Reasons why not to update an Ubuntu version to a newer/older kernel version
Should I upgrade to the "mainline" kernels?
Search for singleton tags on questions INT vs Unique-Identifier for ID field in database The meaning of various equality symbols prove $\frac {ab}{a+b} \geq \sum ^n_{i=1} \frac{a_ib_i}{a_i+b_i}$ How to change SQL Server collation What is AC actually? What is actually alternating current (AC)? And direct current (DC)? I've been reading several books about basic electric circuits analysis and they are contradictory.   Some books say that AC is the same as the sinusoidal stationary state. That is, a sine or cosine function (actually, they are the same only shifted horizontally). For instance, \$v(t) = A \sin(\omega t + \phi)\$. Acording to these books, DC is totally stationary (static), that is, the voltage and current are not time-dependant (\$v(t) = k\$, where \$k = \mathrm{const.}\$). Currents have the same form as voltages on each of these cases. According to other books, AC is any current that is changing (that is alternating) his sign over time (\$t\$). With maths notation: \$i(t_1) &lt; 0\$ and \$i(t_2) &gt; 0\$ for some \$t_1\$ and \$t_2\$ where \$t_1 \neq t_2\$. It could have any shape as long as it's alternating his sign.   I'm inclined to think that in practice wins the first option but maybe it's better the etymology of the second option.  Some other cuestions have relation to this:   Is AC a voltage that is the sum of a sinusoidal stationary state and a constant voltage? For instance, \$v(t) = A \sin(\omega t + \phi) + k\$. Is AC a shawtooth wave? My network icon is always a question mark in both wired and wireless connection but everything network related works correctly. Why is the covariant derivative of the metric tensor zero? Which cyan colored line is produced in the Thomson e/m apparatus? Related:   After reading Lisa Lee’s OP on an electron deflection tube, although she had some misunderstandings on its operation, I still believe that her question is still relevant. If one looks at the Thomson e/m tube filled with helium gas (made by ), the tracer light is created by de-excited electrons, not by an electron beam interacting with a phosphor as in Lisa Lee's OP. That is, the accelerated electrons scatters off of a low pressure helium gas and emit a tracer line to follow the electrons path, as shown below.     Now if you look at the bright line spectrum of helium,     One can clearly see that there are two “cyan” color lines around 500 nm. Following in Lisa Lee’s footsteps, there is a series of question one can ask: (1) which line is emitted by the Helium gas atoms? Or are both lines emitted? (2) How can a variable accelerating voltage for the electrons always produce the same tracer line color? In theory, I assume that if I decreased the energy of the electron beam, I could produce red (around 670 nm) or yellow (around 590 nm) tracer lines, but that doesn’t happen. Somehow, it appears to me that the e/m tube is “tuned” just right so that the emitted light is always this “cyan” color. Why? Baryons have charges that are the result of a polynomial calculation of their building blocks (quarks)'s fractional charges. But what gives these quarks electric charges? What interactions do they have with photons? And what about leptons, like muons and electrons? How do they get their -1 charge? And then, how do positrons and anti-muons get +1 charge? Same goes for quarks: how does up-antiquarks get -2/3 charge? Or I may want to formulate my question this way:  How does any elementary particle interact with the EM-Force to get an electric charge? To be clear on this, I know what is the definition of an inner product space and some properties and theorems about them. What I am asking for is an intuition for this definition in the complex case. In the real case, the intuition (or at least one of them) is  geometric: The inner product of two vectors is the length of the projection of the first to the second scaled by the norms of both vectors so that it is symmetric (modulo some details). In particular I (and everybody else) think of "inner product zero" as geometric orthogonality and of orthonormal bases as, well, orthonormal bases and so on. The question is, what should I think about when working with complex (or should I say hermitian?) inner product spaces? what is the "meaning" of the complex number associated to two vectors called their inner product?  I will be happy to hear all kinds of answers. For example, what physical phenomena does it model or in what mathematical situations does in "naturally" appear. Answers that stress the "nice structure" resulting are also welcome, yet I feel that by itself  it is a bit unsatisfying. INT(5) vs SMALLINT(5): numbers in parenthesis after the numeric type How to embed a text file in a .NET assembly? I would like to embed a text file in an assembly so that I can load the text without having to read it from disk, and so that everything I need is contained within the exe. (So that it's more portable)  Is there a way to do this?  I assume something with the resource files?  And if you can, how do you do it and how do you programaticaly load the text into a string? Divisibility tests and remainder mod $9,11,99,101,999,1001\,$ (casting out nines and elevens) Now I have proved the following two problems:      (1) Prove that a number and the sum of its digits have the same remainder upon division by 9.    (2) Given an integer, consider the difference between the sum of the digits in odd positions (counting from the right) and those in even positions. Show that the difference has the same remainder as the number itself when divided by 11.    Then, I need help on the following problem:      Partition the digits of a number into groups of two and three, respectively, starting from the right. Treat these as two- and three-digit numbers, respectively, and proceed similarly as in the two problems above. What divisibility rules arise?    In fact, I did not quite get what this problem asks for and not clear about this process. Could anyone give me some hints on this, please?  Thanks in advance. Why couldn't the Jedi detect Senator Palpatine as having powers? In Return of the Jedi, when trying to sneak into the base on a shuttle, Luke said he senses Darth Vader's presence and said he shouldn't have come lest he jeopardize the mission. Darth Vader also sensed Luke, but let him in anyways. Also, Yoda and Obi-Wan could detect the Force in young Anakin.  So if Jedi and Sith can detect each other, why couldn't they detect Senator Palpatine to begin with? It seems like a giant plot hole. Consider this situation:  A ball is moving forward and undergoing rotation. Assume that it is not slipping. Eventually, the velocity and rate of rotation of the ball decrease, and it comes to a halt. But if you observe the direction of friction (when the ball is rotating clockwise), you will see that the friction should have provided a clockwise torque to the ball and the angular velocity of the body should have increased. But this doesn't happen. Why? Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$. This is something I've been trying to work out this evening.      Let $R$ be the ring of continuous real-valued functions on $[0,1]$ with pointwise addition and multiplication. For $t\in [0,1]$, the map $\phi_t\colon f\to f(t)$ is a ring homomorphism of $R$ to $\mathbb{R}$. I'm trying to show that every ring homomorphism of $R\to\mathbb{R}$ has this form.   Suppose otherwise, that there is some $\phi\neq\phi_t$, and thus there is some $f_t\in R$ such that $\phi(f_t)\neq \phi_t(f_t)=f_t(t)$. Define $g_t=f_t-\phi(f_t)1\in R$. Here $\phi(f_t)1$ is the constant function sending $[0,1]$ to $\phi(f_t)$. Then $g_t(t)\neq 0$. My first small question is why does $\phi(g_t)=0$? It seems only that $\phi(g_t)=\phi(f_t)-\phi(\phi(f_t)1)$.  I would like to conclude that there are only finitely many $t_i$ such that $g(x)=\sum g_{t_i}^2(x)\neq 0$ for all $x$. Then $g^{-1}=1/g(x)\in R$, but $\phi(g)=0$, contradicting the fact that homomorphisms map units to units. How can we be sure there are only finitely many $g_{t_i}$ such that the sum of their squares is never $0$? Thanks. How do you find all subclasses of a given class in Java? How does one go about and try to find all subclasses of a given class (or all implementors of a given interface) in Java? As of now, I have a method to do this, but I find it quite inefficient (to say the least). The method is:    Get a list of all class names that exist on the class path Load each class and test to see if it is a subclass or implementor of the desired class or interface   In Eclipse, there is a nice feature called the Type Hierarchy that manages to show this quite efficiently. How does one go about and do it programmatically? This question is from a set of optional, much harder problems from my first year analysis course, but the subject material is norms on $\mathbb R^K$.  (c) Show that there exists a constant $C &gt; 0$ such that for all $\mathbf x ∈ \mathbb R^k$, $||\mathbf x||\le C||\mathbf x||_\infty$  Hint: Use the standard unit vectors to write $\mathbf x = x_1\mathbf e_1 +. . .+x_n \mathbf e_n$, and use the triangle inequality.  (d) Show that there also exists a constant $c &gt; 0$ such that for all $x ∈ \mathbb R^k$, $||\mathbf x||_\infty \le c||\mathbf x||$  Hint: If it isn’t true, then you can find a sequence $⟨\mathbf x_n⟩$ such that $||\mathbf x_n||$ is bounded but $c_n := ||x_n||_∞ → ∞$. (Why?) Think about the sequence $⟨\mathbf x_n/c_n⟩$. The Bolzano-Weierstrass theorem may be of assistance.  Note that the unspecified norm represents any norm for $\mathbb R^k$. I've done part c), but am stuck on part d). I've had a look for proofs on other questions on MSE, but none of them seem relevant to the hint given, and frequently the terminology is too advanced for me.  I tried considering the case if it isn't true, as suggested, but I can't see how to bound any sequence using that. Any help would be much appreciated. Probability that median falls within a range? If I draw 5 samples from a distribution that is cont., what is the probability that the median of the population is between the xmin and xmax of the draw samples?  What is the formula to apply here?