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# Unsolved statistics questions from other sites, part II

#### chisigma

##### Well-known member
Like a previous thread also this is opened with the purpose to answer to statistic questions proposed in other sites that didn't receive answer for not less than three days. Let’s start with an interesting problem about ‘Random walking’…

Posted on 11 26 2011 on www.artofproblemsolving.com by the member mr10123 and not yet solved…

 Daniel plays a game with a random number generator. It randomly selects an integer between 1 and n inclusive at the press of a button. If n is selected, he wins n dollars. If any other integer is selected, he loses 1 dollar. He keeps pressing the button until he has more than ‘even’ or he has more money than he begins with. Daniel’s disposable money is unlimited. What is the expected value of the number of times he must press the button?... Kind regards $\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

In my opinion the solution requires the preliminary computation of the following finite sum...

$\displaystyle S_{n}= \sum_{k=1}^{n} k\ x^{k}$ (1)

Starting from the well know formula...

$\displaystyle \sum_{k=0}^{n} x^{k} = \frac{1-x^{n+1}}{1-x}$ (2)

... we obtain in some steps...

$\displaystyle S_{n}= x\ \frac{d}{d x}\ \frac{1-x^{n+1}}{1-x}= \frac{x}{(1-x)^{2}}\ \{1-x^{n+1} -(n+1)\ (1-x)\ x^{n}\} = \frac{x}{(1-x)^{2}}\ -n\ \frac{x^{n+1}}{1-x}$ (3)

Of course is...

$\displaystyle \sum_{k=m}^{n} k\ x^{k}= S_{n}- S_ {m-1}= \frac{(m-1)\ x^{m} -n\ x^{n+1}}{1-x}\$ (4)

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Like a previous thread also this is opened with the purpose to answer to statistic questions proposed in other sites that didn't receive answer for not less than three days. Let’s start with an interesting problem about ‘Random walking’…

Posted on 11 26 2011 on www.artofproblemsolving.com by the member mr10123 and not yet solved…

 Daniel plays a game with a random number generator. It randomly selects an integer between 1 and n inclusive at the press of a button. If n is selected, he wins n dollars. If any other integer is selected, he loses 1 dollar. He keeps pressing the button until he has more than ‘even’ or he has more money than he begins with. Daniel’s disposable money is unlimited. What is the expected value of the number of times he must press the button?...
The first step is the computation of the probability that the iterations end at the k-th trial. Is...

$\displaystyle \text{for}\ k=1\ \text{to}\ n+1 ,\ P_{k}= \frac{1}{n}\ (1-\frac{1}{n})^{k-1}$

$\displaystyle \text{for}\ k=n+2\ \text{to}\ 2n+2 ,\ P_{k}= \frac{1}{n^{2}}\ (1-\frac{1}{n})^{k-2}$

$\displaystyle \text{for}\ k=2n+3\ \text{to}\ 3 n+3 ,\ P_{k}= \frac{1}{n^{3}}\ (1-\frac{1}{n})^{k-3}$

... and in general...

$\displaystyle \text{for}\ k= (j-1)\ n + j\ \text{to}\ j\ (n+1) ,\ P_{k}= \frac{1}{n^{j}}\ (1-\frac{1}{n})^{k-j} = \frac{1}{(n-1)^{j}}\ (1-\frac{1}{n})^{k}$ (1)

... so that the expected value of k can be computed…

$\displaystyle E \{k\}= \sum_{k=1}^{\infty} k\ P_{k}= \sum_{j=1}^{\infty} \frac{1}{(n-1)^{j}}\ \sum_{k=(j-1)\ n + j}^{j\ (n+1) } k\ (1-\frac{1}{n})^{k}$ (2)

The second finite sum can be computed using the result of the previous post and that will be done [possibly! ...] in next posts ...

Kind regards

$\chi$ $\sigma$

#### CaptainBlack

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Like a previous thread also this is opened with the purpose to answer to statistic questions proposed in other sites that didn't receive answer for not less than three days. Let’s start with an interesting problem about ‘Random walking’…

Posted on 11 26 2011 on www.artofproblemsolving.com by the member mr10123 and not yet solved…

 Daniel plays a game with a random number generator. It randomly selects an integer between 1 and n inclusive at the press of a button. If n is selected, he wins n dollars. If any other integer is selected, he loses 1 dollar. He keeps pressing the button until he has more than ‘even’ or he has more money than he begins with. Daniel’s disposable money is unlimited. What is the expected value of the number of times he must press the button?... Kind regards $\chi$ $\sigma$
Is that the exact wording? Could you provide a link to the problem on APS?

I take it n is the index for the play number, but the phrase "He keeps pressing the button until he has more than ‘even’ or .. " is ambiguous. As I read this the stopping condition is satisfied at the begining of the game and so D. never presses the button. Also if he did press the button the game would imeadiatly stop since D. would win and again statisfy the stopping condition. So may be we should assume that n is a fixed integer, but the stopping condition is still satisfied befor the first play.

CB

Last edited:

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Is that the exact wording? Could you provide a link to the problem on APS?

I take it n is the index for the play number, but the phrase "He keeps pressing the button until he has more than ‘even’ or .. " is ambiguous. As I read this the stopping condition is satisfied at the begining of the game and so D. never presses the button. Also if he did press the button the game would imeadiatly stop since D. would win and again statisfy the stopping condition. So may be we should assume that n is a fixed integer, but the stopping condition is still satisfied befor the first play.

CB
The original post is here...

AoPS Forum - Expected value-Random Walk • Art of Problem Solving

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 08 17 2012 on www.mathhelpforum.com by the member pyromania and not yet solved…

A post office has 2 clerks. Alice enters the post office while 2 other customers,Bob and Claire, are being served by the 2 clerks. She is next in line. Assume that the time a clerk spends serving a customer has the exponential (lambda) distribution. What is the expected total time that Alice needs to spend at the post office?...

The answer gives that the expected waiting time(waiting in line) is ½ 1/lambda and the expected time being served in 1/lambda, so the total time is 3/2 1/lambda. I don't understand why the expected waiting time (waiting in line) is ½ 1/lambda…

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 08 17 2012 on www.mathhelpforum.com by the member pyromania and not yet solved…

A post office has 2 clerks. Alice enters the post office while 2 other customers,Bob and Claire, are being served by the 2 clerks. She is next in line. Assume that the time a clerk spends serving a customer has the exponential (lambda) distribution. What is the expected total time that Alice needs to spend at the post office?...

The answer gives that the expected waiting time(waiting in line) is ½ 1/lambda and the expected time being served in 1/lambda, so the total time is 3/2 1/lambda. I don't understand why the expected waiting time (waiting in line) is ½ 1/lambda…
Let suppose to have two exponential r.v. X and Y with...

$\displaystyle f_{x}(t)=f_{y}(t)= \begin{cases} \lambda\ e^{- \lambda\ t}&\text{if}\ t>0 \\ 0 &\text{if}\ t<0 \end{cases}$ (1)

... and we want to find the p.d.f. of the r.v. Z= min (X,Y). Observing the following diagram...

... we have...

$\displaystyle P\{ Z<z\} = 1- \lambda^{2} \int_{z}^{\infty} \int_{z}^{\infty} e^{- \lambda\ (x+y)}\ dx\ dy = 1- e^{-2\ \lambda\ z}$ (2)

... so that is...

$\displaystyle f_{z}(z)= \begin{cases} 2 \lambda\ e^{- 2 \lambda\ z}&\text{if}\ z>0 \\ 0 &\text{if}\ z<0 \end{cases}$ (3)

... and...

$\displaystyle E\{Z\}= \int_{0}^{\infty} z\ f_{z}(z)\ dz = \frac{1}{2\ \lambda}$ (4)

Kind regards

$\chi$ $\sigma$

#### CaptainBlack

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Let suppose to have two exponential r.v. X and Y with...

$\displaystyle f_{x}(t)=f_{y}(t)= \begin{cases} \lambda\ e^{- \lambda\ t}&\text{if}\ t>0 \\ 0 &\text{if}\ t<0 \end{cases}$ (1)

... and we want to find the p.d.f. of the r.v. Z= min (X,Y). Observing the following diagram...

View attachment 304

... we have...

$\displaystyle P\{ Z<z\} = 1- \lambda^{2} \int_{z}^{\infty} \int_{z}^{\infty} e^{- \lambda\ (x+y)}\ dx\ dy = 1- e^{-2\ \lambda\ z}$ (2)

... so that is...

$\displaystyle f_{z}(z)= \begin{cases} 2 \lambda\ e^{- 2 \lambda\ z}&\text{if}\ z>0 \\ 0 &\text{if}\ z<0 \end{cases}$ (3)

... and...

$\displaystyle E\{Z\}= \int_{0}^{\infty} z\ f_{z}(z)\ dz = \frac{1}{2\ \lambda}$ (4)

Kind regards

$\chi$ $\sigma$

Because the exponential distribution is the distribution of the wait for the next arrival for events that arrive at random in time, it is clear that the wait for the first of two events with mean waits of t1 and t2 is exponential with mean wait (t1t2)/(t1+t2). So if t1=t2 the mean wait is t1/2, and the result follows with no integrations since expectations add.

CB

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 12 21 2011 on www.artofproblemsolving.com bythe member ayus_2008 and not yet solved…

Adrunk person walk along the number line as follows : his original position is from x=0 he takes step forward or step backward with equal probability. What isthe probability that he will reach his home which is x=3 before falling into pit which is at x=-2?...

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 12 21 2011 on www.artofproblemsolving.com bythe member ayus_2008 and not yet solved…

A drunk person walk along the number line as follows : his original position is from x=0 he takes step forward or step backward with equal probability. What isthe probability that he will reach his home which is x=3 before falling into pit which is at x=-2?...

Calling $X_{n}$ the sequence of states, is $X_{k}=3$ only if $X_{k-1}=2$ and k is an odd number and it will be...

$\displaystyle P \{X_{2n+1}=3 | X_{2n}=2\}= \frac{1}{2}$ (1)

Now if we set $p_{0}(n) = P\{X_{2n}=0\}$ and $p_{2}(n) = P\{X_{2n}=2\}$ is...

$\displaystyle p_{0}(n+1)= \frac{1}{4}\ \{p_{2}(n) + p_{0} (n)\}$

$\displaystyle p_{2}(n+1)= \frac{1}{4}\ \{p_{2}(n) + p_{0} (n)\}$ (2)

... and from (2) we derive immediately...

$\displaystyle p_{0}(n+1)= p_{2}(n+1)= p(n+1)= \frac{p(n)}{2}$ (3)

The (2) is a difference equation the solution of which with the initial condition $p(0)=\frac{1}{4}$ is $\displaystyle p(n)=\frac{1}{4}\ (\frac{1}{2})^{n}$ so that the probability that the random walker arrives in $X=3$, taking into account (1), is...

$\displaystyle P= \frac{1}{8}\ \sum_{n=0}^{\infty} (\frac{1}{2})^{n}= \frac{1}{4}$ (4)

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 08 12 2012 on www.mathhelpforum.com by the member Newtonian and not yet solved…

Suppose we have independent normally distributed random variables
$X_1 \sim N(c_1,\sigma), X_2 \sim N(c_2,\sigma), \ldots, X_n \sim N(c_n, \sigma)$
where
$\sigma$
and all the
$c_i$
are known. Define
$A=a_1X_1+\ldots+a_nX_n$
and
$B=b_1X_1+\ldots+b_nX_n$
(where all the
$a_i$
and
$b_i$
are known). Form the complex number
$Z=A+Bi$
. What would be a good way of computing the distribution of
$\arg(Z)$
?...

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 08 12 2012 on www.mathhelpforum.com by the member Newtonian and not yet solved…

Suppose we have independent normally distributed random variables
$X_1 \sim N(c_1,\sigma), X_2 \sim N(c_2,\sigma), \ldots, X_n \sim N(c_n, \sigma)$
where
$\sigma$
and all the
$c_i$
are known. Define
$A=a_1X_1+\ldots+a_nX_n$
and
$B=b_1X_1+\ldots+b_nX_n$
(where all the
$a_i$
and
$b_i$
are known). Form the complex number
$Z=A+Bi$
. What would be a good way of computing the distribution of
$\arg(Z)$
?...
The solution of this problem [a little more difficult respect tomost previously posted problems...] require a preliminary computation on thebasis of fig. 1...

fig. 1

The triangle with sides a, b and c of the figure is subject to the ‘sine’s law’so that is…

$\displaystyle \frac {a}{\sin \alpha}=\frac{b}{\sin \beta}= \frac{c}{\sin\theta}$ (1)

… and let’s us suppose that $a$, $\theta$ and$\beta= \pi-\varphi$, so that wecan find from (1) $c$ as function of them…

$\displaystyle c= a\ \frac{\sin \theta}{\sin(\gamma-\theta)}\ ,\ \gamma \ge\theta$ (2)

Now we suppose to have the complex r.v. $A= a +X + i\ Y = a + R\e^{i\ \Gamma}$where $X \sim N (0,\sigma)$ and $Y \sim N(0,\sigma)$ are two independent r.v.The r.v. $R$ and $\Gamma$ have p.d.f. given by…

$\displaystyle f_{R} (\rho) = \frac{\rho}{s}\ e^{- \frac{\rho^{2}}{2\ s^{2}}}$

$\displaystyle f_{\Gamma} (\gamma) =\begin{cases} \frac{1}{2\ \pi}&\text{if}\ -\pi<\gamma<\pi \\ 0&\text{otherwise}\end{cases}$(3)

... where $\displaystyle s^{2}=2\ \sigma^{2}$.From (2) and (3) we derive theprobability that A is in the 'colored' area of fig. 1...

$\displaystyle P \{\text{arg}\ A < \theta\}=\frac{1}{2} + \int_{0}^{\theta}\int_{0}^ {\infty} f_{R}(\rho)\ f_{\Gamma}(\gamma)\ d \rho\ d \gamma +\int_{\theta}^{\pi} \int_{0}^{a\ \frac{\sin\theta}{\sin (\gamma-\theta)}}f_{R}(\rho)\ f_{\Gamma} (\gamma)\ d \rho\ d\gamma =$

$\displaystyle = 1- \frac{1}{2\ \pi}\ \int_{\theta}^{\pi} e^{- \frac{a^{2}\\sin^{2} \theta}{2\ s^{2}\ \sin^{2}(\gamma-\theta)}} d \gamma$ (4)

The possibility of more develop from the (4) will be examined in successive posts...

Kind regards

$\chi$ $\sigma$

#### CaptainBlack

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

The solution of this problem [a little more difficult respect tomost previously posted problems...] require a preliminary computation on thebasis of fig. 1...

View attachment 314

fig. 1

The triangle with sides a, b and c of the figure is subject to the ‘sine’s law’so that is…

$\displaystyle \frac {a}{\sin \alpha}=\frac{b}{\sin \beta}= \frac{c}{\sin\theta}$ (1)

… and let’s us suppose that $a$, $\theta$ and$\beta= \pi-\varphi$, so that wecan find from (1) $c$ as function of them…

$\displaystyle c= a\ \frac{\sin \theta}{\sin(\gamma-\theta)}\ ,\ \gamma \ge\theta$ (2)

Now we suppose to have the complex r.v. $A= a +X + i\ Y = a + R\e^{i\ \Gamma}$where $X \sim N (0,\sigma)$ and $Y \sim N(0,\sigma)$ are two independent r.v.The r.v. $R$ and $\Gamma$ have p.d.f. given by…

$\displaystyle f_{R} (\rho) = \frac{\rho}{s}\ e^{- \frac{\rho^{2}}{2\ s^{2}}}$

$\displaystyle f_{\Gamma} (\gamma) =\begin{cases} \frac{1}{2\ \pi}&\text{if}\ -\pi<\gamma<\pi \\ 0&\text{otherwise}\end{cases}$(3)

... where $\displaystyle s^{2}=2\ \sigma^{2}$.From (2) and (3) we derive theprobability that A is in the 'colored' area of fig. 1...

$\displaystyle P \{\text{arg}\ A < \theta\}=\frac{1}{2} + \int_{0}^{\theta}\int_{0}^ {\infty} f_{R}(\rho)\ f_{\Gamma}(\gamma)\ d \rho\ d \gamma +\int_{\theta}^{\pi} \int_{0}^{a\ \frac{\sin\theta}{\sin (\gamma-\theta)}}f_{R}(\rho)\ f_{\Gamma} (\gamma)\ d \rho\ d\gamma =$

$\displaystyle = 1- \frac{1}{2\ \pi}\ \int_{\theta}^{\pi} e^{- \frac{a^{2}\\sin^{2} \theta}{2\ s^{2}\ \sin^{2}(\gamma-\theta)}} d \gamma$ (4)

The possibility of more develop from the (4) will be examined in successive posts...

Kind regards

$\chi$ $\sigma$

But $$X$$ and $$Y$$ are not independent.

CB

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

But $$X$$ and $$Y$$ are not independent.

CB
That's right... so that my 'preliminary computation' has only illustrative purpose and has to be modified...

Kind regards

$\chi$ $\sigma$

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#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 07 16 2012 on www.artofproblemsolving.com by the member jetix and not yet solved…

Calculate the distribution of the random variable...

... where is Brownian motion...

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 07 16 2012 on www.artofproblemsolving.com by the member jetix and not yet solved…

Calculate the distribution of the random variable...

... where is Brownian motion...

A Wiener Process[know alsoas Brownian Motion…] is a stochastic process$W_{t}$ with the following properties…

a)$\displaystyle W_{0}=0$...

b) $\displaystyle W_{t}$ is continuous in t…

c) $\displaystyle W_{t}$ has increments $\displaystyle W_{t} – W_{s} \sim\mathcal {N} (0, t-s)$...

From the property c) setting s=0 we derive the p.d.f. of $W_{t}$at the time t…

$\displaystyle f(x,t)=\frac{1}{\sqrt{2\ \pi\ t}}\ e^{- \frac{x^{2}}{2\ t}}$ (1)

... and also the basic properties...

$\displaystyle E \{W_{t}\}=0$ (2)

$\displaystyle E \{W_{s} \cdot W_{t}\} =\text{min}\ (s,t)$ (3)

Now if we define $\displaystyle Y(t)=\int_{0}^{t} W_{s}\ d s$, according with (3), we find...

$\displaystyle E \{Y^{2}\} = \int_{0}^{t}\ \int_{0}^{t} E \{W_{\sigma} \cdot W_{\tau}\} d \sigma d \tau =$

$\displaystyle = \int_{0}^{t}\ \int_{0}^{t} \text{min} (\sigma,\tau)\ d \sigma d \tau = \frac{t^{3}}{3}$ (4)

... so that the p.d.f of Y is $\displaystyle \mathcal{N} (0, \frac{t^{3}}{3})$...

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 08 30 2012 on www.mathhelpforum.com by the member nek and not yet solved…

Hello, I'm trying to complete a course on SDE and I need to solve two stochastic differential equations.They are supposed to be easy, but I'm still a beginner and to be honest I'm quite stuck.The equations are the following...

a) $\displaystyle d X_{t} = dt + d W_{t}^{x}$

b) $\displaystyle d Y_{t} = X{t}\ d W_{t}^{y}$

... where $W_{t}^{x}$ and $W_{t}^{y}$ are uncorrelated brownian motions...

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 08 30 2012 on www.mathhelpforum.com by the member nek and not yet solved…

Hello, I'm trying to complete a course on SDE and I need to solve two stochastic differential equations.They are supposed to be easy, but I'm still a beginner and to be honest I'm quite stuck.The equations are the following...

a) $\displaystyle d X_{t} = dt + d W_{t}^{x}$

b) $\displaystyle d Y_{t} = X{t}\ d W_{t}^{y}$

... where $W_{t}^{x}$ and $W_{t}^{y}$ are uncorrelated brownian motions...

Preliminary to the solution of SDE is a short explanation of the so called 'Ito's Integral' , a 'special integral' developed by the Japanese mathematician Kiyoshi Ito. Let's suppose that $W_{t}$ is a Wiener process [or brownian motion...] and we want to compute an integral like this...

$\displaystyle \int_{0}^{t} G(W_{t})\ dW_{t}$ (1)

The 'standard' approach $\displaystyle dW_{t}= \frac {dW_{t}}{dt}\ dt$ fails because one of the properties of the Wiener process is that it is non differentiable respect to t. The general case is quite complex and the interested reader is recommended to access to the specialized lecterature but for our purpose it will be enough to consider the following particular case...

Let $f(x)$ a twice differrentiable function with $\displaystyle f^{'\ '} (x)$ continous. In that case the 'Ito's rule' extablishes that...

$\displaystyle d f(W_{t})= f^{'}(W_{t})\ dW_{t} + \frac{1}{2}\ f^{'\ '}(W_{t})\ dt$ (2)

... and integrating (2) we obtain...

$\displaystyle \int_{0}^{t} f^{'}(W_{t}) dW_{t} = f(W_{t})- f(0) -\frac{1}{2} \int_{0}^{t} f^{'\ '} (W_{s}) ds$ (3)

As simple example let's consider the 'simple' case $f(x)=x$...

$\displaystyle \int_{0}^{t} W_{t} dW_{t} = \frac{W_{t}^{2}}{2} - \frac{1}{2}\ \int_{0}^{t} ds = \frac{W_{t}^{2}}{2}- \frac{t}{2}$ (4)

Two very interesting properties of (4)...

a) respect to the 'traditional integration' there is the 'extra term' $\displaystyle - \frac{t}{2}$...

b) the integral of a 'random process' is the sum of a random variable and a deterministic variable...

Kind regards

$\chi$ $\sigma$

Last edited:

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 08 30 2012 on www.mathhelpforum.com by the member nek and not yet solved…

Hello, I'm trying to complete a course on SDE and I need to solve two stochastic differential equations.They are supposed to be easy, but I'm still a beginner and to be honest I'm quite stuck.The equations are the following...

a) $\displaystyle d X_{t} = dt + d W_{t}^{x}$

b) $\displaystyle d Y_{t} = X{t}\ d W_{t}^{y}$

... where $W_{t}^{x}$ and $W_{t}^{y}$ are uncorrelated brownian motions...

At this point a short description of the solving procedure of linear SDE is presented. Let's start with a 'standard' first order linear ODE...

$\displaystyle \frac{d x_{t}}{d t}= a_{t}\ x_{t} + u_{t}\ ,\ x(0)=x_{0}$ (1)

... the solution of which is...

$\displaystyle x_{t}= \varphi_{t}\ \{x_{0} + \int_{0}^{t} \varphi_{s}^{-1}\ u_{s}\ ds\}$ (2)

... where $\varphi_{t}$ is the solution of the linear ODE...

$\displaystyle \frac{d \varphi_{t}}{d t}= a_{t}\ \varphi_{t}\ ,\ \varphi_{0}=1$ (3)

All that is well known and now we examine how can be used in the solution of a linear in narrow sense SDE that has the form...

$\displaystyle d X_{t}= (a_{t}\ X_{t} + u_{t})\ d t + v_{t}\ dW_{t}\ ,\ X_{0}=x_{0}$ (4)

... and the solution of which is given by...

$\displaystyle X_{t}= \varphi_{t}\ \{ x_{0} + \int_{0}^{t} \varphi_{s}^{-1}\ u_{s}\ ds + \int_{0}^{t} \varphi_{s}^{-1}\ v_{s}\ dW_{s} \}$ (5)

... where $\varphi$ has been defined previously and the second integral is an 'Ito's integral' so that [very important detail...] the solution is the sum of a deterministic variable and a random variable.

Now we are able to solve the first of the SDE proposed by nek...

$\displaystyle d X_{t} = dt + d W_{t}$ (6)

It is a 'narrow sense' linear SDE in the form (4) where $a_{t}=0$, $u_{t}=1$ and $v_{t}=1$ so that is $\varphi_{t}=1$ and the solution is...

$\displaystyle X_{t}= x_{0}+t + \int_{0}^{t} dW_{s}= x_{0}+t+ W_{t}$ (7)

... where the previously described solving procedure of the Ito's integral has been applied...

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 06 07 2012 on www.talkstat.com by the member nounuo and not yet properly solved…

... how can I find the expectation of the distance between any two points uniformly distributed in a square of side 1?... I need a mathematical prove…

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 06 07 2012 on www.talkstat.com by the member nounuo and not yet properly solved…

... how can I find the expectation of the distance between any two points uniformly distributed in a square of side 1?... I need a mathematical prove…
Although at first may seem 'easy', the solution requires several steps. The first step is, given two r.v. X and Y uniformly distributed from 0 to1, the p.d.f. of the r.v. Z=X-Y is...

$\displaystyle f_{Z} (t) =\begin{cases} 1+t\ \text{if}\ -1<t<0 \\ 1-t\ \text {if}\ 0<t<1 \\ 0\ \text{otherwise} \end{cases}$ (1)

... and the demonstration of that is left to the reader. The second step istofind the p.d.f. of the r.v. $U=Z^{2}$ and that is achieved considering that...

$\displaystyle P \{U<t\} = P \{Z<\sqrt t\}= 2\ \int_{0}^{\sqrt t} (1-t)\ dt= 2\ \sqrt t -t$ (2)

... and deriving (2) we have...

$\displaystyle f_{U}(t)= \begin{cases}\frac{1}{\sqrt t}-1\ \text {if}\ 0<t<1 \ \\ 0\ \text{otherwise} \end{cases}$(3)

More steps will be realized in successive posts...

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Although at first may seem 'easy', the solution requires several steps. The first step is, given two r.v. X and Y uniformly distributed from 0 to1, the p.d.f. of the r.v. Z=X-Y is...

$\displaystyle f_{Z} (t) =\begin{cases} 1+t\ \text{if}\ -1<t<0 \\ 1-t\ \text {if}\ 0<t<1 \\ 0\ \text{otherwise} \end{cases}$ (1)

... and the demonstration of that is left to the reader. The second step istofind the p.d.f. of the r.v. $U=Z^{2}$ and that is achieved considering that...

$\displaystyle P \{U<t\} = P \{Z<\sqrt t\}= 2\ \int_{0}^{\sqrt t} (1-t)\ dt= 2\ \sqrt t -t$ (2)

... and deriving (2) we have...

$\displaystyle f_{U}(t)= \begin{cases}\frac{1}{\sqrt t}-1\ \text {if}\ 0<t<1 \ \\ 0\ \text{otherwise} \end{cases}$(3)

More steps will be realized in successive posts...

The r.v. U having p.d.f. (3) is the square of the distance between two random points in the interval (0,1). Now we proceed as in...

http://www.mathhelpboards.com/f23/unsolved-statistics-questions-other-sites-932/index8.html#post7039

... and...

http://www.mathhelpboards.com/f23/unsolved-statistics-questions-other-sites-932/index9.html#post7118

... and we find...

$\displaystyle \mu= E (\delta^{2})= \int_{0}^{1} (\sqrt t -t)\ dt = \frac{1}{6} \implies E (\delta)= \frac{1}{\sqrt{6}}$ (4)

Now we suppose to have two r.v. $U_{1}$ and $U_{2}$ each having p.d.f. (3). In this case if $U=U_{1}+U_{2}$ it will be...

$\displaystyle E (\delta^{2})= 2\ \mu= \frac{1}{3} \implies E (\delta)= \frac{1}{\sqrt{3}}$ (5)

... and (5) is the solution of the proposed problem. Of course in n dimension is...

$\displaystyle E (\delta^{2})= n\ \mu= \frac{n}{6} \implies E (\delta)= \sqrt{\frac{n}{6}}$ (6)

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 10 15 2012 on Math Help Forum - Free Math Help Forums by the user Dinkydoe and not jet solved…

Let $\displaystyle P\ \{X_{k}=1\} = P\ \{X_{k}=0\}=\frac{1}{2}$ (Bernoulli trials) and consider $\displaystyle Y=3\ \sum_{k=1}^{\infty} 4^{-k}\ X_{k}$. Apparently the p.d.f. of Y is constant on $(\frac{1}{4}\ ,\ \frac{3}{4})$, satisfies $\displaystyle f(x)=1-f(x)$ on $(0,1)$ and for $x<\frac{1}{4}$ is $\displaystyle f(x)=2\ f(\frac{x}{4})$...

I’m a bit bewildered…

Kind regards

$\chi$ $\sigma$

Last edited:

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

Posted on 10 15 2012 on Math Help Forum - Free Math Help Forums by the user Dinkydoe and not jet solved…

Let $\displaystyle P\ \{X_{k}=1\} = P\ \{X_{k}=0\}=\frac{1}{2}$ (Bernoulli trials) and consider $\displaystyle Y=3\ \sum_{k=1}^{\infty} 4^{-k}\ X_{k}$. Apparently the p.d.f. of Y is constant on $(\frac{1}{4}\ ,\ \frac{3}{4})$, satisfies $\displaystyle f(x)=1-f(x)$ on $(0,1)$ and for $x<\frac{1}{4}$ is $\displaystyle f(x)=2\ f(\frac{x}{4})$...

I’m a bit bewildered…
The most effective way to attack this problem is the use of 'convolution theorem' that extablishes that, if the r.v. U and V have p.d.f. $f_{U}(t)$ and $f_{V} (t)$, then the r.v. Z=U+V has p.d.f. $f_{Z}(t)= f_{U}(t)*f_{V}(t)$ where '*' means convolution. Each r.v. $Y_{k}= 3\ \frac{X_{k}}{2^{2\ k}}$ has p.d.f. $f_{k}(t)$ the fourier Transform of which is given by...

$\displaystyle \mathcal {F} \{f_{k}(t)\}= e^{- i\ \frac{3\ \omega}{2^{2k+1}}}\ \cos \frac{3\ \omega}{2^{2k+1}}$ (1)

... so that the Fourier Transform od the p.d.f. of the r.v. Y is...

$\displaystyle \mathcal {F} \{f_{Y}(t)\}= \prod_{k=1}^{\infty} e^{- i\ \frac{3\ \omega}{2^{2k+1}}}\ \prod_{k=1}^{\infty} \cos \frac{3\ \omega}{2^{2k+1}} = e^{-i\ \frac{\omega}{2}}\ \prod_{k=1}^{\infty} \cos \frac{3\ \omega}{2^{2k+1}}$ (2)

Observing (2) it is evident enough that the p.d.f. $f_{Y}(t)$ is 'even' respect to $t=\frac{1}{2}$ but for an explicit expression for that requires the computation of the integral...

$\displaystyle \frac{1}{\pi}\ \int_{0}^{\infty} \prod_{k=1}^{\infty} \cos \frac{3\ \omega}{2^{2k+1}}\ \cos \omega\ t\ d \omega$ (3)

... that will be performed [if possible...] in successive posts...

Kind regards

$\chi$ $\sigma$

#### chisigma

##### Well-known member
Re: Unsolved statistic questions from other sites, part II

From…

http://www.mathhelpboards.com/f28/p...ility-distribution-submarine-call-signs-2168/

A hostile naval power possesses a large, unknown number N of submarines. Interception of radio signals yields a small number n of identification numbers $X_{i},\ i=1,2,...,n$ which ate taken to be independent and uniformly distributed over the continuous range from 0 to N. Show that $Z_{1}$ and $Z_{2}$, defined by...

$\displaystyle Z_{1}= \frac{n+1}{n}\ \text{max}\ (X_{1},X_{2},…,X_{n})$ (1)

… and…

$\displaystyle Z_{2}= \frac{2}{n} \sum_{i=1}^{n} X_{i}$ (2)

… both have means equal to N.

Calculate the variance of $Z_{1}$ and $Z_{2}$. Which estimator do you prefer, and why?...

For illustrative purpose let's start with $Z_{1}$ in the particular case N=4 and n=2, so that is $Z_{1}= \text{max}\ (X_{1},X_{2})$, and some aids can come from the following table...

Calling $p_{k,4,2}$ the probability that $\text{max}\ (X_{1}, X_{2})=k$ for the samples $X_{1},\ X_{2}$, it is easy to see from the table that, if $X_{1}$ and $X_{2}$ are independent and uniformely distributed from 1 to 4, is…

$\displaystyle p_{k,4,2} = P \{X_{1} \le k, X_{2} \le k \} - P \{X_{1} \le k-1, X_{2} \le k-1 \}= \frac{k^{2}-(k-1)^{2}}{16}$ (1)

The example now illustrated makes easier to find the general formula...

$\displaystyle p_{k,N,n} = P \{X_{1} \le k, X_{2} \le k, ..., X_{n} \le k \} - P \{X_{1} \le k-1, X_{2} \le k-1, ..., X_{n} \le k-1 \}= \frac{k^{n}-(k-1)^{n}}{N^{n}}$ (2)

... that supplies the probability that $X = \text{max}\ (X_{1}, X_{2}, ..., X_{n})=k$ for the samples $X_{1},\ X_{2}, ...,\ X_{n}$ independent and uniformely distributed from 1 to N.
Using (2) we can evaluate the $E \{ X \}$ as...

$\displaystyle \mu = E \{ X \} = \frac{1}{N^{n}}\ \sum_{k=1}^{N} k\ \{ k^{n}-(k-1)^{n} \}$ (3)
… that, if we consider that is…
$\displaystyle k\ \{ k^{n}-(k-1)^{n} = n\ k^{n} - \frac{n\ (n-1)}{2} k^{n-1} + … + (-1)^{n-1} k$ (4)
... may be written as...

$\displaystyle \mu= E \{ X \} = \frac{1}{N^{n}}\ \{ n\ \sum_{k=1}^{N} k^{n} - \frac{n\ (n-1)}{2}\ \sum_{k=1}^{N} k^{n-1} + ...\} = \frac{1}{N^{n}}\ \{ n\ \frac{B_{n+1} (N+1) - B_{n+1} (0)}{n+1} - \frac{n\ (n-1)}{2}\ \frac{B_{n} (N+1) - B_{n} (0)}{n} + ...\}$ (5)

... where the $B_{i} (*)$ are the Bernoulli Polynomials of order i. Now if we consider that is $\displaystyle \lim_{N \rightarrow \infty} \frac {B_{i} (N+1)}{N^{j}}$ is 1 for i=j and 0 for i<j we obtain that for N 'large enough' is...

$\displaystyle E \{ X \} \sim \frac {n}{n+1}\ N$ (6)

With the goal to arrive to the $\text{Var}\ \{x \}$ now we compute the $E\ \{X^{2} \}$ as...

$\displaystyle E \{ x^{2} \} = \frac{1}{N^{n}}\ \sum_{k=1}^{N} k^{2}\ \{ k^{n}-(k-1)^{n} \}$ (7)

All what we have to do is to repeat the steps from (3) to (6) with $k^{2}$ instead of $k$, obtaining...

$\displaystyle k^{2}\ \{ k^{n}-(k-1)^{n} = n\ k^{n+1} - \frac{n\ (n-1)}{2}\ k^{n} + …$ (8)
... so that is...

$\displaystyle E \{ x^{2} \} = \frac{1}{N^{n}}\ \{ n\ \sum_{k=1}^{N} k^{n+1} - \frac{n\ (n-1)}{2}\ \sum_{k=1}^{N} k^{n} + ...\} = \frac{1}{N^{n}}\ \{ n\ \frac{B_{n+2} (N+1) - B_{n+2} (0)}{n+2} - \frac{n\ (n-1)}{2}\ \frac{B_{n+1} (N+1) - B_{n+1} (0)}{n+1} + ...\}$ (9)

... and 'pushing' N to infinity...

$\displaystyle E \{ x^{2} \} \sim \frac{n}{n+2}\ N^{2} - \frac{n\ (n-1)}{2\ (n+1)}\ N$ (10)

The requested value of $\text {Var} \{ X \}$ is therefore...

$\displaystyle \sigma^{2} = \text {Var} \{ X \} = E \{ X^{2} \} - \mu^{2} \sim \frac{n}{(n+1)^{2}\ (n+2)}\ N^{2} - \frac{n\ (n-1)}{2\ (n+1)}\ N$ (11)

As in previous posts, if would be highly preferable that someone controls my work ...

The r.v. $Z_{2}$ will be treated in succesive post...

Kind regards

$\chi$ $\sigma$


text:
25-30 July 2016
Clock Tower Centennial Hall, Kyoto University
Asia/Tokyo timezone
Home > Contribution List
Displaying 111 contributions out of 111
Session: Pentaquarks
Recently, two hidden-charmed resonances $P_c(4380)$ and $P_c(4450)$ consistent with pentaquark states were observed at the LHCb detector. The two $P_c$ states locate just below the $\bar{D}\Sigma^*_c$ and $\bar{D}^*\Sigma_c$ thresholds with mass of gaps about 5 and 15 MeV, respectively. Inspired by this fact we perform a dynamical investigation about the $\bar{D}\Sigma_c^*(2520)$ and $\bar{D}^*\Si ... More Presented by Jun HE on 27 Jul 2016 at 14:15 Session: Mesons A new$\eta$photoproduction experiment is planned for the determination of the$\eta$-$n$low-energy scattering parameters at the Research Center for Electron Photon Science (ELPH), Tohoku University. The emitted proton is measured at 0 degrees for the$\gamma d\to p eta n$reaction at$E_\gamma \sim 0.9$GeV, which gives the zero relative momentum between the$\eta$meson and the neutron. Two ph ... More Presented by Takatsugu ISHIKAWA on 29 Jul 2016 at 17:50 We study the$¥bar{K}N$system in the Skyrme model in a method based on the bound state approach of Callan-Klebanov but with the kaon around the physical nucleon of the rotating hedgehog. This corresponds to the variation after projection which is opposite to the variation before projection. The new method is considered to be more suited to the study of the weakly interacting$¥bar{K} N$system ... More Presented by Takashi EZOE on 29 Jul 2016 at 18:20 Large N_c QCD in 1+3 dimensional spacetime can be converted into its holographic dual model via gauge/gravity correspondence (called the Sakai-Sugimoto model or holographic QCD)[1]. This QCD-based model well reproduces the mass spectrum of mesons, and also explains many properties of hadron phenomenology such as anomalies, the vector meson dominance, and the Skryme model. In this paper, we conside ... More Presented by Hideo SUGANUMA on 27 Jul 2016 at 15:20 We investigate the H-dibaryon (uuddss) in holographic QCD [1, 2]. Holographic QCD is derived from a QCD-equivalent D-brane system in the superstring theory via the gauge/gravity correspondence. In holographic QCD, all baryons appear as topological chiral solitons of Nambu-Goldstone bosons and (axial) vector mesons [1, 2]. In this framework, the H-dibaryon can be described as an SO(3)-type hedgehog ... More Presented by Kohei MATSUMOTO on 27 Jul 2016 at 15:50 Rare electroweak penguin processes provide a rich platform to search for new physics. Some deviations have recently been found between the rate and angular distribution of these processes measured by the LHCb experiment and theoretical predictions. In addition, LHCb has seen hints of lepton universality breaking in these rare processes. This talk will review these measurements and put them in the ... More Presented by Marcin CHRZASZCZ on 29 Jul 2016 at 15:20 Session: Plenary Knowing the structure of excited baryons is an important gateway to probing non-perturbative QCD. The CLAS system at Jefferson Lab has delivered a wealth of precise photo- and electro-production information about light-quark baryon structure. Examples from photoproduction of strange baryons that lead to insight about the non-strange N* spectrum will be discussed. Examples from electroproduction of ... More Presented by Reinhard SCHUMACHER on 29 Jul 2016 at 11:40 Session: Plenary The nucleon excitation scheme has been under intensive investigation with meson photoproduction experiments during the last few years world wide. Currently, a lot of new experimental results are coming out from the CLAS experiment at Jlab, the Crystal Barrel experiment at the ELSA accelerator in Bonn and the Crystal Ball experiment at the MAMI accelerator in Mainz. These experiments focus on the ... More Presented by Reinhard BECK on 29 Jul 2016 at 11:00 The BESIII Experiment at the Beijing Electron Positron Collider (BEPCII) accumulated the world's largest e+e- collision samples at 3.773 and 4.009 GeV. In this talk, we will report the recent results on charm decays, including semi-leptonic decays, determination of CKM elements |Vcs(d)|, Dalitz plot decays of Ksπ+π0，KsK+K-. Presented by Yi FANG on 29 Jul 2016 at 14:50 Session: Plenary on 30 Jul 2016 at 18:00 We derived the conditions on certain combinations of integrals of the fragmentation functions of pion using HERMES data for the sum of the charged pion multiplicities from semi-inclusive deep-inelastic scattering (SIDIS) off the deuteron target. In our derivation the nucleon parton distribution functions (PDFs) are assumed to be isospin SU(2) symmetric. Similar conditions have also been obtained f ... More Presented by Chung-Wen KAO on 26 Jul 2016 at 15:50 Aiming at quantitative studies of Kbar nuclei, we construct the reliable KbarN local potential. Based on the chiral coupled-channel approach, the chiral unitary approach, we establish a new construction method which respects the behavior of the scattering amplitude in the complex energy plane. This method is employed to the recent experimental data of the energy shift of the kaonic hydrogen by SID ... More Presented by Kenta MIYAHARA on 29 Jul 2016 at 17:50 The HADES experiment at GSI was designed to investigate the properties of hadrons inside dense nuclear matter. The latter is created in heavy-ion collisions at energies of 1-2 AGeV. HADES is currently the only running experiment that studies the region in the QCD phase diagram of very high net-baryon densities and low temperatures. Similar conditions are also present in one of the most fascinating ... More Presented by Celso FRANCO on 26 Jul 2016 at 15:50 Session: Mesons We present a study of the Dalitz decay η → γe + e − . The aim is to determine the transition form factor of the η meson. The transition form factor describes the electromagnetic structure of the meson. The transition form factor is determined by comparing the experimental e + e − invariant mass distribution with QED. The analysis uses proton-proton reaction at 1.4 GeV.The data has been co ... More Presented by Ankita GOSWAMI on 29 Jul 2016 at 18:20 Session: Plenary Our understanding of the theory of strong interaction, quantum chromo-dynamics (QCD), has advanced enormously in the past decades. Both experimentally and theoretically, perturbative regime in QCD has been explored and understood at precision. At the same time, lattice QCD calculations have begun to yield many quantitative results on properties of hadrons. The experimental understanding of how nuc ... More Presented by Rik YOSHIDA on 30 Jul 2016 at 12:20 Session: Baryons The Siegert's theorem states that in a g* N -> N* transition, where N and N* are respectively the nucleon and a nucleon resonance, the electric amplitude, E (defined by the transverse amplitudes) and the scalar amplitude, S, are related in the pseudo-threshold limit by E ~ w/q*S, where w and q are the photon energy and momentum. The pseudo-threshold limit is the limit where q ->0, when the nucleon ... More Presented by Gilberto RAMALHO on 26 Jul 2016 at 17:25 The polarized deuteron has new structure functions in charged-lepton deep inelastic scattering due to its spin-one nature, and they are b1, b2, b3, and b4. The twist-two structure functions b1 and b2 are expressed by tensor-polarized parton distribution functions in the deuteron [1]. There is an approved experiment at JLab to measure them and it is expected to start in 2019. On the other hand, the ... More Presented by Qin-Tao SONG on 26 Jul 2016 at 15:20 Session: Mesons We conducted measurement of excitation spectra in 12C(p,d) reactions near the eta' emission threshold. We employed a 2.5 GeV proton beam accelerated by the synchrotron SIS-18 of GSI impinging on a carbon target. The emitted deuterons at 0 degree were momentum-analyzed by the fragment separator FRS used as a high-resolution spectrometer. We achieved an extremely good statistical sensitivity with a ... More Presented by Kenta ITAHASHI on 29 Jul 2016 at 17:20 In the hadron spectroscopy in the heavy quark region, new symmetry plays an important role. The symmetry is the heavy quark spin symmetry. It manifests the mass degeneracy of the states with different total spin, e.g. degeneracies of$D$and$D^\ast$mesons and$\Sigma_c$and$\Sigma^\ast_c$baryons. It is important to generate the exotic hadron structures found in the heavy quark region. The mass ... More Presented by Yasuhiro YAMAGUCHI on 27 Jul 2016 at 14:15 Session: Pentaquarks We study the possibility that at least one of the two pentaquark structures recently reported by LHCb, can be described as a compact pentaquark state, and we give predictions for new channels that can be studied by the experimentalist if this hypothesis was correct. We use very general arguments dictated by symmetry considerations, in order to describe pentaquark states within a symmetry approach. ... More Presented by Elena SANTOPINTO on 26 Jul 2016 at 14:45 There have been reports on exotic-hadron candidates, especially tetraquark and pentaquark hadrons, in the last several years. However, it is not easy to determine whether they are in fact exotics by low-energy experiments on global properties such as masses, decay widths, spins, and parities. It could be appropriate to determine their internal configurations by high-energy reactions because quark ... More Presented by Shunzo KUMANO on 26 Jul 2016 at 14:15 Session: Baryons The concept of diquark degrees of freedom is expected to be essential to describe hadrons in the excited states as well as in the ground states. Since the spin-dependent interaction between quarks is inversely proportional to the masses of the quarks, the extraction of a light-qq correlation from baryons with one heavy quark is easier than from those with only light flavors. J-PARC E50 experiment ... More Presented by Tomonori TAKAHASHI on 29 Jul 2016 at 15:20 Session: Mesons The COMPASS experiment at CERN has collected a very large data set of 50 million diffractively produced$\pi^-\pi^+\pi^-$events using a$190\,$GeV$/c$negatively charged hadron beam. The partial-wave analysis (PWA) of these high-precision data reveals previously unseen details. The PWA, which is currently limited by systematic uncertainties, is based on the isobar model, in which multi-particle d ... More Presented by Fabian KRINNER on 29 Jul 2016 at 15:50 Session: Few body Systems The structure of the light antikaon-nuclear quasi-bound states is investigated with correlated Gaussian method. We perform full three- to seven-body calculations for the systems which consist of an antikaon (anti-K) and a few nucleons (N) such as anti-KNN, anti-KNNN, anti-KNNNN and anti-KNNNNNN systems without any many-body approximation and investigate how the nuclear structure is changed by inje ... More Presented by Shota OHNISHI on 26 Jul 2016 at 16:50 Session: Baryons Form factors for timelike momentum transfers, determined by hadron-antihadron formation in e+e- annihilation, provide information about spin correlations between the hadron pair produced, information complementary to that provided by spacelike form factors determined by electron scattering from hadronic targets. Timelike form factors at large momentum transfers have only been so far measured for o ... More Presented by Kamal SETH on 26 Jul 2016 at 14:15 We study theoretically the formation of deeply bound pionic atoms to deduce precisely the pion properties in nuclei from the observables. It is important to know the pion properties in nuclei since they are believed to provide valuable information on the aspects of the symmetry of strong interaction at finite density. In this presentation, we show the theoretical formation spectra of deeply bound ... More Presented by Natsumi IKENO on 29 Jul 2016 at 15:15 Session: Plenary In this talk, we shed light upon the mass of the eta' in nuclear matter in the context of partial restoration of chiral symmetry, pointing out that the U_A(1) anomaly effects causes the mass difference of eta'-eta necessarily through the chiral symmetry breaking. As a consequence, the mass of the eta' is expected to be reduced by order of 100 MeV in nuclear matter. We propose several reactions for ... More Presented by Hideko NAGAHIRO on 29 Jul 2016 at 09:55 Session: Mesons We derive gluon fragmentation functions in the Nambu-Jona-Lasinio (NJL) model by approximating a gluon as a fictitious color-octet quark-anti-quark ($q\bar q$) pair. Gluon elementary fragmentation functions are derived from the quark and anti-quark elementary fragmentation functions for emitting specific mesons in the NJL model under the requirement that the$q\bar q$pair maintains in the flavor- ... More Presented by Dong-Jing YANG on 27 Jul 2016 at 15:20 Session: Mesons The KLOE experiment has collected 2.5 fb-1 at the peak of the phi resonance at the e+e- collider DAPHNE in Frascati. A new beam crossing scheme, allowing for a reduced beam size and increased luminosity, is currently operating at DAPHNE. The upgraded detector, named KLOE-2, has already collected 2.0 fb-1 in these new operating conditions, aiming to reach at least 5 fb-1 in the next two years. The ... More Presented by Caterina BLOISE on 29 Jul 2016 at 14:15 Session: Plenary The COMPASS spectroscopy program mostly foots on the use of hadron beams. Large data samples on diffractive production using incoming pions and kaons allow new insights into the spectrum of light and strange mesons. Large data samples also require the development of new analysis methods and close cooperation with phenomenologists. We present new results on the light meson spectrum obtained from 3p ... More Presented by Stephan PAUL on 28 Jul 2016 at 11:40 Session: Mesons Heavy quark spin symmetry (HQSS) partners of the X(3872) 1++ molecule are discussed in a coupled-channel approach with non-perturbative pions. In the strict heavy-quark limit the 1++ molecular state has three degenerate partner states with the 1+-, 0++ and 2++ quantum numbers. In the presence of pions this result is shown to be correct only if all allowed coupled-channel transitions between th ... More Presented by Vadim BARU on 26 Jul 2016 at 17:50 Session: Plenary Observation of two hidden-charm pentaquark-like structures was reported by the LHCb Collaboration. Predictions and post-explanations of them will be reviewed. Further exploration of them and their partners will be discussed. Presented by Bing-Song ZOU on 28 Jul 2016 at 09:55 Session: Plenary A permanent electric dipole moment (EDM) of a fundamental particle violates both parity (P) and time reversal symmetry (T) and therefore combined charge and parity reversal symmetry (CP). It is a very promising place to search for physics beyond the Standard Model. One reason for this is that the Standard Model background is so small. Supersymmetric theories, for example, are already constrained b ... More Presented by Ruediger PICKER on 27 Jul 2016 at 11:40 The$\phi$-$\Lambda(1520)$interference effect in the$\gamma p\to K^+K^-p$reaction has been measured for the first time in the energy range from 1.673 to 2.173 GeV at LEPS/SPring-8. The relative phases between$\phi$and$\Lambda(1520)$production amplitudes were obtained in the kinematic region where the two resonances overlap. The measurement results support strong constructive interference wh ... More Presented by Sun Young RYU on 26 Jul 2016 at 16:50 Session: Plenary The possible existence of strongly-bound$\bar K$nuclear-states has been widely discussed as a consequence of the strongly attractive$\bar K N$interaction in I = 0 channels. Experimentally, however, available information is not sufficient to discriminate between a variety of conflicting interpretations so far. In this situation, we have performed an experimental search for the simplest kaonic n ... More Presented by Fuminori SAKUMA on 26 Jul 2016 at 12:20 Session: Plenary Presented by Marcin KUCHARCZYK on 28 Jul 2016 at 09:15 Session: Plenary More than 99% of the mass of the visible universe is made up of protons and neutrons. Both particles are much heavier than their quark and gluon constituents. The existence and stability of atoms rely on the fact that the mass difference between the neutron and the proton is about 0.14%. A slightly smaller or larger value would have led to a dramatically different universe. I show how theoretical ... More Presented by Zoltan FODOR on 26 Jul 2016 at 10:40 Exclusive Drell-Yan process, \pi^- p \to \mu^+ \mu^- n, may be measured using the high-intensity pion beams at J-PARC, and its QCD description is complementary to that for the deeply virtual meson production, \gamma^* p \to \pi N, at e.g., JLAB. The leading hard exclusive amplitude for exclusive Drell-Yan process was obtained by E.R. Berger, M. Diehl, and B. Pire [Phys. Lett. B523 (2001) 265] in t ... More Presented by Kazuhiro TANAKA on 27 Jul 2016 at 14:15 The amount of u-bar and that of d-bar in the proton were assumed to be the same based on the flavor symmetry. However, the NMC experiment at CERN found, by deep inelastic muon scattering, that d-bar is dominant in the proton. The previous Drell-Yan experiment at Fermilab (E866) measured the ratio of d-bar to u-bar, namely flavor asymmetry, and showed that d-bar/u-bar is as asymmetric as 1.7 at Bjo ... More Presented by Kei NAGAI on 27 Jul 2016 at 15:50 The momentum transfer dependence of the electromagnetic form factors is an important probe of the structure of hadrons at different scales. Using data samples collected with the BESIII detector at the BEPCII collider, we study the process of e+e- -> p bar{p} at 12 center-of-mass energies from 2232.4 to 3671.0 MeV. The Born cross section at these energy points are measured as well as the correspond ... More Presented by Bingxin ZHANG on 29 Jul 2016 at 17:50 Session: Baryons We discuss our dynamical coupled-channels (DCC) model for neutrino-nucleon interaction in the resonance region where single- and double-pion productions are dominant. Our DCC model is based on meson-exchange non-resonant mechanisms, and excitaions of nucleon resonances. By solving a set of coupled-channels scattering equation, we obtain amplitudes for meson productions such as pi N, pi pi N, eta N ... More Presented by Satoshi NAKAMURA on 26 Jul 2016 at 16:50 Session: Few body Systems Understanding of the structure of exotic hadrons is an important topic of the current hadron physics. The existence of many exotic hadrons, especially the XYZ particles, indicates that the internal structure of hadrons can be more complicated than the ordinary hadrons described by qqbar or qqq. For a stable shallow bound state, Weinberg has derived the model-independent relation between the compos ... More Presented by Yuki KAMIYA on 26 Jul 2016 at 17:20 Session: Plenary We present an overview of the recent progress in the spectroscopic study of nucleon resonances within the dynamical coupled-channels analysis of meson-production reactions off the nucleon target, with emphasis on the role of dynamical effects arising from multichannel reaction processes in understanding the mass spectrum, internal structure, and production mechanism of nucleon resonances. Presented by Hiroyuki KAMANO on 29 Jul 2016 at 12:20 Session: Baryons The NA62 experiment at CERN collected a large sample of charged kaon decays with a highly efficient trigger for decays into electrons in 2007. The kaon beam represents a source of tagged neutral pion decays in vacuum. A measurement of the electromagnetic transition form factor slope of the neutral pion in the time-like region from ~1 million fully reconstructed pi0 Dalitz decay is presented. Presented by Enrico GAMBERINI on 26 Jul 2016 at 14:50 The understanding of Quantum Chromodynamics (QCD) at large distances still remains one of the main outstanding problems of nuclear physics. Investigating the internal structure of hadrons provides a way to probe QCD in the non-perturbative domain and can help us unravel the spatial extensions of nature's building blocks. Deeply Virtual Compton Scattering (DVCS) is the easiest reaction that accesse ... More Presented by Carlos MUNOZ CAMACHO on 26 Jul 2016 at 14:50 Session: Baryons Hyperon production in e+e- annihilation provides a clean laboratory for the production of baryons and strangeness in hadronization, and can provide insight into the structure of different hyperons by comparing their production rates. Using 52 pb-1, 805 pb-1, and 586 pb-1 of e+e- annihilation data taken at the psi(2S), psi(3770), and psi(4160) resonances, respectively, with the CLEO-c detector, we ... More Presented by Sean DOBBS on 26 Jul 2016 at 15:50 We propose a new definition of a transverse-momentum-dependent wave function with simpler soft subtraction. The un-subtracted wave function involves two pieces of non-light-like Wilson links oriented in different directions, so that the rapidity singularity appearing in usual$k_T$factorization is regularized, and the pinched singularity from Wilson-link self-energy corrections is alleviated to a ... More Presented by Hsiang-nan LI on 29 Jul 2016 at 18:20 Session: Plenary Meson-photoproduction measurements and their reaction-amplitude analyses can establish more sensitively, and in some cases in an almost model-independent way, the nucleon excitation and non-resonant reaction amplitudes. However, to investigate the strong interaction from explored – where meson-cloud degrees of freedom contribute substantially to the baryon structure – to still unexplored dista ... More Presented by Ralf W. GOTHE on 26 Jul 2016 at 10:00 Octet Baryon Quark Flavor Distribution Functions We investigate the quark flavor distribution functions of the octet baryons. In particular, the valence and sea quark flavor distribution functions of the scalar density matrix elements of octet baryons have been computed explicitly. The implications of chiral symmetry breaking and SU(3) symmetry breaking have been discussed in detail for the sea qu ... More Presented by Harleen DAHIYA on 29 Jul 2016 at 17:20 We study the near-threshold incoherent$\phi$photoproduction on the deuteron based on a model of$\gamma N \to \phi N$, consisting of Pomeron,$(\pi, \eta)$exchanges, and a$J^P = 3/2^-$resonance, which describes the low energy \gamma p \to \phi p$ LEPS data well, including the peak in the forward differential cross section. The calculation is done up to double rescatterings, with the spin depe ... More
Presented by Alvin KISWANDHI on 26 Jul 2016 at 17:50
Recently, a peak structure was observed near the K^- p p threshold in the in-flight 3He (K^- , Lambda p) n reaction of the E15 experiment at J-PARC. This peak could be a signal of the lightest kaonic nuclei, that is, the Kbar N N (I=1/2) state, which has been intensively studied both experimentally and theoretically in the last decade. In this contribution we theoretically investigate what is the ... More
Presented by Takayasu SEKIHARA on 26 Jul 2016 at 15:20
Session: Mesons
The E1 transitions of ψ(3686) and ψ(3770) → γχ_cJ are investigated in a non-relativistic effective field theory (NREFT) where the open charm effects are included systematically as the leading corrections. It also allows a self-consistent inclusion of the S-D mixing in the same framework. It shows that the open charm contributions are essential for understanding the significant deviations of ... More
Presented by Zheng CAO on 29 Jul 2016 at 18:20
Session: Plenary
Presented by Hideto EN'YO on 26 Jul 2016 at 09:40
The Electron Ion Collider was recently accepted by the US Nuclear Science community as their high priority new facility to be built after the completion of FRIB (currently being built at the Michigan State University). The principle physics program of the EIC is aimed at understanding the role of gluons in QCD: structure and dynamics of partons in nucleons and nuclei. This program can be achieved ... More
Presented by Abhay DESHPANDE on 29 Jul 2016 at 14:15
The spectroscopy of charmonium-like states together with the spectroscopy of charmed and strange baryons is discussed. It is a good testing tool for the theories of strong interactions, including: QCD in both the perturbative and non-perturbative regimes, LQCD, potential models and phenomenological models [1, 2, 3]. An understanding of the baryon spectrum is one of the primary goals of non-perturb ... More
Presented by Mikhail BARABANOV on 27 Jul 2016 at 14:50
Session: Pentaquarks
We want to discuss the Pc(4450) structure observed by the LHCb Collaboration in the J/psi proton final states. We want to point out that it is located exactly at the chi_{c1}-proton threshold, and coincides with the leading Landau singularity of the triangle loop Lambda(1890)-chi_{c1}-proton. We also discuss how to distinguish a genuine resonance from the kinematical singularity.
Presented by Feng-Kun GUO on 27 Jul 2016 at 15:15
The phi-meson properties in cold nuclear matter are revisited by implementing resonant phi-N interactions as described in chirally-based approaches including the unitarization of scattering amplitudes. Several N*-like states are dynamically generated in these models around 2 GeV, immediately above the phi N threshold. We find that these states give a sizable contribution to the phi collisional sel ... More
Presented by Astrid HILLER BLIN on 26 Jul 2016 at 15:20
Session: Mesons
New high-precision total and differential cross sections for $\eta$ and $\eta'$ photoproduction on the proton obtained by the A2 Collaboration at the Mainz Microtron are presented. The total cross section for $\eta$ photoproduction demonstrates a cusp at the energy W$\sim$1.9~GeV. Furthermore, we present a new version of the $\eta$MAID model for $\eta$ and $\eta'$ photoproduction. The model includ ... More
Presented by Victor KASHEVAROV on 29 Jul 2016 at 16:50
Session: Plenary
The Hadron Experimental Facility (HEF) of the Japan Proton Accelerator Research Complex (J-PARC) provides the world highest intensity hadron beams, such as kaons, pions, and so on, for various experimental researches in particle and nuclear physics. Currently, HEF operates two charged and one neutral secondary beam lines, K1.8, K1.1, and K0, sharing secondary beams produced at a primary target, T1 ... More
Presented by Hiroyuki NOUMI on 30 Jul 2016 at 16:40
Session: Plenary
Presented by Raffaella DE VITA on 30 Jul 2016 at 14:15
Session: Mesons
Spin correlations for the $\Lambda \Lambda$ and $\Lambda \bar{\Lambda}$ pairs, generated in relativistic heavy-ion collisions, and related angular correlations at the joint registration of space-parity nonconserving hadronic decays of two hyperons are theoretically analyzed. These correlations give important information about the character and mechanism of multiple processes, and the advantage of ... More
Presented by Valery LYUBOSHITZ on 27 Jul 2016 at 14:50
We report our recent experiment of the pionic 121, 116Sn atom using missing-mass spectroscopy of the 122, 117Sn(d, 3He) reaction near the charged pion emission threshold. An established approach for quantitative evaluation of the chiral symmetry breaking in finite density is study of pion-nucleus interaction through the experimental measurement of pionic atoms. So far the 1s pionic states in 205Pb ... More
Presented by Takahiro NISHI on 29 Jul 2016 at 14:15
Session: Mesons
During the past decade, a large number of the so-called $X$, $Y$, $Z$ states have been observed in the heavy flavor sector, as have become candidates for exotic hadrons which may contain more complicated quark-gluon structures than the conventional quark model picture. Among all those exotic candidates, the $Y(4260)$ is undoubtedly one of the most mysterious states and has initiated a lot of exper ... More
Presented by Si-Run XUE on 26 Jul 2016 at 17:20
Session: Plenary
The BESIII experiment at the electron positron collider BEPCII in Beijing is successfully operating since 2008 and has collected large data samples in the tau-mass region, including the world’s largest data samples at the J/psi and psi(2s) resonances. In particular decays of these two resonances provide a rich and clean environment to study hadrons consisting out of light quarks and search for e ... More
Presented by Shuangshi FANG on 27 Jul 2016 at 09:55
Session: Baryons
Based on the large samples of J/ψ and ψ(2s) events accumulated at the BESIII detector, the recent results on baryon spectrosocopy will be presented, including the PWA of ψ(2S)-->p pbar pi0, p pbar eta. Also the perspectives on the baryon spectroscopy at BESIII will be discussed.
Presented by Jingqing ZHANG on 26 Jul 2016 at 15:20
Session: Plenary
I review the recent progress in understanding the decomposition of the nucleon spin into the helicity and orbital angular momentum of quarks and gluons.
Presented by Yoshitaka HATTA on 26 Jul 2016 at 11:40
As a consequence of the attractive KbarN interaction, kaonic nuclei which is bound state of anti-kaon and nucleon has been widely discussed. All theoretical studies support the existence of kaonic nuclei, however, its energy and width are widely spread depending on energy dependence of the KbarN interaction model. The investigation of such bound state would help us to understand the KbarN interact ... More
Presented by Takumi YAMAGA on 26 Jul 2016 at 14:50
Session: Plenary
Presented by Takashi NAKANO on 28 Jul 2016 at 11:00
Session: Plenary
Detector system WASA-at-COSY has been operated at the Cooler Synchrotron COSY in the years from 2006 till 2015. In this presentation we will report on recent results of the analyses of the meson production reactions in deuteron-deuteron and nucleon-nucleon collisions with spin-polarized and unpolarized beams, as well as results of analyses of hadronic and leptonic decays of ground state neutral me ... More
Presented by Pawel MOSKAL on 29 Jul 2016 at 09:15
Session: Mesons
Belle experiment at KEKB $e^+e^-$ collider accumulated data at the energy points around $¥Upsilon(10860)$ and $¥Upsilon(11020)$ as well as at $¥Upsilon(nS)$ $(n=1,2,3)$ resonances. These datasets provide an ideal place to perform bottomonium spectroscopy and search for exotic hadron states in bottomonia decays. In this talk, recent Belle results in the spectroscopy of bottomonium(-like) systems ... More
Presented by Youngjoon KWON on 29 Jul 2016 at 17:20
Session: Baryons
The Charmed baryon is a unique system, considered as a bound state of a charm quark and a light di-quark due to the suppression of the color spin interaction of the heavy charm quark. Belle experiment has led the charmed baryon spectroscopy with the world highest integrated luminosity $e^+e^-$ collision data provided by KEKB accelerator. In this talk, we present the latest results on charmed baryo ... More
Presented by Yuji KATO on 29 Jul 2016 at 14:15
Session: Plenary
Presented by Jianwei QIU on 30 Jul 2016 at 11:40
Session: Plenary
The investigation of the partonic degrees of freedom beyond collinear approximation and towards a 3D description of the hadron structure in the momentum space has been gained increasing interest in the last decade. In the recent years, several first measurements has been made which provide new insights on the parton dynamics within the nucleon or during fragmentation, e.g. related to orbital motio ... More
Presented by Marco CONTALBRIGO on 30 Jul 2016 at 11:00
Session: Plenary
The polarized proton-proton collider at RHIC provides an unique opportunity to study the spin structure of proton. In this talk, I will present recent study high-lights in longitudinal and transverse spin structure of proton at RHIC. The RHIC spin program lately executed the transversely polarized proton-nucleus collision at high energy. We observed strikingly strong atomic mass number dependence ... More
Presented by Itaru NAKAGAWA on 30 Jul 2016 at 09:15
K+->pi+nunu is one of the theoretically cleanest meson decay where to look for indirect effects of new physics complementary to LHC searches. The NA62 experiment at CERN SPS is designed to measure the branching ratio of this decay with 10% precision. NA62 took data in pilot runs in 2014 and 2015 reaching the final designed beam intensity. The quality of data acquired in view of the final measureme ... More
Presented by Elisa MINUCCI on 26 Jul 2016 at 17:20
Session: Plenary
Current progress of lattice QCD to provide theoretical guidance for search for new physics beyond the Standard Model is reported. Focus will be on the hadronic contributions to the anomalous magnetic moment, for which new experiments are starting/planned at FNAL and J-PARC. Calculations for Electric dipole moment of nucleon are also briefly summarized.
Presented by Taku IZUBUCHI on 27 Jul 2016 at 12:20
Presented by Yuping GUO on 26 Jul 2016 at 16:50
Session: Few body Systems
Very recently, four candidates of the tetraneutron state were observed in the 4He(8He,8Be) reaction at RIBF [1]. While the experiment will be continued aiming at higher statistics, the confirmation of such an exotic state with a different reaction is important. We propose a pion DCX (double charge exchange) reaction to populate a tetraneutron state via the 4He(pi-,pi+) reaction. In order to overco ... More
Presented by Hiroyuki FUJIOKA on 26 Jul 2016 at 18:20
The NA48/2 experiment at CERN collected a large sample of charged kaon decays into final states with multiple charged particles in 2003-2004. A new upper limit on the rate of the lepton number violating decay K+- --> pi-+ mu+- mu+- obtained from this sample is reported: 8.6 × 10^−{11} at 90% CL, which improves by more than an order of magnitude upon the previous measurements. Searches for two-b ... More
Presented by Andrey ZINCHENKO on 26 Jul 2016 at 17:50
Λ(1405) is the lightest among negative parity baryon excitation states, which is hardly explained by a simple quark model. Since the Λ(1405) is located just below the KbarN threshold, there is a longstanding argument if it is a KbarN bound state. A chiral unitary model claims that the Λ(1405) consists of two states (KbarN state and Σπ state). According to the model, a pole position of the Kba ... More
Presented by Shingo KAWASAKI on 29 Jul 2016 at 17:20
Spectroscopy of pionic atoms enables us to investigate partial restoration of chiral symmetry at finite density.It is theoretically known that the isovector potential parameter of parameter of the pion-nucleus interaction is related to the chiral condensate.Past experiments with the (d,3He) reaction at GSI showed an evidence of partial restoration of chiral symmetry. For the further study of pioni ... More
Presented by Yuni WATANABE on 29 Jul 2016 at 14:45
A high intensity GeV gamma beam line, LEPS2, was constructed at SPring-8 in Japan in 2013. The LEPS2 beam line provides a highly polarized photon beam up to 3 GeV with one order higher intensity than that of LEPS1 facility. We are constructing a 4$\pi$ solenoidal spectrometer which can detect both of charged particles and photons. The LEPS2 solenoid spectrometer consists of a time projection chamb ... More
Presented by Masayuki NIIYAMA on 26 Jul 2016 at 17:20
An interaction between Kbar and nucleus is studied by using the X-ray from the kaonic atoms for a long time. However, it is difficult to determine the Kbar-nucleus interaction by using only kaonic-atoms data because the value of shift and width of the X-ray depend not only the potential depth but also the type of theoretical model. Thus, we study the Kbar-nucleus interaction by comparing an observ ... More
Presented by Yudai ICHIKAWA on 26 Jul 2016 at 15:50
The production mechanism of a \Sigma \pi pair from a deuteron target gives us an essential information on the interaction between \Lambda(1405) and nucleon. J-PARC E27 group studied the d(\pi+, K+)X reaction, and reported a large mass shift in the hyperon resonance region. Checking the spectrum using the other reaction is helpful to reveal the source of the large shift. We measured the d(gamma, K+ ... More
Presented by Atsushi TOKIYASU on 29 Jul 2016 at 16:50
The COMPASS experiment at CERN is one of the leading experiments studying the nucleon structure. Until 2012 the Parton Distribution Functions (PDFs) and the Transverse Momentum Dependent Parton Distribution Functions (TMDs) were extensively studied at COMPASS using Semi-Inclusive Deep Inelastic Scattering (SIDIS) measurements. In 2015 the data taking was dedicated to the study of the polarised Dre ... More
Presented by Márcia QUARESMA on 27 Jul 2016 at 15:20
Session: Mesons
We study the reaction e+ e− -> gamma_ISR J/psi, where J/psi -> pi+ pi- pi0, J/psi -> K+ K- pi0, and KS K+ pi- using events obtained from the Initial State Radiation process. We measure the relative J/psi branching fraction and perform a Dalitz plot analysis of both J/psi decay modes using an isobar and a Veneziano model. We present also an analysis of the process gamma gamma -> K anti-K pi. We o ... More
Presented by Abner SOFFER on 29 Jul 2016 at 16:50
Session: Mesons
We study the decay constants ($f_M$) of the Charmful and beautifu vector and tensor mesons in the light front quark model. Here, we tried two different distribution amplitudes to study the decay constants. With the known pseudoscalar meson decay constants of $f_{D}$, $f_{D_{s}}$, $f_{B}$ and $f_{B_{s}}$ as the input parameters to determine the light-front wave functions, we obtain that $f_{D^{*}, ... More Presented by Chong-Chung LIH on 29 Jul 2016 at 15:20 Since the winter of 2014, COMPASS collaboration at CERN have performed a series of Drell-Yan experiments using a high-intensity negative hadron beam with momentum 190-GeV/c impinging on a transversely polarised ammonia target and unpolarised aluminum and tungsten targets. The experiment provides the first-ever polarized Drell-Yan data, as well as greatly improved statistics for the unpolarised one ... More Presented by Takahiro SAWADA on 27 Jul 2016 at 14:50 Session: Plenary Presented by Kenichi IMAI on 30 Jul 2016 at 17:20 The spontaneous breaking of chiral symmetry is considered to be the origin of hadron mass. An order parameter of chiral symmetry breaking is a quark anti-quark condensate, but it is not observable. Instead, the spectral function of vector mesons is predicted to be changed in a hot and/or dense medium through the restoration of chiral symmetry. The J-PARC E16 experiment is proposed to study the spe ... More Presented by Yusuke KOMATSU on 26 Jul 2016 at 14:50 Light neutral meson decays provide a unique laboratory to probe fundamental QCD symmetries. A comprehensive Primakoff experimental program at Jefferson Laboratory (JLab) is aimed at gathering high precision measurements on the two-photon decay widths and the transition form factors at low four-momentum transfer squares of pi0, eta and eta’ via the Primakoff effect. Completed experiments on the p ... More Presented by Liping GAN on 29 Jul 2016 at 15:50 Session: Mesons We consider how tetraquarks can affect the chiral phase transition for light quarks coupled to SU(3) color. For two flavors the tetraquark field is an isosinglet, and its effect is minimal. For three flavors, however, the tetraquark field transforms in the same representation of chiral symmetry as the usual chiral order parameter, and so for very light quarks there may be {\it two} chiral phase tr ... More Presented by Robert PISARSKI on 27 Jul 2016 at 14:15 Session: Pentaquarks We study the Λ_b → J/ψ K0 Λ reaction considering both the K0 Λ interaction with its coupled channels and the J/ψΛ interaction. The latter is described by taking into account the fact that there are predictions for a hidden-charm state with strangeness that couples to J/ψΛ. By using the coupling of the resonance to J/ψΛ from these predictions we show that a neat peak can be observed in ... More Presented by Eulogio OSET on 26 Jul 2016 at 14:15 Session: Mesons We study the presence of the the D*s0(2317) resonance in the weak decay process: Bc->J/psi KD. We assume a weak interaction mechanism in which the b quark decays into a c anti-c (J/psi) and anti-s via a W meson. In this process the c anti-s pair hadronizes and the possible final configurations considered are KD and eta Ds. We compute the interaction of these two meson channels in the chiral unitar ... More Presented by PEDRO FERNANDEZ-SOLER on 29 Jul 2016 at 17:50 Session: Plenary The Belle experiment was successfully running in KEK, Tsukuba, Japan until 2010. Now the detector is being upgraded and should start its operation in 2018. The talk is about the detector, SuperKEKB accelerator and physics at the Belle II experiment. Presented by Dmitri LIVENTSEV on 30 Jul 2016 at 14:55 Session: Plenary The physics of strong interactions is undoubtedly one of the most challenging areas of modern science. Quantum Chromo Dynamics is reproducing the physics phenomena only at distances much shorter than the size of the nucleon, where perturbation theory can be used yielding results of high precision and predictive power. At larger distance scales, however, perturbative methods cannot be applied anymo ... More Presented by Johan MESSCHENDORP on 30 Jul 2016 at 15:35 The proton charge radius (Rp) is one of the most fundamental quantities in physics. Precision knowledge of its value is critically important for both nuclear and atomic physics – especially for the spectroscopy of atomic hydrogen. Recent high precision measurements of Rp using the muonic hydrogen atom demonstrated up to eight standard deviation smaller value than the accepted average from all pr ... More Presented by Ashot GASPARIAN on 29 Jul 2016 at 16:50 Session: Plenary After a brief introduction in the handbag approach, generalized parton distributions (GPDs) and hard subprocesses deeply virtual leptoproduction of pions will be discussed in some detail. It will be shown that a leading-twist analysis of this process fails drastically. A successful interpretation of the experimental data on pion production is however achieved by treating the pion-pole contribution ... More Presented by Peter KROLL on 30 Jul 2016 at 09:55 In this presentation, recent results about the behavior of the phi meson in nuclear matter will be presented [1,2,3]. Furthermore, the relation between the phi meson spectral function and QCD condensates, in particular the strange quark condensate, will be discussed. We find a strong correlation between a possible mass shift of the phi-meson in nuclear matter and the strangeness content of the nuc ... More Presented by Philipp GUBLER on 26 Jul 2016 at 14:15 In mesic nuclei, kaonic nuclei have been a hot topic for a decade. Due to so strong KbarN attraction that generates a hyperon resonance Lambda(1405), kaonic nuclei could have various interesting properties, in particular to form a dense matter. To clarify exotic nature caused by anti-kaons, the most essential kaonic nucleus “K-pp” has been studied eagerly from both theoretical and experimental ... More Presented by Akinobu DOTE on 26 Jul 2016 at 14:15 Session: Few body Systems Comparison of theoretical predictions based on a nucleon-nucleon potential with data for elastic nucleon-deuteron scattering and nucleon induced deuteron breakup reveals the importance of the three-nucleon force (3NF). Inclusion of semi-phenomenological 3NF models into calculations in many cases improves the data description. However, some serious discrepancies remain even when 3NF is included. At ... More Presented by Henryk WITALA on 26 Jul 2016 at 17:50 Session: Plenary Presented by Qiang ZHAO on 28 Jul 2016 at 12:20 Session: Baryons Presented by Hai-Qing ZHOU on 26 Jul 2016 at 17:55 Session: Pentaquarks The LHCb collaborations recently reported the observations of two resonance-like structures, which could be the long-searching-for pentaquark states. When studying these heavy pentaquark candidates, usually one will confront two issues, i.e., what their underlying structures are and how to search for them in experiments. We indicated that these resonance-like peaks may be resulted from some kinema ... More Presented by Xiao-Hai LIU on 27 Jul 2016 at 14:45 Session: Mesons I will focus my talk on our recent studies of three-body final state interactions [*]. We considered the decays eta/ω/φ → 3π in the dispersive frameworks that are based on the main constraints of the S-matrix theory, namely unitarity, analyticity, and crossing symmetry. Our results indicated that the final state interactions may be sizable. In my talk, the Dalitz plot distributions and integr ... More Presented by Igor DANILKIN on 29 Jul 2016 at 14:50 Session: Mesons Presented by Bin WANG on 26 Jul 2016 at 16:50 Session: Plenary In Belle experiment, many quarkonium-like exotic hadron candidates have been discovered, X(3872) in B meson decay, Y(4260) in initial state radiation, Zb(10610)+ and Zb(10650)+ in Upsilon(10860) decay and so on. This talk will review recent progress of relevant experimental studies as well as attempts to give a comprehensive interpretation for them. Presented by Kenkichi MIYABAYASHI on 27 Jul 2016 at 09:15 Session: Mesons In this talk we report on two recent works about the Zc(3900) resonance. A coupled channel T-matrix is used in the description of the D*D and J/\psi\pi spectra in which the Zc(3900) peak has been seen. The data can be well reproduced in two different scenarios, in which the Zc(3900) is a resonance or a virtual state. We also put this coupled channel T-matrix in a finite box, with the aim of compar ... More Presented by Miguel ALBALADEJO on 26 Jul 2016 at 18:20 Session: Plenary The possible exotic meson$Z_{c}(3900)$, found in$e^+ e^-$reactions, is studied by the method of coupled-channel scattering in lattice QCD. The interactions among$\pi J/\psi$,$\rho \eta_{c}$and$\bar{D}D^{*}$channels are derived from (2+1)-flavor QCD simulations at$m_{\pi}=410$-$700$MeV. The interactions are dominated by the off-diagonal$\pi J/\psi$-$\bar{D}D^{*}$and$\rho \eta_{c}$-$\ba ... More
Presented by Yoichi IKEDA on 27 Jul 2016 at 10:35
Session: Pentaquarks
Recent LHCb experiments show us that there are two resonances in the N-J/Psi channel, whose spin and parity are most probably (3/2- 5/2+). In this work, we will show that there is a state which gains a large attraction from the color-magnetic interaction in the uudccbar I(JP)=1/2(3/2-) channel, which appears as a resonance in the Lambda_c Dbar* channel, when one employs a quark model. We also foun ... More
Presented by Sachiko TAKEUCHI on 26 Jul 2016 at 15:15
Session: Baryons
The BESIII detector accumulated 567 pb-1 data at the center-of-mass energy of 4.599 GeV, which is the world's largest e+e- collision sample at the Lambda_c pair threshold. By analyzing this data sample, we report the determinations of the absolute branching fractions of the Λc semi-leptonic decay and 12 hadrnoic decays.The precisions of these absolute branching fractions for these decays are impr ... More
Presented by Weimin SONG on 29 Jul 2016 at 14:50

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# How do you find the critical points for the inequality (2x+1)/(x-9)>=0?

Sep 25, 2015

See the explanation.

#### Explanation:

I think the question wants the key numbers or the partition numbers.

These are the values of $x$ at which the sign of the expression MIGHT change.

The sign of a rational function MIGHT change when either the numerator is $0$ or when the denominator is $0$ (where the expression is not defined.)

For the expression $\frac{2 x + 1}{x - 9}$,

the sign MIGHT and does change at $x = - \frac{1}{2}$ (the solution to $2 x + 1 = 0$ and

at $x = 9$ (the solution to $x - 9 = 0$).

In the graph of $y = \frac{2 x + 1}{x - 9}$ below, you can see where the expression changes sign:

graph{y=(2x+1)/(x-9) [-25.9, 39.05, -23.36, 9.1]}

To the left of $x = - \frac{1}{2}$, y is positive. Then at $x = - \frac{1}{2}$, $y$ changes from positive to negative. (You can use a mouse to scroll in and to drag the graph around.)
$y$ stays negative until we get to $x = 9$ where $y$ suddenly becomes very,very positive.


text:
# Tips going rate is supposed to be 15-20%.

#### Ivan Seeking

Staff Emeritus
Gold Member
I just heard that now the going rate is supposed to be 15-20%.

Okay, now why does the percentage keep going up? For a long time, 10% was the standard. Then it went up to 15%. Now 20%??? :surprised Give me a break; I'll take it "to go". :tongue:

Last edited:
Related General Discussion News on Phys.org

#### mattmns

I hear that! Those actors will get only 10% from me, and that is only if they are damn good!

#### JamesU

Gold Member
my family and I will give tips at 20% or more for good service

#### gonpost

Usual rule I've heard is (in restaurants) 10% tip for bad service, 15-17% for average to slightly above, and 20% for amazing service.

at most places in town, they are lucky their tip isn't "stay in school"

#### JamesU

Gold Member
it's better that 'be cool, stay in school' I've heard that too many times. I bet the people who came up with that got their ***** kicked

#### hypatia

What kills me is, people expecting a large tip at a buffet, or when the tip is included in the bill {20%} at the "fine dining steak house". Doesn't matter if the food/service was good or not.
Now the poor pizza boy... they charge me 4 dollars to bring a pizza 3 blocks to my house, and the kid sticks out his hand waiting for a tip. I explain to him, that it took him 5 mins to get to my house, and that the 4 dollar fee is good enough. Now I think next time he gonna spit in my pizza :yuck:

#### Ivan Seeking

Staff Emeritus
Gold Member
Yes, and I wonder who really gets the four bucks.

I don't mind when the bill is twenty bucks...I almost never tip less than four or five dollars for a meal, but when you travel this can really add up for more expensive meals and services.

#### wolram

Gold Member
Ivan Seeking said:
Yes, and I wonder who really gets the four bucks.

I don't mind when the bill is twenty bucks...I almost never tip less than four or five dollars for a meal, but when you travel this can really add up for more expensive meals and services.
You dont know when your in clover you guys, gordon benit, fish and chips
costs about 10 bucks in the uk, and if you go out for a meal the average
per person is twenty bucks, so dont be such skin flints, and spread your
bucks around a bit.

Staff Emeritus
Gold Member
Why should I pay someone $20 for five minute worth of work? Its not about being cheap. Its about getting ripped off if you ask me. This is more than it cost for the services of a skilled craftsman. Last edited by a moderator: #### Ivan Seeking Staff Emeritus Science Advisor Gold Member wolram said: You dont know when your in clover you guys, gordon benit, fish and chips costs about 10 bucks in the uk, and if you go out for a meal the average per person is twenty bucks, so dont be such skin flints, and spread your bucks around a bit. Why did you quote me when I just said that I never tip less than four or five dollars? #### Janus Staff Emeritus Science Advisor Gold Member Ivan Seeking said: Why should I pay someone$20 for five minute worth of work? Its not about being cheap. Its about getting ripped off if you ask me. This is more than it cost for the services of a skilled craftsman.
You know, you've got a point there. I think the problem is in tying the tip to the size of the bill. After all, the wait(er)(ress), does about the same service for you whether you ordered the $10 burger plate or the$50 dollar special.

Maybe the custom needs to be changed to a standard tip per person/order as the baseline.

#### jma2001

Gold Member
Janus said:
You know, you've got a point there. I think the problem is in tying the tip to the size of the bill. After all, the wait(er)(ress), does about the same service for you whether you ordered the $10 burger plate or the$50 dollar special.

Maybe the custom needs to be changed to a standard tip per person/order as the baseline.
The theory is that waiters who work in fancy restaurants in big cities (where the price per plate is much higher) are under more stress, and deserve higher tips, as compared with waiters who work inexpensive suburban diners.

#### TheStatutoryApe

Gale said:
speaking of tipping, i was watching a news program the other day on it. it was about how so many places now expect you to tip. you really can't go many places without tipping. lots of stores have tip jars and stuff... it does get really riddiculous. and it sucks, because tipping traditionally was for an exceptional job or something, and now we're expected to tip every joe-somebody, just for doing their regular job. and at most of these places, they're employees are paid plenty, (unlike the waitstaff at restaurants,) and tips aren't even accounted for in taxes. but you still look like an ass if you don't put a few coins in their tip jar.
Most of those places I don't usually tip. If it's a coffee house I usually tip a buck, it's like a lesser version of a bar to me. In a fast food type place I usually don't unless they are really nice and actually do more than punch something into a register like the chinese food place next to my work.

#### Moonbear

Staff Emeritus
Gold Member
TheStatutoryApe said:
Most of those places I don't usually tip. If it's a coffee house I usually tip a buck, it's like a lesser version of a bar to me. In a fast food type place I usually don't unless they are really nice and actually do more than punch something into a register like the chinese food place next to my work.
In the coffee shop, I just tip whatever coins I get back in change if it's to-go (assuming they actually are making something for me, not just pouring a plain cup of coffee...I don't tip for regular coffee to go), unless I'm actually going to sit there for a while, then I leave at least \$1 tip, more if I get more than just a drink.

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text: Seminar on PDE 主講者: 唐嵐 (華中師範大學) 講題: On a class of boundary homogenization 時間: 2019-08-20 (Tue.)  10:30 - 11:30 地點: 數學所 722 研討室 (台大院區) Abstract: We study a class of boundary homogenization problem related to the p-Laplacian with p ranges from 2 to n. || Close window ||


text:
# DRMacIver's Notebook

Separating Sampling and Removal

Separating Sampling and Removal

This is a weird data structure that as far as I know I invented (it's plausibly a reinvention, but it might also just be too niche a set of requirements for anyone else to have bothered with) and I quite like. It uses a combination of two neat tricks to support all the following operations in O(1):

• Initialize with N elements.
• Sample randomly from one of the remaining elements or raise an error if the collection is empty.
• Remove a single copy of a value from the collection.

It does assume that the values in the collection are hashable, but honestly I've only ever wanted to use it with integers.

It builds on the following trick:

class LazySequenceCopy(object):
"""A "copy" of a sequence that works by inserting a mask in front
of the underlying sequence, so that you can mutate it without changing
the underlying sequence. Effectively behaves as if you could do list(x)
in O(1) time. The full list API is not supported yet but there's no reason
in principle it couldn't be."""

def __init__(self, values):
self.__values = values
self.__len = len(values)
self.__mask = None

def __len__(self):
return self.__len

def pop(self):
if len(self) == 0:
raise IndexError("Cannot pop from empty list")
result = self[-1]
self.__len -= 1
if self.__mask is not None:
self.__mask.pop(self.__len, None)
return result

def __getitem__(self, i):
i = self.__check_index(i)
default = self.__values[i]
if self.__mask is None:
return default
else:
return self.__mask.get(i, default)

def __setitem__(self, i, v):
i = self.__check_index(i)
if self.__mask is None:
self.__mask = {}
self.__mask[i] = v

def __check_index(self, i):
n = len(self)
if i < -n or i >= n:
raise IndexError("Index %d out of range [0, %d)" % (i, n))
if i < 0:
i += n
assert 0 <= i < n
return i

This allows us to make a copy of the initial sequence without actually copying it.

Now if we wanted to do sampling without replacement it's easy: We can just do a lazy fisher yates shuffle:

def sample_without_replacement(random, sequence):
i = random.randrange(0, len(sequence))
j = len(sequence) - 1
sequence[i], sequence[j] = sequence[j], sequence[i]
return sequence.pop()

We pick a random element, swap it to the end, and then pop the last element. This lets us randomly sample and then remove in O(1) because we don't care about preserving the order of the sequence.

The tricky bit is what to do when you want to sample and then decide later whether you want to remove the value or not. I e.g. run into this requirement when randomly but exhaustively exploring a state space - sometimes we discover that a node is fully explored and we want to remove it, but we can't know that at the time of sampling.

The idea is to do deferred deletion. Rather than attempting to actually delete it at the time of deletion, we simply record that we wanted to delete it, and the next time we sample we remove any elements we encounter.

This works as follows:

from collections import Counter

class RemovableSampler(object):
def __init__(self, values):
self.__values = LazySequenceCopy(values)
self.__deletions = Counter()

def sample(self, random):
while True:
i = random.randrange(0, len(self.values))
v = self.values[i]
if self.__deletions[v] > 0:
j = len(sequence) - 1
sequence[i], sequence[j] = sequence[j], sequence[i]
sequence.pop()
self.__deletions[v] -= 1
else:
return v

def delete(self, value):
self.__deletions[value] += 1

i.e. we reuse the procedure from the lazy fisher yates shuffle but we only remove if we're not going to return the value because we've previously deleted it.

We can see that this is ammortized O(1) by using a "debt" model. Each call to delete increases the total debt by one, and each iteration of sample either returns or repays one debt, so the total cost done is never more than O(deletes + samples).


text:
# What can be added to hydrochloric acid to make a gel or paste?

I have a bottle of brick cleaner containing 18-20% hydrochloric acid. What can I add to it to make a gel or paste without unwanted reactions? The application is still just cleaning bricks as the product is intended, I just don't want it to run like a liquid.

• wall paper paste would be a simple choice – porphyrin Feb 20 '17 at 11:10
• You don't want the acid sticking to the brick because washing it off will be a chore. As long as the acid is there it will keep eating at the cement. – MaxW Feb 20 '17 at 16:25
• @MaxW The reason for wanting it to stick to the brick faces is to stop it running into the mortar line, as the acid also eats into the lime mortar which is undesirable. – Paul George Feb 20 '17 at 18:29
• There is another consideration too. Reacting an acid with carbonate yields carbon dioxide gas. So the gas would bubble and splatter the gel outward -- at you. The HCl solution is "thin enough" that it would splatter a lot less. – MaxW Feb 20 '17 at 18:34

I tried the Xanthan Gum method using muratic acid to clean the calcium leaching on my pool, which was bad, having sat for 7-8 months. I used 1 lb. of Xanthan Gum (about \$11 on Amazon) and about 3 gallons of water to make a thick gel. I then added about 1 gallon of it to a 2nd bucket and added muratic acid, 2 then a 3rd gallon to make it stronger. It just didn't work very well. I don't know if it was from it being diluted, but I also wonder if muratic acid, which eats away at organic substances, interacts with Xanthan Gum, being an organic substance, and weakens the acid. It just didn't seem to help. I ended up using 100% muratic acid (33% HCL) and applied it with a home depot acid washing brush, wearing gloves, safety glasses, with a box fan and leaf blower at hand when fumes got bad. Fumes seem to sit in the pool and need to be blown out as you go. I found by dipping the brush and pushing it horizontally away from me, but not pulling back it would leave a nice coating. A little would drip down, especially from the beginning of the stroke, so I'd do a 2nd stroke just below the first to spread it out. You'll see the acid start bubbling with little dripping down. Then repeat starting at the 2nd stroke so it got good coverage. My pool took multiple coats of this. I noticed that after multiple strokes the part still not clean would bubble and the clean parts wouldn't. My surface is diamond brite double blue, with a doubling of the blue put in (quadruple blue for a more durable surface). It would sit for 30-60 minutes then wash it off. Apply sparingly and carefully around light or any other metal fixtures, they will quickly corrode and drip rust. Some may criticize this as being too aggressive, but they weren't here seeing what I was dealing with. It took me all day to do the pool, in south Florida's summer heat. I simply didn't have or want to spend more than a day doing this. And applying it weaker would just take more labor, probably more acid ( I used about 12 gallons), and eventually eat away the same amount. Test your area and find what dilution works for you. I ran a hose constantly to keep the rinsed muratic acid diluted in the deep end. I then used a \$50 utility pump with a hose and pumped it out into the grass. I now have to clean that area where water had pooled up, which I will do, then dilute further with water and pump out. Doing the entire pool I noticed it did eat away about 1 gallon of pool concrete and diamond brite blue specks. Acceptable for a 22k gallon pool. Pool is back to its beautiful blue color.


text:
Pendulum investigation with a stop

1. Dec 6, 2003

exequor

I did this experiment with various values for (d), which is the height from the top of the string to the stop. The length of the string was 0.7m. Since i used 6 differnt values for (d) i got 6 readings.

why i stated all this is because i have to find g from the following expression

$$T = \frac{-\pi^2}{g} (\frac{d}{T}) + 2\Pi \sqrt{\frac {l}{g}}$$

I have tried lots of variations but i just can't find anything close to 9.8m/s^2.

what i did was i tried a single set of results like:
d = 0.5m
T = 1.31
thus d/T = 0.38
and l = 0.7m

could someone use the same and tell me what their result for g was, please.

Last edited: Dec 6, 2003
2. Dec 6, 2003

I got g=9.48

If you're having trouble solving that, try transforming it into a quadratic equation. You could also move T to the right side, plot it as a function of g, and find the roots.