Unity Lighting Problems I've got a problem with the settings of lighting in my unity scene.  The objects have got "dark sides" and it doesn't look natural.  You can see the screenshots and my light settings here:  The screenshot that shows the problem
How to avoid "completely" dark shadow using directional light (as Sun) ? Look at my scene:     Sun is rising and as you can see the scene is realistic; I mean, that what is in shadow is almost completely dark. This is correct, but i would like something less "dark", like an HDR.  These are some parameters i'm using:     This is my unique Light in scene (Sun):     I'm using also a Post-Processing profile with "Eye Adaption" unflagged.  Can you suggest me what i've to change to make my object affected by shadow less.. dark ?   Thanks
The question is:     Are there square matrices $A,B$ over $\mathbb{C}$ s.t. $A^2+B^2=AB$ and $BA-AB$ is non-singular?   From $A^2+B^2=AB$ one could obtain $A^3+B^3=0$. Can we get something from this?  Edit:  $$A^2+B^2=AB\implies\\ A(A^2+B^2)=A^2B \implies\\ A^3+AB^2=A^2B \implies \\ A^3+(A^2+B^2)B=A^2B \implies \\  A^3+A^2B+B^3=A^2B \implies \\ A^3+B^3=0 $$ bases and binary I can not figure this out.   I started off by making a table and putting the base(2) on one side, the number in the middle and the remainder in the third row and for 2010 I got 11111011010 but I cant find the next two numbers please help and please explain in detail.  Thank you =)   to express 2010 in base 2, we use exactly 8 ones and 3 zeros. find the next two integers in base 2 that use the same number of ones and zeros I've recently taken up a position in an all Mac workshop - We have Intel based Apple machines. Can I dual boot Ubuntu on my machine, if so how? Why is there a controversy on whether mass increases with speed? Some people say that mass increases with speed, some people say that the mass of an object is independent of its speed.  I understand how some (though not many) things in physics are a matter of interpretation based on one's definitions. But I can't get my head around how both can be 'true' is any sense of the word.  Either mass increases or it doesn't, right?  Can't we just measure it, and find out which 'interpretation' is right? e.g.: (in some sophisticated way) heat up some particles in a box and measure their weight?  ------------------------------  UPDATE  Right, so I've got two identical containers, each with identical amounts of water, each on identical weighing scales, and each in the same g field. If one container has hotter water, will the reading on its scale be larger than the other? If the answer is yes, and g is constant, does this mean that the m in w=mg has got bigger? Find the exact value of the infinite sum $\sum_{n=1}^\infty \big\{\mathrm{e}-\big(1+\frac1n\big)^{n}\big\}$ Nested Radical of Ramanujan I think I have sort of a proof of the following nested radical expression due to Ramanujan for $x\ge 0$.     $$\large x+1=\sqrt{1+x\sqrt{1+(x+1)\sqrt{1+(x+2)\sqrt{1+\cdots}}}}$$ for $ x\ge -1$   I just want to know if my proof is okay or there is a flaw, and if there is one I request to give some suggestions to eliminate them. Thank you. The proof is the following:  Proof: Let us define $$ a_n(x)=\underbrace{\sqrt{1+x\sqrt{1+(x+1)\sqrt{1+(x+2)\sqrt{1+\cdots}}}}}_{n \ \mbox{terms}}$$ for $x\ge 0$ so that $$ a_1(x)=\sqrt{1+x},\ a_2(x)=\sqrt{1+x\sqrt{1+(x+1)}},\ a_3(x)=\cdots$$    and so on. Since $x\ge 0$ each one of the $a_n$ is defined (I am taking only the positive square root). Also, we note that $$a_{n+1}^2(x)=1+xa_{n}(x+1)$$  Now, we note that $\{a_n(x)\}$ is an increasing sequence and that $$a_n(x)&lt;x+1$$ $\forall n\ge 1$, this is easy to prove by induction as below:  For $n=1$, $a_1(x)=\sqrt{1+x}&lt;1+x$ since $x\ge 0\Rightarrow 1+x\ge 1$. SO it is true for $n=1$. Similarly, the truth can be proved for $n&gt;1$.  Then $a_n(x)$ converges to $$l(x)=\sup_{n}a_n(x)\le x+1$$ Now I make the following claim:  Claim: $l(x)=x+1\quad \forall i\ge 0$  Proof: Fix $x$. Let $l(x)&lt;x+1$. Then, $l(x)=x+1-\epsilon$ for some $\epsilon&gt;0$. Now, I claim that there must be a $n$ such that $$x+1-a_n(x)&lt;\epsilon$$, and if that is true then $$a_n(x)&gt;x+1-\epsilon=l(x)$$ which is a contradiction since $$l(x)=\sup_{n}a_n(x)$$ and then it implies that $$l(x)=x+1$$ To prove my claim it requires $$x+1-a_n(x) &lt;  \epsilon$$ Now, \begin{align} x+1-a_n(x) = &amp; x+1-\sqrt{1+xa_{n-1}(x+1)} \\ \ =&amp; \frac{(x+1)^2-({1+xa_{n-1}(x+1)})}{x+1+\sqrt{1+xa_{n-1}(x+1)} } \\ \ =&amp; x\frac{(x+1)+1-a_{n-1}(x+1)}{x+1+\sqrt{1+xa_{n-1}(x+1)} } \\ \ &lt;&amp; \frac{x}{x+2}((x+1)+1-a_{n-1}(x+1))\\ \ &lt;&amp; \frac{x}{x+2}\cdot\frac{x+1}{x+3}((x+2)+1-a_{n-2}(x+2))\\ \ &lt;&amp; \frac{x}{x+n-1}\cdot \frac{x+1}{x+n} ((x+n-1)+1-a_{1}(x+n-1))\\ \ &lt;&amp; \frac{x}{x+n-1}\cdot \frac{x+1}{x+n}(x+n-\sqrt{x+n})\\ \ &lt;&amp; \frac{x(x+1)}{x+n-1} \end{align}  Now, if one is able to find $n$ such that $$\frac{x(x+1)}{x+n-1}&lt;\epsilon \Rightarrow x&lt; \frac{-(1-\epsilon)+\sqrt{(1-\epsilon)^2+4\epsilon(n-1)}}{2}$$ then we're done.   Now from the upper bound it seems that there always exists some $n$ that satisfies this requirement. Hence the claim is proved. How should a physics student study mathematics? Note: I will expand this question with more specific points when I have my own internet connection and more time (we're moving in, so I'm at a friend's house).  This question is broad, involved, and to some degree subjective.  (I started out as a physics-only student, but eventually decided to add a mathematics major. I am greatly interested in mathematics; the typical curriculum required for physics students is not deep or thorough enough; mathematics is more general (that means work!); and it only requires a few more classes. Naturally, I enjoy  immensely.)  This question asks mainly of undergraduate-level study, but feel free to discuss graduate-level study if you like.  Please do not rush your answer or try to be comprehensive. I realize the StackOverflow model rewards quick answers, but I would rather wait for a thoughtful, thorough (on a point) answer than get a fast, cluttered one. (As you probably know,  produces clear, useful writing; and a properly-done comprehensive answer would take more than a reasonable amount of time and effort.) If you think an overview is necessary, that is fine.  For a question this large, I think the best thing to do is focus on a specific area in each answer.    Update: To Sklivvz, Cedric, Noldorin and everyone else: I had to run off before I could finish, but I wanted to say I knew I would regret this; I was cranky and not thinking clearly, mainly from not eating enough during the day. I am sorry for my sharp responses and for not waiting for my reaction to pass. I apologize.  Re: Curricula:   Please note that I am not asking about choosing your own curriculum in college or university. I did not explicitly say that, but several people believed that was my meaning. I will ask more specific questions later, but the main idea is how a physics student should study mathematics (on his or her own, but also by choosing courses if available) to be a competent mathematician with a view to studying physics.  I merely mentioned adding a mathematics major to illustrate my conclusion that physics student need a deeper mathematical grounding than they typically receive.   And now I have to run off again. Mark or don't mark required fields if all are required? If all fields in a form are required should they be marked somehow (eg. with an asterisk)?  I see this done a lot and find it redundant?  There could be a difference in big forms and small forms, but in big ones I would add a note at the top that all fields are required, but I wouldn't necessarily do that on small ones.  What do you think is the right approach? I got a B1/B2 visa earlier this year when I traveled to the US for a business trip from my company. It expires in 2013 and I'd love to visit the United States again, but for no other purpose than traveling.  I wonder:        If I can legally travel to US with B1/B2 visa without a real business need (assuming I'm honest);   If I have to work at my current company to be able to use it.      I live in Russia. I'm writing a contribution for a double-blind submission system.   Since I would like to supply more data than I could show on a small number of pages, I'm looking for a way to reference supplemental data in my manuscript, such as software scripts, figures or databases.  I could upload on GitHub, RPubs, Figshare and Zenodo, but all of these would expose my real user name (and I don't feel like making a throwaway e-mail account with a new repository for every anonymous publication that I intend to write).  Is there any way to get the above services to do what I want? Or is there a similar service that would allow anonymous hosting of research data?   It would be even better if I could later (e.g. after publication) declassify the information, with the link from the manuscript still being intact. How to make a complete factory reset, without anyone being able to retrieve my data? I will have a few Android phones that I will have to let go.   I would like to make a proper clean wipe of the data, without no one being able to retrieve them, and do a factory reset.  I have read about the , encrypting the device before doing a factory reset, doing both, etc.  Since I am not an Android/adb guru, I would like to know if some of you would have some idea on how to achieve this with certainty.  I know "certainty" is a big word when it comes to proper data erasure on flash memory but still.  I have found some answers here and somewhere else, saying that encrypting and doing a factory reset on your Android device is enough, but I could not find a reliable source.  Just a few information that could be useful:   I'm running Linux as my OS and, therefore, I'm not looking for a Windows-based solution My devices are non-rooted and (almost) identical (Samsung A510F + 1 A510FD) Removing all \n\r characters from a node XSLT? wondered if you could help me please? I have node in xml that is as followed  $LOG: 08880xbpnd $ fhdsafidsfsd df sd fsd f sd fsd  I was wondering is there anyway to make all the text go on to one line so that it then can be passsed through to a javascript function? so it would turn out like this   $LOG: 08880xbpnd $fhdsafidsfsddfsdfsdfsdfsd When I spoke with a friend of mine, I had noticed she used sentences similar to "I need to go buy food."   Is it correct to say "to go buy," or should I say "to go to buy"?    I know that I could say "I need to buy food," but I think that in "I need to go buy food," who is speaking is putting in evidence s/he needs to go and that s/he cannot stay any longer, or that her/his time to stay is limited. Mathoverflow - why so different Curious why  (se site) doesn't have hot questions list on the right.  It also uses the old stackoverflow design.  Why has this site's design and functionality been abandoned (or at least look abandoned?) Weapon damage bonuses and critical hits Need to proof by induction (calculus1 n and n+1) Working with a CSV data file with 100 millions rows (and 30 columns) Google Drive search for part of a file name Is there any way I can search based on the last three digits of a file name?  I have a file with many invoices that are easy to reference with the last three numbers. Is there any way I can search something like *765 to search for ends with 765  Another example.. sometimes files are prefixed with a 0, sometimes not.. 093241251 vs 93241251 and if I just search 93241251 it will not find the 0 prefix version How to check if a macro value is empty or will not create text with plain TeX conditionals? I have a macro which holds some text value, e.g. \macro{some text}. If it is empty, I would like for nothing to appear in the document, but it has some content of any kind which would produce text displayed in the document, I would like a message to appear, "Text: some text".   \macro{} would be considered empty. \def\somedata{}, \macro{\somedata} would be considered empty. \macro{0} would be considered not empty.   I have tried making a TeX conditional which can check if the value is not empty, but nothing I tried works, e.g.:  \ifx #1 {} \else     Text: #1 \fi  \ifx#1{} \else     Text: #1 \fi  \ifx #1 \nil \else     Text: #1 \fi  \ifx#1!="" \else     Text: #1 \fi   What is the correct syntax for creating a conditional in plain TeX with checks if a value is not empty? Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$?