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# Worksheet on Venn diagrams

Question 1
if U = {1,2,3,4,5,6,7,8,9,10}  , A ={1,2,3,4} , B={3,4,5,6}  and C ={2,3,6,7}
Show these on Venn diagram
a.  $A - B$
b. $B - A$
c. $A \cap B \cap C$
d. $A \cup B \cup C$
e. $A \cup C$
f. $B \cup C$
Solution
Here is the Venn diagram

a. A -B

A -B ={1,2}
b. B -A

B -A  ={5,6}
c. $A \cap B \cap C$

$A \cap B \cap C$
={3}
d. $A \cup B \cup C$

$A \cup B \cup C$
=={1,2,3,4,5,6,7}
e. $A \cup C$

$A \cup C$ ={1,2,3,4,5,6}
f. $B \cup C$

$B \cup C$={2,3,4,5,6,7}

Question 2
Draw the Venn diagrams to illustrate the following relationship among sets E, M and U, where E is the set of students studying English in a school, M is the set of students studying Mathematics in the same school, U is the set of all students in that school.
(i) All the students who study Mathematics study English, but some students who study English do not study Mathematics.
(ii) There is no student who studies both Mathematics and English.
(iii) Some of the student’s study Mathematics but do not study English, some study English but do not study Mathematics, and some study both.
(iv) Not all students study Mathematics, but every student studying English studies Mathematics.
Solution
(i)
Since all the students who study mathematics study English, but some students who study English do not study Mathematics. Therefore, M ⊂ E ⊂ U Thus the Venn Diagram is

(ii) Since there is no student who study both English and Mathematics Hence,
E ∩ M = φ.

(iii) Since there are some students who study both English and Mathematics, some English only and some Mathematics only.

(iv) Since every student studying English studies Mathematics. Hence, E ⊂ M ⊂ U

Question 3

a. $A^c \cap B^c$
b. $A \cap B^c$
c. $A^c \cap B$
Solution
a.

b.

c.

Question 4

Study the above Venn diagram and answer below questions
a.  $A \cap B \cap C$
b. $A \cap B$, $B \cap C$
c. $A^c \cap B$
d. $A \cup B \cup C$
e. $A^c \cap B^c \cap C^c$
Solution
a. {8,15}
b. {9,18,8,15}
{6,15,16}
c. {4,10,16}
d. {1,2,3,4,8,9,10,11,12,15,16,18}
e. {5,6,713,14,17,19,20}

Question 5
Study the below Venn diagram

(i)  A and B are disjoint sets. True or False
(ii) $A \cap B$ is an empty set. True or False
(iii) Find the value of $A \cup B$
Solution
(i) True
(ii) True
(iii) {a, b,c,d,e,p,q,r,s}

Question 6
Draw the Venn diagram
a. U = {x: x is a natural number and x < 20}
P = {1,2,3,4,5,6,7}
Q = {2,3,4}
b.  N = {x: x is a natural number}
W = {x: x is whole number}
U = {x: x is a set of real numbers}
c. U = {people who live in India};
V = {people who live in Uttar Pradesh}
W= {people who live in Lucknow}
X= {People who live in Hyderabad}
d.
X = Set of natural numbers,
Y = Set of prime numbers and
Z = Set of even prime numbers.

## Related Topics

Notes Assignments


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# Power series

1. Aug 4, 2003

### iceman

Hello, can anyone help me on this one? I am finding problem pretty tricky indeed.

I know the power series (or Taylor series) for cosx is

1-x^2/2!+x^4/4!-x^6/6!+... (It is convergent for all element x is a member of set R)

Q) Write down the power series for cos(u^2) up to the u^24 term.

2. Aug 4, 2003

Staff Emeritus
First write the cos(x) series you know. Then plug in u^2 for each x in the series. What will that do to the powers of u? What will it do to the coefficients? After you answer those questions try this. What will be the factorial in the denominator when the power of u is 24?

format: plain


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# mean and variance of a gaussian filter mask

This topic is 4757 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

i have a 3 x 3 gaussian filter mask: 1 2 1 2 4 2 1 2 1 does anyone know how to calculate mean and variance of this mask ? thanks, markus

##### Share on other sites
Maybe I'm wrong, but it is a 2d discrete function, so the mean is:

double mean,s=0;int x,y;for (x=0;x<3;x++)   for (y=0;y<3;y++)      s+=filter[x][y];mean=s/9.0;

Variance is:
double v,s=0;int x,y;for (x=0;x<3;x++)   for (y=0;y<3;y++)   {      double diff=(filter[x][y]-mean);      s+=diff*diff;   }}v=s/9.0;

Hope this is right and helps.


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#### Setting Players' Behaviors in World of Warcraft through Semi-Supervised Learning

##### Marcelo Souza Nery, Roque Anderson Teixeira, Victor do Nascimento Silva, Adriano Alonso Veloso

Digital games are one of the major and most important fields on the entertainment domain, which also involves cinema and music. Numerous attempts have been done to improve the quality of the games including more realistic artistic production and computer science. Assessing the player's behavior, a task known as player modeling, is currently the need of the hour which leads to possible improvements in terms of: (i) better game interaction experience, (ii) better exploitation of the relationship between players, and (iii) increasing/maintaining the number of players interested in the game. In this paper we model players using the basic four behaviors proposed in \cite{BartleArtigo}, namely: achiever, explorer, socializer and killer. Our analysis is carried out using data obtained from the game "World of Warcraft" over 3 years (2006 $-$ 2009). We employ a semi-supervised learning technique in order to find out characteristics that possibly impact player's behavior.

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Safe, fallen down this way, I want to be just what I am.safe at lastmore quotes

DNA on 10th — street art, wayfinding and font

# visualization + design

The 2019 Pi Day art celebrates digits of $\pi$ with hundreds of languages and alphabets. If you're a kid at heart—rejoice—there's a special edition for you!

# $\pi$ Day 2014 Art Posters

2019 $\pi$ has hundreds of digits, hundreds of languages and a special kids' edition.
2018 $\pi$ day
2017 $\pi$ day
2016 $\pi$ approximation day
2016 $\pi$ day
2015 $\pi$ day
2014 $\pi$ approx day
2014 $\pi$ day
2013 $\pi$ day
Circular $\pi$ art

On March 14th celebrate $\pi$ Day. Hug $\pi$—find a way to do it.

For those who favour $\tau=2\pi$ will have to postpone celebrations until July 26th. That's what you get for thinking that $\pi$ is wrong. I sympathize with this position and have $\tau$ day art too!

If you're not into details, you may opt to party on July 22nd, which is $\pi$ approximation day ($\pi$ ≈ 22/7). It's 20% more accurate that the official $\pi$ day!

Finally, if you believe that $\pi = 3$, you should read why $\pi$ is not equal to 3.

All art posters are available for purchase.
I take custom requests.

For the 2014 $\pi$ day, two styles of posters are available: folded paths and frequency circles.

The folded paths show $\pi$ on a path that maximizes adjacent prime digits and were created using a protein-folding algorithm.

The frequency circles colourfully depict the ratio of digits in groupings of 3 or 6. Oh, look, there's the Feynman Point!

## frequency circles of $pi$

Some of the posters for this year's Pi Day art expand on the work from last year, which showed Pi as colored circles on a grid.

For those of you who really liked this minimalist depiction of π , I've created something slightly more complicated, but still stylish: Pi digit frequency circles. These are pretty and easy to understand. If you like random distribution of colors (and circles), these are your thing.

Briefly, each set of concentric rings corresponds to a sequence of digits in π , such as 3 ($314 159 265 ...$) or 6 ($314159 265358 ...$). The number of times a given digit is seen within a sequence is encoded by the thickness of the ring. Rings are ordered outward in numerical order of their digits (i.e. 0 on the inside, 9 on the outside).

For some posters, the first digit (3) is offset from the rest of the groups. Look for the high count of 9s at the end of posters showing π up to the Feynman Point (6 9s at digit 762). For posters that show more digits, try to find the Feynman Point somewhere among the groups.

The Feynman point is at an extremely interesting location. If we group the digits of π into groups of 6, then the first $999999$ falls exactly into the 128th group. But, if we group the digits by 3s, then the two groups $999$ and $999$ fall exactly into groups 255 and 256 (a power of 2!), which can be arranged into a perfect square of 16 x 16 groups.

The Feynman point is a specific case of the general case in which the digit d appears n times in a row. I call this the (d=7,n=6) and provide a list of all these points in the first 1,000,000 digits. Points with a large n value will contribute significantly to the frequency distribution of the digit group they fall in. If the sequence is split across groups, its impact is lower.

When split into groups of 4, with the first digit offset, the Feynman point falls into two groups 4999 and 9998. (zoom)
Constructing frequency circles | Frequency distributions of digits in short sequences are turned into stacked ring plots. (zoom)
VIEW ALL

# Genome Sciences Center 20th Anniversary Clothing, Music, Drinks and Art

Tue 28-01-2020

Science. Timeliness. Respect.

Read about the design of the clothing, music, drinks and art for the Genome Sciences Center 20th Anniversary Celebration, held on 15 November 2019.

Luke and Mayia wearing limited edition volunteer t-shirts. The pattern reproduces the human genome with chromosomes as spirals. (zoom)

As part of the celebration and with the help of our engineering team, we framed 48 flow cells from the lab.

Precisely engineered frame mounts of flow cells used to sequence genomes in our laboratory. (zoom)

Each flow cell was accompanied by an interpretive plaque explaining the technology behind the flow cell and the sample information and sequence content.

The plaque at the back of one of the framed Illumina flow cell. This one has sequence from a patient's lymph node diagnosed with Burkitt's lymphoma. (zoom)

# Scientific data visualization: Aesthetic for diagrammatic clarity

Mon 13-01-2020

The scientific process works because all its output is empirically constrained.

My chapter from The Aesthetics of Scientific Data Representation, More than Pretty Pictures, in which I discuss the principles of data visualization and connect them to the concept of "quality" introduced by Robert Pirsig in Zen and the Art of Motorcycle Maintenance.

# Yearning for the Infinite — Aleph 2

Mon 18-11-2019

Discover Cantor's transfinite numbers through my music video for the Aleph 2 track of Max Cooper's Yearning for the Infinite (album page, event page).

Yearning for the Infinite, Max Cooper at the Barbican Hall, London. Track Aleph 2. Video by Martin Krzywinski. Photo by Michal Augustini. (more)

I discuss the math behind the video and the system I built to create the video.

# Hidden Markov Models

Mon 18-11-2019

Everything we see hides another thing, we always want to see what is hidden by what we see.
—Rene Magritte

A Hidden Markov Model extends a Markov chain to have hidden states. Hidden states are used to model aspects of the system that cannot be directly observed and themselves form a Markov chain and each state may emit one or more observed values.

Hidden states in HMMs do not have to have meaning—they can be used to account for measurement errors, compress multi-modal observational data, or to detect unobservable events.

Nature Methods Points of Significance column: Hidden Markov Models. (read)

In this column, we extend the cell growth model from our Markov Chain column to include two hidden states: normal and sedentary.

We show how to calculate forward probabilities that can predict the most likely path through the HMM given an observed sequence.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Hidden Markov Models. Nature Methods 16:795–796.

Altman, N. & Krzywinski, M. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.

# Hola Mundo Cover

Sat 21-09-2019

My cover design for Hola Mundo by Hannah Fry. Published by Blackie Books.

Hola Mundo by Hannah Fry. Cover design is based on my 2013 $\pi$ day art. (read)

Curious how the design was created? Read the full details.

# Markov Chains

Tue 30-07-2019

You can look back there to explain things,
but the explanation disappears.
You'll never find it there.
Things are not explained by the past.
They're explained by what happens now.
—Alan Watts

A Markov chain is a probabilistic model that is used to model how a system changes over time as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another.

Nature Methods Points of Significance column: Markov Chains. (read)

Together with the states, these transitions probabilities define a stochastic model with the Markov property: transition probabilities only depend on the current state—the future is independent of the past if the present is known.

Once the transition probabilities are defined in matrix form, it is easy to predict the distribution of future states of the system. We cover concepts of aperiodicity, irreducibility, limiting and stationary distributions and absorption.

This column is the first part of a series and pairs particularly well with Alan Watts and Blond:ish.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.


text:
For a socket or context using the sub protocol in a publisher/subscriber pattern. Remove a topic from the subscription list.

unsubscribe(con, topic = NULL)

# S3 method for nanoSocket
unsubscribe(con, topic = NULL)

# S3 method for nanoContext
unsubscribe(con, topic = NULL)

## Arguments

con

a Socket or Context using the 'sub' protocol.

topic

[default NULL] an atomic type or NULL. The default NULL unsubscribes from all topics (if all topics were previously subscribed).

## Value

Invisibly, an integer exit code (zero on success).

## Details

Note that if the topic was not previously subscribed to then an 'entry not found' error will result.

To use pub/sub the publisher must:

• specify mode = 'raw' when sending.

• ensure the sent vector starts with the topic.

The subscriber should then receive specifying the correct mode.

## Examples

pub <- socket("pub", listen = "inproc://nanonext")
sub <- socket("sub", dial = "inproc://nanonext")

subscribe(sub, NULL)

send(pub, c("examples", "this is an example"), mode = "raw")
#>  [1] 65 78 61 6d 70 6c 65 73 00 74 68 69 73 20 69 73 20 61 6e 20 65 78 61 6d 70
#> [26] 6c 65 00
recv(sub, "character")
#> $raw #> [1] 65 78 61 6d 70 6c 65 73 00 74 68 69 73 20 69 73 20 61 6e 20 65 78 61 6d 70 #> [26] 6c 65 00 #> #>$data
#> [1] "examples"           "this is an example"
#>
send(pub, "examples will also be received", mode = "raw")
#>  [1] 65 78 61 6d 70 6c 65 73 20 77 69 6c 6c 20 61 6c 73 6f 20 62 65 20 72 65 63
#> [26] 65 69 76 65 64 00
recv(sub, "character")
#> $raw #> [1] 65 78 61 6d 70 6c 65 73 20 77 69 6c 6c 20 61 6c 73 6f 20 62 65 20 72 65 63 #> [26] 65 69 76 65 64 00 #> #>$data
#> [1] "examples will also be received"
#>
unsubscribe(sub, NULL)
send(pub, c("examples", "this example will not be received"), mode = "raw")
#>  [1] 65 78 61 6d 70 6c 65 73 00 74 68 69 73 20 65 78 61 6d 70 6c 65 20 77 69 6c
#> [26] 6c 20 6e 6f 74 20 62 65 20 72 65 63 65 69 76 65 64 00
recv(sub, "character")
#> Warning: 8 | Try again
#> 'errorValue' int 8

subscribe(sub, 2)
send(pub, c(2, 10, 10, 20), mode = "raw")
#>  [1] 00 00 00 00 00 00 00 40 00 00 00 00 00 00 24 40 00 00 00 00 00 00 24 40 00
#> [26] 00 00 00 00 00 34 40
recv(sub, "double", keep.raw = FALSE)
#> [1]  2 10 10 20

close(pub)
close(sub)


text:
# Kinematics - Find position

1. Oct 25, 2016

I've made a drawing in order to visualize the problem better:

1. The problem statement, all variables and given/known data

A car can increase its speed only at 3.00 m/s2, move at constant velocity, or decrease its speed at 7.00 m/s2. Starting at rest, the driver wishes to drive to a road sign located at x=100 m. He increases his speed, then travels at constant velocity and then decreasing his speed.
The driver begins accelerating at t=0 and switches to constant velocity at t=4.50 s. At what position must the driver switch from constant velocity to decreasing speed if he wants to stop the car at the road sign?

2. Relevant equations
These are the kinematic equations I used to solve the problem:
x1=x0+v0(t1-t0) + 1/2a0(t1-t0)2

v1=v0+a0(t1-t0)

v32=v22 + 2a2(x3-x2)

3. The attempt at a solution
x1=x0+v0(t1-t0) + 1/2a0(t1-t0)2
x1=1/2a0t12 =
x1=1/2(3.0m/s2)(4.50s)2 = 30.4m

v1=v0+a0(t1-t0)
v1=(3.0m/s2)(4.50s) = 13.5m/s

Since after v1 the velocity is constant, v2 must be constant and equal to 13.5m/s

v32=v22 + 2a2(x3-x2)
-v22=2a2x3-2a2x2
x2=-[-(v22-2a2x3) / 2a2]
x2 = -[(-182.25+1400)/-14] = 86.98m

Does this result look right?

2. Oct 25, 2016

### PeroK

Can you think of a way to check? Perhaps you may see an easier way to do it.

3. Oct 25, 2016

I only see that I can skip the first step in finding x1, but I can't think of a way to check or find x2 in a different way. Any hints?

4. Oct 25, 2016

### PeroK

Work backwards. Think about stopping distance for the car.

5. Oct 25, 2016

Do you mean to check if x2 is equal to 86.98m or to find x2 in another way? The only way to check if x2 is equal to 86.98m is to use the same formula I used to find this value which is:
v32=v22+ 2a2(x3-x2)
Since we don't have any values for t3 or t2

Also, in order to find x2 working backwards, I think I still need to find v2 first. I'm a little confused. Perhaps I'm missing some relationship in between time and constant velocity.

6. Oct 25, 2016

### PeroK

Suppose the car is moving along at $13.5 ms^{-1}$. It has a fixed deceleration of $7ms^{-2}$. From that you can calculate the stopping distance of the car. Once you know the stopping distance, you can subtract that from $100m$.

7. Oct 25, 2016

The only way I can think of based on the formulas I learned would be subtracting x2-x1. So it would be 86.98m-30.4m=50.6m
However, I don't understand this approach because based on my sketch I uploaded on the first post, I set x2 as the position in which the driver must switch from constant velocity to decreasing speed if he wants to stop the car at the road sign.

8. Oct 25, 2016

### PeroK

A car is moving along at $13.5 ms^{-1}$. It has a fixed deceleration of $7ms^{-2}$.

a) How long does it take to stop (time)?
b) How far does it travel before it stops?

Can you work that out?

9. Oct 25, 2016

Yes.
a)
v1=v0+a0(t1-t0)
t1=1.93 s

b)
v12=v02+2a0(x1-x0)
-182.25=-14x1
x1=13.02 m

10. Oct 26, 2016

### PeroK

So, you need to start decelerating $13.02m$ before the point you want to stop. And what is $100m - 13.02m$?

11. Oct 26, 2016

So 100m - 13.02m = 86.98 m would be the position in which the driver must switch from constant velocity to decelerating in order to stop the car at 100m correct?

12. Oct 26, 2016

### PeroK

Yes, exactly. And now you have a much simpler solution to the original problem.

13. Oct 26, 2016


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# why people don't use the same generators?

i want to make many pederson commitments $$C=g^s h^r$$ for a long time , do i have to change the generators $$g$$ and $$h$$ or its ok if i always used the same ones

You can use the same $$g$$. However, if the discrete log of $$h$$ relative to $$g$$ is known, then Pedersen is no longer binding. Thus, you cannot use an $$h$$ if there is any possibility of someone else knowing that discrete log.


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# Infinite cubic grid of resisrors

Can we find net resistance between the body diagonal points of a infinite cubic lattice ?

The objective is to find net resistance between A & B of the given cube which is part of infinite grid. Let the resistance between any two adjacent vertices is R

Note by Pranjal Prashant
5 years, 8 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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see 2nd answer to the question in the link https://physics.stackexchange.com/questions/2072/on-this-infinite-grid-of-resistors-whats-the-equivalent-resistance It's for n dimensional grid

- 11 months, 1 week ago

It must be R/3

- 5 years, 1 month ago

- 5 years ago

Solution ?

- 5 years, 1 month ago

Yes, I know about 2 d version for resistors and fourier series for getting across square diagonal 2r/pi.[you know that Ishan :D ] But this is quite different fom those, much more difficult in getting the approach. You should share this so that someone reaches at the final ansWeR.

- 5 years, 8 months ago

Oh my.

Staff - 5 years, 8 months ago

Staff - 5 years, 8 months ago

A simpler version would be two find the equivalent resistance between two diagonally opposite points in an infinite grid of resistors, which is still quite difficult. See the page I have linked Infinite grid of resistors

- 5 years, 8 months ago

Total resistance (across points A and B) = ( 5/6 ) * R
I can't post a picture of my solution here

- 5 years, 8 months ago

Incorrect, This answer holds if there was a single cube of resistances rather than an infinite one.

- 5 years, 8 months ago

but infinite series of resistors just push the "single cube value" to an exact number so my idea is that effective resistance is near (5/6)R (like 0.85R or 0.9R max but not less than (5/6)R). Please notify me if there is a mistake in my assumption.

- 5 years, 8 months ago

Now what significance pushing values is of, the question is not an mcq, I want to know how it can be done, and I am sure that it is solvable. {although answer would not be beautiful perhaps}.

- 5 years, 8 months ago

got it but I dont know how to solve the way you told and yes the answer sure will be weird

- 5 years, 8 months ago

NO, IT IS NOT SO. In the fourier series , steps of integration are nasty, but answer is simply 2r/ $\pi$

- 5 years, 8 months ago

thanks for the info I will surely try to get the steps for your answer.

- 5 years, 8 months ago

I could not understand "push the single cube value to an exact number". Also think of 2-D grid of infinite resistors in which we have to find the equivalent resistance between adjacent points which everyone knows to be R/2. What will be your argument in this one? Just because other resistances are present does not mean that the net would be greater than 5R/6 because resistances in parallel decrease the value

- 5 years, 8 months ago

Yes it is haha, I considered only a 'cube'.

- 5 years, 8 months ago


text:
I believe that is what is happening in regards to Free Power motor that needs no external power to operate. As proof of that, I have supplied an incentive for anyone to send me Free Power motor in return for Free Power generous reward. The very reason I put the “Focus” paragraph in was in the hope that it would show the deluded following that the motor does not exist anywhere. Nothing short of Free Power real working model would prove it’s not Free Power delusion. Stay focused on that and you will see the truth of what I am saying. Harvey1A magical magnetic motor? Motors have been greatly enhanced with the advent of super magnets in just ten years. Smaller and more powerful to say the least. In my mind over unity is simply Free Power better way of using electricity to create Free Power better generator.

Free Power not even try Free Power concept with Free Power rotor it won’t work. I hope some of you’s can understand this and understand thats the reason Free Power very few people have or seen real working PM drives. My answers are; No, no and sorry I can’t tell you yet. Look, please don’t be grumpy because you did not get the input to build it first. Gees I can’t even tell you what we call it yet. But you will soon know. Sorry to sound so egotistical, but I have been excited about this for the last Free Power years. Now don’t fret………. soon you will know what you need to know. “…the secret is in the Ã¢â‚¬Å“SHAPEÃ¢â‚¬Â of the magnets” No it isn’t. The real secret is that magnetic motors can’t and don’t work. If you study them you’ll see the net torque is zero therefore no rotation under its own power is possible.
Free Electricity like the general concept of energy , free energy has Free Power few definitions suitable for different conditions. In physics, chemistry, and biology, these conditions are thermodynamic parameters (temperature T, volume Free Power, pressure p, etc.). Scientists have come up with several ways to define free energy. The mathematical expression of Helmholtz free energy is.
This is not Free Power grand revelation. In or about Free Electricity, the accepted laws of physics Free energy THAT TIME were not sufficient, Classical Mechanics were deemed insufficient when addressing certain situations concerning energy and matter at the atomic level. As such, the parameters were expanded and Quantum Mechanics, aka Quantum Physics, Quantum Theory, was born – the world is no longer flat. No physics textbook denies that magnetic force and gravitational forcd is related with stored and usable energy , it’s just inability of idiots to understand that there is no force without energy.
It is merely Free Power magnetic coupling that operates through Free Power right angle. It is not Free Power free energy device or Free Power magnetic motor. Not relevant to this forum. Am I overlooking something. Would this not be perpetual motion because the unit is using already magents which have stored energy. Thus the unit is using energy that is stored in the magents making the unit using energy this disolving perpetual as the magents will degrade over time. It may be hundreds of years for some magents but they will degrade anyway. The magents would be acting as batteries even if they do turn. I spoke with PBS/NOVA. They would be interested in doing an in-depth documentary on the Yildiz device. I contacted Mr. Felber, Mr. Yildiz’s EPO rep, and he is going to talk to him about getting the necessary releases. Presently Mr. Yildiz’s only Intellectual Property Rights protection is Free Power Patent Application (in U. S. , Free Power Provisional Patent). But he is going to discuss it with him. Mr. Free Electricity, then we do agree, as I agree based on your definition. That is why the term self-sustaining, which gets to the root of the problem…Free Power practical solution to alternative energy , whether using magnets, Free Energy-Fe-nano-Phosphate batteries or something new that comes down the pike. Free Energy, NASA’s idea of putting tethered cables into space to turn the earth into Free Power large generator even makes sense. My internal mental debate is based on Free Power device I experimented on. Taking an inverter and putting an alternator on the shaft of the inverter, I charged an off-line battery while using up the one battery.
I am doing more research for increasing power output so that it can be used in future in cars. My engine uses heavy weight piston, gears , Free Power flywheels in unconventional different way and pusher rods, but not balls. It was necessary for me to take example of ball to explain my basic idea I used in my concept. (the ball system is very much analogous to the piston-gear system I am using in my engine). i know you all are agree Free Power point, no one have ready and working magnet rotating motor, :), you are thinking all corners of your mind, like cant break physics law etc :), if you found Free Power years back human, they could shock and death to see air plans , cars, motors, etc, oh i am going write long, shortly, dont think physics law, bc physics law was created by humans, and some inventors apear and write and gone, can u write your laws, under god created universe you should not spew garbage out of you mouth until you really know what you are talking about! Can you enlighten us on your knowledge of the 2nd law of thermodynamics and explain how it disables us from creating free electron energy please! if you cant then you have no right to say that it cant work! people like you have kept the world form advancements. No “free energy magnetic motor” has ever worked. Never. Not Once. Not Ever. Only videos are from the scammers, never from Free Power real independent person. That’s why only the plans are available. When it won’t work, they blame it on you, and keep your money.
Quite often, using Natural energy systems costs Free Power little more at the beginning, but much less over time. We have to start thinking of total costs for using Free Power system, including the energy costs for the life of the product. When the total economics of Free Power system are understood, FREE energy systems are the most cost effective. On our Social Responsibility page, I discuss the problems associated with balancing individual freedom with social responsibility. Society cannot provide the individual with rights and freedoms if the individual is unwilling to provide the society with responsible behavior in return. The arrival of unlimited amounts of low-cost, clean energy could be extremely destabilizing to an uncivil society. These developments provide unparalleled opportunities for both economic disruption or rapid innovation. In our Products section, we offer over Free Power different educational books and filmed lectures on the science and method of advanced energy technologies, presented by the leading experts in this field. Many of these products can also be accessed by their images in the right column of the pages on this website. Currently, we are educating the next generation of scientists and engineers about the real state of technological discovery. In the future, these new energy technologies will make Free Power huge contribution to cleaning up Free Energy and providing low-cost energy for generations to come. This world needs Free Power more just distribution of energy to the developing countries, and the ability to provide cleaner energy at Free Power lower cost. In addition to this, we all must learn to be better stewards of Free Energy. That means pollute less and recycle more. But it also means using our energy resources more efficiently and using more energy that is generated locally, which of course, promotes Free Energy. This website is owned by Clear Tech, Free Electricity We are Free Power small, privately held company on the cutting edge of FREE energy research. Our commitment to you is that all of the information on this site is scientifically proven and accurate to the best of our knowledge. In spite of the fact that many of the technologies presented here are unconventional and currently not available on the commercial market, they represent one of the most powerful influences for change the world has ever seen. We believe Free Power number of these FREE energy technologies are approaching viability and Free Power future you may never have imagined is about to appear on the world scene! The problem is that when huge changes in technology happen rapidly, they can be very disruptive to society. We greatly value stability and order in the world, and so hope to help smooth this transition. In the late 1880’s, trade journals in the electrical sciences were predicting free electricity and free energy in the near future. Incredible discoveries about the nature of electricity were becoming common place. Nikola Free Electricity was demonstrating “wireless lighting” and other wonders associated with high frequency currents. There was an excitement about the future like never before. Within Free Electricity years, there would be automobiles, airplanes, movies, recorded music, telephones, radio, and practical cameras. The Victorian Age was giving way to something totally new. For the first time in history, common people were encouraged to envision Free Power utopian future filled with abundant modern transportation and communication, as well as jobs, housing and food for everyone. Disease would be conquered, and so would poverty. Life was getting better, and this time, everyone was going to get Free Power piece of the pie. Actually, the answer to that question is no. In fact, the opposite is true. Spectacular energy technologies were developed right along with the other breakthroughs. Since that time, multiple methods for producing vast amounts of energy at extremely low cost have been developed. None of these technologies have made it to the consumer market as an article of commerce, however. Exactly why this is true will be discussed shortly. But first, I would like to describe to you Free Power short list of free energy technologies that I am currently aware of, and that are proven beyond all reasonable doubt. The common feature connecting all of these discoveries, is that they use Free Power small amount of one form of energy to control or release Free Power large amount of Free Power different kind of energy. Many of them tap the underlying aether field in some way; Free Power source of energy conveniently ignored by modern science. Radiant energy. Nikola Free Electricity’s magnifying transmitter, T. Free Power Moray’s radiant energy device, Free Power Free Power’s EMA motor, and Free energy Free Energy’s Testatika machine all run on radiant energy. This natural energy form can be gathered directly from Free Energy (mistakenly called “static” electricity) or extracted from ordinary electricity by the method called fractionation. Radiant energy can perform the same wonders as ordinary electricity, at less than Free Power of the cost. It does not behave exactly like electricity, however, which has contributed to the scientific community’s misunderstanding of it. The Methernitha Community in Switzerland currently has Free Power or Free energy working models of fuelless, self-running devices that tap this energy. Permanent Magnets. Dr. Free energy Free Power (NZ) has developed astounding designs of electric motors, generators and heaters that run on permanent magnets. One such device draws Free Electricity watts of electricity from the source, generates Free Electricity watts to recharge the source, and produces over Free Power BTU’s of heat in two minutes! Dr. Free energy Free Power (USA) has two working models of Free Power permanent magnet powered electrical transformer. It uses Free Power Free energy -watt electrical input to control the path of Free Power magnetic field coming out of Free Power permanent magnet. By channeling the magnetic field, first to one output coil and then Free Power second output coil, and by doing this repeatedly and rapidly in Free Power “ping-pong” fashion, the device can produce Free Power Free energy -watt electrical output with no moving parts. Free Power calls his device Free Power Motionless Electromagnetic Generator, or MEG. Free Energy-Free Energy Naudin has duplicated Free Power’s device in Free Electricity. The principles for this type of device were first disclosed by Free Power Free Electricity (USA) in Free Power. Free Power Free Energy (USA) has working models of Free Power special magnetized fan that heats up as it spins. It takes exactly the same amount of energy to spin the fan whether it is generating heat or not. Beyond these developments, multiple inventors have identified working mechanisms that produce motor torque from permanent magnets alone. Mechanical Heaters. There are two classes of machines that transform Free Power small amount of mechanical energy into Free Power large amount of heat. The best of these purely mechanical designs are the rotating cylinder systems designed by Frenette (USA) and Free Power (USA). In these machines, one cylinder is rotated within another cylinder with about an eighth of an inch of clearance between them. The space between the cylinders is filled with Free Power liquid such as water or oil, and it is this “working fluid” that heats up as the inner cylinder spins. Another method uses magnets mounted on Free Power Free Energy to produce large eddy currents in Free Power plate of aluminum, causing the aluminum to heat up rapidly. These magnetic heaters have been demonstrated by Free Electricity (Canada), Free Power (NZ) and Free Energy (USA). All of these systems can produce ten times more heat than standard methods using the same energy input. Super-Efficient Electrolysis. Water can be broken into hydrogen and oxygen using electricity. Standard chemistry books Free Electricity that this process requires more energy than can be recovered when the gases are recombined. This is true only under the worst case scenario. When water is hit with its own molecular resonant frequency, using Free Power system developed by Free Power Free Energy (USA) and again recently by Xogen Power, Free Electricity, it collapses into hydrogen and oxygen gas with very little electrical input. Also, using different electrolytes (additives that make the water conduct electricity better) changes the efficiency of the process dramatically. It is also known that certain geometric structures and surface textures work better than others do.

Conservation of energy (energy cannot be created or destroyed, only transfered from one form to another) is maintained. Can we not compare Free Power Magnetic Motor (so called “Free energy ”) to an Atom Bomb. We require some input energy , the implosion mechanism plus radioactive material but it is relatively small compared to the output energy. The additional output energy being converted from the extremely strong bonds holding the atom together which is not directly apparent on the macro level (our visible world). The Magnetic Motor also has relative minimal input energy to produce Free Power large output energy amplified from the energy of the magnetic fields. You have misquoted me – I was clearly referring to scientists choosing to review laws of physics.
Not Free Power lot to be gained there. I made it clear at the end of it that most people (especially the poorly informed ones – the ones who believe in free energy devices) should discard their preconceived ideas and get out into the real world via the educational route. “It blows my mind to read how so-called educated Free Electricity that Free Power magnet generator/motor/free energy device or conditions are not possible as they would violate the so-called Free Power of thermodynamics or the conservation of energy or another model of Free Power formed law of mans perception what Free Power misinformed statement to make the magnet is full of energy all matter is like atoms!!”


text:
Solutions of sum-type singular fractional q-integro-differential equation with $m$-point boundary value using quantum calculus
• +1
• Shahram Rezapour,
• Soheil Salahshour,
Mediterranean University of Reggio Calabria Department of Informatics Mathematics Electronics and Transport
Author Profile
Shahram Rezapour
Author Profile
Soheil Salahshour
Bahcesehir Universitesi
Author Profile
Bu Ali Sina University
Author Profile

## Abstract

In this study, we investigate the sum-type singular nonlinear fractional q-integro-differential $m$-point boundary value problem. The existence of positive solutions is obtained by the properties of the Green function, standard Caputo $q$-derivative, Riemann-Liouville fractional $q$-integral and the means of a fixed point theorem on a real Banach space $(\mathcal{X}, \|.\|)$ which has a partially order by using a cone $P \subset \mathcal{X}$. The proofs are based on solving the operator equation $\mathcal{O}_1 x + \mathcal{O}_2 x = x$ such that the operator $\mathcal{O}_1$, $\mathcal{O}_2$ are $r$-convex, sub-homogeneous, respectively and define on cone $P$. As applications, we provide an example illustrating the primary effects.
20 Jan 2020Submitted to Mathematical Methods in the Applied Sciences
25 Jan 2020Submission Checks Completed
25 Jan 2020Assigned to Editor
25 Jan 2020Reviewer(s) Assigned
01 Feb 2020Review(s) Completed, Editorial Evaluation Pending
02 Feb 2020Editorial Decision: Revise Major


text:
# 34Understanding How it Works

The publication system used in this online guide is based on version controlling all the content – text, tables and figures – and on automatically generating from each version – in parallel – both website and PDF renderings of the guide.

This [work in progress] chapter gives an overview of the project and the role of each tool.

Essentially, the project is divided in two top-level folders: the /guide and the /generator.

The first has the files for the entire contents of the guide (text, images, tables, etc). The text is written in a simple but powerful format, that at the same allows ease of use, independence of content from style and is compatible with version control.

The second contains the source-code for the special purpose generation tool – manu – that takes the text for the guide and the assets and builds the PDF and the complete website.

All content is versioned in Git, a powerful and proved distributed version control system used extensively in software development, and the project lives in GitHub, a platform for collaboration on projects using git.

A robot that lives in our server constantly monitors GitHub for events in this project – such as new commits or changes in pull requests – and automatically runs manu for each new version.


text:
### Identification of Predictive Sub-Phenotypes of Acute Kidney Injury using Structured and Unstructured Electronic Health Record Data with Memory Networks

Acute Kidney Injury (AKI) is a common clinical syndrome characterized by the rapid loss of kidney excretory function, which aggravates the clinical severity of other diseases in a large number of hospitalized patients. Accurate early prediction of AKI can enable in-time interventions and treatments. However, AKI is highly heterogeneous, thus identification of AKI sub-phenotypes can lead to an improved understanding of the disease pathophysiology and development of more targeted clinical interventions. This study used a memory network-based deep learning approach to discover predictive AKI sub-phenotypes using structured and unstructured electronic health record (EHR) data of patients before AKI diagnosis. We leveraged a real world critical care EHR corpus including 37,486 ICU stays. Our approach identified three distinct sub-phenotypes: sub-phenotype I is with an average age of 63.03$\pm 17.25$ years, and is characterized by mild loss of kidney excretory function (Serum Creatinne (SCr) $1.55\pm 0.34$ mg/dL, estimated Glomerular Filtration Rate Test (eGFR) $107.65\pm 54.98$ mL/min/1.73$m^2$). These patients are more likely to develop stage I AKI. Sub-phenotype II is with average age 66.81$\pm 10.43$ years, and was characterized by severe loss of kidney excretory function (SCr $1.96\pm 0.49$ mg/dL, eGFR $82.19\pm 55.92$ mL/min/1.73$m^2$). These patients are more likely to develop stage III AKI. Sub-phenotype III is with average age 65.07$\pm 11.32$ years, and was characterized moderate loss of kidney excretory function and thus more likely to develop stage II AKI (SCr $1.69\pm 0.32$ mg/dL, eGFR $93.97\pm 56.53$ mL/min/1.73$m^2$). Both SCr and eGFR are significantly different across the three sub-phenotypes with statistical testing plus postdoc analysis, and the conclusion still holds after age adjustment.

### The Use of NLP to Extract Unstructured Medical Data From Text - insideBIGDATA

When working in healthcare, a lot of the relevant information for making accurate predictions and recommendations is only available in free-text clinical notes. Much of this data is trapped in free-text documents in unstructured form. This data is needed in order to make healthcare decisions. Hence, it is important to be able to extract data in the best possible way such that the information obtained can be analyzed and used. State-of-the-art NLP algorithms can extract clinical data from text using deep learning techniques such as healthcare-specific word embeddings, named entity recognition models, and entity resolution models.

### Unsupervised Learning for Computational Phenotyping

With large volumes of health care data comes the research area of computational phenotyping, making use of techniques such as machine learning to describe illnesses and other clinical concepts from the data itself. The "traditional" approach of using supervised learning relies on a domain expert, and has two main limitations: requiring skilled humans to supply correct labels limits its scalability and accuracy, and relying on existing clinical descriptions limits the sorts of patterns that can be found. For instance, it may fail to acknowledge that a disease treated as a single condition may really have several subtypes with different phenotypes, as seems to be the case with asthma and heart disease. Some recent papers cite successes instead using unsupervised learning. This shows great potential for finding patterns in Electronic Health Records that would otherwise be hidden and that can lead to greater understanding of conditions and treatments. This work implements a method derived strongly from Lasko et al., but implements it in Apache Spark and Python and generalizes it to laboratory time-series data in MIMIC-III. It is released as an open-source tool for exploration, analysis, and visualization, available at https://github.com/Hodapp87/mimic3_phenotyping

### How companies are Using AI in the Field of Patient Data Mining

One of the ways AI is and will continue t be helpful in the field of healthcare is allowing medical professionals the ability to create treatment plans as well as discovering the best suited methods for helping their patients; instead of having to battle the tread-wheel of bureaucracy, nurses and physicians can focus on doing their actual jobs. Since we are in the age of big data, patient information is becoming valuable as tech giants, such as IBM and Google, are becoming more involved in acquiring this information; therefore, companies are using AI in the field known as patient data mining in a variety of ways. The AI research branch of the company recently launched a project known as Google Deepmind Health which focuses on mining medical records with the goal of providing faster and better health services; the project can go through hundreds of thousands of medical data within minutes. Also, Google's life sciences are working on a data-collecting initiative that aims to apply some of the same algorithms used to power Goggle's search button to analyze what it is that makes a person healthy. Included in this is experimenting with technologies that monitor diseases such as a digital contact lens that might detect levels of blood sugar.

### Big Data, Deep Learning and Blockchain Enhancing Healthcare Industry Analytics Insight

In spite of noteworthy headway in innovation in various fields, health management and authoritative frameworks leave a ton of opportunity to get better. At present, in the greater part of the healthcare enterprises, the health record of a patient is put away manually which makes it harder to keep up such colossal measure of data. It is so difficult to keep up this healthcare information precisely. As a matter of first importance, all these information changes constantly, doctors are always moving all through systems, they are continually adopting new insurance coverage, they're changing office areas and changing their affiliations with facilities and clinics and the patient is analyzed at different health associations. So, the information keeps on changing except if doctors are great about reaching their systems each time one of those information fields changes which will drop out of synchronizing rapidly.


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# Minimum ratio cover of matrix columns by extreme rays of its induced cone

2 BAMBOO - An algorithmic view on genomes, cells, and environments
LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558, Inria Grenoble - Rhône-Alpes
Abstract : Given a matrix S∈ℝm ×n and a subset of columns R, we study the problem of finding a cover of R with extreme rays of the cone $\mathcal{F}=\{v \in \mathbb{R}^n \mid Sv=\mathbf{0}, v\geq \mathbf{0}\}$, where an extreme ray v covers a column k if vk>0. In order to measure how proportional a cover is, we introduce two different minimization problems, namely the minimum global ratio cover (MGRC) and the minimum local ratio cover (MLRC) problems. In both cases, we apply the notion of the ratio of a vector v, which is given by $\frac{\max_i v_i}{\min_{j\mid v_j > 0} v_j}$. We show that these two problems are NP-hard, even in the case in which |R|=1. We introduce a mixed integer programming formulation for the MGRC problem, which is solvable in polynomial time if all columns should be covered, and introduce a branch-and-cut algorithm for the MLRC problem. Finally, we present computational experiments on data obtained from real metabolic networks.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [11 references]

https://hal.inria.fr/hal-00763453
Contributor : Marie-France Sagot <>
Submitted on : Monday, December 10, 2012 - 6:56:59 PM
Last modification on : Tuesday, August 24, 2021 - 4:52:01 PM
Long-term archiving on: : Monday, March 11, 2013 - 12:51:00 PM

### File

Minimum_ratio_cover_of_matrix_...
Files produced by the author(s)

### Citation

Alexandre da Silva Freire, Vicente Acuña, Pierluigi Crescenzi, Carlos Eduardo Ferreira, Vincent Lacroix, et al.. Minimum ratio cover of matrix columns by extreme rays of its induced cone. Proceedings of the Second international Symposium on Combinatorial Optimization (ISCO), Apr 2012, Athens, Greece. pp.165--177, ⟨10.1007/978-3-642-32147-4_16⟩. ⟨hal-00763453⟩

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text:
Essential University Physics: Volume 1 (3rd Edition)

$-3 \ MW$
We use the known equation for H to obtain: $H = \frac{-kA \Delta T}{\Delta x}$ $H = \frac{-(.61)(1.5\times 10^6)(26)}{8}\approx 3 \ MW$


text:
# Compact Linear Transformation is Bounded

Jump to navigation Jump to search

## Theorem

Let $H, K$ be Hilbert spaces.

Let $T \in B_0 \left({H, K}\right)$ be a compact linear transformation.

Then $T$ is also a bounded linear transformation.

That is, $B_0 \left({H, K}\right) \subseteq B \left({H, K}\right)$.


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# Simplification II

• November 4th 2008, 09:55 AM
Simplicity
Simplification II
Would this simplification be correct?

$\sqrt{\frac{A^2 - 2A^2B^2+A^2B^4+4A^2B^2C^2}{1-2B^2+B^4+4B^2C^2}} = \sqrt{\frac{A^2(1-2B^2+B^4+4B^2C^2)}{1-2B^2+B^4+4B^2C^2}} = \sqrt{{A^2}} = A$
• November 4th 2008, 10:20 AM
Moo
Hello,
Quote:

Originally Posted by Air
Would this simplification be correct?

$\sqrt{\frac{A^2 - 2A^2B^2+A^2B^4+4A^2B^2C^2}{1-2B^2+B^4+4B^2C^2}} = \sqrt{\frac{A^2(1-2B^2+B^4+4B^2C^2)}{1-2B^2+B^4+4B^2C^2}} = \sqrt{{A^2}} = {\color{red}|}A{\color{red}|}$

This would be better (Tongueout)
• November 4th 2008, 10:59 AM
Simplicity
... And what if it was:

$\sqrt{\frac{A^2 - 2A^2B^2+A^2B^4+4A^2B^2C^2}{(1-2B^2+B^4+4B^2C^2)^2}}$

How would I simplify that?
• November 4th 2008, 11:02 AM
Moo
Quote:

Originally Posted by Air
... And what if it was:

$\sqrt{\frac{A^2 - 2A^2B^2+A^2B^4+4A^2B^2C^2}{(1-2B^2+B^4+4B^2C^2)^2}}$

How would I simplify that?

Hmmm well, you'd have :

$\sqrt{\frac{A^2}{|1-2B^2+B^4+4B^2C^2|}}$ after simplifying :) (what's in a square root must be positive)

$=\frac{|A|}{\sqrt{|1-2B^2+B^4+4B^2C^2|}}$

now if you know that one or another is positive, you can remove the absolute values


text:
Wednesday, October 25, 2017 0

In the modern study of Ethics one debate has dominated almost all the others, it is the question of whether morals are discovered or invented, in other words whether moral values exist independently of us, whether they are entirely a product of the human mind, or whether there can be a set of moral values universally accepted. In TOK, this is an issue which you will encounter in different forms and in different places. TOK requires us to address the ...

Monday, October 23, 2017 0

It's sometimes hard to define whether a puzzle can be classified as "mathematical" or not. They certainly are if they require mathematical techniques or knowledge to solve them. Today's puzzles don't, but I would still class them as mathematical: firstly, because they use numbers or geometrical space or logic; and secondly because they tickle the mathematical bits of your brain and so, in a very small way, hone your skills. 1. The two jugs Solve this in under 30 seconds - excellent. ...

Friday, October 20, 2017 0

Clerics in Saudi Arabia, the birthplace of Islam, have long struggled to justify the kingdom’s decades-old ban on women driving. None could cite a verse in the Koran to justify barring women from driving a vehicle. On September 26th the Kingdom decided to lift the ban. The decision was welcomed by women and many men. It will give Saudi women a freedom that others take for granted. It will have economic benefits, too, sparing families the cost of hiring a (male) ...

Wednesday, October 18, 2017 0

Most understandably, there was a small delay in the release of the subject report.  With all new assessments, there was much to report on and the examiners responsibly clearly wanted to provide clarity on the expectations of the assessments, and advice for future candidates.  A lot of work goes into these reports, and in IB history, with nearly 50,000 students writing 10 different exams and completing an internal assessment, there are a lot of variables to consider. (Please note that as of ...

Wednesday, October 11, 2017 0

When I opened the paper today (yes, some of us still do that), there was a brief interview with some of the members of the Little Rock 9.  60 years ago today, 9 African-American teenagers entered Central High School, in Little Rock, Arkansas, USA, in a bid to begin the end of segregation in education.  If you look at the photo of the students that the Associated Press/Fox News used in its article, you see a group of pleasant, well-dressed young people on ...

Monday, October 9, 2017 0

Often, IB teachers of the Group A Language and Lit courses regret that there is not much opportunity to do more creative work with their classes. But short exercises can be incorporated into our classes and many of us do that.  Here is one exercise which has not only produced some very lively original pieces with my students, but also raised their consciousness and refined their sense of how prose is constructed and how different effects are created. Obviously there ...

Friday, October 6, 2017 0

In September I posted some thoughts about the Comparative Study – Six of the Best (comparative study issues and advice) This month I’m continuing that theme but focusing on criterion F, so I’m only talking really to those of you who are taking HIGHER LEVEL Visual Arts. Criterion F deals with making connections to your own art-making practice. *In July I posted a blog about what NOT to do in your exhibition - “When NOT to…” (Visual Arts Exhibition No Nos) Now I am posting ...

Wednesday, October 4, 2017 1

This post is primarily aimed at the IB1 crowd. Right about now you should be well along your Frustration Curve - it looks something like this over the first year:   Should be fairly self-explanatory but maybe a few words about where you are heading. Your first tests should be reasonably straightforward - let's face it, we are not rocket surgeons - and you should be able to deal with supply, demand, markets and elasticities with reasonable confidence. The initial shell-shock, and ...

Monday, October 2, 2017 0

You will have learnt that there are three types of average: the mean, the median, and the mode. Let's look at them closely - why we need all three, what you can do with them, and when to use each one. The Mean The mean is calculated by adding all the values and dividing by the number of values. Using sigma notation, where the sigma sign means "the sum of", we can write: $m = {{\sum x } \over n}$. The best way ...

Monday, October 2, 2017 0

I've just started to teach this topic to my students. It doesn't take too long but I do find it an enjoyable topic to teach. But how do you teach it? I always warn the students that the topic is jargon heavy - the words / phrases used in the topic such as  chiral, racemic, racemate, optically active are all pretty specific to optical isomers and are not used outside of the topic. In my teaching I have found that students understand the ...


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## arXiv Analytics

### arXiv:2302.01322 [cond-mat.stat-mech]AbstractReferencesReviewsResources

#### Universality in the tripartite information after global quenches: (generalised) quantum XY models

Published 2023-02-02Version 1

We consider the R\'enyi-$\alpha$ tripartite information $I_3^{(\alpha)}$ of three adjacent subsystems in the stationary state emerging after global quenches in noninteracting spin chains from both homogeneous and bipartite states. We identify settings in which $I_3^{(\alpha)}$ remains nonzero also in the limit of infinite lengths and develop a field theory description. We map the calculation into a Riemann-Hilbert problem with a piecewise constant matrix for a doubly connected domain. We find an explicit solution for $\alpha=2$ and an implicit one for $\alpha>2$. In the latter case, we develop a rapidly convergent perturbation theory that we use to derive analytic formulae approximating $I_3^{(\alpha)}$ with outstanding accuracy.

Related articles: Most relevant | Search more
Universality in the tripartite information after global quenches
arXiv:cond-mat/0203455 (Published 2002-03-22, updated 2002-03-29)
Universality of Zipf's Law
arXiv:cond-mat/9811018 (Published 1998-11-02)
Universality of quantum Brownian motion


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# 7.3 Input/Output¶

The logging and I/O features are provided mainly by the MOSEK task and to some extent by the MOSEK environment objects.

## 7.3.1 Stream logging¶

By default the solver runs silently and does not produce any output to the console or otherwise. However, the log output can be redirected to a user-defined output stream or stream callback function. The log output is analogous to the one produced by the command-line version of MOSEK.

The log messages are partitioned in three streams:

These streams are aggregated in the streamtype.log stream. A stream handler can be defined for each stream separately.

A stream handler is simply a user-defined function of type streamfunc that accepts a string, for example:

def myStream(msg):
sys.stdout.write(msg)
sys.stdout.flush()

It is attached to a stream as follows:

task.set_Stream(streamtype.log,myStream)

The stream can be detached by calling

task.set_Stream(None)

After optimization is completed an additional short summary of the solution and optimization process can be printed to any stream using the method Task.solutionsummary.

## 7.3.2 Log verbosity¶

The logging verbosity can be controlled by setting the relevant parameters, as for instance

Each parameter controls the output level of a specific functionality or algorithm. The main switch is iparam.log which affect the whole output. The actual log level for a specific functionality is determined as the minimum between iparam.log and the relevant parameter. For instance, the log level for the output produce by the interior-point algorithm is tuned by the iparam.log_intpnt; the actual log level is defined by the minimum between iparam.log and iparam.log_intpnt.

Tuning the solver verbosity may require adjusting several parameters. It must be noticed that verbose logging is supposed to be of interest during debugging and tuning. When output is no more of interest, the user can easily disable it globally with iparam.log. Larger values of iparam.log do not necessarily result in increased output.

By default MOSEK will reduce the amount of log information after the first optimization on a given problem. To get full log output on subsequent re-optimizations set iparam.log_cut_second_opt to zero.

## 7.3.3 Saving a problem to a file¶

An optimization problem can be dumped to a file using the method Task.writedata. The file format will be determined from the filename’s extension (unless the parameter iparam.write_data_format specifies something else). Supported formats are listed in Section 17 (together with a specification of problem types various formats support).

For instance the problem can be written to an OPF file with

task.writedata("data.opf")

All formats can be compressed with gzip by appending the .gz extension, for example

task.writedata("data.task.gz")

Some remarks:

• Unnamed variables are given generic names. It is therefore recommended to use meaningful variable names if the problem file is meant to be human-readable.
• The task format is MOSEK‘s native file format which contains all the problem data as well as solver settings.

## 7.3.4 Reading a problem from a file¶

A problem saved in any of the supported file formats can be read directly into a task using Task.readdata. The task must be created in advance. Afterwards the problem can be optimized, modified, etc. If the file contained solutions, then are also imported, but the status of any solution will be set to solsta.unknown (solutions can also be read separately using Task.readsolution). If the file contains parameters, they will be set accordingly.

task = env.Task()
try:


text:
Re: Issues about the semantics of the ontology-lexicon interface [was: Re: Why not to shortcut the "sense" object]

From: Philipp Cimiano <cimiano@cit-ec.uni-bielefeld.de>
Date: Tue, 30 Oct 2012 10:39:25 +0100
Message-ID: <508FA04D.7070805@cit-ec.uni-bielefeld.de>

Dear all,

thanks for the contributions of Guido, Aldo et al. Apologies for the
silence in the last days. Some times I do other things than ontolex
(ehm) ;-)

It seems that we are converging on a two-level formalization:

Layer 1: senses are constants representing a linguistic meaning

Pro: i) cognitive simplicity, ii) LOD-compliance (navigate from lexical
entry to concept and from concept to lexical entry), iii) easy retrieval
of all lexicalizations of a concept without subsumption reasoning, iv)
easy to implement (DB, simple RDF store without reasoning, etc).
Contra: i) limited joint reasoning over lexicon and ontology

Layer 2: senses are (sub-classes)

Pro:  i) joint reasoning over lexicon and ontology, ii) senses are
subclasses (in line with the lemon model)
Contra: i) increased cognitive complexity, ii) no shortcut possible anymore

We will need to state how both layers are related to each other in some
sort of "glue theory".

I think this is a proposal that we can discuss on Friday, possibly
finally agreeing to follow this path. The implications of this will have
to be worked out of course in the near future.

Concerning the axiomatization of lexical relations: we could axiomatize
lexical relations also in layer one, i.e.

\forall s_1, s_2  Sense(s_1) & Sense(s_2) & synonyms(s_1,s_2)
\rightarrow \forall l LinguisticContext(l) & partOf(s_1,l) \rightarrow
semEquivalent(l[s_1/s_2],l).

where l[s_1/s_2] is that linguistic context where s_1 is replaced by
s_2. Of course, the question is what semEquivalent means, but that is
not somehting that I even intend to formalize or capture in this WG.

I will make a concrete proposal that we can discuss and agree on (or
not) on Friday.

Best regards,

Philipp.

Am 26.10.12 14:42, schrieb Guido Vetere:
> Aldo Gangemi <aldo.gangemi@cnr.it> wrote on 26/10/2012 10:04:29:
>
> > Dear Guido, some more comments: I think we have cut the problem to
> > the bones now, and can proceed to a concrete list of alternatives.
> >
> > On Oct 23, 2012, at 5:58 PM, Guido Vetere <gvetere@it.ibm.com> wrote:
> >
> >> Of course if you can elaborate the axiomatization of sense and sense
> >> relationships in the model, then there are many solutions like
> >> yours, I was just comparing the specific models we were discussing.
> >
> > Ehm, do you mean: "your solution is just one of those that naïve
> > people can easily produce during pasta cooking by using their pinky
> toes"? ;)
>
> exactly :-)
>
> > I'd say that my solution is based on a design pattern that works
> > well with this kind of data. If you know about "many" others, please
> > share them with us, so we can evaluate those that fit best.
> >
>
> Sorry, I meant 'ideally, there are many solutions' etc.
>
> >
> >> However, as part of such axiomatization, you would be expected to
> >> introduce logical lexical relations as first order properties (as in
> >> fact you did) and to specify, for instance, whether if
> >> <s1,synonym_of,s2> implies that lexemes associated to s1 are
> >> available as a substitute for those associated to s2, like if they
> >> were logically equivalent. In sum, you would have to reconstruct a
> >> fragment of the same logic in which your ontology is specified, and
> >> to implement part of the standard DL reasoning as (e.g.) SPARQL
> >> queries. In sum, I want to 'transform' senses into a full-fledged
> >> ontology (by the way, what are them 'originally'?), but you want to
> >> reimplement logics in SPARQL!
> >
> > It seems you are putting another requirement into your use case,
> > i.e. that lexical relations *must* be formalized within a (FOL or
> > HOL) logic. I am not sure this is something we can achieve in this
> > WG, neither that it is worth doing it just for the sake of jointly
> > reasoning with lexical and ontological data (but see below).
> > And of course, I do not want to reimplement logics in SPARQL: I'm
> > showing a possible solution for a relatively simple use case,
> > without resorting to DL reasoning gunboats. Maurizio Lenzerini, who
> > you often quote, reminds knowledge engineers to use basic data
> > models like relational DB when you do not really need more than
> > that. I agree with him here: what you call "logical lexical
> > relations" are not necessarily logical in the sense of being in the
> > meta-theory of OWL, at least because we do not commit to a deep
> > formalization of any linguistic/lexical resource, do we?
> >
>
> I'm totally with you and our friend Maurizio. Let's go on with data
> structures for now.
>
> >
> >> Seriously, of course there are pros and cons in every choice, I
> >> think that we should just draw a number of possible alternatives. I
> >> think that M2 allows a smooth exploitation of ontological axioms on
> >> the lexical side without requiring an elaborated semiotic model. It
> >> is clear that lexical relationships cannot be trivially mapped to
> >> logical ones and that a complete semiotic model should probably
> >> provide an account for this. But as far as users in concrete use
> >> cases are just interested in exploring the relationship between
> >> existing ontologies and (mapped) lexical resources (e.g. to discover
> >> how disjunction is reflected on antonymy), M2 is good enough - and
> >> could be further refined, but this is for the next game :-)
>
> >
> > You stress the importance of a logical treatment of lexical
> > relations. Good enough, I deem this an important issue, which we are
> > studying e.g. for the FRED text2rdf tool. But here the use case is
> > directly "reasoning on textually-derived data/ontologies", not the
> > one we are discussing here. Also this use case is part of the
> > interface between language and ontologies, but a more challenging
> > one. BTW, it does not concern how we map lexical relations to
> > description logics, but how to represent natural language semantics
> > (and pragmatics) into logic.
> >
>
> Just to make it clear, I'm not advocating the logical formalisation of
> lexical relations in general, I'm just (trivially) saying that if you
> want to exploit standard DL reasoning on senses with respect to
> ontology classes, then you'd better treat senses as classes rather
> than instances. Of course, if you are not interested in the premise,
> then the consequence is irrelevant to you.
>
> > Bottom line, I agree on the alternative patterns idea, but with
> > compatibility statements.
> > I think this WG can deliver a comprehensive proposal that delivers
> > pairs of requirements/use cases and ontology modules.
> > We should also consider the valuable observations of John's about
> > the actual reception/sustainability from average users. We clearly
> > need different layers or modules, with the complication that we need
> > compatibility among them: as John said, clarifying those
> > compatibilities is not trivial.
> >
>
> Agree with you and John.
>
>
> Guido Vetere
> Manager, Center for Advanced Studies IBM Italia
> _________________________________________________
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>
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>
> (Salvo che sia diversamente indicato sopra / Unless stated otherwise
> above)

--
Prof. Dr. Philipp Cimiano
Semantic Computing Group
Excellence Cluster - Cognitive Interaction Technology (CITEC)
University of Bielefeld

Phone: +49 521 106 12249
Fax: +49 521 106 12412
Mail: cimiano@cit-ec.uni-bielefeld.de

Room H-127
Morgenbreede 39
33615 Bielefeld

Received on Tuesday, 30 October 2012 09:39:58 UTC

This archive was generated by hypermail 2.3.1 : Monday, 23 October 2017 10:57:26 UTC


text:
# K3 Surfaces : Derivations and automorphisms

The literature about K3 surfaces is extensive. Let us consider the fact that the zero locus of any smooth homogeneous degree 4 equation is a K3 surface.

Let $$R$$ the quotient ring of a homogeneous polynomial in $$4$$ variables and degree $$4$$.

I am not being succesfull to find anything related to the study of derivations and locally nilpotent derivations on these sort of ring. What could be a reference for

1. a description of the derivations on $$R$$?
2. a description of the locally nilpotent derivations on $$R$$?
3. a description of the automorphism groups of $$R$$?
4. any condition for the group of automorphisms of $$R$$ to be finite/finitely generated?
• What do you call a derivation on a surface? If you mean a tangent vector field, they do not exist ($\neq 0$) on a K3.
– abx
Dec 27 '19 at 17:20
• @abx: "do not exist" means "=0". But the question is, indeed, quite unclear. Dec 27 '19 at 19:38
• It was really bad written and it was missing an essential part of the data. Sorry for my mistake in not double checking it. I tried to clarify now... Dec 28 '19 at 3:52
• 1. is just given by the Euler sequence. They are just derivations of the polynomial ring (which are obvious) which takes the equation of the hypersurface to a multiple of the same equation. Dec 29 '19 at 15:57
• @Mohan It is pretty clear that the derivations should have this property related to the polynomial ideal that we are taking the quotient, but I want to know a characterization (if it exists). Dec 31 '19 at 5:14

I can try to say a little about your first question, on derivations of $$R$$, in characteristic 0. As Mohan said, the derivations of $$R$$ are just derivations of the polynomial ring taking the defining equation to itself, but I'd add that it's a bit subtle what the collection of such derivations looks like. It's clear we have derivations of every positive degree $$k$$, for example by first applying the Euler operator and then multiplying by a polynomial of degree $$k$$. So, one natural question you can ask is whether there's a derivation of $$R$$ of negative degree. Note that such a derivation is locally nilpotent (though not all locally nilpotent derivations have negative degree).
The general context for your question is that we're given a ring $$R=S(X,L):=\bigoplus H^0(X,L^m)$$, which is naturally the section ring of a (smooth) projective variety with a chosen ample line bundle. By a theorem of J.M. Wahl ("A cohomological characterization of $$\mathbb P^n$$") if $$R$$ admits a derivation of negative degree, then $$X$$ must in fact be $$\mathbb P^n$$. Thus, in your example there will be no derivations of negative degree. (This crucially uses the characteristic 0 hypothesis.)
In fact, one can rule out differential operators of negative degree of any order on your $$R$$, not just derivations: one can show that the existence of a differential operator of order $$m$$ and degree $$-e$$ gives rise to an element of $$H^0(X,(\mathrm{Sym}^m T_X)(-e))$$, and in turn to an ample subsheaf of $$\mathrm{Sym}^m T_X$$. By powerful results of Miyaoka (Corollary 8.6 of "Deformations of a Morphism along a Foliation and Applications") this in turn forces $$X$$ to be uniruled (again, in characteristic 0!), which your K3 surface is not.


text:
# atomic number of helium

Therefore, the atomic number of Helium is 2. If you are looking for other crossword clue solutions simply use the search functionality in the sidebar. The number of protons is identical to the atomic number (as well as electrons, but these don't matter right now). What is the atomic number of Helium? In its elemental form helium's CAS number is 7440-59-7. So, let's take helium. The helium atom has a covalent radius of 28.pm and it's Van der Waals radius is 140.pm. Share. Asked by Rachit gupta, Last updated: May 24, 2020 + Answer. The atomic … What is the atomic number of Helium? The chemical symbol for Helium is He . THE COMMUNIST MANIFESTO; In The Communist Manifesto, co-authors Karl Marx and Friedrich Engels proposed that the… As we are limited in space, below are a few ideas to help get you started.In Chapter 1, titled “Bourgeois and Proletarians” of Karl Marx and Friedrich Engels’s The Communist Manifesto, both authors… 1 educator From the Greek word helios, the sun. Request. Helios, lit. Here is the answer for: Helium’s atomic number crossword clue. Below you may find the answer for: Helium's atomic number crossword clue.This clue was last seen on Wall Street Journal Crossword December 16 2020 Answers In case the clue doesn’t fit or there’s something wrong please let us know and we will get back to you. look up a periodic table to see the square for helium. 5. Helium. Its boiling point is the lowest among all the elements. The atomic number, equal to the number of protons in the nucleus, locates an element's position in the table. Properties. This is because the atomic number is the number of protons in the nucleus, and an ion is formed when an atom gains or loses electrons, which are located in the electron cloud surrounding the nucleus. The atomic number of an element is usually written in front of and slightly below the element's symbol, like in the Figure below for helium. Ask your question. It’s the second lightest element. Commercial helium is extracted from natural gas. So a helium ion would have an atomic number of 2, which is the atomic number for helium. A subset of exotic light nuclei, the exotic helium isotopes have larger atomic masses than helium's natural isotopes. Wannia Jamil. Helium can be found on the periodic table at atomic number two. manirohith2008 manirohith2008 3 days ago Chemistry Secondary School +5 pts. The abundance of 3 He in air of 0.000 137 % as determined by Nier had a negligible effect on the atomic weight of helium. The principal commercial use of helium is for MRI scanners. The units of the atomic weight are grams/mole. Log in. LEARNING APP; ANSWR; CODR; XPLOR; SCHOOL OS; STAR; answr. what occurs as the atomic number of the elements in period 2 increases? Gaseous chemical element, symbol: He, atomic number: 2 and atomic weight 4,0026 g/mol. The precise estimation of atomic polarizabilities impinges upon a number of areas and processes in physical sciences. The nucleus of the helium atom contains 2 massive, positively charged particles. The number of protons in an atom is called its atomic number ($$Z$$). It should have elements with atomic numbers from 1 (Hydrogen) to the vicinity of 118 (Oganesson). Here is a collection of facts about this lightweight, interesting element: Helium Element Facts . One mole of any atom or molecule is equal to Avogadro's Number. It's supposed to be 2, not 3.The third element is Lithium. It is a noble gas, non metal that is second most common element in the universe after Hydrogen. All helium atoms have two protons, and no other elements have atoms with two protons. Join Now. Answered Nov 17, 2018. A helium ion would have an atomic number of 2. Thus, Z, the atomic number = 2. Z thus defines the identity of the element: Z=1, hydrogen; Z=2, helium; Z=3, lithium;.....Z=80, mercury. Number of protons in Calcium is 20. The other number is the atomic weight. It's average atomic mass is 4.003, and has 2 protons  (because that is the same as the atomic number). 1 3. Helium (from Greek: ἥλιος, translit. By signing up, you'll get thousands of step-by-step solutions to your homework questions. D. 1. Solved: What is the atomic number of helium-4? Ask your question. It has 2 electrons (since the number of electrons is the same as the number of protons) and 2 neutrons in regular atoms (since it's the atomic mass, 4, subtracted by the number of protons, 2). 0. A. Follow. C. 1. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas, the first in the noble gas group in the periodic table. Answer Anonymously; Answer Later; Copy Link ; 5 Answers. 0. Helium is one of the noble gases of group O in the periodic table. Answer Anonymously; Answer Later; Copy Link; 2 Answers. Follow. This number clearly shows you how many protons an element’s nucleus contains. the atomic number is greater. This question is part of Atomic Number of the First 20 Elements On The Periodic Table. Helium is atomic number 2 on the periodic table, with the element symbol He. However, some helium atoms have more or less than two neutrons. Molar mass of Helium … A nucleus with two protons will always be helium. read more This crossword clue was last seen on Wall Street Crossword December 16 2020 Answers. Atomic number of helium is 2 Share Reply. 'Sun') is a chemical element with symbol He and atomic number 2. as the elements in period 2 of the periodic table are considered in succession from left to right, there is a decrease in atomic radius with increasing atomic number. Helium is most commonly used in diving, welding and for inflating balloons. Melting point of Calcium is 839 °C and its the boiling point is 1487 °C. The number of electrons in each of Helium's shells is 2 and its electronic configuration is 1s 2. Helium is the element that is atomic number 2 on the periodic table. megabunny. For example, all helium atoms have two protons, and no other elements have atoms with two protons. Answers (2) Lunamia 24 June, 03:14. B. I believe the answer is C. (: Comment ; Complaint; Link; Margaux 24 June, 04:36. Although all exotic helium isotopes decay with a half-life of less than one second , researchers have eagerly created exotic light isotopes through particle accelerator collisions to create unusual atomic nuclei for elements such as helium, lithium , and nitrogen . Answer. There are no overlaps in this regard. 0. 0. Correct answer to the question What is the atomic number for helium DOES ANYBODY WANT TO RP - e-eduanswers.com The element is also used as a purge gas, to grow silicon wafers and other crystals, and as a protective gas for welding. Atomic Number: 2: Atomic Radius: 140 pm (Van der Waals) Atomic Symbol: He: Melting Point:-272.2 °C: Atomic Weight: 4.003: Boiling Point:-268.93 °C: Electron Configuration: 1s 2 : Oxidation States: 0: History. Helium is a chemical element with atomic number 2 which means there are 2 protons and 2 electrons in the atomic structure. Helium Atomic Number: 2 Helium Symbol: He Helium Atomic Weight: 4.002602(2) Helium Discovery: Janssen, 1868, some sources … Helium is a Block S, Group 18, Period 1 element. Likewise, helium atoms contain two protons despite the conditions or state they are found in. rachit gupta . 0 5 0. It is a colorless, flavorless gas, best known for its use in filling floating balloons. Share. Haha but it doesn’t matter xD Because when identifying atomic number of an atom, you ONLY need to know what element it is Atomic number of an atom is its number of protons. 0. Log in. This question is part of atomic number of the first 20 elements on the periodic table. The number of neutrons can vary to produce isotopes, which are atoms of the same element that have different numbers of neutrons. The number of protons is called the atomic number of any element. Atomic Number. Asked on December 26, 2019 by Pari Rithvick. 1. » Boiling Point » Melting Point » Abundant » State at STP » Discovery Year About Calcium . Since there are two protons in the nucleus of helium, the atomic number of helium is two. Atomic Number of Calcium is 20. The main helium source in the world is a series of fields of natural gas in the United States. This number is very important because it is unique for atoms of a given element. The atomic number does not change when an atom becomes an ion. For example, carbon’s atomic number (Z) is six because it has 6 protons. Rachit gupta. chemistry. Atomic number 2 is used for party balloons, but it's primary use is in the cryogenic industry for cooling superconducting magnets. Janssen obtained the first evidence of helium during the solar eclipse of 1868 when he detected a new line in the solar spectrum. Sources, facts, uses, scarcity (SRI), podcasts, alchemical symbols, videos and images. helium does not have an atomic number. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas, the first in the noble gas group in the periodic table. Element Helium (He), Group 18, Atomic Number 2, s-block, Mass 4.003. 0. The number of electrons can also be different in atoms of the same element, thus producing ions (charged atoms). Wannia Jamil. Join now. Atomic number of hydrogen is 1 and that of helium is 2. but an atom of helium is 5 times denser than hydrogen. Approved by eNotes Editorial Team We’ll help your grades soar. Asked by Megabunny, Last updated: Dec 19, 2020 + Answer. Join now. Therefore the mass of most helium atoms is 4 atomic mass units ($$2 \: \text{amu}$$ for the protons + $$2 \: \text{amu}$$ for the neutrons). This isotope is present in natural sources of helium with a smaller abundance than that of any other stable isotope relative to its elemental composition. Helium (He) is a colorless, odorless gas that has the atomic number 2 and the symbol He. The atomic number is specifically tied to a single element. The orbital in which two electrons are present is called s-orbital. 0. The maximum accommodating capacity of s-orbital is two electrons. Request. This number is … Login. Calculate the number of moles of helium present in 52g of Helium. Answered Oct 01, 2017. Answer:follow me Explanation:atomic number of hellium= 2 mark me Brainilist please 1. How do atomic mass and atomic number compare for helium? A. the atomic mass is greater. the atomic mass and atomic number is qual. Atoms with the same number of protons but different numbers of neutrons are called isotopes. Click hereto get an answer to your question  Calculate the number of moles of helium present in 52g of Helium. Atomic weight of Calcium is 40.078 u or g/mol.  Helium, with an atomic number of 2 and He as its element symbol, is a unique element. 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# [FOM] Is the derivability sign a metalinguistic sign?

Arnon Avron aa at tau.ac.il
Fri Oct 20 15:10:51 EDT 2006

> A simple problem about language and metalanguage in formal theory.
> It is usually stated that |- (sign of derivability) is a
> metalinguistic sign denoting (in a sequent calculus) a
> relation between sets of formulas and formulas.

It is a conceptual mistake to use |- (which is otherwise used
as a meta-language symbol for denotsing consequence
Unfortunately, some authors are doing this confusing mistake -
but no serious book in Proof theory is doing it. Gentzen
himself, as well as Takeuti in "Proof Theory", Troelstra
and Schwichtenberg in "Basic Proof Theory" (and Kleene in
"introduction to Metamathematics") are all using a special
formal symbol (like =>) to separate the two sides of a sequent,
never |-. Then one can write |-\Gamma=>\delta to denote
that \Gamma=>\delta is a theorem of the system, and
S|-\Gamma=>\delta to denote the dertivability in the system
of \Gamma=>\delta from the set of sequents S.

Arnon Avron


text:
## Taiwanese Journal of Mathematics

### GRAPHS WITH 4-STEINER CONVEX BALLS

Tanja Gologranc

#### Abstract

Recently a new graph convexity was introduced, arising from Steiner intervals in graphs that are a natural generalization of geodesic intervals. The Steiner tree of a set $W$ on $k$ vertices in a connected graph $G$ is a tree with the smallest number of edges in $G$ that contains all vertices of $W$. The Steiner interval $I(W)$ of $W$ consists of all vertices in $G$ that lie on some Steiner tree with respect to $W$. Moreover, a set $S$ of vertices in a graph $G$ is $k$-Steiner convex, denoted $g_k$-convex, if the Steiner interval $I(W)$ of every set $W$ on $k$ vertices is contained in $S$. In this paper we consider two types of local convexities. In particular, for every $k \gt 3$, we characterize graphs with $g_k$-convex closed neighborhoods around all vertices of the graph. Then we follow with a characterization of graphs with $g_4$-convex closed neighborhoods around all $g_4$-convex sets of the graph.

#### Article information

Source
Taiwanese J. Math., Volume 19, Number 5 (2015), 1325-1340.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133711

Digital Object Identifier
doi:10.11650/tjm.19.2015.4403

Mathematical Reviews number (MathSciNet)
MR3412008

Zentralblatt MATH identifier
1357.05031

#### Citation

Gologranc, Tanja. GRAPHS WITH 4-STEINER CONVEX BALLS. Taiwanese J. Math. 19 (2015), no. 5, 1325--1340. doi:10.11650/tjm.19.2015.4403. https://projecteuclid.org/euclid.twjm/1499133711

#### References

• B. Bre\ptmrs šar, M. Changat, J. Mathews, I. Peterin, P. G. Narasimha-Shenoi and A. Tepeh Horvat, Steiner intervals, geodesic intervals, and betweenness, Discrete Math., 309 (2009), 6114-6125.
• B. Bre\ptmrs šar and T. Gologranc, On a local 3-Steiner convexity, European J. Combin., 32 (2011) 1222-1235.
• J. Cáceres and O. R. Oellermann, On 3-Steiner simplicial orderings, Discrete Math., 309 (2009) 5828-5833.
• J. Cáceres, O. R. Oellermann and M. L. Puertas, Minimal trees and monophonic convexity, Discuss. Math. Graph Theory, 32 (2012) 695-704.
• M. Changat, H. M. Mulder and G. Sierksma, Convexities related to path properties on graphs, Discrete Math., 290 (2005), 117-131.
• F. F. Dragan, F. Nicolai and A. Brandstädt, Convexity and HHD-free graphs, SIAM J. Discrete Math., 12 (1999) 119-135.
• M. Henning, M. H. Nielsen and O. R. Oellermann, Local Steiner convexity, European J. Combin., 30 (2009) 1186-1193.
• M. Farber and R. E. Jamison, Convexity in graphs and hypergraphs, SIAM J. Algebr. Discrete Methods, 7 (1986) 433-444.
• M. Farber and R. E. Jamison, On local convexity in graphs, Discrete Math., 66 (1987) 231-247.
• E. Kubicka, G. Kubicki and O. R. Oellermann, Steiner intervals in graphs, Discrete Math., 81 (1998) 181-190.
• M. H. Nielsen and O. R. Oellermann, Local 3-monophonic convexity, J. Combin. Math. and Combin. Comput., 80 (2012) 11-24.
• M. H. Nielsen and O. R. Oellermann, Steiner trees and convex geometries, SIAM J. Discrete Math., 23 (2009) 680-693.
• O. R. Oellermann and M. L. Puertas, Steiner intervals and Steiner geodetic numbers in distance-hereditary graphs, Discrete Math., 307 (2007) 88-96.
• M. J. L. van de Vel, Theory of Convex Structures, Amsterdam, North-Holland, 1993.


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Question 03 | Maths Made Easy

# GCSE Maths Functions

## Question 03

If $f(x)=\dfrac{2}{x+1}$ and $g(x)=5x+2$, find the value of $gf(x)$

Select the correct answer from the list below:

A: $\dfrac{17-3x}{x+1}$

B: $\dfrac{x+1}{2x+5}$

C: $\dfrac{5x+2}{x+1}$

D: $\dfrac{2x+12}{x+1}$