Which pronoun is correct to use in this sentence and why?
When is a gerund supposed to be preceded by a possessive adjective/determiner?
How to effectively deal with Imposter Syndrome and feelings of inadequacy: "I've somehow convinced everyone that I'm actually good at this" Increasing the maximum number of TCP/IP connections in Linux How to recenter an object's origin? So, I'm working creating a lamp... yes, newbie here.  After modeling for a bit, I noticed that my point of origin was no longer the center of my object:    How to I reset an object origin point to the center of it's geometry? Why is Dictionary preferred over Hashtable in C#? In most programming languages, dictionaries are preferred over hashtables. What are the reasons behind that? I wish to show that $\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$.    What I did so far was to show that $\mathbb{Q}(\sqrt2,\sqrt3) =\text{span}\{1,\sqrt2,\sqrt3,\sqrt6\}$.  Assuming they are isomorphic, denoting $f$ the isomorphism, then $f(1) = 1$, so $x^2-3$ has a root in $\mathbb{Q}(\sqrt2,\sqrt3)$ so $\sqrt 3\in\mathbb{Q}(\sqrt[4]2)$. ($\sqrt2 \in \mathbb{Q}(\sqrt[4]2)$, $\sqrt[4]2\cdot\sqrt[4]2=\sqrt2)$.   Thus under the assumption, $\mathbb{Q}(\sqrt2, \sqrt3)\subseteq \mathbb{Q}(\sqrt[4]2)$. As a vector spaces of the same dimension over $\mathbb{Q}$, it means that $\mathbb{Q}(\sqrt2, \sqrt3)= \mathbb{Q}(\sqrt[4]2)$.  Now all is left to do it to show a contradiction: $\sqrt[4]2\in\mathbb{Q}(\sqrt2,\sqrt3)$, then $\sqrt[4]2 = a+b\sqrt2+c\sqrt3+d\sqrt6$ so $2=(a+b\sqrt2+c\sqrt3+d\sqrt6)^4$, I believe that opening the expression, I would find out that it can't be an element of $\mathbb{Z}$. However this is a really inelegant way (if it really works), and I wish for a better way to do so.  An other approach: $\mathbb{Q}(\sqrt2,\sqrt3) = \mathbb{Q}(\sqrt2 + \sqrt3)$ by the irreducibility of $x^4-10x^2+1$ over $\mathbb{Q}$ (an some dimension theorem usage). Also, $x^4-10x^2+1$ splits in $\mathbb{Q(\sqrt2, \sqrt3)}$.   Is there a way to show that this polynomial doesn't split over $\mathbb{Q}(\sqrt[2]4)$? with different method then assuming that $\sqrt3\in\mathbb{Q}(\sqrt[4]2)$ and getting a contradiction? Maybe the fact that $\sqrt[4]2$ has complex roots might help? Will using 'var' affect performance? Earlier I asked a question about  and got the answer that while it is only necessary for anonymous types, that it is used nonetheless to make writing code 'quicker'/easier and 'just because'.  Following  I saw that var gets compiled down to the correct type in the IL (you will see it about midway down article).  My question is how much more, if any, IL code does using the var keyword take, and would it be even close to having a measurable level on the performance of the code if it was used everywhere? What does it mean to "program to an interface"? I have seen this mentioned a few times and I am not clear on what it means. When and why would you do this?   I know what interfaces do, but the fact I am not clear on this makes me think I am missing out on using them correctly.   Is it just so if you were to do:  IInterface classRef = new ObjectWhatever()   You could use any class that implements IInterface? When would you need to do that? The only thing I can think of is if you have a method and you are unsure of what object will be passed except for it implementing IInterface. I cannot think how often you would need to do that.   Also, how could you write a method that takes in an object that implements an interface? Is that possible? I want to describe my business and want to refer to it in a sentence.  I am trying to say:      "In 2015 we established a business (that is) named X".   Intuitively, the "that is" part is redundant, and makes the sentence more cumbersome. But I cannot think of a reason why we should be able to drop the verb.  Is the version without the "that is" part grammatically correct? How can it be explained? Solution for A/C Condensate Drain Line that doesn't require emptying a bucket of water every day? $e^{mx}$ in solving second order differential equations In a book I am reading on differential equations, the author writes about the solution to a homogenous, linear, second order differential equation with constant coefficients. The author says something like, "Let us suppose that the solution is of the form $y=e^{mx}$ " . After this the author introduces the characteristic equation of a differential equation of the form mentioned above, and proceeds to describe how to solve it w/ undetermined coefficients, variation of parameters, etc.   How did mathematicians first come up with this "assumption" that the solution was of the form $y=e^{mx}$? And, are there any other forms of solutions for these types of equations? How do I convert my PhD dissertation so that it can be published as a book? Why do database guys go on about normalisation?    What is it? How does it help?    Does it apply to anything outside of databases? Tight bound for $T(n) = T(n^{1/2}) + 1$ I followed  to create a soccer ball.  Now I want to texture it in a way that every pentagon has an image inside itself and the exagons are white, but I also want everything to be a little glossy. I managed to successfully UV Map the ball and paint the texture in photoshop but now I am having big problems in applying the texture material to the mesh.    I've created a new material in Blender Render mode with Diffuse and the texture applied to it. I also set the Texture mapping to UV. I've gone in edit mode, selected all the mesh and applied the material. Unfortunately in Texture View Mode I see just a white ball and while rendering I see everything's black.      If I try to do this in Cycles Render and use a Mix Shader with the FAC set to the texture image I get what I want in the Texture View Mode but while rendering I just see everything black and white of my colored images.        I hope I've been clear enough and that someone will help me in this easy/difficult task! Thank you in advance How did Thanos know about the power of "The Snap"? In the scene on Titan with Doctor Strange in Avengers: Infinity War, Thanos said,     With all six Infinity Stones, I will simply snap my fingers and it would all cease to exist.   Then again, in the very first scene with Thor and Loki, when Maw gave Thanos the Space Stone, he said that no one has ever worn two Infinity Stones together.   So how come Thanos knew about the power of the Snap? Because as Wong puts it to Tony, the Big Bang hurled the six Infinity Stones across the universe.   So if no one had collected all the six stones before Thanos, then how did he know about the ability to "Snap"? Error: could not start the command in Texmaker when I run makeindex I'm trying to create a nomenclature but I'm getting the following error when I run makeindex:     Error: Could not start the command   This error appears even with this basic example:  \documentclass{article} \usepackage[refpage]{nomencl}  \makenomenclature  \begin{document} Example of nomenclature \nomenclature{A}{Area}  \printnomenclature \end{document}   In the Configure Texmaker editor I wrote: makeindex %.nlo -s nomencl.ist -o %.nls in the makeindex slot. Then I run:   PdfLaTeX MakeIndex   And the error appears... I also tried all suggestions , but nothing seems to work.  I have installed MacTex 2012 distribution, Mac OS X 10.7.5 Proving $\lim_{x\to 1} x^3=1$ with $\epsilon$-$\delta$ definition Problem: I need to formally prove that $$\lim_{x\to 1} x^3 = 1.$$ My work: This is what I have so far and I'm generally a bit stuck with these proofs from here onwards. Because$$-\epsilon &lt; x^3-1 &lt; \epsilon  =  | x^3-1 | &lt; \epsilon,$$ then $$ -\epsilon &lt; x^3-1 &lt; \epsilon$$ $$-\epsilon+1 &lt; x^3 &lt; \epsilon +1$$ $$ \sqrt[3]{-\epsilon+1}&lt; x &lt; \sqrt[3]{\epsilon+1}.$$ Hoping that what I have done so far is correct. Am I right in thinking that $$ \sqrt[3]{-\epsilon+1}&lt; x &lt; \sqrt[3]{\epsilon+1}$$ is giving me an interval where $x$ is going to give me a $f(x)$ value that falls within the distance $\epsilon$ from the limit on the $y$-axis ? Or is this interval smaller than the $\epsilon$-distance on the $y$-axis? Keyword for the outer class from an anonymous inner class In the following snippet:  public class a {     public void otherMethod(){}     public void doStuff(String str, InnerClass b){}     public void method(a){         doStuff("asd",             new InnerClass(){                 public void innerMethod(){                     otherMethod();                 }             }         );     } }   Is there a keyword to refer to the outer class from the inner class?  Basically what I want to do is outer.otherMethod(), or something of the like, but can't seem to find anything. Journal of Finance Template German '*.bst' Does $x^{y^z}$ equal $x^{(y^z)}$? If so, why?   Why not simply apply the order of the operation from left to right? Meaning $x^{y^z}$ equals $(x^y)^z$?  I always get confused with this and I don't understand the underlying rule. Any help would be appreciated!