How to find the missing dependencies for all packages?
Undo apt-get remove open* ubuntu 12.04
Why is Lightroom not rendering what I see in every other JPG viewer? Can I use a higher rank tensor field as the metric field? What a metric should necessarily do is it should give me a way to associate a frame invariant number with a given pair of spacetime events. Now, if I use a higher rank tensor field (say, for example, a tensor field of rank 3: $g_{\mu \nu \rho}$) then also I can certainly produce a frame invariant scalar out of a given displacement $\vec{A}$ in this trivial way: $ I := g_{\mu \nu \rho} A^{\mu}A^{\nu}A^{\rho}$. Since the components of the higher rank tensor and that of the displacement vector are going to transform in a covariant and a contravariant manner respectively, the cooked up quantity is certainly a scalar.   Another crucial property, which I think has more direct physical content than the previous one, is that between two inertial frames, at least one such transformation should exist that leaves at least one metric invariant. i.e., There should exist at least one combination of transformation matrix $\displaystyle\frac{\partial{x^{\alpha}}}{\partial{x^{\mu '}}}$ and metric $g_{\alpha \beta \gamma}$ that satisfies the following equation:      $\displaystyle\frac{\partial{x^{\alpha}}}{\partial{x^{\mu '}}}\displaystyle\frac{\partial{x^{\beta}}}{\partial{x^{\nu '}}}\displaystyle\frac{\partial{x^{\gamma}}}{\partial{x^{\rho '}}} g_{\alpha \beta \gamma} - \delta_{\mu '}^{\alpha}\delta_{\nu '}^{\beta}\delta_{\rho '}^{\gamma} g_{\alpha \beta \gamma} =0$    The last thing I can think of that can put a restriction on the choice of a tensor as a metric is the existence of a possibility of finding a metric compatible symmetric connection field. Following the usual procedure of finding the expression for a metric compatible symmetric connection field, I reached following condition (unlike the case of the usual two rank metric where we get a full-fledged expression) for the connection in the terms of the metric:      $g_{\nu \rho k_1} \Gamma^{k_1}_{\mu \lambda} - g_{\lambda \mu k_2} \Gamma^{k_2}_{\rho \nu} = \displaystyle\frac{1}{2} (\partial_{\nu}g_{\rho \lambda \mu} + \partial_{\rho}g_{\lambda \mu \nu}  - \partial_{\lambda}g_{\mu \nu \rho}  - \partial_{\mu}g_{\nu \rho \lambda}) $   My question is that if it is possible to satisfy the two highlighted conditions then can we use such a 3 rank (or even higher rank tensors with similarly produced conditions) tensor fields as metric fields?   PS: This is NOT a proposal for a new home-production theory of gravity (or that of anything for that matter) but rather it is just that I am trying to understand why a two rank tensor is used in General Relativity as the metric. Thank you. One part of the render layer glowing? How can I find non-ASCII characters in MySQL? I'm working with a MySQL database that has some data imported from . The data contains non- characters (em dashes, etc.) as well as hidden carriage returns or line feeds. Is there a way to find these records using MySQL? How to nest code within a list using Markdown If $\vec{a},\vec{b},\vec{c},\vec{d}$are unit vectors, $(\vec{a}\times\vec{b}).(\vec{c}\times\vec{d})=1$ and $\vec{a}.\vec{c}=\frac{1}{2}$,then If $\vec{a},\vec{b},\vec{c},\vec{d}$are unit vectors such that $(\vec{a}\times\vec{b}).(\vec{c}\times\vec{d})=1$ and $\vec{a}.\vec{c}=\frac{1}{2}$,then $(A)\vec{a},\vec{b},\vec{c}$ are non-coplanar $(B)\vec{a},\vec{b},\vec{d}$ are non-coplanar $(C)\vec{b},\vec{d}$ are non-parallel. $(D)\vec{a},\vec{d}$ are parallel and $\vec{b}$ and $\vec{c}$ are parallel.    My Attempt: $(\vec{a}\times\vec{b}).(\vec{c}\times\vec{d})=1$ $(\vec{a}.\vec{c})(\vec{b}.\vec{d})-(\vec{a}.\vec{d})(\vec{b}.\vec{c})=1$ $\frac{1}{2}(\vec{b}.\vec{d})-(\vec{a}.\vec{d})(\vec{b}.\vec{c})=1$    Book's Solution which i did not understand: $(\vec{a}\times\vec{b}).(\vec{c}\times\vec{d})=1$ is possible only when $|\vec{a}\times\vec{b}|=|\vec{c}\times\vec{d}|=0$ and $(\vec{a}\times\vec{b})$ is parallel to $(\vec{c}\times\vec{d})$ And the correct option given is $(C)$.  I could not solve this problem after some efforts.Please help me.Thanks. VHDL Transition Function The characteristic and minimal polynomial of a companion matrix of a monic polynomial $f \in \mathbb F\left[x\right]$ in $1$ variable $x$ over a field $\mathbb F$ plays an important role in understanding the structure of finite dimensional $\mathbb F[x]$-modules.  It is an important fact that the characteristic polynomial and the minimal polynomial of $C(f)$ are both equal to $f$. This can be seen quite easily by induction on the degree of $f$.  Does anyone know a different proof of this fact? I would love to see a graph theoretic proof or a non inductive algebraic proof, but I would be happy with anything that makes it seem like more than a coincidence! Find $\sum_{n=1}^\infty \frac{n^3}{n!}$. I have to find the sum of the following series:  $$\sum\limits_{n=1}^\infty \frac{n^3}{n!}$$  I know how to prove the convergence of this series, but how do i find the sum. I can't use the properties of derivation or integration of the series, i have to do it using the definition that a series converges iff it's sequence of partial sum converges. How to measure supply currents ranging from 1μA to 10mA? Assume that $0 &lt; a_n \leq 1$ and that $\sum a_n=\infty$. Is it true that  $$ \sum_{n \geq 1} \frac{a_n}{(a_1+\ldots+a_n)^2} &lt; \infty $$ ?  I think it is but I can't prove it. Of course if $a_n \geq \varepsilon$ for some $\varepsilon &gt; 0$ this is obvious.  Any idea? Thanks. Extruding Vector Files in Blender I am sure this has been discussed quite a few times, but I found a tutorial recently doing the exact same thing as I did, but in my case my logo is messing up!  Here is the link to the workflow:   This is what it looks like after adding the solidify modifier:   I already recalced the normals of my spline, but besides that it messes up my spline shape, it had no effect.  Any suggestions on how to fix it? I'm trying to evaluate $(\hat{a}+\hat{a}^\dagger)^k|n\rangle$ Where $\hat{a}$ and $\hat{a}^\dagger$ are ladder operators and $|n\rangle$ the $n$th Fock state. For this, I separated the problem in three parts: $k&lt;n$, $k=n$ and $k&gt;n$. In this part I'm a bit confused: Is it possible to evaluate such operations? Some tips on how to start would be really great. What is the difference between "gerund" and "infinitive"? What is the difference between "gerund" and "infinitive"? I do not understand the differences.Can you explain them? Why current in series circuit is the same? I have read in the internet that the charges do not have any other path to go and they must go through the same in a series circuit,hence the current is same.  It was quite convincing but what confused me was: "A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. Resistors act to reduce current flow..."(according to the Wikipedia). This means that the resistors slow down the rate of flow of charges. By definition, electric current is the rate of flow of charges. Then must not the current be reduced in a resistor even when the amount of charge is same? OrderBy and OrderByDescending are stable? I have to prove the  by tomorrow and I am really unconfident about what I did:  $$\sum_{n=1}^\infty a_n\text{ converges } \iff \sum_{n=1}^\infty 2^n a_{2^n}\text{ converges}$$  I did the following:  Let $(b_n)$ be a sequence as follow: $b_{2^k+m}:=a_{2^k}$ with $k\in\mathbb N_0$ and $0\leq m&lt;2^k$.  It's $a_{n+1}\leq a_n$ and so $0\leq a_{n+p}\leq a_n$ for all $n,p\in\mathbb N$.  So $\sum\limits_{n=1}^\infty b_n$ converges by the majorizing series $\sum\limits_{n=1}^\infty a_n$. And it's $\sum\limits_{n=0}^\infty b_n=\sum\limits_{n=0}^\infty\sum\limits_{m=0}^{2^n-1}a_{2^{n+1}}=\sum\limits_{n=1}^\infty 2^{n-1}a_{2^n}$ so $\Rightarrow$ is done.  For $\Leftarrow$ consider $c_{2^k+m}:=a_{2^k}$ with $k\in\mathbb N_0$ and $0\leq m&lt;2^k$.  It's $|a_n|\leq c_n$ and $\sum\limits_{n=0}^\infty c_n=\sum\limits_{n=0}^\infty\sum\limits_{m=0}^{2^n-1}a_{2^{n}}=\sum\limits_{n=1}^\infty 2^{n}a_{2^n}$ and so $\sum\limits_{n=1}^\infty a_n$ converges by the majorizing series $\sum\limits_{n=0}^\infty c_n$.  Is this in form and content correct? I have a collection of files and directories with strange names, they contain spaces and the special characters \, *, ), ( and ?. All of them cause problems when I try to use them in the command line or scripts, e.g.:    $ cd space dir bash: cd: space: No such file or directory  $ cat space file cat: space: No such file or directory cat: file: No such file or directory  $ cat ( bash: syntax error near unexpected token `newline'  $ echo content &gt;\ &gt; ^C  $ ls ? (  )  *  ?  \   How do I enter file or directory names that contain special characters in the terminal? Skip empty rasters in ArcGIS I'm trying to write some code to skip over empty raster sets when converting rasters to point (the empty sets stop the conversion, leaving me with a half complete model run).  I know that I can identify empty rasters using the ALLNODATA result from "Get Raster Properties" .  I know I can delete rasters using the Delete.management tool.  I know I should be able to create a branch using calculate value.  But I'm inexperienced with python and modelbuilder, and haven't been able to put this all together. Could someone help me figure out what I am doing wrong? My code and an image of the modelbuilder setup are below.  def fn(Property):  #Import modules      import arcpy  #ifelse statement if Property == "1":             return "true" elif Property == "0":            return "false" My LAN server won't let my cousin join me or me join my cousin. It won't show up on the multiplayer screen - it keeps saying "scanning for LAN servers" but it never finds it. I am at his house and we use different computers but it won't connect. How can I fix this?