2015 Definition and 215 Threads

Hello. I was wondering if there have been any further developments on the topic of B-modes in the CMB polarization since this 2015 paper? https://arxiv.org/abs/1502.00612 A Joint Analysis of BICEP2/Keck Array and Planck Data The above paper declares that... 'We find strong evidence for dust...

I am reading Planck 2015 results. In particular, I focused on "Power law potentials" subsection. The issues I have are 1. I do not understand why the validity of the model can be determined by the value of the ##B## mode. 2. Why the ##B## mode values ##\ln B = −11.6## and ##\ln B = −23.3## for...

I was browsing a antineutrino map and was wondering if there was a meltdown in 2015 when it was taken. I never heard about it in the news; but, here are some pictures from the paper: https://www.nature.com/articles/srep13945 Thoughts?

Hi, I'm hoping someone can point me in the right direction please. I'm using the Planck 2015 CMB temperature (intensity) SMICA pipeline maps (Nside = 2048) and am trying to determine the temperature variance of each individual pixel. Variance and hit-count were provided with the 2013 CMB maps...

Homework Statement 2. Homework Equations [/B]The Attempt at a Solution so i was thinking i could take a look at small number of points and then generalize it but my method soon breaks down in the diagram i have denoted the resistance of the segment beside it if there is a bracket it means...

Is there a set of $2015$ consecutive positive integers containing exactly $15$ prime numbers?

https://www.physicsforums.com/threads/new-lhc-results-2015-tuesday-dec-15-interesting-diphoton-excess.84798 and status from Monday CMS released their conference note a bit earlier. They see absolutely nothing at the mass range where the excess appeared in 2015. It is a bit curious that they...

Homework Statement Here are the free response questions:[/B] https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap15_frq_physics_c-m.pdf Here are the solutions: https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap15_physics_cm_sg.pdf I do not understand how they solved a...

Here is this week's POTW: ----- Show that a connected subspace of a topological group $\pi$ which contains the identity must algebraically generate another connected subspace of $\pi$. ----- Remember to read the...

Please indicate the papers you think will prove most significant for future Loop-and-allied QG research. The poll is multiple choice, so it's possible to vote for several. Abstracts follow in the next post. http://arxiv.org/abs/1512.09010 Implications of Planck2015 for inflationary, ekpyrotic...

Happy New Year everyone! Here is this week's POTW: ----- Calculate the principal, Gaussian, and mean curvatures of the quadric surface $$z = 2x^2 - xy + 3y^2$$ at the origin.----- Remember to read the...

Here is this week's POTW: ----- Let $c>0$ be a constant. Give a complete description, with proof, of the set of all continuous functions $f:\mathbb{R}\to\mathbb{R}$ such that $f(x)=f(x^2+c)$ for all $x\in\mathbb{R}$. ----- Remember to read the...

Thanks to all MHB members who have participated this year in the Graduate POTWs. (Happy) Here is the last problem of the year, concerning homotopy groups: ----- Explain why $\pi_r(S^m \lor S^n) \approx \pi_r(S^m) \oplus \pi_r(S^n)$ for $2 \le r < m + n - 1$. ----- Remember to read the...

Here is this week's POTW: ----- A man chooses two positive integers $a$ and $b$. He then defines a positive integer $k$ to be good if a triangle with side lengths $\log a$, $\log b$ and $\log k$ exists. He finds that there are exactly $100$ good numbers. Find the maximum possible value of...

I seek comprehensive lists of the best or most recommended popular books on particle physics, astronomy, astrophysics, cosmology and mathematics published in 2014 and 2015. These lists should be freely accessible on the web and not hidden behind any paywall or limited to subscribers only...

It's December 23rd, and 55 degrees in the northern Midwest. Does anyone know why? If this is because of climate change, will this become the norm? Thanks.

Here is this week's POTW: ----- Let $X$ be a domain in $\mathbb C$, and let $f : X \to \Bbb R$ be a harmonic function such that $f^2$ is harmonic. Prove $f$ is constant. -----Remember to read the...

Here is this week's POTW: ----- For $n\ge 1$, let $d_n$ be the greatest common divisor of the entries of $A^n-I$, where $$A=\begin{bmatrix}3&2\\4&3\end{bmatrix} \qquad \text{and} \qquad I=\begin{bmatrix}1&0\\0&1\end{bmatrix}.$$ Show that $\displaystyle \lim_{n\to\infty}d_n=\infty$. -----...

Here is this week's POTW: ----- Minimize $|x+2|+2|x-5|+|2x-7|+|0.5x-5.5|$, given $x$ is a real number. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to...

Here is this week's POTW: ----- Let $\mathcal{C} = \{C_n\}_{n\ge 0}$ be a chain complex. Compute the homology spectral sequence associated with the filtration $F_m := \sum_{n = 0}^m C_n$, $m\ge 0$. ----- Remember to read the...

Here is this week's POTW: ----- Let $f(x)$ be a polynomial with degree $2008$ and leading coefficient $1$ such that $$f(0)=2007,\,f(1)=2006,\,f(2)=2005,\,\cdots\,f(2007)=0$$ Determine the value of $f(2008)$. ----- Remember to read the...

Here is this week's POTW: ----- For which real numbers $c$ is there a straight line that intersects the curve $x^4+9x^3+cx^2+9x+4$ in four distinct points? ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to...

After a slow start, the LHC and its detectors worked nicely and collected a lot of data this year (~3.5/fb). While many analyses are still ongoing, both ATLAS and CMS will report several results on Tuesday 3 pm (CET)*. The presentations will probably appear here, a...

Here is this week's POTW: ----- Let $F : \Bbb R \to \Bbb R$ be given by $$F(x) = \sum_{n\, =\, -\infty}^\infty \frac{1}{1 + (x + n)^2}.$$ Prove that $$\int_0^1 F(x)\cos(2\pi x)\, dx = \pi e^{-2\pi}.$$ ----- Remember to read the...

Here is this week's POTW: ----- Suppose $A, B, C,$ and $D$ are points in the plane such that no three of them are collinear. If $D$ is in the interior of $\triangle ABC$, show that $| AB |+| BD |+| CD | < | AB |+| BC |+| CA |$. Note here that $|XY|$ denotes the length of segment $XY$...

Here is this week's POTW: ----- Let $(a,\,b)$ be a pair of real numbers satisfying $33a-56b=\dfrac{a}{a^2+b^2}$ and $56a+33b=-\dfrac{b}{a^2+b^2}$ Determine the value of $|a|+|b|$. ----- Remember to read the...

Here is this week's POTW: ----- What is the largest absolute value attained by the function $f(z)=z^{2000}-z^4+1$ as $z$ ranges over the unit circle in the complex plane? ----- Remember to read the...

I realized that I haven't yet given MHB members a Galois problem to solve. ;) So here is this week's POTW: ----- Let $f(x)$ be an irreducible prime degree polynomial with rational coefficients, such that only two of its roots are nonreal complex numbers. Determine the Galois group of $f(x)$...

Here is this week's POTW: ----- Solve the equation $\sqrt{x+\sqrt{4x+\sqrt{16x+\sqrt{\cdots+\sqrt{2^{4016}x+3}}}}}=\sqrt{x}+1$. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to...

Here is this week's POTW: ----- Evaluate the integral $$\int_{-\infty}^\infty \frac{\cos x - \cos 2x}{x^2}\, dx.$$ Justify the major steps of your calculation. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines...

Here is this week's POTW: ----- It has been snowing heavily and steadily. At noon, a snow plow starts out and travels 2 miles the first hour, and 1 mile the second hour. When did it start snowing? ----- Remember to read the...

Here is this week's POTW: ----- Point $Q$ lies at $(3,\,8)$ and point $P$ lies at $(0,\,4)$. Find the $x$ coordinate of the point $X$ on the $x$ axis maximizing $\angle PXQ$. ----- Remember to read the...

as it is nearly the end of the year , thought we should start this thread so what has been everyone's favourite moments during the last year?

Here is this week's POTW: ----- Classify the primes $p$ for which the ring $\Bbb Z[x]/(p, x^2 + 3)$ is a field, and for those primes, find the number of elements in the ring. ----- Remember to read the...

Many thanks to anemone for sending me some very helpful source links for problems. Here is this week's POTW: ----- Cowboy Joe wants to climb an absolutely slippery glacier of the round conical form. He has a lasso (with a loop of a fixed size) which he can throw over the top and pull himself...

Here is this week's POTW: ----- Find all integral values of $a$ such that $\sqrt{a+8-6\sqrt{a-1}}+\sqrt{a+3-4\sqrt{a-1}}=1$. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to...

Here is this week's POTW: ----- Prove or disprove that the series $$\sum_{\substack{(m,n)\in \Bbb N^2\\ m\neq n}}\frac{\cos(mn x)}{m^2 - n^2}$$ converges for all $x \in [-1,1]$. ----- Remember to read the...

Here is this week's POTW: ----- For any integer $n\ge 2$, prove that $n^5-n$ is divisible by $30$. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to...

Here is this week's POTW: ----- This week's high school POTW uses the same context as last week's problem (http://mathhelpboards.com/potw-secondary-school-high-school-students-35/problem-week-188-november-3rd-2015-a-16779.html), but we have cranked up the difficulty level and we hope members...

Here is this week's POTW: ----- Let $X$ and $Y$ be random variables. Suppose $-\infty < q < 0$ and $p > 0$ such that $\frac{1}{p} + \frac{1}{q} = 1$. Show that if $X$ and $Y$ have finite $p$-th and $q$-th absolute moments, respectively, then $$\left(\Bbb E[|X|^p]\right)^{1/p} \cdot \left(\Bbb...

Here is this week's POTW: ----- Let $a_1, \dots, a_{2015}$ be real numbers such that $a_1=2015$ and $$\sum_{j=1}^{n}a_{j}=n^2 \, a_n$$ for all $1\le n \le 2015$. Compute $a_{2015}$. ----- Remember to read the...

Here is this week's POTW: ----- Consider a polynomial $$P(x)=a_0+a_1x+\cdots+a_{2011}x^{2011}+x^{2012}$$ Nigel and Jessica are playing the following game. In turn, they choose one of the coefficients $a_0,\,\cdots,\,a_{2011}$ and assign a real value to it. Nigel has the first move. Once a...

Five Things to Know About the 'Halloween Asteroid' https://gma.yahoo.com/5-things-know-halloween-asteroid-002900478--abc-news-Halloween.html This asteroid was only discovered days ago. Coming within 1.3 lunar distances -- or ~310,000 miles (49000 km) -- the asteroid, called 2015 TB145 (width...

Here is this week's POTW: ----- Factorize $a(b^2+c^2-a^2 )+ b(c^2+a^2-b^2 )+ c(a^2+b^2-c^2 )-2abc$. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to...

Here is this week's POTW: ----- Show that $$\frac{1}{\Gamma(s)} = -\frac{1}{2\pi i} \int_\gamma (-z)^{-s}e^{-z}\, dz,$$ where $\gamma$ is a contour which is the union of a line from $+\infty$ to $\epsilon$ (where $\epsilon > 0$), an $\epsilon$-circle about the origin, and a line from...

Here is this week's POTW: ----- A dart, thrown at random, hits a square target. Assuming that any two parts of the target of equal area are equally likely to be hit, find the probability that the point hit is nearer to the center than to any edge. ----- Remember to read the...

Why did Hurricane Patricia become a monster so quickly? http://news.yahoo.com/why-did-hurricane-patricia-become-monster-quickly-202419311.html Patricia slams Mexico Pacific Coast as Category 5 hurricane http://news.yahoo.com/mexicos-pacific-coast-braces-monster-hurricane-patricia-040315825.html

Here is this week's POTW: ----- Let $(M,g)$ be a Riemannian manifold. A vector field $X$ on $M$ is a Killing field if the Lie derivative of $g$ along $X$ is zero, i.e., $\mathcal{L}_Xg = 0$. Show that the Lie bracket of two Killing fields on $M$ is a Killing field. ----- Remember to read the...

Here is this week's POTW, which marks my first anniversary of being the University POTW Director: ----- Given three distinct digits, six numbers can be formed such that each of the given digits appears exactly once in any of them; e.g., using 1, 2, and 5, you can form 125, 152, 215, 251, 512...

Here is this week's POTW: ----- Find $A$ and $B$ such that the product $$\prod_{n=1}^{15} (n+1)!$$ can be written in the form $A^2B!$, where $A,\,B$ are positive integers. ----- Remember to read the...