2016 Definition and 207 Threads

2016 (MMXVI) was a leap year starting on Friday of the Gregorian calendar, the 2016th year of the Common Era (CE) and Anno Domini (AD) designations, the 16th year of the 3rd millennium, the 16th year of the 21st century, and the 7th year of the 2010s decade.
2016 was designated as:

International Year of Pulses by the sixty-eighth session of the United Nations General Assembly.
International Year of Global Understanding (IYGU) by the International Council for Science (ICSU), the International Social Science Council (ISSC), and the International Council for Philosophy and Human Sciences (CIPSH).

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  1. J

    How to have "Excel for Mac 2016" Auto-convert entry of yymmdd to yyyy-mm-dd

    Hi, 
 I want to type, say, 20201008 or 201008 into a cell and as soon as I press the enter or tab key have "Excel for Mac 2016" immediately convert and display either entry as 2020-10-08. 
 I don't want to have another column set up that uses a formula to convert 20201008 or 201008 to...
  2. A

    A Confusion about 2016 Unruh paper - fluctuating vacuum energy density?

    Hi all, Just had a look at the 2016 paper by Wang, Zhu, and Unruh, "How the huge energy of quantum vacuum gravitates to drive the slow accelerating expansion of the Universe," Qingdi Wang, Zhen Zhu, and William G. Unruh, Phys. Rev. D 95, 103504 – Published 11 May 2017 The paper states...
  3. almostvoid

    Virtual Revolution Sci Fi Movie [2016]

    for once not a Hollywood ending. Looks like Blade Runner at first, the plot is not unfamiliar but the ending is.
  4. pixel

    Arrival (2016): What Do You Think? SPOILER ALERT

    SPOILER ALERT. I saw this movie recently and, as usual, there are some things that I found puzzling and was wondering what other people thought. For one thing, the aliens were very much more advanced than us, so why didn't they figure out our language, instead of us having to figure out their...
  5. N

    Schools Math Reu Season 2016: Results & Questions

    Please post results or questions on this Math Reu season. See last years discussionhttps://www.physicsforums.com/threads/math-reus-2016.858490/
  6. V

    MHB How can the sum of digits of a multiple of 2016 equal 2016?

    What is the least multiple of 2016 such that the sum of its digits is 2016. I think the answer must be a 225 digit long number ending in 8 but do not know the exact value nor how to prove it. Any ideas. Thanks beforehand.
  7. BillTre

    538's Awards for Best and Worst Data Stories of 2016

    Link awards: Statistical Fortitude Best Use of Data to Speak Truth to Power "Word of the Year" of the Year Trudeau Prize for Governance The Barest Minimum of Progress Achieved Boldest Sacking of Experienced Humans in Favor of Untested Algorithm The "Are We Still Doing This for Willful...
  8. jim mcnamara

    2016 seems long to me (Leap second)

    Now I know why: http://phys.org/news/2016-12-extra_1.html We are getting a leap second! 2016 really is too long. :cry: If you are an astronomer or programmer you know about these corrections to NIST atomic clock time (UTC). The Earth's period of rotation is not constant over long periods...
  9. Euge

    MHB Can Uniformly Bounded Functions Converge Weakly to Zero in $\mathscr{L}^p$?

    Here is this week's POTW: ----- Let $1 < p < \infty$, and let $(f_n)$ be a sequence of real-valued functions in $\mathscr{L}^p(-\infty, \infty)$ which converges pointwise a.e. to zero. Show that if $\|f_n\|_p$ is uniformly bounded, then $(f_n)$ converges weakly to zero in...
  10. Ackbach

    MHB What Are the Conditions for This Putnam Problem's Sum to Equal Zero?

    Here is this week's POTW: ----- Find necessary and sufficient conditions on positive integers $m$ and $n$ so that \[\sum_{i=0}^{mn-1} (-1)^{\lfloor i/m \rfloor +\lfloor i/n\rfloor}=0.\] ----- Remember to read the...
  11. anemone

    MHB What is the decimal part of the sixth power of the sum of two square roots?

    Here is this week's POTW: ----- Given that the decimal part of $X=\left(\sqrt{13}+\sqrt{11}\right)^6$ is $Y$, find the value of $X(1-Y)$. ----- 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...
  12. Euge

    MHB How can you prove that a retract of a Hausdorff space is always closed?

    Here is this week's POTW: ----- Give two different proofs of the following result: Every retract of a Hausdorff space is closed. ----- 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...
  13. anemone

    MHB Can You Solve This Week's Math Challenge Equation?

    Here is this week's POTW: ----- Solve the equation x^3=4+\left\lfloor{x}\right\rfloor. ----- 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 http://www.mathhelpboards.com/forms.php?do=form&fid=2!
  14. Ackbach

    MHB What is the minimum perimeter of a triangle with given vertices?

    Here is this week's POTW: ----- Given a point $(a,b)$ with $0<b<a$, determine the minimum perimeter of a triangle with one vertex at $(a,b)$, one on the $x$-axis, and one on the line $y=x$. You may assume that a triangle of minimum perimeter exists. ----- Remember to read the...
  15. anemone

    MHB Problem of the week #245 Dec 14th, 2016

    Here is this week's POTW: ----- Prove that \frac{aca}{acb}\lt \frac{bca}{bcb} for any digits $a\ne b$ and for any digit number $c$, where $xyz$ represents a 3-digit number. ----- Remember to read the...
  16. Euge

    MHB Can the center of a finite group determine the size of its conjugacy classes?

    Here is this week's POTW: ----- Let $Z$ be the center of a finite group $G$. Prove that there are at most $(G : Z)$ elements in each conjugacy class of $G$. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to...
  17. Ackbach

    MHB What is the minimum value of a complex expression?

    Here is this week's POTW: ----- Find the minimum value of \[\frac{(x+1/x)^6-(x^6+1/x^6)-2}{(x+1/x)^3+(x^3+1/x^3)}\] for $x>0$. ----- 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...
  18. davenn

    6 Dec 2016 M 6.5 Quake northern Sumatera, Indonesia

    My live gram ... http://www.sydneystormcity.com/seismograms.htm saved file ... This quake on just offshore ESE of Banda Aceh city it has been severely damaging and last report I heard around 19 fatalities M6.5 - 19km SE of Sigli, Indonesia 2016-12-06 22:03:32 UTC 5.281°N 96.108°E 8.2 km...
  19. Euge

    MHB Can an Entire Function Be Non-Zero with Finite Double Integral?

    Here is this week's POTW: ----- Show that if $f$ is an entire function such that $\int_{-\infty}^\infty \int_{-\infty}^\infty \lvert f(x + yi)\rvert^2\, dx\, dy < \infty$, then $f$ is identically zero.----- Remember to read the...
  20. anemone

    MHB Probability of |x-y|>=6 for Two Numbers in Range [0,10]

    Here is this week's POTW: ----- Two real numbers $x$ and $y$ are chosen in the range $[0,\,10]$. What is the probability that $|x-y|\ge 6$. ----- 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...
  21. Ackbach

    MHB Can three points form a square?

    Here is this week's POTW: ----- Let $A, B, C$ denote distinct points with integer coordinates in $\mathbb R^2$. Prove that if \[(|AB|+|BC|)^2<8\cdot [ABC]+1\] then $A, B, C$ are three vertices of a square. Here $|XY|$ is the length of segment $XY$ and $[ABC]$ is the area of triangle $ABC$...
  22. Euge

    MHB Why is $M/(N\cap P)$ Artinian when $M/N$ and $M/P$ are Artinian?

    Here is this week's POTW: ----- Let $R$ be a commutative ring. If $N$ and $P$ are submodules of an $R$-module $M$ such that $M/N$ and $M/P$ are Artinian, show that $M/(N\cap P)$ is Artinian. ----- Remember to read the...
  23. anemone

    MHB What Are the Last Two Digits of the Sum of Factorials from 7! to 2016!?

    Here is this week's POTW: ----- What are the last two digits in $7! + 8! + 9! + ... + 2016 !$? ----- 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...
  24. Ackbach

    MHB What is the expected length of the shorter segment when the stick snaps?

    Here is this week's POTW, a problem submission by Track. Thanks, Track! ----- I thought y'all could use some more stochastic love. Requires knowledge of calculus-based probability theory. Suppose a $12$-inch, uniformly-shaped wooden stick is held securely at both ends, such that the stick...
  25. Euge

    MHB What is the Homological Degree of a Fixed Point Free Continuous Map?

    Here is this week's POTW: ----- Let $n$ be a positive integer, and let $\Bbb S^n \to \Bbb S^n$ be a fixed point free continuous map. Show that the map's homological degree is $(-1)^{n+1}$. ----- Remember to read the...
  26. anemone

    MHB Can You Find a Function That Satisfies This Integral Equation?

    Here is this week's POTW: ----- Determine a continuous function f:\left[0,\,\frac{1}{3}\right]\rightarrow \left(0,\,\infty\right) with the property such that 27\int_{0}^{\frac{1}{3}} f(x) \,dx+16\int_{0}^{\frac{1}{3}} \frac{1}{\sqrt{x+f(x)}} \,dx=3----- Remember to read the...
  27. Ackbach

    MHB Can a finite collection of open discs cover a given set in two dimensions?

    Here is this week's POTW: ----- Let $\mathcal F$ be a finite collection of open discs in $\mathbb R^2$ whose union contains a set $E\subseteq \mathbb R^2$. Show that there is a pairwise disjoint subcollection $D_1,\ldots, D_n$ in $\mathcal F$ such that \[E\subseteq \cup_{j=1}^n 3D_j.\] Here...
  28. Euge

    MHB Is $\omega^2$ nowhere vanishing on the four-sphere?

    Here is this week's POTW: ----- If $\omega$ is a two-form on the four-sphere, is $\omega^2$ (i.e., $\omega \wedge \omega$) nowhere vanishing? ----- 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...
  29. anemone

    MHB Can You Solve This Complex Quadratic Expression by Hand?

    Here is this week's POTW: ----- Evaluate \left\lfloor{\left(-\sqrt{2}+\sqrt{3}+\sqrt{6}\right)\left(\sqrt{2}-\sqrt{3}+\sqrt{6}\right)\left(\sqrt{2}-\sqrt{3}-\sqrt{6}\right)}\right\rfloor without using a calculator. ----- Remember to read the...
  30. S

    News Reaction to Trump winning the 2016 US Presidential Election

    Hi everyone! I know that the Election Day thread has now been locked by the moderators, but I felt I had to respond to Donald Trump winning the 2016 US Presidential Election. I had a swirl of emotions floating inside of me, from shock (despite knowing that there was a reasonable chance that...
  31. Euge

    MHB Is every $S^{-1}R$-module flat?

    Here is this week's POTW: ----- Let $R$ be a commutative ring with unity. Show that if $S$ is multiplicatively closed in $R$ and if every $R$-module is flat, then every $S^{-1}R$-module is flat. ----- Remember to read the...
  32. Ackbach

    MHB What are the solutions to Problem of the Week #240 - Nov 07, 2016?

    So, I am ashamed to admit it, but this is the very first break in the weekly POTW since it started. I have a good excuse, though: my twin brother was visiting, and I was quite distracted by the wonderful company. So here is this week's POTW: ----- Let $A_1=0$ and $A_2=1$. For $n>2$, the...
  33. anemone

    MHB Can xyz Exceed 1 Given x^2 + y^2 + z^2 + xyz = 4?

    Here is this week's POTW: ----- If $x,\,y$ and $z$ are non-negative reals such that $x^2+y^2+z^2+xyz=4$, prove that $xyz\le 1$. ----- 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...
  34. Euge

    MHB How to Prove Convergence in Sequence $(x_n)_{n=1}^\infty$?

    Here is this week's POTW: ----- Consider a sequence of real numbers $(x_n)_{n = 1}^\infty$ such that $\sum\limits_{n = 1}^\infty \lvert x_n y_n\rvert$ converges for every real sequence $(y_n)_{n = 1}^\infty$ such that $\sum\limits_{n = 1}^\infty y_n^2$ converges. Prove that $\sum\limits_{n =...
  35. kaliprasad

    MHB Showcase of 2016 Consecutive Numbers w/ 100 Primes

    Show that there exists 2016 consecutive numbers that contains exactly 100 primes.
  36. anemone

    MHB What Are the Solutions for the Exponential Equation \( x^{(y^z)} = (x^y)^z \)?

    Here is this week's POTW: ----- Determine all triples $(x,\,y,\,z)$ of positive integers with $x^{(y^z)}=\left(x^y\right)^z$. ----- 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...
  37. Ackbach

    MHB Problem of the Week # 239 - Oct 28, 2016

    Here is this week's POTW: ----- Let $f$ be a real function on the real line with continuous third derivative. Prove that there exists a point $a$ such that \[f(a)\cdot f'(a) \cdot f''(a) \cdot f'''(a)\geq 0 .\] ----- Remember to read the...
  38. George Jones

    Walter Greiner: October 1935 - October 2016

    Author and coauthor of an incredibly useful series of physics books.
  39. Euge

    MHB How Do You Prove the Boundedness of an Integral Operator in Measure Spaces?

    Here is this week's POTW: ----- Show that if $(X,\mathcal{M},\mu)$, $(Y,\mathcal{N},\nu)$ are finite measure spaces, $1 < p < \infty$, and $K$ is a measurable function on $X\times Y$, there is a bounded integral operator $I(K) : \mathscr{L}^p(\nu) \to \mathscr{L}^p(\mu)$ given by $$I(K)(f) :x...
  40. Evo

    News POTUS Election 2016- a Fresh Start

    Let's please keep this civil and within the rules. This is Current News Events, not Politics, so if you have an article posted in the current news in a mainstream source, you may post it to be discussed as long as you stay within the guidelines. This replaces the old POTUS thread...
  41. anemone

    MHB Can You Solve the Triangle $PQR$ Equation from POTW #238?

    Here is this week's POTW: ----- In a triangle $PQR$ with its sides $p,\,q$ and $r$ where $2\angle P=3\angle Q$, prove that $(p^2-q^2)(p^2+pr-q^2)=q^2r^2$. ----- Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to...
  42. ChrisVer

    B What is the significance of the 2016 Nobel Prize in Physics?

    Well, this was awarded to Condensed matter physics this year, so I think this is the appropriate thread to post my question... So far I've only read through the official site's press release ( https://www.nobelprize.org/nobel_prizes/physics/laureates/2016/press.html ), however it is still...
  43. N

    Testing One Week to Physics GRE 2016: Tips from past exam takers?

    There's about one week to the Physics GRE. I've worked through all five past exams and corrected mistakes. What would those of you that scored well recommend I do in this last week or so before the exam? Should I retake the five exams timed? Work through the 500 exam questions slowly? Just...
  44. Ackbach

    MHB Problem of the Week # 238 - Oct 20, 2016

    Here is this week's POTW: ----- Let $s$ be any arc of the unit circle lying entirely in the first quadrant. Let $A$ be the area of the region lying below $s$ and above the $x$-axis and let $B$ be the area of the region lying to the right of the $y$-axis and to the left of $s$. Prove that...
  45. Euge

    MHB Can an invertible sheaf be isomorphic to the structure sheaf?

    Here is another chance to solve a sheaf problem! ----- Let $(X,\mathscr{O})$ be a ringed space. Suppose $\mathscr{F}$ is an invertible sheaf over $\mathscr{O}$. That is, $\mathscr{F}$ is a rank one locally free module over $\mathscr{O}$. Prove that there is an isomorphism between the tensor...
  46. CapnGranite

    National Academies Science Literacy book 2016

    https://www.nap.edu/catalog/23595/science-literacy-concepts-contexts-and-consequences Science Literacy: Concepts, Contexts, and Consequences "Science is a way of knowing about the world. At once a process, a product, and an institution, science enables people to both engage in the construction...
  47. Ackbach

    MHB How can a cube be inscribed in a right circular cone?

    Here is this week's POTW: ----- A right circular cone has base of radius 1 and height 3. A cube is inscribed in the cone so that one face of the cube is contained in the base of the cone. What is the side-length of the cube? ----- Remember to read the...
  48. Euge

    MHB Is This Week's Math Problem of the Week Still Unsolved?

    Here is this week's POTW: ----- Call an $S$-space over a topological space $B$ a pair $(E,p)$ where $E$ is a topological space and $p$ is a local homeomorphism from $E$ into $B$. A morphism of $S$-spaces $(E_1,p_1)$, $(E_2,p_2)$ over $B$ is a continuous mapping $\phi : E_1 \to E_2$ such that...
  49. anemone

    MHB Can You Solve the Trigonometry Puzzle of the Week?

    Here is this week's POTW: ----- Prove that $\cot 13^\circ \cot 23^\circ \tan 31^\circ \tan 35^\circ \tan 41^\circ =\tan 75^\circ$ ----- 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...
  50. Ackbach

    MHB What is the solution to Problem B-5 in the 1997 Putnam Competition?

    Here is this week's POTW: ----- Prove that for $n\geq 2$, \[ \overbrace{2^{2^{\cdots^{2}}}}^{\mbox{$n$ terms}} \equiv \overbrace{2^{2^{\cdots^{2}}}}^{\mbox{$n-1$ terms}} \quad \pmod{n}. \] ----- Remember to read the...
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