What is 2015: Definition and 219 Discussions

2015 (MMXV) was a common year starting on Thursday of the Gregorian calendar, the 2015th year of the Common Era (CE) and Anno Domini (AD) designations, the 15th year of the 3rd millennium, the 15th year of the 21st century, and the 6th year of the 2010s decade.
2015 was designated by the United Nations as:

International Year of Light
International Year of Soil

View More On Wikipedia.org
Recent contents Top users
  1. Cerenkov

    B B-Modes in CMB Polarization - any change since BICEP2 in 2015?

    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...
  2. V

    B Videos from Big Event 2015 (Växjö): Loophole free Bell test

    vhttps://play.lnu.se/media/t/0_hgz7034c A.Zeilinger: The Future of Bell Experiments. https://play.lnu.se/media/t/0_6jkhpefo G. Weihs: Violation of Bell’s Inequality under Strict Einstein Locality Conditions https://play.lnu.se/media/t/0_q2r30syq R. Hanson: From the first loophole-free Bell...
  3. JD_PM

    A Exploring Planck 2015 Results on Power Law Potential Models

    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...
  4. TimeSkip

    Nuclear meltdown in 2015 on antineutrino map?

    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?
  5. T

    A Planck 2015 CMB temperature individual pixel variance

    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...
  6. T

    Equivalent resistance of 2015 points

    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...
  7. lfdahl

    MHB Set of 2015 Consecutive Positive Ints with 15 Primes

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

    I New LHC Results 2015: Interesting Diphoton Excess?

    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...
  9. M

    Unable to create rendered view - Etabs 2015

    I completed one model on Etabs, everything is okay except one issue. after completed the detailing, whenever i clicked on "Reinforcement Cage Views", and then on any of beams, i got the subject error. any advise?
  10. RoboNerd

    Question on theory for solving 2015 AP Physics C Free Response Questions

    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...
  11. Euge

    MHB What is the solution to POTW #190?

    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...
  12. marcus

    A Poll: Fourth quarter 2015 MIP (most important QG papers)

    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...
  13. Euge

    MHB What Are the Curvatures of the Quadric Surface at the Origin?

    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...
  14. Ackbach

    MHB What are the properties of continuous functions satisfying $f(x)=f(x^2+c)$?

    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...
  15. Euge

    MHB How does homotopy groups of wedge sums relate to the individual spheres?

    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...
  16. anemone

    MHB Maximizing ab with 100 Good Numbers: POTW #196 (Dec. 29, 2015)

    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...
  17. R

    Popular Physics & Math Books 2014 & 2015

    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...
  18. Isaac0427

    Unusually warm winter for 2015

    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.
  19. Euge

    MHB Is a Harmonic Function Constant if its Square is Also Harmonic?

    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...
  20. Ackbach

    MHB What is the Limit of the Greatest Common Divisor in a Matrix Sequence?

    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 $\displaystyle \lim_{n\to\infty}d_n=\infty$. -----...
  21. anemone

    MHB Minimizing Absolute Value Expressions with Real Numbers - POTW #195

    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...
  22. Euge

    MHB What is the Homology Spectral Sequence for a Chain Complex with Filtration?

    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...
  23. anemone

    MHB Polynomial Problem of the Week #194: Find $f(2008)$ for a Degree 2008 Polynomial

    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...
  24. Ackbach

    MHB Can a Straight Line Intersect a Curve in Four Distinct Points?

    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...
  25. mfb

    New LHC results 2015: Tuesday Dec 15 - interesting diphoton excess

    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...
  26. Euge

    MHB Prove that $$\int_0^1 F(x)\cos(2\pi x)\, dx = \pi e^{-2\pi}.$$

    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...
  27. Ackbach

    MHB Is There a Geometric Solution for the Interior Point Problem?

    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 $XY$...
  28. anemone

    MHB POTW #193: Solving for Real Numbers (December 8th, 2015)

    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...
  29. Ackbach

    MHB What is the largest absolute value attained by the function?

    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...
  30. Euge

    MHB What is the Galois group of a prime degree polynomial with two nonreal roots?

    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 $f(x)$...
  31. anemone

    MHB Can You Tackle This Infinite Nested Radical Equation?

    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...
  32. Euge

    MHB Can You Solve POTW #182 for November 24, 2015?

    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...
  33. Ackbach

    MHB What is the start time of the snowstorm?

    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...
  34. anemone

    MHB Optimizing Angle PXQ with Point Q at (3,8) and Point P at (0,4)

    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...
  35. H

    What are your highlights of 2015?

    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?
  36. Euge

    MHB What is the ring structure of $\Bbb Z[x]/(p, x^2 + 3)$ for certain primes $p$?

    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...
  37. Ackbach

    MHB What is the critical cone angle for Cowboy Joe's lasso?

    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...
  38. anemone

    MHB Find Integral Solutions for Square Root Equation | POTW #190 11/17/2015

    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...
  39. Euge

    MHB Problem of the Week #180 - November 10, 2015

    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...
  40. Ackbach

    MHB How can you prove that $n^5-n$ is divisible by $30$ for any integer $n\ge 2$?

    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...
  41. anemone

    MHB POTW #189: High School Polynomial Game Strategy for Divisibility by x^2+1

    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...
  42. Euge

    MHB Can You Solve This Week's POTW on Finite Moments of Random Variables?

    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...
  43. Ackbach

    MHB What is the value of $a_{2015}$ in a sequence with given conditions?

    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...
  44. anemone

    MHB Playing the Polynomial Game: POTW #188 - November 3rd, 2015

    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...
  45. Astronuc

    NEO 2015 TB145: 5 Facts About "Halloween Asteroid

    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...
  46. anemone

    MHB Factorization Problem #187: October 28th, 2015 POTW - Math Help Boards

    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...
  47. Euge

    MHB How to use Euler's reflection formula for POTW #178?

    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...
  48. Ackbach

    MHB What is the Probability of Hitting the Center of a Square Target?

    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...
  49. Astronuc

    Hurricane Patricia - October 22-24, 2015

    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
  50. Euge

    MHB Problem of the Week #177 - October 20, 2015

    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...
Back
Top