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What gear do I need for a newborn photography session? I am an amateur photographer and I have a newborn session coming up for a family friend.   My current gear is:   Canon T5i (crop sensor) Canon 18-55 IS STM Kit lens 85mm f/1.8 lens   I plan on buying a reflector for the shoot and will be using natural light as my light source.  So my question is: is this enough gear to get some nice photos? Should I get another prime lens besides the 85mm? I don't really use the kit lens.  I also have another 8 month old baby shoot coming up and an informal wedding shoot coming up so it would be nice to use the lenses in all situations. I don't need a telephoto at the moment and will probably not use one any time soon. How to include a document into another document? Reference template variable within Jinja expression How can I boot with an older kernel version? The latest kernel is causing problems with my sound, which worked fine with an older version. As I have only Ubuntu installed, Grub is not getting displayed while booting. How can I manually choose my kernel version while booting? I just installed Dufour on my Windows 7 Lenovo ThinkCentre desktop. When I open 2.0.1 I get this error window:    And when I try to add the 'Add Delimited Text Layer' plugin I get this message:    When I click 'OK' the program closes.   Any help is greatly appreciated - thanks. Proof that a formula $\theta$ is valid if and only if $\forall x \theta$ is valid I need to prove for first-order logic that $\vDash\theta$ if and only if $\vDash\forall x \theta$. The proof for the forward direction seems simple enough:  Suppose $\theta$ is valid. Let $\mathfrak{A}$ be an arbitrary structure and let $s:V\to |\mathfrak{A}|$ be an arbitrary function assigning values of the universe of $\mathfrak{A}$ to variables. Then we know by assumption that $\vDash_\mathfrak{A}\theta[s]$.  But since $s$ is arbitrary, it follows that $\vDash_\mathfrak{A}\theta[s(x|c)]$, for all $c\in|\mathfrak{A}$. But this means that $\vDash_\mathfrak{A}\forall x\theta[s]$. Since $\mathfrak{A}$ and the function assigning elements of the structure to variables are arbitrary, it follows that $\vDash\forall x\theta$.   Now we have to show that if $\vDash\forall x\theta$, then $\vDash\theta$, and this is where I'm stuck. I understand why it makes sense that this should be true, I'm just having a hard time writing it rigorously. Any suggestions would be greatly appreciated. Does Metal have to be Hemalurgically charged for Ruin to control someone? Ways to prove Euler's formula for $\zeta(2n)$ induction with 2 recursive sequnces I'm having trouble solving this problem. I have relation for two sequences of natural numbers.   $$a(n)+\sqrt3\cdot b(n)=\left(1+\sqrt3\right)^n$$  and I have to prove that recursions:  $$\begin{align*} &amp;a(n+1)=a(n)+3b(n)\\ &amp;b(n+1)=a(n)+b(n) \end{align*}$$  will satisfy relation mentioned above. I tried solve it using induction but I failed. Can anybody help with some other ideas? What causes an electric shock - Current or Voltage? Though voltage and current are two interdependent physical quantity, I would like to know what gives more "shock" to a person - Voltage or Current? In simple words, will it cause more "electric - shock" when the voltage is high or Current is more? Finding roots/zeros for collision detection? For the most simple of 2D games, I have implemented a posteriori collision detection (overlapping rectangles) on the x/y Cartesian plane, but am now interested in understanding the basics of a priori collision detection...  In the link , I noticed the reference to Newton’s Method.  So, I want to better understand the link b/w finding zeros of an equation and detecting a posteriori collision.    Let's start with the most obvious case of finding roots of an equation:  If you have a projectile's trajectory modeled as a quadratic function, you can find the roots to predict at what time the height will equal zero (or any other constant height, actually, by just solving f(x)=C to be f(x)-C=0 and then finding roots of that expression).    So, as I understand, finding the root can tell me the time at which the object will be at any chosen height.  More broadly, we basically know the (x,y) location of the object for any given time.  But how does root finding, in particular, translate to detecting collisions with another object?  (The other object may be stationary, or be moving.  If the latter, do you also determine roots/location of this moving object as well? Calculate the (x,y) trajectory of both objects and determine where they will intersect?)  Again, the basic question is where does root finding come into play?  Any links to a basic primer on this topic, with a simple example would also be greatly appreciated. Plotting bell shaped curve in TikZ-PGF I want to create some bell shaped curves for demonstrating hypothesis testing in statistics. Can anybody help me drawing curves like shown in the following picture? How to make a blank page in Google Chrome at start-up? Why AUC =1 even classifier has misclassified half of the samples? Find the center of the symmetry group $S_n$.   Attempt:  By definition, the center is $Z(S_n) = \{ a \in S_n : ag = ga \forall\  g \in S_n\}$. Then we know the identity $e$ is in $S_n$ since there is always the trivial permutation. Suppose $a$ is in $S_n$, but not equal to identity. Now we can imagine the permutation as bijective function that maps from $\{1,2,\dotsc,n\}$ to $\{1,2,\dotsc,n\}$.  So suppose $p$ is a permutation map. Then $p$ maps from a location $i$ to a location $j$. Take $p(i) = j$ where $i\neq j$. Let $k$ be in $\{1,2,\dotsc,n\}$, where $k$, $i$ and $j$ are all different elements. The cycle $r = (jk)$, then we will see if this commutes.  $rp(i) = rj$    Can someone please help me, I am stuck?  Thank you. Doubly stochastic matrix proof A transition matrix $P$ is said to be doubly stochastic if the sum   over each column equals one, that is $\sum_i P_{ij}=1\space\forall i$.   If such a chain is irreducible and aperiodic and consists of $M+1$   states $0,1,\dots,M$ show that the limiting probabilities are given by   $$\pi_j=\frac{1}{1+M},j=0,1,\dots,M$$   I have no idea how to prove it but   If a chain is irreducible then all states communicate i.e $$P_{ij}&gt;0\space \text{and}\space P_{ji}&gt;0\space\forall i,j$$ If $d$ denotes the period of any state, if a chain is irreducible aperiodic, then $d(i)=1\forall i$   If $P_{(M+1)\times (M+1)}$ matrix and $\pi$ is the stationary distribution  $$\pi_j=\sum_iP_{ij}\pi_i\space j=0,1,\dots,M+1$$  but how I can get this expression? Proof that a sequence is convergent I'm asked to prove the convergence of the sequence $$X_n=\left(1+\frac12\right)\left(1+\frac14\right)\left(1+\frac18\right)\cdots\left(1+\frac{1}{2^n}\right)$$   I proved that it is increasing through the ratio test and then I want to prove that it is bounded.  My question is the following : is it enough to say that $X_n&lt;\left(\frac32\right)^n$ for $n&gt;1$ or not ? Namely, can we say that a sequence is bounded if $\forall$  $n$ ,  $\exists$ a $N$ such that $X_n&lt;N$ or do I have to find a N such that $\forall$  $n$ , $X_n&lt;N$?  In other words, can a bound depend on $n$ ?  Thanks for your help. C++ cout hex values? Is there a number whose absolute value is negative? Why won't this ocelot do anything but breed?