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).
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...
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...
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...
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.
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...
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...
Here is this week's POTW:
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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...
Here is this week's POTW:
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Find necessary and sufficient conditions on positive integers $m$ and $n$ so that
\[\sum_{i=0}^{mn-1} (-1)^{\lfloor i/m \rfloor +\lfloor i/n\rfloor}=0.\]
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Remember to read the...
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Given that the decimal part of $X=\left(\sqrt{13}+\sqrt{11}\right)^6$ is $Y$, find the value of $X(1-Y)$.
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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:
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Give two different proofs of the following result: Every retract of a Hausdorff space is closed.
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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:
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Solve the equation x^3=4+\left\lfloor{x}\right\rfloor.
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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!
Here is this week's POTW:
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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.
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Remember to read the...
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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.
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Remember to read the...
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Let $Z$ be the center of a finite group $G$. Prove that there are at most $(G : Z)$ elements in each conjugacy class of $G$.
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to...
Here is this week's POTW:
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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 $x>0$.
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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...
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...
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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...
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Two real numbers $x$ and $y$ are chosen in the range $[0,\,10]$.
What is the probability that $|x-y|\ge 6$.
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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:
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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 $ABC$...
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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.
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Remember to read the...
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What are the last two digits in $7! + 8! + 9! + ... + 2016 !$?
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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, a problem submission by Track. Thanks, Track!
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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...
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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 $(-1)^{n+1}$.
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Remember to read the...
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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...
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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...
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If $\omega$ is a two-form on the four-sphere, is $\omega^2$ (i.e., $\omega \wedge \omega$) nowhere vanishing?
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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:
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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.
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Remember to read the...
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...
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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.
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Remember to read the...
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:
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Let $A_1=0$ and $A_2=1$. For $n>2$, the...
Here is this week's POTW:
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If $x,\,y$ and $z$ are non-negative reals such that $x^2+y^2+z^2+xyz=4$, prove that $xyz\le 1$.
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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:
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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 =...
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Determine all triples $(x,\,y,\,z)$ of positive integers with $x^{(y^z)}=\left(x^y\right)^z$.
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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:
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Let $f$ be a real function on the real line with continuous third derivative. Prove that there exists a point $a$ such that \[f(a)\cdot f'(a) \cdot f''(a) \cdot f'''(a)\geq 0 .\]
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Remember to read the...
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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...
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...
Here is this week's POTW:
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In a triangle $PQR$ with its sides $p,\,q$ and $r$ where $2\angle P=3\angle Q$, prove that $(p^2-q^2)(p^2+pr-q^2)=q^2r^2$.
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to...
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...
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...
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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...
Here is another chance to solve a sheaf problem!
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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...
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...
Here is this week's POTW:
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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?
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Remember to read the...
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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...
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Prove that $\cot 13^\circ \cot 23^\circ \tan 31^\circ \tan 35^\circ \tan 41^\circ =\tan 75^\circ$
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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:
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Prove that for $n\geq 2$,
\[
\overbrace{2^{2^{\cdots^{2}}}}^{\mbox{$n$ terms}} \equiv
\overbrace{2^{2^{\cdots^{2}}}}^{\mbox{$n-1$ terms}} \quad \pmod{n}.
\]
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Remember to read the...