text:
\section{Introduction}

We consider the family of parameterized polynomials
$$
f_{a}(x)=x^3-ax^2-(a+3)x-1,
$$
with parameter $a\in \mathbb{Z}$.
It is easy to show that for any $a\in \mathbb{Z}$ the polynomial $f_a$ is irreducible with a real root~$\rho$ and discriminant $D=(a^2+3a+9)^2$.
Therefore, the field $K=K_a=\mathbb{Q}(\rho)$ is Galois with cyclic Galois group generated by $\sigma$. In particular, the Galois group is given by $\Gal(K_a/\mathbb{Q})=\langle \sigma\rangle$ where $\sigma (\rho)=-1-1/\rho$.
This family of cubic fields $K_a$ was first studied systematically by Shanks \cite{Shanks1974}, who called it a family of simplest cubic fields.
As already Shanks noted, $\rho$ and $\sigma(\rho)$ are multiplicatively independent units, which makes estimating the regulator of $K_a$ particularly easy.

This rather simple structure of the family of fields $K_a$, and in particular the simple form of a multiplicatively independent system of units, yield a nice underlying background structure to study various types of families of Diophantine equations. In particular, Thomas \cite{Thomas:1990} and subsequently Mignotte \cite{Mignotte:1993}  studied the family of Thue equations
$$ N_{K_a/\mathbb{Q}}(X-\rho Y)=X^3-aX^2Y-(a+3)XY^2-Y^3=\pm 1.$$
Families of twisted Thue equations were first studied by Levesque and Waldschmidt \cite{Levesque:2015}, who considered the family
$$N_{K_a/\mathbb{Q}}(X-\rho^t Y)=\pm 1.$$
We also want to mention that the integral points of the family of elliptic curves
$$\mathcal E_a:\quad Y^2=f_a(X)$$
have been studied by Duquesne \cite{Duquesne:2001}.

In this paper we want to study the family of unit equations
\begin{equation}\label{eq:unit}
u_1+u_2=n,\qquad n\in \mathbb{Z},\;\; u_1,u_2\in \mathcal{O}_{K_a}^*,
\end{equation}
where $\mathcal{O}_{K_a}$ is the maximal order of $K_a$.

\section{Equivalent solutions, trivial solutions and main result}

Before we state our main result we make some observations.
As mentioned above, for any $a\in \mathbb{Z}$ the number field $K_a=\mathbb{Q}(\rho)$ corresponding to $f_a(x)$ is Galois and the Galois group is cyclic and generated by $\sigma(\rho)=1-1/\rho$.

Let $(u_1,u_2,n)$ be a solution to \eqref{eq:unit}. Then we can apply $\sigma$ to \eqref{eq:unit} and since $\sigma$ maps units to units and integers to integers, we see that $(\sigma(u_1),\sigma(u_2),n)$ is another solution to \eqref{eq:unit}. In fact,
\begin{align*}
 &(u_1,u_2,n),& &(\rho(u_1),\rho(u_2),n),& &(\rho^2(u_1),\rho^2(u_2),n),\\
 &(-u_1,-u_2,-n),& &(-\rho(u_1),-\rho(u_2),-n),& &(-\rho^2(u_1),-\rho^2(u_2),-n),\\
 &(u_2,u_1,n),& &(\rho(u_1),\rho(u_2),n),& &(\rho^2(u_1),\rho^2(u_2),n),\\
 &(-u_2,-u_1,-n),& &(-\rho(u_2),-\rho(u_1),-n),& &(-\rho^2(u_2),-\rho^2(u_1),-n)
\end{align*}
are each solutions to \eqref{eq:unit}. Note that these solutions are obtained by a combination of change of sign, permutation of $u_1$ and $u_2$ and application of some $\tau\in\Gal(K_a/\mathbb{Q})$ to \eqref{eq:unit}.
That is, with one solution usually come eleven more solutions that can easily be obtained from the first one.
We shall call solutions that are obtained from $(u_1,u_2,n)$ in this way \textit{equivalent} to $(u_1,u_2,n)$.

Next, note that there are some obvious solutions to \eqref{eq:unit}. Clearly,
\begin{equation}\label{eq:trivial1}
	(1,1,2)
	\quad \text{and} \quad
	(u, - u , 0) \text{ with } u\in \mathcal{O}_{K_a}^*
\end{equation}
are solutions to \eqref{eq:unit}. Moreover, one can check that $\rho$ and $\rho+1$ are also in $\mathcal{O}_{K_a}^*$. Thus
\begin{equation}\label{eq:trivial2}
(\rho+1, -\rho, 1)
\end{equation}
is also a solution to \eqref{eq:unit}. We shall call all solutions that are equivalent to solutions from \eqref{eq:trivial1} and \eqref{eq:trivial2} \textit{trivial solutions}. All non-trivial solutions will be called \textit{sporadic}.

Further, note that $f_a(x)=-x^3f_{-a-3}(1/x)$, so if $\rho$ is a root of $f_a(x)=x^3-ax^2-(a+3)x-1$, then $1/\rho$ is a root of $f_{-a-3}(x)$. Hence $K_a=K_{-a-3}$. Therefore, we may assume that $a\geq -1$ when considering Equation \eqref{eq:unit}.

Finally, let us point out that in this paper we will not consider the units of the maximal order $\mathcal{O}_{K_a}$ but of the order $\mathbb{Z}[\rho]$. The reason for this is that for the maximal order $\mathcal{O}_{K_a}$ a parametrisation of the system of fundamental units is in general not known, while for $\mathbb{Z}[\rho]$ Thomas \cite{Thomas1979} showed that $\rho$ and $\sigma(\rho)$ form a system of fundamental units.
 However, we have $\mathbb{Z}[\rho]=\mathcal{O}_{K_a}$ whenever the discriminant $D=(a^2+9a+3)^2$ is a square of a prime, and this is conjecturally (e.g. by Bunyakovsky's conjecture) infinitely often the case.

Now we state our main result.

\begin{thm}\label{thm:main}
Let $a\geq -1$, let $\rho$ be a root of $f_a(x)$ and consider the Diophantine Equation
\begin{equation}\label{eq:main}
 u_1+u_2=n,
 \qquad
 u_1,u_2\in \mathbb{Z}[\rho]^*, \;
 n\in \mathbb{Z}, \; |n|\leq \max\{|a|^{1/3},1\}.
\end{equation}
Then for $a\geq 3$ Equation \eqref{eq:main} has only trivial solutions. For $a\leq 2$ every solution is either trivial or equivalent to one of the 10 sporadic solutions $(u_1,u_2,1)$ presented in Table \ref{tab:sporadicSols} in Section \ref{sec:smallSols}.
\end{thm}

Let us outline the strategy of our proof. As mentioned above, $\epsilon:=\rho$ and $\delta:=-\sigma(\rho)$ form a fundamental system of units of $\mathbb{Z}[\rho]$. Therefore, we can write
$$u_1=\pm \epsilon^{x_1}\delta^{y_1},\qquad u_2=\pm \epsilon^{x_2}\delta^{y_2}$$
for some $x_1,x_2,y_1,y_2\in \mathbb{Z}$. Assume that $(u_1,u_2,n)$ is a solution to \eqref{eq:main} and let $X:=\max\{|x_1|,|x_2|,|y_1|,|y_2|\}$. Our first goal is to show that it is always possible to find a solution $(\bar u_1,\bar u_2,n)$ equivalent to $(u_1,u_2,n)$ such that $|\bar u_2|>a^{X/2}$ (Section \ref{sec:embedding}). In Section \ref{sec:specialCases} we deal with some special cases that yield the three families of trivial solutions.
Established these preliminary results we apply lower bounds for linear forms in logarithms to obtain an upper bound for $X$ of the form $X\ll \log a \, (\log \log a)^2$ (Section \ref{Sec:upper}). On the other hand, using a similar trick as in \cite{Thomas:1990} we obtain a lower bound for $X$ of the form $X\gg a \log a$ (see Section \ref{Sec:lower}). These two bounds yield an absolute upper bound for $a$. Using continued fractions we show that there are no sporadic solutions provided that $a> 100$. The case $a\leq 100$ is dealt with in the next section.

\section{Small solutions}\label{sec:smallSols}

For technical reasons we want to exclude small values of the parameter $a$ and start by proving the following proposition:

\begin{prop}\label{prop:smallSols}
For $a\leq 100$ the only solutions to Equation \eqref{eq:main} are those stated in Theorem~\ref{thm:main}.
\end{prop}

\begin{proof}
The computations were done with Magma \cite{Magma}. The function \verb|UnitEquation| was used to solve the unit equation \eqref{eq:main} over the maximal order of $K_a$ for $-1 \leq a \leq 100$ and $1 \leq n\leq \max\{|a|^{1/3},1\}$.
This took only a couple of seconds and revealed a total of $693$ solutions.

Then the trivial solutions were filtered out as well as those not lying in $\mathbb{Z}[\rho]$. Thus 60 solutions remained and in each of them we had $n=1$. Up to equivalence they correspond to the $10$ sporadic solutions presented in Table~\ref{tab:sporadicSols}.
\end{proof}

In Table \ref{tab:sporadicSols} the sporadic solutions to Equation \eqref{eq:main} are represented in terms of $\rho$ as well as powers of fundamental units $\varepsilon=\rho$ and $\delta=-\sigma(\rho)$.

\begin{table}[h]
\[
\begin{tabular}{ >{$}c<{$}  >{$}r<{$} @{\hspace{2pt}} >{$}l<{$} >{$}r<{$} @{\hspace{2pt}}
	>{$}l<{$}}
\hline
a & &u_1 & &u_2  \\
\hline
-1 &
-\rho -1  & =  - \varepsilon^{ 1 } \delta^{ 1 } &
\rho +2  & =   \varepsilon^{ 0 } \delta^{ 2 } \\
&
-\rho^2+3  & =   \varepsilon^{ -1 } \delta^{ 1 } &
\rho^2 -2  & =  - \varepsilon^{ -1 } \delta^{ -1 } \\
&
-\rho^2+\rho +1  & =   \varepsilon^{ 1 } \delta^{ -1 } &
\rho^2 -\rho   & =   \varepsilon^{ 0 } \delta^{ -2 } \\
&
-549\rho^2 -305\rho +1234  & =  - \varepsilon^{ -11 } \delta^{ -8 } &
549\rho^2 +305\rho -1233  & =   \varepsilon^{ -8 } \delta^{ 3 } \\
&
-6\rho^2 -3\rho +14  & =   \varepsilon^{ -3 } \delta^{ 1 } &
6\rho^2 +3\rho -13  & =   \varepsilon^{ -4 } \delta^{ -3 } \\
&
-3\rho^2 -2\rho +7  & =  - \varepsilon^{ -3 } \delta^{ -2 } &
3\rho^2 +2\rho -6  & =   \varepsilon^{ -2 } \delta^{ 1 } \\
\hline
0 &
-21\rho^2 +7\rho +61  & =  - \varepsilon^{ -5 } \delta^{ -2 } &
21\rho^2 -7\rho -60  & =   \varepsilon^{ -2 } \delta^{ 3 } \\
&
-2\rho^2 +\rho +6  & =   \varepsilon^{ -1 } \delta^{ 1 } &
2\rho^2 -\rho -5  & =   \varepsilon^{ -2 } \delta^{ -1 } \\
\hline
1 &
-21\rho^2 +27\rho +77  & =   \varepsilon^{ -1 } \delta^{ 3 } &
21\rho^2 -27\rho -76  & =   \varepsilon^{ -4 } \delta^{ -1 } \\
\hline
2 &
-603\rho^2 +1340\rho +2718  & =   \varepsilon^{ -1 } \delta^{ 5 } &
603\rho^2 -1340\rho -2717  & =   \varepsilon^{ -6 } \delta^{ -1 } \\
\hline
\end{tabular}
\]
\caption{Sporadic solutions $(u_1,u_2,1)$}
\label{tab:sporadicSols}
\end{table}

From now on, we assume that $a> 100$.

\section{Further notations and finding a good solution in the equivalence class}\label{sec:embedding}

First, we note that $f_a(x)$ has three real roots $\rho=\rho_1,\rho_2,\rho_3$. Let us choose the ordering of the roots such that $\rho$ is the largest root,
$\rho_2=\sigma(\rho)=-1 - 1/\rho$ and $\rho_3=\sigma^2(\rho)=-1/(1+\rho)$.
Then we have the following estimates:
\begin{align*}
	a+1 < & \rho_1 < a+2,\\
	-1 - \frac{1}{a+2} < & \rho_2 < -1 - \frac{1}{a+3},\\
	-\frac{1}{a+2} < & \rho_3 < -\frac{1}{a+3}.
\end{align*}
The estimates can easily be checked e.g. by inserting the upper and lower bounds in $f_a(x)$ and observing that the sign changes.

Since $\rho_1\rho_2\rho_3=1$, the roots $\rho_1,\rho_2,\rho_3$ are indeed units in the maximal order $\mathcal{O}_{K_a}$ of $K_a$.

Next, observe that $\sigma(\rho)=-\rho^2+a\rho + a+2 \in \mathbb{Z}[\rho]$, which implies $\mathbb{Z}[\rho]=\mathbb{Z}[\rho_2]=\mathbb{Z}[\rho_3]$. Thus $\rho_1,\rho_2,\rho_3$ are indeed units in the order $\mathbb{Z}[\rho]$. Moreover, Thomas \cite{Thomas1979} showed that
$\epsilon:=\rho_1$ and $\delta:=-\rho_2$ form a fundamental system of units of the order $\mathbb{Z}[\rho]$.

\medskip

Now let $(u_1,u_2,n)$ be a solution to Equation \eqref{eq:main}. In the following we will find a $\tau\in \Gal(K_a/\mathbb{Q})$ such that $|\tau(u_2)|$ is ``large''.

 Since $\varepsilon$ and $\delta$ are a fundamental system of units, we can write
\[
	u_1= \pm \varepsilon^{x_1}\delta^{x_1}, \quad
	u_2= \pm \varepsilon^{x_2}\delta^{y_2}.
\]
Consider the set of all solutions $(\bar u_1,\bar u_2, n)$ equivalent to $(u_1,u_2,n)$ and let $X$ be the maximum of all absolute values of exponents of $\epsilon$ and $\delta$ in $\bar u_1$ and $\bar u_2$. By choosing an appropriate solution equivalent to $(u_1,u_2,n)$ we may assume without loss of generality that
\[
	X=\max\{|x_2|, |y_2|\}.
\]
Next, we find a ``good'' $\tau\in \Gal(K_a/\mathbb{Q})$. Therefore we prove first

\begin{lem}\label{lem:embedding}
There is a $\tau\in \Gal(K_a/\mathbb{Q})$ such that
$\tau(u_2)=\bar u_2=\pm \varepsilon^{\bar{x}_2}\delta^{\bar{y}_2}$
and the exponents satisfy one of the following conditions:
\begin{enumerate}[label=(\alph*)]
\item \label{case:X-X}$\bar{x}_2=X$ and $\bar{y}_2\geq -X$,
\item \label{case:X2-X2}$\bar{x}_2\geq X/2$ and $\bar{y}_2\geq -X/2$.
\end{enumerate}
\end{lem}
\begin{proof}
We distinguish between several cases, according to the size of the exponents $x_2$ and~$y_2$.

\caselI{Case 1:} $X=x_2$. Then condition \ref{case:X-X} is immediately satisfied with $\tau=\id_{K_a}$.

\caselI{Case 2:} $X=-x_2$.
We distinguish between two subcases.

\caselII{Case 2.1:} $y_2 \geq -X/2$.
If we choose $\tau=\sigma^2$, then we have
\[
	|\tau(u_2)|
	=|\rho_3|^{x_2}|\rho_1|^{y_2}
	=|\rho_1 \rho_2|^{-x_2}|\rho_1|^{y_2}
	=\varepsilon^{-x_2+y_2} \delta^{-x_2}
	=\varepsilon^{\bar{x}_2}\delta^{\bar{y}_2}.
\]
Thus condition \ref{case:X2-X2} is satisfied:
\begin{align*}
	\bar{x}_2
	&=-x_2 + y_2
	\geq X - X/2
	= X/2,\\
	\bar{y}_2
	&= -x_2 = X \geq -X/2.
\end{align*}

\caselII{Case 2.2:} $y_2 < - X/2$. In this case we choose $\tau=\sigma$. Then we have
\[
	|\tau(u_2)|
	= |\rho_2|^{x_2} |\rho_3|^{y_2}
	= |\rho_2|^{x_2} |\rho_1\rho_2|^{-y_2}
	= \varepsilon^{-y_2} \delta^{-y_2+x_2}
	=\varepsilon^{\bar{x}_2}\delta^{\bar{y}_2}
\]
and condition \ref{case:X2-X2} is satisfied:
\begin{align*}
	\bar{x}_2
	&=-y_2
	> X/2,\\
	\bar{y}_2
	&= -y_2 + x_2
	> X/2 - X
	= -X/2.
\end{align*}

\caselI{Case 3:} $X=y_2$. Again, we distinguish between two subcases.

\caselII{Case 3.1:}
$x_2 \geq X/2$. Then condition \ref{case:X2-X2} is immediately satisfied with $\tau=\id_{K_a}$.

\caselII{Case 3.2:}
$x_2 < X/2$.
If we take $\tau=\sigma^2$, then as in Case 2.1 we have
\[
	|\tau(u_2)|
	=\varepsilon^{-x_2+y_2} \delta^{-x_2}
	=\varepsilon^{\bar{x}_2}\delta^{\bar{y}_2}
\]
and condition \ref{case:X2-X2} is satisfied:
\begin{align*}
	\bar{x}_2
	&=-x_2 + y_2
	> -X/2 + X
	= X/2,\\
	\bar{y}_2
	&= -x_2
	> -X/2.
\end{align*}

\caselI{Case 4:} $X=-y_2$. We choose $\tau=\sigma$. Then as in Case~2.2 we have
\[
	|\tau(u_2)|
	= \varepsilon^{-y_2} \delta^{-y_2+x_2}
	=\varepsilon^{\bar{x}_2}\delta^{\bar{y}_2}
\]
and condition \ref{case:X-X} is satisfied:
\begin{align*}
	\bar{x}_2
	&=-y_2
	=X,\\
	\bar{y}_2
	&= -y_2 + x_2
	\geq X - X = 0 \geq - X.
\end{align*}
\end{proof}

Now we can prove that $|\bar u_2|$ is ``large''.

\begin{lem}\label{lem:u2gross}
Let $\bar u_2 = \tau (u_2)$ be as stated in Lemma \ref{lem:embedding}. Then we have
\[
	|\bar u_2|>a^{X/2}.
\]
\end{lem}
\begin{proof}
First assume that condition \ref{case:X-X} of Lemma \ref{lem:embedding} is satisfied, i.e. $\bar x_2=X$ and $\bar y_2 \geq -X$. Then we have
\[
	|\bar u_2|
	=\varepsilon^{\bar x_2}\delta^{\bar y_2}
	> (a+1)^{X}\left(1+\frac{1}{a+2}\right)^{-X}
	= \left( \frac{(a+1)(a+2)}{a+3}\right)^{X}
	> a^{X}.
\]
Now assume that condition \ref{case:X2-X2} is satisfied, i.e. $\bar x_2\geq X/2$ and $\bar y_2\geq -X/2$. Then we have
\[
	|\bar u_2|
	= \varepsilon^{\bar x_2}\delta^{\bar y_2}
	> (a+1)^{X/2} \left(1+\frac{1}{a+2}\right)^{-X/2}
	= \left( \frac{(a+1)(a+2)}{a+3}\right)^{X/2}
	> a^{X/2}.
\]

\end{proof}

Now consider the solution $(\bar u_1 , \bar u_2, n)= (\tau(u_1),\tau(u_2),n)=(\pm \varepsilon^{\bar x_1} \delta^{\bar y_1}, \pm \varepsilon^{\bar x_2} \delta^{\bar y_2},n)$.
Since $\max\{|\bar x_1|,|\bar x_2|,|\bar y_1|,|\bar y_2|\}\leq X$ we immediately obtain the following proposition. (Note that after a possible change of signs we may assume $\bar u_1$ to be positive.)

\begin{prop}\label{prop:good}
Every solution to \eqref{eq:main} is equivalent to a solution $(u_1,u_2,n)$ satisfying
$|u_2|>a^{X/2}$, where $X=\max\{|x_1|,|x_2|,|y_1|,|y_2|\}$ and
$u_1=\varepsilon^{x_1}\delta^{y_1}$, $u_2=\pm \varepsilon^{x_2}\delta^{y_2}$.
\end{prop}

From now on, we will only consider the solutions from Proposition \ref{prop:good}, i.e. we will always assume without loss of generality that a solution  $(u_1,u_2,n)$ is of the form $u_1=\varepsilon^{x_1}\delta^{y_1}$, $u_2=\pm \varepsilon^{x_2}\delta^{y_2}$ and that $|u_2|>a^{X/2}$. Moreover, $X$ shall denote the maximum of the exponents $X=\max\{|x_1|,|x_2|,|y_1|,|y_2|\}$.

\section{Some special cases}\label{sec:specialCases}

In this section we treat the special case $x_1=x_2$, finding the trivial solutions to Equation~\eqref{eq:main}.

\begin{lem}\label{lem:einfacheL}
Let $(u_1,u_2,n)=(\varepsilon^{x_1}\delta^{y_1}, \pm \varepsilon^{x_2}\delta^{y_2},n)$ be a solution to \eqref{eq:main} with $x_1=x_2$ and $y_1-y_2 \in \{0,\pm 1\}$. Then $(u_1,u_2,n)$ is a trivial solution.
\end{lem}
\begin{proof}
First, assume that $x_1=x_2$ and $y_1-y_2=0$. Then we have $u_1=\pm u_2$.
If $u_1 = -u_2$, then we have the trivial solution $(u_1, -u_1 ,0)$.
If $u_1= u_2$, then we have $2 \varepsilon^{x_1} \delta^{y_1} = n$, which is only possible if $x_1=y_1=0$, i.e. $u_1=u_2=1$ and $n=2$.

Now consider the case that $x_1=x_2$ and $y_1-y_2=1$. Then we have
\[
	\varepsilon^{x_1}\delta^{y_2+1} \pm \varepsilon^{x_1}\delta^{y_2}
	=\varepsilon^{x_1}\delta^{y_2}(\delta \pm 1)
	=n.
\]
On the one hand, one can check that $N_{K_a/\mathbb{Q}}(\delta+1)=-2a-3$. Since $\varepsilon$ and $\delta$ are units and $n\in \mathbb{Z}$ with $|n|\leq a^{1/3}$, we obtain a contradiction considering the norm of the above equation:
\[
	2a+3
	=|N_{K_a/\mathbb{Q}}(u_1+u_2)|
	=|N_{K_a/\mathbb{Q}}(n)|
	=|n|^3
	\leq a.
\]
On the other hand, $N_{K_a/\mathbb{Q}}(\delta -1)=1$ and there is a solution for $n=1$:
We have	$\varepsilon^{x_1}\delta^{y_2}(\delta-1)=1$ if and only if $\varepsilon^{x_1}\delta^{y_2}=1/(\delta-1)=\varepsilon $, i.e. $x_1=x_2=1$, $y_1=1$ and $y_2=0$. Thus we have $u_1= \varepsilon \delta=\varepsilon + 1$ and $u_2= -\varepsilon$, which is the trivial solution $(\rho+1,-\rho,1)$.

The case $x_1=x_2$ and $y_1-y_2=-1$ is analogous to the above case.
\end{proof}

In the more general cases we will also argue via the norm, using the following lemma.

\begin{lem}\label{lem:norm}
For $x\in \mathbb{Z}\setminus\{0,\pm1 \}$ we have
\[
	|N_{K_a/\mathbb{Q}}(\varepsilon^x \pm 1)|>a.
\]
\end{lem}
\begin{proof}
First, assume that $x\geq 2$. Then
\begin{align*}
	|N_{K_a/\mathbb{Q}}(\varepsilon^x \pm 1)|
	&= |\rho_1^x \pm 1|\cdot|\rho_2^x \pm 1|\cdot|\rho_3^x \pm 1|\\
	&> ((a+1)^2 - 1) \left( \left( 1 + \frac{1}{a+3}\right)^2 - 1 \right)
		\left( 1- \left( \frac{1}{a+2}\right)^2 \right)\\
	&=\frac{a(1+a)(7+2a)}{(2+a)(3+a)}
	> a.
\end{align*}
For $x\leq -2$ we have
\begin{align*}
	|N_{K_a/\mathbb{Q}}(\varepsilon^x \pm 1)|
	&> (1- (a+1)^{-2}) \left( 1 - \left( 1 + \frac{1}{a+3}\right)^{-2} \right)
		\left( \left( \frac{1}{a+2}\right)^{-2} - 1 \right)\\
	&=\frac{a(a+2)(a+3)(2a+7)}{(a+1)(a+4)^2}
	> a.
\end{align*}
\end{proof}

Now we can prove

\begin{prop}\label{prop:specialCases}
Any solution $(u_1,u_2,n)=(\varepsilon^{x_1}\delta^{y_1}, \pm \varepsilon^{x_2}\delta^{y_2},n)$ to Equation \eqref{eq:main} with $x_1=x_2$ is trivial.
\end{prop}
\begin{proof}
By Lemma \ref{lem:einfacheL} we only need to check the cases where $x_1=x_2$ and $y_1-y_2 \notin\{0,\pm 1\}$.
Under these assumptions Equation \eqref{eq:main} becomes
\[
	n
	= \varepsilon^{x_1} \delta^{y_1} \pm \varepsilon^{x_1} \delta^{y_2}
	= \varepsilon^{x_1} \delta^{y_2} (\delta^{y_1-y_2} \pm 1).
\]
Considering the norm, we obtain a contradiction with Lemma \ref{lem:norm}:
\[
	a
	\geq |n|^3
	=| N_{K_a/\mathbb{Q}}(\delta^{y_1-y_2} \pm 1)|
	>a.
\]
\end{proof}

From now on, we assume that $x_1\neq x_2$ and in particular $X\geq 1$.

\section{Obtaining an upper bound for $X$}\label{Sec:upper}

In this section we use a lower bound for linear forms in logarithms by  Laurent \cite[Cor. 2]{Laurent2008} in order to obtain a bound of the form $X\ll \log a \,(\log \log a)^2$. To state Laurent's result we have to introduce the notion of height. Let $\alpha \neq 0$ be an algebraic number of degree $d$ and let
\[
	a_0(x-\alpha_1)\cdots (x-\alpha_d) \in \mathbb{Z}[x]
\]
be the minimal polynomial of $\alpha$. Then the absolute logarithmic Weil height is defined by
$$h(\alpha):=\frac 1d \left(\log |a_0|+\sum_{i=1}^d \max\{0,\log|\alpha_i|\}\right).$$
With this notation we have

\begin{knownthm}[Laurent]\label{thm:Laurent}
Let $\alpha_1, \alpha_2 \geq 1$ be two multiplicatively independent real algebraic numbers, let $b_1$ and $b_2$ be two positive integers and let
\[
	\Lambda := b_2 \log \alpha_2 - b_1 \log \alpha_1.
\]
Then
\[
	\log |\Lambda|
	\geq - 17.9 D^4 (\max\{ \log b' + 0.38, 30/D, 1\})^2 \log A_1 \log A_2,
\]
where
\begin{align*}
	D&=[\mathbb{Q}(\alpha_1,\alpha_2):\mathbb{Q}],\\
	b'&=\frac{b_1}{D \log A_2} + \frac{b_2}{D \log A_1},\\
	\log A_i &\geq \max \{ h(\alpha_i),|\log \alpha_i|/D,1/D\}
		\qquad (i=1,2).
\end{align*}
\end{knownthm}

\begin{prop}\label{prop:upperBound}
Let $a > 100$ and $(u_1,u_2,n)$ be a solution with the properties from Proposition~\ref{prop:good} and $x_1 \neq x_2$.
Then for the maximum of exponents $X$ we have the upper bound
\begin{equation}\label{eq:upperBound}
	X < 343 \log a \cdot (10 +  1.7 \log \log a)^2.
\end{equation}
\end{prop}
\begin{proof}
First, note that Inequality \eqref{eq:upperBound} is trivially fulfilled if $X\leq 200\,000$. Thus we may assume $X> 200\,000$.

We start with the unit equation $u_1+u_2=n$.
Taking absolute values and dividing by $|u_2| > a^{X/2}$
we obtain
\begin{equation*}\label{eq:uB_preLinform}
	\left|\frac{u_1}{u_2} - 1 \right|
	= |\varepsilon^{x_1-x_2} \delta^{y_1-y_2} \pm 1 |
	= \frac{|n|}{|u_2|}
	< \frac{a^{1/3}}{a^{X/2}}.
\end{equation*}
Since we are assuming $X\geq 1$ and $a>100$,
the right-hand side of the above inequality is smaller than $0.5$. Since $\varepsilon$ and $\delta$ are positive, the ``+'' sign cannot hold and we have
\begin{equation*}
	|\varepsilon^{x_1-x_2} \delta^{y_1-y_2} - 1 |
	<  \frac{a^{1/3}}{a^{X/2}}.
\end{equation*}
Since $|\log x|< 2 |x-1|$ for $|x-1|<0.5$, this implies
\begin{equation}\label{eq:uB_linform}
	|\Lambda|
	:=|(x_1-x_2)\log \varepsilon - (y_1-y_2) \log \delta|
	< \frac{2a^{1/3}}{a^{X/2}}.
\end{equation}
Note that $\varepsilon, \delta$ are multiplicatively independent and larger than 1. Further, note that $x_1-x_2$ and $y_1-y_2$ are integers.
Since $|\Lambda|<0.5$, $\log \varepsilon>1$ and $x_1-x_2\neq 0$, it is easy to see that $y_1-y_2$ is nonzero and of the same sign as $x_1-x_2$.
Therefore, we may apply \hyperref[thm:Laurent]{Laurent's} theorem. First, we estimate the height of $\alpha_1:=\varepsilon$ and $\alpha_2:=\delta$:
\begin{align*}
	h(\alpha_1)=h(\alpha_2)
	= h(\rho_1)
	&=\frac{1}{3}(\log 1 + \log \max\{1, |\rho_1|\} + \log \max\{1, |\rho_2|\} + \log \max\{1, |\rho_3|\} )\\
	&=\frac{1}{3}(\log|\rho_1| + \log |\rho_2|\}\\
	&< \frac{1}{3}\left(\log (a+2) +\log \left(1+ \frac{1}{a+2}\right)\right)
	= \frac{1}{3}\log (a+3).
\end{align*}
Now we have
\begin{align*}
D &= [\mathbb{Q}(\alpha_1,\alpha_2):\mathbb{Q}]=3,\\
\log A_1 =\log A_2
	&:= \frac{1}{3}\log (a+3)
	\geq \max \{ h(\alpha_i),|\log \alpha_i|/D,1/D\},\\
b' &= \frac{|x_1-x_2|}{D\log A_2} + \frac{|y_1-y_2|}{D\log A_1} =\frac{|x_1-x_2|+|y_1-y_1|}{\log(a+3)}.
\end{align*}
Thus we obtain
\begin{multline}\label{eq:uB_LaurentApplied}
	-17.9 \cdot 3^4 \left( \max \left\{
		\log \left( \frac{|x_1-x_2|+|y_1-y_1|}{\log(a+3)} \right) + 0.38,
		\frac{30}{3}, 1
	\right\} \right)^2
	\left(\frac{1}{3}\log(a+3) \right)^2\\
	\leq \log |\Lambda|
	< \log 2 + \frac{1}{3}\log a - \frac{X}{2}\log a.
\end{multline}
Next, note that
\begin{align*}
	\log \left( \frac{|x_1-x_2|+|y_1-y_2|}{\log(a+3)} \right) + 0.38
	&\leq \log \left(\frac{4X}{\log(a+3)}\right) + 0.38\\
	&= \log 4 + \log X - \log \log (a+3) + 0.38\\
	&\leq \log 4 + \log X - \log \log 103 + 0.38\\
	< \log X + 0.24.
\end{align*}
Moreover, since we are assuming $X>200\,000$, we have in particular $\log X > 12$, so
\[
	\max \left\{\log \left( \frac{|x_1-x_2|+|y_1-y_1|}{\log(a+3)} \right) + 0.38,
		\frac{30}{3}, 1 \right\}
	<\log X + 0.24
	< 1.02 \log X.
\]
Therefore, we obtain from \eqref{eq:uB_LaurentApplied}
\[
	-167.61 (\log X)^2 (\log (a+3))^2
	<  \log 2 + \frac{1}{3}\log a - \frac{X}{2}\log a,
\]
which implies
\[
	\frac{X}{2}\log a
	< 167.61 (\log X)^2 (\log (a+3))^2 + \log 2 + \frac{1}{3}\log a
	< 168 (\log X)^2 (\log (a+3))^2.
\]
Multiplying by $2(\log a)^{-1}$ we obtain
\begin{equation}\label{eq:uB_preBound}
\begin{split}
	X
	&< 168 (\log X)^2 (\log (a+3))^2 \cdot 2 (\log a)^{-1} \\
	&< 168 (\log X)^2 (1.01 \log a)^2 \cdot 2 (\log a)^{-1} \\
	&< 343 \log a \cdot (\log X)^2 .
\end{split}
\end{equation}
This implies (note that we are assuming $X>200\,000$)
\begin{align*}
	\log X
	&< \log 343 + \log \log a + 2\log \log X \\
	&< 5.9 +  \log \log a + 0.41 \log X
\end{align*}
and therefore
\[
	\log X
	< \frac{5.9}{0.59} + \frac{\log \log a}{0.59}
	< 10 +  1.7 \log \log a.
\]
Thus \eqref{eq:uB_preBound} implies
\[
	X < 343 \log a \cdot (10 +  1.7 \log \log a)^2.
\]
\end{proof}

\section{Obtaining a lower bound for $X$}\label{Sec:lower}

Next, we do some elementary estimations in order to obtain the following lower bound for $X$.

\begin{prop}\label{prop:lowerBound}
Let $a > 100$ and $(u_1,u_2,n)$ be a solution with the properties from Proposition~\ref{prop:good} and $x_1\neq x_2$.
Then for the maximum of exponents $X$ we have the lower bound
\begin{equation*}
 X > \frac{1}{2}(a+2)(\log (a+1) - \log 2).
\end{equation*}
\end{prop}
\begin{proof}
As in the proof of Proposition \ref{prop:smallSols}, assuming $X\geq 1$ and $a> 100$ we have
\[
	|\varepsilon^{x_1-x_2} \delta^{y_1-y_2}- 1 |
	< \frac{a^{1/3}}{a^{X/2}}
	< 0.5.
\]
Since we assume $x_1-x_2\neq 0$, we can distinguish between the two cases $x_1-x_2\leq -1$ and $x_1-x_2\geq 1$.

\caselI{Case 1:} $x_1-x_2 \leq -1$. Then we have
\begin{align*}
	0.5
	< \varepsilon^{x_1-x_2} \delta^{y_1-y_2}
	\leq (a+1)^{-1} \delta^{y_1-y_2},
\end{align*}
so we must have $y_1-y_2 > 0$ and
\[
	\frac{1}{2}
	< (a+1)^{-1} \left( 1+ \frac{1}{a+2}\right)^{y_1-y_2}
	\leq (a+1)^{-1} \left( 1+ \frac{1}{a+2}\right)^{2X}.
\]
This implies
\begin{align*}
	X
	> \frac{\log (a+1) - \log 2}{2 \log \left( 1+ \frac{1}{a+2}\right)}
	> \frac{1}{2}(a+2)(\log (a+1) - \log 2),
\end{align*}
where we used that $\log (1+x)<x$ and therefore $\frac{1}{\log(1+x)}>\frac 1x$ for all $x>0$.

\caselI{Case 2:} $x_1-x_2 \geq 1$. In this case we have
\[
	1.5
	> \varepsilon^{x_1-x_2} \delta^{y_1-y_2}
	\geq (a+1)\, \delta^{y_1-y_2},
\]
so we must have $y_1-y_2<0$ and
\[
	1.5
	> (a+1) \left( 1+ \frac{1}{a+2}\right)^{y_1-y_2}
	\geq (a+1) \left( 1+ \frac{1}{a+2}\right)^{-2X}.
\]
This implies
\begin{align*}
	X
	> \frac{\log (a+1) + \log 1.5}{2 \log \left( 1+ \frac{1}{a+2}\right)}
	> \frac{1}{2}(a+2)(\log (a+1) - \log 2).
\end{align*}
\end{proof}

\section{Finishing the proof of Theorem \ref{thm:main}}

Combining Proposition \ref{prop:upperBound} and Proposition \ref{prop:lowerBound} we obtain
an absolute bound for~$a$:

\begin{prop}\label{prop:largeBound}
There are no sporadic solutions for
$a > 1.48 \cdot 10^5$.
\end{prop}
\begin{proof}
The statement follows from Propositions \ref{prop:good}, \ref{prop:specialCases}, \ref{prop:upperBound} and \ref{prop:lowerBound}. The bound is obtained by solving the inequality
\[
	\frac{1}{2}(a+2)(\log (a+1) - \log 2)
	< 343 \log a \cdot (10 +  1.7 \log \log a)^2.
\]
\end{proof}

Finally, we use continued fractions to deal with all $100<a\leq 1.48\cdot 10^5$ and thus finish the proof of Theorem \ref{thm:main}.

Recall Inequality \eqref{eq:uB_linform} from the proof of Proposition \ref{prop:smallSols}:
\[
	|(x_1-x_2)\log \varepsilon - (y_1-y_2) \log \delta|
	< 2a^{\frac{1}{3}-\frac{X}{2}}.
\]
Note that by Proposition \ref{prop:specialCases} we may assume $x_1-x_2\neq 0$ and therefore it is easy to check that $y_1-y_2\neq 0$ as well.
Dividing by $\log \varepsilon > \log a$ we obtain
\begin{equation}\label{eq:red_ineq}
	\left| (x_1-x_2)-(y_1-y_2)\frac{\log \delta}{\log \varepsilon} \right|
	< \frac{2a^{\frac{1}{3}-\frac{X}{2}}}{\log a}.
\end{equation}
We proceed for each $a$ with $100< a \leq 1.48 \cdot 10^5$ as follows.
First we compute $\frac{\log \delta}{\log \varepsilon}$ and find the smallest convergent $\frac{p}{q}$ to $\frac{\log \delta}{\log \varepsilon}$ such that
\[
	q
	\geq 2 \cdot 343 \log a \cdot (10 +  1.7 \log \log a)^2
	> 2X
	\geq |y_1-y_2|.
\]
Then by the best approximation property of continued fractions we have
\[
	c:= \left|p - q\, \frac{\log \delta}{\log \varepsilon}\right|
	<\left|(x_1-x_2) - (y_1-y_2) \frac{\log \delta}{\log \varepsilon}\right|
	< \frac{2a^{\frac{1}{3}-\frac{X}{2}}}{\log a},
\]
which implies a new bound
\[
	X
	< \frac{2}{\log a} \log \left( \frac{2a^{1/3}}{c \log a} \right) .
\]
On the other hand, we have
\[
	X> \frac{1}{2}(a+2)(\log (a+1) - \log 2)
\]
and if upper and lower bounds for $X$ contradict each other, we deduce that no non-trivial solution for this specific $a$ exists. Indeed, the computations for $100 < a \leq 1.48 \cdot 10^5$ revealed that the bounds contradict each other for every $a$. Thus there are no sporadic solutions to Equation \eqref{eq:main} for $a>100$. Since the case  $a \leq 100$ has already been treated in Proposition \ref{prop:smallSols}, this completes the proof of  Theorem \ref{thm:main}.

Finally, let us remark that the computations described above were done in Sage \cite{Sage} and took about 5 minutes on a usual pc.

\section{Further problems}

In Theorem \ref{thm:main} we assumed for technical reasons $|n|\leq \max\{|a|^{1/3},1\}$. The question is, whether this assumption is necessary.

For small $a$ there actually do exist further solutions if we omit this assumption. E.g. for $a=-1$ there is a total of 15 sporadic, pairwise non-equivalent, solutions with the largest $n$ being $22$.

However, a search in the range $- 1 \leq a \leq 400$ and $1\leq n \leq 400$ revealed no sporadic solutions for $a\geq 3$.
Therefore, we suspect that indeed a much stronger result holds.

\begin{con}\label{con:unit-eq}
The Diophantine equation
\begin{equation*}
 u_1+u_2=n,
 \qquad
 u_1,u_2\in \mathbb{Z}[\rho]^*, \;
 n\in \mathbb{Z}
\end{equation*}
has exactly 24 sporadic solutions that are pairwise non-equivalent.
Moreover, each sporadic solution $(u_1,u_2,n)$ satisfies $a\leq 2$ and $|n|\leq 22$.
\end{con}

Another natural question is whether our result can be extended to units of the maximal order  of $K_a$ instead of the order $\mathbb{Z}[\rho]$. In the range $-1\leq a \leq 400$ and $1\leq n \leq 400$ there are only 66 pairwise non-equivalent sporadic solutions and all of them satisfy $a\leq 66$ and $|n|\leq 22$.
Therefore, we make the following (perhaps wild) conjecture.

\begin{con}\label{con:strong}
Unit Equation \eqref{eq:unit} has exactly 66 sporadic solutions that are pairwise non-equivalent.
\end{con}

\section*{Acknowledgement}

We want to thank Attila B\'erczes for his help with the computations verifying Conjectures~\ref{con:unit-eq} and \ref{con:strong} in the range $- 1 \leq a \leq 400$ and $1\leq n \leq 400$.

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


Kent State University at Tuscarawas is sponsoring Super Science Saturday from 9 a.m. to noon on Oct. 8 in the Science and Advanced Technology Center. Designed for students in grades four through seven, participants will perform and observe more than a dozen exciting chemistry experiments. A few of the experiments include t-shirt chromatography, crayon art and making ice cream in a baggie, which can be taken home as completed projects.
Registration fee is $10 per participant, which includes a t-shirt students will decorate. Registrations can be made online at Super Science Saturday.
Kent State Tuscarawas, 330 University Dr NE, New Philadelphia, OH 44663.
Registrations are limited to the first 100 responders and must be received by Sept. 29. For questions about the program, contact Pam Patacca at ppatacca@kent.edu or 330-308-7473.
Super Science Saturday is an activity of the Conceptual Chemistry graduate level education course and is coordinated by Kent State University at Tuscarawas.


text:
Estragol ist ein Phenylpropanoid und ein Isomer von Anethol.

Vorkommen

Estragol ist ein aromatischer Bestandteil ätherischer Öle, die aus Estragon (60–75 % Estragol), Kerbel (60 % Estragol), Basilikum (23–88 % Estragol), Anis, Anis-Duftnessel, Koreaminze, Sternanis, Bay, Avocado, Fenchel, Piment, Muskatnuss, Pinie, Waldkiefern oder Terpentin gewonnen werden.

Eigenschaften
Estragol ist eine viskose, farblose Flüssigkeit von anisartigem Geruch, die unter Normaldruck bei 216 °C siedet. Die Dampfdruckfunktion ergibt sich nach Antoine entsprechend log10(P) = A−(B/(T+C)) (P in bar, T in K) mit A = 5,03793, B = 2246,739 und C = −41.799 im Temperaturbereich von 326 K bis 488 K. Die Verbindung löst sich nur geringfügig (0,178 g/l) in Wasser.

Verwendung
Der Stoff wird in Parfüms, Likören und Lebensmitteln als Duftstoff bzw. Aroma verwendet.
Die europäische Verordnung (EG) Nr. 1334/2008 (Aromenverordnung) (Anhang III, Teil A) regelt die Verwendung von Estragol in Aromen und Lebensmitteln. Als Reinsubstanz darf Estragol Aromen und Lebensmitteln nicht zugesetzt werden – sofern aber dieser Stoff über natürliche Quellen wie Estragonöl oder Basilikumöl Eingang in Aromen und Lebensmitteln findet, sind für die wichtigsten Lebensmittel, die häufig diese Extrakte zur Geschmacksgebung enthalten, Höchstmengen zu beachten. Diese betragen 50 mg pro kg verzehrfertiges Lebensmittel für Milcherzeugnisse, verarbeitetes Obst und Gemüse (incl. Pilze, Wurzelgemüse, Knollen, Hülsenfrüchte, Leguminosen), verarbeitete Nüsse und Samen und für Fischerzeugnisse und 10 mg pro kg für alkoholfreie Getränke.

Gesundheitsrisiken
Da die Substanz vielfach in Teeaufgüssen festgestellt wurde und in Tierstudien krebserzeugend wirkt, hat das Bundesinstitut für Risikobewertung auf die Dringlichkeit hingewiesen, dass in derartigen Teeerzeugnissen Estragol nicht nachweisbar sein darf. Vor allem weil diese Getränke häufig an Säuglinge und Kleinkinder verabreicht werden, erscheint dem Institut die Absenkung des Estragol-Gehaltes dringend erforderlich.

Weblinks
 Estragol im Riechstofflexikon

Einzelnachweise

Alkenylbenzol
Methoxybenzol
Allylverbindung
Phenylpropanoid
Flüchtiger Pflanzenstoff

redpajama_set_name: RedPajamaWikipedia


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It is the worst, you go to get your brows done and the take off too much or give you a shape you did not ask for! Can this be avoided?? Absolutely! This is my recommendation to you and to any professional that has a new client or a client you are just "learning". I prep the skin, draw in the shape of the brows using a pencil or powder per my consultation. Once you and the client agree on the brow shape, then I wax or tweeze around it. Brows are sisters not twins so powder or pencil correction is often needed anyway. This allows you to consult with your client to make them more uniform and often invites a purchase of the product and tools you are using.
Using Heat & Acne together! Don't miss out!


text:
Cleveland Clinic and IBM hope their tech partnership could help prevent the next pandemic
Updated: 10:35 AM EDT Mar 30, 2021
By Clare Duffy, CNN Business
IS LIVE IN BOSTON WITH THAT MESSAGE. JEN? JENNIFER: EVEN AS VACCINATIONS RAMP UP AT SITES LIKE THIS ONE, THE CDC DIRECTOR IS SOUNDING THE ALARM. THE FORMER MGH DOCTOR WARNING THE U.S. IS ON A COLLISION COURSE WITH, IN HER WORDS, IMPENDING DOOM. >> WE HAVE SO MUCH TO LOOK FORWARD TO, SO MUCH PROMISE AND POTENTIAL OF WHERE WE ARE, AND SO MUCH REASON FOR HOPE. BUT RIGHT NOW, I'M SCARED. JENNIFER: SOME PARTS OF THE COUNTRY ARE SEEING A STEADY RISE IN CASES, FUELED BY TRAVEL, YOUNG PEOPLE AND RELAXED RULES, INCLUDING HERE IN MASSACHUSETTS. >> GOVERNOR BAKER'S NEW RELAXATION RULES AROUND WHERE PEOPLE CAN CONGREGATE -- AGAIN, IF PEOPLE DO IT SAFELY, IT IS OK. JENNIFER: YESTERDAY, PRESIDENT BIDEN MOVED UP HIS VACCINATION GOAL, AS THESE CONCERNS MOUNT. HE SAYS HE WANTS TO SEE 90% OF ADULTS ELIGIBLE FOR VACCINATION BY APRIL 19. THAT'S WHEN MASSACHUSETTS IS SET TO OPEN SHOTS UP TO THE GENERAL PUBLIC. AGAIN, THE CDC DIRECTOR IS EXPECTED TO SPEAK WITH THE NATION'S GOVERNORS TO
Video above: CDC director warns of 'impending doom' if U.S. eases COVID-19 restrictionsAfter a year in which scientists raced to understand COVID-19 and develop treatments and vaccines to stop its spread, Cleveland Clinic is partnering with IBM to use next-generation technologies to advance health care research — and potentially prevent the next public health crisis.The two organizations on Tuesday announced the creation of the "Discovery Accelerator," which will apply technologies such as quantum computing and artificial intelligence to pressing life sciences research questions. As part of the partnership, Cleveland Clinic will become the first private-sector institution to buy and operate an on-site IBM quantum computer, called the Q System One. Currently, such machines only exist in IBM labs and data centers.Quantum computing is expected to expedite the rate of discovery and help tackle problems with which existing computers struggle.The accelerator is part of Cleveland Clinic's new Global Center for Pathogen Research & Human Health, a facility introduced in January on the heels of a $500 million investment by the clinic, the state of Ohio and economic development nonprofit JobsOhio to spur innovation in the Cleveland area.The new center is dedicated to researching and developing treatments for viruses and other disease-causing organisms. That will include some research on COVID-19, including why it causes ongoing symptoms (also called "long Covid") for some who have been infected."Covid-19 is an example" of how the center and its new technologies will be used, said Dr. Lara Jehi, chief research information officer at the Cleveland Clinic."But ... what we want is to prevent the next COVID-19," Jehi told CNN Business. "Or if it happens, to be ready for it so that we don't have to, as a country, put everything on hold and put all of our resources into just treating this emergency. We want to be proactive and not reactive."The promise of quantumQuantum computers process information in a fundamentally different way from regular computers, so they will be able to solve problems that today's computers can't. They can, for example, test multiple solutions to a problem at once, making it possible to come up with an answer in a fraction of the time it would take a different machine.Applied to health care research, that capability is expected to be useful for modeling molecules and how they interact, which could accelerate the development of new pharmaceuticals. Quantum computers could also improve genetic sequencing to help with cancer research, and design more efficient, effective clinical trials for new drugs, Jehi said.Ultimately, Cleveland Clinic and IBM expect that applying quantum and other advanced technologies to health care research will speed up the rate of discovery and product development. Currently, the average time from scientific discovery in a lab to getting a drug to a patient is around 17 years, according to the National Institutes of Health."We really need to accelerate," Jehi said. "What we learned with the COVID-19 pandemic is that we cannot afford, as a human race, to just drop everything and focus on one emergency at a time."Part of the problem: It takes a long time to process and analyze the massive amount of data generated by health care, research and trials — something that AI, quantum computing and high-performance computing (a more powerful version of traditional computing) can help with. Quantum computers do that by "simulating the world," said Dario Gil, director of IBM Research."Instead of conducting physical experiments, you're conducting them virtually, and because you're doing them virtually through computers, it's much faster," Gil said.What this means for IBMFor IBM, the partnership represents an important proof point for commercial applications of quantum computing. IBM currently offers access to quantum computers via the cloud to 134 institutions, including Goldman Sachs and Daimler, but building a dedicated machine on-site for one organization is a big step forward."What we're seeing is the emergency of quantum as a new industry within the world of information technology and computing," Gil said. "What we're seeing here in the context of Cleveland Clinic is ... a partner that says, 'I want the entire capacity of a full quantum computer to be to my research mission."The partnership also includes a training element that will help educate people on how to use quantum computing for research — which is likely to further grow the ecosystem around the new technology.Cleveland Clinic and IBM declined to detail the cost of the quantum system being installed on the clinic's campus, but representatives from both organizations called it a "significant investment." Quantum computers are complex machines to build and maintain because they must be stored at extremely cold temperatures (think: 200 times colder than outer space).The Cleveland Clinic will start by using IBM's quantum computing cloud offering while waiting for its on-premises machine to be built, which is expected to take about a year. IBM plans to later install at the clinic a more advanced version of its quantum computer once it is developed in the coming years.Jehi, the Cleveland Clinic research lead, acknowledged that quantum computing technology is still nascent, but said the organization wanted to get in on the ground floor."It naturally needs nurturing and growing so that we can figure out what are its applications in health care," Jehi said. "It was important to us that we design those applications and we learn them ourselves, rather than waiting for others to develop them."
Video above: CDC director warns of 'impending doom' if U.S. eases COVID-19 restrictions
After a year in which scientists raced to understand COVID-19 and develop treatments and vaccines to stop its spread, Cleveland Clinic is partnering with IBM to use next-generation technologies to advance health care research — and potentially prevent the next public health crisis.
The two organizations on Tuesday announced the creation of the "Discovery Accelerator," which will apply technologies such as quantum computing and artificial intelligence to pressing life sciences research questions. As part of the partnership, Cleveland Clinic will become the first private-sector institution to buy and operate an on-site IBM quantum computer, called the Q System One. Currently, such machines only exist in IBM labs and data centers.
Quantum computing is expected to expedite the rate of discovery and help tackle problems with which existing computers struggle.
The accelerator is part of Cleveland Clinic's new Global Center for Pathogen Research & Human Health, a facility introduced in January on the heels of a $500 million investment by the clinic, the state of Ohio and economic development nonprofit JobsOhio to spur innovation in the Cleveland area.
The new center is dedicated to researching and developing treatments for viruses and other disease-causing organisms. That will include some research on COVID-19, including why it causes ongoing symptoms (also called "long Covid") for some who have been infected.
President Biden, CDC director warn of virus rebound if nation lets up
"Covid-19 is an example" of how the center and its new technologies will be used, said Dr. Lara Jehi, chief research information officer at the Cleveland Clinic.
"But ... what we want is to prevent the next COVID-19," Jehi told CNN Business. "Or if it happens, to be ready for it so that we don't have to, as a country, put everything on hold and put all of our resources into just treating this emergency. We want to be proactive and not reactive."
The promise of quantum
Quantum computers process information in a fundamentally different way from regular computers, so they will be able to solve problems that today's computers can't. They can, for example, test multiple solutions to a problem at once, making it possible to come up with an answer in a fraction of the time it would take a different machine.
Applied to health care research, that capability is expected to be useful for modeling molecules and how they interact, which could accelerate the development of new pharmaceuticals. Quantum computers could also improve genetic sequencing to help with cancer research, and design more efficient, effective clinical trials for new drugs, Jehi said.
Biden announces 90% of adults will be vaccine eligible in three weeks
Ultimately, Cleveland Clinic and IBM expect that applying quantum and other advanced technologies to health care research will speed up the rate of discovery and product development. Currently, the average time from scientific discovery in a lab to getting a drug to a patient is around 17 years, according to the National Institutes of Health.
"We really need to accelerate," Jehi said. "What we learned with the COVID-19 pandemic is that we cannot afford, as a human race, to just drop everything and focus on one emergency at a time."
Part of the problem: It takes a long time to process and analyze the massive amount of data generated by health care, research and trials — something that AI, quantum computing and high-performance computing (a more powerful version of traditional computing) can help with. Quantum computers do that by "simulating the world," said Dario Gil, director of IBM Research.
"Instead of conducting physical experiments, you're conducting them virtually, and because you're doing them virtually through computers, it's much faster," Gil said.
What this means for IBM
For IBM, the partnership represents an important proof point for commercial applications of quantum computing. IBM currently offers access to quantum computers via the cloud to 134 institutions, including Goldman Sachs and Daimler, but building a dedicated machine on-site for one organization is a big step forward.
"What we're seeing is the emergency of quantum as a new industry within the world of information technology and computing," Gil said. "What we're seeing here in the context of Cleveland Clinic is ... a partner that says, 'I want the entire capacity of a full quantum computer to be [dedicated] to my research mission."
The partnership also includes a training element that will help educate people on how to use quantum computing for research — which is likely to further grow the ecosystem around the new technology.
Cleveland Clinic and IBM declined to detail the cost of the quantum system being installed on the clinic's campus, but representatives from both organizations called it a "significant investment." Quantum computers are complex machines to build and maintain because they must be stored at extremely cold temperatures (think: 200 times colder than outer space).
The Cleveland Clinic will start by using IBM's quantum computing cloud offering while waiting for its on-premises machine to be built, which is expected to take about a year. IBM plans to later install at the clinic a more advanced version of its quantum computer once it is developed in the coming years.
Jehi, the Cleveland Clinic research lead, acknowledged that quantum computing technology is still nascent, but said the organization wanted to get in on the ground floor.
"It naturally needs nurturing and growing so that we can figure out what are its applications in health care," Jehi said. "It was important to us that we design those applications and we learn them ourselves, rather than waiting for others to develop them."

redpajama_set_name: RedPajamaCommonCrawl


Whether you're in to product design and style, software engineering, construction or any other sector, there is generally even more than one way to get things done. Regarding projectmanagement, each of the most high profile methods with regards to getting details done are definitely the classic waterfall style of project operations as well as the innovative youngster in the mass, acuto task operations. To decide which is best for your needs, you need to establish a valuable knowledge of the advantages and limitations of each and every type of project administration technique. In this article we all look what is diverse about the two schools of thought, and compare side simply by side the huge benefits and restrictions of every single.
Waterfall task control mimics the conventional work method in any development or engineering project since it is a continuous process. All the stages occurs in remoteness, and once total, the team will leave your site and go to the subsequent level in the string. Waterfall job management is dependent upon meticulous record saving. This means we have a clear paper trek to follow, enabling the task to be white and improved upon in the future. From the beginning, the customer may have a clear concept of what is certainly going to happen during task delivery. They will be aware of approximately what the cost, timescales and size of the job will probably be, and will have a good idea of what to expect basically we. Once a level in the procedure has been completed, there is zero way to get back and change facts without scrapping the total project and beginning again. The full process relies on refined initial requirements; any time these kinds of are flawed then the project is doomed to inability from the outset. The product is designed found in stages and only tested fully towards the end, meaning glitches may always be hence ingrained worth merchandise that they can be unattainable to take out. Finally, this sort of job control won't allow for adjustments to the brief, hence if the customer understands they need to improve the quick half approach through, surrender will will need to become made in terms of spending budget and timescales.
Snello was once recognized as being the perfect solution to many belonging to the problems in waterfall job management. Instead of following a order of measures in solitude, this approach relies upon a great pregressive strategy to the project delivery. Project groups start shut off which has a very simple idea of where they are going, and consequently work on unobtrusive web theme in short 'sprints'. At the end of each and every sprint the modules are tested to see any drive or weaknesses and customer comments is got ahead of the up coming sprint happens. Plenty of adjustments can be built after preliminary plans are developed, in fact rewrites and major changes are practically anticipated. This will make it less difficult to put features and maintain abreast of modifications in our market, actually while the job will be sent. Frequent screening assures blemishes will be acknowledged in early stages, meaning that the product can become ready for unveiling more quickly and is more likely to be a quality merchandise. Using this method requires a solid project manager to keep tasks about track and balance out creativeness with job delivery requirements. Since of the haziness of the main project program, the last merchandise can often be wildly different to what was at first supposed.
Both the strategies of project management both have their time and place, and the one which in turn ideal your needs depends entirely with your specific brief. When you know very well what a final item should always be and are confident your client will never have to transformation the range half method through, design project supervision is the good friend. Even so in the event that acceleration of development is even more essential than the top quality of the finished item as well as the customer chooses to be in a position to alter scope part way through, agile provides for more versatility and is usually among the things just about every job manager ought to know about. To find out more go through in this article www.akhbarqena.com .


Hemorrhoids should not be a cause of embarrassment as there are several Hemorrhoids remedy methods available.Hemorrhoids remedy or treatments are of various types.
The most common of hemorrhoids remedy are creams, sitz bath, home remedies and finally surgical removal. Hemorrhoids remedy can be of the following types.
Soft and easy bowel movements- Don't strain you bowel it's one of the best curative and preventive measures for Hemorrhoids remedy.
Diet and food habits- Eat food, which helps to ease digestion and smooth stool passage. For example have more fluids, fruits and vegetables rather than bread, soda, etc.
Applying ice on the area, Sitz bath, herbal remedies like horse chest nut extract, etc are some of the home treatment methods of Hemorrhoids remedies.
Creams- Another common Hemorrhoids remedy that helps to curb swelling of irritated hemorrhoidal tissues are Hemorrhoids creams.
It also gives immediate and temporary relief from the painful burning, itching and discomfort of hemorrhoids.
1. The hemorrhoids may be removed surgically or through other methods in extreme cases.
1. Rubber Band Ligation - In this process a small rubber band is placed at the base of the internal hemorrhoid. The blood supply to the hemorrhoid is cut off hence resulting in it to shrink up and fall off in about four to seven days.
2. Injection Sclerotherapy - A chemical solution is injected into the mucous membrane near the hemorrhoid resulting in inflammation and closure of the veins, thereby shrinking the hemorrhoid.
3. Infrared Photocoagulation - An infrared is directed to clot the dilated veins of the hemorrhoid. The hemorrhoids shrink since the blood does not flow through the coagulated blood vessels.
4. Laser Coagulation - An electric current is applied to the hemorrhoids triggering a chemical reaction that shuts down the blood supply in the hemorrhoid and causes the inflamed tissue to shrink.
5. Hemorrhoidectomy - Here the hemorrhoid groups are surgically removed with a scalpel, cattery device or laser. What should the Hemorrhoids remedy doIt should relieve pain and discomfort from hemorrhoids.
Reduce itching, prevents bleeding, eliminate swelling and burning. It should heal and shrinks the hemorrhoid and prevent hemorrhoids from returning due to its power to strengthen the veins tone. In case of surgery caution must be taken.It should do the appropriate repair of damaged tissues.


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Q: Как работать с javascript с другим(внешним) сайтом? Вопрос такой.
Как подключить javascript со внешнего ресурса?
Или, если точнее, нужно при помощи javascript (например ajax) отправить и получить данные с другого сайта.
PS: проблема возникает со встроенной защитой браузеров.
A: Получить можно через JSONP, а отправить AJAX напрямую не получиться, если только на внешнем ресурсе не поддерживается CORS. Еще как вариант можно на клиенте (на своём ресурсе) сделать что-то вроде proxy, через который принимать/отправлять запросы на внешний ресурс, на мой взгляд самый стабильный вариант.

redpajama_set_name: RedPajamaStackExchange


We'll emblaze the fuel of our inventive creative energies by investigating and specifying the advantages of wood-based designs. This isn't going to solely rotate upon wooden houses, yet the utilization of wood inside designs and development too. Wood is a wondrous material; ideally, you'll concur upon its decision.
Some building materials, for example, steel, inorganic materials which are non-burnable, grow when warmed which can debilitate and fall the structure. Wood responds in a relatively inverse way to this. Whenever warmed, wood dries and really turns out to be considerably harder.
We should make a few correlations here. Glass conducts warm 23 times quicker than wood, marble 90 times speedier, take 1650 times quicker and aluminum an astounding 7000 times speedier. This implies less vitality 'spillage' from a home. In the event that you need the glow (or coolness) to stay in your home, and you need to spend less cash on warming (or cooling), wood is an enormous contrasting option to block, concrete or stone. Contrasted with other development materials, wood, financially is a star offspring of protection.
At the point when contrasted and block, stone or solid, wood developments absolutely do spare time, and inalienably with that come reserve funds in labor. This is particularly pertinent in brutal climate conditions, for example, overwhelming precipitation, snow, and cold conditions, where wood development can proceed without impediment. It has additionally been said from a developer companion of dig that gets ready for wooden structures are less demanding to take after than block, cement or utilizing steel outlines.
Wood-confined houses empower simple adjustments amid and after the building procedure and this is a result of the simplicity, flexibility and cost-viability which makes it such a well known and modest decision. Protected solid shape homes can be expensive, troublesome and tedious to modify post assemble.
Green is the enormous thing nowadays so obviously this will be a major component in this article. Houses produced using trees are maintainable, inexhaustible and naturally inviting. Did you realize that wooden structures ingest and store air CO2 and that wood, notwithstanding considering haulage, is carbon nonpartisan (truth be told, it's the main carbon unbiased development material).
With more than 5000 unique woods to browse, there is totally going to be something that'll suit ones development or configuration wants. A few woods are perfect for protection, some for acoustics, grain, shading, appearance, and others for basic casings, dividers, floors, roofs and furniture.
The grain on a bit of wood is a standout amongst the most entrancing delights in the common world, where diverse shades of shading and surfaces move once again into each other like a charming move. Wood can be painted in any shading and can be waxed and varnished which display its common artfulness. It can be cut, cut, stuck and nailed.
One of the numerous reasons why wood is as yet utilized today, regardless of gigantic walks in designing greatness, is its strength weight and security. Wood has a tad of give in it which implies it can twist marginally, which is a property which blocks don't have. In this way, if the establishments move somewhat, the aesthetic wood works in home can flex and move with the change as opposed to break. Indeed, even the littlest move in the establishments of a block house will case breaks to show up in the mortar (not a decent look).
While numerous woods absorb dampness and water, making them swell, there are a few assortments of wood which are very water safe. An investigation has been directed into the assimilation rates of four distinct assortments of wood, Western Red Cedar, Douglas Fir, Western Hemlock and Sitka Spruce. Following multi year, the dampness level of Western Cedar was between 9-11%, while the others went between 14-21%. The expansion in dampness assimilation from the untreated cedar wood was insignificant.
Despite the fact that wood doesn't go about as an immaculate sound cover, it prevents echoes from ricocheting around the room by engrossing sound waves. At the point when contrasted with its productive rivals, wood ends up being significantly more compelling at sound protection, particularly with regards to protecting between various rooms.


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Пётр Михайлович Казначеев (1854—1931) — действительный статский советник и уездный предводитель окружного суда города Владимир, генеральный делегат Ордена мартинистов в России (с 1915 года), глава мартинистской ложи (1910—1917), член дикой ложи «Семен Гамалея к кубическому камню» (10.1917—06.1918).

Биография
15 мая 1876 года окончил Императорское училище правоведения. Пётр Казначеев со студенческих лет увлекался философией Шопенгауэра, гностицизмом, масонством, мистикой, читая много литературы этой тематики, о чём впоследствии написал в своих дневниках. Вместе с женой и дочерью переводил для себя иностранную религиозно-философскую литературу. Близко дружил с масонами, изучал масонское учение и был им страстно увлечён. Его считали примером «отличной нравственности», имел крайне правые убеждения.

Участие в мартинизме
В 1905 году, когда Казначеев работал во Владимире, он получил приглашение от масона В. С. Арсеньева посетить его в Москве.

В этом же году Казначеев написал письмо Седиру и Папюсу, что хочет вступить в Орден мартинистов. Папюс направил его к делегату в Санкт-Петербурге графу В. В. Муравьёву-Амурскому.

Муравьёв-Амурский и его помощник Исаев пригласили Казначеева с его сыном в Петербург, куда последние и прибыли в мае 1906 года. А летом 1907 года Муравьёв и Исаев приехали во Владимир, где приняли в Орден мартинистов Казначеева с сыном (возведя их в 3-ю степень), его жену и дочь (возведя их во 2-ю степень), и нескольких знакомых семьи Казначеевых.

В 1910 году Казначеев приезжает в Петербург, где в редакции журнала «Изида» знакомится с Мёбесом и Антошевским. В результате этих поездок Казначеева назначили специальным делегатом Ордена мартинистов для Средней России.

В том же 1910 году Г. О. Мёбес становится главой петербургской мартинистской ложи, приезжает во Владимир и открывает там [во имя Св. Иоанна] мартинистскую ложу, основу которой составила семья П. М. Казначеева и их ближайшие друзья.

В июне 1911 года Казначеев уходит в отставку с государственной службы и переезжает в Москву.

В августе 1912 года в среде российских мартинистов произошёл раскол. Мёбес пытается изменить на свой лад ложу русских мартинистов, о чём в резких тонах переписывается с П. М. Казначеевым, который сообщает это Чинскому. Чинский отстраняет Мёбеса от управления петербургской ложей и назначает Казначеева учреждающим делегатом Ордена мартинистов в России. Петербургская часть ордена во главе с Г. Мёбесом объявила о своей независимости от Парижа.

Зимой 1913—1914 года Чинский уезжает из России, временно передав должность генерального делегата Казначееву. А в 1915 году в Варшаве у Чинского проявляются проблемы со здоровьем, и он отходит от активной деятельности в мартинизме. По этой причине Папюс передаёт титул генерального делегата Ордена мартинистов Казначееву.

В 1912 году Казначеев выдал патент С. К. Маркотуну на учреждение мартинистской ложи «Св. апостола Андрея» в Киеве.

Участие в масонстве
В январе 1906 года в ряде московских газет («Русское слово», «Русские ведомости») было опубликовано анонимное объявление, в котором приглашались все желающие принять участие в воссоздании франкмасонства в России. Обратный адрес был указан — Почтамт, до востребования. В ответ на это объявление пришло 63 письма. В числе отозвавшихся был П. М. Казначеев и его сын Дмитрий, ответившие 12 января 1906 года.

Московское отделении полиции вело наблюдение за Казначеевым, в связи с его мартинистской деятельностью, и перлюстрировало его переписку с сыном Дмитрием. В марте 1910 года Дмитрий в своём письме уведомлял отца о том, что на начальном этапе возрождения масонства в России потребуется организовать философский кружок, для этого просил рекомендовать ему нескольких человек.

Утверждается, что в 1916—1917 гг. мартинисты якобы создавали масонские ложи. Так, в 1916 году на основе мартинистской ложи «Св. апостола Андрея» киевские мартинисты во главе с Маркотуном образовали масонскую ложу с одноимённым названием.

В 1917 году в Москве на основе ранее полученных от испанских братьев-масонов псевдопатентов 33 градуса шотландского масонства и 6 степени философского масонства Казначеев образовал дикую ложу «Семен Гамалея к кубическому камню». Кроме П. М. Казначеева, первыми членами её стали Ю. К. Терапиано и Леон Гольторп. Эта ложа начала свою деятельность в октябре 1917 года, когда членами ложи стали: барон А. Ф. Каульбарс, генерал И. В. Новицкий, Л. Хорват, Н. А. Назарьев и Ф. И. Шилов. Ложа «Семен Гамалея к кубическому камню» просуществовала до 13 июня 1918 года.

Примечания

Литература

 ЦГАОР СССР, ф. 102, 00, 1905, д. 12, ч. 2

Мартинисты


text:
Carttec (Cart Technology SL) was created in 2007 as a company dedicated to the distribution of supermarket and hypermarket equipment as a representative of the French company Caddie.
The company starts with a team of 6 people in an industrial warehouse in Alcobendas, Madrid.
In 2008, the company moved to a larger industrial building of 600m2 in Avenida Valgrande 29, Alcobendas, Madrid, with a warehouse area and offices.
In 2009, Carttec entered into an agreement with Gatekeeper for the exclusive distribution in Spain and Portugal of its products, including car anti-theft systems.
In 2010, the company agrees to represent the products of the American company Mart Cart, including a vehicle for people with reduced mobility.
In 2011, Carttec begins to collaborate with international companies and manufacturers.
In 2012, Carttec starts new business lines including the marketing of equipment for the hospitality and airport sectors.
In 2013, following the international crisis, the company establishes international agreements with Asian manufacturers especially for the trolley market.
In 2014, Carttec formalizes the first cart projects manufactured in China.
In 2016 the logistics centre is created in Ribarroja del Turia, Valencia, with facilities of more than 6000 m2 in response to the growing demand of our customers.
In 2017, the headquarters are moved to a new office in Calle Corazón de María 67, Madrid, keeping the facilities in Alcobendas as a support logistic centre.
In 2019, Carttec strengthened its relationship with the University of Salamanca by promoting the creation of innovative products seeking to revolutionise the world of retail at its R&D&I centre.


The discovery of neutrino oscillations is so far the only direct experimental evidence of physics beyond the standard model, making neutrinos a torch which can illuminate the path forward to reveal the deep secrets of nature. Unlocking these secrets requires a new era of precision measurements of neutrino oscillations. The elusive nature of neutrinos demands the finest instruments in order to reach high precision. The Liquid Argon Time Projection Chamber (LArTPC) is the chosen detector technology for the next generation of neutrino physics mega-projects. I will describe the current MicroBooNE experiment, a pioneer in the use of the LArTPC technology, designed to address the previously observed MiniBooNE low energy excess anomaly and perform detector R&D. Leveraging experience in data analysis in MicroBooNE, I will then discuss the physics goals and latest status of the future short and long-baseline neutrino oscillation programs, which will be providing unprecedented neutrino data to search for new physics.


Legend Of The Supreme Soldier - Chapter 132 - AnythingNovel.com Read online any english novel around the world.
"Fifteenth from the left in the thirteenth row, that's the mech's main body;seventh from the left on the fifth row, eighth from the left on the twenty second row … These are for the first combination." Mu's voice was steady and resolute.
Hei Zi stared stupidly at Ye Chong with bulging eyes. A moment earlier, Ye Chong began to pick his way through the parts like a butterfly flitting from flower to flower. The huge mech parts weighed like nothing in Ye Chong's hands. "This … This is ridiculous!" Hei Zi massaged his temples in disbelief. While these were relatively lightweight skeleton parts, they were still parts for a mech;to lift them so effortlessly - was he human?
Ye Chong seemed to move with purpose. Hei Zi was confused - wasn't he listening to him all the while earlier? He was not eyeing those mech parts back then!
"What a strange guy!" Hei Zi muttered to himself!
Ye Chong looked at the three piles of mech parts laid before him. The three combinations that Mu proposed were now fully grouped together.
Ye Chong walked to the first pile of mech parts, frowned slightly in thought for a moment, and set down to work! One by one, the mech parts assembled themselves like magic through his hands. He moved adeptly like a professional mech assembler, and the whole process went smoothly. The mech presented itself before him, and it grew taller and taller from the legs upwards, giving the illusion of something growing rapidly upwards.
Hei Zi could feel his brain giving up!
Ye Chong stared with knitted brows at the three mechs before him.
While he was unsure of the performance of these three mechs, he knew just from their appearance that they were all excellent products, definitely outstanding! Hei Zi stared dumbfounded at the three mechs without a word.
The three mechs had peculiar designs. They lacked the common metallic gleam found on average mechs, and had a unique quality of skeleton texture. Ye Chong believed that Mu's proposed combinations were most logical, but still, he felt that something was wrong!
"Strange, what is it?" Ye Chong frowned, studying the three mechs closely!
The three mechs were made of parts of all colors - since they were not originally part of the same set, they looked like a colorful mess, but these three combinations were excellent. Unlike Master's complete unfamiliarity with mechs, Hei Zi understood mechs at a deep level. The way he saw it, these parts, arranged artfully by Ye Chong, fit very well with each other, unlocking the potential of these parts to their maximum. They were perfect!
"Guy's a true genius!" Hei Zi grew respectful of Ye Chong. From his perspective, Ye Chong was only improvising, but this improvisation had led to such a degree of perfection. He knew all the parts here like the back of his hand, and had tried to assemble them together. However, no matter which combination he came up with, they cannot be compared with any of Ye Chong's three mechs. Besides, it took only a short moment for three mechs of this perfection to be produced!
Hei Zi believed that Ye Chong must be infinitely more knowledgeable about mechs than him!
Ye Chong was still deeply frowning, deep in thought.
Hei Zi did not noticed Ye Chong's perplexity;his eyes were only for the three mechs. If Shang were here and saw how the black-faced burly man could look at the three mechs with tender eyes, he would definitely not stop himself from snickering!
Ye Chong pondered over it, unsure of himself, and moved quickly towards the first mech.
"Ye, is there a problem?" Mu also thought it strange.
"Mu, don't you think there's something wrong with these three mechs?" Ye Chong's voice was uncertain.
"Wrong? In what sense?" Mu was curious.
After some hesitation, Ye Chong said, "I don't know, but I can feel that something is wrong."
"How is that possible? My calculations should be infallible!" Mu's voice held an arrogant undertone!
Ye Chong did not reply, but walked towards the first mech and began to disassemble it. "What's this?" Seeing Ye Chong suddenly beginning to disassemble the first mech, Hei Zi grew baffled and could not help but asked, "What're you disassembling it for?"
"Reassembling? He's really out of the ordinary, to strive for perfection even with mechs of this perfection, no wonder he's miles ahead of me!" The honest Hei Zi grew even more respectful of Ye Chong.
Ye Chong disassembled the mech quickly. At least, Hei Zi had never seen anyone work as fast as him.
"Could I have assembled them wrong?" Ye Chong doubted himself first of all, since he was more likely to be at fault compared to Mu. Ye Chong even thought that the sense of wrongness was an illusion, since he could not exactly point out what was wrong about the mechs!
The fact was, Ye Chong was exposed to a great variety of mechs;with his own expertise, these exposures gradually developed a sense not unlike the intuition in him, and he could quickly evaluate a mech subconsciously. Like learning any language, when a person studies up till a certain point, he would develop a grammar sense;when constructing a sentence, he might not know exactly why, but through a vague decision process, he may choose to replace a word with another more appropriate vocabulary. Of course, this vague decision is not completely infallible, but is still usually quite accurate.
Through unceasing practice and learning, this vague decision making process could be honed to a higher accuracy. It would also mean that the person has advanced to a higher plane of understanding.
These three mechs were obviously styled from mechs of the Orbits, and Mu's calculations and enhancements were based on physics. This method of combination was more suited for mechs like the MPA's, where mech technology was more advanced, and the mech models were the result of extensive calculations. Mechs from the Orbits mostly had a natural feel to them, and so the combinations based purely on mechanical and performance-enhancing factors were not in harmony with the design style.
Mu was only a PSI, and emotions were his weakness;hence, things like style, which were not data driven, were naturally not part of a mech's considerations.
Ye Chong was different. While he was always a logical thinking person, but it was inevitable as a human for him to have emotional senses. Due to his long experience with mechs, he had developed an acute awareness for them. While he could not pinpoint the exact source of the problem, he could sense the discord inside him.
Hei Zi, however, had not yet reached this level of sensitivity, and so did not notice it.
This vague feeling did not leave Ye Chong. He had reassembled the first mech thrive, but still could not see the problem. Ye Chong felt like he had reached a bottleneck, the solution to his troubles were ever closer but unreachable.
Ye Chong was vexed, but could not put his trouble into words for Mu.
If Ye Chong could one day understand his apparent intuition in great detail, it would mean that his knowledge in mechs would have reached a whole new level.
However, as Ye Chong was now, it would take him a very long time to reach that level by himself!
An ancient voice suddenly broke Ye Chong's increasingly confused thoughts, "Oh, these three mechs look good, only that the style is a little incompatible!"
Style! Ye Chong's eyes shone brightly as he realized then. "That's right! It's the style! The style!" he thought. Every mech has its own unique style. While these three mechs would perform well, their styles were not in harmony! No wonder he felt a little uncomfortable with them.
How should he proceed since he currently realized that style was the problem? Ye Chong's initial excitement gradually receded to calmness. Ideas flew past his mind, but only aimlessly;even if he knew that style was the problem, how should he proceed?
Ye Chong could not help but lift his head to the voice that triggered his realization, and found it to be Nan Nan's grandfather. He had focused intensely on disassembling the mech, and did not notice the time. The old man had already awakened from his nap and, upon returning to his workshop, found the three assembled mechs. The old man was a skeleton carver all his life, and had deep insights in abstract concepts such as mech styles. As he noticed the mechs, he could not help but comment on them, lending a hand to Ye Chong.
The old man saw Ye Chong turning to him, and smiled, "Who'd have thought you to be so knowledgeable in mechs. Looks like Hei Zi has much to learn from you, it's hard to have huge ambitions with just skeleton carving skills in this line of work!" The old man ended his sentence blandly, probably dispirited from his inability to attain those huge ambitions that he had. The old man had become a master in skeleton carving, but his lack of knowledge in mechs had increasingly become a handicap for him.
Ye Chong lowered his head as though in thought, his expression hidden from the others.
They would not have guessed that Ye Chong was having an intense conversation with Mu.
"Mu, I want to learn how to make these skeleton parts!"
"Ye, our priority right now is to treat your illness, your current situation is very dangerous! Based on Lu Caite's information, we first have to leave the Orbits and find his teacher. That's what we should do now!" Mu was exceedingly calm.
"Hmm, you're right, but the incident with Guardian raised a huge ruckus, they're probably searching all over the Orbits for us now. It's not a good choice to leave the Orbits now. Besides, all the starships in the Orbits are under the control of the Sanctuary. Without the starships, it's impossible for us to leave the Orbits!" Ye Chong was equally in control of himself.
"You're right! Based on Lu Caite's information, you have to pass the so-called 5 tests by the Sanctuary! As it is, this is not a good time for us to take the tests! However, Ye, your health might suffer!" Mu was worried about Ye Chong's physical condition.
"Nothing we can do about that! As long as it's not fatal, I can handle it!" Ye Chong's plain words were spoken with incredible determination!


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AtrocitiesAgainst MuslimsFeatured
Bihar: Muslims attacked in different incidents on Dussehra night
BY MEER FAISAL
Three Muslim men are reportedly attacked by Hindu Mob on the last day of Dussehra [Hindu festival] in different incidents in Bihar Sharif, Bihar's Nalanda district on Friday night. Police have filed FIR in at least one attack.
Md Raza, Saddam Qureshi and Md Aasif were attacked on Dashmi, last day of Dussehra, after being identified as Muslims, the victims told Maktoob.
23-year-old Md Raza was attacked while returning from market.
"There was a rush of Dashmi. Someone from the crowd asked me: 'Are you a Hindu or a Muslim?' I replied: 'Muslim.' Then someone said from the crowd "Maar Miya Saale ko" [Attack Muslims] and then they started beating me".
Raza claims that the mob looted him and raised anti-Muslim slurs while beating mercilessly.
Another victim, Saddam Qureshi, who was brutally attacked on the head while visiting his in-laws' house.
"I had gone to in-laws house, Moth Mahua Tola, Bihar Sharif to meet my wife. Around 7:30 pm, I was standing at the gate of the road then suddenly 15-20 people came and asked my name, as I told my name, they started beating me while calling me Miya".
"Is it a crime for me to be a Muslim in this country?" asks Qureshi.
Aasif was attacked in similar manner when he asked the crowd about the occasion.
Qureshi has demanded police to check footage from the CCTV installed in the locality and arrest the assailants.
State president of Social Democratic Party of India (SDPI), Shamim Akhtar condemned the attack.
"One man's condition was very critical. He had a deep injury on his head and eye. After informing the police, the police came and took them to Sadar Hospital."
Akthar claims that police was reluctant to file FIR initially but upon putting pressure the FIR is filed but no arrest is made so far.
Police informed Maktoob that investigation is ongoing and the CCTV footage is checked.
"Every month 2-3 lynching incidents are happening here. We want strict law for lynching so that Muslims do not lose their lives every day," he added.
Hindutva January 18, 2022
By Anagha Subhash Nair and Ananta Agarwal India's Supreme Court says it will investigate after complaints that Hindu nationalist leaders called on followers to take up arms against the country's Muslim...
By Syeda Faiza Kirmani Goons of the Hindutva outfit, Hindu Jagran Manch, have destroyed another shrine in Himachal Pradesh, videos of which were widely shared...


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Kids, Work and Games Android Development
One other RPG game obtainable on Android phones is Dungeon Defenders: First Wave. The sport is an online cooperative action-RPG much like Torchlight and Baldur's Gate. The sport is free to download for many phones. The graphics are in full 3D and looks stunning for a recreation that costs nothing to download. Up to 4 gamers can play collectively on-line. It could be clich?�d and borrows parts from most other RPG games, nonetheless its visuals and multiplayer is what makes it fairly enjoyable.
As regards to the programming language, the iPhone app growth language is Goal-C which is based on C and consists of various extensions together with interfaces, dynamic typing, messages and many more. However, Android revolves around Java. Many really feel that Java is a complete no-brainer programming device. That's precisely the reason why coders go for iPhone application growth which they would find extra thrilling than Android app improvement.
That works great for me there simply no charging.
This game simulates an entire racing world for you. You enter the sport as a novice racer and eventually graduate to the extent of a champion racer. The game is very addictive, and there are two issues you are able to do to progress: either play all of the games, cross all the degrees, understand the gaming world; or you may merely pay some real money and purchase your strategy to the top. People actually spend actual money to level up in GT Racing; this says loads in regards to the recognition of the game.
Sudoku took the world by storm when it was first revealed in newspapers. Those who jumped on the Sudoku train are probably still taking part in and that is the very best such app available for obtain in your Android. It has a bunch of different talent ranges and it will keep track of all the puzzles you've got began and accomplished. As everyone knows, generally it's best to return back to it after taking a bit of day without work and this app permits you to just do that!
Keep monitor of your information utilization
It must reduce the app development costs significantly as in comparison with others. Tools which are easy to make use of Discover what's happening right now, anyplace on the planet with the official Twitter for Android app. Realtime search, trending subjects and maps present what's taking place now. Tweet, What's in the Field?
This Android recreation is much like the slide puzzles you may remember as a child. The object of this recreation is to get the yellow automotive out of the site visitors jam. How do you do it? By dragging the automobile to maneuver around all the other cars so it could actually get out of the display. It's loopy, but there are over 5000 levels and more on the best way! There's a variety of enjoyable available with this free Android puzzle game.
To this point I love the EVO (and will adore it more as soon because the Android 2.2 OS – additionally referred to as Froyo – turns into accessible). However, I've to confess that in reviewing the WWDC rollout I started to query whether or not I should make the most of Dash's 30-day satisfaction assure.
Tags: android, development, games
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What Is Google Glass Really About?
There has been a lot of buzz about Google Glass lately. What's with this dorky, sci-fi looking gadget that only a geek could love? Glass is something you wear on your head like a pair of glasses. It's a computer that projects an image right in front of your eye and you control it with voice commands.
Along with the new wrist watch computers, Google Glass is part of the latest trend of wearable computing devices. No, a mobile phone in your pocket just isn't close enough to you! SIDE NOTE: this trend won't stop until we can embed computing devices *in* you (i.e. Matrix style) and we eventually turn cyborg… oops, I wasn't suppose to tell everyone about the final chapter yet. Is it too late to flash a 'Spoiler Alert!' warning?
I give Google credit, they are really starting to get the "slow release" marketing tactic in order to generate buzz. First they started talking about it at their conferences and generating interest with impressive sky jumping demos, now industry celebs are getting beta versions in order to validate the concept and generate gadget envy, and they are discussing plans to release a year from now in what is sure to be a "we can't keep up with the demand" distribution timed just before Christmas where desperate rich people will bid up the device to infinity on Ebay so their kid can have one too. All this keeps the gadget in the headlines and most importantly makes our feeble human brains forget just how stupid this will look sitting on your head!
Yes, mobile phones changed all that. We can now answer all these questions while driving, ahem riding, in the car and the world is just so much more productive now! For this productivity increase we are willing to pay thousands of dollars annually for that ubiquitous internet connection just so siri can tell us "No, there aren't any disco's near you" when you are in need of a taco.
Wearable computers offer this same amazing productivity increase. Mobile phones no longer require us to stop our car to answer a question on the go while wearable computers will allow us to get answers without reaching into our pockets. Go ahead, get up off the floor, I'll wait.
For the most part I don't think the difference between pulling out your phone, checking your wrist, or just having the relevant information projected right onto your retina is going to make that much difference to justify the idea that you could "never live a day without them". Dork.
Despite poking fun at it, I do think this could be a game changer in some scenarios. Actually, I'm really excited about the promise of wearable computers, especially the one's like Glass which are in your line of sight.
Facial recognition. The glasses have a forward facing camera (because a rear facing camera would produce some awful selfies, sorry duck-face girls this device won't help you there) and that means they can see whatever I see. With facial recognition and an internet connection glass could instantly poll my social graph and present me a detailed interaction history for the person approaching me with their hand out whose first name escapes me. I would love to see the LinkedIn profile of everyone sitting at the conference table in a meeting while on a customer site. If Glass could connect us, ala Terminator style, with the people around us in a seamless way I think it would be huge.
Second Screen at live sporting events. I'm a season ticket holder for UT Football. I love the college atmosphere. I've noticed in recent years that some people will turn down tickets to the game with me because their TV experience is so good with all the replays, stats, and commentary. Glass could provide the TV experience at the live game in a fairly unobtrusive way so you get the atmosphere and second screen. Winship.
Places recognition. Last, imagine walking down a busy urban street lined with shops and eateries. Glass could overlay what I'm seeing on the street with Yelp summaries of everything I'm seeing. In fact, it could show me that I'm looking at a bunch of 3.5 star restaurants but if I'm willing to turn my head to my right I will see that 4.5 star restaurant where I'd be much better off.
The only question is whether these things become socially acceptable or not. I think the use cases will be there once we get the software that exploits what we have. However I know we are a long ways from that day. I'm a product manager for an enterprise mobile startup and I've been trying to tell the world that we are just scratching the surface on leveraging the capabilities of the modern mobile phone and that's been here 6 years already (a lifetime in technology these days). How many years before the software catches up with the capabilities of Glass?
Google Glass? Two thumbs up in about 5 years. Great technology but let the early adopters take the hit to their social status before it becomes acceptable to wear in public.
Posted on April 30, 2013 April 30, 2013 Categories DevelopmentTags Google Glass, Wearable Computing3 Comments on What Is Google Glass Really About?


The Subaru Forester has been a popular model at Canon Subaru for many years, long before other carmakers started creating vehicles that look like an SUV, but park as easily as a car. The Forester was one of the first real car-SUV crossovers that caught our attention, and it's still an eye-catching, beloved model.
The Subaru Forester has undergone many changes over the years since it first debuted on our Lakeland, FL lots. But, many things about this steadfast and true model have remained the same. It still has four doors and seats five people comfortably. It still offers the latest in innovative and modern features, and it still has the legendary Subaru reliability and standard all-wheel drive.
While the Subaru Forester comes in your choice of trim levels, with a list of six to select from, you don't have to splurge on high trim levels to get the quality and features you want in your new vehicle. Sure, moving up trims will always net you more and more features, but, every Subaru Forester comes with a great list already, without spending a lot of extra money.
If you do choose to move up in trim levels, look for such features as heated front seats, a power-operated liftgate, a heated steering wheel, and automatic climate control.
Plus, Subaru has a number of optional packages and add-on, standalone features that can be used to customize various Forester models. The availability of these options is dependent on the trim level, so be sure to speak to a Subaru expert at our dealership for the most up-to-date information.
Of course, Subaru shines when it comes to safety technology on their vehicles, and the Forester is no different. In addition to the peace of mind and sense of security that accompanies standard all-wheel drive, the Forester has a number of other safety features that are available either standard or optional.
With so many great safety features for this model, it can be hard to know which would be best for you. Visit our team for more information about which features come with which Subaru Forester trims.
Every Forester trim designated with the number code 2.5i comes equipped with a 2.5-liter engine rated for 170 horsepower, while the 2.0XT designates models that have a turbocharged 2.0-liter engine that offers 250 horsepower.
Browse this collection of available Subaru Forester models. When you're ready to meet this versatile vehicle in person, we can help. We'll set you up for a test drive, and help you find the perfect Forester for your needs, and your budget. Stop by soon, and see all of the traits that make the Subaru Forester such an enduring favorite around the Lakeland area.
Which 2018 Forester Trim Level Fits You Best?
The new Subaru Forester offers an excellent trim selection that consists of a variety of options designed to fit your particular driving needs and style. Here's a brief insight into which Forester trim option fits your driving style for the roads of Lakeland.
At the Base level, the 2.5i is an affordable option that covers all your bases for an enhanced driving experience. Explore the Subaru Starlink™ multimedia platform, standard all-wheel drive, and Bluetooth® capability with USB and IPOD® control. This standard Forester trim level also hold 8.7-inches of ground clearance which is ideal for adventurous terrain shall you ever come across any.
The next step up from the base trim level, and drivers can look forward to 17-inch aluminum-alloy wheels, an automatic climate control system, powered rear gate, and a panoramic moonroof. If you're seeking the peace of mind while commuting on the Florida roads and highways, the availability for the EyeSight® Driver Assist technology is available within this trim level and enhances your response time and awareness.
Drivers can look forward to the plush comfort of the leather-trimmed upholstery of the Forester 2.5i Limited and with the All-Weather Package, the included heated front seats offer warmth when cold winter fronts start entering central Florida in December. Fog lights and a leather-wrapped steering wheel are also included with and shifter handle which creates an interactive driving experience when the weather elements are not up to par.
Take the next step up with the 18-inch aluminum-alloy wheels which give a broader stance to the exterior and relish within the warmth of a heated steering wheel and the 8-way power driver's seat w/ memory. Great for the drivers who are seeking long-term reliability and comfort within their next SUV purchase.
Gain the sporty appearance with the 2.0XT Premium trim level which hosts a sport design front fascia, unique 18-inch alloy wheels, and the All-Weather Package with heated front seats. You'll stand out from the ordinary and experience a confident commute with this Forester trim level!
The top model of the Forester is the 2.0XT Touring trim level, and it has everything necessary for a comfortable and durable commute. Experience the convenience of the one-touch folding rear seatback, powered driver's seat with memory, along with Dual-Zone automatic climate control which maintains a fresh and clean circulation of air on those humid summer days. Experience everything the Forester is capable of with the 2.0XT Touring trim level and schedule your test drive today!


Be A Friend To Wildlife! Help Our Cause Today!
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Thank you so very much for your contribution.
Your generous donation to the Friends of Homosassa Springs Wildlife Park will be used to directly support the Park in its mission to provide quality resource-based recreation through visitor services, interpretive programs, and wildlife exhibits. Listed below are several examples of how generous donations, such as yours, volunteerism, and funds raised by the "Friends" special events have benefited the Park, its visitors and its wildlife inhabitants.
Donations of $500 and up are eligible for recognition on our Giving Tree.
The Giving Tree, located in the Visitor Center provides a beautiful display of engraved leaves that recognize donors.
Donations of $500 – $999 receive a Small Leaf.
Donations of $1,000 and up receive a Large Leaf.
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