How to make eyeglass lens material
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Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$ Consider the space $C^1([0,1])$ and the function $d:C([0,1])\times C([0,1]) \to \mathbb R$ defined as $d(f,g)=|f(0)-g(0)|+sup_{x \in [0,1]}|f'(x)-g'(x)|$. Decide whether the metrics $d$ and $d_{\infty}$ are topologically equivalent in $C^1([0,1])$ (where $d_{\infty}=sup_{x \in [0,1]}|f(x)-g(x)|)$  My attempt at a solution:  If two metrics are topologically equivalent, then they have the same convergent sequences. Honestly, I couldn't do anything. I am trying to define a sequence of functions $\{f_n\}_{n \in \mathbb N}$ such that $f_n \to f$ in, for instance, $(C^1([0,1]),d)$ but $f_n \not \to f$ in $(C^1([0,1]),d_{\infty})$. Could it be this two metrics are topologically equivalent? If this is the case, how could I prove it? If not, I would appreciate any hint to find an adequate sequence of functions that works for what I am trying to prove. "Require Installation Of Untrusted Packages" while upgrading with the update manager It didn't fixed the error. So, how do I fix my GUI update?  For every software I have to install it from command line because I got same error when install software from Ubuntu Software Center. Show that $X^2$ and $X^3$ are irreducible but not prime in $K[X^2,X^3]$.   My reasoning is as follows:  Since the only ways $X^2$ and $X^3$ can be factored in $K[X^2,X^3]$ are $X^2 = X^2 * 1$ and $X^3=X^3*1$ it follows that $X^2$ and $X^3$ are irreducible.  To show that they are not prime in $K[X^2,X^3]$ I argue that $X^2\mid X^3*X^3$ but $X^2\nmid X^3$ and $X^3\mid X^4*X^2$ but $X^3\nmid X^4$ or $X^3\nmid X^2$.  Is that correct? Polygamma reflection formula Merging two xml files in C# without appending and without deleting anything (example given) How do I disable auto-maximizing of newly launched windows in GNOME? Each time I open any application, it zooms to fill-up the entire desktop and so I am always forced to use "Unmaximize" using Alt+Space menu. Solve $\lim_{x\to 0} \frac{\sin x-x}{x^3}$ Software/App for electronic research notebooks I want to keep a research notebook for my computational "experiments". Basically, I should at least be able to write text and attach images like plots. Other nice features to have would be   linking to past experiments/pages latex equations uploading papers, or other urls being able to transfer data dating and version control open-source tool   I am already familiar with trello and tiddlywiki. Trello is good for attaching stuff and organising tasks, but I need a notebook where I attach a plot, write stuff around it, attach another below it. It doesn't have a paper or canvas. Tiddlywiki is a little painful for attaching pics and equations, the file bloats, it seems I am keeping a blog.  What is a good, free electronic notebook tool for research/lab work? My understanding is that a question is historically locked because the information in it is too valuable for the question to be deleted.   But if the "valuable information" becomes obsolete, what happens then?  We cannot modify the question content, or the answers for a historically locked question, right? Why cannot fermions have non-zero vacuum expectation value? In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory take non-zero vacuum expectation value? What forbids fermions to take vevs? Consider these two sentences: "I gave him a pencil," and, "I gave a pencil to him."  Is it correct that the important part of the sentence is placed at the end? When we want to emphasize the pencil that I gave him, must we say, "I gave him a pencil?" When we want to emphasize that it is him to whom I gave a pencil, must we say, "I gave a pencil to him?" How do I loop through or enumerate a JavaScript object? How do you declare an interface in C++? How do I setup a class that represents an interface?  Is this just an abstract base class? Prevent VLC from starting a new instance every time a media file is opened mkdir error: no such file or directory on a linux machine running CENTOS v 7.8.2003 I am in a directory Neutrinos I now do  mkdir /pionloop/ this works. I then go to into this new directory pionloop and do mkdir /E_0.3 and this works as well. I thus have as a result a directory Neutrinos/pionloop/E_0.3.  Now, starting in Neutrinos I want to do this in one command and therefore do mkdir /pionloop/E_0.3 and get: `mkdir: cannot create directory ‘/pionloop/E_3.0’: No such file or directory  What is going wrong here?? Effective Refractive Index in Paper I am reading the paper, entitled "Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings" by Eric B. Grann, M. G. Moharam, and Drew A. Pommet.   In the paper they mention this formula:        Do you know how it can be derived and where it comes from ? java.sql.SQLException Parameter index out of range (1 > number of parameters, which is 0) Is there a way to mount a disk directly to a specific folder? Proving a triangle with different edge colors exists in a graph. This is again some homework translated (hopefully not too badly) from my book  The graph $K_{n}$ is colored using $n$ different colors, in a way that each color is used at least once. Prove that there exists a triangle with its edges colored in different colors. I am interested in publishing a GML file as a WFS. I don't want to use a database like PostgreSQL. What would be the rough steps I need to do for that? I like to use open source software (geoserver). I don't have much experience. I am just looking for a rough guide what kind of software I should look into and which step follows which step..