I have been using a domain name for the last few years. A larger company is threatening to sue me for using my initials as my company name!  So as an answer to this I have created a new domain URL with the addition of my location in the URL. So I now have redirected my old URL to my new URL.  But...I want Google to acknowledge this is really then same site and to keep any rankings, or to transfer the rankings from the old URL to the new URL!  Is this possible?
We have to shift our web-site to a new domain due to some unavoidable circumstances. The portal has been up and running there since 2009.  It has good index in various search engines and we are getting a good number of page hits on daily basis.  Losing the search hits and index are our big concern. We are not sure how best we can handle this.  What all can be done to preserve as much as possible while shifting to new domain name.
Pullback of a Volume Form Under a Diffeomorphism. I have an exercise here, which I have no idea how to do.     Problem: Let $ U $ and $ V $ be open sets in $ \mathbb{R}^{n} $ and $ f: U \to V $ an orientation-preserving diffeomorphism. Then show that   $$   {f^{*}}(\text{vol}_{V}) = \sqrt{\det \! \left( \left[   \left\langle {\partial_{i} f}(\bullet),{\partial_{j} f}(\bullet) \right\rangle   \right]_{i,j = 1}^{n} \right)} \cdot   \text{vol}_{U}. $$   Notation:         $ \text{vol}_{U} $ and $ \text{vol}_{V} $ denote the volume forms on $ U $ and $ V $ respectively.   $ f^{*}: {\Lambda^{n}}(T^{*} V) \to {\Lambda^{n}}(T^{*} U) $ denotes the pullback operation on differential $ n $-forms corresponding to $ f $. Need intuition about independence of events Suppose that we have the situation as depicted in the figure: a random experiment which has 4 outcomes $x_1, ..., x_4$ and two events $A$ and $B$. Also assume that $P(x_i)=0.25$.  Now, since $P(A \cap B) = P(A)P(B) = 0.25$, by definition the events $A$ and $B$ are independent. This does not make sense to me. Why are they independent? Is there an intuitive explanation?  Another thing is, suppose that there is a 5th outcome, $x_5$, outside of $A \cup B$, in that case the events $A$ and $B$ are no longer independent since  $P(A \cap B) \ne P(A)P(B)$. This result also does not make sense to me. nginx support for .htaccess / rewrite rules? Differences from Apache? Do you really answer "How do you do?" with "How do you do?" Should methods in a Java interface be declared with or without a public access modifier? Should methods in a Java interface be declared with or without the public access modifier?  Technically it doesn't matter, of course. A class method that implements an interface is always public. But what is a better convention?  Java itself is not consistent in this. See for instance Collection vs. Comparable, or Future vs. ScriptEngine. Is there an example of a ring $S$ with identity $1_S$ containing a non-trivial subring $R$ which itself has an identity $1_R$, but $1_R\neq 1_S$ (or equivalently $1_S\notin R$). I'd also like to know under what conditions the identities have to be equal. I know they must be equal if $S$ has no zero divisors, since for every $r\in R$ we have $(1_S-1_R)r=0$  In other words: Is the category of unital rings with identity-preserving morphisms a full subcategory of the category of rings (where morphism are only required to respect addition and multiplication)? AIC versus Likelihood Ratio Test in Model Variable Selection The software that I am currently using to build a model compares a "current run" model to a "reference model" and reports (where applicable) both a chi-squared p-value based on likelihood ratio tests and AIC values for each model.  I know that one advantage of AIC over likelihood ratio tests is that AIC can be compared on non-nested models.  However, I am not aware of any reason why AIC couldn't or shouldn't be compared on nested models.  In my model, when comparing nested models for variable selection, I'm finding several cases where the likelihood ratio test and the AIC comparison are suggesting opposite conclusions.  Since both are based on likelihood calculations, I'm struggling to interpret these results.  However the documentation of my software says (without explaining),   "If two models are nested (i.e. one is a sub-set of the other) then the more usual chi-squared test is the most appropriate to use. If the models are not nested, the AIC can be used..."  Can anyone elaborate on this and/or explain why AIC is not as helpful as likelihood ratio tests on nested models? So I have an SQL dump file that needs to be loaded using mysql_query(). Unfortunately, it's not possible to execute multiple queries with it.  -> It cannot be assumed that the mysql command-line client (mysql --help) is installed -- for loading the SQL file directly  -> It cannot be assumed that the mysqli extension is installed  /* contents of dump.sql, including comments */ DELETE FROM t3 WHERE body = 'some text; with semicolons; scattered; throughout'; DELETE FROM t2 WHERE name = 'hello'; DELETE FROM t1 WHERE id = 1;   The explode() below won't work because some of the dump content's values contain semicolons.  $sql = explode(';', file_get_contents('dump.sql')); foreach ($sql as $key =&gt; $val) {     mysql_query($val); }   What's the best way to load the SQL without modifying the dump file? Conditional Expectation of Bernoulli R.V. Let $X_1, X_2,\ldots, X_n$ be iid bernoulli r.v. with parameter $p$. Let $S=X_1+\cdots+X_n$ and $Y=X_1X_2$. Compute $\mathbb{E}(Y\mid S)$.  I know that $\mathbb{E}(X_1\mid S) = S/n$. So If I could split $\mathbb{E}(Y\mid S)$ into two then I would be done. But I don't think that is allowed. How to proceed? vertical alignment of a turned cell I know using turn command and a sample code like this:  \usepackage{rotating}  \begin{turn}{90} Supervised Learning \end{turn}}   we can rotate a text inside a cell, however, I couldn't find a way to vertically center this rotated text. Any suggestions is appreciated.  Here is the sample MWE:  \begin{table}[]     \centering     \begin{tabular}{|&gt;{\centering\arraybackslash}m{0.5cm}|c|&gt;{\centering\arraybackslash}m{8cm}|}         \hline         \multicolumn{2}{|c|}{Classification} &amp; References \\ \hline         %\multirow{2}{*}{{\begin{turn}{90}Supervised Learning\end{turn}}}            \multirow{2}{*}{\rotatebox[origin=c]{90}{Supervised Learning}}  \end{tabular}     \caption{A Classification}     \label{tab:Machine_Learning_models} \end{table} I'm having some trouble understanding a proof on  on Number Theory and I was wondering if you guys could give me some help. The problem is that I don't understand the last implication on the proof for example 1.1     Example 1.1. Let x and y be integers. Prove that 2x + 3y is divisible by 17 iff 9x + 5y is divisible by 17.      Solution. 17 | (2x + 3y) ⇒ 17 | [13(2x + 3y)], or 17 | (26x + 39y) ⇒ 17 | (9x + 5y)       conversely, 17 | (9x + 5y) ⇒ 17 | [4(9x + 5y)], or 17 | (36x + 20y) ⇒ 17 | (2x + 3y).   My problem is that I don't understand how does 17 | (26x + 39y) imply 17 | (9x + 5y). If you could elaborate on this step I would be most grateful.  I'm sorry if this is an obvious question but I am a beginner and I just can't get it.  Thanks for your help in advance. CAML query daterange not working jQuery 1.9 checkbox not checked second time after once it unchecked In Star Trek TOS, we see the Defiant disappear to unknown parts  ('The Tholian Web'), and Star Trek: Enterprise revealed that the Defiant went back in time to the mirror universe ('In a Mirror Darkly', parts 1 &amp; 2).   Because of this, one might wonder why (in-universe) the mirror universe didn't obtain (and maintain) technological superiority over the main timeline. (Granted, the out of universe answer is that TOS depicted the two universes as having essentially the same level of tech)  So does any work (whether STO, or a pocket books work) address why the mirror universe didn't simply leap frog the main universe's technology?   (Or to put it another way, why did the mirror universe's technology appear to stagnate for a century after obtaining access to the Defiant's advanced technology?) At the start of A New Hope are Yoda and Obi-Wan really the last remaining Jedi? I have never read any Star Wars books and have no knowledge outside of the Star Wars films, but after seeing Episode III I am left wondering if there are any other Jedi that escape death and remain in hiding like Yoda did. I mean with regard to the "official" events in the Star Wars universe. Why does the collada exporter not export texture references? I've been having trouble exporting collada objects from blender, so I stripped everything back and textured a single cube, and exported it.  This is a completely trivial model, one cube, with one material assigned to it, the material has a single 'g.png' texture assigned to it.   The exported collada data looks like this:    &lt;library_materials&gt;     &lt;material id="Material-material" name="Material"&gt;       &lt;instance_effect url="#Material-effect"/&gt;     &lt;/material&gt;   &lt;/library_materials&gt;   Where:    &lt;library_effects&gt;     &lt;effect id="Material-effect"&gt;       &lt;profile_COMMON&gt;         &lt;technique sid="common"&gt;           &lt;phong&gt;             &lt;emission&gt;               &lt;color sid="emission"&gt;0.2879998 0.2879998 0.2879998 1&lt;/color&gt;             &lt;/emission&gt;             &lt;ambient&gt;               &lt;color sid="ambient"&gt;0 0 0 1&lt;/color&gt;             &lt;/ambient&gt;             &lt;diffuse&gt;               &lt;color sid="diffuse"&gt;0.2163267 0.1845119 0.2121569 1&lt;/color&gt;             &lt;/diffuse&gt;             &lt;specular&gt;               &lt;color sid="specular"&gt;0.5 0.5 0.5 1&lt;/color&gt;             &lt;/specular&gt;             &lt;shininess&gt;               &lt;float sid="shininess"&gt;50&lt;/float&gt;             &lt;/shininess&gt;             &lt;index_of_refraction&gt;               &lt;float sid="index_of_refraction"&gt;1&lt;/float&gt;             &lt;/index_of_refraction&gt;           &lt;/phong&gt;         &lt;/technique&gt;         &lt;extra&gt;           &lt;technique profile="GOOGLEEARTH"&gt;             &lt;double_sided&gt;1&lt;/double_sided&gt;           &lt;/technique&gt;         &lt;/extra&gt;       &lt;/profile_COMMON&gt;       &lt;extra&gt;&lt;technique profile="MAX3D"&gt;&lt;double_sided&gt;1&lt;/double_sided&gt;&lt;/technique&gt;&lt;/extra&gt;     &lt;/effect&gt;   &lt;/library_effects&gt;   This seems to be missing the texture data associated with the object.   By comparsion, exporting a wavefront object generates this .mtl file:  # Blender MTL File: 'basic.blend' # Material Count: 1  newmtl Material Ns 96.078431 Ka 0.000000 0.000000 0.000000 Kd 0.790000 0.790000 0.790000 Ks 0.500000 0.500000 0.500000 Ni 1.000000 d 1.000000 illum 0 map_Kd g.png   &lt;----- ie. Blender is aware of this texture   So... is the collada exporter for blender just broken, or does it require some kind of special config in order to function correctly?  If the latter, how/what is required to make this work?  (NB for what it's worth, the UV coordinates are exported in the .dae, abit they obviously are completely useless without a texture assigned to them; I've also tried adding two different textures to see if the exporter needs that because it naively assumes 'one texture = don't bother, it's one texture for the whole model'. That didn't work either) On company 401k matching. Clarification needed I realized I don't fully understand something. It almost embarrassing to admit.  In 2016 we have 18k max contribution limit for 401k. Does this mean that employee can contribute at most 18k or that total contributions made on behalf of employee should not exceed 18k (company match)  To make is simple, if you make 100k, by contributing 18% you got your limit. But if your company matches 5%, actual contributions will be 18.9k. In the above example, if one wants to maximize benefit should one contribute 18% or less? A word for "mercy killing" "Mercy killing" is an act of killing someone who is already dying and in terrible pain, in order to reduce his or her suffering.    Is there any single word for "mercy killing"? How do I get the subscribers of an event? I need to copy the subscribers of one event to another event. Can I get the subscribers of an event (like MyEvent[0] returning a delegate)?  If this is not possible I would use the add accessor to add the delegates to a list. Would that be the best solution? I just added a PPA repository for the development version of the GIMP, but I get this error:  $ apt-get update &amp;&amp; apt-get upgrade ... The following packages have been kept back:   gimp gimp-data libgegl-0.0-0 libgimp2.0   Why and how can I solve it so that I can use the latest version instead of the one I have now?