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The following simple circuit gives the following error message when running ERC check: <pre><code>ErrType(3): Pin connected to some others pins but no pin to drive it @ (2.5000 ",4.0000 "): Cmp #PWR01, Pin 1 (power_in) not driven (Net 5) </code></pre> <img src="https://i.stack.imgur.com/AZ9nR.png" alt="schema"> The...
I think the power flag is preferred and is what I usually use (and what the documentation recommends IIRC) to stop ERC errors if pins are not set to power output (see below) In the above you just need to put a power flag on pin 2 of the fuse and the warning should go away. Also, you can set a component pin to a powe...
In KiCad Schematic, if you connect a pin which is defined as Input , to another pin which was defined as input , and there is not third wire providing any voltage / current / signal input , its a logical contradiction. Isnt it ? This is what exactly "No Driven Means" To get rid of the error , change any of two pin typ...
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441,390
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I am reading Tanenbaum's Modern Operating Systems. I want to understand a particular concept regarding processes and blocking system calls, specifically with regards to I/O. I assume threads might complicate the discussion somewhat, so please assume that I am asking about single-threaded processes only. The book states...
A blocking system call will simply not return control to the process that called it. Either the data will become available during the time slice that the scheduler allocated to that process, so that it will be able to execute some more instructions, or its time slice will simply expire and it gets added to the collecti...
The actual situation in any real operating system can actually be quite a bit more complicated than what is described by Tanenbaum. Today, &quot;an I/O operation&quot; could be addressed to a real, physical device ... or to some network resource ... or even to a <em>virtual</em> resource. So, basically, when a process...
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95,280
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In programming languages, when numbers (either integer, or real) are printed out, are they firstly converted to the codes of the readable characters that are meant to represent the numbers, and then the codes are then decoded into the readable characters? For example, in C, functions such as <code>printf</code> can pr...
printf() does the first half of what you say, with the "%d" print spec. A number in a variable is typically in Ones-complement binary (although other conventions exist, and have been used) and code in printf() does convert a number 1 into an ASCII code, and usually in 8-bits. It's up to the output device, xterm, prin...
Generally yes. Output to the console is usually done using ASCII Characters. The rendering engine in the BIOS/OS(depending which is doing the rendering) intrprets the ASCII Character and sets the proper pixels to display. Technically the computer only knows 1's and 0's. The compilers writes the code to convert the...
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12,715
[ "https://mechanics.stackexchange.com/questions/12715", "https://mechanics.stackexchange.com", "https://mechanics.stackexchange.com/users/7204/" ]
I have a Craftsman Snowblower, model 247.889702. Unit is a few years old, and I can't get it to start. Unfortunately, I left gas in it one winter and over the summer and of course when I tried to get it to start last winter it wouldn't work. I'm a definite novice when it comes to troubleshooting issues like this, but ...
Your best bet is to get a replacement carb. Some have had good luck rebuilding them, but for the trouble of it, it's just a lot easier to buy a new one off the internet. Personally, I can never get them to run right after a rebuild. You can usually get one for less than $50 depending on the model. After you put a new ...
Does it have a vacuum operated fuel valve? If so you need to suck on the vacuum pipe to allow fuel to flow into carburetor. You should then see it gush out if the bowl is removed
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266,798
[ "https://mathoverflow.net/questions/266798", "https://mathoverflow.net", "https://mathoverflow.net/users/8628/" ]
What is an example of two bounded lattices $L, K$ such that there exist surjective lattice homomorphisms $f:L\to K$ and $g:K\to L$, but there are no injective lattice homomorphisms between $L, K$?
Let $\bf n$ be the $n$-element antichain. Define $L_{m,n}$ to be the lattice that is the ordinal sum ${\bf 1}+{\bf m}+{\bf 1}+{\bf n}+{\bf 1}+{\bf m}+{\bf 1}+{\bf n}+\cdots$, with $\omega$-many summands. Let $L_{m,n}^*$ be the bounded lattice obtained by adding a top element $1$ to $L_{m,n}$ and letting the original bo...
I think you can remove the assumption of 0-preservation in @KeithKearnes' answer by replacing $\mathbf 3$, $\mathbf 4$, and the 0 element of each lattice by three mutually non-embeddable bounded lattices, thereby obtaining an answer to the question as originally stated.
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142,418
[ "https://mathoverflow.net/questions/142418", "https://mathoverflow.net", "https://mathoverflow.net/users/11142/" ]
Suppose I have the convex hull $P$ of a finite collection of points in $\mathbb{R}^d,$ and I want to see whether a point $p$ is contained in $P.$ This is a standard (some would say <em>the</em> standard linear programming problem: we are determining whether $p = \sum_{i=1}^{V(p)} \lambda_i v_i,$ with $\lambda_i \geq 0,...
Take your linear program and add the objective function <strong>max</strong> $x$, and the inequalities $\lambda_i - x \geq 0$. If the point is on the exterior, the optimum solution has $x=0$. Otherwise, there is a solution with $x &gt; 0$.
One can minimize $\sum_j \lambda_j^2$ subject to the constraints listed in the question. Then the minimizer has all entries non-zero if and only if $p$ is in the interior. This is convex quadratic programming, can be done in polynomial time, solvers readily are available, if you actually need to solve these kinds of pr...
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299,913
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Imagine you are trying to explain the purpose of <strong>f1</strong>, <strong>precision</strong> and <strong>recall</strong> to a person? How would you proceed on why do we need such measures instead of simply computing incorrect / correct ratio? I tried traditional explanation with false/true positives/negatives but ...
F1, precision and recall aren't really relevant to classification problems with equivalent and equally prevalent classes, such as "blue" vs "red" in your example, when you care as much about a red ball being mis-classified as blue as you do the other way around. In that case you would indeed just use the overall accura...
Here is one possible generalisation on how to choose the appropriate metric for classification problem. Basically, we want a metric that <ul> <li>the higher the better. Possibly (and more preferably???) bounded but I don't have a convincing argument why it should be, but I believe it's not necessary to have something ...
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6,172
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What was your worst electronics workbench accident involving equipment, voltage, soldering irons, chemicals, or whatever else, and what changes have you made to prevent that type of accident from happening again?
Here are some precautions I take... they might be a little excessive but I'd rather play it safe. Soldering: <ul> <li>Cheap solder extractor.</li> <li>Simple, clear glasses to protect my eyes against bits of metal flying away from my side-cutters.</li> </ul> PCB Manufacture: <ul> <li>All-round protection goggles to...
Only a switch that cut the power to everything, so that I don't forget something turned on (like the soldering iron...) <img src="https://i.stack.imgur.com/iPhj0.jpg" alt="http://thumbs.dreamstime.com/thumblarge_519/12784118163hDBbE.jpg">
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230,877
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I'm in the early stages of my programming career and I've been working with MVC for just about a year now. I've spent much time learning about the pattern and the concepts behind it, but as the projects I'm working with get larger I'm starting to think that maybe I don't have the best understanding of how the model lay...
You asked exactly the right question: "Why?" MVC, MVP, MVVM, and probably a thousand minor deviations of those... There are so many design patterns out there, and the differences are very subtle. The only way to get clear grasp of how to design the GUI layer of your application is probably to lean back, collect your r...
A rather general answer. Traditionally the View in MVC would request the information it needs from the Model, and the Model knows nothing about the View. Data binding (very popular in Microsoft UIs) ties the View quite closely to the underlying Model, which conflicts with the traditional MVC. So the solution is to hav...
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