prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What are the stability conditions for a solution of $-\Delta u = f(u)$?

Read the following text and answer briefly.

Context 1: \section{Introduction and main results}


In this note we are interested in the existence versus non-existence of stable sub- and super-solutions of equations of the form
\begin{equation} \label{eq1}
-div( \omega_1(x) \nabla u ) = \omega_2(x) f(u) \qquad \mbox{in $ {\mathbb{R}}^N$,}
\end{equation} where $f(u)$ is one of the following non-linearities: $e^u$,  $ u^p$ where $ p>1$ and $ -u^{-p}$ where $ p>0$   We assume that $ \omega_1(x)$ and $ \omega_2(x)$, which we call \emph{weights},  are smooth positive functions (we allow $ \omega_2$ to be zero at say a point) and which satisfy various growth conditions at $ \infty$     Recall that we say that a solution $ u $ of $ -\Delta u = f(u)$ in $ {\mathbb{R}}^N$ is stable provided
\[ \int f'(u) \psi^2 \le \int | \nabla \psi|^2, \qquad \forall \psi \in C_c^2,\] where $ C_c^2$ is the set of $ C^2$ functions defined on $ {\mathbb{R}}^N$ with compact support   Note that the stability of $u$ is just saying that the second variation at $u$ of the energy associated with the equation is non-negative      In our setting this becomes:  We say a $C^2$ sub/super-solution $u$ of (\ref{eq1}) is \emph{stable} provided
\begin{equation} \label{stable}
\int \omega_2 f'(u) \psi^2 \le \int \omega_1 | \nabla \psi|^2 \qquad \forall \psi \in C_c^2 
\end{equation}
One should note that (\ref{eq1}) can be re-written as
\begin{equation*}
- \Delta u  + \nabla \gamma(x) \cdot \nabla u ={ \omega_2}/{\omega_1}\ f(u) \qquad \text{ in $ \mathbb{R}^N$},
\end{equation*}
where
$\gamma = - \log( \omega_1)$ and on occasion we shall take this point of view 


\begin{remark} \label{triv} Note that  if $ \omega_1$ has enough integrability then it is immediate that if $u$ is a stable solution  of (\ref{eq1}) we have $ \int \omega_2 f'(u) =0 $  (provided $f$ is increasing)    To see this let $ 0 \le \psi \le 1$ be supported in a ball of radius $2R$ centered at the origin ($B_{2R}$) with $ \psi =1$ on $ B_R$ and such that $  | \nabla \psi | \le \frac{C}{R}$ where $ C>0$ is independent of $ R$    Putting this $ \psi$ into $ (\ref{stable})$ one obtains
\[ \int_{B_R} \omega_2 f'(u) \le \frac{C}{R^2} \int_{R < |x| <2R} \omega_1,\] and so if the right hand side goes to zero as $ R \rightarrow \infty$ we have the desired result 

\end{remark}





The existence versus non-existence of stable solutions of  $ -\Delta u =  f(u)$ in $ {\mathbb{R}}^N$ or $ -\Delta u = g(x) f(u)$ in $ {\mathbb{R}}^N$ is now quite well understood, see  \cite{dancer1, farina1, egg, zz, f2, f3, wei, ces, e1, e2}   We remark that some of these results are examining the case where $ \Delta $ is replaced with $ \Delta_p$ (the $p$-Laplacian) and also in many cases the authors are interested in finite Morse index solutions or solutions which are stable outside a compact set 
  Much of the interest in these Liouville type theorems  stems from the fact that the non-existence of a stable solution is related to the existence of a priori estimates for stable solutions of a related equation on a bounded domain 




       In \cite{Ni}  equations similar to  $ -\Delta u = |x|^\alpha u^p$  where examined on the unit ball in $ {\mathbb{R}}^N$ with zero Dirichlet boundary conditions   There it was shown that for $ \alpha >0$ that  one can obtain positive solutions for $ p $ supercritical with respect to Sobolev embedding and so one can view that the term $ |x|^\alpha$ is restoring some compactness       A similar feature happens for equations of the form
\[ -\Delta u = |x|^\alpha f(u) \qquad \mbox{in $ {\mathbb{R}}^N$};\]    the value of $ \alpha$ can vastly alter the existence versus non-existence of a stable solution,  see \cite{e1, ces, e2, zz, egg} 

We now come to our main results and for this we need to define a few quantities:

\begin{eqnarray*}
I_G&:=& R^{-4t-2} \int_{ R < |x|<2R} \frac{ \omega_1^{2t+1}}{\omega_2^{2t}}dx , \\
 J_G&:=& R^{-2t-1} \int_{R < |x| <2R} \frac{| \nabla \omega_1|^{2t+1} }{\omega_2^{2t}} dx  ,\\I_L&:=& R^\frac{-2(2t+p-1)}{p-1}  \int_{R<|x|<2R }{ \left(   \frac{w_1^{p+2t-1}}{w_2^{2t}}    \right)^{\frac{1}{p-1} }  }  dx,\\ J_L&:= &R^{-\frac{p+2t-1}{p-1} }  \int_{R<|x|<2R }{ \left(   \frac{|\nabla w_1|^{p+2t-1}}{w_2^{2t}}     \right)^{\frac{1}{p-1} }  }  dx,\\
I_M  &:=&   R^{-2\frac{p+2t+1}{p+1} }  \int_{R<|x|<2R }{ \left(   \frac{w_1^{p+2t+1}}{w_2^{2t}}    \right)^{\frac{1}{p+1} }  } \ dx, \\
J_M  &:= &  R^{-\frac{p+2t+1}{p+1} }  \int_{R<|x|<2R }{ \left(   \frac{|\nabla w_1|^{p+2t+1}}{w_2^{2t}}     \right)^{\frac{1}{p+1} }  }  dx 
\end{eqnarray*}


The three equations we examine are
\[ -div( \omega_1 \nabla u ) = \omega_2 e^u \qquad \mbox{ in $ {\mathbb{R}}^N$ } \quad  (G), \]
\[  -div( \omega_1 \nabla u ) = \omega_2 u^p \qquad \mbox{ in $ {\mathbb{R}}^N$ } \quad  (L), \]
\[ -div( \omega_1 \nabla u ) = - \omega_2 u^{-p} \qquad \mbox{ in $ {\mathbb{R}}^N$ } \quad  (M),\]  and where we restrict $(L)$ to the case $ p>1$ and $(M)$ to $ p>0$     By solution we always mean a $C^2$ solution    We now come to our main results in terms of abstract $ \omega_1 $ and $ \omega_2$     We remark that our approach to non-existence of stable solutions is the approach due to Farina, see \cite{f2,f3,farina1} 

\begin{thm} \label{main_non_exist} \begin{enumerate}


\item   There is no  stable sub-solution of $(G)$ if $ I_G, J_G \rightarrow 0$ as $ R \rightarrow \infty$   for some   $0<t<2$ 
 \item    There is no positive   stable sub-solution (super-solution) of $(L)$  if  $ I_L,J_L \rightarrow 0$ as $ R \rightarrow \infty$   for some   $p- \sqrt{p(p-1)}   < t<p+\sqrt{p(p-1)} $  ($0<t<\frac{1}{2}$) 
\item   There is no positive   stable super-solution of (M) if  $ I_M,J_M \rightarrow 0$ as $ R \rightarrow \infty$  for some $0<t<p+\sqrt{p(p+1)}$ 

\end{enumerate}

\end{thm}     If we assume that $ \omega_1$ has some monotonicity we can do  better    We will assume that the monotonicity conditions is satisfied for big $x$  but really all ones needs is for it to be satisfied on a suitable sequence of annuli 

\begin{thm} \label{mono}  \begin{enumerate} \item There is no  stable sub-solution of $(G)$ with $  \nabla \omega_1(x) \cdot  x \le 0$ for big $x$ if  $ I_G \rightarrow 0$ as $ R \rightarrow \infty$   for some   $0<t<2$ 

\item There is no positive  stable sub-solution of  $(L)$ provided  $  I_L \rightarrow 0$ as $ R \rightarrow \infty$ for either:
\begin{itemize}
\item  some $  1 \le t < p + \sqrt{p(p-1)}$ and $  \nabla \omega_1(x) \cdot x \le 0$ for big $x$,  or  \\

\item some $ p - \sqrt{p(p-1)} < t \le 1$ and $ \nabla \omega_1(x) \cdot x \ge 0$ for big $ x$ 
\end{itemize}
 There is no positive super-solution of $(L)$ provided $ I_L \rightarrow 0$ as $ R \rightarrow \infty$ for some $ 0 < t < \frac{1}{2}$ and $ \nabla \omega_1(x) \cdot x \le 0$ for big $x$ 



\item  There is no positive stable super-solution of $(M)$ provided  $ I_M \rightarrow 0$ as $ R \rightarrow \infty$  for some  $0<t<p+\sqrt{p(p+1)}$ 

\end{enumerate}

\end{thm}


\begin{cor}  \label{thing}  Suppose $ \omega_1 \le C  \omega_2$  for big $ x$, $ \omega_2 \in L^\infty$,  $ \nabla \omega_1(x) \cdot  x \le 0$ for big $ x$ 
\begin{enumerate} \item There is no stable sub-solution of $(G)$ if $ N \le 9$ 

\item  There is no positive stable sub-solution of $(L)$ if  $$N<2+\frac{4}{p-1} \left( p+\sqrt{p(p-1)}  \right) $$

\item  There is no positive stable super-solution of $(M)$ if $$N<2+\frac{4}{p+1} \left( p+\sqrt{p(p+1)}  \right) $$

\end{enumerate}

\end{cor}


If one takes $ \omega_1=\omega_2=1$ in the above corollary, the results obtained for $(G)$ and  $(L)$,  and for some values of $p$ in $(M)$, are optimal, see \cite{f2,f3,zz} 





We now drop all monotonicity conditions on $ \omega_1$ 

\begin{cor} \label{po} Suppose  $ \omega_1 \le C \omega_2$ for big $x$, $ \omega_2 \in L^\infty$, $ | \nabla \omega_1| \le C \omega_2$ for big $x$ 
\begin{enumerate} \item  There is no stable sub-solution of $(G)$ if $ N \le 4$ 

\item  There is no positive stable sub-solution of $(L)$ if $$N<1+\frac{2}{p-1} \left( p+\sqrt{p(p-1)}  \right) $$

\item There is no positive super-solution of $(M)$ if $$N<1+\frac{2}{p+1} \left( p+\sqrt{p(p+1)}  \right) $$

\end{enumerate}

\end{cor}

Some of the conditions on $ \omega_i$ in Corollary \ref{po} seem somewhat artificial   If we shift over to the advection equation (and we take $ \omega_1=\omega_2$  for simplicity)
\[ -\Delta u + \nabla \gamma \cdot \nabla u = f(u), \] the conditions on $ \gamma$ become: $ \gamma$ is bounded from below and has a bounded gradient 



In what follows we examine the case where $ \omega_1(x) = (|x|^2 +1)^\frac{\alpha}{2}$ and $ \omega_2(x)= g(x) (|x|^2 +1)^\frac{\beta}{2}$,  where $ g(x) $ is positive except at say a point, smooth and where $ \lim_{|x| \rightarrow \infty} g(x) = C \in (0,\infty)$      For this class of weights we can essentially obtain optimal results 


\begin{thm} \label{alpha_beta}   Take $ \omega_1 $ and $ \omega_2$ as above 
\begin{enumerate}

\item If $ N+ \alpha - 2 <0$ then there is no stable sub-solution for $(G)$, $(L)$ (here we require it to be positive) and in the case of $(M)$ there is no positive  stable  super-solution  This case is the trivial case, see Remark \ref{triv}   \\



\textbf{Assumption:} For the remaining cases we assume that $ N + \alpha -2 > 0$ 

  \item If  $N+\alpha-2<4(\beta-\alpha+2)$ then there is no  stable sub-solution for $ (G)$ 

\item If $N+\alpha-2<\frac{ 2(\beta-\alpha+2)   }{p-1} \left( p+\sqrt{p(p-1)}  \right)$ then there is  no positive stable sub-solution of $(L)$ 

\item If $N+\alpha-2<\frac{2(\beta-\alpha+2)   }{p+1} \left( p+\sqrt{p(p+1)}  \right)$ then there is no positive stable super-solution of $(M)$ 

\item Further more 2,3,4 are optimal in the sense if $ N + \alpha -2 > 0$ and the remaining inequality is not satisfied (and in addition we assume we don't have equality in the inequality) then we can find a suitable function $ g(x)$ which satisfies the above properties and a stable sub/super-solution $u$ for the appropriate equation 

\end{enumerate}

\end{thm}

\begin{remark}  Many of the above results can be extended to the case of equality in either the $ N + \alpha - 2 \ge 0$ and also the other inequality which depends on the equation we are  examining   We omit the details because one cannot prove the results in a unified way 

\end{remark}






















In showing that an explicit solution is stable we will need the   weighted Hardy inequality given in \cite{craig} 
\begin{lemma} \label{Har}
Suppose $ E>0$ is a smooth function   Then one has
\[ (\tau-\frac{1}{2})^2 \int E^{2\tau-2} | \nabla E|^2 \phi^2 + (\frac{1}{2}-\tau) \int (-\Delta E) E^{2\tau-1} \phi^2 \le \int E^{2\tau} | \nabla \phi|^2,\] for all $ \phi \in C_c^\infty({\mathbb{R}}^N)$ and $ \tau \in {\mathbb{R}}$ 
\end{lemma}  By picking an appropriate function $E$ this gives,

\begin{cor} \label{Hardy}
For all $ \phi \in C_c^\infty$ and $ t , \alpha \in {\mathbb{R}}$  We have
  \begin{eqnarray*}
\int (1+|x|^2)^\frac{\alpha}{2} |\nabla\phi|^2 &\ge& (t+\frac{\alpha}{2})^2 \int |x|^2 (1+|x|^2)^{-2+\frac{\alpha}{2}}\phi^2\\
&&+(t+\frac{\alpha}{2})\int  (N-2(t+1)   \frac{|x|^2}{1+|x|^2}) (1+|x|^2)^{-1+\frac{\alpha} {2}} \phi^2 
\end{eqnarray*}
 \end{cor}























\section{Proof of main results}

\textbf{ Proof of Theorem \ref{main_non_exist} }   (1)  Suppose $ u$ is a stable sub-solution of $(G)$ with $ I_G,J_G \rightarrow 0$ as $ R \rightarrow \infty$ and  let $ 0 \le \phi \le 1$ denote a smooth compactly supported function   Put $ \psi:= e^{tu} \phi$ into (\ref{stable}), where $ 0 <t<2$, to arrive at
\begin{eqnarray*}
\int \omega_2 e^{(2t+1)u} \phi^2 &\le & t^2 \int \omega_1 e^{2tu} | \nabla u|^2 \phi^2 \\
&& +\int \omega_1 e^{2tu}|\nabla \phi|^2 + 2 t \int \omega_1 e^{2tu} \phi \nabla u \cdot \nabla \phi 
\end{eqnarray*}  Now multiply $(G)$ by $ e^{2tu} \phi^2$ and integrate by parts to arrive at
\[ 2t \int \omega_1 e^{2tu} | \nabla u|^2 \phi^2 \le \int \omega_2 e^{(2t+1) u} \phi^2 - 2 \int \omega_1 e^{2tu} \phi \nabla u \cdot \nabla \phi,\]
and now if one equates like terms they arrive at
\begin{eqnarray} \label{start}
\frac{(2-t)}{2} \int \omega_2 e^{(2t+1) u} \phi^2  & \le & \int \omega_1 e^{2tu} \left( | \nabla \phi |^2 - \frac{ \Delta \phi}{2} \right) dx \nonumber \\
&& - \frac{1}{2} \int e^{2tu} \phi \nabla \omega_1 \cdot \nabla \phi 
\end{eqnarray}   Now substitute $ \phi^m$ into this inequality for $ \phi$ where $ m $ is a big integer to obtain
\begin{eqnarray} \label{start_1}
\frac{(2-t)}{2} \int \omega_2 e^{(2t+1) u} \phi^{2m}  & \le & C_m \int \omega_1 e^{2tu} \phi^{2m-2}  \left( | \nabla \phi |^2 + \phi |\Delta \phi|  \right) dx \nonumber \\
&& - D_m \int e^{2tu} \phi^{2m-1} \nabla \omega_1 \cdot \nabla \phi
\end{eqnarray} where $ C_m$ and $ D_m$ are positive constants just depending on $m$    We now estimate the  terms on the right but we mention that when ones assume the appropriate monotonicity on $ \omega_1$ it is the last integral on the right which one is able to drop 

\begin{eqnarray*}
\int \omega_1 e^{2tu} \phi^{2m-2} | \nabla \phi|^2 & = & \int \omega_2^\frac{2t}{2t+1} e^{2tu} \phi^{2m-2}  \frac{ \omega_1 }{\omega_2^\frac{2t}{2t+1}} | \nabla \phi|^2  \\
& \le &  \left( \int \omega_2 e^{(2t+1) u} \phi^{(2m-2) \frac{(2t+1)}{2t}} dx \right)^\frac{2t}{2t+1}\\ &&\left( \int \frac{ \omega_1 ^{2t+1}}{\omega_2^{2t}} | \nabla \phi |^{2(2t+1)} \right)^\frac{1}{2t+1} 
\end{eqnarray*}
Now, for fixed $ 0 <t<2$ we can take $ m $ big enough so $ (2m-2) \frac{(2t+1)}{2t} \ge 2m $ and since $ 0 \le \phi \le 1$ this allows us to replace the power on $ \phi$ in the first term on the right with $2m$   and hence we obtain
 \begin{equation} \label{three}
 \int \omega_1 e^{2tu} \phi^{2m-2} | \nabla \phi|^2  \le \left( \int \omega_2 e^{(2t+1) u} \phi^{2m} dx \right)^\frac{2t}{2t+1} \left( \int \frac{ \omega_1 ^{2t+1}}{\omega_2^{2t}} | \nabla \phi |^{2(2t+1)} \right)^\frac{1}{2t+1} 
 \end{equation}    We now take the test functions $ \phi$ to be such that $ 0 \le  \phi \le 1$ with $ \phi $ supported in the ball $ B_{2R}$ with $ \phi = 1 $ on $ B_R$ and $ | \nabla \phi | \le \frac{C}{R}$ where $ C>0$ is independent of $ R$    Putting this choice of $ \phi$ we obtain
 \begin{equation} \label{four}
 \int \omega_1 e^{2tu} \phi^{2m-2} | \nabla \phi |^2 \le \left( \int \omega_2 e^{(2t+1)u} \phi^{2m} \right)^\frac{2t}{2t+1} I_G^\frac{1}{2t+1} 
 \end{equation}  One similarly shows that
 \[ \int \omega_1 e^{2tu} \phi^{2m-1} | \Delta \phi| \le \left( \int \omega_2 e^{(2t+1)u} \phi^{2m} \right)^\frac{2t}{2t+1} I_G^\frac{1}{2t+1} \]
 So, combining the results we obtain

 \begin{eqnarray} \label{last} \nonumber \frac{(2-t)}{2} \int \omega_2 e^{(2t+1) u} \phi^{2m} &\le& C_m \left( \int \omega_2 e^{(2t+1) u} \phi^{2m} dx \right)^\frac{2t}{2t+1} I_G^\frac{1}{2t+1}\\
 &&- D_m \int e^{2tu} \phi^{2m-1}  \nabla \omega_1 \cdot \nabla \phi 
 \end{eqnarray}
 We now estimate this last term   A similar argument using H\"{o}lder's inequality shows that
 \[ \int e^{2tu} \phi^{2m-1} | \nabla \omega_1| | \nabla \phi| \le \left(  \int \omega_2 \phi^{2m} e^{(2t+1) u} dx \right)^\frac{2t}{2t+1} J_G^\frac{1}{2t+1}  \] Combining the results gives that
\begin{equation} \label{last}
(2-t) \left( \int \omega_2 e^{(2t+1) u} \phi^{2m} dx \right)^\frac{1}{2t+1} \le I_G^\frac{1}{2t+1} + J_G^\frac{1}{2t+1},
\end{equation} and now we send $ R \rightarrow \infty$ and use the fact that $ I_G, J_G \rightarrow 0$ as $ R \rightarrow \infty$ to see that
\[ \int \omega_2 e^{(2t+1) u} =0, \] which is clearly a contradiction    Hence there is no stable sub-solution of $(G)$ 

(2)    Suppose that $u >0$ is a stable sub-solution (super-solution) of $(L)$   Then a similar calculation as in (1) shows that for  $ p - \sqrt{p(p-1)} <t < p + \sqrt{p(p-1)}$,  $( 0 <t<\frac{1}{2})$ one has

\begin{eqnarray}   \label{shit}
(p  -\frac{t^2}{2t-1}   )\int \omega_2 u^{2t+p-1} \phi^{2m} & \le & D_m \int \omega_1 u^{2t} \phi^{2(m-1)} (|\nabla\phi|^2  +\phi |\Delta \phi |) \nonumber \\
&& +C_m \frac{(1-t)}{2(2t-1)} \int u^{2t} \phi^{2m-1}\nabla \omega_1 \cdot  \nabla \phi 
 \end{eqnarray}    One now applies H\"{o}lder's argument as in (1) but the terms $ I_L$ and $J_L$ will appear on the right hand side of the resulting
 equation       This shift from a sub-solution to a super-solution depending on whether $ t >\frac{1}{2}$ or $ t < \frac{1}{2}$ is a result from the sign change of $ 2t-1$ at $ t = \frac{1}{2}$    We leave the details for the reader 


(3)   This case is also similar to (1) and (2) 


\hfill $ \Box$

 \textbf{Proof of Theorem \ref{mono} }   (1)   Again we suppose there is a stable sub-solution $u$ of $(G)$   Our starting point  is (\ref{start_1}) and we wish to be able to drop the term
 \[ - D_m \int e^{2tu} \phi^{2m-1} \nabla \omega_1 \cdot \nabla \phi, \] from (\ref{start_1})     We can choose $ \phi$ as in the proof of Theorem \ref{main_non_exist} but also such that $ \nabla \phi(x) = - C(x) x$ where $ C(x) \ge 0$      So if we assume that $ \nabla \omega_1 \cdot x \le 0$ for big $x$ then we see that this last term is non-positive and hence we can drop the term   The the proof is as before but now we only require that $ \lim_{R \rightarrow \infty} I_G=0$ 

 (2)      Suppose that $ u >0$ is a stable sub-solution of $(L)$  and so (\ref{shit}) holds for all $  p - \sqrt{p(p-1)} <t< p + \sqrt{p(p-1)}$    Now we wish to use monotonicity to drop the term from (\ref{shit}) involving the term $ \nabla \omega_1 \cdot \nabla \phi$       $ \phi$ is chosen the same as in (1)  but here one notes that the co-efficient for this term changes sign at $ t=1$ and hence by restriction $t$ to the appropriate side of 1 (along with the above condition on $t$ and $\omega_1$) we can drop the last term depending on which monotonicity we have and hence to obtain a contraction we only require that $ \lim_{R \rightarrow \infty} I_L =0$    The result for the non-existence of a stable super-solution is similar be here one restricts $ 0 < t < \frac{1}{2}$ 


(3)   The proof here is similar to (1) and (2) and we omit the details 




 \hfill $\Box$













\textbf{Proof of Corollary \ref{thing} }   We suppose  that $ \omega_1 \le C  \omega_2$  for big $ x$, $ \omega_2 \in L^\infty$,  $ \nabla \omega_1(x) \cdot  x \le 0$ for big $ x$      \\
(1)     Since $ \nabla \omega_1 \cdot x \le 0$ for big $x$ we can apply Theorem \ref{mono} to show the non-existence of a stable solution to $(G)$    Note that  with the above assumptions on $ \omega_i$ we have that
\[ I_G \le \frac{C R^N}{R^{4t+2}} \]  For $ N \le 9$  we can take $ 0 <t<2$  but close enough to $2$ so the right hand side goes to zero as $ R \rightarrow \infty$ 

Both (2) and (3) also follow directly from applying Theorem \ref{mono}    Note that one can say more about (2) by taking the multiple cases as listed in Theorem \ref{mono} but we have choice to leave this to the reader 


\hfill $ \Box$


\textbf{Proof of Corollary \ref{po} }   Since we have no monotonicity conditions now we will need both $I$ and $J$ to go to zero to show the non-existence of a stable solution    Again the results are obtained immediately by applying Theorem \ref{main_non_exist}  and we prefer to omit the details 


\hfill $\Box$
















\textbf{Proof of Theorem \ref{alpha_beta} }  (1)   If $ N + \alpha -2 <0$ then using Remark \ref{triv}  one easily sees there is no stable sub-solution of $(G)$ and $(L)$ (positive for $(L)$) or a positive stable super-solution of $(M)$    So we now assume that $ N + \alpha -2 > 0$      Note that the monotonicity of $ \omega_1$ changes when $ \alpha $ changes sign and hence one would think that we need to consider separate cases if we hope to utilize the monotonicity results    But a computation shows that in fact $ I$ and $J$ are just multiples of each other in all three cases so it suffices to show, say, that $ \lim_{R \rightarrow \infty} I =0$  \\
(2)    Note that for $ R >1$ one has
\begin{eqnarray*}
I_G & \le  & \frac{C}{R^{4t+2}} \int_{R <|x| < 2R} |x|^{ \alpha (2t+1) - 2t \beta} \\
& \le  &  \frac{C}{R^{4t+2}}  R^{N + \alpha (2t+1) - 2t \beta},
\end{eqnarray*} and so to show the non-existence we want to find some $ 0 <t<2$ such that
$  4t+2 > N  + \alpha(2t+1) - 2 t \beta$,   which is equivalent to  $ 2t ( \beta - \alpha +2) > (N + \alpha -2)$     Now recall that we are assuming that $ 0 < N + \alpha -2 < 4 ( \beta - \alpha +2) $ and hence we have the desired result by taking $  t <2$ but sufficiently close 
The proof of the non-existence results for
(3) and (4) are similar and we omit the details    \\
(5)   We now assume that $N+\alpha-2>0$   In showing the existence of stable sub/super-solutions we need to consider  $ \beta - \alpha + 2 <0$ and $ \beta - \alpha +2 >0$ separately 

\begin{itemize} \item $(\beta - \alpha + 2 <0)$  Here we take $ u(x)=0$ in the case of $(G)$ and $ u=1$ in the case of $(L)$ and $(M)$  In addition we take $ g(x)=\E$   It is clear that in all cases $u$ is the appropriate sub or super-solution   The only thing one needs to check is the stability     In all cases this reduces to trying to show that we have
\[ \sigma \int       (1+|x|^2)^{\frac{\alpha}{2}  -1}    \phi^2 \le \int      (1+|x|^2)^{\frac{\alpha}{2}}   | \nabla\phi  |^2,\]  for all $ \phi \in C_c^\infty$ where  $ \sigma $ is some small positive constant; its either $ \E$ or $ p \E$ depending on which equation were are examining 
To show this we use the result from Corollary \ref{Hardy} and we drop a few positive terms to arrive at
\begin{equation*}
\int (1+|x|^2)^\frac{\alpha}{2} |\nabla\phi|^2\ge (t+\frac{\alpha}{2})\int \left (N-2(t+1)   \frac{|x|^2}{1+|x|^2}\right) (1+|x|^2)^{-1+\frac{\alpha} {2}}
\end{equation*} which holds for all $ \phi \in C_c^\infty$ and $ t,\alpha \in {\mathbb{R}}$ 
  Now, since $N+\alpha-2>0$, we can choose $t$ such that $-\frac{\alpha}{2}<t<\frac{n-2}{2}$   So, the integrand function in the right hand side is positive and since for small enough $\sigma$ we have
  \begin{equation*}
\sigma \le  (t+\frac{\alpha}{2})(N-2(t+1)   \frac{|x|^2}{1+|x|^2})  \ \ \ \text {for all} \ \ x\in \mathbb{R}^N
\end{equation*}
 we get stability 



\item ($\beta-\alpha+2>0$) In the case of $(G)$ we take   $u(x)=-\frac{\beta-\alpha+2}{2} \ln(1+|x|^2)$ and $g(x):= (\beta-\alpha+2)(N+(\alpha-2)\frac{|x|^2}{1+|x|^2})$  By a computation one sees that $u$ is a sub-solution of $(G)$ and hence we need now to only show the stability, which amounts to showing that
\begin{equation*}
\int \frac{g(x)\psi^2}{(1+|x|^{2   })^{-\frac{\alpha}{2}+1}}\le \int\frac{|\nabla\psi|^2}{    (1+|x|^2)^{-\frac{\alpha}{2}}     },
\end{equation*} for all $ \psi \in C_c^\infty$   To show this we use  Corollary \ref{Hardy}   So  we  need to choose an appropriate $t$ in   $-\frac{\alpha}{2}\le t\le\frac{N-2}{2}$  such that for all $x\in {\mathbb{R}}^N$ we have
 \begin{eqnarray*}
 (\beta-\alpha+2)\left(    N+  (\alpha-2)\frac{|x|^2}{1+|x|^2}\right)         &\le& (t+\frac{\alpha}{2})^2 \frac{ |x|^2 }{(1+|x|^2}\\
&&+(t+\frac{\alpha}{2}) \left(N-2(t+1)   \frac{|x|^2}{1+|x|^2}\right) 
\end{eqnarray*}
With a  simple calculation one sees we need just to have
   \begin{eqnarray*}
 (\beta-\alpha+2)&\le& (t+\frac{\alpha}{2}) \\
  (\beta-\alpha+2)     \left(    N+  \alpha-2\right)      &   \le&  (t+\frac{\alpha}{2}) \left(N-t-2+\frac{\alpha}{2}) \right) 
 \end{eqnarray*}     If one takes $ t= \frac{N-2}{2}$ in the case where $ N \neq 2$ and $ t $ close to zero in the case for $ N=2$ one easily sees the above inequalities both hold, after considering all the constraints on $ \alpha,\beta$ and $N$ 

 We now consider the case of $(L)$   Here one takes $g(x):=\frac {\beta-\alpha+2}{p-1}(    N+  (\alpha-2-\frac{\beta-\alpha+2}{p-1})
\frac{|x|^2}{1+|x|^2})$ and $ u(x)=(1+|x|^2)^{ -\frac  {\beta-\alpha+2}{2(p-1)} }$    Using essentially the same approach as in $(G)$ one shows that $u$ is a stable sub-solution of $(L)$ with this choice of $g$    \\
For the case of $(M)$ we take   $u(x)=(1+|x|^2)^{ \frac  {\beta-\alpha+2}{2(p+1)}   }$ and $g(x):=\frac {\beta-\alpha+2}{p+1}(    N+  (\alpha-2+\frac{\beta-\alpha+2}{p+1})
\frac{|x|^2}{1+|x|^2})$ 



\end{itemize}


\hfill  $  \Box$









Context 2: My Aspergers Child: COMMENTS & QUESTIONS [for Feb , 2017]
I emailed you a while back and you mentioned that I could email when I needed to  Thank you  I last wrote you in December that my son became involved in a dispute involving the local police  We have had 3 court dates  It keeps delaying due to not being able to come to an agreement  But the attorney, even though he was just vaguely familiar with Aspergers, has been very good with Craig  He has the compassion and excellence that is needed here  What started out very bad is turning into a good thing  It will probably take another 90 days or more 
But Craig is working hard  Too hard sometimes  He goes to therapy 3 times a week  Doing excellent  He's more focused and can calm down easier  He's got a lot on his plate but has support from his family  From his attorney  From therapy  And from his work 
He has been renting a room from a lady who has a son with ADHD  It is good for him  I'm a little worried though because since she smokes he wants to find his own place  With all the costs he has to balance it out financially  That is good  I can't help him more than I am which is good  He is stepping up and taking responsibility  He is listening much better 
He is going to have an evaluation today to get an accurate diagnosis  I understand that is a little difficult since he is an adult  Also the PTSD may cover it over  The attorney stated it would help to have the diagnosis 
Aware this is a long update, but thanks for reading  I am fighting much guilt still but I have a lot of peace now  My daughter and her 4 year old son also have Aspergers symptoms  So my life chapters may not close for a while  :-)
My name is Mac  I'm sure you're quite busy, so I'll get right to it I just wanted to pass on compliments on My Aspergers Child and your post, How to Implement the GFCF Diet: Tips for Parents of Autistic Children 
Me and my wife absolutely loved it!
I got a facebook message from him today begging to be able to come home saying he misses home and he will change  He says he will follow rules now  I stated to him the simple rules he has to follow which were - No weed in my house, or smoked in my house, coming home at curfew, going to school, no skipping, no drugs at school, and to drop the attitude of I am 17 I can do whatever I want 
I have made it very clear that if I see any drugs in my home I will be calling the police, as well as if I see signs of it being sold by him I will report him  (He has never had selling amounts in my house,     I believe it's being kept at his "friends" which of course I have no proof of    I just know it is not here 
I know my battle is not over by a long shot, I am sure we will have more consequences and possibly another being kicked out, but I am going to think positive and hope that he learned some form of a valuable lesson here 
Thank you so much for the guidance, never in a million years did I ever think I'd be on this side, (the one needing the help, as I am the one who helps )
I am going to go back to the start of the program like I said earlier and keep notes close by for reference 
Thanks for all you do, helping us all with ODD children/teens
I have a small company providing educational support services to a few families who have children with various disabilities in Ohio  One of the families has multiple adopted children of whom several have significant attachment disorders including RAD  As an experienced teacher and foster parent I have some experience in working with children who have extensive trauma backgrounds  However, I could use additional training  Also working with these children are two staff members with minimal background in attachment disorders who would also benefit from training primarily in behavior management  The primary caregiver to the children does a wonderful job managing their needs  In order to further develop team cohesion, I'm hoping to include her in any training as well 
Is it possible to schedule such a training session with you? If so, please let us know what will work for you including time, place, and cost  Thank you for your assistance 
I just listed to your tapes on dealing with an out of control, defiant teen  I'd like to ask your advice on a particular situation we have  Our 15 year old daughter is smoking pot almost every day at school  Because we had no way to control the situation, we told her, fine, go ahead and smoke weed  However, you will no longer receive the same support from us  You will not have your phone, lunch money to go off campus (she has an account at the school for the cafeteria she can use), and you will be grounded until you can pass a drug test  We will not be testing you except for when you tell us you are ready to be tested  She is now saying she's suicidal because she feels so isolated, yet she continues to smoke weed  In fact, she tried to sneak out last night but was foiled by our alarm system  For the particular drug test we have, I read it takes about 10 days of not smoking to pass the test  What would you do? Please advise 
I am having a problem with my 18 year old son, Danny, with high functioning autism  We finally had him diagnosed when he was 16 years old  I always knew something was going on with him but the doctors misdiagnosed him as bipolar  It's been 2 years now and he will not accept his diagnosis  He won't talk about it and when I try to bring it up he gets very angry  I've tried telling him that it's not a bad thing, that there's been many, many very successful people with Aspergers  He won't tell anyone and refuses to learn about managing life with it  He once shared with me that the other kids at school use it as an insult, like saying someone is so autistic when they do something they don't approve of  So he doesn't want anyone to know  He's turned down services that could help him  He has a girlfriend, going on 8 months  He won't tell her and they're having problems arguing a lot and I wonder if it would help for her to know 
I'm sad that he thinks it's a life sentence to something horrible instead of accepting, embracing it and learning about it more so he maybe can understand why he's struggling  I told him that he doesn't need to shout it out to the whole world but he won't even accept it himself 
I don't know how to help him with it and because he's almost 19 I have limited control now  It's made my life easier knowing what we're dealing with and I think his life would be easier is he accepted it 
Please help me help him 
I am a clinical psychologist in NYC who now has several (!!) children I see who have RAD  In 20 years of practice, I’d seen only one case  Now, I have at least three children with this  I have no training, per se, in working with this children though I know about setting structure, consistency, etc  I do a lot of work with parents about parenting  I work primarily within the school setting in a charter school whose mission is to educate children on the autism spectrum in a mainstream setting  We use Michelle Garcia Winner’s social thinking program with our ASD kids  I also work with gen ed kids in the school who are at-risk; the school is in the inner city from where the majority of our non-ASD kids live 
It would have been so much easier to mention to my adult son that I think (I know he does, but want to ease into the subject)
he has Asperger's when we were living together two years ago  He has since moved to Tennessee working in his field of interest
which is 3-D printing and software development  I am so happy for him that he has found his way into a job that he truly enjoys
even though he's socially isolated 
He's not diagnosed and does not know he has it  How I know is his classic symptoms being sensory issues (fabric feeling like sandpaper)
communication difficulties, meltdowns and much more  Throughout his childhood I just felt he was a bit different  Nothing major stood out and time
just passes, misdiagnosis of ADHD, low frustration, etc  We've talked about his ADHD numerous times (which I now know he doesn't have) 
It's so much easier to communicate with him now that I know he has Asperger's  I keep it "slow and low" in talking, with long moments
of silence and then we connect  It's really too bad that Asperger's got a diagnostic code back in the 90's, yet all the so called doctors,
physiologist's, etc, didn't know how to diagnose it  Too bad 
There seems to be no one answer to "should I tell my adult son he has Asperger's" from a few specialists I asked  He is typical Asperger,
complicated, highly intelligent (high IQ), anxiety at times, socially isolated, hard to make friends  Not knowing how he will react is the hard part 
How will he be better off knowing he has it? Do I wait to tell him in person, or ease into it with him over Skype? He likes direct, honest, concrete communication 
Why is this so hard for me? Maybe because no one know's if he is going to be better off knowing or not  Do you know if people are better off
knowing? I try to get up the courage to just let him know, then I back down 
I have been searching the web looking for advice and came upon your site  I am trying to read blogs, websites, books, and articles to help guide me  I was so happy when you said that I could ask you a question  My husband and I are struggling with my 27 year old son who lives with us 
Kyle is the youngest of 4 sons  He is a college graduate but never could find the "right" job  He has always been quiet and never had a lot of friends  Two years ago, his girlfriend broke up with him  Kyle had an online gambling addiction and was using pot all the time  After the breakup, Kyle was very depressed and started using heroin and finally told my husband he was using  He is now seeing a psychiatrist who has him on suboxone and antidepressants  He is also seeing a psychologist weekly for counseling but it does not seem to be helping 
Last October,, Kyle lost his job, got drunk, and was agitated and came home , fighting with us, damaging our home and being verbally abusive  My other son , age 32, who also lives with us called the police and Kyle got arrested  He is currently in the family court system  He went through an anger management course and now is in substance abuse classes  Kyle continues to verbally abusive to me and blame me for everything  He says he "hates me "and calls me terrible names  At times, he pushes my husband and intimidates me  My husband and I are so upset  We just hired an attorney for him because since he has been going to these classes, he is getting more depressed and not getting better  Kyle continues to drink while taking his meds prescribed by the psychiatrist and then he has his "moods " My husband and I have met once with the psychiatrist just to give him background information when Kyle started with him 
At this point, we do not know what to do  We never thought at this stage of our life, we would be supporting and spending our retirement money on adult children  I do not know why Kyle hates me, I could not have been a better mom  My husband and I have no life and just do not know what it the right path we should take  Kyle does not want anything to do with us  He spends all his time in his room playing football online We have tried tough love versus caring and love and understanding  Do you have any advice for me?
This whole ODD and ADHD is killing me as a parent  I work in the field of adult psych and addictions so I am well educated  I have been dealing with my teen being like this for almost 3 years and I totally lost my cool today with my 17-year-old son to the point I told him he is out of the house  He can never simple rules, comes and goes as he pleases sometimes doesn't come home, just recently back in school from several suspension for drug related    I am just so exhausted  He has made me hate life, hate being a parent and sometimes I just feel like not even being here  I bought your program in hopes to it would help, I am at week three and I feel things are getting worse    what am I doing wrong??
My partner hasn't been diagnosed yet but I know he has aspergers   day to day is a struggle   I feel I'm going crazy with how he makes me feel Feel let down constantly  He lies alot but I've been told they can't but I know he does I just feel trapped and unloved We have a 4yr old daughter together and my main worry with how he is that it will effect our daughter ; (his skills as a parent are so weak He can't disapline at all Feel so alone  he hides it well too I just wondered if things will get worse? He's angry so quick in arguments Scares me etc I can't leave as he's the main bread winner and our daughter loves him to bits Don't know why I'm writing this  Sorry if I'm going on and not making sense :(
I wanted to let you know about a research opportunity for children, teens, and young adults with autism  I am studying the effects of Brazilian Jiu Jitsu, and psychotherapy on helping people with autism develop subjective awareness of others 
I am writing you to see if this might help someone in your practice, or to see if you might know of someone with autism who may benefit from participating in this study  The requirements of the study will be:
1  A participant should be between 7-21 years of age and have a diagnosis of Autism Spectrum Disorder 
2  The participant should enroll in an approved Jiu Jitsu Academy and attend at least two sessions a week for a period of six months 
3  The participant should enroll in social skills groups, provided by my office or be in a steady psychotherapeutic relationship in your office, at least once a week, or minimally two to three times a month 
4  The participant will be given a SRS (Social Responsiveness Scale) test at the beginning of the study, at three months, and again at six months 
If you know of anyone who might benefit from this novel approach to helping to develop social awareness in autism, please do not hesitate to contact me for further information 
I have a 10 year old daughter who has outbursts with prolonged crying almost like tantrums that 2 year olds have when they cannot express themselves 
I had her in therapy from age 6-8 years old for the same thing but I feel that the sessions didn't really help much 
She has severe sensitivities to light, sound, vibration, frequencies which trigger irritability and crying 
We changed her diet and tried getting her involved with activities but she is anti-social and prefers reading than being social  She is terrified of change even in daily routine (even that will trigger prolonged crying) 
It frustrates me because I don't know what else to do with her behavior 
I've tried acupuncture (she refused at the first session); she refuses massage too 
She is an honor-roll student at school and has very minimal issues at school but if she has had a bad day it does result in a tantrum or crying and defiance 
How can I get her tested for Asperger's Syndrome?
Last night our 24 year old son with Aspergers told his dad and I that he is pulling out of the 4 college classes that he recetnly enrolled in because he has not been attending class or turning in his assignments  He paid $2800 (his own money) for tuition and I reminded him of this when he told us but it did not seem to bother him 
This is the 3rd time he has started college courses and has not completed them  (He also took some concurrent college classes while he was in high school that he failed)  This is a son who basically had a 4 0 grade point average through 10th grade and got a 34 on the ACT the first time he took it 
With the news that he was once again not sticking with college courses I did not sleep well  When I got up this mornning I began looking online for help in how to deal with his situation  I found your "Launching Adult Children With Aspergers" and purchased it  Most of what is included are things we have done or did with our son throughout his life  I was hoping for more help so I am emailing you now in hopes of more specific ideas 
We noticed some things with our son, Taylor, as a yound child but as we had not heard of Aspergers at that time we just did what we thought would help him  As a toddler and a child at pre-school he generally went off on his own to play  When I talked to his pre-school teacher about my concerns (that I was worried he would end up a hermit) she said she did not see him being a loner and that he seemed to interact fine with others in many situations  We worked with him on making eye contact when talking with others  We explained different emotions in people's faces and mannerisms to help him know how to interact with others  We discussed the fact that people would say things that did not mean what they souneded like - such as "I'm so hungry I could eat a horse"  As we did these things he worked hard to better understand communication with others 
During his 4th grade year I had a teacher from the gifted program ask me if I had ever heard of Aspergers  I told her that I had not heard of it  She proceeded to read me some of the charateristics and so many of them described my son  So we had him tested by the school district during the summer between 4th and 5th grade and they did find that he had Aspergers but that he was high functioning  We then set him up with and EIP which stayed with him until his sophomore year  We pulled him from it at that time because we had moved and the new district was requiring him to take one class a day that was a study class  This reduced the number of required classes he could take and he was doing fine with his studies at the time 
It was during the 2nd half of his Junior year that we noticed some of his grades going down  Then during his Senior year is when he started skipping classes and not doing assignments  We had not realized it before then but we soon became aware that he was addicted to gaming  He would go to the library or somewhere else on campus and play games on the computer rather than go to class  It was also at this time that he began lying about his actions (so as not to get in trouble) 
Based on his grades and his ACT score he received offers from colleges for full tuition scholarships  He chose the college where he had taken concurrent classes during his high school years  But he proceeded to skip class and not turn in assignments so he lost his scholarship and quit attending college  During this time he was only able to find employment through an employment agency where he was mostly sent to manuel labor type jobs (which is not something he enjoys but he did it anyway)  It was during this time that at one place had gone to on numerous occasions he was told if he came late one more time they would tell the emplyment agency they did not want him to come there anymore  (This seemed to make an impression on him because he has continued to be reliable and responsbile at his places of employment) 
At 19 1/2 he left to serve a 2 year full-time mission for our church  He completed his mission successfully  (I don't think it was without some struggle, stress and depression, but he was able to pick himself up and move on from those times) 
When he came home he started working for the employment agency again but began looking for employment elsewhere  He got a job at a local Chick Fil-A where he has worked for 3 years  He started college again shortly after he came home but as before it was short lived  He did finish out the semester but failed most of the classes due to his skipping class and not turning in assignments



ground_truth: $\int f'(u) \psi^2 \le \int | \nabla \psi|^2, \forall \psi \in C_c^2$.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the research opportunity that is mentioned?

Read the following text and answer briefly.

Context 2:  When he skipped class he would usually sleep in his car 
Taylor's life consists of working (where to the best of our knowledge) he does well, he is reliable and his employer likes him  When he comes home from work he either sleeps or plays video games or other games - such as kakuro  He spendes most of his time in the basement where his bedroom is and this is where he games  Taylor owns his own car, bought his own laptop and very rarely spends money  He pays us $200 /month to still live at home, unloads the dishwasher on a regular basis and does the weekly garbage  However, his room is a mess and he only cleans his bathroom when I tell him he needs to clean it 
Taylor used to read quite a bit and loved to learn  It has just been in his adult years that he has not read as much - I think because of his gaming addiction  Taylor goes to church on a regular basis but sleeps through the main meeting  In Sunday class room settings he stays awake - I think because he is able to particpate in discussions 
Taylor has only had 2 real friends since entering Junior High school  And as of now he only keeps in contact with one of them who still lives in Georgia  We have lived in Utah since the summer of 2007 and he has never had a friend to do things with since we have lived here  He has two younger siblings, a brother 22 and a sister 20  They love Taylor and spend time with him when they are home  They are both at college and doing well 
Throughout Taylor's school years he has seen a counsleor on a fairly regular basis  One summer during junior high he attended a weekly class where he interacted with other kids with Aspergers  We did see a lot of change in him from this group  After he returned from his mission he went to see a counselor for a short period - this counselor tried to help him with some social skills  His dad and I went with him the first 3 or 4 times but we found out that after we quit going with him he only went a few more times and then scheduled appointments but did not show a couple of the times  We only found this out when a bill came for a "no show" appointment 
I don't know if this is too much information but were are in dire need of help for him  In the information that we purchased from you you mentioned that you do coaching for Aspergers adults  I don't know if you can help us but I thought I would check with you just in case 
Alas I think I have found your information too late to save my marriage but I am hoping to save myself 
I am currently going through a very very painful separation after a 27 year relationship with my husband whom I am convinced has aspergers syndrome  It is a long and painful story and I am desperately trying to process it all alongside dealing with a very conflictual separation  My partner is angry non communicative and totally dismissive of me and our long shared history 
He walked out last year after I discovered he had been visiting massage parlours and developed a relationship with an illegal Chinese escourt whom he subsequently moved in with  He had been seeing this woman behind my back for over 18 months  The pain of all this indescribable and his dismissal of my pain and very existence beyond belief 
Leading up to this I had been battling anxiety and depression which my husband found very hard to cope with 
Over the years of our relationship I knew something was off but I just could not put my finger on it  I often felt a complete lack of validation and empathy  Communication was also difficult as my husband was defensive and unwilling to look at issues in our marriage 
Please Mark could you help me validate some of this pain and try and make dense of 27 years of my life without drowning in fear guilt and despair about my future 
Thank you for listening and your site 
I have had problems with drunkenness, being late for school, not handing in school work, buying pot from a dealer etc  I chose to focus on the drinking and did the grounding then (grounding happened 3 times)  I also stopped sleep overs at friends 100%  I have stopped handing out money for no reason or even buying treats like chocolate 
I did lose it one evening (and didn't do the poker face) when I was trying to unplug the internet at midnight on a school night (she’s always late for school so I am trying to get her to sleep at a reasonable hour)  I was physically stopped and pushed around so I slapped my daughter (it was not hard)  This ended up with her saying she didn’t want to come home (the next day after school)  By this stage, I also had enough and didn’t go get her  I thought I am not begging  You will run out of money soon  It was quite a relief to have some peace  Daughter’s Dad was in town (from another country) and called a family meeting with the counsellor  To cut a long story short, daughter and her counsellor put it on the table that daughter wants to go live somewhere else (with her friends family) because of the stress at home with me (we live on our own) (i e  stricter rules and her bucking up against it) 
I didn’t really want this but made a compromise that daughter would go there Tues morning – Friday afternoon as the friend is an A student whereas my daughter is failing  They do the same subjects  I made the decision at the end of the day based on what is good for me – some time away from the daughter  I also thought of your book when the child went to live with the grandparents – daughter will dig her own hole over at the friend’s house  They have a week day no going out policy which made me think it is OK  I went and discussed with them the problems experienced (drinking, pot, late nights, not handing in work)
I am also trying to follow the let go of school thing per your book  I find it really difficult to remain calm when I can see daughter on her phone and watching series (when I have her on the weekends) when I know there are projects due  I hired her a private tutor once a week for help with a subject  The tutor has just fired my daughter for not handing in work and being not committed  It’s not the first time private tutoring has not been appreciated  The school give me a report back on a Friday as to whether everything is handed in  The deal is – if the work is not handed in – no pocket money and no Friday night out)  Her school is a "progressive" school and there are no repercussions for her being late or not handing in work  I would change schools if I could but there are only 8 months left of school (she turns 18 in August) 
We have just completed the first week and beginning week two of your material  We are agreeing with your take and see our son and ourselves in most of what you are saying  Prior to finding your material and starting your program we had been having extreme out of control behaviors and had to call the police because he was breaking things in our house and pushed my husband  This happened three weeks ago  After that incident we took away privileges ie  PS4, phone (which had already been taken for a few days), and friends  So, last week while doing your program he already didn’t have privileges and has continued with poor behavior – name calling, throwing things, slamming doors  We are not sure when to give privileges back  He has been given the privilege of playing with friends on occasion  His 13th birthday is tomorrow  This past weekend, for his birthday my husband and he went boar hunting  Of course we debated about it but decided to go ahead since it was his bday  We are cooking some of the meet on the grill tomorrow night for his bday and inviting a couple of his friends over for a cookout  No more gifts other than cards and balloons  We are wondering if we should go ahead and give him his privileges back and not sure how to do it  Last Friday morning we attempted to talk giving him a date to return privileges and that conversation ended with him getting angry but he gathered from our conversation that he is getting his stuff back on his bday  We are starting week 2 assignments today but not sure how to handle what was already in place  Of course, we aren’t seeing the respect and responsibility we are looking for but realize it has been a long time  We were wanting him to pay for his phone and thought it might be a good time to introduce that idea  Allowing him to earn his phone  We expect that he will be angry with this idea and not sure how to implement 
My son and myself are interested in a inpatient Aspergers program  We line in Calif which is preferable  My son is very high functioning and was diagnosed dry late  He was eight years old  He has never been in or attended a full day of class  Partially due to depression,anxiety, and trouble with his ADHD also his aversion and being bullied and of course his Aspergers  He will not attend his freshmen year due to surgery on both Achilles' tendons from walking on his toes  With physical therapy he should be ready by his sophomore year! We all feel he needs in patient therapy to give him the tools on how to work with his issues in a structured setting and a place that will give him tools for the rest of his life 
In my utter desperation to find a way to get some help for my daughter's increasingly challenging behaviour I trawled the internet to see if I could find some strategies that would provide specific methods on dealing with teenagers with Asperger's syndrome  When I came across your website, I couldn't believe that every statement you made was exactly what I have been going through with my daughter  She has just turned 14 last week, and was diagnosed with Asperger's/ Autism Spectrum Disorder 15 months ago  I have already been seeing a child psychologist for the past five months, however the methods she has been advising have not been very effective 
Our main difficulty with our daughter is her overwhelming obsession to use her cell phone (and to a lesser extent her laptop) constantly  Without any restriction, she will be on it every minute of the day, and will be awake until the early hours every day  We have tried to incorporate her input around rules as to when she has to give in her phone, but she is unwilling to compromise on a time that she should give it to us, believing that she should have unlimited use  I believe she is unable to do any adequate study or homework, as she is constantly having to look at the phone  We have tried to put rules in place that she has to give in her phone and laptop on school nights at 22:15  If she is able to do this then she is given rewards, and if she doesn't then she knows that there will be consequences  The consequence has been restricted use the following day  However, this is usually where we fail, because taking her phone away from her results in tantrums, screaming, and even threatening to harm herself  This behaviour is relentless to the point where the whole family becomes deeply distressed, and inevitably results in her getting the phone back 
This obsession is affecting her schoolwork, and more severely her eyesight  She has become very shortsighted, and her eyesight continues to deteriorate as a result of holding the phone or laptop very close, and mostly in the dark without any lights on  My husband and I have a constant battle on our hands daily, in all areas of discipline with our daughter, but our main concern is that we have been unable to find a way to minimise this obsessive behaviour centred around her phone and laptop  Please can you provide some strategies that can help us specifically with this problem 
First of all, I thank you for developing this program and I am only at the first stage of assignment 1  I have loads of books I have bought, attended psychiatrists for my son and myself, family therapy, occupational therapy, begged and prayed for change but have been dealing with behavioural issues for so long I am definitely exhausted and resentful 
I am a mum to a 15 yr old boy with ASD, dyslexia, OCD and ODD  Sorry to focus on the labels but just to give you an idea of what I am dealing with  I also have a 13 yr old son whom finds his brother’s behaviours difficult, embarassing and challenging  My husband whom is not in great health ( he had a cerebral aneurysm clamped two years ago and has two further aneurysms that are inoperable so endures fatigue, headaches and stress)  We have however a pet cat that is very social and a calming influence in the home! I was fortunate enough to have loving parents but I lost both my mum and dad in 2008 and 2015  My inlaws are elderly and quite directly say they are too old to help us so it feels we are alone in dealing with the issues we have 
I am desperate for change as the household is one of stress and anger and I feel all the control lies in my son Patrick’s hands  I am hopeful your programme can make life better for all of us but I wonder if it is too early to ask you two questions?
The first lies with what to do when Patrick goes into my other son Brendan’s room and will either turn on a light when he is sleeping, yell when he is on his phone or create some disturbance  He will not leave the room when asked to do so and the situation always escalates into yelling and Brendan attempting to physically remove him  This happens regularly and always ends badly with doors slamming, my husband being woken and myself in tears feeling the lack of control and also I admit I seem to think “Why me?” which rationally I know is of no help 
The second problem is leaving the house for school  Patrick refuses personal hygiene (either morning or night) and any request to even brush his teeth is fraught with swearing and abuse  If I can get him to shower, he will watch the water roll down the drain and turn up the water really high temp (mu husband has had to turn down the thermostat on the hot water service) without so much as getting wet  My husband leaves for work at 6am but I leave at 745 to work as a nurse in a busy outpatients department in the Alfred Hospital (Melbourne)  My work is my sanity as it is a paid break from home but most days I am late which is causing considerable stress and anxiety not to mention my responsibility to do my job  Patrick simply refuses to leave the house and as much as I am tempted to just walk out and leave I know the house would be left unlocked and wonder if Patrick would even attend school  The time I need to leave is not negotiable but Patrick uses this to his advantage and seems to delight in stressing me out and subsequently speeding to work in a frazzled mess 
The interesting and frustrating element in all of this is that although he is socially isolated at school (he has no friends) and academically challenged his behaviour at school is not a problem  He is quiet and his teachers report he does his best and is compliant and well mannered  It is like a Jekyll and Hyde situation where another side of him at home is so angry and abusive yet at school this behaviour does not happen 
I’m Jackie, I now work primarily as a freelance tech writer, after starting my career in software development and moving on to teach IT to young adults at a variety of colleges and schools 
My freelance work is pretty varied and looks at many aspects of the computer industry as a whole, and I’ve just recently completed a piece which gives help and advice to anyone wanting to become a game designer, which you can read here: http://www gamedesigning org/become-a-game-designer/  It highlights the hard work and effort it takes to get into such a role, and also how you can further your career and continue to learn and improve as you go  I hope you’ll agree it shows that starting work in the industry takes dedication and skill and that becoming a game designer isn’t just a fly-by-night job!
If you’d be interested in sharing a quick mention of my work on your blog that would be really wonderful and I’d appreciate the chance to get my work out there to a wider audience  Alternatively, I’d be happy to write a short blurb or paragraph or two (or a longer piece - just let me know) highlighting the key points because I think some of your readers might get a lot of value from it 
My son just turned 15 and is a freshman in high school  Although this is his first year in a general ed environment, he is struggling with behaviors in school  He has meltdowns and does not express why he would have them until much later  Once we all know what caused it, the school will accommodate him and try to "change up" things so as not to cause his meltdown  Once that is resolved, another issue comes up and causes him to melt down  He is a high functioning and academically does well, when he wants to do the work  We battle at home over homework  He does not care how it is done, as long as he hands it in  He thinks failing a test is ok, at least he took the test  Homework is never on his mind when he gets home from school  If I never prompt him, he would never open is backpack  He can be aggressive but is never intentionally trying to hurt anyone  He may push over a chair in school, but it is not directed at anyone  We know how that in itself could hurt someone who gets hit by it though  He is defiant in that he only wants to do what interests him  He does not go out by himself (still immature), or abuse alcohol or drugs and never curses  He is a very funny kid and very talented  His main problems are task avoidance and seeking attention  He can be disrespectful to adults in that he is "cheeky" with them, trying to be funny or cute  And he has no "filters" 
I’ve just finished reading your Living with an Aspergers Partner ebook  I found it so informative, thank you 
You offered some personal advise, and i wanted to run a situation past you and seek your input as to a strategy for what to do next 
I’ve been seeing a guy for about 7 months now who I believe has Aspergers  I came to this conclusion months ago and I don’t think he realizes, (or acknowledges) although he is aware he has some traits 
He’s highly intelligent and successful, a pattern seeker, has a tendency to focus on the project to hand to the total exclusion of all else for as long sit takes (work or home) socially awkward (has learned coping strategies), sensitive to loud noise, high anxiety with control strategies, black and white thinking etc  He’s currently not working and I’ve seen a slow withdrawal over the last 6 weeks, including the need to ‘escape’ and leave a situation at least once 
He also has a bipolar ex overseas who has primary custody one daughter where there has been ongoing patterns of drama which has recently increased 
Over the past couple of months (since stopping work and drama increase) I’ve gone from being ‘wonderful’ in his eyes to him now being sorry and not having the ‘urge’ to spend close/intimate time with me and offering friendship  Since he shared that with me in a message he’s stonewalled and has retreated to the safety of minimal messages and talks about not knowing what best to say and not being able to find the right words somehow 
He’s a good kind man who I feel is struggling  I’m concerned about his anxiety and possibly the risk of depression  I’m fairly resilient and whilst i’m disappointed he doesn’t want to pursue a relationship with me, i’m concerned for him and his well being  One of his very few close friends is also just leaving the country to live overseas 
The strategy I’ve used so far is simply to back off and give him space  I’ve asked to take him up on an original offer he made to talk but haven’t pushed it  I also haven’t been aggressive or accusatory in the few messages i’ve sent 
Any advise you could give would be greatly appreciated,
Carli who is 10 years old and has had behavioral issues her whole life  The other night she came home very upset after having a conflict with a friend  She was at her friend's house and her and her friend wanted to get on the computer and the older sister was using it  Carli made up a story that someone was at the door to get the older sister off the computer  Her friend didn't understand that she was making up a story to get the sister off the computer  She got excited that someone was at the door and ran downstairs to answer the door  In the process of getting the door, she fell and yelled at Carli  Carli became extremely upset  She was able to control her feelings at her friend's house, but when she came home, she proceeded to cry extremely loudly for over an hour  Her dad spent most of that time with her, talking to her and trying to calm her down  After an hour, I asked him if he could please tell her to be more quiet because the other members of the household were trying to go to sleep 
My question is    how do I as the girlfriend, handle this? He did not like that I asked her to be quiet  We have a rule that if she is having bad behavior, and can't calm down in 5 minutes, he takes her out of the house because her yelling doesn't stop for a long time and is very upsetting to everyone in the household  I would like to ask him to do this with this kind of situation as well  Is this a reasonable request? His thought was that she shouldn't be made to calm down, because everyone handles being upset in a different way  But, she was literally sobbing and wailing very loudly 
My other question is should she have been told that if she wouldn't have lied, this wouldn't have happened? She has a history of lying and of not accepting responsibility for her actions  My boyfriend became very upset with me when I brought this up  He was being very sympathetic and understanding to her  I feel like he was giving her negative attention, and being an over indulgent parent by not putting his foot gown and saying, "you can't carry on like this, even though you are upset"  Please let me know how we can handle these situations better 
I am contacting you for help with adult AS  I am taking initiative to pre screen potential therapists to help my current boyfriend get therapy and help with Adult AS 
He has seen many therapists, but it seems like they aren’t really helping him with his problems  They don’t seem to understand how his (undiagnosed) AS would affect therapy approaches  For example, he may not share enough in therapy session and I’m assuming an AS therapist would recognize that is part of the AS and employ strategies to get information from him that helps with treatment  Sometime he tunes out when he is processing something heavy or that he doesn’t want to hear necessarily, or he gets distracted and I’m hoping an As therapist would recognize that and get that he may need repeated something for example, if this is happening 
He is currently suffering from depression that appears clinical in nature as well as reoccurring negative thoughts about something specific that has been worrying him about our relationship  Today he told me these reoccurring thoughts happen during all waking hours unless he watches TV, he never gets a break from them and they make him feel like he is going crazy  As his girlfriend, I am extremely concerned that he cannot get relief from these thoughts and that the therapists he is seeing are unable to help him with his problems  Therefore, I am taking initiative to try and help him find better therapy options, because I want to see him someone who can better help him get to the bottom of things and help him with the challenges he is facing  He really needs an advocate that will help him go deep to figure things out and not just assume therapies are working well, without seeing changes or getting supporting feedback from him in that regard 
Here are some questions I am trying to ask in advance to find the right people to help us with this  As you may know, insurance for these therapies are not often available  We don’t have a lot of money to go from therapist to therapist to find the right person and are hoping prescreening will help 
I recently downloaded your e-book and listened to your talks and your information is by far the most helpful I have been able to find to date  It's very accurately describes my situation as an NT wife married to a very probable AS husband  I think you for taking the time to write this and sharing your insights as well as the experiences of many of your clients  It has really helped me understand the last 32 years of our marriage and get a grasp on how to move forward 
One area that is of primary concern to me, that I did not see addressed, is stimming  I believe that is the behavior my husband is showing through constant vocal singing, repetition of words, shouting out, as well as slapping himself in the chest and general nervous activity  It is very loud and disruptive to our household and it is often a relief when he is not at home  I think there may be a level of Tourette's syndrome as well 
I did some searches on the Internet and could not find anything that really describes his behavior  Most of what I found was flapping or children's behavior  I understand that it is a release of nervous tension but I am really trying to find some strategies to help him stop this behavior as it is extremely frustrating and builds my resentment in dealing with it daily  A lot of it is embarrassing as well and sounds childish to me 
He usually does this when close family members are around and will reign himself in if he is around other people besides us  When we are home it is constant  He also has a lot of anger, mostly at himself, and blows up at unimportant things, it is as if he has a ton of negative energy inside him that need to get out and stimming is one outlet 
I will try to build my acceptance of it, but I also would just like him to stop especially the loudest and most annoying portions  Would you have any resources you could point me to?
Context 3: Do you know the difference between V T  and T V?
Like any exclusive club, heart disease has its own jargon, understandable only by other members of the club, particularly by cardiac care providers  For example, I remember lying in my CCU bed (that’s the Coronary Intensive Care Unit), trying to memorize the letters LAD (that’s the Left Anterior Descending, the large coronary artery whose 99% blockage had caused my MI (myocardial infarction – in my case, the so-called ‘widowmaker’ heart attack) 
To help others needing simultaneous translation of this new lingo in your research or in your own medical records, here’s a helpful list of some of the most common acronyms/terms you’ll likely find around the cardiac ward 
NOTE from CAROLYN: This entire patient-friendly, jargon-free glossary (all 8,000 words!) is also part of my book “A Woman’s Guide to Living with Heart Disease“ (Johns Hopkins University Press, November 2017) 
AA – Anti-arrhythmic: Drugs used to treat patients who have irregular heart rhythms 
Ablation – See Cardiac Ablation 
ACE Inhibitor – Angiotension Converting Enzyme inhibitor: A drug that lowers blood pressure by interfering with the breakdown of a protein-like substance involved in regulating blood pressure 
ACS – Acute Coronary Syndrome: An emergency condition brought on by sudden reduced blood flow to the heart  The first sign of acute coronary syndrome can be sudden stopping of your heart (cardiac arrest) 
AED – Automatic External Defibrillator: A portable defibrillator for use during a cardiac emergency; it can be used on patients experiencing sudden cardiac arrest by applying a brief electroshock to the heart through electrodes placed on the chest 
AF or Afib – Atrial Fibrillation: An irregular and often rapid heart rate that can cause poor blood flow to the body  Afib symptoms include heart palpitations, shortness of breath, weakness or fainting  Episodes of atrial fibrillation can come and go, or you may have chronic atrial fibrillation 
AFL – Atrial Flutter: A type of arrhythmia where the upper chambers of the heart (the atria) beat very fast, causing the walls of the lower chambers (the ventricles) to beat inefficiently as well 
A-HCM – Apical Hypertrophic Cardiomyopathy: Also called Yamaguchi Syndrome or Yamaguchi Hypertrophy, a non-obstructive form of cardiomyopathy (a disease of the heart muscle that leads to generalized deterioration of the muscle and its pumping ability) in which a portion of the heart muscle is hypertrophied (thickened) without any obvious cause although there may be a genetic link  It was first described in individuals of Japanese descent 
AI – Aortic Insufficiency: A heart valve disease in which the aortic valve does not close tightly, leading to the backward flow of blood from the aorta (the largest blood vessel) into the left ventricle (a chamber of the heart) 
AIVR – Accelerated Idioventricular Rhythm: Ventricular rhythm whose rate is greater than 49 beats/min but less than 100 beats/min, usually benign  (Ventricles are the two main chambers of the heart, left and right) 
Angina (stable) – A condition marked by distressing symptoms typically between neck and navel that come on with exertion and go away with rest, caused by an inadequate blood supply to the heart muscle typically because of narrowed coronary arteries feeding the heart muscle  Also known as Angina Pectoris  Unstable angina (UA) occurs when fatty deposits (plaques) in a blood vessel rupture or a blood clot forms, blocking or reducing flow through a narrowed artery, suddenly and severely decreasing blood flow to the heart muscle  Unstable angina is not relieved by rest; it’s dangerous and requires emergency medical attention 
Antiplatelet drugs – Medications that block the formation of blood clots by preventing the clumping of platelets (examples: Plavix, Effient, Brillinta, Ticlid, etc)  Heart patients, especially those with implanted stents after PCI, are often prescribed dual antiplatelet therapy (DAPT) which includes one of these prescribed meds along with daily low-dose aspirin 
Aorta – The main artery of the body, carrying blood from the left side of the heart to the arteries of all limbs and organs except the lungs 
Aortic Stenosis: A disease of the heart valves in which the opening of the aortic valve is narrowed  Also called AS 
Aortic valve – One of four valves in the heart, this valve allows blood from the left ventricle to be pumped up (ejected) into the aorta, but prevents blood from returning to the heart once it’s in the aorta 
AP – Apical Pulse: A central pulse located at the apex (pointy bottom) of the heart 
Apex – the lowest (pointy) tip of the heart that points downward at the base, forming what almost looks like a rounded point 
Apical Hypertrophic Cardiomyopathy (A-HCM): Also called Yamaguchi Syndrome or Yamaguchi Hypertrophy, a non-obstructive form of cardiomyopathy (a disease of the heart muscle that leads to generalized deterioration of the muscle and its pumping ability) in which a portion of the heart muscle is hypertrophied (thickened) without any obvious cause  There may be a genetic link  It was first described in people of Japanese descent 
Arrhythmia – A condition in which the heart beats with an irregular or abnormal rhythm 
AS – Aortic Stenosis: A disease of the heart valves in which the opening of the aortic valve is narrowed 
ASD – Atrial Septal Defect: See Septal Defect 
Atrial Flutter – A heart rhythm problem (arrhythmia) originating from the right atrium, most often involving a large circuit that travels around the area of the tricuspid valve (between the right atrium and the right ventricle (this is called typical atrial flutter)  Less commonly, atrial flutter can also result from circuits in other areas of the right or left atrium that cause the heart to beat fast (called atypical atrial flutter) 
Atrial Septum, the membrane that separates the left and the right upper chambers of the heart (the atria) 
Atrium – A chamber of the heart that receives blood from the veins and forces it into a ventricle or ventricles  Plural: atria 
AV – Atrioventricular: A group of cells in the heart located between the upper two chambers (the atria) and the lower two chambers (the ventricles) that regulate the electrical current that passes through it to the ventricles  Also Atrioventricular Block: An interruption or disturbance of the electrical signal between the heart’s upper two chambers (the atria) and lower two chambers (the ventricles)  Also Aortic valve: The valve that regulates blood flow from the heart into the aorta 
AVNRT – Atrioventricular Nodal Re-entry Tachycardia: a heart rhythm problem that happens when there’s an electrical short circuit in the centre of the heart, one of the most common types of SVT, most often seen in people in their twenties and thirties, and more common in women than in men 
BAV – Bicuspid Aortic Valve: The most common malformation of the heart valves in which the aortic valve has only two cusps instead of three 
BB – Beta Blocker: A blood pressure-lowering drug that limits the activity of epinephrine, a hormone that increases blood pressure 
BBB – Bundle Branch Block: – A condition in which parts of the heart’s conduction system are defective and unable to normally conduct the electrical signal, causing an irregular heart rhythm (arrhythmia) 
BMI – Body mass index: A number that doctors use to determine if you’re overweight  BMI is calculated using a formula of weight in kilograms divided by height in meters squared (BMI =W [kg]/H [m2])  Better yet, just click here to figure out your own BMI 
BNP blood test – BNP (B-type Natriuretic Peptide) is a substance secreted from the ventricles or lower chambers of the heart in response to changes in pressure that happen when heart failure develops and/or worsens  The level of BNP in the blood increases when heart failure symptoms worsen, and decreases when the heart failure condition is stable 
BP – Blood Pressure: The force or pressure exerted by the heart in pumping blood; the pressure of blood in the arteries  See also hypertension 
BrS – Brugada Syndrome: Brugada syndrome is a genetic heart disease that is characterized by distinctively abnormal electrocardiogram (EKG/ECG) findings and an increased risk of sudden cardiac arrest 
CAA – Coronary artery anomaly: A congenital defect in one or more of the coronary arteries of the heart 
CABG – Coronary Artery Bypass Graft: A surgical procedure that reroutes blood flow around a diseased or blocked blood vessel that supplies blood to the heart by grafting either a piece of vein harvested from the leg or the artery from under the breastbone 
CA – Coronary Artery: The arteries arising from the aorta that arch down over the top of the heart and divide into branches  They provide blood to the heart muscle 
CAD – Coronary Artery Disease: A narrowing of the arteries that supply blood to the heart  The condition results from a plaque rupture/blood clot or spasm and greatly increases the risk of a heart attack 
Cardiac Ablation – A procedure performed by an Electrophysiologist (EP) – a cardiologist with specialized training in treating heart rhythm problems – that typically uses catheters — long, flexible tubes inserted through a vein in the groin and threaded to the heart — to correct structural problems in the heart that cause an arrhythmia  Cardiac ablation works by scarring or destroying the tissue in your heart that triggers an abnormal heart rhythm 
Cardiac Arrest – Also known as Sudden Cardiac Arrest: The stopping of the heartbeat, usually because of interference with the electrical signal that regulates each heartbeat (often associated with coronary heart disease)  Can lead to Sudden Cardiac Death 
Cardiac Catheterization – An invasive procedure in which a catheter is inserted through a blood vessel in the wrist/arm or groin with x-ray guidance  This procedure can help provide information about blood supply through the coronary arteries, blood pressure, blood flow throughout the chambers of the heart, collection of blood samples, and x-rays of the heart’s ventricles or arteries  It’s typically performed in the cath lab during angiography 
Cardiac Resynchronization Therapy (CRT) also called bi-ventricular pacemaker: an electronic pacing device that’s surgically implanted in the chest to treat the delay in heart ventricle contractions that occur in some people with heart failure 
Cardiac Tamponade – Pressure on the heart that occurs when blood or fluid builds up in the space between the heart muscle (myocardium) and the outer covering sac of the heart (pericardium)  Also called Tamponade 
Cardiomyopathy – a chronic disease of the heart muscle (myocardium), in which the muscle is abnormally enlarged, thickened, and/or stiffened 
Cardioversion – A medical procedure in which an abnormally fast heart rate (tachycardia) or cardiac arrhythmia like atrial fibrillation is converted to a normal rhythm using electricity or drugs  Synchronized electrical cardioversion uses a therapeutic dose of electric current to the heart at a specific moment in the cardiac cycle  Chemical cardioversion uses medications to convert to normal rhythm 
Cath lab – the room in the hospital/medical clinic where cardiac catheterization procedures take place (for example, when a stent is implanted into a blocked coronary artery) 
CCB – Calcium Channel Blocker: A drug that lowers blood pressure by regulating calcium-related electrical activity in the heart 
CDS – Cardiac Depression Scale: A scale that can help assess the effects of depression occurring as a result of a heart disease diagnosis 
CHF – Heart Failure (also called Congestive Heart Failure): A condition in which the heart cannot pump all the blood returning to it, leading to a backup of blood in the vessels and an accumulation of fluid in the body’s tissues, including the lungs 
CM – Cardiomyopathy: A disease of the heart muscle that leads to generalized deterioration of the muscle and its pumping ability 
CO – Cardiac Output: The amount of blood the heart pumps through the circulatory system in one minute 
Collateral arteries – These extra coronary blood vessels are sometimes able to bypass a blockage in an artery in order to supply enough oxygenated blood to enable the heart muscle to survive when in danger of being damaged because of blockage(s) 
Collateral arteries – Blood vessels that provide an alternative arterial supply of blood to an area of the heart that’s in danger of being deprived of oxygenated blood because of one or more blocked arteries 
Congenital heart defect – one of about 35 different types of heart conditions that happen when the heart or the blood vessels near the heart don’t develop normally before a baby is born (in about 1% of live births)  Because of medical advances that treat babies born with heart defects, there are now for the first time more adults with congenital heart disease than children 
Congestive heart failure (CHF) – a chronic progressive condition that affects the pumping power of your heart muscle  Often referred to simply as heart failure, CHF specifically refers to the stage in which fluid builds up around the heart and causes it to pump inefficiently 
COPD – Chronic Obstructive Pulmonary Disease: A lung disease defined by persistently poor airflow as a result of breakdown of lung tissue (known as emphysema) and dysfunction of the small airways Often associated with smoking, it typically worsens over time 
Coronary Microvascular Disease – A heart condition that causes impaired blood flow to the heart muscle through the small vessels of the heart  Also called Microvascular Disease or Small Vessel Disease 
Coronary Reactivity Test – An angiography procedure specifically designed to examine the blood vessels in the heart and how they respond to different medications  Physicians use these images to distinguish different types of blood vessel reactivity dysfunction (such as Coronary Microvascular Disease) 
Costochondritis– the cause of severe chest pain, but NOT heart-related; it’s an inflammation of the cartilage that connects a rib to the breastbone 
Coumadin – A drug taken to prevent the blood from clotting and to treat blood clots  Coumadin is believed to reduce the risk of blood clots causing strokes or heart attacks  See also Warfarin 
Cox Maze procedure – A complex “cut-and-sew” surgical procedure done to treat atrial fibrillation through a complicated set of incisions made in a maze-like pattern on the left and right atria (the upper chambers of the heart) to permanently interrupt the abnormal electrical signals that are causing the irregular heartbeats of Afib  See also: Mini-Maze 
CP – Chest Pain (may also be felt as squeezing, pressure, fullness, pressure, heaviness, burning or tightness in the chest) 
CPR – Cardiopulmonary Resuscitation: An emergency procedure in which the heart and lungs are made to work by manually compressing the chest overlying the heart and forcing air into the lungs, used to maintain circulation when the heart stops pumping during Cardiac Arrest  Current guidelines suggest hands-only CPR  See also AED 
CQ10 – Co-enzyme Q10: A dietary supplement sometimes recommended for heart patients taking statin drugs 
CRP – C-reactive protein: A byproduct of inflammation, produce by the liver, found in the blood in some cases of acute inflammation 
CRT – Cardiac Resynchronization Therapy also called bi-ventricular pacemaker: an electronic pacing device that’s surgically implanted in the chest to treat the delay in heart ventricle contractions that occur in some people with heart failure 
CT – Computed tomography (CT or CAT scan): An x-ray technique that uses a computer to create cross-sectional images of the body 
CTA – Computerized Tomographic Angiogram: An imaging test to look at the arteries that supply the heart muscle with blood  Unlike a traditional coronary angiogram, CT angiograms don’t use a catheter threaded through your blood vessels to your heart but instead rely on a powerful X-ray machine to produce images of your heart and heart vessels 
CV – Coronary Vein: One of the veins of the heart that drain blood from the heart’s muscular tissue and empty into the right atrium 
CV – Cardiovascular: Pertaining to the heart and blood vessels that make up the circulatory system 
DBP – Diastolic blood pressure: The lowest blood pressure measured in the arteries  It occurs when the heart muscle is relaxed between beats 
DCM – Dilated Cardiomyopathy: A disease of the heart muscle, primarily affecting the heart’s main pumping chamber (left ventricle)  The left ventricle becomes enlarged (dilated) and can’t pump blood to your body with as much force as a healthy heart can 
DDI – Drug-drug interaction: A situation in which a medication affects the activity of another medication when both are administered together 
DIL – Diltiazem: A calcium channel blocker drug that acts as a vasodilator; used in the treatment of angina pectoris, hypertension, and supraventricular tachycardia 
Diuretic – A class of drugs used to lower blood pressure  Also known as “water pills” 
Dobutamine stress echocardiography: This is a form of a stress echocardiogram diagnostic test  But instead of exercising on a treadmill or exercise bike to stress the heart, the stress is obtained by giving a drug that stimulates the heart and makes it “think” it’s exercising  The test is used to evaluate your heart and valve function if you are unable to exercise  It is also used to determine how well your heart tolerates activity, and your likelihood of having coronary artery disease (blocked arteries), and it can evaluate the effectiveness of your cardiac treatment plan  See also TTE and Stress Echocardiogram 
Dressler’s syndrome – Happens to a small number of people three to four weeks after a heart attack  The heart muscle that died during the attack sets the immune system in motion, calling on lymphocytes, one of the white blood cells, to infiltrate the coverings of the heart (pericardium) and the lungs (pleura)  It also starts generating antibodies, which attack those two coverings  Chest pain (CP) is the predominant symptom; treated with anti-inflammatory drugs 
Dual Antiplatelet Therapy – Medications that block the formation of blood clots by preventing the clumping of platelets (examples Plavix, Effient, Brillinta, Ticlid, etc ) are often prescribed along with aspirin as part of what’s known as dual antiplatelet therapy, especially to patients who have undergone PCI and stent implantation 
DVT – Deep Vein Thrombosis: A blood clot in a deep vein in the calf 
ECG / EKG – Electrocardiogram: A test in which several electronic sensors are placed on the body to monitor electrical activity associated with the heartbeat 
Ectopic beats – small changes in an otherwise normal heartbeat that lead to extra or skipped heartbeats, often occurring without a clear cause, most often harmless 
EF – Ejection Fraction: A measurement of blood that is pumped out of a filled ventricle  The normal rate is 50-60% 
EKG/ECG – Electrocardiogram: A test in which several electronic sensors are placed on the body to monitor electrical activity associated with the heartbeat 
Endothelium: A single-cell layer of flat endothelial cells lining the closed internal spaces of the body such as the inside of blood vessels  Endothelial dysfunction affects the ability of these cells to help dilate blood vessels, control inflammation or prevent blood clots  The endothelium is associated with most forms of cardiovascular disease, such as hypertension, coronary artery disease, chronic heart failure, peripheral vascular disease, diabetes, chronic kidney failure, and severe viral infections 
Enhanced External Counterpulsation – EECP is an FDA-approved non-invasive, non-drug treatment for angina  It works by promoting the development of collateral coronary arteries  The therapy is widely used in prominent heart clinics such as the Cleveland Clinic, Mayo Clinic and Johns Hopkins – especially for patients who are not good candidates for invasive procedures such as bypass surgery, angioplasty or stenting 
EP – Electrophysiologist: A cardiologist who has additional training in diagnosing/treating heart rhythm disorders 
EPS – Electrophysiology Study: A test that uses cardiac catheterization to study patients who have arrhythmias (abnormal hear rhythm)  An electrical current stimulates the heart in an effort to provoke an arrhythmia, which is immediately treated with medications  EPS is used primarily to identify the origin of the arrhythmia and to test the effectiveness of medications used to treat abnormal heart rhythms 
EVH – Endoscopic Vessel Harvesting: To create the bypass graft during CABG open heart surgery, a surgeon will remove or “harvest” healthy blood vessels from another part of the body, often from the patient’s leg or arm  This vessel becomes a graft, with one end attaching to a blood source above and the other end below the blocked area  See CABG 
Exercise stress test – An exercise test (walking/running on a treadmill or pedalling a stationary bike) to make your heart work harder and beat faster  An EKG is recorded while you exercise to monitor any abnormal changes in your heart under stress, with or without the aid of drugs to enhance this assessment  See also: MIBI, Echocardiogram, Nuclear Stress Test 
Familial hypercholesterolemia (FH) – A genetic predisposition to dangerously high cholesterol levels  FH is an inherited disorder that can lead to aggressive and premature cardiovascular disease, including problems like heart attacks, strokes, or narrowing of the heart valves 
Femoral Artery: a major artery in your groin/upper thigh area, through which a thin catheter is inserted, eventually making its way into the heart during angioplasty to implant a stent; currently the most widely used angioplasty approach in the United States, but many other countries now prefer the Radial Artery access in the wrist 
FFR – Fractional Flow Reserve: A test used during coronary catheterization (angiogram) to measure pressure differences across a coronary artery stenosis (narrowing or blockage) defined as as the pressure behind a blockage relative to the pressure before the blockage 
HC – High Cholesterol: When fatty deposits build up in your coronary arteries 
HCTZ – Hydrochlorothiazide: A drug used to lower blood pressure; it acts by inhibiting the kidneys’ ability to retain water  Used to be called “water pills” 
Heart Failure – a chronic progressive condition that affects the pumping power of your heart muscle  Sometimes called Congestive Heart Failure (CHF) 
Holter Monitor – A portable monitoring device that patients wear for recording heartbeats over a period of 24 hours or more 
HTN – Hypertension: High blood pressure, the force of blood pushing against the walls of arteries as it flows through them 
Hypokinesia – Decreased heart wall motion during each heartbeat, associated with cardiomyopathy, heart failure, or heart attack  Hypokinesia can involve small areas of the heart (segmental) or entire sections of heart muscle (global)  Also called hypokinesis 
ICD – Implantable Cardioverter Defibrillator: A surgically implanted electronic device to treat life-threatening heartbeat irregularities 
IHD – Ischemic Heart Disease: heart problems caused by narrowing of the coronary arteries, causing a decreased blood supply to the heart muscle  Also called coronary artery disease and coronary heart disease 
INR – International Normalized Ratio: A laboratory test measure of blood coagulation, often used as a standard for monitoring the effects of the anti-coagulant drug, warfarin (coumadin) 
IST – Inappropriate sinus tachycardia: A heart condition seen most often in young women, in which a person’s resting heart rate is abnormally high (greater than 100 bpm), their heart rate increases rapidly with minimal exertion, and this rapid heart rate is accompanied by symptoms of palpitations, fatigue, and/or exercise intolerance 
Interventional cardiologist – A cardiologist who is trained to perform invasive heart procedures like angiography, angioplasty, percutaneous coronary intervention (PCI), implanting stents, etc 
IVS – Interventricular Septum: The stout wall that separates the lower chambers (the ventricles) of the heart from one another 
IVUS – Intravascular Ultrasound: A form of echocardiography performed during cardiac catheterization in which a transducer (a device that can act as a transmitter (sender) and receiver of ultrasound information) is threaded into the heart blood vessels via a catheter; it’s used to provide detailed information about the blockage inside the blood vessels 
LAD – Left Anterior Descending coronary artery: One of the heart’s coronary artery branches from the left main coronary artery which supplies blood to the left ventricle 
LAFB – Left Anterior Fascicular Block: A cardiac condition,distinguished from Left Bundle Branch Block because only the anterior half of the left bundle branch is defective and more common than left posterior fascicular block 
LAHB – Left Anterior Hemiblock: The Left Bundle Branch divides into two major branches – the anterior and the posterior fascicles  Occasionally, a block can occur in one of these fascicles 
Left Circumflex Artery – The artery carries oxygenated blood from the heart to the body; it’s a branch of the Left Main Coronary Artery after the latter runs its course in between the aorta and the Main Pulmonary Artery 
Left Main Coronary Artery – The artery that branches from the aorta to supply oxygenated blood to the heart via the Left Anterior Descending Artery (LAD) and the Left Circumflex Artery 
Lipids – fat-like substances found in your blood and body tissues; a lipid panel is a blood test that measures the level of specific lipids in blood to help assess your risk of cardiovascular disease, measuring four types of lipids: total cholesterol, HDL cholesterol, LDL cholesterol, and triglycerides 
Lipoprotein-a or Lp(a) – molecules made of proteins and fat, carrying cholesterol and similar substances through the blood  A high level of Lp(a) is considered a risk factor for heart disease; detectable via a blood test 
Long QT syndrome (LQTS): A heart rhythm disorder that can potentially cause fast, chaotic heartbeats that may trigger a sudden fainting spell or seizure  In some cases, the heart may beat erratically for so long that it can cause sudden death 
LV – Left Ventricle – One of four chambers (two atria and two ventricles) in the human heart, it receives oxygenated blood from the left atrium via the mitral valve, and pumps it into the aorta via the aortic valve 
LVAD – Left ventricular assist device: A mechanical device that can be placed outside the body or implanted inside the body  An LVAD does not replace the heart – it “assists” or “helps” it pump oxygen-rich blood from the left ventricle to the rest of the body, usually as a bridge to heart transplant 
LVH – Left Ventricular Hypertrophy: A thickening of the myocardium (muscle) of the Left Ventricle (LV) of the heart  
Lumen – The hollow area within a tube, such as a blood vessel 
Main Pulmonary Artery – Carries oxygen-depleted blood from the heart to the lungs 
MIBI – Nuclear Stress Test/Cardiac Perfusion Scan/Sestamibi: tests that are used to assess the blood flow to the heart muscle (myocardium) when it is stressed by exercise or medication, and to find out what areas of the myocardium have decreased blood flow due to coronary artery disease  This is done by injecting a tiny amount of radionuclide like thallium or technetium (chemicals which release a type of radioactivity called gamma rays) into a vein in the arm or hand 
Microvascular disease – a heart condition that causes impaired blood flow to the heart muscle through the small blood vessels of the heart  Symptoms mimic those of a heart attack  Also called Coronary Microvascular Disease or Small Vessel Disease  I live with this diagnosis and have written more about it here, here and here 
Mini-Maze – a surgical procedure to treat atrial fibrillation, less invasive than what’s called the Cox Maze III procedure (a “cut-and-sew” procedure), and performed on a beating heart without opening the chest 
Mitral Valve: One of four valves in the heart, the structure that controls blood flow between the heart’s left atrium (upper chamber) and left ventricle (lower chamber)  The mitral valve has two flaps (cusps)  See also MV and/or Valves 
Mitral valve prolapse: a condition in which the two valve flaps of the mitral valve don’t close smoothly or evenly, but instead bulge (prolapse) upward into the left atrium; also known as click-murmur syndrome, Barlow’s syndrome or floppy valve syndrome 
MR – Mitral regurgitation: (also mitral insufficiency or mitral incompetence) a heart condition in which the mitral valve does not close properly when the heart pumps out blood  It’s the abnormal leaking of blood from the left ventricle, through the mitral valve and into the left atrium when the left ventricle contracts 
MRI – Magnetic Resonance Imaging: A technique that produces images of the heart and other body structures by measuring the response of certain elements (such as hydrogen) in the body to a magnetic field  An MRI can produce detailed pictures of the heart and its various structures without the need to inject a dye 
MS – Mitral Stenosis: A narrowing of the mitral valve, which controls blood flow from the heart’s upper left chamber (the left atrium) to its lower left chamber (the left ventricle)  May result from an inherited (congenital) problem or from rheumatic fever 
MUGA – Multiple-Gated Acquisition Scanning: A non-invasive nuclear test that uses a radioactive isotope called technetium to evaluate the functioning of the heart’s ventricles 
Murmur – Noises superimposed on normal heart sounds  They are caused by congenital defects or damaged heart valves that do not close properly and allow blood to leak back into the originating chamber 
MV – Mitral Valve: The structure that controls blood flow between the heart’s left atrium (upper chamber) and left ventricle (lower chamber) 
Myocardial Infarction (MI, heart attack) – The damage or death of an area of the heart muscle (myocardium) resulting from a blocked blood supply to the area  The affected tissue dies, injuring the heart 
Myocardium – The muscular tissue of the heart 
New Wall-Motion Abnormalities – Results seen on an echocardiogram test report (see NWMA, below) 
Nitroglycerin – A medicine that helps relax and dilate arteries; often used to treat cardiac chest pain (angina)  Also called NTG or GTN 
NSR – Normal Sinus Rhythm: The characteristic rhythm of the healthy human heart  NSR is considered to be present if the heart rate is in the normal range, the P waves are normal on the EKG/ECG, and the rate does not vary significantly 
NSTEMI – Non-ST-segment-elevation myocardial infarction: The milder form of the two main types of heart attack  An NSTEMI heart attack does not produce an ST-segment elevation seen on an electrocardiogram test (EKG)  See also STEMI 
Nuclear Stress Test – A diagnostic test that usually involves two exercise stress tests, one while you’re exercising on a treadmill/stationary bike or with medication that stresses your heart, and another set while you’re at rest  A nuclear stress test is used to gather information about how well your heart works during physical activity and at rest  See also: Exercise stress test, Nuclear perfusion test, MIBI 
Open heart surgery – Any surgery in which the chest is opened and surgery is done on the heart muscle, valves, coronary arteries, or other parts of the heart (such as the aorta)  See also CABG 
Pacemaker – A surgically implanted electronic device that helps regulate the heartbeat 
PAD – Peripheral Artery Disease: A common circulatory problem in which narrowed arteries reduce blood flow to the limbs, usually to the legs  Symptoms include leg pain when walking (called intermittent claudication) 
PAF – Paroxysmal Atrial Fibrillation: Atrial fibrillation that lasts from a few seconds to days, then stops on its own  See also Atrial Fibrillation 
Palpitations – A noticeably rapid, strong, or irregular heartbeat due to agitation, exertion or illness 
Paroxysmal Atrial Fibrillation – An unusual heart arrhythmia of unknown origin, at one time believed to be associated with an unusual sensitivity to alcohol consumption 
PDA – patent ductus arteriosus: A persistent opening between two major blood vessels leading from the heart  The opening is called ductus arteriosus and is a normal part of a baby’s circulatory system before birth that usually closes shortly after birth  But when it remains open, it’s called a patent ductus arteriosus  If it’s small, it may never need treatment, but a large PDA left untreated can allow poorly oxygenated blood to flow in the wrong direction, weakening the heart muscle and causing heart failure or other complications 
Pericardium: two thin layers of a sac-like tissue that surround the heart, hold it in place and help it work 
PET – Positron Emission Tomography: A non-invasive scanning technique that uses small amounts of radioactive positrons (positively charged particles) to visualize body function and metabolism  In cardiology, PET scans are used to evaluate heart muscle function in patients with coronary artery disease or cardiomyopathy 
PFO – Patent Forman Ovale: An opening between the left and right atria (the upper chambers) of the heart  Everyone has a PFO before birth, but in 1 out of every 3 or 4 people, the opening does not close naturally as it should after birth 
Plaque – A deposit of fatty (and other) substances in the inner lining of the artery wall; it is characteristic of atherosclerosis 
POTS – Postural Orthostatic Tachycardia Syndrome: A disorder that causes an increased heart rate when a person stands upright 
PPCM – Post-partum cardiomyopathy: A form of cardiomyopathy that causes heart failure toward the end of pregnancy or in the months after delivery, in the absence of any other cause of heart failure 
Preeclampsia – a late-pregnancy complication identified by spikes in blood pressure, protein in the urine, possible vision problems  Women who experience pregnancy complications like preeclampsia are at significantly higher risk for heart disease 
Prinzmetal’s Variant Angina – Chest pain caused by a spasm in a coronary artery that supplies blood to the heart muscle 
PSVT – Paroxysmal Supraventricular Tachycardia: – An occasional rapid heart rate (150-250 beats per minute) that is caused by events triggered in areas above the heart’s lower chambers (the ventricles)  “Paroxysmal” means from time to time  See also supraventricular tachycardia (SVT) 
Pulmonary Valve: One of the four valves in the heart, located between the pulmonary artery and the right ventricle of the heart, moves blood toward the lungs and keeps it from sloshing back into the heart 
PV – Pulmonary Vein: A vein carrying oxygenated blood from the lungs to the left atrium of the heart 
PVC – Premature Ventricular Contraction: An early or extra heartbeat that happens when the heart’s lower chambers (the ventricles) contract too soon, out of sequence with the normal heartbeat  In the absence of any underlying heart disease, PVCs do not generally indicate a problem with electrical stability, and are usually benign 
RA – Right Atrium: The right upper chamber of the heart  The right atrium receives de-oxygenated blood from the body through the vena cava and pumps it into the right ventricle which then sends it to the lungs to be oxygenated 
Radial Artery: the artery in the wrist where a thin catheter is inserted through the body’s network of arteries in the arm and eventually into the heart during a procedure to implant a stent  Doctors may also call this transradial access, the transradial approach, or transradial angioplasty  Because it’s associated with fewer complications, this is increasingly considered the default access approach in most countries, except in the U S  where the traditional Femoral Artery (groin) approach is still the most popular access 
RBBB – Right Bundle Branch Block: A delay or obstruction along the pathway that electrical impulses travel to make your heart beat  The delay or blockage occurs on the pathway that sends electrical impulses to the right side of your heart  See also Left Bundle Branch Block 
RCA – Right Coronary Artery: An artery that supplies blood to the right side of the heart 
Restenosis – The re-closing or re-narrowing of an artery after an interventional procedure such as angioplasty or stent placement  Sometimes called “stent failure” 
RHD – Rheumatic Heart Disease: Permanent damage to the valves of the heart caused especially by repeated attacks of rheumatic fever 
RM – Right Main coronary artery: A blood vessel that supplies oxygenated blood to the walls of the heart’s ventricles and the right atrium 
RV – Right Ventricle: The lower right chamber of the heart that receives de-oxygenated blood from the right atrium and pumps it under low pressure into the lungs via the pulmonary artery 
SA – Sinus node: The “natural” pacemaker of the heart  The node is a group of specialized cells in the top of the right atrium which produces the electrical impulses that travel down to eventually reach the ventricular muscle, causing the heart to contract 
SB – Sinus Bradycardia: Abnormally slow heartbeat 
SBP – Systolic Blood Pressure: The highest blood pressure measured in the arteries  It occurs when the heart contracts with each heartbeat  Example: the first number in 120/80 
SCAD – Spontaneous Coronary Artery Dissection: A rare emergency condition that occurs when a tear forms in one of the blood vessels in the heart, causing a heart attack, abnormalities in heart rhythm and/or sudden death  SCAD tends to strike young healthy women with few if any cardiac risk factors 
SD – Septal defect: A hole in the wall of the heart separating the atria (two upper chambers of the heart) or in the wall of the heart separating the ventricles (two lower chambers) 
Sestamibi stress test – See MIBI 
Short QT intervals (SQT): An abnormal heart rhythm where the heart muscle takes a shorter time to recharge between beats  It can cause a variety of complications from fainting and dizziness to sudden cardiac arrest 
Sick Sinus Syndrome (also known as sinus node dysfunction) is caused by an electrical problem in the heart; a group of related heart conditions that can affect how the heart beats, most commonly in older adults, although it can be diagnosed in people of any age  “Sick sinus” refers to the sinoatrial node (see below)  In people with sick sinus syndrome, the SA node does not function normally 
Sinoatrial node (SA): also commonly called the sinus node; it’s a small bundle of neurons situated in the upper part of the wall of the right atrium (the right upper chamber of the heart)  The heart’s electrical impulses are generated there  It’s the normal natural pacemaker of the heart and is responsible for the initiation of each heartbeat 
Spontaneous Coronary Artery Dissection (SCAD) – A rare emergency condition that occurs when a tear forms in one of the blood vessels in the heart, causing a heart attack, abnormalities in heart rhythm and/or sudden death  SCAD tends to strike young healthy women with few if any cardiac risk factors 
SSS – Sick Sinus Syndrome: The failure of the sinus node to regulate the heart’s rhythm 
ST – Sinus Tachycardia: A heart rhythm with elevated rate of impulses originating from the sinoatrial node, defined as greater than 100 beats per minute (bpm) in an average adult  The normal heart rate in the average adult ranges from 60–100 bpm  Also called sinus tach or sinus tachy 
Statins – Any of a class of drugs that lower the levels of low-density lipoproteins (LDL) – the ‘bad’ cholesterol in the blood – by inhibiting the activity of an enzyme involved in the production of cholesterol in the liver  Examples of brand name statins: Lipitor, Crestor, Zocor, Mevacor, Levachol, Lescol, etc  Also available as a cheaper generic form of the drug 
STEMI – ST-elevation heart attack (myocardial infarction)  The more severe form of the two main types of heart attack  A STEMI produces a characteristic elevation in the ST segment on an electrocardiogram (EKG)  The elevated ST segment is how this type of heart attack got its name  See also NSTEMI 
Stent – An implantable device made of expandable, metal mesh (looks a bit like a tiny chicken wire tube) that is placed (by using a balloon catheter) at the site of a narrowing coronary artery during an angioplasty procedure  The stent is then expanded when the balloon fills, the balloon is removed, and the stent is left in place to help keep the artery open  TRIVIA ALERT: the coronary stent was named after Charles Stent (1807-1885), an English dentist who invented a compound to produce dentures and other things like skin grafts and hollow tubes (essentially what a metal coronary stent is)  His real claim to fame occurred when he suggested using his material to coat underwater trans-Atlantic cable, which had broken several times as a result of corrosion by seawater  You’re welcome 
Stint – a common spelling mistake when what you really mean is the word “stent” (see above) 
Stress Echocardiography – A standard echocardiogram test that’s performed while the person exercises on a treadmill or stationary bicycle  This test can be used to visualize the motion of the heart’s walls and pumping action when the heart is stressed, possibly revealing a lack of blood flow that isn’t always apparent on other heart tests  The echocardiogram is performed just before and just after the exercise part of the procedure  See also TTE 
Sudden Cardiac Arrest – The stopping of the heartbeat, usually because of interference with the electrical signal (often associated with coronary heart disease)  Can lead to Sudden Cardiac Death 
Takotsubo Cardiomyopathy – A heart condition that can mimic a heart attack  Sometimes called Broken Heart Syndrome, it is not a heart attack, but it feels just like one, with common symptoms like severe chest pain and shortness of breath  It sometimes follows a severe emotional stress  Over 90% of reported cases are in women ages 58 to 75  Also referred to as Broken Heart Syndrome, stress cardiomyopathy, stress-induced cardiomyopathy or apical ballooning syndrome 
TAVR – Transcatheter aortic valve replacement: A minimally invasive procedure to repair a damaged or diseased aortic valve  A catheter is inserted into an artery in the groin and threaded to the heart  A balloon at the end of the catheter, with a replacement valve folded around it, delivers the new valve to take the place of the old  Also called TAVI (Transcatheter aortic valve implantation) 
Tetralogy of Fallot – A rare condition caused by a combination of four heart defects that are present at birth, affecting the structure of the heart and causing oxygen-poor blood to flow out of the heart and into the rest of the body  Infants and children with Tetralogy of Fallot usually have blue-tinged skin because their blood doesn’t carry enough oxygen  Often diagnosed in infancy, but sometimes not until later in life depending on severity 
Tg – Triglycerides: The most common fatty substance found in the blood; normally stored as an energy source in fat tissue  High triglyceride levels may thicken the blood and make a person more susceptible to clot formation  High triglyceride levels tend to accompany high cholesterol levels and other risk factors for heart disease, such as obesity 
TIA – Transient Ischemic Attack: A stroke-like event that lasts only for a short time and is caused by a temporarily blocked blood vessel 
TEE – Transesophageal echocardiogram: This test involves an ultrasound transducer inserted down the throat into the esophagus in order to take clear images of the heart structures without the interference of the lungs and chest 
Treadmill Stress Test – See Exercise Stress Test 
troponin – a type of cardiac enzyme found in heart muscle, and released into the blood when there is damage to the heart (for example, during a heart attack)  A positive blood test that shows elevated troponin is the preferred test for a suspected heart attack because it is more specific for heart injury than other blood tests, especially the newer high sensitivity troponin tests (hs-cTnT) 
TTE – Transthoracic Echocardiogram: This is the standard echocardiogram, a painless test similar to X-ray, but without the radiation, using a hand-held device called a transducer placed on the chest to transmit high frequency sound waves (ultrasound)  These sound waves bounce off the heart structures, producing images and sounds that can be used by the doctor to detect heart damage and disease 
TV – Tricuspid Valve: One of four one-way valves in the heart, a structure that controls blood flow from the heart’s upper right chamber (the right atrium) into the lower right chamber (the right ventricle) 
UA or USA – Unstable Angina: Chest pain that occurs when diseased blood vessels restrict blood flow to the heart; symptoms are not relieved by rest; considered a dangerous and emergency crisis requiring immediate medical help 
Valves: Your heart has four one-way valves that keep blood flowing in the right direction  Blood enters the heart first through the tricuspid valve, and next goes through the pulmonary valve (sometimes called the pulmonic valve) on its way to the lungs  Then the blood returning from the lungs passes through the mitral (bicuspid) valve and leaves the heart through the aortic valve 
Vasodilator: A drug that causes dilation (widening) of blood vessels 
Vasospasm: A blood vessel spasm that causes sudden constriction, reducing its diameter and blood flow to the heart muscle  See also Prinzmetal’s Variant Angina 
VB – Ventricular Bigeminy: A heart rhythm condition in which the heart experiences two beats of the pulse in rapid succession 
Vena Cava – a large vein that carryies de-oxygenated blood into the heart  There are two in humans, the inferior vena cava (carrying blood from the lower body) and the superior vena cava (carrying blood from the head, arms, and upper body) 
Ventricle – each of the two main chambers of the heart, left and right 
VF – Ventricular Fibrillation: A condition in which the ventricles (two lower chambers of the heart) contract in a rapid, unsynchronized fashion  When fibrillation occurs, the ventricles cannot pump blood throughout the body  Most sudden cardiac deaths are caused by VF or ventricular tachycardia (VT) 
VLDL – Very Low Density Lipoprotein: Molecules made up of mostly triglycerides, cholesterol and proteins  VLDL, also known as the “very bad” cholesterol, carries cholesterol from the liver to organs and tissues in the body  It may lead to low density lipoproteins (LDL), associated with higher heart disease risks  VLDL levels are tricky to measure routinely, and are usually estimated as a percentage of your triglyceride levels  By reducing triglycerides, you are usually also reducing your VLDL levels 
Warfarin – A drug taken to prevent the blood from clotting and to treat blood clots  Warfarin is believed to reduce the risk of blood clots causing strokes or heart attacks  Also known as Coumadin 
Widowmaker heart attack – The type of heart attack I survived, since you asked  A nickname doctors use to describe a severely blocked left main coronary artery or proximal left anterior descending coronary artery of the heart  This term is used because if the artery gets abruptly and completely blocked, it can cause a massive heart attack that will likely lead to sudden cardiac death  Please note the gender imbalance here: despite the number of women like me who do experience this type of cardiac event, doctors are not calling this the widowermaker, after all 
WPW – Wolff-Parkinson-White Syndrome: A condition in which an extra electrical pathway connects the atria (two upper chambers) and the ventricles (two lower chambers)  It may cause a rapid heartbeat 
NOTE FROM CAROLYN: I was very happy when we were able to include this entire glossary in my book, “A Woman’s Guide to Living with Heart Disease“ (Johns Hopkins University Press, 2017) 
Are we missing any important heart acronyms/terms from this list? Let me know!
Please can someone explain something for me  I am a 53 yr old woman and generally fit and healthy  Had 2 ECG’s due to a one off dizzy spell during a stressful time dealing with my fathers terminal diagnosis  The 2nd ECG request did give me concern as i did not know why i had to have one  On 24/01/19 at my doctors appointment she explained that on 3 the leads it showed inverted T waves  And she explained that it may suggest angina  I was so shocked  Wasn’t expecting that  She gave me a GNT (nitroglycerin) spray in case I do get pain and take 75Mg of aspirin  I’m now waiting for a Cardiology referral 
I am so stressed and consumed by what might be wrong  My maternal grandmother had angina and valve issues  Her 3 brothers all had double bypasses  Could I have inherited this? I am not overweight at 63kg and 5 ft 9  I walk 20-25 miles a week at work and general walking here and there  I started HRT (patches evorol 25 -50) in July as menopause pain was making me feel like I was 90 and was getting me down 
I am worried so much now and analysing every ache/ twinge I get  I feel like a hypochondriac at the moment  I’m worried what will happen at the cardiologist and what the test will entail and tell me  I am waiting on cholesterol test which I had on 25/01/19  Can I have inverted T waves and be fine  Please help I am so scared and crying far too much 
Hello Colleen – the first thing is: please take a big deep breath before you read another word here! I’m not a physician so of course cannot comment on your specific case, but I can tell you generally that the definition of “angina” (as this glossary lists above) is “distressing symptoms”, typically chest pain that gets worse with exertion, and goes away with rest  That’s classic stable angina… typically caused by something that’s reducing blood flow to the heart muscle (causing the chest pain of angina) 
A family history that might make a difference for you personally is only in what’s called your ‘first degree’ relatives: for example, if your mother or sister were diagnosed with heart disease before age 65, or if your Dad or brother were diagnosed before age 55, then doctors would consider that you have a family history as a risk factor for heart disease  There’s little if any scientific evidence that a grandparent or uncle’s heart disease history has any effect on your own risk 
It is a very good thing that you’re having further tests and a referral to a cardiologist, if only to ease your mind  There are many reasons for inverted T-waves, ranging from cardiac issues to completely benign conditions  One way of looking at this is choosing to believe that seeing a cardiologist will ease your mind one way or the other – so this is something to look forward to, not dread  If the cardiologist spots something suspicious, a treatment plan will be created  If not, you can wave goodbye and go back to happily living your life 
Try thinking of this cardiology appointment just as you would if your car were making some frightening noises and you were bringing it to your mechanic for a check up  You could work yourself into a complete state worrying ahead of time if the car trouble is going to be serious, or you could look at this appointment as the solution – at last! – to figuring out what’s wrong so the mechanic can recommend the next step 
Thank you for this list of so many definitions provided in plain English  what a valuable resource this is  THANK YOU, I have been looking for translations FOR PATIENTS not med school graduates– like this for three years 
My family doctor had me wear a 24 hr EKG  After reading the results, she has scheduled a scope to look inside my heart by a specialist  Completely forgoing a stress test  Said I have major changes in the EKG, what type of changes could they be looking at? Had LAD STENT INSERTED 7 YRS AGO – WHAT COULD THEY BE LOOKING FOR?
This is a great wealth of information, Carolyn! I looked and did not see my diagnosis, which is aortic stenosis  I looked under aortic as well as stenosis  Did I just miss it somehow?
I learned some new information, I am a bit familiar now, but not when I had my MI, it was like learning a new language  But, my favorite part was seeing SCAD on this list! Thank you 
Thanks and welcome! I was thinking of editing that SCAD definition actually: I suspect that that it isn’t so much that SCAD is “rare”, but it’s more that it’s “rarely correctly diagnosed” 
I totally agree that SCAD is not as rare as I believed for many years  Once awareness is spread to all medical staff, I believe many lives will be saved  Hoping for a brighter future for all SCAD patients 
I hope so too, Cathy  Perhaps when more SCAD studies (like Mayo Clinic’s) are published and read by more and more MDs, it will no longer be “rarely correctly diagnosed” 
It’s great to see IST on here  I was diagnosed with it 9 years ago and the lack of awareness is frustrating 
What a great resource for heart patients and their families!
Thanks so much, Ashley  I recently updated my original 2011 list after the world-famous Cleveland Clinic tweeted their glossary recently and I noticed that their list had a few glaring omissions (like SCAD and Brugada Syndrome) so this made me wonder what my list might be missing, too  Let me know if there’s anything else you think should be included, okay?
How is your health these days? How are you feeling?
New for me too  I have just been diagnosed with A-HCM: Apical Hypertrophic Cardiomyopathy 
I’ll add that one to my list, Kathleen – thanks!
Just saw this, Carolyn, and you’ve compiled a great resource  One note on A-HCM: Present thinking is that it’s due to a genetic modification  Runs in families though sometimes occurs spontaneously  I have not as yet done genetic testing, though it’s been offered 
Thanks Kathleen – like many cardiac diagnoses, it sounds like a moving target… Good luck to you!
This list is great  I’ve just been diagnosed and am utterly overwhelmed  Even in the WomenHeart online support community, I often have no clue most days what others are talking about with all these initials about their heart tests and specific disease  This is VERY helpful, thank you SO MUCH  Love your website which has been a godsend since my diagnosis 



ground_truth: A study on the effects of Brazilian Jiu Jitsu and psychotherapy on people with autism.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the purpose of an ICD?

Read the following text and answer briefly.

Context 4:  The systematic error includes the unknown phase between the
two resonances  Work is in progress on extracting the two Breit-Wigner
amplitudes 


\begin{figure}[htb]
\vspace*{-2mm}
\hspace*{-3mm}
\includegraphics[height=0 28\textheight,width=8 3cm]  {B08F02 eps}

\vspace*{-1cm}
\caption{Mass difference $\Delta M = M(B\pi)-M(B)$ for exclusive $B$ decays 
The background-subtracted signal is a sum of 
$B^*_1 \rightarrow B^* \pi$, $B^* \rightarrow B \gamma $ (open area)
and $B^*_2 \rightarrow B^*\pi$ $B^*\rightarrow B \gamma$ (lower peak in the shaded area)
and $B^*_2 \rightarrow B \pi$ (upper peak in the shaded area)  
(D\O) }
\label{fig:d0_bexc}
\end{figure}


\begin{figure}[htb]
\includegraphics[height=0 25\textheight,width=7 5cm]  {B05F03 eps}

\vspace*{-1cm}
\caption{The invariant mass distribution of
$(D^*,\pi)$ pairs, opposite sign (points) and same-sign (solid histogram) }
\label{fig:d0_dstst}
\end{figure}






\subsection{Lifetimes}


CDF and D\O\ have measured  lifetimes of $b$ hadrons through the exclusively
reconstructed decays $B^+ \rightarrow J/\psi K^+$, $B^0 \rightarrow J/\psi K^{*0}$,
$B_s \rightarrow J/\psi \phi$, 
and $\Lambda_b \rightarrow J/\psi \Lambda$
(Fig  \ref{fig:d0_lbctau}) 
The latest results are:  \\



 $\tau(B^+)$=1 65 $\pm$ 0 08 $^{+0 096}_{-0 123}$  ps ~(D\O\ 2003),

 $\tau(B^+)$=1 662 $\pm$ 0 033  $\pm$ 0 008  ps ~(CDF),

 $\tau(B^0_d)$=1 473  $^{+0 052}_{-0 050}$ $\pm$ 0 023    ps ~(D\O) 

 $\tau(B^0_d)$=1 539 $\pm$ 0 051  $\pm$ 0 008  ps ~(CDF),

 $\tau(B^0_s)$=1 444   $^{+0 098}_{-0 090}$ $\pm$ 0 020   ps ~(D\O),

 $\tau(B^0_s)$=1 369 $\pm$ 0 100 $\pm$ $^{+0 008}_{0 010}$  ps ~(CDF),


 $\tau(\Lambda_b)$=1 221 $^{+0 217}_{-0 179}$ $\pm$ 0 043  ps ~(D\O),


 $\tau(\Lambda_b)$=1 25 $\pm$ 0 26 $\pm$ 0 10  ps ~(CDF 2003) \\



The measured lifetimes correspond to the following lifetime ratios:\\

$\tau(B^+)/\tau(B^0_d)$   =  1 080$\pm$0 042     ~(CDF),
 
$\tau(B^0_s)/\tau(B^0_d)$ =  0 890$\pm$0 072    ~(CDF),

$\tau(B^0_s)/\tau(B^0_d)$ = 0 980$ ^{+0 075}_{-0 070}   \pm$0 003    ~(D\O),

$\tau(\Lambda_b)/\tau(B^0_d)$ =  0 874$ ^{+0 169}_{-0 142}   \pm$0 028    ~(D\O) \\



\begin{figure}[htb]
\includegraphics[height=0 3\textheight,width=8 2cm]  {d0_lbctau_B11F02 eps}
\vspace*{-1cm}

\caption{ Fit projection on  $c\tau$ for the $\Lambda_b$ candidates   (D\O)}
\label{fig:d0_lbctau}
\end{figure}


The $B_s$ lifetime measurements listed above are results of
a single-lifetime fit to data, integrated over the decay angles 
Because  of the presence of  final
states  common to ${B_s^0}$\ and its charge conjugate ${\overline{B}_s^0}$,
the two meson states   are expected
to mix in such a way that the two CP  eigenstates may have a relatively
large lifetime difference 
It is possible to
separate the two CP components of ${B_s^0 \rightarrow J/\psi \phi}$\ and thus to measure the
lifetime difference by studying the time evolution of the
polarization states of the vector mesons in the final state 
CDF has carried out a combined analysis of $B_s$ lifetimes 
and polarization amplitudes  The results for the lifetimes of the
low mass (CP even) and high mass (CP odd) eigenstates, and the relative 
width difference are:\\

 $\tau_L = 1 05 ^{+0 16}_{-0 13} \pm 0 02$ ~ps,
 
 $\tau_H = 2 07 ^{+0 58}_{-0 46} \pm 0 03$ ~ps,

 $\Delta \Gamma /\overline \Gamma   = 0 65 ^{+0 25}_{-0 33} \pm 0 01$ \\

Figure \ref{fig:cdf_dg} shows  the scan of the likelihood function 
for $\Delta \Gamma /\overline \Gamma$ 
Pseudoexperiments tossed with $\Delta \Gamma /\overline \Gamma =0$
yield the betting odds for observing the above results at
1/315  For $\Delta \Gamma /\overline \Gamma = 0 12$ (SM prediction,
which has recently been updated to 0 14$\pm$0 05~\cite{dg_un}) the betting odds are
1/84 

\begin{figure}[htb]
\vspace*{-1mm}
\includegraphics[height=0 3\textheight,width=8 2cm]  {cdf_scan-dg-un eps}

\vspace*{-1cm}
\caption{Scan of the likelihood function 
for $\Delta \Gamma /\overline \Gamma$ (CDF) 
}
\label{fig:cdf_dg}
\end{figure}




D\O\ has used a novel technique to  measure the lifetime ratio
of the charged and neutral $B$ mesons, exploiting the large
semileptonic sample  $B$ hadrons were reconstructed in the channels
$B\rightarrow \mu^+ \nu D^*(2010)^-X$, which are dominated by $B^0$ decays, 
and  $B\rightarrow \mu^+ \nu D^0X$, which are dominated by $B^+$ decays 
The lifetime ratio was
obtained from the variation of the ratio of the number of events in these two
processes at different decay lengths 
The result is \\


$\tau(B^+)/\tau(B^0_d)$   =  1 093$\pm$0 021$\pm$0 022       ~(D\O)




\subsection{Towards $B_s$ mixing}

Measurement of the $B_s$ oscillation frequency via ${B_s^0}$ -${\overline{B}_s^0}$ ~mixing
will provide an important constraint on the CKM matrix  The oscillation
frequency is proportional to the mass difference between the mass eigenstates,
$\Delta m_s$, and is related to the CKM matrix through 
$\Delta m_s \propto |V_{tb}V_{ts}|$  When combined with the
$B_d$ mass difference, $\Delta m_d$ it helps in extraction of $|V_{td}|$,
and thereby the CP violating phase  

As a benchmark for future $B_s$ oscillation measurement, both groups
study  $B_d$ mixing, gaining an understanding of the different components
of a $B$ mixing analysis (sample composition, flavor tagging, vertexing,
asymmetry fitting)  For a sample of partially reconstructed decays
$B\rightarrow D^*(2010)^+\mu^-X$, D\O\ obtains 
$\Delta m_d = 0 506 \pm 0 055 (stat) \pm  0 049 (syst))$ ps$^{-1}$ and
$\Delta m_d = 0 488 \pm 0 066 (stat) \pm  0 044 (syst))$ ps$^{-1}$
when employing  opposite side muon tagging and the same side tagging,
respectively 

The CDF result for semileptonic channels is
$\Delta m_d = 0 536 \pm 0 037 (stat) \pm  0 009 (s c ) \pm 0 015 (syst)$ ps$^{-1}$ 
CDF also reports a result on $B$ oscillations using fully reconstructed
decays:
$\Delta m_d = 0 526 \pm 0 056 (stat) \pm  0 005 (syst))$ ps$^{-1}$ 

Reconstructing $B_s$ decays into different final states is another
important
 step in the ${B_s^0}$ -${\overline{B}_s^0}$ ~mixing analysis 
Thanks to the  large muon and tracking coverage,   D\O\ is accumulating
a  high statistics sample of semileptonic $B_s$ decays 
D\O\ reconstructs the $B_s \rightarrow D^+_s \mu^- X$ decays, with
$D^+_s \rightarrow \phi \pi^+ $ and
$D^+_s \rightarrow K^* K^+ $,
at a rate of $\approx$ 40(25) events per pb$^{-1}$,  respectively 
Figure \ref{fig:d0_bsdsphipi} shows the mass distribution of the
$D^+_s \rightarrow \phi \pi$ candidates 


\begin{figure}[htb]
\vspace*{-5mm}
\includegraphics[height=0 3\textheight,width=8 0cm]  {blds-250 eps}
\vspace*{-1 2cm}
\caption{  $D^+_s \rightarrow \phi \pi^+$  signal  (D\O)}
\label{fig:d0_bsdsphipi}
\end{figure}


\begin{figure}[htb]
\vspace*{-10mm}
\hspace*{-4mm}
\includegraphics[height=0 35\textheight,width=7 9cm]  {cdf_Bs-DsPi-PhiPi eps}

\vspace*{-1 0cm}
\caption{ $B_s \rightarrow D_s \pi$, $D_s \rightarrow \phi \pi$  signal   (CDF)}
\label{fig:cdf_bsdsphipi}
\end{figure}


CDF has clean signals for fully hadronic, flavor-specific  $B_s$ decays,
providing the best sensitivity to $B_s$ oscillations at high
$\Delta m_s$  Figure \ref{fig:cdf_bsdsphipi} shows the signal for
the best channel, $B_s \rightarrow D_s \pi$, $D_s \rightarrow \phi \pi$ 

\clearpage


\subsection{Rare decays}

The purely leptonic decays $B_{d,s}^0 \rightarrow \mu^+
\mu^-$ are flavor-changing neutral current (FCNC) processes 
In the standard model, these decays are forbidden at the tree level and
proceed at a very low rate through higher-order diagrams 
The latest SM prediction~\cite{sm_ref3}
is ${\cal B}(B^0_s \rightarrow \mu^+ \mu^-)=(3 42\pm 0 54)\times
10^{-9}$, where the error is dominated by non-perturbative uncertainties  The
leptonic branching fraction of the $B_d^0$ decay is suppressed by CKM matrix elements $|V_{td}/V_{ts}|^2$
leading to a predicted SM branching fraction of $(1 00\pm0 14)\times 10^{-10}$ 
The best published experimental bound (Fig ~\ref{fig:cdf_bsmumu})
 for the branching fraction
of $B^0_s$ $(B^0_d)$ is presently
${\cal B}(B^0_s \, (B^0_d) \rightarrow \mu^+\mu^-)<7 5\times 10^{-7}\, 
(1 9\times 10^{-7})$ at the 95\% C L ~\cite{cdfII} 
The decay amplitude of $B^0_{d,s} \rightarrow \mu^+ \mu^-$ can be
significantly enhanced in some extensions of the SM  

\begin{figure}[htb]
\includegraphics[height=8 3cm,width=7 9cm]  {cdfbsmumu_results_prl eps}

\vspace*{-1cm}
\caption{Invariant mass for the events passing all requirements  (CDF)}
\label{fig:cdf_bsmumu}
\end{figure}


Assuming no contributions 
from the decay $B^0_d\rightarrow \mu^+\mu^-$ in the signal region,
D\O\  finds the conservative upper limit on the branching fraction 
to be ${\cal B}(B^0_s \rightarrow \mu^+ \mu^-) \leq 4 6\times 10^{-7}$ 
at the 95\% C L  (Fig ~\ref{fig:d0_bsmumu}) 






\begin{figure}[htb]
\includegraphics[height=5 0cm,width=8 0cm]  {B06F03 eps}
\vspace*{-1cm}
\caption{Invariant mass for the events  passing all requirements  (D\O)}
\label{fig:d0_bsmumu}
\end{figure}





ground_truth: Implantable Cardioverter Defibrillator (ICD) is a surgically implanted electronic device to treat life-threatening heartbeat irregularities.