I'm trying to buy a used Merida Scultura Road frame, but the current owner does not know the year of manufacturing. It is possible to extract this information from serial number?  Serial:   WC 93055 B  BI - 1582 BR
This is a canonical question that will hopefully encompass all of the questions we get asking us to determine what year a bicycle was manufactured (how old is my bike, how old is my frame, etc.). Each "answer" should address a different way to determine the manufacturing year of a bicycle. To some extent, these will also help you narrow down the model as well as it will tell you what distinguishing features to look at.  The span of answers would include things such as:      Skiptooth cranks Cartridge bottom brackets (BB30/90 etc) Elliptical chainring Quick releases versus contemporary through-axles How the steerer attaches to the fork (quill vs. threadless)  Braking system (especially with mountain bikes: v-brake, direct pull, etc.)   Shifting ramps and pins on cassettes/sprockets and chainrings (versus flat sprockets) Frame material (e.g., shift from tubular steel to use of CF and hydroformed aluminium)  Frame tubing type (e.g. Reynolds 531 tubing introduced around 1934, still used today; Reynolds 501 tubing introduced around 1983). So a frame with an original 501 decal can't be from the 70', 531 decal doesn't help as much because of the range of years produced. Also, see Decals.   *Decals: style/design, amount, placement, color, etc. can help not only determine models, but also year of manufacture. Many changed decal design for the same model bike often yearly, with special/limited editions even more specific. This applies only if decals are original or have been replaced with the identical design. Tubing decals (Reynolds, Columbus, etc.) also changed designs for same tubing made in different years, although the changes aren't made as often, and manufacturers didn't always put tubing Brand decals on every model. Earlier bikes tended to have less fancy, less colorful, less quantity of decals.   Headbadges: most early bikes had actual "badges", often quite detailed and fancy, made of metal, then plastic, and finally just using decals on the headtube. Most bikes lost their metal badges in the 60's and early 70's, although some brands still have actual badges to this day, but in general a real badge indicates an earlier model bike. Dropout style (including the later inclusion of lawyers lips) Presence or absence of CPSC reflectors (USA only) Manufacturing method (shift from lugs to TIG welding, for example)  Number of gears (shift from 2x5 ten-speed to 3x8, 2x9, 1x11, etc.)  Inspection of lug design: pantographs, cut-out, stampings, custom brazing/filing, chrome, fork crow n sweep, etc. Frame/Fork Braze-ons. Race bikes tended have less braze-ons the earlier the year of manufacture. Most 60's racers and earlier had few or none with cable guides/stops, shifters, bidons, etc. being clamp-on. By the 80's if it was clamp-on, it was a sign of very cheap models and most frames had braze-ons for all cables, with multiple bottle and accessory bosses depending on style and use.   and so forth. Please edit this question if you have an answer that isn't in the index above.   A couple of caveats:   A previous owner could have replaced or upgraded components on a bicycle, so this guide only applies to original equipment There is a delay between the introduction of a technology (such as indexed shifting) and when manufacturers start selling products that use it. Low-end manufacturers may continue using technology that is severely outdated (such as one-piece cranks, freewheels, or quill stems) because it is cheaper to do so. A number of bikes are built in a Retro style, but with modern components.  Dutch bikes, trendy coffee cruisers, and beach cruisers may be modern but appear to be 1950s styling.  These tend to have modern rims and brakes as a giveaway.     Note that bicycles.stackexchange does not do valuations of bicycles. How much your bicycle is worth depends on the location of the buyer and seller, how much the buyer wants the bike, etc. etc. etc.
Uniform convergence of $\sum_{n=1}^{\infty}\frac{1}{n(1+(x-n)^2)}$ Is $$\sum_{n=1}^{\infty}\frac{1}{n(1+(x-n)^2)}$$ uniformly convergent on $(0,+\infty)$? Sadly, Weierstrass' criterion nor Cauchy's condition don't seem to work here and I just ran out of ideas. SEO in Stack Overflow In the book on Brownian Motion by Yuval Peres, he makes the following claim:     Suppose that $\{ B(t); \ t \geq 0 \}$ is a Brownian Motion and $U$ is an independent random variable, uniformly distributed on $[0, 1]$. Then the process $\{ \tilde{B} (t); \ t \geq 0 \}$ defined as,   $$\tilde{B}(t) = \begin{cases} B(t)  &amp; \mbox{ if $t \neq U$} \\ 0  &amp; \mbox{ if $t = U$} \end{cases}$$      has the same finite-dimensional distributions as a Brownian motion, but is discontinuous if $B(U) \neq 0$, i.e. with probability one, and hence this process is not a Brownian motion.   I'm having difficulty in proving that the finite dimensional joint distribution ( basically the joint distribution of $( \ \tilde{B}(t_1), \ \tilde{B}(t_2), \tilde{B}(t_3), \dots \tilde{B}(t_n) \ )$ ) is the same as the finite dimensional distribution of $B(t)$. Can you please give me some clues. What is the difference between [0-9]+ and [0-9]++? Now that Unity is gone, the usual way of setting a Compose Key (via Keyboard Preferences > Layout) no longer works (because in Ubuntu 18.04, Devices > Keyboard has no Layout tab).  How do we set a Compose Key in Ubuntu 18.04 Bionic Beaver? Preview on mobile page I suggest a preview on the mobile page. For questions, answers and edits to both, like on the desktop page.  I messed up formatting often enough to be annoyed that there is no preview on the mobile page and I'm surprised that noone suggested it before (at least I didn't find anything).  If it's too performance heavy to have a live preview update after every change in the text box, there could be a preview button next to the save button which leads to a page with only the preview, a back button and a save button (and the title bar and so on). What Thunderbolt to USB 3.0 cables/adapters exist for OS X and Mac hardware? I have the Late 2013 Macbook Pro, which has two USB 3.0 ports and two Thunderbolt 2 ports. I currently use both USB 3.0 ports and one TB2 port. I want to connect a third USB 3.0 device to the machine, but I don't want to use a USB splitter on one USB port as I'm concerned the devices would draw too much power from the bus. I have no current use for the second TB2 port and I would love to be able to use it for this purpose.   Browsing extensively online, I've found numerous docks, such as , that connect via a Thunderbolt cable. This would work, but it's an expensive, 'bulkier' solution (and not the one I'm looking for).   I'm aware that a USB 3.0 device wouldn't be able to take advantage of Thunderbolt's I/O speeds, but it's certainly compatible, which is all I'd need. After all, Apple even sells a . I also know that Thunderbolt is not only used for digital video purposes (along with the TB > Firewire option, there exists ).   There are almost no Thunderbolt to USB 3.0 cables/adapters on the market. I'd think this hardware would be more prevalent given the prominence of USB devices out there. What adapters are available for OS X? I realize I am taking a risk by reopening what seems to be an old, hoary, and thorny discussion. However, it seems that in all the long discussions about Meta Stack Exchange reputation, what it means, and why it's separate from reputation on other sites, I have never seen a complete answer to this question:  If reputation on Meta Stack Exchange is used by the community to indicate agreement with an opinion instead of the quality of a post, why is it still tied to site privileges?  The association between reputation and privileges makes sense on other Stack Exchange sites, where reputation is a measure of your participation in the site and the quality of your questions and answers. If you contribute positively to the community your reward is increased privileges, whereas your punishment for "polluting" the site with bad questions or unhelpful answers is a loss of privileges.  However, on Meta Stack Exchange, reputation is a measure of the popularity, not the quality, of your contributions. Tying reputation to privileges means that losing privileges on the site is a punishment for expressing an unpopular opinion, and gaining them is a reward for agreeing with the majority.   My opinion:  I don't think that tying privileges to popularity makes sense as a feedback system. It doesn't really encourage quality contributions, and even worse, acts to suppress minority opinions through the threat of losing privileges. As a user with fairly low reputation, I am afraid of asking a question that may be controversial, because if enough other members disagree with me I will be stripped of the ability to vote and chat. Even if I had higher reputation, I would still be concerned that expressing a controversial opinion would cause me to lose helpful privileges like editing and viewing close votes.   The FAQ tells new users "not to be concerned" by downvotes because all it means is that the community disagrees with them. However, I think new users have every right to be concerned about downvotes, because they still mean the loss of privileges. Install suspension forks on non-suspension bike If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism. Let $X$ and $Y$ be metric spaces, $X$ compact, and $T:X \to Y$ bijective and continuous. Show that $T$ is a homeomorphism.   My attempt:  We need only show that $T^{-1}$ is continuous.  Let $M \subset Y$ be closed. Then, from the surjectiveness of $T$, there exists a $A \subset X$ such that $T(A)=M$. Since $M$ is closed, by the continuity of $T$, we must have that $A$ is closed.  Now $$T^{-1}(T(A))=T^{-1}(M)$$ i.e, $A=T^{-1}(M)$. Since $A$ and $M$ are closed, we must have that $T^{-1}$ is continuous.  My problem with this, however, is that I am not using the fact that $X$ is compact anywhere in the proof. Is there perhaps another way that I can show this, using the compactness of $X$?   Any hints will be appreciated. I have gcc 7.3.0 on Ubuntu 18.04. But I am working on a project where I need gcc less than version 6. When I tried to install gcc 5.4 using sudo apt install gcc-5.4, I got this error:  Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package gcc-5.4 E: Couldn't find any package by glob 'gcc-5.4' E: Couldn't find any package by regex 'gcc-5.4'     What is the appropriate way to install gcc 5.4? How do you take profit from stock trading while keeping capital invested? Is it possible to skip Skyrim's new game introduction cinematic? I don't want to watch the prisoner cart ride to the execution: is it possible to skip this?   If so, how? Can I replace the intro movie file by some empty video? When programming interfaces, I've found I'm doing a lot of casting or object type conversion.  Is there a difference between these two methods of conversion?  If so, is there a cost difference or how does this affect my program?  public interface IMyInterface {     void AMethod(); }  public class MyClass : IMyInterface {     public void AMethod()     {        //Do work     }      // Other helper methods.... }  public class Implementation {     IMyInterface _MyObj;     MyClass _myCls1;     MyClass _myCls2;      public Implementation()     {         _MyObj = new MyClass();          // What is the difference here:         _myCls1 = (MyClass)_MyObj;         _myCls2 = (_MyObj as MyClass);     } }   Also, what is "in general" the preferred method? Sum of independent Gamma distributions is a Gamma distribution If $X\sim \Gamma(a_1,b)$ and $Y \sim \Gamma(a_2,b)$, I need to prove $X+Y\sim\Gamma(a_1+a_2,b)$ if $X$ and $Y$ are independent. I am trying to apply formula for independence integral and just trying to multiply the gamma function but stuck ? Finding the limit of $(1-\cos x)/x^2$ How do I find out which dlls an executable will load? If I have a Windows executable, how can I find out which dlls it will load?  I'm just talking about which ones that will be loaded statically, not ones it might load dynamically with something like LoadLibrary. Convergence of the series $\sum_n \frac{n^{\log(n)}}{\log(n)^n}$ I have a rough outline of a proof. Is this correct?  $$\sum_{n \geq 2} \frac{n^{\log(n)}}{\log(n)^n} \to a \in \mathbb{R} \iff  \sum_{n \geq 2} 2^n \frac{(2^n)^{\log(2^n)}}{\log(2^n)^{2^n}} \to b \in \mathbb{R}$$ via dyadic criterion (or Cauchy condensation test).  Analyzing the right-hand side:  $$\sum_{n \geq 2} 2^n \frac{(2^n)^{\log(2^n)}}{\log(2^n)^{2^n}} = \sum_{n \geq 2} 2^n \frac{(2^n)^{n\log2}}{(n\log2)^{2^n}} = \sum_{n \geq 2} \frac{(2^n)^{n\log2 + 1}}{(n\log2)^{2^n}} = \sum_{n \geq 2} \frac{2^{n^2\log2 + n}}{(n\log2)^{2^n}} = (\ast). $$  We know for some sufficiently large $N$, $n \log 2 \ge 2$ for all $n\ge N$, so we can bound the series above by:  $$(\ast) \leq C_N + \sum_{n \geq N} \frac{2^{n^2\log2 + n}}{2^{2^n}} = \sum_{n \geq N} 2^{n^2\log2 + n - 2^n} = (\ast\ast),$$  where $C_N$ is the finite sum of the original series until $N$. And once again, for sufficiently large $M$, $m^2\log2+m - 2^m \leq -m^2$ for all $m \ge M$. Hence  $$ (\ast\ast) \leq C_{\max(N,M)} + \sum_{n \geq \max(N,M)} 2^{-n^2} &lt; \infty.$$  We then use the $p$-test to conclude that the sequence does converge. Finding an example of a discrete-time strict local martingale. For example, this regex  (.*)&lt;FooBar&gt;   will match:  abcde&lt;FooBar&gt;   But how do I get it to match across multiple lines?  abcde fghij&lt;FooBar&gt;