For example, I have a string s and the MD5 of s is m. So is it possible for s=m.  Now it can be found by iterating through all possible combinations but there are 2^128 combinations to check through and I do not have the resources to do so. Is any such case possible and if it is possible then what is the case?
Is there a fixed point in the MD5 transformation, i.e. does there exist x such that md5(x) == x?
How to disable gedit side panel? How do i disable this stupid side panel of gedit, that somehow appeared? There is nothing in the settings or plugins. Tried rm -r -f ~/.config/gedit as well, with no success. I don't have big screen and i find it totally useless and eating up what little free space for editing documents i have. See Screenshot How to solve the diffencial equation for power series $(1+x²)y'' - 6xy=0$ in $x_{0}=0$ I have tried for the power series but when suppose the solution is $y(x)=\sum _{n=0}^\infty a_nx^n$ appeared sums dependents of $a_n$,  $a_{n+2}$ and $a_{n-1}$ and this is not possible. Take a look at this example schematic:  The chip in question is the  and as you can see power is provided on both sides (with a 100nF cap to smooth noise I guess). Is this strictly required or could you put power into one side and just ignore the other? I know that I have just put power in one side and everything still seems to work fine but I feel uneasy with doing that. I feel that they would not waste pins that could be doing something useful by having an extra pair of power in/out pins. For what purpose does this PIC MCU (and others like it) have multiple power pins? QR factorization of complex matrix If you have two complex numbers $a,b$ how can you find the QR factorization of   $ M = \begin{bmatrix}        aI_n\\          bI_n \end{bmatrix} $,  I can't seem to be able to do it. I tried an earlier trick, but I now know it's not necessary true for complex numbers. Is there anyway to do this?  I think if I use a Givens algorithm I should be able to reduce it to a QR factorization. I need to find the caller of a method. Is it possible using stacktrace or reflection? How can I block all traffic *except* Tor? Difference between Session and HttpContext.Current.Session Why didn't Dumbledore remove Quirrell from DADA teaching when he realized something was wrong with him? In "Harry Potter and the Deathly Hallows", from Snape's memory that Harry views, we learn that Dumbledore had misgivings about Quirrell, when he said to Snape:     Keep an eye on Quirrell, won't you?   If he knew something was off, why not remove him from a very sensitive position of teaching DADA to kids? How do I generate the upper triangular indices from a list? Is there anything like “cubic formula”? Just like if we have any quadratic equation which has complex roots, then we are not able to factorize it easily. So we apply quadratic formula and get the roots.  Similarly if we have a cubic equation which has two complex roots (which we know conjugate of each other) and one fractional root, then we are not able to find its first root by hit &amp; trial.  So my question is like quadratic formula, is there exist any thing like cubic formula which help in solving cubic equations?  For example, I have an equation $$2x^3+9x^2+9x-7=0\tag{1}$$ and I have to find its solution which I am not able to find because it has no integral solution. Its solutions are $\dfrac {1}{2}$, $\dfrac{-5\pm \sqrt{3}i}{2} $, I know these solutions because this equation is generated by myself.  So how can I solve equations like these?  Also while typing this question, I thought about the derivation of quadratic formula, which is derived by completing the square method.  So I tried to apply ‘completing the cube’ method on the general equation $ax^3+bx^2+cx+d=0$ but it didn't help.  So please help me in finding a cubic formula or to solve the equations like given in example by an alternative method. Get Response header when 401 occurred Test for existence of nested JavaScript object key Using Illustrator CS6 to create shape out of multiple paths I am very new to Illustrator, in fact I am only experimenting with it in an attempt to help my friend develop a logo for a new business venture. I managed to draw out the shell of the logo using the line tool and modifying the lines with the anchor tool to get the shape I wanted.  However, I would like to somehow take all of these paths and create one object, or symbol which I can then apply a drop shadow, fill and various other effects too. Currently when I try to do this I get unwanted effects...  I'd appreciate any help on the subject. What is the difference between these two:     Suzuki was nearly close to go out of business just after the World War period.   Vs.     Suzuki was nearly close to going out of business just after the World War period.(from a video)   When talking about the past, do these two sentences different from each other? Like, if you use verbing(going) with infinitive(to) in the past, does it mean that there is another event happening? Or none. Is it possible to set start-up applications to initialize in certain workspaces? I'd like to not have to manually distribute my start-up applications across my numerous workspaces every time I boot up my machine. I'm running Ubuntu 12.04 .  Any Help ? Let $F:\mathbb{R^2}\rightarrow \mathbb{R}$ be a function, such as : $$F(x,y)=\begin{cases}        0 &amp; (x,y)=(0,0) \\       \frac{xy}{x^2+y^2} &amp; (x,y)\neq (0,0)    \end{cases}$$      Is $F$ differentiable at $(0,0)$?   My attempt :  Consider the limit, $\lim_{(x,y)\rightarrow (0,0)} F(x,y)$ along the line $y=x$. The limit equals to $\frac{1}{2}$. However, $F(0,0)=0$. Hence $F$ is not continuous at $(0,0)$ which implies that $F$ isn't differentiable as well.  Is this approach okay ? How to choose a good research problem? I am working to get a PhD, maybe next year this time around. Currently, this is my second year. I have published 3 papers. All of them are not about one problem but consider different problems. My strategy to find a research idea/problem is given below.  1 - Read papers whose titles are either interesting or I have some apriori understanding of those titles.  2 - Understand those papers as best as I can. That is, I try to understand each detail presented in the paper except the simulation results (this is because I think simulation results are hard to reproduce).  3 - I analyze the paper and try to find a very small problem which can be addressed (i.e. I can solve it) by the methodology of the paper.  4 - If I am successful at step 3 I start working on that problem otherwise I repeat the process from step 1.  By applying this strategy I have been able to write 3 papers and I have submitted a fourth (I am not satisfied with those papers because at very best they can be considered average papers). But my concern is that the problems addressed in those papers do not belong to one area. As far as I have seen, for the profiles of some of the renowned researchers in my field their PhD work is focused on one area. One main thing I console myself with is that almost all of those researchers had good supervisors. My supervisor does not even read the draft/reviews of my papers and the suggestions that he provides during the meetings are so broad that the problem becomes intractable. Under these circumstances what are your opinions: Is there any better strategy to do research?   I will be very thankful to you for providing me suggestions or commenting on my dilemma. Parse PHP code to extract function names? Double limit of $\cos^{2n}(m! \pi x)$ at rationals and irrationals I stumbled upon this "relation" (is the name correct?):  $$ \lim_{m \to \infty} \lim_{n \to \infty} \cos^{2n}(m! \pi x) = \begin{cases} 1,&amp;x\text{ is rational}\\ 0,&amp;x\text{ is irrational}\end{cases} $$  How is it called and why is it so? I'm really not asking for a proof since I fear it would be too complicated for me to understand, but rather for an "intuition". How do I recover my Google account (or Gmail) password or username? I have forgotten the password or username for my Google account, or I'm unable to access my account for other reasons.  How can I recover my account?  (This Q&amp;A is meant as a general description for all Google and Gmail username/password questions. See: )