text:
I want to review the URL routing for my appengine webapp:

routes = [
(r'/', CyberFazeHandler),
(r'/vi/(eyes|mouth|nose)', CyberFazeHandler),
(r'/realtime', RealtimeHandler),
('/serve/([^/]+)?', ServeHandler),
('/file/([0-9]+)', FileInfoHandler),
('/file/set/([0-9]+)', SetCategoryHandler),
('/file/([0-9]+)/success', AjaxSuccessHandler),
]

app = webapp2.WSGIApplication(routes,
debug=os.environ.get('SERVER_SOFTWARE', '').startswith('Dev'
))

Does it look alright to you? Can you recommend an improvement? Should I use the 'r prefix to my regexes?

Have you considered using named Route templates instead of capturing regular expressions? It could make the code more readable. Consider

Route("/task/refresh-user/<username>", RefreshUserHandler)

(r'/task/refresh-user/(.*)', RefreshUserHandler)

for example. (Of course, I don't know what kwargs RefreshUser actually wants, but you can change the angle-bracketed part to the appropriate name.)


text:
# Where to \definecolor?

When I put color definitions in the preamble, I get an error, e.g.

\documentclass[12pt]{article}

\usepackage{xcolor}

\definecolor{es-bg}{HTML}{e7edf4ff}% (cornflower light blue background at the top)
\definecolor{es-aqua}{HTML}{00ffffff}% (bright aquaish, matches)
\definecolor{es-lb}{HTML}{0090d4ff}% (lighter blue, matches)
\definecolor{es-db}{HTML}{003b74ff}% (darker blue, matches)

\begin{document}

\colorbox{es-aqua}{This should be a color.}

\end{document}

gives an error of "Missing \begin{document}".

If I put the definitions after \begin{document}, it compiles but there is an extra line "FFFFFFFF" in the document, e.g.

\documentclass[12pt]{article}

\usepackage{xcolor}

\begin{document}
\definecolor{es-bg}{HTML}{e7edf4ff}% (cornflower light blue background at the top)
\definecolor{es-aqua}{HTML}{00ffffff}% (bright aquaish, matches)
\definecolor{es-lb}{HTML}{0090d4ff}% (lighter blue, matches)
\definecolor{es-db}{HTML}{003b74ff}% (darker blue, matches)

\colorbox{es-aqua}{This should be a color.}

\end{document}

It's completely fine to define colors in the preamble. But the HTML format asks for 6 numbers/letters, not 8:

\documentclass[]{article}

\usepackage{xcolor}
\definecolor{es-bg}{HTML}{0df400}

\begin{document}
\textcolor{es-bg}{Hello}

\end{document}

The xcolor HTML color model takes 6 uppercase hex digits so

\documentclass[12pt]{article}

\usepackage{xcolor}

\definecolor{es-bg}{HTML}{E7EDF4}% (cornflower light blue background at the top)
\definecolor{es-aqua}{HTML}{00FFFF}% (bright aquaish, matches)
\definecolor{es-lb}{HTML}{0090D4}% (lighter blue, matches)
\definecolor{es-db}{HTML}{003B74}% (darker blue, matches)

\begin{document}

\colorbox{es-aqua}{This should be a color.}

\end{document}

• Thanks! (I selected the other answer because it was slightly ahead of you and the poster doesn't have 626k karma, however you answer indicates that the trailing ff is the problem in the colors).
– yoyo
Sep 17 at 19:12

format: plain


text:
# Convergence and almost sure properties in Hardy spaces of Dirichlet series

Abstract : Given a frequency $\lambda$, we study general Dirichlet series $\sum a_n e^{-\lambda_n s}$. First, we give a new condition on $\lambda$ which ensures that a somewhere convergent Dirichlet series defining a bounded holomorphic function in the right half-plane converges uniformly in this half-plane, improving classical results of Bohr and Landau. Then, following recent works of Defant and Schoolmann, we investigate Hardy spaces of these Dirichlet series. We get general results on almost sure convergence which have an harmonic analysis flavour. Nevertheless, we also exhibit examples showing that it seems hard to get general results on these spaces as spaces of holomorphic functions.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-03103584
Contributor : Frédéric Bayart <>
Submitted on : Friday, January 8, 2021 - 11:20:34 AM
Last modification on : Thursday, February 25, 2021 - 10:32:06 AM

### Files

gendir5.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-03103584, version 1
• ARXIV : 2101.02990

### Citation

Frédéric Bayart. Convergence and almost sure properties in Hardy spaces of Dirichlet series. 2021. ⟨hal-03103584⟩

Record views


text:
# Preface

This book provides worked-out solutions to the exercises given in Advanced R1 and reflects our efforts to understand and acquire its content.

Advanced R covers R2 and programming. It presents the specific characteristics of the R language to programmers and helps R users to improve their understanding of general programming concepts.

When we came across Advanced R, it gave us a more thorough understanding of the R code we worked with daily and helped us to see the underlying principles more clearly. The content helped us to get a more complete picture of R’s programming landscape.

We soon re-discovered that reading about programming is not enough and that it helps greatly to open the editor and write some code along the way. The clear structure of Advanced R and the exercises given provided a great starting point for this.

We think of this book as a solutions manual, which intends to supplement and support your own study of the R language through Advanced R. We hope that it will help you to stay on track and allow you to check your understanding and progress along the way. The solutions may also give you another perspective on some of the presented material.

## How this book came to be

The solutions in this book are written from our personal perspective and current level of understanding. We both came from mathematics and statistics backgrounds preparing us more carefully for data analysis than for programming. So, we were R users first and improved as programmers in our day jobs and through working on projects like this one.

By taking advantage of the bookdown package3 to structure our process, we created this book almost as a by-product. While the initial progress was fun and motivating, actually providing solutions to all of the 284 exercises took slightly longer than originally expected (and Hadley’s rewrite of Advanced R halfway in between didn’t really make the journey shorter).

As the project matured, we strived to provide solutions that were as clean, straightforward, and expressive as possible. As well-written code is often more expressive than lengthy explanations, many of the solutions are rather code heavy. The written explanations aim to provide context and motivation, discuss important implementation details, or relate to the practical work of being an R programmer.

Hadley Wickham wrote Advanced R and created the exercises which form the substructure of this book. We took the task to solve them as correctly and idiomatically as possible. When we finished a chapter, we asked Hadley to review it. His feedback included many comments (which we then had to resolve), corrections, and suggestions, as well as a few complete solutions. We repeated this process until each exercise was reviewed and approved. As a result, we feel pretty good about the quality of the solutions in the book. However, any remaining mistakes or inconsistencies are certainly on us.

## How to use this book

Since this book builds so heavily on Advanced R, we think it should be read together with the textbook, either as a hardcopy or the online version (https://adv-r.hadley.nz). Working on an exercise first by yourself should in general give you the biggest benefit.

It may be a good idea to start with the parts of Advanced R that are most relevant to your work and interest. You can certainly read the book cover to cover, but we think that you don’t have to, though it’s probably a good idea to start with the foundations part.

Of the more difficult exercises in the book, only a few were completed in one go. Often we had to reread the question or look up the related content in Advanced R and started by writing a few lines of code first or consulting the documentation. Reading the source code (preferably with syntax highlighting) and searching the web were typically quite helpful.

To support your study, you may also be interested in the R4DS Advanced R book club, where groups of readers regularly discuss a different chapter of Advanced R.

In case you want to do more or have a special interest in the mechanics of base R, you may be interested in checking out the first edition of Advanced R (http://adv-r.had.co.nz/).4 Some additional solutions related to that edition can be found at https://advanced-r-solutions-ed1.netlify.app/.

There is one recommendation from Advanced R that we’d like to echo: reading source code can be tremendously helpful in developing your programming skill! For example, you can just head to GitHub and start looking into the source code of packages you love and developers you admire. While reading, it’s not necessary to understand every line of code right away. Keeping this a regular practice (for a while) will expose you to many new ideas, patterns, and design choices, and also expand your R vocabulary.

We don’t necessarily apply many of the concepts taught in Advanced R in daily programming and that’s okay! But we hope that the code we write has become more robust, expressive, and readable, and it’s actually quite easy to see the progress when we take a look at the earlier drafts of our own code.

## Acknowledgements

Many open source projects are the result of the work of a lot of people; so is this. We would like to explicitly mention and thank everybody who contributed solutions, raised questions, or helped to fix spelling and grammar to improve this work:

@3zhang, Anne (@ahoffrichter), Anh N Tran (@anhtr), Arash (@arashHaratian), Leon Kim (@BetweenTwoTests), Jun Cai (@caijun), @Charles926, Safouane Chergui (@chsafouane), Corrado Lanera (@CorradoLanera), @davidblitz, Zhuoer Dong (@dongzhuoer), @Elucidase, Fabian Scheipl (@fabian-s), @HannesOberreiter, @its-gazza, Jorge Aranda (@jorgearanda), @lotgon, @MajoroMask, Maya Gans (@MayaGans), Øystein Sørensen (@osorensen), Peter Hurford (@peterhurford), @philyoun, PJ (@pieterjanvc), Robert Krzyzanowski (@robertzk), Emily Robinson (@robinsones), Tanner Stauss (@tmstauss), @trannhatanh89, and Yihui Xie (@yihui).

Tobias Stalder (@toeb18) designed the beautiful cover, which visualizes the structure of Advanced R and its exercises.

Thanks to CRC Press for the interest in the project and our editor, Rob Calver, and his assistant, Vaishali Singh, for their patience and support in making this book a reality.

Thanks to our managers and companies for granting us some flexibility with our work schedules and generally supporting the completion of this project.

## Conventions

A brief overview of conventions we followed and decisions we made.

• Some chapters and sections in Advanced R do not contain exercises. In our book you will see that we skipped these chapters and sections. This decision introduces some gaps in the numbering, but we feel that keeping the numbers in sync with those of Advanced R will provide the most practical value.
• We strived to follow mostly the tidyverse style guide. The {styler} package5 helped us to check many of the rules automatically.
• Each chapter of this book was rendered in a separate R session via the bookdown package. We configured this process to initially:
• set %>% <- magrittr::%>% to unlock the pipe operator without specifically loading the magrittr package6 every time,
• set a random seed (1014) to improve reproducibility (similar as in Advanced R), and
• define a few ggplot2 and knitr options.
You can check out the exact code on GitHub.
• We chose to keep the code in this book as self-contained as possible.
• The packages used are usually loaded in the beginning of each chapter.
• We repeat all code from Advanced R that is necessary to work on an exercise but not explicitly part of the exercise. When some longer code passages (from Advanced R) are omitted, this is explicitly stated in the solution.
• The printed version of the book was rendered with R version 4.0.3 (2020-10-10) and the most recent available package versions as of December 2020. (The print version of Advanced R was rendered with R version 3.5.2.)
• Emoji images in the printed book come from the open-licensed Twitter Emoji.
• Benchmarks are computed when the book is rendered. While this improves reproducibility, the exact results will depend on the system creating the document.

## Closing remarks

We are so happy to finish this exciting project that in fact neither of us really had the time for. We probably wouldn’t have made it to the finish line if we hadn’t worked on it together.

Collaboration is powerful and it’s fun to build and share. The various backgrounds represented in the R community generally make this exchange much more interesting and meaningful. Much of this success is possible because R is free software. At least in theory, everyone can contribute and no one can take away your freedom to do so.

The automated systems we build using these tools are not neutral and the rapid adoption of data-driven processes in business and technology does clearly affect our everyday lives and societies. It’s important that everyone has a fair say in the discussions about these systems and participates in their design. Against this background, we chose to donate half of our royalties from this book to https://rladies.org/, an organization empowering minority genders in the R community.

Thank you for your interest in this project and we hope the solutions will be of value to you.

See you around!

Malte Grosser @malte_grosser

Henning Bumann @henningsway


text:
Normally distributed rain drops problem

About 50% of raindrops land downtown, downtown is a perfectly circular space around the city centre. Assuming the coordinates of the raindrops are independent and distributed according to the standard normal about the city centre. What is the percentage of rain drops that land within a radius twice that of downtown?

Since around 50% of the raindrops land downtown, clearly the percentage landing within a radius twice that of downtown must be less than or equal to 50, but beyond this I am not sure how to approach/solve this problem, can someone help? Thanks!

Let us look at a normal distribution in one dimension first, then proceed into two dimensions.

According to your statement, 50% of the raindrops land in downtown. Without loss of generality, let's assume that 'downtown' is one kilometer in radius. Let's model that in one dimension: $$Pr(\mu-n\sigma\leq X\leq\mu+n\sigma)=\Phi(n)-\Phi(-n)=0.5$$ In this case, looking at a z-table gives $$0.67. Now, we'll double n to find the standard deviation for the raindrops that land exactly two kilometers from downtown. We get in that case $$n\approx1.35$$. Now we plug that back in: $$Pr(\mu-2n\sigma\leq X\leq\mu+2n\sigma)\approx\Phi(1.35)-\Phi(-1.35)\approx0.823$$ again using the z-table.

Now, since we are talking about two dimensions rather than one, we square the resultant probability to obtain $$(0.823)^2\approx0.677$$.

Hope this works! Not sure if I'm correct, I'm no expert. (Not 100% confident about the last step.)

I believe you can use standard z-tables (e.g. https://en.wikipedia.org/wiki/Standard_normal_table) to work out the various percentages for the radius in question. The z-table will tell you the probability contained by the standard normal curve from 0 to whatever z-value you choose. Now, if you make the equivalence of rain percentage to probability and z to radius, then you should be able to solve the problem.

For example, if you look at the z-table for the standard normal, you will see that the z-value for 0.25 (25% - remember this is going to be 1/2 the total 50% because it is measured from the center), is about z=0.68. Now, if you double this (double the radius), you will get $$z=2(0.68)=1.36$$. This z-value corresponds to 0.413 or 41.3%. Then, you'll need to double this to get 82.6% which I believe should correspond to the final answer.

I hope this helps.

• Thank you a lot. Does this not contradict with the fact that 50% of the raindrops land downtown though? Since 50+81.6>100? Or am I missing something here? – gb4 Dec 5 '19 at 20:05
• @g The raindrops that fall downtown form a subset of the set of raindrops that fall in the circle twice the radius of down town. – saulspatz Dec 5 '19 at 20:08
• From my interpretation of the question, it seems like what is being asked is the percentage contained in a radius twice that of downtown. This will include the 50% of downtown, so you don't need to count that again. 81.6% should be the final answer. I hope this helps. – ad2004 Dec 5 '19 at 20:09
• Ah right okay that makes much more sense to me now, thank you a lot for your help. Should the final answer not be $41.6\times 2 = 82.6\%$ instead of $81.6\%$ then? – gb4 Dec 5 '19 at 20:14
• Yes. Good catch. 41.3(2)=82.6. I hope this helps. – ad2004 Dec 5 '19 at 20:16


text:
Eric Chapdelaine
Student at Northeastern University Studying Computer Science.
Notes
Projects
Articles
Resume

Email
GitHub

# Introduction and Fundamentals

## Definitions, Theorems, and Proofs

Mathematical Reasoning: Rigorous math based on logic

Statement: Declarative sentence that has a definite truth value

3 Types of Statements

1. Definition: Gives precise meaning. Always true.
2. Theorem: Have to prove to be true (8 is an even number).
3. Proof: Logical arguments to show a theorem is true

Proposition (more modest than theorem) = result. Another word is fact.

Undefined terms/Axioms: Don’t need to explicit state in proof.

1. Numbers: Integer, Real Number (We will define even, odd, rational, etc.)
2. Operations: Addition, Subtraction, Multiplication, and Division. (We will prove even + even = even)
3. Basic Properties of Arithmetic
4. Ordering of Real Numbers

When in doubt, prove it (or ask).

## Logical Connectives

NOTE:

The rows of a truth table can be determined by $2^{\text{number of compnent statements}}$

### Not

Takes one component statement

Notation: $\sim p$

Truth Table:

$p$ $\sim p$
T F
F T

### And

Conjunction

Takes 2 component statements

Notation: $p \wedge q$

Truth Table:

$p$ $q$ $p \wedge q$
T T T
T F F
F T F
F F F

### Or

Disjunction

Takes 2 component statements

Notation: $p \vee q$

Truth Table:

$p$ $q$ $p \vee q$
T T T
T F T
F T T
F F F

### If then

Conditional statement

Another way to say it is $p$ implies $q$.

• In this case, $p$ is the condition/hypothesis/premise/assumption and $q$ is the conclusion.

Truth Table:

$p$ $q$ $p \rightarrow q$
T T T
T F F
F T T
F F T

Warning:

It doesn’t say anything about the condition when $\sim p$ is true.

$p \rightarrow q$

• Inverse: $\sim p \rightarrow \sim q$
• Converse: $q \rightarrow p$

Note, the inverse and the converse have the same truth table and therefore they are the same.

### if and only if

Also called iff or biconditional

Notation: $p \leftrightarrow q$

• = $(p \rightarrow q) \wedge (q \rightarrow p)$
• = $(p \rightarrow q) \wedge (\sim p \rightarrow \sim q)$

Truth Table:

$p$ $q$ $p \leftrightarrow q$
T T T
T F F
F T F
F F T

NOTE:

All definitions are bidirectional. That is, if a definition has “if … then”, it means “if and only if”.


text:
# Introduction to Linear Regression in Machine Learning

## What is Linear Regression in Machine Learning ?

In general, Linear Regression is about fitting a straight line through the data and using that line to make predictions that minimizes the error between the observed value and the predicted value. The goal is to predict the value of an outcome variable (dependent variable) using one or more predictor variables ( or independent variables ). When we use a single predictor variable the method is called simple linear regression and when we use several predictor variables, the method is called multiple regression.

A linear regression line has an equation of the form Y = mX + b, where X is the independent variable and Y is the dependent variable. The slope of the line is m, and b is the intercept (the value of y when x = 0).

### How to fit a straight line through the data ?

To fit a straight line through the data we start with some data and we fit a line to it using least squares. In other words we measure the residuals, the distance between the data and the line and then squares them so that negative values do not cancels out positive values and then we add them all up. Then we rotate the line a little bit and we do the same thing. We measure the residuals, square them and add them. And the line with the smallest sum of squared residuals ( the least square) is the line chosen to fit best.

## How to train a Linear Regression model ?

Let’s read a dataset to work with.

import pandas as pd
import numpy as np
from sklearn import datasets

housing = datasets.fetch_california_housing()
X = pd.DataFrame(housing.data, columns=housing.feature_names)
y = housing.target
X.head()

Now, split the data into training and test set.

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

Now, let’s train a linear regression model.

from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error

# create a linear regression model
lin_reg = LinearRegression()

# fit a linear regression model
lin_reg.fit(X_train, y_train)

# make prediction on test set
y_pred = lin_reg.predict(X_test)

# measure error
mse = mean_squared_error(y_test, y_pred)
rmse = np.sqrt(mse)
rmse
# output
0.7455813830127762

### Related Posts –

Rating: 1 out of 5.


text:
## Isothermal expanision and deltaU [ENDORSED]

$\Delta U=q+w$

Liam Maxwell 2E
Posts: 53
Joined: Fri Sep 29, 2017 7:07 am

### Isothermal expanision and deltaU

Why is it that when there is an isothermal expanison, and thus deltaT=0, that deltaU also equals 0?

Vincent Tse 1K
Posts: 30
Joined: Fri Sep 29, 2017 7:05 am
Been upvoted: 1 time

### Re: Isothermal expanision and deltaU

I think it's b/c internal energy is directly related to change in temp.

Forgot where exactly, but there's a derivation somewhere in the book that uses the equipartition theorem and says that molar internal energy is U = 3/2 RT.
Therefore, ΔU = 3/2 RΔT. If ΔT is 0, then ΔU is also 0.

Erica Nagase 1H
Posts: 30
Joined: Sat Jul 22, 2017 3:00 am

### Re: Isothermal expanision and deltaU  [ENDORSED]

Isothermal means that temperature is constant. For an ideal gas (ideal = isothermal conditions), $\Delta U = \frac{3}{2}nR\Delta T$. Because $\Delta T$ = 0, $\Delta U$ = 0,


text:
# give the difference between three subatomic particles

By | 30. 12. 2020
How many candles are on a Hanukkah menorah? The difference between atoms is found in the numbers of each of these particles. • Protons, including neutrons, give the atom mass but are not involved in chemical reactions. Beta particles are named after the second letter in Greek alphabet the letter β. Subatomic particle, also called elementary particle, any of various self-contained units of matter or energy that are the fundamental constituents of all matter. and electron is negative. The Importance of these three subatomic particles are given below. Which subatomic particles contribute most directly in chemical bonding? What happens to an atom is you alter the number of protons, neutrons or electrons? Protons have a positive electrical charge, so they are often represented with the mark of a "+" sign. Give an example of a chemical or physical process that illustrates the law of conservation of mass. Why don't libraries smell like bookstores? Matt Strassler [April 15, 2013] At the center of every atom lies its nucleus, a tiny collection of particles called protons and neutrons.In this article we’ll explore the nature of those protons and neutrons, which are made from yet smaller particles, called quarks, gluons, and anti-quarks (the anti-particles of quarks.) When did organ music become associated with baseball? Performance & security by Cloudflare, Please complete the security check to access. They have different charges and differ in their masses. 2.photons. Although 15 isotopes of carbon are known, the natural form of the element consists of a mixture of only three of them: carbon-12, carbon-13, and carbon-14. : 1.1 It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. The main three subatomic particles are Protons, electrons and neutrons. Please enable Cookies and reload the page. In Chemical reactions, it is the electrons in the outer shells that take part in the reaction. The Importance of these three subatomic particles are given below. In contrast, the electron has a negligible mass of .0005 amu. An atom is the basic building block of matter, the smallest molecule of an element that exists and that cannot be chemically divided by ordinary means. Who is the longest reigning WWE Champion of all time? If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. 3. Most of the atoms are carbon-12. Find answers now! Protons, neutrons, and electrons are the three main subatomic particles found in an atom. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. No. Virtual particles are those that represent the average step to the disintegration of an unstable particle and exist for a … Join today and start acing your classes! The Bohr model shows the three basic subatomic particles in a simple manner. Protons carry positive electric charge and make up a nucleus of … The number of protons in the nucleus, which is generally equal to the number of orbiting electrons, is what distinguishes atoms of one element from atoms of another element. In the physical sciences, subatomic particles are smaller than atoms. It cannot be broken down or sectioned. Cloudflare Ray ID: 609620147a39cd83 What are some samples of opening remarks for a Christmas party? Log in or sign up to leave a comment log in sign up. Subatomic particles are so numerous and varied that physicists have used the term "particle zoo" to describe them. 3. What is the difference between subatomic particles? Protons are the positively charged particles, electrons are the negatively charged particles, and neutrons are electrically neutral, which means that they do not possess any charge. Subatomic particles are so numerous and varied that physicists have used the term "particle zoo" to describe them. The main differences are proton and neutron are in the nucleus, Instead of writing their actual masses in kilograms, we often use their relative masses. The main three subatomic particles are Protons, electrons and neutrons. Measuring the difference in the ratio between carbon-12 and carbon-14 is useful for dating the age of organic matter since a living organism is exchanging carbon and maintaining a certain ratio of isotopes. In particle physics, a pion (or a pi meson, denoted with the Greek letter pi: π) is any of three subatomic particles: π 0 π +, and π −Each pion consists of a quark and an antiquark and is therefore a meson.Pions are the lightest mesons and, more generally, the lightest hadrons.They are unstable, with the … Each atom … An easy way to remember this is to remember that both proton and positive start with the letter "P." Neutrons have no electrical charge. List the three subatomic particles of the atom. That means all the matters are made up of these fundamental particles. What is the difference between the three subatomic particles? The electron microscope is able to resolve detail at the subatomic level. A subatomic particle is an elementary or composite particle smaller than an atom. Describe covalent bonding. Neutrons and protons are both located in the nucleus of the atom; neutrons are neutrally charged particles, and protons are positively charged particles. An atom consists of three types of subatomic particles: neutrons, protons, and electrons. Depending on which definition of "matter… Subatomic particles are particles that are smaller than the atom. For simplicity, we will use the amu unit for the three subatomics. Actually, fundamental subatomic particles are electrons,protons and neutrons. The resulting particles are endowed with an amount of kinetic energy equal to the difference between the rest mass of the products of the annihilation and the rest mass of the original particle–antiparticle pair, which is often quite large. What is the difference between an atom, molecule, isotope and ion? What are the physical differences between subatomic particles that give them different charges? The key difference between proton and electron is that proton is a subatomic particle found in a nucleus of an atom, whereas electrons are particles orbiting the nucleus.. 1) Name the three subatomic particles and their charge? It has a charge of +1; It has a mass of 1; It is found in nucleus Neutrons. 1) All mater is made up of small particles called atoms 2)All atoms of any given typer ar similar to one another and significantly different from all other types 3) The relative number and arrangement of different atoms in a pure substrance determine its identity. The mass of a neutron is nearly equal to the mass of a proton. There are four known gauge bosons - the photon, W and Z bosons, and gluon.Two additional bosons, which almost certainly exist, … There are three known subatomic particles: Electrons, Protons and Neutrons Electrons It has a charge of -1; It has negligible mass; it is found outside the nucleus Protons. Best Answers. Protons, neutrons and electrons make up the subatomic particles of an atom. Protons have a positive (+) charge. In the domain of leptons, there are 3 types of electron - electron, muon and tau - 3 types of neutrino, and their antiparticles, making 12 leptons. Chemistry Lesson #6 – Subatomic Particles – The Difference between Mas – Genius Games Subatomic particle - Subatomic particle - Investigating neutrinos: Other hints of physics beyond the present Standard Model concern the neutrinos. Atoms consist of electrons, protons, and neutrons. According to modern atomic theory, an atom has a nucleus, which is present in its center or core. Answer to: 1. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. Atoms are made up of three subatomic particles. Click here to Register!. Protons – Protons are particles that are positively charged and are also located in the nucleus. Three Main Subatomic Particles. Out of which, electrons are leptons,while protons and neutrons are hadrons which are made up of quarks( the smallest elementary particle up to now). subatomic particles list in order of discovery, 2. Electrons are indivisible; they are, as far as we know, dimensionless points having a $-1$ electrical charge. The three particles that atoms are composed of are protons, neutrons, and electrons. Some properties of these subatomic particles are summarized in Table $$\PageIndex{1}$$, which illustrates three important points: Volume, Mass 3) Combination of 2 or more components that retain their identity Mixture 4) What is the difference between a covalent and ionic bond? In the Standard Model these particles have zero mass, so any measurement of a nonzero mass, however small, would indicate the existence of processes that are outside the Standard Model. Protons – positive Neutrons – neutral Electron – negative 2) Matter is anything that has ___ and ___. Protons and neutrons form the nucleus of an atom, and a cloud of electrons orbits the nucleus. What does contingent mean in real estate? Two of the types of particles carry an electrical charge, while the third is neutral. Beta Particle. In the next lesson, we will talk more about the actual mass of each of these three subatomic particles in greater detail. By joining Chemistry Steps, you will gain instant access to the answers and solutions for all the Practice Problems including over 20 hours of problem-solving videos, Multiple-Choice Quizzes, and t he powerful set of Organic Chemistry 1 and 2 Summary Study Guides.. How long will the footprints on the moon last? Most of the atoms are carbon-12. 5. Out of all of these subatomic particles, there are three main particles of interest – the electrons, protons and neutrons. Electrons are present outside the nucleus of an atom. Neutrons are neutral. If you have to name three subatomic particles of an atom, they are protons, electrons and neutrons. An atomic mass unit ($$\text{amu}$$) is defined as one-twelfth of the mass of a carbon-12 atom. Experiments with magnetic fields showed … Particle Charge : Relative Charge**: Mass Relative mass** : Location : Proton +1.60 x 10-19 C +1: 1.672 x 10-24 g: 1 amu: nucleus: Electron-1.60 x 10-19 C-1: 9.05 x 10-28 g: 0 amu ~(1/1840 amu) They can be composite particles, such as the neutron and proton; or elementary particles, which according to the standard model are not made of other particles. So let's go back to middle school physics and start with the three subatomic particles most people have heard of: electrons, protons, and neutrons, the three components of any atom. neutron and the charge on a proton is positive, neutron is neutral A "free" electron and "free" proton are placed in an ide… 00:25. The atom is the smallest unit on Earth. Explain Electronegativity Subatomic particles: The atoms consist of three types of subatomic particles and these subatomic particles are proton, neutron and electron respectively. between a hundred and a thousand times less of that of a proton and he three main subatomic particles that form an atom are protons, neutrons, and electrons. How many protons, electrons and neutrons does the ion 35C1-1 possess? In the domain of leptons, there are 3 types of electron - electron, muon and tau - 3 types of neutrino, and their antiparticles, making 12 leptons. (physics) Relating to particles that are constituents of the atom, or are smaller than an atom; such as proton, neutron, electron, etc. ... What is the difference between Alpha Particle and Beta Particle? Masses for the three subatomic particles can be expressed in amu (atomic mass units) or grams. These nucleus contain subatomic particles like protons and neutrons. I think you probably mean the mass of the classical subatomic particles, Proton, Neutron and Electron. The difference between atoms, ions and isotopes is the number of subatomic particles. If you have to name three subatomic particles of an atom, they are protons, electrons and neutrons. 2. Although this is an oversimplification that ignores the other subatomic particles that have been discovered, it is sufficient for discussion of chemical principles. List should include: model electron nucleus atom proton neutron atomic particles II Models of the Atom Activity V - Objective: to give background information of the discovery of the subatomic particles, with students, given … 2. Atoms are the building blocks of all existing substances. What are the physical differences between subatomic particles that give them different charges? Difference between subatomic particles are as follows : Electron 1. While the magnitudes of the charge are the same the polarity … Explain the difference between the … 2. Describe briefly the functions and characteristics of the three main subatomic particles (protons, neutrons, electrons). 0 comments. Enroll in one of our FREE online STEM bootcamps. Other particles exist as well, such as alpha and beta particles (which are discussed below). List the three subatomic particles that compose atoms and give the basic properties (mass and charge) of each. There are four known gauge bosons - the photon, W and Z bosons, and gluon.Two additional bosons, which almost certainly exist, … All Rights Reserved. They are both subatomic particles. • What are difference between subatomic particles and elementary particles? Particle physics and nuclear physics study these particles and how they interact. That means all the matters are made up of these fundamental particles. List the three subatomic particles that compose atoms and give the basic pro… 00:55. Describe the difference between the subatomic particles, including their masses, locations, and charges. The three subatomic particles determine the overall charge of an atom, the chemical characteristics it can possess and its physical properties. For quite a while, the atom was thought to be the smallest part of matter that could exist. 3.quarks. Protons have a positive (+) charge. Alpha particles can be broken down to more fundamental subatomic particles with high energy collisions. These differences are:: Neutron 1. This content is for registered users only. Electrons are negatively charged particles which orbit the nucleus of the atom. These nucleus contain subatomic particles like protons and neutrons. Copyright © 2020 Multiply Media, LLC. What is the difference between the three subatomic particles. (Gluons, like photons, are their own anti-particles). To recap, we know that everything you can see and touch, literally every physical object around you can be made from only three particles, called subatomic particles: protons, neutrons and electrons. Subatomic particles: A subatomic particle is a structural and functional unit of the matter. List should include: model electron nucleus atom proton neutron atomic particles II Models of the Atom Activity V - Objective: to give background information of the discovery of the subatomic particles, with students, given … For comparison, the radius of a typical bacterium is 1 × 10-6 m and the radius of a human hair is about 1 × 10-4 m. The masses of subatomic particles are very tiny. Close • Posted by 1 minute ago. Subatomic particles include electrons, negatively charged, nearly massless particles that account for much of the atom’s bulk, that include the stronger building blocks of the atom’s compact yet very dense nucleus, the protons that are positively charged, and the strong neutrons that are electrically neutral. The masses of subatomic particles are very tiny. Subatomic particles: The atoms consist of three types of subatomic particles and these subatomic particles are proton, neutron and electron respectively. 3. List the three subatomic particles that compose atoms and give the basic pro… 02:33. What is an Isotope? What is the difference between the three subatomic particles? It has no electrical charge The weight of an electron is between a hundred and a thousand times less of that of a proton and … Protons, including neutrons, give the atom mass but are not involved in chemical reactions. The subatomic particles they are those that are smaller than the atom. The mass of an electron is considered to negligible. The atom consists of three types of subatomic particles: protons, neutrons, and electrons. Neutrons are present in the nucleus of an atom. In ordinary matter, there are three subatomic particles: electrons, protons and neutrons. The magnitude of the charge on each particle is 1.60x10^(-19) In a neutral atom or molecule the number of protons = the number of electron. The electron is by far the lightest of the three, while the much heavier proton and neutron have masses very similar to each other. And that is how the atoms preserve their identity and uniqueness. Differences. The first three particles were known to be the building blocks from which atoms are made: protons and neutrons in atomic nuclei and electrons in orbit around those nuclei. Nuclear reactions are reactions where the nuclei of atoms take part in the reaction. Subatomic particles are particles that are smaller than the atom. It is the basic component of any type of matter. A typical atom consists of three subatomic particles: protons, neutrons, and electrons (as seen in the helium atom below). In 1940, the number of subatomic particles known to science could be counted on the fingers of one hand: protons, neutrons, electrons, neutrinos, and positrons. What is an ionic bond and what is the difference between a cation and an anion? These are the subatomic particles that make up the building blocks of the universe – atoms. 4. Also, the roles of each of the sub-atomic particles are quite different from each other. Difference Between Nuclear Reaction and Chemical Reaction Definition. Both neutrons and protons are assigned as having masses of 1 amu each. There are composite particles and elementary particles; On the other hand, the existence of virtual particles is also known. Subatomic Particles. Although 15 isotopes of carbon are known, the natural form of the element consists of a mixture of only three of them: carbon-12, carbon-13, and carbon-14. subatomic particles list in order of discovery, 2. 3. For quite a while, the atom was thought to be the smallest part of matter that could exist. All protons are identical to each other, and all neutrons are identical to each other. The main difference between Proton, Neutron and Electrons can be found in The third column shows the masses of the three subatomic particles in "atomic mass units." Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. Typically, an atom can be broken down into three subatomic particles, namely: protons, electrons, and neutrons. Indicate the charge of each. The modern classification of subatomic particles is divided into three type: 1.leptons. What is the difference between polar and nonpolar covalent bonds? Answered January 19, 2018 Subatomic particles like proton and neutron only differ from eachother in their composition of elementary particles (Quarks) but electron itself a elementary particle Proton - made of 2 up quarks and a down quark (elementary particles) Neutron - made of 2 down quark and a up quark (elementary particles) Calculate What is the difference expressed in kilograms between … What are Subatomic Particles? 100% Upvoted. Protons – Protons are particles that are positively charged and are also located in the nucleus. The difference between an atom and a molecule is that atoms are single neutral particles whereas molecules are formed from two or more atoms that are bonded to each other. The atom is the smallest part of matter that represents a particular element. The atom is the smallest part of matter that represents a particular element. Subatomic particle, also called elementary particle, any of various self-contained units of matter or energy that are the fundamental constituents of all matter. We explain Subatomic Particles with video tutorials and quizzes, using our Many Ways(TM) approach from multiple teachers. Give the difference between three subatomic particles. https://www.differencebetween.com/difference-between-proton-and-vs-electron save hide report. Covalent – sharing of electrons Your IP: 151.80.44.89 Protons and neutrons make up the nucleus of an atom. A Subatomic particle is nothing but a particle which is smaller than an atom in size. So to recap: The mass of an object is the quantity or amount of actual matter (or physical stuff) within that object. 4. rest mass = 1 Electron 1. The first subatomic particle was identified in 1897 and called the electron A subatomic particle with a negative electric charge..It is an extremely tiny particle, with a mass of about 9.109 × 10 −31 kg. You may need to download version 2.0 now from the Chrome Web Store. According to modern atomic theory, an atom has a nucleus, which is present in its center or core. Protons, neutrons, and electrons are the three main subatomic particles found in an atom. Atoms are divisible into smaller particles called subatomic particles. Protons are the positively charged particles, electrons are the negatively charged particles, and neutrons are electrically neutral, which means that they do not possess any charge. Elemental Composition Which subatomic particles contribute to atomic mass? Another way to prevent getting this page in the future is to use Privacy Pass. Subatomic particles are: neutron, proton, electron. Electrons are negatively charged. The main differences are proton and neutron are in the nucleus, electrons are outside of the nucleus. 1 Questions & Answers Place. Subatomic particles include the atomic constituents electrons, protons, and neutrons. share. Relating to any length or mass that is smaller in scale than a the diameter of a hydrogen atom. The weight of an electron is An easy way to remember this is to remember that both proton and positive start with the letter "P." Neutrons have no electrical charge. electrons are outside of the nucleus. Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. Particle physics and nuclear physics are concerned with the study of these particles, their interactions, and non-atomic matter composed from them. Give the difference between three subatomic particles. Unit for the three subatomic particles ( protons, neutrons, and charges by cloudflare, Please complete security! And that is smaller in scale than a the diameter of a chemical or process. 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Let’s suppose, for the moment, you’re interested in the function $f(x) = \frac{\pi\sin(x)}{x}$. It’s a perfectly respectable function, defined everywhere except for $x = 0$, where the bottom is 0. The top is also zero there (because $\sin(0) = 0$), so its value is, strictly speaking, indeterminate - $\frac{0}{0}$ could, in reality, be anything.

However, if you draw the graph of $y = \frac{\pi\sin(x)}{x}$, you’ll see that near $x=0$, the value gets closer and closer to $\pi$, and it’s the same on either side, so saying $\frac{\pi \sin(0)}{0} “=“ \pi$ seems legit. Unfortunately, we can’t write that, because of the whole dividing by 0 problem, but we can say that as $x \rightarrow 0$ (“$x$ approaches zero”), $\frac{\pi \sin(0)}{0} \rightarrow \pi$. Our answer gets as close to $\pi$ as we could possibly want.

One way to show this is to use something called L’Hôpital’s rule, which I’ve always liked because it has two apostrophes and a circumflex. I’ve recently come to appreciate it more, on the ground that L’Hôpital didn’t discover it, Bernoulli did - and L’Hôpital bought the rights.

Here’s what it says:

If $u(x_0) = 0$ and $v(x_0) = 0$ for some value of $x_0$, and if you can differentiate $u(x)$ and $v(x)$ at $x_0$, then the limit of $\frac{u(x)}{v(x)}$ as $x \rightarrow x_0$ is $\frac{u’(x_0)}{v’(x_0)}$.

I’m not going to go into many of the subtleties of that here, but focus on the main result: if you’ve got a function that gives an indeterminate fraction somewhere, you can find the value that makes sense by dividing the derivatives.

### Danger! Danger!

Under no circumstances should you confuse L’Hôpital’s rule with the quotient rule. Different things with different uses. Be careful.

### In this case…

So, in this case, we’ve got $u(x) = \pi \sin(x)$, which gives $u’(x) = \pi \cos(x)$. Meanwhile, $v(x) = x$, so $v(x) = 1$.

Divide them to get $\frac{u’(0)}{v’(0)} = \frac{\pi \times 1}{1} = \pi$, which is what we wanted. Hooray.

### But why?

The pirate proof is very simple, if you know your Taylor series. You know that $u(x_0 + \epsilon) \simeq u(x_0) + \epsilon u’(x_0) + …$, where $\epsilon$ is small and everything after that is really small - so small we can ignore it.

Similarly, $v(x_0 + \epsilon) \simeq v(x_0) + \epsilon v’(x_0) + …$, where again $\epsilon$ is small and everything else is too small to worry about.

So that means $f(x_0 + \epsilon) \simeq \frac{ u(x_0) + \epsilon u’(x_0)}{v(x_0) + \epsilon v’(x_0)}$. However, we also know that $u(x_0) = v(x_0) = 0$, because $f(x)$ is indeterminate. So, that’s all the same as $f(x_0 + \epsilon) = \frac{ \epsilon u’(x_0) + \epsilon^2(\text{stuff})}{ \epsilon v’(x_0) + \epsilon^2 (\text{stuff})}$.

We can divide the top and bottom by $\epsilon$ (which, remember, is small):

$f(x_0 + \epsilon) \simeq \frac{ u’(x_0) + \epsilon(\text{stuff})}{ v’(x_0) + \epsilon(\text{stuff})}$.

Lastly, we see what happens when we let $\epsilon$ approach zero: the “stuff” all becomes zero, so $f(x_0 + \epsilon) \rightarrow \frac{u’(x_0)}{v’(x_0)}$ as $\epsilon \rightarrow 0$ - or, better still:

$f(x) \rightarrow \frac{u’(x_0)}{v’(x_0)}$ as $x \rightarrow x_0$


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# Will the work be positive or negative if i move a positive test charge away from a positive point charge?

Assume we have apositive source charge And near it a positive test charge And we moved this test charge away from the source charge to a certain point, will the external work be positive or negative

• Hint: work done along path $C$ is given by $W = \int_{C} \vec{F} \cdot d\vec{s}$. In your case $\vec{F}$ is given by Coulomb's law, and $d\vec{s}$ is the infinitesimal displacement. – K_inverse Sep 10 '18 at 1:01


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# 3.1: Discrete Random Variables

Difficulty Level: At Grade Created by: CK-12

Learning Objectives

• Demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses.

You are in statistics class. Your teacher asks what the probability is of obtaining five heads if you were to toss 14 coins.

(a) Determine the theoretical probability for the teacher.

(b) Use the TI calculator to determine the actual probability for a trial experiment for 20 trials.

Work through Chapter 3 and then revisit this problem to find the solution.

Whenever you run and experiment, flip a coin, roll a die, pick a card, you assign a number to represent the value to the outcome that you get. This number that you assign is called a random variable. For example, if you were to roll two dice and asked what the sum of the two dice might be, you would design the following table of numerical values.

These numerical values represent the possible outcomes of the rolling of two dice and summing of the result. In other words, rolling one die and seeing a while rolling a second die and seeing a . Adding these values gives you a ten.

The rolling of a die is interesting because there are only a certain number of possible outcomes that you can get when you roll a typical die. In other words, a typical die has the numbers 1, 2, 3, 4, 5, and 6 on it and nothing else. A discrete random variable can only have a specific (or finite) number of numerical values.

A random variable is simply the rule that assigns the number to the outcome. For our example above, there are 36 possible combinations of the two dice being rolled. The discrete random variables (or values) in our sample are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12, as you can see in the table below.

We can have infinite discrete random variables if we think about things that we know have an estimated number. Think about the number of stars in the universe. We know that there are not a specific number that we have a way to count so this is an example of an infinite discrete random variable. Another example would be with investments. If you were to invest \$1000 at the start of this year, you could only estimate the amount you would have at the end of this year.

Well, how does this relate to probability?

Example 1: Looking at the previous table, what is the probability that the sum of the two dice rolled would be 4?

Solution:

Example 2: A coin is tossed 3 times. What are the possible outcomes? What is the probability of getting one head?

Solution:

If our first toss were a heads...

If our first toss were a tails...

Therefore the possible outcomes are:

Alternate Solution:

We have one coin and want to find the probability of getting one head in three tosses. We need to calculate two parts to solve the probability problem.

Numerator (Top)

In our example, we want to have 1 H and 2Ts. Our favorable outcomes would be any combination of HTT. The number of favorable choices would be:

Denominator (Bottom)

The number of possible outcomes

We now want to find the number of possible times we could get one head when we do these three tosses. We call these favorable outcomes. Why? Because these are the outcomes that we want to happen, therefore they are favorable.

Now we just divide the numerator by the denominator.

Remember:

Possible outcomes where number of tosses.

Here we have tosses. Therefore,

Possible outcomes

Possible outcomes

Possible outcomes

Possible outcomes

Note: The factorial function (symbol: !) just means to multiply a series of descending natural numbers.

Examples:

Note: It is generally agreed that . It may seem funny that multiplying no numbers together gets you 1, but it helps simplify a lot of equations.

Example 3: A coin is tossed 4 times. What are the possible outcomes? What is the probability of getting one head?

Solution:

If our first toss were a heads...

If our first toss were a tails...

Therefore there are 16 possible outcomes:

Alternate Solution:

We have one coin and want to find the probability of getting one head in four tosses. We need to calculate two parts to solve the probability problem.

Numerator (Top)

In our example, we want to have 1 H and 3 Ts. Our favorable outcomes would be any combination of HTTT. The number of favorable choices would be:

Denominator (Bottom)

The number of possible outcomes

We now want to find the number of possible times we could get one head when we do these four tosses (or our favorable outcomes).

Remember:

Possible outcomes where number of tosses.

Here we have tosses. Therefore,

Possible outcomes

Possible outcomes

Possible outcomes

Possible outcomes

Now we just divide the numerator by the denominator.

Technology Note:

Let’s take a look at how we can do this using the TI-84 calculators. There is an application on the TI calculators called the coin toss. Among others (including the dice roll, spinners, and picking random numbers), the coin toss is an excellent application for when you what to find the probabilities for a coin tossed more than 4 times or more than one coin being tossed multiple times.

Let’s say you want to see one coin being tossed one time. Here is what the calculator will show and the key strokes to get to this toss.

Let’s say you want to see one coin being tossed ten times. Here is what the calculator will show and the key strokes to get to this sequence. Try it on your own.

We can actually see how many heads and tails occurred in the tossing of the 10 coins. If you click on the right arrow (>) the frequency label will show you how many of the tosses came up heads.

We could also use randBin to simulate the tossing of a coin. Follow the keystrokes below.

This list contains the count of heads resulting from each set of 10 coin tosses. If you use the right arrow (>) you can see how many times from the 20 trials you actually had 4 heads.

Now let’s go back to our original chapter problem and see if we have gained enough knowledge to answer it.

You are in statistics class. Your teacher asks what the probability is of obtaining five heads if you were to toss 14 coins.

(a) Determine the theoretical probability for the teacher.

(b) Use the TI calculator to determine the actual probability for a trial experiment for 20 trials.

Solution:

(a) Let’s calculate the theoretical probability of getting 5 heads for the 14 tosses.

Numerator (Top)

In our example, we want to have 5 H and 9 Ts. Our favorable outcomes would be any combination of HHHHHTTTTTTTTT. The number of favorable choices would be:

Denominator (Bottom)

The number of possible outcomes

The number of possible outcomes

Now we just divide the numerator by the denominator.

The probability would be 12% of the tosses would have 5 heads.

b)

Looking at the data that resulted in this trial, there were 4 times of 20 that 5 heads appeared.

or 20%.

Lesson Summary

Probability in this chapter focused on experiments with random variables or the numbers that you assign to the probability of events. If we have a discrete random variable, then there are only a specific number of variables we can choose from. For example, tossing a fair coin has a probability of success for heads = probability of success for tails . Using tree diagrams or the formula , we can calculate the probabilities of these events. Using the formula requires the use of the factorial function where numbers are multiplied in descending order.

Points to Consider

• How is the calculator a useful tool for calculating probability in discrete random variable experiments?
• Are TREE Diagrams useful in interpreting the probability of simple events?

Vocabulary

Discrete Random Variables
Only have a specific (or finite) number of numerical values.
Random Variable
A variable that takes on numerical values governed by a chance experiment.
Factorial Function
(symbol: !) – The function of multiplying a series of descending natural numbers.
Theoretical Probability
A probability calculated by analyzing a situation, rather than performing an experiment, given by the ratio of the number of different ways an event can occur to the total number of equally likely outcomes possible. The numerical measure of the likelihood that an event, , will happen.

Tree Diagram
A branching diagram used to list all the possible outcomes of a compound event.

Review Questions

1. Define and give three examples of discrete random variables.
2. Draw a tree diagram to represent the tossing of two coins and determine the probability of getting at least one head.
3. Draw a tree diagram to represent the tossing of one coin three times and determine the probability of getting at least one head.
4. Draw a tree diagram to represent the drawing two marbles from a bag containing blue, green, and red marbles and determine the probability of getting at least one red.
5. Draw a tree diagram to represent the drawing two marbles from a bag containing blue, green, and red marbles and determine the probability of getting at two blue marbles.
6. Draw a diagram to represent the rolling two dice and determine the probability of getting at least one 5.
7. Draw a diagram to represent the rolling two dice and determine the probability of getting two 5s.
8. Use randBin to simulate the 6 tosses of a coin 20 times to determine the probability of getting two tails.
9. Use randBin to simulate the 15 tosses of a coin 25 times to determine the probability of getting two heads.
10. Calculate the theoretical probability of getting 4 heads for the 12 tosses.
11. Calculate the theoretical probability of getting 8 heads for the 10 tosses.
12. Calculate the theoretical probability of getting 8 heads for the 15 tosses.

2. .
3. (two 5's)
5. The number of possible outcomes The number of possible outcomes Now we just divide the numerator by the denominator.
6. The number of possible outcomes The number of possible outcomes Now we just divide the numerator by the denominator.

Answer Key for Review Questions (even numbers)

2.

4.

6.

(at least one 5)

8.

10.

The number of possible outcomes

The number of possible outcomes

Now we just divide the numerator by the denominator.

12.

The number of possible outcomes

The number of possible outcomes

Now we just divide the numerator by the denominator.

### Notes/Highlights Having trouble? Report an issue.

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text:
On the polynomiality of orbifold Gromov–Witten theory of root stacks

@article{Tseng2021OnTP,
title={On the polynomiality of orbifold Gromov–Witten theory of root stacks},
author={Hsian-hua Tseng and Fenglong You},
journal={Mathematische Zeitschrift},
year={2021},
volume={300},
pages={235-246}
}
• Published 1 January 2020
• Mathematics
• Mathematische Zeitschrift
In [ 25 ], higher genus Gromov–Witten invariants of the stack of r -th roots of a smooth projective variety X along a smooth divisor D are shown to be polynomials in r . In this paper we study the degrees and coefficients of these polynomials.
4 Citations
A new approach to the operator formalism for Gromov-Witten invariants of the cap and tube
• Mathematics
• 2021
Based on Johnson’s operator formula for the equivariant Gromov-Witten theory of P-orbifolds, we give a new approach to the operator formalism by Okounkov and Pandharipande regarding the
A Gromov-Witten theory for simple normal-crossing pairs without log geometry
• Mathematics
• 2020
We define a new Gromov-Witten theory relative to simple normal crossing divisors as a limit of Gromov-Witten theory of multi-root stacks. Several structural properties are proved including relative
A mirror theorem for multi-root stacks and applications.
• Mathematics
• 2020
Given a smooth projective variety $X$ with a simple normal crossing divisor $D:=D_1+D_2+...+D_n$, where $D_i\subset X$ are smooth, irreducible and nef. We prove a mirror theorem for multi-root stacks

References

SHOWING 1-10 OF 31 REFERENCES
Higher genus relative Gromov–Witten theory and double ramification cycles
• Mathematics
Journal of the London Mathematical Society
• 2020
We extend the definition of relative Gromov–Witten invariants with negative contact orders to all genera. Then we show that relative Gromov–Witten theory forms a partial CohFT. Some cycle relations
Curve counting in genus one: Elliptic singularities and relative geometry
• Mathematics
Algebraic Geometry
• 2021
We construct and study the reduced, relative, genus one Gromov-Witten theory of very ample pairs. These invariants form the principal component contribution to relative Gromov-Witten theory in genus
Orbifold Gromov-Witten Theory
• Mathematics
• 2001
In this article, we introduce the notion of good map and use it to establish Gromov-Witten theory for orbifolds.
Structures in genus‐zero relative Gromov–Witten theory
• Mathematics
Journal of Topology
• 2020
In this paper, we define genus‐zero relative Gromov–Witten invariants with negative contact orders. Using this, we construct relative quantum cohomology rings and Givental formalism. A version of
Higher genus relative and orbifold Gromov–Witten invariants
• Mathematics
Geometry & Topology
• 2020
Given a smooth target curve $X$, we explore the relationship between Gromov-Witten invariants of $X$ relative to a smooth divisor and orbifold Gromov-Witten invariants of the $r$-th root stack along
Double ramification cycles on the moduli spaces of curves
• Mathematics
• 2016
Curves of genus g$g$ which admit a map to P1$\mathbf {P}^{1}$ with specified ramification profile μ$\mu$ over 0∈P1$0\in \mathbf {P}^{1}$ and ν$\nu$ over ∞∈P1$\infty\in \mathbf {P}^{1}$ define a
A quantum Leray–Hirsch theorem for banded gerbes
• Mathematics
Journal of Differential Geometry
• 2021
For a gerbe $\Y$ over a smooth proper Deligne-Mumford stack $\B$ banded by a finite group $G$, we prove a structure result on the Gromov-Witten theory of $\Y$, expressing Gromov-Witten invariants of
Relative and orbifold Gromov-Witten invariants
• Mathematics
• 2010
We prove that genus zero Gromov--Witten invariants of a smooth scheme relative to a smooth divisor coincide with genus zero orbifold Gromov--Witten invariants of an appropriate root stack


text:
# The shortest distance between the line $\dpi{100} y-x = 1$ and the curve $\dpi{100} x=y^{2}$ is Option 1) $\frac{2\sqrt{3}}{8}$ Option 2) $\frac{3\sqrt{2}}{5}$ Option 3) $\frac{\sqrt{3}}{4}$ Option 4) $\frac{3\sqrt{2}}{8}$

As we learnt in

Perpendicular distance of a point from a line -

$\rho =\frac{\left | ax_{1}+by_{1}+c\right |}{\sqrt{a^{2}+b^{2}}}$

- wherein

$\rho$  is the distance from the line $ax+by+c=0$ .

Let (a2 , a) be a point on x = y2

Distance between (a2, a) and x- y+ 1= is

$\frac{a^{2}-a+1}{\sqrt{2}}= \frac{1}{\sqrt{2}}[(a-\frac{1}{2})^{2}+\frac{3}{4}]$

It is minimum when $a=\frac{1}{2}$

So minimum distance = $\frac{3}{4\sqrt{2}}$

Option 1)

$\frac{2\sqrt{3}}{8}$

This is incorrect.

Option 2)

$\frac{3\sqrt{2}}{5}$

This is incorrect.

Option 3)

$\frac{\sqrt{3}}{4}$

This is incorrect.

Option 4)

$\frac{3\sqrt{2}}{8}$

This is incorrect.

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text:
Thévenin and Norton Equivalents
Fall 2018

ECE 110

Course Notes

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Learn It!

Almost all electronic devices we use are "black boxes": we do not have to know what they contain or how exactly they work, but we do have to know how they will behave when we use them.

Figure 1

Fig. 1: Battery charger. This subcircuit is literally concealed in a black box with $+$ and $-$ terminals exposed. Inserting a battery pack as a load subcircuit completes the circuit. Image source.

A black box subcircuit is an unknown subcircuit that can be connected to another subcircuit. As long as we know how the unknown subcircuit behaves when it is connected to any other subcircuit, we can determine how the completed circuit operates. The information we need about the unknown subcircuit is its I-V characteristic because we can use it to find the completed circuit's operating point using the load line method.

Figure 2

Fig. 2: Black box subcircuit. The contents of this subcircuit are unknown, but the subcircuit can be used predictably if the I-V characteristic across its terminals is known.

If two subcircuits have identical I-V characteristics, they behave exactly the same from the point of view of a connected subcircuit, so we say they are equivalent. The Thévenin theorem states that any black box subcircuit containing exclusively sources and resistors is equivalent to a subcircuit containing a voltage source in series with a resistor.

Figure 3

Fig. 3: Thévenin equivalent subcircuit. This subcircuit is equivalent to an unknown subcircuit (like the one in Fig. 2) made exclusively of sources and resistors for appropriate values of Thévenin voltage $V_T$ and effective resistance $R_{\text{eff}}$.

The Norton theorem states that any black box subcircuit containing exclusively sources and resistors is equivalent to a subcircuit containing a current source in parallel with a resistor.

Figure 4

Fig. 4: Norton equivalent subcircuit. This subcircuit is equivalent to an unknown subcircuit (like the one in Fig. 2) made exclusively of sources and resistors for appropriate values of Norton current $I_N$ and effective resistance $R_{\text{eff}}$.

The Thévenin and Norton equivalent subcircuits are also equivalent to each other for appropriate values of $V_T$, $I_N$ and $R_{\text{eff}}$. Note that the effective resistance $R_{\text{eff}}$ is the same value for both of these subcircuits.

The following table describes how to find the values of $V_T$, $I_N$ and $R_{\text{eff}}$ from the unknown subcircuit.

Value Diagram/Equation Method
$V_T$
• Keep the terminals of the unknown subcircuit open (i.e. disconnected) so that the open-circuit current $I_{\text{oc} }=0$.
• Find the open-circuit voltage $V_{\text{oc} }$ across the terminals. Note that $V_{\text{oc} }$ can be measured in lab using a voltmeter across the terminals since an ideal voltmeter's infinite resistance keeps the circuit open.
• Set $V_T=V_{\text{oc} }$.
$I_N$
• Short the terminals of the unknown subcircuit so that the short-circuit voltage $V_{\text{sc} }=0$.
• Find the short-circuit current $I_{\text{sc} }$ between the terminals. Note that $I_{\text{sc} }$ can be measured in lab using an ammeter across the terminals since an ideal ammeter's zero resistance shorts the circuit.
• Set $I_N=I_{\text{sc} }$.
$R_{\text{eff} }$
$V_T$, $I_N$ or $R_{\text{eff} }$ $R_{\text{eff}}=\frac{V_T}{I_N}$ Given any two of $V_T$, $I_N$ and $R_{\text{eff} }$, solve $R_{\text{eff}}=V_T/I_N$ to find the other one.
Table 1: Methods for finding Thévenin and Norton equivalent subcircuit values.

Most of the results in Table 1 can be derived by comparing the I-V characteristic of an unknown subcircuit consisting of sources and resistors with those of the Thévenin and Norton subcircuits.

Subcircuit Schematic I-V Characteristic Explanation
Unknown subcircuit Any subcircuit containing exclusively sources and resistors has a linear I-V characteristic. This line has $V$-intercept equal to $V_{\text{oc} }$ since $I_{\text{oc} }=0$, and it has $I$-intercept equal to $I_{\text{sc} }$ since $V_{\text{sc} }=0$. Therefore, the slope is $-I_{\text{sc} }/V_{\text{oc} }$.
Thévenin subcircuit This line is the I-V characteristic of a voltage source and resistor in series.
Norton subcircuit This line is the I-V characteristic of a current source and resistor in parallel.
Table 2: Comparison of I-V characteristics of unknown, Thévenin and Norton subcircuits.

For the three subcircuits in Table 2 to be equivalent, their I-V characteristics must be identical. Therefore, we equate the intercepts and slopes to obtain three of the results in Table 1.
\begin{align}
V_T&=V_{\text{oc} } & & \text{by equating }V\text{-intercepts} \label{TNE:EQ1}\\
I_N&=I_{\text{sc} } & & \text{by equating }I\text{-intercepts} \label{TNE:EQ2} \\
R_{\text{eff}}&=\frac{V_{\text{oc}}}{I_{\text{sc}}}=\frac{V_T}{I_N} & & \text{by equating slopes} \label{TNE:EQ3}
\end{align}
Note that, in Table 2, we chose to label the voltage drop $V$ across the terminals with $+$ label at the top and $-$ label at the bottom and we chose to label the current $I$ with current arrow label pointing out of the terminal at the top. These choices are consistent with the labeling in Fig. 2 to Fig. 4 and in Table 1. If $V$ and $I$ are labeled differently, then the I-V characteristics appear horizontally and/or vertically flipped and some of the equations $\eqref{TNE:EQ1}$ to $\eqref{TNE:EQ3}$ change sign. It is better to reason about the labeling and signs than to try to memorize formulas and that is why we do not list all the cases.

We have seen that Thévenin and Norton equivalents can represent unknown subcircuits, but they can also be used to simplify known subcircuits. Consider two subcircuits connected together as shown below.

Figure 5

Fig. 5: Circuit consisting of two subcircuits. Either of the known subcircuits can be replaced by a simpler Thévenin or Norton equivalent without changing the behavior of the other known subcircuit.

The table below gives example procedures for determining the Thévenin and Norton equivalents of the two subcircuits in Fig. 5.

Step Subcircuit 1 Subcircuit 2
Draw known subcircuit
Find one of the values $V_T$, $I_N$ or $R_{\text{eff} }$
Find another value out of $V_T$, $I_N$ or $R_{\text{eff} }$
Find the remaining value $V_T$, $I_N$ or $R_{\text{eff} }$ $I_N=\frac{V_T }{R_{\text{eff} } }=\frac{3 \text{ V}}{2\text{ k}\Omega} =\frac{3}{2} \text{ mA}$ $V_T=I_N R_{\text{eff} }=\left( 2 \text{ mA} \right)\left( 5\text{ k}\Omega \right)= 10\text{ V}$
Draw Thévenin equivalent
Draw Norton equivalent

Explore More!


text:
# IEEE Sensors Journal

## Filter Results

Displaying Results 1 - 25 of 34
• ### Table of contents

Publication Year: 2007, Page(s): C1
| PDF (106 KB)
• ### IEEE Sensors Journal publication information

Publication Year: 2007, Page(s): C2
| PDF (36 KB)
• ### Table of contents

Publication Year: 2007, Page(s):313 - 314
| PDF (46 KB)
• ### Search Strategy Optimization for Intruder Detection

Publication Year: 2007, Page(s):315 - 316
Cited by:  Papers (1)
| | PDF (95 KB) | HTML

Sensors can take advantage of environmental information to sweep for a moving intruder in a manner that will look random to an intruder, but that will maximize the probability of detection. We show how likelihood information about intrusion from particular sectors can be used to design a sweep strategy View full abstract»

• ### Photonic Demodulator With Sensitivity Control

Publication Year: 2007, Page(s):317 - 318
Cited by:  Papers (11)  |  Patents (5)
| | PDF (511 KB) | HTML

A current assisted photonic demodulator for use as a pixel in a 3-D time-of-flight imager shows nearly 100% static demodulator contrast and is operable beyond 30 MHz. An integrated tunable sensitivity control is also presented for increasing the distance measurement range and avoiding unwanted saturation during integration periods. This is achieved by application of a voltage on a dedicated drain ... View full abstract»

• ### Using Environmental Models to Optimize Sensor Placement

Publication Year: 2007, Page(s):319 - 320
Cited by:  Papers (10)
| | PDF (130 KB) | HTML

Sensors used in protective applications are conventionally placed on perimeters or over areas in an evenly distributed pattern. However, such patterns may actually be suboptimal, since environmental factors may make some forms of attack more or less likely than others. We describe a protective application of sensors for detecting underwater threats in an urban estuary environment. We demonstrate t... View full abstract»

• ### Dual-Channel Quartz-Crystal Microbalance for Sensing Under UV Radiation

Publication Year: 2007, Page(s):321 - 322
Cited by:  Papers (2)
| | PDF (367 KB) | HTML

In situ measurements of interfacial phenomena with subatomic resolution under environmental disturbances have been a major goal of engineers and scientists engaged in the development of a microbalance sensor. Here, we demonstrate in situ measurements of the photooxidization process of alkanethiol self-assembled monolayers using dual-channel quartz-crystal microbalance (D-QCM) sensor that uses sphe... View full abstract»

• ### Sol-Gel Synthesis of Palladium-Doped Silica Nanocomposite Fiber Using Triton X-100 Micelle Template and the Application for Hydrogen Gas Sensing

Publication Year: 2007, Page(s):323 - 328
Cited by:  Papers (6)
| | PDF (1485 KB) | HTML

Palladium-doped silica nanocomposites were synthesized via a sol-gel technique combined with a template of Triton X-100 micelle. The freshly prepared sol sample of Pd-doped silica nanocomposites was investigated by TEM. Determined from the TEM image, the sizes of the Pd nanoparticles are narrowly distributed, which are around 30 nm in diameter. The prepared sol solution of the sample was injected ... View full abstract»

• ### Solvent Detection and Water Monitoring With a Macroporous Silicon Field-Effect Sensor

Publication Year: 2007, Page(s):329 - 335
Cited by:  Papers (10)
| | PDF (1221 KB) | HTML

Integration of electrical and fluidic systems for the design and fabrication of a system-on-chip (SOC) capable of sensing various liquid phase solvents is reported. A monolithic integration strategy makes use of macroporous silicon (MPS) as a gateway to interface the electrical and fluidic domains. In this application, the MPS material, acting as a sensing membrane, is used in a flow-through struc... View full abstract»

• ### Numerical Development of ZnO/Quartz Love Wave Structure for Gas Contamination Detection

Publication Year: 2007, Page(s):336 - 341
Cited by:  Papers (7)
| | PDF (220 KB) | HTML

Love wave structures are encouraging devices for sensing applications in gaseous or liquid media because of their high sensitivity. In this paper, we first investigate basic properties of a ZnO/quartz Love wave device by the use of theoretical considerations in order to get a good gas sensor. Second, experimental results of the developed structure, ZnO(2.1 mum)/90deg ST-cut quartz, confirm the sui... View full abstract»

• ### 2-D Wavelet Segmentation in 3-D T-Ray Tomography

Publication Year: 2007, Page(s):342 - 343
Cited by:  Papers (19)
| | PDF (284 KB) | HTML

In this letter, segmentation techniques for terahertz (T-ray) computed tomographic (CT) imaging are investigated. A set of linear image fusion and novel wavelet scale correlation segmentation techniques is adopted to achieve material discrimination within a 3-D object. The methods are applied to a T-ray CT image dataset taken from a plastic vial containing a plastic tube. This setup simulates the ... View full abstract»

• ### Calibration of Multi-Axis MEMS Force Sensors Using the Shape-From-Motion Method

Publication Year: 2007, Page(s):344 - 351
Cited by:  Papers (33)
| | PDF (949 KB) | HTML

Precise calibration of multi-axis microelectromechanical systems (MEMS) force sensors is difficult for several reasons, including the need to apply many known force vectors at precise orientations at the micro- and nanoNewton (nN) force scales, and the risk of damaging the small, fragile microdevices. To tackle these challenges, this paper introduces the shape-from-motion calibration method. A new... View full abstract»

• ### Measurements of the Degree of Comprehensive Cooling in Stochastically Quenched Microstructures

Publication Year: 2007, Page(s):352 - 360
Cited by:  Papers (1)
| | PDF (2421 KB) | HTML

We clarify the atomistic behavior of a micromechanical structure whose thermally driven stochastic motion has been quenched, using force-feedback techniques. The quenching is observed, via both qualitative and quantitative measurements, to optically clamp one of the vibrational modes of the lever such that the overall body temperature is only reduced slightly. The degree of comprehensive cooling i... View full abstract»

• ### Biomimetic Sonar and Neuromorphic Processing Eliminate Reverberation Artifacts

Publication Year: 2007, Page(s):361 - 369
Cited by:  Papers (16)
| | PDF (1174 KB) | HTML

A biomimetic sonar is configured using two conventional sensors that generate point processes related to echo waveform intensity, resembling biological action potential spikes. The sensors point slightly outward from the sonar axis, similar to pinnae in some bats, to acquire slightly different views of the environment during a rotational scan. Artifacts in sonar maps are points that do not relate ... View full abstract»

• ### Nonlinear Dynamic Analysis of Electrostatically Actuated Resonant MEMS Sensors Under Parametric Excitation

Publication Year: 2007, Page(s):370 - 380
Cited by:  Papers (64)  |  Patents (9)
| | PDF (1190 KB) | HTML

Electrostatically actuated resonant microelectromechanical systems (MEMS) sensors have gotten significant attention due to their geometric simplicity and broad applicability. In this paper, nonlinear responses and dynamics of the electrostatically actuated MEMS resonant sensors under two-frequency parametric and external excitations are presented. The presented model and methodology enable simulat... View full abstract»

• ### Analysis of Nonideal Effects on a Tomography-Based Switched-Capacitor Transducer

Publication Year: 2007, Page(s):381 - 391
Cited by:  Papers (5)
| | PDF (872 KB) | HTML

This paper presents a nonideal analysis of a fully-integrated switched-capacitor capacitive transducer for electrical capacitance tomography system. The investigation establishes different types of error source models as well as practical mismatch effects in the derivation of second-order analytical expressions. The analyses are conducted on the basis of heavy stray capacitances of 150 pF typicall... View full abstract»

• ### Optimal Estimation of the Acceleration of a Car Under Performance Tests

Publication Year: 2007, Page(s):392 - 400
Cited by:  Papers (7)
| | PDF (787 KB) | HTML

In this paper, a recursive least-squares lattice (RLSL) adaptive filter was used to carry out the optimal estimation of the relevant signal coming from an accelerometer placed in car under performance tests. Here, the signal of interest is buried in a broadband noise background where we have little knowledge of the noise characteristics. In addition, due to the fact that the noise and the relevant... View full abstract»

• ### A Novel Needle-Type SV-GMR Sensor for Biomedical Applications

Publication Year: 2007, Page(s):401 - 408
Cited by:  Papers (20)
| | PDF (1676 KB) | HTML

Cancer is the most deadly disease in the world today. There is a variety of different treatment methods for cancer, including radiotherapy and chemotherapy with anticancer drugs that have been in use over a long period of time. Hyperthermia is one of the cancer treatment methods that utilizes the property that cancer cells are more sensitive to temperature than normal cells. The control of tempera... View full abstract»

• ### Agarose-Gel Based Guided-Mode Resonance Humidity Sensor

Publication Year: 2007, Page(s):409 - 414
Cited by:  Papers (18)  |  Patents (2)
| | PDF (367 KB) | HTML

A photonic relative-humidity (RH) sensor employing the guided-mode resonance effect is designed, fabricated, and characterized. An agarose-gel transduction layer is integrated with a periodic silicon-nitride film to form a sensitive optical resonance structure. As the agarose-gel humidifies, the resonance wavelength shifts. Comparison with rigorous diffraction models allows quantification of the g... View full abstract»

• ### Detection of Chemiluminescence Using an Amorphous Silicon Photodiode

Publication Year: 2007, Page(s):415 - 416
Cited by:  Papers (28)
| | PDF (166 KB) | HTML

A hydrogenated amorphous silicon photodiode is used for the integrated, real-time detection of chemiluminescent reactions in solution. The light emission at 425 nm, resulting from the horseradish peroxidase-catalyzed oxidation of luminol, is detected by a p-i-n amorphous silicon photodiode operated at zero bias. The sensitivity achieved is in the range of nanomole of horseradish peroxidase per lit... View full abstract»

• ### An Optical Thermometer Exploiting Periodically Poled Lithium Niobate for Monitoring the Pantographs of High-Speed Trains

Publication Year: 2007, Page(s):417 - 425
Cited by:  Papers (2)
| | PDF (950 KB) | HTML

Optical thermometers have been widely investigated. Here, the temperature behavior of second harmonic generation (SHG) in periodically poled lithium niobate (PPLN) substrates is analyzed; indeed, the QPM tuning in PPLN devices and the obtained SHG efficiency depend on the crystal thermal expansion and dispersion, particularly in the case of guided propagation. Therefore, such devices are suitable ... View full abstract»

• ### A Multimodal Tomography System Based on ECT Sensors

Publication Year: 2007, Page(s):426 - 433
Cited by:  Papers (44)  |  Patents (3)
| | PDF (993 KB) | HTML

A new noninvasive system for multimodal electrical tomography based on electrical capacitance tomography (ECT) sensor hardware is proposed. Quasistatic electromagnetic fields are produced by ECT sensors and used for interrogating the sensing domain. The new system is noninvasive and based on capacitance measurements for permittivity and power balance measurements for conductivity (impedance) imagi... View full abstract»

• ### Ammonia Sensing Resistors Based on ${\rm Fe}_{2}{\rm O}_{3}$-Modified ZnO Thick Films

Publication Year: 2007, Page(s):434 - 439
Cited by:  Papers (15)
| | PDF (1242 KB) | HTML

Thick films of ZnO were prepared by a screen printing technique. Unmodified ZnO thick film was almost insensitive to NH3. ZnO thick films were surface modified with Fe3+ by dipping them into an aqueous solution of ammonium ferric sulfate for different intervals of time and fired at 500degC for 24 h. The ammonium ferric sulfate would transform into ferric oxide Fe2O... View full abstract»

• ### On-Chip Capacitance Sensing for Cell Monitoring Applications

Publication Year: 2007, Page(s):440 - 447
Cited by:  Papers (51)  |  Patents (3)
| | PDF (1921 KB) | HTML

We describe an integrated circuit for sensing the substrate coupling capacitance of anchorage-dependent living cells in a standard culture environment. Capacitance is measured using charge redistribution in response to weak, low frequency electric field excitations. The underlying biophysical phenomenon results primarily from the insulating nature of the cell structure and the counterionic polariz... View full abstract»

• ### Low–Temperature Hydrogen Sensors Based on Au Nanoclusters and Schottky Contacts on ZnO Films Deposited by Pulsed Laser Deposition on Si and ${\hbox{SiO}}_{2}$ Substrates

Publication Year: 2007, Page(s):448 - 454
Cited by:  Papers (22)
| | PDF (1609 KB) | HTML

Unintentionally doped n-type ZnO thin films deposited on Si and SiO2 substrates by pulsed laser deposition (PLD) techniques, were functionalized as H2 gas sensors by a) incorporating Au nanoclusters in the surface, and b) developing Au Schottky diodes on ZnO. The influence of the catalytic action of the Au nanoclusters on the sensing properties of the devices was examined and... View full abstract»

## Aims & Scope

The IEEE Sensors Journal is a peer-reviewed, semi-monthly online journal devoted to sensors and sensing phenomena.

Full Aims & Scope

## Meet Our Editors

Editor-in-Chief
Sandro Carrara
École Polytechnique Fédérale de Lausanne (EPFL)
Lausanne, CH-1015 Switzerland
sandro.carrara@epfl.ch


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# Tag Info

Let's recap: upper indices are vectors ($x^\mu$), the inner product on Minkowski space is given by $g_{\mu \nu}$ so "dual vectors" have lower indices $x_\nu = g_{\nu \rho} x^\rho.$ Then you see that a matrix (in the sense of linear map between vectors) has one upper and one lower index, because it maps a vector to another vector: $$x^\mu \mapsto ... 2 I) Pragmatically speaking, the most important property of \sqrt{-g} for model building purposes, is not per se the fact that \sqrt{-g}d^{4}x measures the volume element of a 4-dimensional Parallelepiped with infinitesimal edges dx^0, \ldots, dx^3. II) A more important property is that \sqrt{-g}d^{4}x transforms as a scalar (i.e. is invariant) under ... 4 A variation of a tensor is always a tensor and the formula for the value above doesn't show otherwise. What you probably find surprising is that \delta g_{\mu\nu} and \delta g^{\rho\sigma} are not related to each other by simply raising the indices \mu,\nu or lowering the indices \rho,\sigma. Indeed, they're not related in this way. In this case, ... 3 A perfect fluid is defined by the property that, in the local rest frame, it allows no energy fluxes and no anisotropic stresses. Thus, at a given space-time point, in the local rest frame [in which the components of the 4-velocity are u^{\alpha} = (1, 0, 0, 0)^{\mathsf{T}}], the energy momentum tensor components are T^{\alpha\beta} = \mathrm{diag}(e, p, ... 3 First off, please don't use units with c\ne 1 in GR. It makes everything horribly messy. What we normally think of as a ruler or clock measurement is represented in GR by an upper index quantity like \Delta x^\mu. Therefore in a Cartesian coordinate system in the fluid's rest frame, we are guaranteed that u^\mu=(1,0,0,0), not (-1,0,0,0). This is ... 1 As soon as you get something like \delta_{bd}, alarm bells should ring, as this is not a tensor. The inverse metric g^{ac} is defined by the identity$$ g^{ac}g_{cb} = \delta^a_b $$If you plug this into your expression (and use the fact that g is symmetric), you will obtain the correct equation. 0 It can be show easily by the next reasoning.$$ DA_{i} = g_{ik}DA^{k}, $$because DA_{i} is a vector (according to the definition of covariant derivative). On the other hand,$$ DA_{i} = D(g_{ik}A^{k}) = g_{ik}DA^{k} + A^{k}Dg_{ik}. $$So,$$ g_{ik}DA^{k} + A^{k}Dg_{ik} = g_{ik}DA^{k} \Rightarrow Dg_{ik} = 0.  So, it isn't a condition, it is a ...
The elements of this particular metric tensor do not depend on time. $dx^j$ and $dt$ are treated as constants when you take the time derivative. You should also have $\Gamma^{\lambda}_{00} = -\frac{1}{2} g^{\nu \lambda} \frac{\partial g_{00}}{\partial x^\nu}$.