My teacher said "Red apple is red because it absorb all light and reflect only red while our eyes can detect all light"  I know that all object/thing made of atoms so different atoms are the source of different color.   My main question is: "How can atoms reflect different colors? Is it because electron excitation and de-excitation?"
I'm confused, does the absorption and emission determine the color of something? Or does that only happen when something is emitting energy?  When light hits an object, the photons get absorbed, then emitted with a different wavelength right?
How to prove $\sum_{k=1}^{n}F_k = F_{n+2}-1$ by induction when $F_n$ is the Fibonacci sequence Let $F_n$ be the Fibonacci sequence where  $F_0$ = 0  , $F_1$ = 1 and  $F_n$ = $F_{n-1}$ + $F_{n-2}$.                   I want to prove the following by induction. $$\sum_{k=1}^{n}F_k = F_{n+2}-1$$ Here is what I have so far.  Can anybody tell me if I am right?  Base case = n=1  $F_k$ = 1 = LHS  $F_{1+2}$ - 1 = 2 - 1 = 1 = RHS  Statement is true for n=1.  Assume statement is true for n=i.  $$\sum_{k=1}^{i}F_k = F_{i+2}-1$$  Prove statement is true for n=i+1.  $$\sum_{k=1}^{i+1}F_{k} = F_{((i+1)+2)}-1$$  $F_1$ + $F_2$ +...+ $F_i$ + $F_{i+1}$ = $F_{((i+1)+2)}-1$  $F_{i+2}$ - 1 + $F_{i+1}$ = $F_{((i+1)+2)}-1$  $F_{((i+1)+2)}-1$ = $F_{((i+1)+2)}-1$  Statement holds for n=i+1 How to create a Wi-Fi Hotspot (in Access Point mode)? I have a directory full of images:  image0001.png image0002.png image0003.png ...   And I would like a one-liner to rename them to (say).  0001.png 0002.png 0003.png ...   How do I do this? Identify a catastrophic sci fi story written before 1980: ruptured spleen, alien moon base, time and space travel, antimatter tool I read a sci fi short story sometime between 1974-1980 but it may have been written long before that.  I believe it was in a paper back anthology of sci fi stories, but I'm not certain.  I think the protagonist is facing the final climactic conflict when we meet him.  Most of the story is memories and flashbacks.  The first flashback is to his childhood.  He and his younger brother are sled riding.  His brother crashes, ruptures his spleen and dies.  He feels responsible and is wracked with guilt.  Much later, as an adult, he is exploring a long-deserted alien base on the moon.  There are unfamiliar artifacts on the base, including a time-travel device/vehicle, and a tool with an anti-matter tip.  It carves neat holes and eliminates matter simply by moving it through matter.  He accidentally drops the tool, which plummets unimpeded to the center of the moon.  He realizes that over time, it will consume and destroy the moon, which will be catastrophic for Earth.  He uses the time-travel device to travel to the moon at an earlier time so that he can prevent himself from dropping the tool.  He makes bigger problems for himself, forcing him to travel back further and further in time.  He travels so far back that he encounters the original alien inhabitants of the base.  Now we are at the present time in the story.  This is his final conflict, he has to escape, travel forward in time and resolve all of the problems he created.  Unfortunately, the alien inhabitants capture him, and the story ends.  Can anyone identify the story and author? I was trying to fit my data into various models and figured out that the fitdistr function from library MASS of R gives me Negative Binomial as the best-fit. Now from the  page, the definition is given as:     NegBin(r,p) distribution describes the probability of k failures and r   successes in k+r Bernoulli(p) trials   with success on the last trial.   Using R to perform model fitting gives me two parameters mean and dispersion parameter. I am not understanding how to interpret these because I cannot see these parameters on the wiki page. All I can see is the following formula:    where k is the number of observations and r=0...n. Now how do I relate these with the parameters given by R? The help file does not provide much information either.   Also, just to say a few words about my experiment: In a social experiment that I was conducting, I was trying to count the number of people each user contacted in a period of 10 days. The population size was 100 for the experiment.   Now, if the model fits the Negative Binomial, I can blindly say that it follows that distribution but I really want to understand the intuitive meaning behind this. What does it mean to say that the number of people contacted by my test subjects follows a negative binomial distribution? Can someone please help clarify this? In Stein's Fourier Analysis i'm having trouble Justifying the following calculations for the Fourier Coefficients in $(1.)$  $(1.)$  Let $f(\theta) = \theta$ for $ -\pi \leq \theta \leq \pi$ in the case when $n \neq 0$:  $$f(n)=\frac{1}{2 \pi}\int_{-\pi}^{\pi}\theta e^{-in \theta} d \theta = \frac{1}{2 \pi}[-\frac{\theta}{in}e^{-in \theta}]_{-\pi}^{\pi} + \frac{1}{2 \pi in} \int_{-\pi}^{\pi}e^{-in\theta}d \theta = \frac{(-1)^{n+1}}{in} $$  Then the Fourier Series of $f$ is given by:  $$ f(n) = \sum_{n \neq 0}  \frac{(-1)^{n+1}}{in}$$ SQL Servers has Traces and XEvents. These are used to capture and analyze what is going on with our SQL Server Instances. Events are stored in the stack for later analysis. For example,  If I decide to monitor any dead lock in the database, I just query the trace file to see the history of deadlock for a period of time. Here is my question:  While events occur, in our example deadlock event, is there a way to get an email notification using msdb.dbo.xp_send_dbmail? Which versions of C++ redistributables can I remove? I have a number of Microsoft Visual C++ 2005 and 2008 Redistributable and I would like to know which ones are safe to remove, because there are actually more than 10 installed on my computers.   Microsoft Visual C++ 2005 ATL Update kb973923 - x64 8.0.50727.4053 Microsoft Visual C++ 2005 Redistributable Microsoft Visual C++ 2005 (x64) Microsoft Visual C++ 2008 ATL Update kb973924 - x64 9.0.30729.4148 Microsoft Visual C++ 2008 Redistributable - x64 9.0.30729.17 Microsoft Visual C++ 2008 Redistributable - x86 9.0.30729.17 Microsoft Visual C++ 2008 Redistributable - x86 9.0.30729.4148 Microsoft Visual C++ 2008 Redistributable - x86 9.0.30729.4974 Microsoft Visual C++ 2010 x64 Runtime - 10.0.30319   It could be that these versions are all different, but a confirmation of that is fine for me as well. Thanks in advance.  PS. I'm using an x64 machine one windows 7. How do I add CSS & JavaScript to ? I want to add the following code in my  section of the front page using a Drupal 8 sub theme of Bartik.   Can anybody help how to do it? What is the best way to do it in this new twig version of theme? Where is page.tpl?  &lt;script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.3.2/jquery.min.js"&gt;&lt;/script&gt; &lt;script type="text/javascript" src="stepcarousel.js"&gt;&lt;/script&gt; Do I require airport transit visa at Frankfurt? How long can a temporary suspension be? I ran into a user profile that states:  This account is  to cool down. The suspension period ends on Apr 27 '24 at 7:54  At first, it seemed like a somewhat longish suspension period.  Referring to  reveals:  Depending on the severity of the problem behavior — and at the complete discretion of the moderator — your account will be placed in timed suspension for anywhere from 1 to 365 days.  This indicates that temporary suspensions can last upto a year.  Additionally, the  doesn't give any other information about the timed suspension other than the link to the wiki above. I am keen to know whether the example above (wherein the account has been suspended until 2024) is a one-off case or is it a case of documentation being obsolete? Say I have a Python function that returns multiple values in a tuple:  def func():     return 1, 2   Is there a nice way to ignore one of the results rather than just assigning to a temporary variable? Say if I was only interested in the first value, is there a better way than this:  x, temp = func() Does the logistic map have an attractor for a particular value of the parameter? Background:  Currently I am studying a course on non-linear dynamics. We have been studying about attractors only intuitively, so I do not have a definition for an attractor. Let me give you a couple of examples.  Consider a problem where a ball is slipping in a parabolic valley. It is clear intuitively and quantitatively that the lowermost point of the parabola is the attractor for it.   Say we are talking about a . We may not guess intuitively that there is an attractor, a priori, but using simulations for different values of initial conditions, we may qualitatively (and maybe quantitatively too) compare the trajectories for different initial conditions and convince ourselves that we have an attractor.  Problem:  Consider the  given as   $$x_n = ax_{n-1}{(1-x_{n-1})}.$$  Let us fix a value of the parameter where we "know" that the logistic map exhibits chaos. Say $a=3.9$.  Let us take the definition for the term attractor from :  An attractor is a subset $A$ of the phase space characterized by the following three conditions:   $A$ is forward invariant under $f$: if $a$ is an element of $A$ then so is $f(t,a)$, for all $t &gt; 0$. There exists a neighborhood of $A$, called the basin of attraction for $A$ and denoted $B(A)$, which consists of all points $b$ that "enter $A$ in the limit $t → ∞$". More formally, $B(A)$ is the set of all points $b$ in the phase space with the following property: For any open neighborhood $N$ of $A$, there is a positive constant $T$ such that $f(t,b) ∈ N$ for all real $t &gt; T$. There is no proper subset of $A$ having the first two properties.   How might we demonstrate/convince ourselves of/disprove the statement that the logistic map does have an attractor for a particular choice of the parameter at which the map exhibits chaos? Terminal command 'login' fails with error message Coming from Mac OS X, there is a possibility for every ordinary user to open Terminal and type in 'login' to change to a different user account.  When I do this with Ubuntu, it provides the following error message:  login: Cannot possibly work without effective root   Is there any way to remedy this?  Which file do I need to edit and with what to enable the use of this command (even for a standard user)? "one of the cables that runs" or "one of the cables that run"? Recently at work I was writing the following, and I have not been able to get a firm answer on which version is the most grammatically correct. The sentence is:     We would like to use one of the cables that _________ between rooms.   Is the correct conjugation run or runs?  I think 'run' is correct, because I think that the verb in the prepositional phrase is referring to 'cables' not 'one.' However, a number of colleagues have said that 'runs' is correct because one is singular. Is it legal/well-defined C++ to call a non-static method that doesn't access members through a null pointer? I'm trying to process some data in Excel. The data includes numeric account numbers and other long numeric strings (like cell phone MEIDs). I am not doing math operations on these strings, so I want Excel to treat them as plain text.  Here is what is making me nuts (this is Excel 2010):   Take a long number like 1240800388917 and paste it in a cell in a new worksheet. Excel's default cell format is general, so the string is presented in scientific notation as 1.2408E+12 Right click on the cell, select Format Cells, set the format to Text   The cell is still displayed in scientific notation, even though the format has been set to text.  Now, if I do the steps in a different order:   Format an empty cell as text. Right click on the cell, select Format Cells, set the format to Text Take a long number like 1240800388917 and paste it in to the text formatted cell   Now, the cell is displayed as a string and not in scientific notation.  The results remaining in scientific notation even though the cell is formatted as text just seems broken to me. I've seen suggested work-arounds like: use CSV import and set the format to text, add a space character to the beginning of each numeric string, and others.  Is there a simple good work around to easily keep these strings formatted as text?  Why on earth does Excel do this?  Related SU questions I found:  and What causes close votes to be annotated with "(deleted)"? In the "Votes Cast" section of my profile, my vote to close  is annotated with "(deleted)":    However, the close vote does not appear to have been deleted: it successfully closed the question:    Why was this vote marked as "(deleted)"?    If the vote was deleted my some internal process after the question was closed and the closers were recorded, I call that a . Regardless of what happens internally, it's irrelevant to users if close votes are deleted after they have taken effect. Show that a set is dense in $[-1,1]$ Show that $\{\cos\ n:n \in \mathbb{N}\}$ is dense in $[-1,1]$ by using the fact below:      Suppose $x$ is irrational. Then there exists $p_n,q_n \in \mathbb{Z}$   such that $\bigg|x -\frac{p_n}{q_n}\bigg| &lt; \frac{1}{q_n^2}$   I have no idea on how to apply the fact above to show the set is dense in $[-1,1]$. Can anyone help me? Assign points within 150 meter buffer of each other the same unique identifier? I have a bunch of points on a QGIS map. Each point is a unique sampling event. However, some of these points have been sampled multiple times but there is no common identifier in the attribute data to determine this. The only way we can see this is by looking at the map and seeing points very close to each other.   I am wondering if anyone has a method to assign points within a 150 meters of each other a common identifier?