text stringlengths 0 6.23M | __index_level_0__ int64 0 419k |
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TITLE: How to show if $m$ and $n$ are coprime and $m-n$ is odd, then $(m^2-n^2)^2$, $(2mn)^2$, $(m^2+n^2)^2$ have a common factor?
QUESTION [1 upvotes]: We know that the Pythagorean triples can be generated by the Euclid's formula $a=m^2-n^2$, $b=2mn$, $c=m^2+n^2$ for any positive integers $m,n$ and $m>n$.
I am trying ... | 105,903 |
Name
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Snore No More by Kristian on April 19, 2021 at 00:00 Chapter: Comic It was either this or dropping a gigantic nasal spray onto earth. Oh, and a sawing log is the universal image used for snoring, right? I was alternatively gonna go for just “ZzZ” instead. Liked it? Take a second to support Kristian on Patreon! └ Tags: ... | 157,691 |
TITLE: How do I solve $x=1.1^x$? Is it possible?
QUESTION [2 upvotes]: I'm trying to find the intersection of $y=x$ and $y=1.1^x$. I've tried logging both sides and doing every log law on it, but can't figure it out. I know these equations intersect twice thanks to desmos. Using desmos, when I set y=nx, where n is a bi... | 1,588 |
TITLE: Roots of a special polynomial
QUESTION [3 upvotes]: I have a question that seems tricky to me. So, let $P_n$ be the polynomial defined by $P_n(x+1/x)=x^n+x^{-n}$. And let $Q$ be some polynomial with $\sup_{x\in [-2,2]}|Q(x)|<2$. Then $P_n-Q$ has at least $n$ different roots. I have no idea yet. It's clear that $... | 12,255 |
Microsoft Outlook is a personal information manager software system. You will find it inside the Microsoft 365 suite of tools. This powerful application does more than create and send emails. Its design helps you keep your workspace organized, even when you’re busy.
Our latest video shows you some fantastic time-saving... | 26,237 |
(*
Title: Budan-Fourier theorem
Author: Wenda Li <wl302@cam.ac.uk / liwenda1990@hotmail.com>
*)
section \<open>Budan-Fourier theorem\<close>
theory Budan_Fourier imports
BF_Misc
begin
text \<open>
The Budan-Fourier theorem is a classic result in real algebraic geometry to over-approximate
real roo... | 220,516 |
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Virtual, Inc. Expands Staff To Serve Growing Needs Of Association Clients
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I'm thankful for my trip this last weekend (and that I can write in a blog with whatever type of punctuation I feel like):
being met by the crisp, Fall air and a best friend with a smile stretched across her face
fall leaves floating haphazardly across the street as we drove to meet another best friend for dinner
a sea... | 308,745 |
Can I just say that I love being able to get out of my office and heading downstairs (to the Concourse, or Plaza) for lunch. Because I enjoy reading Kristi Gustafson’s blog On The Edge, I have the opportunity to meet some new people. Last month (or so) I went to one of the evening meet-up’s where several of the frequen... | 392,316 |
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If there’s one thing I remember from growing up in the Eighties, it’s the proliferation of commercials for Star Wars action figures and accessories that played every 3.5 minutes on every channel on Saturday morning. Ironically enough, I never owned a Star Wars action figure – not because I didn’t desperately want them,... | 376,367 |
TITLE: Convergence of the powers of stochastic matrices
QUESTION [3 upvotes]: I want prove that for a $n
\times n$ left stochastic matrix $P$ with dominant eigenvector $v$ and any
nonzero vector $x$ with non-negative entries, $P^kx \to \alpha v$ as $k\to\infty$ for some real $\alpha > 0$.
I know how to do the proof whe... | 50,387 |
TITLE: Number of possible functions using minterms that can be formed using n boolean variables.
QUESTION [2 upvotes]: Consider 3 boolean variables $x, y$ and $z$. Then you can form a total of 8 expressions using each variable or its complements exactly once in each expression i.e. $xyz$, $xyz′$, $xy′z$, $xy′z′$, $x′yz... | 83,548 |
TITLE: A basis in the space of all tempered distributions over $\mathbb{R}^n$
QUESTION [1 upvotes]: What is a(n uncountable) basis in the topological vector space $\mathcal{S}' \left(\mathbb{R}^n\right)$ ? How can any tempered distribution be expanded in terms of such a basis?
REPLY [2 votes]: You said "uncountable" w... | 173,886 |
MiniserverItem no.: 100001
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TITLE: A polynomial $x^2 + ax + b$ with three distinct roots modulo $4$
QUESTION [1 upvotes]: Give an example of a polynomial $x^2 + ax + b \in R[x]$, where $R = \mathbb{Z}$ / $4\mathbb{Z}$, which has 3 distinct roots in $R$.
My immediate thought is that there is no such polynomial because the degree of of the polynom... | 30,164 |
TITLE: Determining when $3 \cdot 5^a \cdot 7$ is abundant.
QUESTION [0 upvotes]: I would like to determine the values of $a$ for which $3 \cdot 5^a \cdot 7$ is abundant.
My work so far:
$$\sigma(3 \cdot 5^a \cdot 7) > 2 \cdot 3 \cdot 5^a \cdot 7 = 42 \cdot 5^a \Leftrightarrow$$
$$ \sigma(3) \cdot \sigma (5^a) \cdot ... | 85,500 |
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To see if your business is a fit with our membership goals, please complete the Membership Fit Assessment.
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TITLE: Cardinality of the set of infinite binary sequences
QUESTION [3 upvotes]: Let $B := \{ (x_n) \mid x_n \in \{0, 1\}, n \in \mathbb N \}$ then prove that $|B| = 2^{\aleph_0}$.
I know that the given set $B$ is uncountable. This can be deduced by proving that any countable subset of sequences of $B$ will be a prope... | 116,896 |
Control your sites as well as the content by controlling individual preference 'friend' and who you allow to reply to your profile sites. This could include anything from filing cease and desist orders to buying domain names, in fact it is an important element of modern marketing.
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Kaduna State Water Corporation (KADSWAC) Shortlisted Candidates For Aptitude Test 2018
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\begin{document}
\title{Jet Schemes and Singularities}
\author{Lawrence Ein}
\address{Department of Mathematics \\ University of
Illinois at Chicago, 851 South Morgan Street (M/C 249)\\
Chicago, IL 60607-7045, USA} \email{ein@math.uic.edu}
\thanks{The first author was supported in part by NSF under Grant DMS-0200... | 181,811 |
TITLE: Reference request : table of quantum Clebsch-Gordan coefficient
QUESTION [5 upvotes]: From a quick Google search, one can find a table of the first Clebsch-Gordan coefficient. For example this table. Those are used to pass between the tensor product bases and the bases as sum of irreducible of the tensor product... | 107,008 |
TITLE: Invertiblity of ST and TS for linear maps
QUESTION [0 upvotes]: Could somebody explain why for any given linear maps S and T over a finite dimensional vector space V, ST is invertible if and only if TS is? Why is it so important that V is finite dimensional for this to hold true?
Edit: I am looking for an approa... | 133,740 |
No Comparison
Stephanie Cutter.
No Affordable Choices
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TITLE: Find all zero divisors and all inverses in polynomial quotient ring
QUESTION [1 upvotes]: I'm trying to study algebra at IUM and I stuck on this question:
Let $\mathbb{F_4} := \mathbb{F_2}[\alpha]/(\alpha^2+\alpha+1)$ -- a field that consists of 4 elements $\{0,1,\alpha, \alpha+1\}$. Find all zero divisors and ... | 193,761 |
Where's the Beef?
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As a long-time fan of the Pokemon series let me tell you, Pokemon Ultra Moon represents both the highs and lows of being a Poke-fan. The graphical leaps the series has made since Red and Blue in 1996 are impressive, but the 3DS’s limitations become ever more apparent as designers try to push beyond them. Graphically th... | 28,232 |
INEOS Group
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3,279 ft
Distance
63 ft
Climb
-130 ft
Descent
00:04:15
Avg time
Wright of Way Details
Fredericton's first machine built flow-trail!
Local Trail AssociationRiver:15
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\documentclass{article}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{amsmath}
\newtheorem{definition}{Definition}
\newtheorem{proposition}{Proposition}
\newtheorem{theorem}{Theorem}
\newtheorem{corollary}{Corollary}
\newtheorem{lemma}{Lemma}
\newtheorem{remark}{Remark}
\def\address{Kyiv Taras Shevchenko Univ... | 214,463 |
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Criminal Justice: Police Science
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The other real housewives insist: It's 'not all about the Salahis'
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\subsection{Edge density and degree distribution in the projected graph}
To study the edge density and degree distribution in the projected graph,
we use the following quantity:
\begin{equation}
p_{u_1 u_2} := \frac{M_{R2}}{M_{R1} ^2} \frac{w_{u_1} w_{u_2}}{n_R}.
\end{equation}
The following theorem shows that $p_{u_1 ... | 43,112 |
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\begin{document}
\begin{abstract}
The general stability problem of truncations for a family of functions concentrating mass at the origin is described and a concrete example in the framework of entire optimizers for the fractional Hardy-Sobolev inequality is given. In this short note we point out some quantitative sta... | 62,146 |
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September
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September 2014
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MEMPHIS, Tenn. — Twelve gang members have been arrested in a major drug bust involving the seizure of marijuana, cocaine, illegal weapons and $1 million in cash, authorities said this morning.
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TITLE: Composition of Two Galois extension is Galois Extension
QUESTION [0 upvotes]: Question:
Let $K$ and $L$ be extensions of $F$. Show that $KL$ is Galois over $F$ if both $K$ and $L$ are Galois over $F$.
This question has been already asked here. But People provided incomplete solution to the problem.
I have trie... | 197,573 |
TITLE: Prove or disprove each of the follow function has limits $x \to a$ by the definition $\lim_{(x, y) \to (0, 0)} \frac{x^2y}{x^2 + y^2}$
QUESTION [0 upvotes]: Prove or disprove each of the follow function has limits $x \to a$ by the definition
$\lim_{(x, y) \to (0, 0)} \frac{x^2y}{x^2 + y^2}$
Let $y = x^2$
$\f... | 142,082 |
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R&B Singer Brandy Dines at Martorano’s in Las Vegas
April 12, 2012 by VegasNews.com
R&B singer Brandy was spotted on Wednesday night having dinner with her boyfriend at Martorano’s at Rio All-Suite Hotel & Casino.
She enjoyed the South Philly cheesesteak, and after dinner signed Steve Martorano’s photo with, “The food ... | 270,626 |
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Storrs Ice & Coal Co., Bridge St. Shed in 1905 shows existing building on Bridge Street, with Walter Storrs in white and long row of horsecarts with drivers. Photo originally contributed by Isabel Hogg and now part of the Hannibal Arts Council's Hannibal as History collection.
Days Gone By horsecarts
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TITLE: Is $\mathbb{R}[x^2,x^3]=\{f=\sum_{i=0}^n a_ix^i\in\mathbb{R}[x]:a_1=0\}$ is Euclidean Domain?
QUESTION [1 upvotes]: Is $\mathbb{R}[x^2,x^3]=\{f=\sum_{i=0}^n a_ix^i\in\mathbb{R}[x]:a_1=0\}$ an Euclidean Domain ?
My answer : I know that it is integral domain ,by theorem R is integral domain then $\Bbb R[x... | 181,870 |
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TITLE: Is multiplication implicitly definable from successor?
QUESTION [44 upvotes]: A relation $R$ is implicitly definable in a structure $M$ if there is a formula $\varphi(\dot R)$ in the first-order language of $M$ expanded to include relation $R$, such that $M\models\varphi(\dot R)$ only when $\dot R$ is interprete... | 172,915 |
\subsection{Tight completions of groups}
Consider an arbitrary group $G$ as a category $\GGg$ with a single object, i.e., $|\GGg| =\{o\}$ and $\GGg(o,o) = G$, with the group operation $\mmult$ as the composition and the group unit $\iota$ as the identity. Starting from the loose completions again, we note (as explained... | 193,086 |
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\begin{document}
\title{A Variable Sample-size Stochastic Quasi-Newton Method
for Smooth and Nonsmooth Stochastic Convex Optimization}
\author{Afrooz Jalilzadeh, Angelia Nedi{\'{c}}, Uday V. Shanbhag\footnote{Authors contactable at \texttt{azj5286@psu.edu,Angelia.Nedich@asu.edu,udaybag@psu.edu,farzad.yousefian@ok... | 7,295 |
Denise McLothlin, a nurse practioner with the Lehigh Medical Group, which includes Lehigh Regional Medical Center, has become only the second person to sign up so far for the honorary mayor’s race......
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\section{Technical results}
In this section we prove our cohomological theorem on Selmer growth.
The larger body of results we draw upon comes from \Nekovar's
formalism of Selmer complexes, which expresses the arithmetic local
and global dualities in the language of derived categories. Since
familiarity with these i... | 14,934 |
Wilson, James William
17 Dec. 1832–2 July 1910
James William Wilson, engineer, was born in Granville County, the son of the Reverend Alexander, a noted Presbyterian clergyman and educator, and Mary Willis Wilson. He grew up in Alamance County, attended the Caldwell Institute in Greensboro, and was graduated from The Un... | 188,799 |
\begin{document}
\newcounter{prop}
\newtheorem{theorem}{Theorem}
\newtheorem{proposition}[prop]{Proposition}
\newtheorem{corollary}[prop]{Corollary}
\newtheorem{lemma}[prop]{Lemma}
\newcounter{rem}
\newtheorem{remark}[rem]{Remark}
\newtheorem*{remarknonumb}{Remark}
\newcounter{exerc}
\newtheorem{exercise}[exerc]{Exer... | 85,607 |
TITLE: Candy machines and optimal strategy in terms of expected value
QUESTION [2 upvotes]: Problem
We have three candy machines: call them G (good), B (bad) and M (mixed) . G always gives you a candy when you put 1\$. B never gives you a candy when you put 1\$. M gives you a candy with probability $1/2$ when you put 1... | 108,893 |
\begin{document}
\title[On ELSV, Hurwitz numbers and topological recursion]{On ELSV-type formulae, Hurwitz numbers and topological recursion}
\author[D.~Lewanski]{D.~Lewanski}
\address{D.~L.: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Postbus 94248, 1090 GE Amsterdam, The Netherlands}
\emai... | 86,638 |
bfs<<
Haiku Getting UserlandFS, NetFS
We.
In its current state, UserlandFS is coded to work in BeOS R5, but it will soon be ported to work with the new Haiku file system interface (which is slightly modified implementation from that of BeOS R5). It is hoped that the availability of UserlandFS will accelerate developmen... | 413,163 |
hifi in Virginia Beach, VA
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Access Innovations Incorporated3631 Virginia Beach Blvd, Virginia Beach, VA map
- Write a review
- 1.4 MI
Audio Connection1657 Laskin Rd, Virginia Beach, VA map
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- 3.8 MI
APS Inc700 Military Highway, Virginia Beach, VA map
Se... | 73,417 |
A Última Minoria (19??)
The Last Minority
45 min
Documentário Actualidades
Outros: · Helena Balsa [Jornalista]
This stubborness belong to around 1 thousand inhabitants of Goa; they are still one thousand in a country which is a subcontinent with more than 800 million inhabitants.
You are therefore invited to watch that... | 47,499 |
NOLA Itinerary - Comments and Suggestions Please!
I am going with a friend to New Orleans May 25 (arriving 10:00 am) – May 30 (leaving 4:00 pm) and could really use some insider advice/guidance on my food itinerary. My friend will be attending a conference so for some lunches and breakfasts I will be alone. We really w... | 380,399 |
At least I'm telling myself it will be fun! On the agenda today...the frame. What else? I will also be brainstorming the trilogy. We're still trying to come up with an idea editorial likes. At least we're closer and things are not so, well, sexy now.
Hubby's been gone this week (second week this month) and I'm going to... | 51,836 |
Specialized AX2012 skills in Process Manufacturing, focused on:
• Formula management
• Co-product and by-product planning and management, including allocating costs for unplanned co-products and by-products
• Multi-dimensional inventory capability
• Containerized packaging
• First expired/first out (FEFO) and shelf lif... | 4,719 |
\begin{document}
\maketitle
\begin{abstract}
We point out to a connection between a problem of invariance of power series families of probability distributions under binomial thinning and functional equations which generalize both the Cauchy and an additive form of the Go\l \k ab-Schinzel equation. We solve these equa... | 131,597 |
Occasions
Just Because**CLEAR CREEK FLOWERS & GIFTS** in Crystal Springs**CLEAR CREEK FLOWERS & GIFTS** in Crystal Springs.
Get Well FlowersWhether **CLEAR CREEK FLOWERS & GIFTS**. Whether it's roses, the class flower or any other arrangement, we can help you make this special occasion even more memorable. Need to send... | 302,404 |
Keeping up with the current mortgage rates is almost like riding a rollercoaster lately. For the longest time, the rates were holding fairly steady a few months ago. Then they started to decline. In fact, they declined for several weeks in a row. A couple weeks ago, they went back up slightly and now the current mortga... | 337,385 |
TITLE: Probability that a symmetric random walk returns to $0$ exactly $k$ times in $2n$ steps
QUESTION [2 upvotes]: I'm trying to find a formula to find the probability of exactly k returns in 2n steps of a symmetric random walk. More specifically, I am trying to show that the probability of 2 returns is exactly equal... | 20,675 |
X-Wing: Imperial Aces Expansion PackTalk0
114,677pages on
this wiki
this wiki
The X-Wing: Imperial Aces Expansion Pack—also called the TIE Interceptor Aces Expansion—is a supplement to the tactical ship-to-ship combat game, X-Wing: Core Set, published by Fantasy Flight Games. The expansion features 2 detailed TIE Inter... | 364,610 |
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