When I use Spectracalc.com to calculate the peak wavelength at 500 Kelvin, I am told the peak is at 5.79551 µm.  When I switch the calculation result to wavenumber the peak is said to be at 980.506 cm-1.  But if I were to simply convert wavelength to wavenumber I do not get this value.  1/(5.79551E-6) = 172,547.3 m-1 = 1725.47  cm-1  What is going on here?    Edit:   Several people have answered that this has to do with the differentials not being the same size.  I don't think this answers my question.  I get that a wavenumber increment is not the same size as a wavelength increment.  That isn't the question at all.  The question is more about the physical meaning of what is measured.  Let me restate it more clearly.  Say I measure with a highly accurate physical instrument and get a value of the peak at 5.8 µm.  This is a physical quantity. It is the distance between two sequential peaks of the wave of the light measured as coming from the body at the temperature of 500 K.  This physical quantity, that describes a physical thing, also can be described by looking at the number of times the wave cycles in a unit distance. The wave that has a wavelength of 5.8 µm cycles 1/5.8 µm times in a unit distance, giving it a wavenumber of 1724.1 1/cm.  This is also a physically meaningful way a to describe the exact same wave I measured as the peak.  They are interchangeable descriptions of the same physical thing.  Now, say I had used a different instrument to measure the exact same physical body in the exact same state, an instrument that instead measured wavenumber. According to the wavenumber form of Planck's law, I should measure a wavenumber of 980.5 1/cm when earlier I had measured a wave with a wavelength of 1724.1 1/cm. This is supposed to be the exact same physical thing that was measured.  Yet the exact same physical thing cannot have two different values for the same measure!  So, which is it: Is one of the forms of Planck's law wrong, or are the two measures of the same wave not in fact interchangeable, i.e., is it false that a wave with a wavelength X has a wavenumber 1/X?  If the peak is a real physical phenomenon that corresponds to a real physical wavelength of X, then this physical wave MUST have a wavenumber of 1/X, unless that relation is just false. But if that relation is not false, then how on earth can we get two different values for the same physical phenomenon? The hot body knows which instrument I am using and moves the peak around accordingly?  Something is not right about this.
I read that it makes a difference whether you calculate $\frac{dE(\lambda) }{d \lambda}=0$ or $\frac{dE(\omega)}{d \omega}=0$ in the sense that the maximum energy density with respect to the wavelength does not coincide with the frequency maximum that one would assume to be at $\omega_{max} = \frac{c}{\lambda_{max}}$. Actually, I do not understand why this is so ( Now, I am only interested in a pure physical explanation, mathematically this is clear and due to the chain rule). Does anybody know how to explain this odd thing?  Somehow I feel that the core of the question has not been completely answered. Although I can easily look up wikipedia, where the need for the chain rule is explained, I am rather interested in understanding where the following argument breaks down, which seems to be why this question has caused some confusion in the past(as you can see by googling this question):  So we have $E(\omega)$ the energy radiated at a given frequency. Now this function has a maximum somewhere, so there is a frequency where a maximal amount of energy is emitted. In other words: If you add the sum of the photon's energies at each frequency that are emitted, you will notice that the maximum is reached at this frquency. Now $E(\lambda)$ tells you basically the same for the wavelength, but again: We know where at which frequency the maximal amount of energy is radiated, so we know the corresponding wavelength.   I think there is a need to explain this.   If anything is unclear, please let me know.
I have an app that's been out for a couple of weeks. Its not exactly selling like hot cakes yet, but I'm pretty sure I've gotten a rating or a review by now. But nothing shows when viewing either in iTunes or directly on the AppStore on the iPhone.  Is there a standard delay as to when ratings/reviews show up, that Apple imposes, especially for new apps? Or do you think there is some problem with Apple's system? Try to do something vs. Try doing something Is there any differences between      Try to do   And     Try doing   Thank you in advence. I am working on a git repository with a master branch and another topic branch. I have switched to topic branch and modified a file. Now, if I switched to master branch that same file is shown as modified.   For example:  git status in git-build branch:  # On branch git-build # Changes to be committed: #   (use "git reset HEAD &lt;file&gt;..." to unstage) # #       modified:   cvsup_current #   Switch to master branch  [root@redbull builder_scripts (git-build)]# git co master M       builder_scripts/cvsup_current Switched to branch "master"   git status in master branch  [root@redbull builder_scripts (master)]# git status # On branch master # Changes to be committed: #   (use "git reset HEAD &lt;file&gt;..." to unstage) # #       modified:   cvsup_current #   Why is that the file is shown as modified in master branch even though it was modified in git-build branch?   My understanding was that the branches are independent of each other and when I change from one branch to another the changes do not "spill over" from one branch to another. So I am obviously missing some thing here.   Anyone got a clue stick? Checking for a null int value from a Java ResultSet I was working on a problem that resulted in the calculation: $20 \equiv 10x \pmod{11}$.  I got the answer $x \equiv 2 \pmod{11}$ with the thought process: Since $10$ is a factor of $20$ I can rewrite $20 \pmod{11}$ as $10x \pmod{11}$ with $x=2$. But isn't this basically the same as using division, which we aren't supposed to do in modular spaces?  If I solve by multiplying $20$ by the multiplicative inverse of $10 \pmod{11}$ which is $10$, I get $200 \pmod{11}$ which simplifies to $2 \pmod{11}$ anyway. Did these numbers just happen to be the same or is my original method valid? My brother owns Skyrim on steam. We use Steam Family Share, but we were wondering how both of us could play it at the same time? I gave a scammer my telephone number, address, and name. How bad is it? Updated question because old one was embarassing: I saw a spam email from "PayPal" and I didn't realize that it was a phishing attempt. I gave the phishing site my name, telephone number, and email. What could he do with them?  Old question: Well, I saw a spam email, but I didn't realize that it's really a scam at first. I gave him my telephone number, address, and name. What would he do with them? Could he ruin ALL of my reputation with it? Is it possible to create individual power settings for each hard drive? I have a number of different drives that I use for different purposes but I only use two of them frequently. I would like for the others to enter sleep mode when not in use, but never my main two.  Is there any way to edit power saving settings for individual drives? How do I add a Pokestop to an area that has none? It is an area where there are tons of businesses but unless I drive about a mile from my work area there are no Pokestops.   I want to add one since we have 1000's of people in the work area, a lot of them play Pokemon Go, and we all can't leave work to drive a mile away to get to a Pokestop area.   Plus it would be nice to be able to capture Pokemon on our breaks. Is the concept of even/odd numbers applicable to decimal numbers? For e.g. - 4.222 is a even number? Why was Peeves in Hogwarts? Peeves was a poltergeist. It generally irritated people and rather then helping them as well as making fun of them.   Why was Peeves in the school? What is/was the job or work assigned to Peeves? How can I render an edge only mesh as solid lines? I have a schematic of a raspberry pi that is completely flat, no solid faces, just connected vertices.  Is it possible to render these lines somehow, so that it looks like a 2D drawing?  Maybe with freestyle? Let $X_1$ and $X_2$ be two independent exponential random variables with the PDFs $f_{X_1}(x_1)=\lambda_1 \exp(-\lambda_1 x_1)$ and $f_{X_2}(x_2)=\lambda_2 \exp(-\lambda_2 x_2)$.   Let $X= \frac{X_1X_2}{X_1+X_2+a}$ be a r.v. for which I want to derive the CDF, where $a$ is a positive constant.  In other words, I need to calculate $\mathbb{P}\{X &lt;x \}$.  Any ideas or hints?  Edit (attempt):  Using a similar approach to that used , we have $X_1 \in [0, \infty)$ and  $X_2 \in [0, \frac{x(x_1+a)}{x_1-x})$. The latter interval results from: $\frac{x_1x_2}{x_1+x_2+a} &lt; x$, thus $x_2(x_1-x)&lt;x(x_1+a)$ which implies $x_2 &lt; \frac{x(x_1+a)}{x_1-x}$; but I am not sure if this is correct since $x_1-x$ can sometimes be negative (?). Based on the above, we can write: \begin{align}  \mathbb{P} \{ \frac{X_1X_2}{X_1+X_2+a} &lt; x \}  &amp; = \int_{x_1=0}^\infty \int_{x_2=0}^{ \frac{x(x_1+a)}{x_1-x}} \lambda_1 \exp(-\lambda_1 x_1) \lambda_2 \exp(-\lambda_2 x_2)  dx_2 dx_1  \\ &amp;= \int_{x_1=0}^\infty \left(1-\exp(-\lambda_2\frac{x(x_1+a)}{x_1-x}) \right) \lambda_1 \exp(-\lambda_1 x_1) dx_1  \\ &amp; = 1-\lambda_1 \int_{x_1=x}^\infty \exp(-\lambda_2\frac{x(x_1+a)}{x_1-x} ) \exp(-\lambda_1 x_1)   dx_1 \end{align} In the last equality: for the integral of $\lambda_1 \exp(-\lambda_1 x_1) dx_1$, I suppose that $x_1 \in [0,\infty)$, whereas for the second term I suppose that $x_1 \ge x$ (since $x_2$ should be positive) (?).  Is my approach correct ? Permutation module of $S_n$ Let $G=S_n$ and let $V$ be the permutation module of $G$ with basis $\{x_1,\ldots,x_n\}.$  Let $\lambda, \mu \in \mathbb{C}$ to allow one to define a $\mathbb{C}G$-homomorphism $\rho:V \to V$ by $$\rho(x_j):=\lambda x_j+\mu\sum_{i \neq j}x_i.$$  By using the above fact or otherwise, how can we prove that $V$ is the direct sum of two non-isomorphic irreducible $\mathbb{C}G$ -submodules?  I tried to prove this by construction. A familiar irreducible submodule in this case is the $1$-dimensional space $U:=\operatorname{span}\{x_1+\cdots+x_n\}$. I intend to find another $(n-1)$-dimensional submodule $W$  which makes $V=U\oplus W$ hold, but it's hard to do so. Is there a way to use the fact instead of a random construction? Should I mention my Canadian visa refusal in my UK visa application? How to install MySQL workbench? Installing MySQL workbench on 10.04 or 10.10 is not a problem, as the deb packages are available on MySQL's website.  But there is no 11.04 deb package available.  So, how do I install MySQL workbench on 11.04 and keep it updated automatically when updates become available to ubuntu via apt-get update. I am trying to follow the best practice design patterns for triggers but get the error Constructor not defined: [CaseTriggerHandler].(). What am I missing?  Trigger  trigger CaseTrigger on Case (before insert, before update, before delete, after insert, after update, after delete, after undelete) {      CaseTriggerHandler handler = new CaseTriggerHandler();      //Before Insert     if(Trigger.isInsert &amp;&amp; Trigger.isBefore){         handler.OnBeforeInsert(Trigger.new);     }     //After Insert     else if(Trigger.isInsert &amp;&amp; Trigger.isAfter){         handler.OnAfterInsert(Trigger.new);     }     //Before Update     else if(Trigger.isUpdate &amp;&amp; Trigger.isBefore){         handler.OnBeforeUpdate(Trigger.old, Trigger.new, Trigger.newMap);     }     //After Update     else if(Trigger.isUpdate &amp;&amp; Trigger.isAfter){         handler.OnAfterUpdate(Trigger.old, Trigger.new, Trigger.newMap);     }     //Before Delete     else if(Trigger.isDelete &amp;&amp; Trigger.isBefore){         handler.OnBeforeDelete(Trigger.old, Trigger.oldMap);     }     //After Delete     else if(Trigger.isDelete &amp;&amp; Trigger.isAfter){         handler.OnAfterDelete(Trigger.old, Trigger.oldMap);     }     //After Undelete     else if(Trigger.isUnDelete){         handler.OnUndelete(Trigger.new);     } }   Handler      public with sharing class CaseTriggerHandler {      private boolean isExecuting = false;      public CaseTriggerHandler(boolean isExecuting){         this.isExecuting = isExecuting;     }      public void OnBeforeInsert(List&lt;Case&gt; newCases){         //EXECUTE BEFORE INSERT LOGIC     }      public void OnAfterInsert(List&lt;Case&gt; newCases){         //EXECUTE AFTER INSERT LOGIC     }      public void OnBeforeUpdate(List&lt;Case&gt; oldCases, List&lt;Case&gt; updatedCases, Map&lt;Id, Case&gt; CaseMap){         //BEFORE UPDATE LOGIC     }      public void OnAfterUpdate(List&lt;Case&gt; oldCases, List&lt;Case&gt; updatedCases, Map&lt;Id, Case&gt; CaseMap){         //AFTER UPDATE LOGIC     }      public void OnBeforeDelete(List&lt;Case&gt; CasesToDelete, Map&lt;Id, Case&gt; CaseMap){         //BEFORE DELETE LOGIC     }      public void OnAfterDelete(List&lt;Case&gt; deletedCases, Map&lt;Id, Case&gt; CaseMap){         //AFTER DELETE LOGIC     }      public void OnUndelete(List&lt;Case&gt; restoredCases){         //AFTER UNDELETE LOGIC     }      public boolean IsTriggerContext{         get{ return isExecuting;}     } } How can Planck units be consistent with conflicting dimensions of mass? I suspect I'm missing something obvious, but I'm coming up blank. I've gotten pretty comfortable with so-called natural units over the years: in doing quantum mechanics/QFT, it's common to set $c = \hbar = 1$ and in GR, it's common to set $c = G = 1$. I'm told that quantum gravity researchers are fond of , where (according to that Wiki page) we set $c = \hbar = G = 1$, along with a couple other fundamental constants. I don't know what to make of this, though: it's dimensionally inconsistent in 3+1 dimensions. That same article gives the dimensions of each constant:  $$\begin{align} [c] &amp;= L T^{-1} \\ [G] &amp;= L^3 M^{−1} T^{−2} \\ [\hbar] &amp;= L^2 M T^{−1} \end{align}$$  Setting $c$ and $G$ to 1 implies $L=T=M$. Setting $c$ and $\hbar$ to 1 implies $L=T=M^{-1}$. Hence, making all three unity is internally inconsistent: mass cannot simultaneously have dimensions of length and reciprocal length. So, how do Planck units work? What's the mathematics definition of the F value in Analysis of Variance Table? Suppose I have a linear regression model Y ~ b1*x1 + b2*x2 with the sample data:          x1      x2        y 0  -0.7251 -0.6033  10.2508 1  -1.3148  3.7067  10.3054 2  -1.2818 -5.8136   7.2010 3   0.6154  3.6336  11.2807 4   1.4887 -2.8337  10.6299 5  -2.0224 -0.3931   7.4502 6   0.5419 -1.7807  10.7339 7  -1.0745 -5.0296   5.8734 8   3.2116 -0.4681  11.7184 9   1.6767 -4.6040   9.0145 10 -1.3355 -2.6874   6.5014 11  0.8296  2.6793  11.8295 12 -2.8647  4.2916   7.8414 13  1.8445 -3.3924   9.6520 14 -0.1036  2.4273  11.9766 15  1.0886 -3.5636  10.6023 16 -3.3026 -6.9837   4.9962 17  1.4050 -3.8453  10.4630 18 -0.3111 -1.4278   9.2283 19 -3.5454  2.4960   7.3720   And using the following R code to get the Analysis of Variance Table:  &gt; df &lt;- read.csv('f:/data.csv', header=T, sep=",") &gt; model_All &lt;- lm(y ~ x1 + x2, data=df) &gt; anova(model_All) Analysis of Variance Table  Response: y           Df Sum Sq Mean Sq F value    Pr(&gt;F)     x1         1 44.440  44.440  58.277 6.865e-07 *** x2         1 26.640  26.640  34.934 1.711e-05 *** Residuals 17 12.964   0.763                       --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1   And I can calculate the F value of hypothesis test H0： b2=0 via:  &gt; model_Drop2 &lt;- lm(y ~ x1, data=df) &gt; SSR_All = sum(resid(model_All)^2) &gt; SSR_Dp2 = sum(resid(model_Drop2)^2) &gt; F_x2 = ((SSR_Dp2 - SSR_All) / 1) / (SSR_All / (20 - 3)) &gt; F_x2 [1] 34.93434   We can see that F_x2 is equal to F value of x2 in Analysis of Variance Table. However, the value F_x1 calculated as follow is not equal to F value of x1, I can't understand why:  &gt; model_Drop1 &lt;- lm(y ~ x2, data=df) &gt; SSR_Dp1 = sum(resid(model_Drop1)^2) &gt; F_x1 = ((SSR_Dp1 - SSR_All) / 1) / (SSR_All / (20 - 3)) &gt; F_x1 [1] 70.30392   So, what is the mathematics definition of the F value in table?  EDIT The result of the features reversed as commented by @Michael M:  &gt; model_All2 &lt;- lm(y ~ x2 + x1, data=df) &gt; anova(model_All2) Analysis of Variance Table  Response: y           Df Sum Sq Mean Sq F value    Pr(&gt;F)     x2         1 17.468  17.468  22.907 0.0001718 *** x1         1 53.612  53.612  70.304 1.914e-07 *** Residuals 17 12.964   0.763                       --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Fontconfig warning: "/etc/fonts/conf.d/90-fonts-unfonts-core.conf" I am getting the following error frequently. (Example: when running zenity,firefox etc. commands / applications.)  Fontconfig warning: "/etc/fonts/conf.d/90-fonts-unfonts-core.conf", line 11: Having multiple values in &lt;test&gt; isn't supported and may not work as expected   Here is contents of file /etc/fonts/conf.d/90-fonts-unfonts-core.conf:  &lt;?xml version="1.0"?&gt; &lt;!DOCTYPE fontconfig SYSTEM "fonts.dtd"&gt; &lt;fontconfig&gt;     &lt;match target="font"&gt;         &lt;test name="family" qual="any"&gt;             &lt;string&gt;은 바탕&lt;/string&gt;&lt;string&gt;UnBatang&lt;/string&gt;                 &lt;string&gt;은 돋움&lt;/string&gt;&lt;string&gt;UnDotum&lt;/string&gt;                 &lt;string&gt;은 궁서&lt;/string&gt;&lt;string&gt;UnGungseo&lt;/string&gt;                 &lt;string&gt;은 필기&lt;/string&gt;&lt;string&gt;UnPilgi&lt;/string&gt;                 &lt;string&gt;은 그래픽&lt;/string&gt;&lt;string&gt;UnGraphic&lt;/string&gt;         &lt;/test&gt;          &lt;edit name="antialias" mode="assign" binding="strong"&gt;&lt;bool&gt;true&lt;/bool&gt;&lt;/edit&gt;         &lt;edit name="hinting"   mode="assign" binding="strong"&gt;&lt;bool&gt;false&lt;/bool&gt;&lt;/edit&gt;         &lt;edit name="autohint"  mode="assign" binding="strong"&gt;&lt;bool&gt;true&lt;/bool&gt;&lt;/edit&gt;         &lt;edit name="hintstyle" mode="assign" binding="strong"&gt;&lt;const&gt;hintslight&lt;/const&gt;&lt;/edit&gt;     &lt;/match&gt; &lt;/fontconfig&gt;   How to solve it?