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TITLE: Sum and product of linear recurrences
QUESTION [6 upvotes]: Given
$a_n = \alpha_1 a_{n-1} + \cdots + \alpha_k a_{n-k}$
and
$b_n = \beta_1 b_{n-1} + \cdots + \beta_l b_{n-l}$ are linear recurrences with complex coefficients, how can I find linear recurrences for $a_n + b_n$ and $a_n b_n$?
REPLY [8 votes]: It wil... | 134,953 |
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Toxic subcultures are thriving in the medical profession, often putting patients at risk. Everyone who works in the NHS has met these people, but dealing with the problem is a huge management challenge.
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Improve your snare sound without having to spend hundreds on a new drum.
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TITLE: Compute $ \sum\limits_{k=0}^{m}(-1)^k {n \choose k} {n \choose m-k}$ and $\sum\limits_{A,B\subseteq X} |A\cup B|$ for some given finite set $X$
QUESTION [6 upvotes]: I've got a problem with deducing closed-form expressions for sums:
$1) \ \sum_{k=0}^{m}(-1)^k {n \choose k} {n \choose m-k}$
$2) \ \sum_{A,B\subset... | 15,351 |
TITLE: $f(f(x))=f(x),$ for all $x\in\Bbb R$ suppose $f$ is differentiable, show $f$ is constant or $f(x)=x$
QUESTION [4 upvotes]: $f(f(x))=f(x),$ for all $x\in\Bbb R$ suppose $f$ is differentiable, show $f$ is constant or $f(x)=x$
Clearly, $f'(f(x))f'(x)=f'(x)$. This implies for each $x$, $f'(f(x))=1$, or $f'(x)=0$. B... | 164,745 |
You can always tell the masters from those just trying to be a master. There are several in music that come to my mind, Sandi Patti, George Strait, Rosemary Clooney....all masters and the list could go on. It is amazing how a duet between one of the masters and one of those trying to be a master reveals the truth of pu... | 67,989 |
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TITLE: Finitely many ideals of given norm in rings of integers
QUESTION [4 upvotes]: I'm trying to prove that there are only finitely many ideals of any given norm in the ring of integers $\mathcal{O}_k$ over a numberfield $K$.
I know there are "standard proofs" (e.g. How many elements in a number field of a given norm... | 118,210 |
WASHINGTON — President Trump is about to score a big win, but not the kind he promised.
The luxury hotel builder who campaigned as a champion of the “forgotten” middle class is poised this week to sign his first major bill — a tax overhaul that could deliver its biggest benefits to the wealthy and big corporations.
The... | 148,061 |
In-what-way-do-socioeconomic-factors-effect-the-attitude-of-women-towards-their-dressing-style-in-India
Answer by Balaji Viswanathan:
Continuing the discussion from here: Why are North Indian city girls more stylish in comparison to South Indian girls?
- Where they live: In big cities, women tend to be freer when it co... | 340,476 |
OK, that was bad. But, was it bad enough to generate these comments from Utah Republican Party Chairman Dave Hansen (via today's Political Cornflakes)?
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TITLE: Closed analytic form of $\int x^x\,\mathrm{d}x$
QUESTION [2 upvotes]: I have been struggling to find a closed analytic form for the indefinite integral:
$$
\int x^x\,\mathrm{d}x
$$
After a number of failed attempts I am thinking that only a numerical solution exists given bounded limits of integration.
Main atte... | 183,787 |
\section{Background on the geodesic flow}\label{s=background}
Let $M$ be a Riemannian manifold. As usual $\langle v,w\rangle$ denotes the inner product of two vectors and $\nabla$ is the Levi-Civita connection defined by the Riemannian metric. It is the unique connection that is symmetric and compatible with the met... | 100,072 |
TITLE: Symmetric Group and Alternating Subgroup
QUESTION [2 upvotes]: Prove that $A_{4}$ is the only subgroup of $S_{4}$ of order $12$.
-So far I know that the best way to prove this is by contradiction, assuming that there exists another subgroup in $S_{4}$ of order $12$:
Suppose $H$ is an subgroup of $S_{4}$ of order... | 28,242 |
TITLE: Kahler differentials on a smooth projective plane curve
QUESTION [4 upvotes]: Let $C = \{f=0\} \subset \mathbb{P}_k^2$ be a smooth plane curve of degree $d$.
I'm trying to find an explicit basis for $H^0(C,\Omega^1_{C/k})$. I know it should be $\frac{(d-1)(d-2)}{2}$ - dimensional. What I'm trying to find is an... | 108,446 |
TITLE: Renormalization of mass of an electron inside the crystal
QUESTION [4 upvotes]: In Cheng and Li's book, Gauge theory of Elementary Particle Physics, he essentially says that renormalization has nothing to do with infinities. Even in a totally finite theory, we would still have to renormalize physical quantities.... | 140,988 |
\newpage
\tableofcontents
\newpage
\section*{Appendix}
\addcontentsline{toc}{part}{Appendix}
\section{Notation and organization of the Appendix}
\paragraph{Structure.} In the first Sections~\ref{APP_Section_Lin_Sys},~\ref{APP_Section_Stat} we review results from system theory and statistics. These include the main too... | 47,714 |
Figure 2
From: BRCA-Monet: a breast cancer specific drug treatment mode-of-action network for treatment effective prediction using large scale microarray database
BRCA-MoNet. Each node represents a drug. A group of nodes linked by edges of the same color represent a MoA. The black edge linked two MoAs that show correla... | 164,953 |
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\begin{document}
\begin{abstract}
According to a well-known theorem of Cram\'er and Wold,
if $P$ and $Q$ are two Borel probability measures on $\RR^d$
whose projections $P_L,Q_L$ onto each line $L$ in $\RR^d$ satisfy $P_L=Q_L$, then $P=Q$.
Our main result is that, if $P$ and $Q$ are both elliptical distributions,
then... | 138,044 |
\section{Introduction}
The study of patterns in a word is
related to several topics and it has
various applications in several research domains, ranging from practical applications to theoretical considerations.
Among these patterns, we can mention palindromes and repetitions such as squares, cubes, periods, overlap... | 145,822 |
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Whipped Cream for Valentine Cake
This recipe for whipped cream is for our romantic valentine cake.
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Ingredients
- 2 cups heavy cream
- 2 tablespoons confectioners' sugar
- 1 teaspoon pure vanilla extract
Directions
Step 1
In the bowl of an electric mixer fitted with the whisk a... | 406,765 |
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One morning, at 4 a.m., I go to Rungis with Bernard Noel, the daytime chef at Chez Denise, to shop … Continu... | 160,960 |
National Geographic (NatGeo), the international news magazine, dedicated its April 2019 issue to the challenges of urban living and the progression of big cities. When I came across the hard copy of this issue, entitled "Cities: Ideas for a Brighter Future", my heart reached out for Dhaka, the city where I was born and... | 286,526 |
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Vivica A. Fox has sparked quite a fire on social media, after she suggested that her ex-boyfriend, 50 Cent might be gay.
The actress went on Watch What Happens Live this weekend, where she claimed that her famous ex was a “booty snatcher,” and as well as questioned his sexuality whi... | 254,369 |
TITLE: Orthogonality of summed wave functions
QUESTION [4 upvotes]: Problem. I know that the two wave functions $\Psi_1$ and $\Psi_2$ are all normalized and orthogonal. I now want to prove that this implies that $\Psi_3=\Psi_1+\Psi_2$ is orthogonal to $\Psi_4=\Psi_1-\Psi_2$.
My naive solution. From the premises, we kn... | 153,732 |
And still, each day begins with a sense of removal and distance. As if I put myself in exile, broken only if the will is there to do it.
Again I am up at dawn. You’d think I’ve seen all there is to be seen at sunrise, but that’s not so. Today, for instance, there are wisps of cloud that filter light in new ways. When t... | 128,483 |
TITLE: $P(X=c)=0$ for normally distributed $X$?
QUESTION [1 upvotes]: Let $X$ be norm $(a, b)$-distributed and let $c$ be some real number. Does this imply $P(X=c)=0$? What if $b=0$?
REPLY [2 votes]: If $X$ is any continuous random variable (e.g. normally distributed), then $P(X=c) = 0$ for all $c$ in $\mathbb{R}$, no... | 152,864 |
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TITLE: Is $\mathbb{F}_{2011^2}[x]/(x^4-6x-12)$ a field?
QUESTION [5 upvotes]: I'm studying for my qualifying exam and this was one of the questions in the question bank under Field and Galois theory section. I'm currently stuck on this question.
Is $\mathbb{F}_{2011^2}[x]/(x^4-6x-12)$ a field?
I'm guessing the answer... | 173,010 |
TITLE: If $f(z)$ analytic in the domain $D$ and $f'(z)=0$ so $f(z)=$constant?
QUESTION [2 upvotes]: I've been thinking how to prove that an analytic function $f$ in the domain $D$ is a constant if $f'(z)=0$ in every point in $D$, but I haven't figured it out yet.
What I was thinking is to use Cauchy-Riemann equations,... | 103,761 |
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Books in Film Studies
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Edited by Susan Ingram
One of the most dynamic capital cities of the twenty-first century, Berlin also has one of the most tumultuous modern histories. A city that came of age, in many senses, with the cinema, it has been captured on film dur... | 201,734 |
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Are you managing your dealership’s workforce compliance on spreadsheets, or worse, paper? Not only is that a lot of unnecessary work, it’s hides compliance gaps at your dealership that could cause serious problems. Lawsuits, fines, high turnover, reputation damage – poor workforc... | 281,441 |
\chapter{Simplicial techniques}\label{Chapt:simp}
The theory of simplicial sets and simplicial spaces is classical.
Simplicial sets were first defined in~\cite{EilenbersZilber:50}. The geometric realization
was defined in~\cite{Milnor:57}. Other references to simplicial techniques
are~\cite{May:67},~\cite{GoerssJardin... | 4,925 |
TITLE: Divergence of inverse of metric tensor
QUESTION [2 upvotes]: I know that the Levi-civita connection preserves the metric tensor. Is the divergence of the inverse of metric tensor zero, too?!
I'm not so familiar with the divergence of the second ranked tensor. However, I think one can write
$$\nabla_j g^{ij}=\par... | 67,695 |
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NOAA Climate Change Data Manipulation Charge: Scandal or Nothing to See Here?
Settled science and confirmation bias all the way down
Did National Oceanic and Atmospheric Administration researchers rush and manipulate data back in 2015 in order to publish a high-impact study in Science disproving the notion that the rat... | 162,746 |
TITLE: Proving properties of a family of measurable sets
QUESTION [0 upvotes]: Let $m$ be a lebesgue measure and $\{A_n\}_{n\in \mathbb{N}}$ a family of measurable sets on $[0,1]$,and $F=\{x:\forall n\in\mathbb{N} \exists k\geq n \text{ s.t } x\in A_k \}$
Prove the following:
$F=\bigcap_{n=1}^{\infty}\bigcup_{k=n}^{\... | 207,733 |
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/-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Anatole Dedecker
-/
import topology.separation
/-!
# Extending a function from a subset
The main definition of this file is `extend_from A f` where `f : X → Y`
and ... | 113,109 |
The Botswana Congress Party, BCP, says it wants the Directorate of Public Prosecution (DPP) to prosecute the minister who allegedly attempted to rape a senior government official during an official trip.
“Allegations of rape concerning a minister are matters of national importance,” said a press statement, issued by BC... | 392,408 |
Kobe Bryant has two jerseys retired by the Lakers. Five NBA championship winning legend. Sadly, I only saw him play once in the Staples. 2009 against the Denver Nuggets. Carmelo Anthony was a nightmare but Kobe won out the duel. Trevor Ariza had a great game but left next season. Ron Artest replaced him and a second Ch... | 41,190 |
TITLE: Proof by induction that $x_{n} + by_{n} = a$
QUESTION [1 upvotes]: I have an algorithm where a and b $\in$ Z+
MUL(a,b)
x = a
y = 0
WHILE x >= b DO
x = x-b
y = y+1
IF x = 0 THEN
RETURN(y)
ELSE
RETURN(-1)
I need to prove by induction that
$x_{n} + by_{n} = a$
is true if $x_{n}$ and $y_{n}$ are ... | 192,007 |
121 Comments
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Vanuatu Accommodation
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What do you get when you have a popular fastfood restaurant make a game console that could have competed against the likes of PlayStation 5 and Xbox Series X?
A prank, of course.
The notion comes from a recently launched ad by no other than KFC itself via Twitter which came with the #PowerYourHunger that depicts an alm... | 302,161 |
TITLE: Help proof by induction
QUESTION [1 upvotes]: I just got my first induction assignment in a new course. They want me to prove by induction that:
$$\sum_{s=1}^k s*s! = (K+1)!-1.$$
The way I understand induction is that I test for the first value. Then for n and then n+1, to show the given expression is true.
I've... | 133,115 |
Early ride on the Zamboni – Sunday, January 9th
Jan 9, 2011, 8:59 PM EST
It seems like we’re in the time of year in which teams play games with some pretty odd start times, so let’s take a look at some of the contests that finished a little earlier this Sunday.
Carolina 4, Atlanta 3 (OT)
All of a sudden, it’s looking l... | 230,248 |
DEVELOPMENT OF FLUID-SEDIMENT-SEABED INTERACTION MODEL AND ITS APPLICATION
Abstract
Keywords
References
Bear, J. 1972. Dynamics of Fluids in Porous Media, American Elsevier Pub. Co., New York, 764 p.
Jiang, Q., S. Takahashi, Y. Muranishi, and M. Isobe. 2000. A VOF-FEM model for the interaction among waves, soils and st... | 255,543 |
TITLE: Sharkovskii's theorem
QUESTION [0 upvotes]: the Sharkovskii's theorem states that for any continuous function $f:I\rightarrow I$, where $I = [0,1]$, if $\exists x$ such that $f\circ f\circ f (x) = x$, then for all $n\in \mathbb{N},\; \exists x,\; \underbrace{f\circ f\circ \dots \circ f}_{n \;\text{times}}(x) = x... | 140,330 |
Whether you are feeling happy, angry, silly or just bored, Netflix has a show that will match your every mood. In fact, to save you time, OK! Magazine has picked the top Netflix shows to match your every mood. As the cherry on top, you can watch just one show or binge the entire series in the comfort of your own home.
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Where Do You Stand: Raising Children in a Two-Religion Household
In today's world, it's not uncommon to marry outside of your race, culture, or religion. That's all fine and well when you don't have kids. But when children are brought into the mix, deciding how to raise them, religiously speaking, could be problematic.... | 72,114 |
MINATEC construction projects right on track
Categorie(s) : Life @ MINATEC, MINATEC, News
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\subsubsection*{Discrete polygons}
A \textit{discrete polygon} is a simply connected subgraph $\Omega$ of $\Z^2$,
{or $\delta \Z^2$,}
with $2N$ marked boundary points $x_1, x_2, \ldots , x_{2N}$ in counterclockwise order, whose precise definition is given below.
Firstly, we define the \textit{medial polygon}. We g... | 218,122 |
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Japan Credits Overseas TV Content Sales With Triggering Tourism Boom
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\begin{document}
\title{Some abstract versions of G\"odel's second incompleteness theorem based on non-classical logics}
\author{Lev Beklemishev and Daniyar Shamkanov \\
Steklov Mathematical Institute, Moscow\\
Moscow M.V.~Lomonosov State University \\
National Research University Higher School of Economics, Moscow\\... | 6,559 |
En español | WASHINGTON—Today, residents of all ages.
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View the full list of grantees: Jessica Winn, jwinn@aarp.org, 202-434-2506, @AAARPMedia | 338,479 |
TITLE: Can We Write the Differential in Terms of Covectors?
QUESTION [3 upvotes]: Let $f:\mathbf R^n\to \mathbf R$ be a smooth map.
We can write $df:T\mathbf R^n\to \mathbf R$ neatly as
$$
df = \sum_{i=1}^n(\partial f/\partial x_i) dx_i
$$
For a function $f:M\to \mathbf R$ defined on a smooth manifold $M$, given local ... | 63,454 |
\section{Introduction}
\label{sec:introduction}
In digital communication systems, data detection and decoding is a fundamental task at the receiver. The maximum a-posteriori (MAP) decoding approach is the optimal one to minimize the symbol or sequence error probability. If the channel model is known, the decoder can be... | 75,618 |
TITLE: Prove that a given CFG grammer $G$ is equivalent to language $L$
QUESTION [1 upvotes]: I need help to prove that the given CFG grammar $G$ is equivalent to language $L$:
as
$S\to 0S1 \mid SS \mid \varepsilon$
and
$L=\{w\in\{0,1\}^* \mid \#_0(w)=\#_1(w)\text{ and for any prefix } u \text{ of } w:\ \#_0(u)\ge\#_1... | 116,770 |
TITLE: How to Treat Coefficient as Constant To Approximately Solve PDE?
QUESTION [0 upvotes]: I am interested in analytically deriving an approximate solution to $\frac{\partial}{\partial t}f(x,t)=c(x,t) \frac{\partial}{\partial x^2}f(x,t)$ subject to given initial and boundary conditions. If the coefficient $c(x,t)$ w... | 109,221 |
\begin{document}
\theoremstyle{plain}
\newtheorem{thm}{Theorem}[section]
\newtheorem{theorem}[thm]{Theorem}
\newtheorem*{theorem*}{Theorem}
\newtheorem{lemma}[thm]{Lemma}
\newtheorem{corollary}[thm]{Corollary}
\newtheorem{proposition}[thm]{Proposition}
\newtheorem{addendum}[thm]{Addendum}
\newtheorem{variant}[thm]{Va... | 1,877 |
TITLE: Construction of new ellipse
QUESTION [6 upvotes]: Using a pencil, the thread was pulled on the ellipse. Then the pencil started to rotate around the ellipse. How to prove that the new geometric figure which the pencil drew is also an ellipse (with the same foci as the first ellipse)?
REPLY [2 votes]: Partial an... | 132,210 |
Tesla Is Bringing Autonomous Cars to Dubai
This move could ultimately lead to safer roadways everywhere.
Tesla is now in the United Arab Emirates (UAE). The electric vehicle manufacturer and sustainable technology innovator has brought its charging, service, and support infrastructures, as well as autonomous models to ... | 102,647 |
Wimpy gamma-ray burst delights astronomers
A new type of cosmic explosion that occurred late last year could shed light on the death of massive stars, astronomers say.
The explosion was more powerful than supernovae, explosions marking the death of a huge star, but weaker than gamma-ray bursts (GRB), the mysterious and... | 319,629 |
<< < alp off > >>
A short distance from the target, in right ascension, where
the telescope is pointed for various purposes.
→ alpha; → offset.
In → CCD detectors, same as
→ bias and → offset.
→ bias; → offset.
A.
A short distance from the target, in → declination,
where the → telescope is pointed for various purposes.... | 173,940 |
\begin{document}
\title[A simple algorithm to compute link polynomials]{A simple algorithm to compute link polynomials defined by using skein relations}
\author{Xuezhi Zhao}
\address{Department of Mathematics \& Institute of mathematics and interdisciplinary
science, Capital Normal University, Beijing 100048, CHINA... | 116,997 |
Special topics
Upstream Petroleum Operations in Ghana: An Overview of Activities and Environmental Impacts.
For an undeniable fact, exploitation of petroleum resources has sumptuous economic implications for a country, as well as in most countries has also reduced enormously natural oil pollution from oil seeps. Howeve... | 238,485 |
LHOTEL
262 rue St-Jacques Ouest, Montréal, Québec H2Y 1N1, Canada
Andy Warhol, Roy Lichtenstein, Robert Rauschenburg—you’ll find their art here, among other pop treasures. LHOTEL brings the glamor of the international art scene to Old Montreal.
YOU SHOULD KNOW While the location is great for exploring the Old Port, rue... | 96,763 |
.
The first blog of this TfL series showed that a key difference between the public transport funding models in London and Paris is that dependency on fare revenues is particularly low in the latter. Of the five cities analysed, the French capital is the only one where fare revenues accounted for less than 30 per cent ... | 407,280 |
$ 108.99 SALE: $ 98.99.
customer shoe reviews | 313,055 |
TITLE: Non-associative commutative "group"
QUESTION [4 upvotes]: When dealing with some hash functions that I was trying to speed up, I toyed with a binary operation with the goal to "approximate" the addition on $\{0,1\}^*$ when seen as binary representation of the positive integers:
$$(a,b) \in (\{0,1\}^*)^2 \mapsto ... | 211,788 |
The Day Thou Gavest : Lyrics.
Suitable for Evensong. Meter: 98 98. Lyricist: John Ellerton (1826 -1893). Public Domain.
The Day Thou Gavest : Recording & Download
- Tune: St Clement, composed by Charles Cotterill Scholefield (1839 – 1904). Public Domain.
- Performance ℗ and Facebook.Click Here to Download
Please Right-... | 88,309 |
Printable PDF
Vendor: EXIN
Certifications: ITIL OSA
Exam Name: ITIL Service Capability Operational Support and Analysis Exam
Exam Code: ITILSC-OSA
Total Questions: 26 Q&As
Last Updated: Mar 14, 2017
Us
This dump is still valid. I passed mine yesterday. Thanks so much guys.
Teressa
Still valid! Go get it now!!!
LoL
hi a... | 195,532 |
\begin{document}
\date{June 3, 2018}
\title{Erratum to ``Deformed Calabi--Yau Completions''}
\author{Bernhard Keller}
\address{Universit\'e Paris Diderot -- Paris 7\\
UFR de Math\'ematiques\\
Institut de Math\'ematiques de Jussieu--PRG, UMR 7586 du CNRS \\
Case 7012\\
B\^{a}timent Chevaleret\\
7520... | 158,617 |
At VitaminBungalow.Com we offer the lowest prices, all at or below wholesale prices Ordering is Fast and Easy. All orders over $150 receive Free Super Saver Shipping.
All orders in stock ship within 24 Hours,98% ship same day and arrive within 1-4 days! If you are having trouble finding a product, use our Search (top r... | 417,382 |
It’s unlike us to post an entire album, but then again it’s unlike albums to be as good as this. Even at almost a year old Submotion Orchestra‘s Finest Hour still rolls and breaks along, perfectly full of energy and yet still almost absurdly understated. The sound reminds me of Belleruche in that it combines the tradit... | 272,203 |
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