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\chapter{Introduction}
\epigraph{
Por qu\'e los \'arboles esconden\\el esplendor de sus ra\'{\i}ces?}{
Neruda, {\em El libro de las preguntas}}
\section{Root numbers of elliptic curves}
Let $E$ be an elliptic curve over $\mathbb{Q}$. The reduction $E$ mod $p$
can
\begin{enumerate}
\item be an elliptic curve over $\math... | 139,072 |
\section{Application to convolutional linear network}\label{conv-tree}
\begin{figure}
\centering{
\begin{picture}(15,10)
\put(1,10){\shortstack{edges of depth}}
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\put(10,10){\shortstack{$2$}}
\multiput(10.2,9.7)(0,-0.1){90}{\line(0,-1){0.... | 64,403 |
In Brief: Wal-Mart Woes … Roddick, Reebok Split
WAL-MART WOES: Wal-Mart has pulled the plug on millions in stock options and other benefits for former vice chairman Thomas Coughlin, who was forced off the board in March after an internal investigation uncovered the possible...
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\begin{document}
\title{Local convergence analysis of inexact Newton-like \\ methods under majorant condition\thanks{IME/UFG, Campus II- Caixa
Postal 131, CEP 74001-970 - Goi\^ania, GO, Brazil.}}
\author{ O. P. Ferreira\thanks{E-mail:{\tt
orizon@mat.ufg.br}. The author was supported in part by
CNPq ... | 127,697 |
\begin{document}
\title[Real-Analyticity of Generalized Sine]{Real-Analyticity of Generalized Sine Functions with Two Parameters}
\author{Pisheng Ding}
\address{Department of Mathematics, Illinois State University, Normal, Illinois 61790}
\email{pding@ilstu.edu}
\subjclass[2020]{ 26E05, 33E20, 30B40}
\date{}
\keywords{... | 214,945 |
\begin{document}
\title {Bicategories and Weakly Globular Double Categories}
\author{Simona Paoli}
\address{Department of Mathematics,
University of Leicester,
LE17RH, UK}
\email{sp424@le.ac.uk}
\author{Dorette Pronk}
\address{Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 4R2, Ca... | 81,182 |
TITLE: Prove that $E \subset [0,1] \times [0,1]$ is not a Borel set.
QUESTION [4 upvotes]: Suppose $E$ is a subset of the unit square $[0,1] \times [0,1]$ such that each vertical line through the square intersects $E$ in a countable set and each horizontal line through the square intersects the complement of $E$ in a c... | 22,495 |
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TITLE: Converse of Taylor expansion theorem
QUESTION [1 upvotes]: The Taylor theorem states, that if a function $f$ is $n$-times differentiable at point $a$, it has a unique expansion
$$f(x) = \sum_{k=0}^n f^{(k)}(a) \frac{(x-a)^k}{k!} + o((x-a)^n)$$
Suppose now we are given a function $g$, which can be written in the ... | 43,643 |
TITLE: Do all the particles acquire mass in the Standard Model due to the Higgs mechanism only?
QUESTION [7 upvotes]: I know that a mass term for an intermediate boson is not compatible with the gauge symmetry. But in principle a mass term for the electron field does not violate a gauge symmetry. However to build an el... | 216,606 |
TITLE: Fermionic occupation for an inhomogeneous tight-binding model
QUESTION [1 upvotes]: The model
Consider the simple one-dimensional fermionic tight-binding chain of $N$ sites with inhomogenous hopping couplings $t_n$:
$$ H = - \sum_n t_n c^\dagger_{n+1} c_n + \text{h.c.} \equiv \sum_{n,m} c^\dagger_n h_{nm} c_m$$
... | 78,632 |
\chapter*{Preface}
These lectures were a part of the geometry course held during the Fall 2011 Mathematics Advanced Study Semesters (MASS) Program at Penn State (\url{http://www.math.psu.edu/mass/}).
The lectures are meant to be accessible to advanced undergraduate and early graduate students in mathematics.
We have... | 179,842 |
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TITLE: How to compute direct images of ramified covering maps?
QUESTION [1 upvotes]: Let $X$ be a smooth projective variety, $L$ a line bundle on $X$, and $s \in \Gamma(X,L) $ a non-zero section whose zero locus $D$ is smooth.
Let $\pi: Y \to X$ be the $n$-sheeted ramified cover given in local coordinates by taking the... | 131,258 |
\subsubsection{Consistent lockdown}
\label{sec:nom_oc_1_1}
In the following, we argue that a consistent lockdown strategy necessitates strong lockdown measures over a long time horizon to fully eradicate the virus as otherwise, dropping the social distancing measures too early leads to a second outbreak wave.
Based o... | 69,288 |
Houses for Sale in Easley, SC
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\begin{document}
\centerline{\bf International Journal of Algebra, Vol. 8, 2014, no. 4, 195 - 204}
\centerline{\bf HIKARI Ltd, \ www.m-hikari.com}
\centerline{\bf http://dx.doi.org/10.12988/}
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\centerline {\Large{\bf Induced Representations of Hopf Algebras}}
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\begin{document}
\title[Shock profiles and rarefaction waves under periodic perturbations]{Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-d convex scalar viscous conservation laws}
\author[Z. Xin]{Zhouping XIN}
\thanks{This research is partially supported by Zheng Ge... | 219,529 |
\begin{document}
\title{Torsion points and the Latt\`es family}
\author{Laura De Marco}
\address{Department of Mathematics, Northwestern University, USA}
\email{demarco@math.northwestern.edu}
\author{Xiaoguang Wang}
\address{Department of Mathematics, Zhejiang University, P.R.China}
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This dish is not very in-tune with the season as the cooking parts will heat your kitchen up on the QT and takes a bit of forethought (those poblanos don’t roast themselves), but we’ve had a few chilly days here in the Kawarthas, my BFF was visiting and doesn’t often get to eat shrimp, and it combines three of my favor... | 24,283 |
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TITLE: Prove that the limit $\lim_{x\to 0^+}\frac{1}{x}\sin{(\frac{\pi}{x})}$ does not exist
QUESTION [2 upvotes]: I have to prove that $\lim_{x\to 0^+}\frac{1}{x}\sin{\left(\frac{\pi}{x}\right)}$ does not exist.
My idea: from the definition of function limit, if I found $x_n\to\infty$ and $y_n\to\infty$ and $x_n,y_n\n... | 45,657 |
TITLE: Finding short vectors in $\mbox{GF}(2)$
QUESTION [4 upvotes]: Suppose we have a system of $n$ linear equations in $m$ unknowns over $\mbox{GF}(2)$ (binary field) $$Av=b$$ Let $V = \mbox{GF}(2)^m$ be the vector space of possible assignments of the variables. For $v \in V$, let $|v|$ be the number of non-zero valu... | 28,992 |
Police are worried teens using the leaves and seeds of a local plant to get high may not realize the potentially fatal effects of the plant.
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TITLE: Tiling a board with domino pieces
QUESTION [2 upvotes]: Let $m$ and $n$ be natural numbers such that $m\geqslant n>1$ and that the numbers $m$ and $n$ are not both odd. Consider a board with $m$ columns and $n$ rows. Obviously, the board can be tiled with domino pieces (as usual, I am assuming that each domino p... | 184,157 |
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TITLE: Proofing That $\int_0^a(f(x) + f^{-1}(x))dx \geq a^2$ for $a > 0$
QUESTION [1 upvotes]: Hello everyone $f(x)$ is a increasing function that for $f(0) = 0$ and $f^{-1}(x)$ is the opposite function of $f(x)$
How can I proof that $\int_0^a(f(x) + f^{-1}(x))dx \geq a^2$ for $a > 0$
Thanks!
REPLY [1 votes]: $\int_{... | 123,488 |
… Read more
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“Success leaves clues.” -Tony Robbins Tony was right. The clues are everywhere, in any business or field you choose to pursue. You just have to notice them and follow them to your desired destination. And if you want to succeed in business, here are 4 key principles that will get you where… Re... | 263,066 |
\begin{document}
\title[Random Polynomials ]{A review of some recent results on Random Polynomials over $\R$ and over $\C$.}
\author{Diego Armentano}
\date{}
\keywords{Random Polynomials; System of Random Equations; Bernstein Basis, Logarithmic Energy, Elliptic Fekete Points.}
\address{Centro de Matem\'atica, Universid... | 179,276 |
11 December 2020
China's power market is undergoing a fundamental energy transition.
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Maligned, misunderstood and often feared, nuclear will play a significant role in Northeast Asia’s pursuit of carbon neutrality
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TITLE: Longest consecutive runs of sums of $k$-subsets of first $n$ primes
QUESTION [4 upvotes]: Table of contents
[$1.$] Definition
[$2.$] Implication. (Motivation.)
[$3.$] Question. & Computed data.
[$4.$] Solutions of simplified variations.
[$5.$] Progress on solving the question.
[$6.$] Characterization of critica... | 157,085 |
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\begin{document}
\title[Point-like perturbed fractional Laplacians with shrinking potentials]
{Point-like perturbed fractional Laplacians through shrinking potentials of finite range}
\author[A.~Michelangeli]{Alessandro Michelangeli}
\address[A.~Michelangeli]{International School for Advanced Studies -- SISSA \\ via B... | 106,222 |
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TITLE: Math theory behind the slope formula of Least Squares
QUESTION [3 upvotes]: When studying linear regression, I see the slope formula of least squares like this: least squares. But I couldn't find the math theory behind it, i.e. how mathematicians came up with this equation, or why this equation gives out the bes... | 210,981 |
World
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By Vincent Fung
GENEVA/NAIROBI, 24 January 2013 -. | 35,183 |
The Australian accent is the result of heavy drinking by the first colonial settlers, a communication expert has controversially claimed. Dean Frenkel, a lecturer in public speaking and communications at Victoria University, has said that the "drunken slur" is "not related to class".
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Wednesday, March 5, 2014
GARLICZOOM
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Mithun brings you Nehi
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The wild boar was standing beside a tree, sharpening his tusks. The fox asked him why he was sharpening his tusks now, when there was no immediate need for him to do so. The wild boar replied, ‘I have my reasons! This way, when danger threatens, I won’t have to take time to whet my tusks but will instead have them read... | 164,171 |
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\begin{document}
\title[Capacity \& Perimeter from $\alpha$-Hermite Bounded Variation]
{Capacity \& Perimeter from $\alpha$-Hermite Bounded Variation}
\author[Jizheng Huang]{Jizheng Huang}
\address{ School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, P.R.China. }
\email{hjzheng@16... | 119,811 |
TITLE: Is there a known representation for this set derived from a Lie group $\subseteq \text{SU}(n)$?
QUESTION [0 upvotes]: Let $G \subseteq \text{SU}(n)$ be a Lie group for $n \in \mathbb{N}$, with a proper Lie subgroup $H \subset G$ having Lie algebra $\mathfrak{h}$ such that $H = e^{\mathfrak{h}}$. Let $g_0 \in G$ ... | 104,066 |
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TITLE: Are the following identities well known?
QUESTION [19 upvotes]: $$
x \cdot y = \frac{1}{2 \cdot 2 !} \left( (x + y)^2 - (x - y)^2 \right)
$$
$$
\begin{eqnarray}
x \cdot y \cdot z &=& \frac{1}{2^2 \cdot 3 !} ((x + y + z)^3 - (x + y - z)^3 \nonumber \\
&-& (x - y + z)^3 + (x - y - z)^3 ),
\end{eqnarray}
$$
$$
\be... | 181,925 |
Chiropractic Care
The Chiropractic profession is often poorly misunderstood, and many people have no experience with Chiropractors..
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MACKINAW CITY — With oil again flowing through side-by-side pipelines beneath the waterway that connects Lake Huron and Lake Michigan and inspections of damage to Line 5 and electric transmission lines underway, Michigan Attorney General Bill Schuette said he intends to bring civil action against the company believed t... | 239,110 |
TITLE: Why is this derivation of rotational kinetic energy wrong?
QUESTION [0 upvotes]: I was trying to derive the rotational kinetic energy of a solid sphere with radius $R$ using the following idea.
Each infinitesimally small shell volume $4\pi r^2 \cdot dr$ at radius $r$ within the sphere has a mass $m$ of $m(r) = \... | 209,720 |
\begin{document}
\title{The second homology group of current Lie algebras}
\author[P.~Zusmanovich]{Paul Zusmanovich}
\thanks{\noindent S.~M.~F. Ast\'erisque 226 (1994)}
\maketitle
\setcounter{section}{-1}
\section{Introduction}
It is a well known fact that the current Lie algebra
$\mathcal G \otimes \mathbb C[[t... | 42,853 |
UPDATED HAMILTON COUNTY FAMILY LAW RULES
credit to
The Hamilton County Family Law Rules were updated on July 1, 2019. This post discusses those rules:
To Whom do these Rules Apply?
The rules shall apply in all divorce, post-divorce, paternity and post-paternity cases.
What is Required by Litigants in These Cases?
Parti... | 121,971 |
Can you reopen an injury settlement in the future if there are additional diagnosed injuries, symptoms or expenses after coming to terms with an insurance company? It is important to fully understand every issue surrounding your injuries after any motor vehicle accident due to the negligence of another person. Once you... | 17,547 |
BPAP: Work Abroad. Live Here.
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Brexit & Beyond: U.K. Investment and Immigration Slow, Brexit Weighs on Rural Land, Investors Look to Draghi
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TITLE: Does the direct sum decomposition of a p-group tell you the number of Prüfer subgroups?
QUESTION [0 upvotes]: My understanding is that every countable Abelian $p$-group can be written as a direct sum of at most countably many finite cyclic groups and at most countably many copies of the Prüfer $p$-group.
Suppose... | 53,528 |
TITLE: On the clarification of Manin's remark about Gödel’s incompleteness theorems
QUESTION [13 upvotes]: In his paper Georg Cantor and his heritage Yuri I. Manin writes (see page 7, 3rd paragraph),
Baffling discoveries such as Gödel’s incompleteness of arithmetics
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TITLE: Efficient method to find the center of the $SL(2, 3)$
QUESTION [0 upvotes]: We consider the group $G$ of $2 × 2$ invertible matrices with determinant 1 over the the field $Z/3Z = ${$0, 1, 2$} (i.e., the entries of the matrix are taken from {$0, 1, 2$}, and addition and multiplication are performed modulo $3$, e.... | 86,450 |
TITLE: Is a MIMO system with a pole $s=0$ stable?
QUESTION [1 upvotes]: Is a MIMO (multi-input-multi-output) system $G(s)$ with a pole $s=0$ stable? Or what will happen if the MIMO system has a $s=0$ pole?
REPLY [2 votes]: @Kwin van der Veen
I agree that controllability of unstable poles can be checked if you test a s... | 169,508 |
TITLE: Why isn't an observer on earth considered to be accelerating in the twin paradox?
QUESTION [0 upvotes]: This question has a duplicate, but answers to that question went miles above my head. Well, that was supposed to happen since I have just previewed special relativity that too on a high school level, but I did... | 180,400 |
TITLE: Period of the decimal expression for the rational number $\frac{1}{n}$ is at most $n-1$
QUESTION [1 upvotes]: Proposition: Show that for an integer $n\geq 2$, the period of the decimal expression for the rational number $\frac{1}{n}$ is at most $n-1$. I'm unsure of where to start. This is my first class on proof... | 5,334 |
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Ceramic braces are made of clear materials and are therefore less visible on your teeth than metal braces.
Invisalign is simple. The aligners are comfortable and have no metal to cause mouth abrasions during treatment. | 54,189 |
PHIL Duncan has joined the Natural Resources Access Regulator board, the first Aboriginal man to become part of the four-member team.
With decades of exprience working between Aboriginal people and government, Mr Duncan joins chairman Craig Knowles, Ilona Millar and Bruce Brown on the board.
He is sombre in his assessm... | 404,897 |
The Whitehall-Coplay School District is planning to sell a 28-acre tract in Egypt back to the man who owned it 18 years ago when the district condemned the land to build an elementary school.
The school board last night authorized district officials to sell the tract to Stephen Schwartz of Whitehall for $150,000. The s... | 93,937 |
This group is a place for people involved or interested in homeland security to converse. IDGA’s Annual Border Management Summit offers the most comprehensive update on border security initiatives you will experience this year. Attend and get up-to-date with what’s happening at our borders.
By registering to be a membe... | 70,253 |
\begin{document}
\title[Rigidity of limit sets for geometrically finite Kleinian groups]{Rigidity of limit sets for nonplanar geometrically finite Kleinian groups of the second kind}
\authorlior\authordavid\authormariusz
\begin{abstract}
We consider the relation between geometrically finite groups and their limit s... | 35,188 |
TITLE: How do I find the closed form of a recurrence relation?
QUESTION [2 upvotes]: I'm stuck on how to find closed forms of recurrence relations. My current problem is:
An employee joins a company in 1999 with a starting salary of $50,000. Every year this employee receives a raise of 1,000 plus 5% of the salary of t... | 61,686 |
TITLE: Stochastic integral of Poisson process
QUESTION [2 upvotes]: I want a way to calculate or approximate the stochastic integral
$$
\int_{0}^{t} e^{\lambda (t - s)}dW_s
$$
where $\lambda > 0$ is a real number, and $W_s$ is a Poisson process with intensity $\mu e^{\lambda s}$, where $\mu > 0$ is a real number. I wa... | 15,423 |
Apple rejects writing lesson for links to Amazon, then for mentioning Amazon a fine fury, Lisle writes:.
On the bright side, pulling all of her (self-published) content from the store will probably not affect her bottom line all that much—as she says herself, 90% of her income is going to come from Amazon anyway. Nonet... | 417,690 |
Science graduates 'lack skills needed by business'
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Universities are not producing enough science graduates with the skills needed by UK industry, a report says.
The Lords Science and Technology Committee calls for immediate action to boost student numbers in science, technology, engineering and maths at undergrad... | 103,545 |
Amazon’s first live TV show lets you shop as you watch
Amazon is debuting its first live TV show tonight – a 30-minute daily fashion and beauty segment featuring a former Miss America, an ex-Big Brother star and an MTV presenter as its hosts.
From the ‘Style Code Live‘ trailer it looks insufferably cheerful, with Rache... | 24,826 |
The Bristol Press Monday, March 31, 2003 | A7 THE TATTOO against terrorism,” said Justin Garren, Selena Chu, a Virginia 16-year-old, said that Hussein probably has hidden weapons of mass destruction. “I think that something needs to be
tattoo soulja girl international harvester bleed it out hot lip gloss me love remix ... | 56,586 |
TITLE: Prove inner-product inequality $\Bigl (\sum_{i=1}^k \langle u\;,\;e_i \rangle \langle v\;,\;e_i \rangle \Bigr)^2≤ \Vert u \Vert^2 \, \Vert v \Vert^2$
QUESTION [3 upvotes]: The Question:
For the real vector space $V$, let $u,v \in V$ and $\{ e_1,\dots,e_k \}$ being a set of orthonormal vectors wrt to the inner pr... | 146,735 |
A few weeks ago, I wrote about a spat between the House of Commons Procedure Committee and the Department for Exiting the European Union. The issue concerned what happens if the Government chooses to ignore a recommendation of one of the new ‘sifting committees’ established to consider Brexit-related delegated legislat... | 388,555 |
November 11, 2008 7:24 AM
Deborah L. Schwartz has been named a member of the Rotary Club of Montecito. Ms.
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