issue with mirrior modifier
Why does the mirror modifier sometimes give me an overlapping mesh?
I thought this would be really simple, but it's presenting some difficulties. If I have std::string name = &quot;John&quot;; int age = 21;  How do I combine them to get a single string &quot;John21&quot;? Physical meaning of this integral in $k$-space I am trying to solve an integral in $k$-space where I want to calculate the ratio of the average energy of an arbitrary electronic band ($E(k)=k^n)$ to the square of average group velocity of electrons($v_g   = k^{n-1})$ approximately in the form of this expression given by $$L=\frac{\frac{\sum_{\mathbf{k}}k^{n}}{\sum_{\mathbf{k}}1}}{\left(\frac{\sum_{\mathbf{k}}k^{n-1}}{\sum_{\mathbf{k}}1}\right)^2}\;.$$  Now, I want to do this for $d$-dimensions, so I convert this sum to integral.  $$L=\frac{\dfrac{\int_{0}^{k_f}k^{n} d^d k}{\int_{0}^{k_f}1d^d k}}{\left(\dfrac{\int_{0}^{k_f}k^{n-1}d^d k}{\int_{0}^{k_f}1d^d k}\right)^2}$$ where $d^dk  = \dfrac{d \pi^{d/2}}{\Gamma(\frac{d}{2}+1)}k^{d-1}dk$ is the volume element in $d$-dimensional space.  I want to get a simple expression for $L$ and how it depends with $k_f,n$ and $d$. any physical insight into this integral could also be helpful. How to understand "with" in the following sentence? Not every job will end up with a success.   What is the meaning of "with" here? Why not use other preposition?  Could native speakers please describe the scene of this sentence for me? Thx. Mouse acceleration seems to be on by default, and I can't find anywhere in the launcher settings or the in game settings to turn it off.  It's very annoying as it makes it feel as if the mouse is lagging. Is there any way to turn it off? Assuming there are 5 items in the settings file (MySetting1 to MySetting5), why does PropertyValues have 0 items while Properties has the correct number?   Console.WriteLine( Properties.Settings.Default.PropertyValues.Count); // Displays 0 Console.WriteLine( Properties.Settings.Default.Properties.Count);     // Displays 5 What are useful websites for scouting GIS related jobs? Error 404 : While using flag Except when we use right to denote direction, what is the difference between these two terms?  Also, which one is the preferred construction between these two     Am I right?   or     Am I correct? Find the first occurrence/starting index of the sub-array in C# Scanf skips every other while loop in C How check with SOQL if a picklist value is available or not for a specified record type How check if a picklist value is available or not for a specified record type ( through SOQL)? Thanks in advance How to troubleshoot unwanted white spaces smartly? Why is there a white space on the left side?  \documentclass{standalone} \usepackage{asymptote} \begin{document} \noindent \begin{asy} size(10cm,10cm); draw((0,0)--(100,100)); draw((0,100)--(100,0)); dot((50,50)); \end{asy} \end{document} If a field $F$ is such that $\left|F\right|>n-1$ why is $V$ a vector space over $F$ not equal to the union of $n$ proper subspaces of $V$ Why won't Amanita move in and settle down? Finding the roots of complex numbers $(2i)^{1/2}$  $(1-\sqrt{3}i)^{1/2}$  $(-1)^{1/3}$  $(-16)^{1/4}$  How can I find the roots of the complex numbers above? Returning an unevaluated expression with values substituted in Evaluating a PDF to find an unkown constant Evaluate the PDF to find K  $1 = \int_0^{\infty} \frac{k}{(1+x)^4}$  using u substitution I got:  $u=1+x$ and $du= dx$  $\int_0^{\infty} \frac{k}{u^4} \to \frac{k}{\frac{-1}{3} u^3}$   Since $u^4 du = \frac{u^{-4+1}}{-4+1}=$ $\frac{u^{-3}}{-3}$  which evaluating gives:  $1=\frac{k}{\frac{-1}{3(1+x)^3}} \vert_0^{\infty} \to \frac{-3k}{(1+x)^3} \vert_0^{\infty} = 0 -3k$   and $k= \frac{-1}{3}$  somehow though they came up with $\frac{-k}{3} \frac{1}{(1+x)^3}$ after integrating $\int_0^{\infty} \frac{k}{(1+x)^3}$   Was my approach correct to use substitution? Where does my work go wrong? Let $A∈\mathscr{M}_{3×2}(\mathbb{R})$ and $B∈\mathscr{M}_{2\times3}(\mathbb{R})$ be matrices satisfying   $AB =\begin{bmatrix} 8 &amp;2 &amp;−2\\ 2 &amp;5 &amp;4\\ −2 &amp;4&amp; 5 \end{bmatrix}$. Calculate $BA$. (Golan, The Linear Algebra a Beginning Graduate Student Ought to Know, Exercise 426.)   Maybe it can be solved by solving a system of equations, but I think there is a shorter way since this problem was in my exam.  Thanks. MATLAB/OCTAVE Extracting elements from different sized vectors in a cell array Using Integration By Parts results in 0 = 1 I've run into a strange situation while trying to apply Integration By Parts, and I can't seem to come up with an explanation.  I start with the following equation:  $$\int \frac{1}{f} \frac{df}{dx} dx$$  I let:  $$u = \frac{1}{f} \text{ and } dv = \frac{df}{dx} dx$$  Then I find:  $$du = -\frac{1}{f^2} \frac{df}{dx} dx \text{ and } v = f$$  I can then substitute into the usual IBP formula:  $$\int udv = uv - \int v du$$  $$\int \frac{1}{f} \frac{df}{dx} dx = \frac{1}{f} f - \int f \left(-\frac{1}{f^2} \frac{df}{dx}\right) dx$$  $$\int \frac{1}{f} \frac{df}{dx} dx = 1 + \int \frac{1}{f} \frac{df}{dx} dx$$  Then subtracting the integral from both sides, I've now shown that:  $$0 = 1$$  Obviously there must be a problem in my derivation here...  What wrong assumption have I made, or what error have I made?  I'm baffled.