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TITLE: Can we improve the given 3x3 matrix-vector multiplication further? Or is there a better way?
QUESTION [2 upvotes]: Suppose we have
$$ \begin{bmatrix} a & 2c & 2b \\ b & a & 2c \\ c & b & a\end{bmatrix} \times \begin{bmatrix} e \\ f \\g \end{bmatrix}
=
\begin{bmatrix} B+C+D \\ A+C+E \\A+B+F \end{bmatrix}$$
Wher... | 211,335 |
SN 14 | EP 5 | Caravans, Tuning Forks, Ice Resurfacers, and Festival of Lights
Find out how to build the world's toughest mobile home, how an ice rink is resurfaced in minutes, how tuning forks are made, and how they put on the world's biggest festival of lights.
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\begin{document}
\begin{center}{\bf \large Fundamental solutions for Schr\"{o}dinger operators with \\[2mm]
general inverse square potentials }\medskip
\bigskip\medskip
{\small
Huyuan Chen\footnote{chenhuyuan@yeah.net} \ \,
Suad Alhomedan\footnote{shemedan@ksu.edu.sa}\ \, Hichem Hajaiej\footnote{hich... | 187,825 |
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\begin{document}
\title{Key Rate of the B92 Quantum Key Distribution Protocol
with Finite Qubits\thanks{
Accepted for presentation in 2015 IEEE International
Symposium on Information Theory, Hong Kong,
June 14--19, 2015.}}
\author{Hiroaki Sasaki\IEEEauthorrefmark{1},
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TITLE: About Groups and Isomorphic Quotients
QUESTION [7 upvotes]: So I was studying some group theory and I came up with this question: Say you have a group $G$ and two isomorphic normal subgroups $A,B$, is it true then that $$\dfrac{G}{A}\cong\dfrac{G}{B}$$ Turn out, it is not, take $G=\mathbb{Z}_4\times\mathbb{Z}_2$... | 95,088 |
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An exotic love story becomes an empowering portrait of two highly gifted women who defy social convention
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TITLE: Prove the formula for the Lie derivative of a differential form
QUESTION [2 upvotes]: If $X$ is a vector field then by $\mathcal F^t_X$ I will denote it's flow. If $\alpha \in \Lambda^k$ then by definition
$$
\mathcal L_X \alpha = \frac{d}{dt}(\mathcal F^t_X)^*\alpha \, \biggr|_{t=0}. \tag{1}
$$
The following... | 155,488 |
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Children are Hungry after School; the Food Bank is Feeding Them
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Hundreds of volunteers are working across the state to feed hungry families. We're getting a glimpse at the fruits of their labor tonight.
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Did you know that the average smart phone user looks at their phone 150 times a day? That's staggering! While there are more and more studies being published on what has been dubbed "digital addiction," it's not just affecting children and teenagers, but people of all ages.
If you or someone you know has small children... | 85,378 |
TITLE: Strange/Unexpected behavior of an Infinite product
QUESTION [2 upvotes]: Some friends and I were playing around with this continued fraction:
We noticed when writing it out for each next step, the end behavior went either to 1 (when there was an even number of terms) or to a linear dependence on x (when there w... | 42,747 |
\begin{document}
\title[The homotopy type of unions of arrangements and pencils]{On the homotopy type of the complement of an arrangement that is a 2-generic section of the parallel connection of an arrangement and a pencil of lines}
\author{Kristopher Williams}
\address{Department of Mathematics, Doane College, Cret... | 99,912 |
\begin{document}
\maketitle
\begin{abstract}
The Schwarz map of the hypergeometric differential equation is studied
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hyperbolic Schwarz map}, whose target is the hyperbolic 3-space. This
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TITLE: How can I prove $y^2-(x-z^2)^3$ is irreducible?
QUESTION [0 upvotes]: Suppose $F$ is an algebraically closed field.
I'm trying to find the set of singular points of the algebraic set $X=V(y^2-(x-z^2)^3)$. So I may need to prove the polynomial $y^2-(x-z^2)^3 \in F[x,y,z]$ is irreducible. If I can do that, then I ... | 209,386 |
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TITLE: What Are the Limitations in Diophantine Equations?
QUESTION [2 upvotes]: I read a bit about Diophantine equations, and I learned Hilbert tried to see if a solution exists for problems such as
$x^2y^3z^5-23x^5y^4+11x^2=176$
Apparently, rather than the notion our mathematics has not caught up yet it is actually th... | 105,117 |
\begin{document}
\title{Spectral edge detection in two dimensions using wavefronts}
\author{L. Greengard and C. Stucchio}
\maketitle
\begin{abstract}
A recurring task in image processing, approximation theory, and the
numerical solution of partial differential equations is to
reconstruct a piecewise-smooth real-val... | 37,639 |
Image Credit: Valarie Jean/Getty ImagesThis sure has been an interesting summer to follow Amanda Bynes’ Twitter feed. In June, she announced her retirement from acting on her beloved Twitter account, and in July, she simply announced that she “unretired” from acting on her Twitter. In the few weeks in between, Amanda t... | 168,608 |
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{\bf Problem.} The sum of the first $n$ terms in the infinite geometric sequence $\left\{1,\frac{1}{3},\frac{1}{9},\frac{1}{27},\dots \right\}$ is $\frac{121}{81}$. Find $n$.
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Heidi, an orphan, is sent to live with her grumpy grandfather in the Swiss Alps. Here, she falls in love with the snow-covered mountains. Soon, she is sent to Frankfurt, Germany, where she meets a differently abled girl named Clara. Will this mark the beginning of an everlasting friendship? Read Johanna Spyri�s classic... | 387,298 |
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I just read an article in TimesWarp, a site that reports biased coverage in the New York Times of human rights violations in occupied Palestine. But never ever mention Palestine.
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\begin{document}
\title{Squares, ascent paths, and chain conditions}
\author{Chris Lambie-Hanson}
\address{Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel}
\urladdr{http://math.biu.ac.il/~lambiec/}
\author{Philipp L\"ucke}
\address{Mathematisches Institut, Universit\"at Bonn,
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\begin{document}
\begin{center}
\LARGE \textbf{COBRA: A Nonlinear Aggregation
Strategy}\\
\vspace{0.6cm}
\end{center}
{\bf G\'erard Biau}\\
{\it Universit\'e Pierre et Marie Curie\footnote{Research partially
supported by the French National Research Agency (grant
ANR-09-BLAN-0051-02 ``CLARA'') and by the... | 86,177 |
Lawrenceburg Speedway’s grandstand, pictured with a full house during the 2018 season, will look different at 50 percent capacity, due to COVID-19 restrictions, for its delayed season opener coming Saturday, June 20. (Brandon Murray)
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TITLE: Probability of a letter coming from a city
QUESTION [1 upvotes]: I got this question:
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Anonymous Americas
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?
Read this poem in other languages
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Read Chris Lima’s report on Dave´s session on Internet Genre analysis .
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In this section we introduce the third term of our sequence, the group of Galois objects. We introduced it in \cite{CF} taking advantage of the construction of the group of biGalois objects due to Schauenburg, \cite{Sch1}. We will present here the main results on Galois objects and this group without proofs to keep thi... | 67,419 |
Quantum theory and the beginning of the Universe
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\begin{document}
\maketitle
\begin{abstract}
\paragraph{Abstract.}
We present a beautiful interplay between combinatorial topology and homological
algebra for a class of monoids that arise naturally in algebraic combinatorics.
We explore several applications of this interplay.
For instance, we provide a new interpreta... | 191,592 |
TITLE: Show that $s_z^2 = s_x^2.$
QUESTION [0 upvotes]: Let $x_1, \ ... \, x_n \in \Bbb R$ and $b \in \Bbb R$. Assume that $z_k = x_k + b, \ k = 1, \ ... \, n$ and $\bar z = \bar x + b$.
Show that
$s_z^2 = s_x^2.$
Here,
$$\bar x = {1 \over n} \sum_{k=1}^n x_k$$
and
$$s_x^2 = {1 \over n - 1} \sum_{k=1}^n (x_k - \bar x)... | 168,768 |
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LSU Dining gets A+ in Beanology
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Publications & Documents
- The Texas Longleaf Pine Implementation Team Conservation Plan
- Appendix A: List of Agencies and Organizations - Contributors to the Conservation Plan
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TITLE: Cofactors and determinant
QUESTION [0 upvotes]: Anyone can explain to me why $\det(C)=\det(A)^{n-1}$
where $A$ is $n$-by-$n$ matrix and $C$ is the matrix of cofactors of $A$.
I have been thinking, anyone can help? Thanks!
REPLY [0 votes]: As $C$ is the matrix of cofactors of $A$ , so $CA=\text{det}(A)I_{n}$ and... | 213,289 |
Global and Local Learning
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- Engage individuals at... | 126,155 |
\begin{document}
\baselineskip=17pt
\title{Continua having distal minimal actions by amenable groups}
\author{Enhui Shi}
\address[E.H. Shi]{School of Mathematical Sciences, Soochow University, Suzhou 215006, P. R. China}
\email{ehshi@suda.edu.cn}
\begin{abstract}
Let $X$ be a non-degenerate connected compact me... | 154,062 |
\begin{document}
\parindent 0pt
\title{\textbf{Asymptotic development for the CLT\\in total variation distance}}
\author{ \textsc{Vlad Bally}\thanks{
Universit\'e Paris-Est, LAMA (UMR CNRS, UPEMLV, UPEC), MathRisk INRIA, F-77454
Marne-la-Vall\'{e}e, France. Email: \texttt{bally@univ-mlv.fr} }\smallskip \\
\textsc{Luc... | 135,800 |
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According to the ABI, Bankruptcy Judge Redfield T. Baum rejected Canadian billionaire Jim Balsillie’s offer to purchase the Phoenix Coyotes hockey team and move it to Hamilton, Ontario, as well as the NHL’s purchase offer, the Associated Press reported today. However, Judge Baum upheld the league's right to decide who ... | 318,528 |
There is a lot of publicity at the moment about Fibromyalgia with the British Fibromyalgia Awareness Week September 4th 11th nearly with us.
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Jordan & Harley
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\begin{document}
\title{\textrm On the Roots of Characteristic Equations of Delay Differential Systems}
\author{Jia-Yuan Dai}
\date{ }
\maketitle
\begin{abstract}
We prove that characteristic equations of certain types of delay differential systems, under some mild conditions on their coefficients, can posses... | 204,402 |
\begin{document}
\pagenumbering{arabic}
\pagestyle{headings}
\def\sof{\hfill\rule{2mm}{2mm}}
\def\llim{\lim_{n\rightarrow\infty}}
\title[Generalizations of Bell number formulas]{Generalizations of Bell number formulas of Spivey and Mez\H{o}}
\maketitle
\begin{center}Mark Shattuck\\
Department of Mathematics, Univers... | 30,152 |
TITLE: The spectrum of a commutative unital Banach algbra having linearly dense idempotents is totally disconnected
QUESTION [5 upvotes]: I don't know how should I start to show:
If $A$ is an arbitrary abelian Banach algebra in which the idempotents have dense linear span, its specrum (the space of characters on $A$) i... | 163,934 |
TITLE: What is the expectation value of this random variable?
QUESTION [2 upvotes]: Let s be a positive integer. Do the following:
Step 1: choose a random natural number $s_1 \in \{0, \ldots,s\}$ (uniformly distributed)
If $s_1 = 0$, stop.
Otherwise, step 2: choose a random number $s_2 \in \{0, \ldots, s_1\}$
Continue... | 7,069 |
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\begin{document}
\begin{center}
{\Large\bf Skein theory and the Murphy operators}
\bigskip
HUGH R. MORTON
\medskip
{\it Department of Mathematical Sciences, University of Liverpool,\\
Peach St, Liverpool, L69 7ZL, England. }\\
{\tt morton@liv.ac.uk}
\end{center}
\vskip 1cm
\begin{abstract}
The Murphy op... | 79,070 |
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TITLE: How to prove this result with sequences and series?
QUESTION [1 upvotes]: Let $\left(v_n\right)_{n\geqslant1}$ and $\left(w_n\right)_{n\geqslant1}$ be two real sequences with strictly positive values, i.e., $v_n> 0$ and $w_n >0$. Assume that $v_n\sim w_n$ and the series $\sum_k v_k$ diverges.
Hence: $\sum_kv_k\s... | 57,994 |
CHESTERTOWN, Maryland, November 3. SENIOR Caroline Coolidge and sophomore Jason Potter won two events apiece, leading the Gettysburg College swimming teams to a sweep over host Washington College in their Centennial Conference openers Saturday afternoon.
The-freestyle (2:04.53) and the 500-freestyle (5:35.55) while anc... | 338,340 |
TITLE: Linearly independence of a family of linear functionals
QUESTION [1 upvotes]: I'm solving the following exercise of linear algebra
Recall that $\Bbb{R}_n[X]$ denotes the space of polynomials of degree inferior or equal to $n$. Let $a_0,...,a_n\in\Bbb{R}$ be distinct real numbers. Show that there exists a unique... | 154,298 |
Yonex has improved the V-Core to become an even more spin-friendly frame with the new Yonex V-Core 100 Lite (280 maneuverable racquet designed for great spin and power.
- Web Description: Yonex V-Core 100 Lite (280g) Red (No Cover)
- Sport: Tennis
- Headsize: 100 sq. in.
- Length: 27"
- Beam Width: 24/25/22mm
- Weight ... | 416,417 |
Coffee For Dogs
Inside a review in Italy, it absolutely was established that that brewed espresso contains several antioxidants and use of antioxidant-rich brewed espresso may possibly inhibit diseases prompted by oxidative damages. When compared to other caffeine made up of drinks like tea and cocoa, espresso proved t... | 130,935 |
Elon Musk's SpaceX let go 10% of its 6,000 person staff today. In May of last year, the company stated that it has had "many years" of continuing profitability and in recent weeks raised $273 million so far in a planned $500 million funding round.
"To continue delivering for our customers and to succeed in developing i... | 203,582 |
Phonofone by Science & Sons. October 10, 2007
Ceramics + Music = Design Beauty. I want a Phonofone by Science & Sons. The Phonofone is clever piece of applied science, a beautiful icon of nostalgia, and an ironic twist on the insular nature of personal listening devices. Through passive amplification alone, the Phonofo... | 297,069 |
The last few weeks have been incredible across the High Country. In Victoria we passed into spring with fantastic snowmass and in the last few weeks we’ve had sunny days and mostly cold nights. The resorts are still going, at least until this weekend, and there’s lots of backcountry terrain which is accessible with lit... | 384,998 |
\begin{document}
\pagestyle{fancy}
\title{The Two-fold Role of Observables\\ in Classical and Quantum Kinematics}
\author[1,2]{Federico Zalamea
\thanks{This work has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013 Grand Agreement n$^\circ$... | 169,630 |
New Music: Mary J. Blige – ‘A Mary Christmas’ [Album Snippets]
Mary J. Blige has a gift for her fans this holiday season. The Queen of Hip-Hop Soul has unwrapped the star-studded tracklisting for her first-ever Christmas album.
Blige joins forces with David Foster, the Grammy-winning producer behind multi-platinum Chri... | 30,740 |
When I agreed to write for the National Teachers Alliance, I suggested that the best way to get to know the success of Country Day’s technology program was through its people. Rob Baker, our Director of Technology, is a man who uses pithy, insightful statements to help others understand what works at Country Day. Rob w... | 376,075 |
TITLE: Expected number of distinct sums of two sets modulo an integer
QUESTION [2 upvotes]: Let $m$ be a fixed integer and $r,s\ll m$ given integers. We pick uniformly at random two sets $A$ and $B$ of classes modulo $m$ the first with $r$ elements and the second with $s$ elements. I would like to know what is the expe... | 90,471 |
The Howling Lords: Bad For Me
- Posted on
- 10.11.16
-
The most impressive fresh blues rock fix you could get today, is brought to you courtesy of British duo, The Howling Lords, who were formed in 2015 at the Western Isles and whose debut single off their upcoming 2017 album, has dropped today and it rocks like a kick... | 351,226 |
TITLE: If $A$ is idempotent then $A$ is similar to a diagonal matrix with only $0$'s and $1$'s on the diagonal.
QUESTION [3 upvotes]: I am trying to use Jordan normal form to show that if $A^2 = A$ then it is similar to a diagonal matrix with only $0$'s and $1$'s. I've proved that the eigenvalues of $A$ have to be eith... | 167,236 |
TITLE: How to construct a locally injective entire holomorphic function such that the modulus is axially symmetric?
QUESTION [3 upvotes]: Let $f$ be an entire holomorphic function, with $f'$ vanishing nowhere in the complex plane. Is it possible to construct such a function such that $|f(z)|$ is symmetric with respect ... | 133,410 |
TITLE: Definition of Tensor Laplacian
QUESTION [4 upvotes]: Let $(M,g)$ be an orientable Riemannian manifold, $\nabla$ its Levi-Civita connection and $\epsilon$ its volume form. Let $f\in C^\infty(M)$ be a scalar field. Then we know that we can define its Laplacian by $$\nabla^2f=\star d\star df.\tag{1}$$
Now let $T \i... | 153,103 |
Protect your investment – migrate to the cloud…
The ProTelesis managed data center platform is designed specifically for Mitel MiVoice Business (3300) or MiVoice Connect (ShoreTel) customers who want to "cloud enable" their communications solution but want to maintain the financial investment they have already made in ... | 194,743 |
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