text:
Gluten-free post
This post is gluten-free.
A seven month-old baby in Belgium died from malnutrition after his parents put him on an alternative gluten-free diet despite no actual medical diagnosis or recommendation. The child weighed only 9 pounds, about half the size of an average child his age, and was extremely dehydrated. The story brings to light just how dangerous alternative diets can be for very young children.
The baby, identified only as "Lucas" by The Daily Mail, was raised on a gluten-free diet consisting of quinoa milk, rice milk, oat milk, and other alternative milk products. Upon noticing their child's diminishing health—the boy was described as extremely thin and "gasping for air"—his parents, named only as Peter S and Sandrina V, took him to visit a homeopathic doctor. The homeopath however immediately sent the family to a hospital.
(full article here: Baby Dies of Malnutrition).
And some people still don't believe in natural selection. I think that's proof in itself of natural selection.
Behind Her Eyes by Sarah Pinborough. Yuck!
Behind Her Eyes by Sarah Pinborough
I can't believe I stuck with this book to the end. It's a positive insult to the reader's intelligence. I saw the ending coming way in advance, although, admittedly, not the very last twist. I couldn't believe the publishers would ever put such crap in a book, so I kept reading in the hope that I had it wrong. It wasn't just the ridiculous ending that was bad; the writing was, too. The author used the same sentences with only minor variations dozens, perhaps scores, of times. The same thoughts running through the same heads over and over. I wanted to scream "get on with it!" at least fifty times. Enough said. Don't waste your time on this one.
Breakdown by Jonathan Kellerman
Child psychologist Alex Delaware is summoned to treat Zelda, a psychotic former actress whose child he once evaluated. She's on a 5150 hold in a dubious facility and is soon released. Days later she is found dead on a palatial estate in Bel Air, poisoned from ingesting some toxic plant material. With his homicide lieutenant buddy Milo, Delaware goes about tracking down what happened to her and trying to find her missing son. The plot is classic police procedural, my favorite mystery genre, and the author has a knack for description. Put simply, he writes well. I enjoyed the book and recommend it. If you are looking for an idea of a book to read this summer, and you like police procedurals, then you can stop reading here and put this on your list. It's a good one.
Now, if you'd like my take as an ex-FBI agent, lawyer, and crime novelist as to what wasn't done quite right, keep reading. For starters, it was realistic, or at least plausible, for Alex to go from person A to person B to person C to gather leads. Pure procedural. But when it got to person Q or R, the serendipity became ludicrous. Everybody he talked to just happened to have one person to suggest who might have information, and all of them were alive, easy to find, and available and willing to talk. He also met every one in person, mostly over a meal. Have they no telephones in L.A.? What that really was was a lot of filler trying to turn a 120-page book into a 350-page book.
Now for the forensic part. The author really slipped here. I think he just got lazy. Take this quote where Alex has just looked up a location on Google Earth:
"In seconds I had full-color, one-year-old, 3-D satellite photos of the property at a variety of angles, the forest-like area … revealed in high definition."
I use Google Earth constantly for my geocaching and a camera designer for Google involved in Google Earth used to be my next-door neighbor. It does not actually show satellite photos over L.A., although it does over many non-urban or forbidden areas like North Korea. Over L.A. and other U.S. cities they use low-flying airplanes. Okay, I forgive the use of the word satellite. But you can't look at the area from different angles from that view. The pictures are all taken from directly overhead. Google has given the terrain a sort of 3-D look using clever algorithms and elevation data, but you're still only going to see the same exact view no matter how you tilt the screen view. Think of it this way: imagine they printed the overhead view on a flat, flexible piece of paper and then pasted that paper over a 3-D model of the surface, complete with hills. That's what is displayed. Despite the 3-D effect you only see the roofs of the houses. Of course if you use Street View, then you can see various angles at ground level because the Google photo car does have multiple cameras photographing from different angles, but that view wouldn't show the plants in this scenario.
Next, Alex has a retired cop fly over the property in a helicopter and a plant biologist is able to identify several different species of ground-level shrubs from the infrared photos. This information is used to obtain a search warrant. There are several problems with this. First, IR photography identifies heat, and has very poor resolution. A biologist would not be able to identify various different species from IR signatures no matter how low the helicopter flew. Even if he also used standard photography, he'd have to practically land on the property to be close enough to identify these various species among a very tangled growth area, which would be a 4th Amendment violation and render the search warrant void. I rather doubt it could be done at all without taking a sample back to a lab. A low flight of that nature would also destroy the secrecy of the surveillance, which supposedly went undetected in the story.
There were several other legal hurdles that seem to have been magically vanished in the story, like how does Alex, a civilian, get access to crime scenes and all kinds of evidence only police can get (and even they often can't), but I'm not going to go into further detail. These quibbles did not destroy the overall enjoyment of the story, although they diminish my rating from 5 stars to 4. This is the first book from any of the prolific Kellerman clan that I've read, although the library shelves are full of them. I expect to read more in the future.
Cached Out free this weekend
My best-selling Cliff Knowles mystery, Cached Out, will have a free promotion (Kindle download) on Amazon this weekend, the first in a year. Spread the word.
Cached Out
I welcome comments on my posts, but they sometimes take a while to appear. Why? I have a spam filter on my site. It does a pretty good job, but it's not perfect. The majority of comments that get past it are fake, spam posts. For that reason I have set restrictions so that comments do not appear until I approve them. However, WordPress does not "push" notify me that a comment has come. It just adds a little number next to an icon on the dashboard page. I have to remember to look for that as it is not obvious and hides among a lot of clutter on that page. I typically see the dashboard page only when I'm ready to post something new myself. The long and short of it is that it sometimes takes me a few days to notice that a comment has come in and to approve it. I don't know how that looks on the reader's end, i.e. whether he or she is notified that the comment has been approved and appears. So if you look for your comment and it is not there, don't think you're being snubbed. Just look again in a few days. If you want to reach me immediately, you can use the About the Author/Contact link at the top menu and I will get an email in my inbox.
Consider these two maps:
This data is taken from the IRS based on the number of taxpayers (and their children, since it includes exemptions on the returns) who moved into or out of California between 2015 and 2016. California had slightly more people leave than enter. The top map shows the states from which people come to California, the bottom the states to which they go. In both cases, darker green means more people.
In both cases it is unsurprising that the largest number of migrants both in and out come primarily from the states that are the most populous and the ones geographically closest to California. The maps resemble each other to a large extent, but there are subtle differences. For example, the upper Midwest like Minnesota and Michigan are darker in the upper map, indicating that more of those people want to come to California than the other way around. It looks like more Californians prefer to stay in the Pacific or far west states when they do move. Now compare these maps to the next one:
This map shows a net migration into or out of California as a percent of the population of the other state. I set California at zero for comparison purposes even though it had a net outflow. Every state that is darker than California had a net migration into California with the darkest having the highest percent of their population migrating. Everything that is lighter than California shows a net migration from California to that state with the lightest receiving the biggest bump to their population as a percent. The top maps show raw numbers while this bottom map shows the biggest effect on population percentage-wise. It seems there is still a westward migration going on, especially from the Northeast. It also appears that Californians are moving to adjacent states, probably in many cases motivated by the high housing, taxes, and other costs. There was a net flow of about 14,000 to Nevada, 9,000 to Oregon and a net inflow of almost 6,000 from New York to California. Bear in mind that the IRS data does not show movement of those who don't pay federal income taxes, like the poor, unless they are taken as dependents on someone's return. The maps also don't show movement to or from foreign countries. Even so, it seems reasonable to assume that these trends are consistent with population movement as a whole.
Idiocy or lack of education?
I have two short anecdotes about the sad state of knowledge in America today. My wife went to the store to buy some fish for tonight's dinner, a fish soup we both enjoy. She ordered a quarter pound of one particular fish. The new clerk at the meat counter scooped a bunch of it and placed it on butcher paper on the scales. It read .41 pounds. She asked if that was the right amount. My wife told her no, she wanted a quarter pound. The clerk, a young woman, asked if that was more or less than what she had on the scale. My wife had to give her instructions to take some off until it reached .25 pounds.
Now I just learned that a large freeway sign has been erected on Interstate 280 in San Jose near the Saratoga Avenue exit. These signs cost over $10,000 each. The sign reads "Saratogo Ave". I understand that whoever made the sign may not be from this area, but Saratoga is a common place name and has other uses. The Wikipedia page has 31 entries for it on its disambiguation page, including a fish, several battles, and a Chrysler model. CalTrans blames it on a contractor. Perhaps we can't expect laborers to be able to spell, but I think we can expect them to paint the same letters on the sign as written on the order from CalTrans and we certainly expect those guys to be able to spell the names on roadway signs. Considering the cost of these signs, we also should expect the CalTrans staff and the contractor's staff (which may be the Department of Corrections) to have close oversight over the spelling and overall accuracy of the signs before they are committed to metal.
I don't know whether to wallow in dismay at the stupidity of the world or rejoice in the fact I'm not that stupid. Did I just get a better education? Am I just more careful? Have I made any typos in this post? Better check.
Why all the smoking and drinking?
Would someone please send a 2017 calendar to all the publishers and producers out there. Somehow they haven't gotten the word that people don't smoke anymore, not most sane, admirable people anyway. I've noticed a trend in books and movies recently that feature leading characters, i.e. the "heroes" and "heroines" of the stories, who smoke and get drunk all the time. Supposedly these are sympathetic characters. These behaviors, however, do not make them look very admirable.
The days of Mad Men cocktail parties and chain smoking are long gone. I cannot remember the last time I saw anyone smoking in real life. It has been months, maybe years. I can't think of anyone I know who smokes. It's interesting that you can tell the demographic a movie or TV show is going for by who smokes. For the mainstream broadcast channels now like ABC, NBC, CBS, if a character smokes in one of their series, he or she is probably a bad guy. They've figured out that it is mostly the low-lifes who do (no offense to the non-low lifes who do as I know you exist). In fact, often the person doesn't smoke until it is revealed that the person is a bad guy. However, in many movies and on the cable channels or "arty" or counterculture channels, the lead characters smoke. Supposedly they are, or look, cool by doing this. I don't get it. They just look like idiots, definitely not sympathetic. Maybe the demographic they are targeting is the low-life demographic.
Examples of this trend in books: Behind Her Eyes by Sarah Pinborough, The Girl Before by JP Delaney, The Muse by Jessie Burton. All three of these are written by British women, but Pleasantville by Attica Locke, and American, can be added to the list. On TV, examples of shows where the "cool" leads smoke are Better Call Saul and Sneaky Pete. All of these drink quite a bit, too, although that varies. I'm afraid series and books like these will inspire some impressionable young people to take up smoking. The only good thing I can say about them is that these lead characters are all pretty much losers in life. If these kids pay close attention (good luck with that) maybe they'll see that smoking is not the way to a good life.
Two Chopin pieces on guitar
Two piano pieces arranged for guitar. Very short. The first one is a Waltz in A minor (Op. 34 No.2) and the second is Nocturne (Op. 9 No. 2). I think I play the second one a little better.
The Girl Before by J. P. Delaney
The Girl Before by J.P. Delaney
One star seems a bit harsh since it wasn't badly written, but in Goodreads, that merely means I didn't like it, not that it was terrible. I didn't get all the way through this one. It just got too creepy and graphic with the sex to be enjoyable. I got the feeling the whole plot was devised just to provide some soft-core porn gussied up as drama so that readers could pretend to themselves they were reading it for its literary value, like men who used to tell their wives they read Playboy for the articles.
Since this blog is about language, this recent Facebook thread of mine may be of interest to readers. Click on the image to get a larger version if you can't read it.
The Muse by Jessie Burton
Odelle is from Trinidad, living in London in the 1960s, trying to make it as a writer as she makes a living as a clerk in a shoe store. She manages to acquire a position as a typist at an art gallery and is taken under the wing of Marjorie Quick, an executive there. The story shifts to prewar Spain where Olive Schloss, a young woman, falls in love with Isaac Robles, an artist and revolutionary. Isaac and his half-sister Teresa are working as servants to the Schloss family. Olive's father is a renowned Austrian art dealer, her mother a disturbed British woman. Central to the story is a remarkable painting of a young woman carrying her own severed head while a lion looks on. The two stories merge, of course, as the plot reveals itself.
The author writes with erudition bordering on pretentiousness, but succeeds in giving a credible picture of both settings. The story is engaging the whole way. I listened to the audiobook version. The actress who reads the London portions is excellent, with a wonderfully charming Caribbean accent (when portraying Odelle) and upper class English accent (when portraying Quick or other Brits). On the other side, the actress who reads the Spanish portions is terrible. She can't act and her English so poor she mispronounces words constantly. Orange rhymes with flange. It's clear she is a native Spanish speaker. This choice may have provided us with an authentic Spanish accent, but at what price? She sounds like she's reading to three-year-olds, overacting and reading at a pace designed for a slow-witted Braille transcriber. She's more than a ham; she's bacon. I don't understand the choice since there is very little Spanish in the story, just a few words here and there.
For a long time I had a hard time believing the same author wrote the two threads of the story, the Spanish thread seeming so badly written. It just shows how important the reader is. Despite this drawback, I enjoyed the book. I thought the attempt to create a surprise ending by letting us know that Marjorie Quick had a secret failed, as I was able to guess the secret quite quickly (no pun intended), but the ending was still a mostly satisfying one.


text:
\section{Introduction}\label{intro}
\setcounter{equation}{0}

Let $\O$ be a bounded, open, connected subset in $\rm I\kern-.19emR^d$ ($d=2$ or $3$) with a Lipschitz continuous boundary $\partial \O$.
This paper studies a posteriori error estimates of nonconforming and discontinuous finite element methods for the following
interface problems (i.e., diffusion problems with discontinuous coefficients):
 \begin{equation}\label{scalar}
 -\nabla\cdot \,(\alpha(x)\nabla\, u) = f
 \quad \mbox{in} \,\,\Omega
 \end{equation}
with homogeneous Dirichlet boundary condition, $u = 0$ on $\partial\O$, for simplicity.

Here, $f \in L^{2}(\O)$ is a given function;
and diffusion coefficient $\alpha(x)$ is positive
and piecewise constant on polygonal subdomains of $\O$ with possible
large jumps across subdomain boundaries (interfaces):
\[
 \alpha(x)=\alpha_i > 0\quad\mbox{in }\,\O_i
 \quad\mbox{for }\, i=1,\,...,\,n.
\]
Here, $\{\Omega_i\}_{i=1}^n$ is a partition of the domain $\O$ with
$\O_i$ being an open polygonal domain. It is well-known \cite{Kel:74} that problem (\ref{scalar}) has a unique solution
$u$ in $H^{1+s}(\O)$ with possibly very small $s>0$.

Recently, in \cite{CaZh:15apriori} we obtained a priori error estimates for the nonconforming, the mixed, and the discontinuous
finite element approximations. Those estimates are robust with respect to the diffusion coefficient and optimal with respect to
local regularity of the solution with no assumption on the distribution of the diffusion coefficient.
This paper is a continuation of \cite{CaZh:15apriori} on the a posteriori error estimates. We refer readers to \cite{CaZh:15apriori}
for definitions of commonly used notations.

For the conforming finite element approximation  to the interface problem in (\ref{scalar}),
by using the diffusion coefficient to properly weight
the element residual and the edge flux jump, Bernardi and Verf\"urth in \cite{BeVe:00} (see also \cite{Pet:02})
showed that the resulting residual
based error estimator is locally efficient and globally reliable with the efficiency constant independent of
the jump of the diffusion coefficient.
Moreover, under the assumption of the quasi-monotone distribution of the diffusion coefficient
(see section 1.1 of \cite{CaZh:15apriori} on the QMA),
the reliability constant is proved to be uniform with respect to the jump as well.
Since then, various robust a posteriori error estimators have been constructed, analyzed, and implemented
(see, e.g., \cite{LuWo:04, CaZh:08a, Voh:11} for the conforming elements, \cite{Ain:05, CaZh:10a}
for the nonconforming elements,
\cite{Ain:07, Kim:07, CaZh:10a, DuLinZhang:16} for the mixed elements,  \cite{CaYeZh:09,ErSt:08,ErStZu:08} for the discontinuous elements, \cite{MuJa:13,MuJa:14} for the finite volume methods).
The robustness for those estimators was theoretically established again under the QMA.
However, numerical results by many researchers including ours strongly suggest that those estimators are robust
even when the diffusion coefficients are not quasi-monotone.

The purpose of this paper is to theoretically establish robust reliability bounds of the residual estimators
without the QMA for nonconforming and discontinuous finite element approximations.
The QMA is imposed to guarantee the desired approximation and stability properties of the Cl\'ement type interpolation (see  \cite{BeVe:00} for details), which is one of the key steps in obtaining the reliability bound of the residual based estimator.

For the conforming elements, this type of interpolations is defined on vertex patches through averaging and, hence, the QMA is required. One reason of using the Cl\'ement interpolation is due to its minimum regularity requirement of the approximated function as in the commonly used reliability analysis (see, e.g., \cite{BeVe:00}).
For the nonconforming and discontinuous elements, one may construct a modified
Cl\'ement interpolation satisfying the desired properties without the QMA (see \cite{CaHeZh:14}).
Due to the lack of the error equation, the reliability bound for discontinuous approximations is commonly
analyzed through the Helmholtz decomposition of the true error. Application of the Helmholtz decomposition, in turn,
leads to establishment of the reliability bound for conforming approximations and, hence, the requirement of the QMA.

In \cite{CaHeZh:14}, we introduced a new and direct analysis, that does not involve the Helmholtz decomposition,
for the two-dimensional nonconforming elements. In particular, we derived an $L^2$ representation of the error in the energy norm
that naturally contains three terms: the element residual, the face flux jump, and the face solution jump.
Due to a technical difficulty, the solution jump was modified at elements where the QMA is not satisfied.
The modified estimator was proved to be robustly reliable without the QMA. Unfortunately, robustness of local efficiency of the modified indicator requires the QMA.

With the help of our newly developed trace inequality in \cite{CaZh:15apriori},
we are able to bound the solution jump without any modification.
Moreover, instead of using the nonconforming Cl\'ement type interpolation as in \cite{CaHeZh:14}, we use the standard nonconforming interpolation and the piecewise constant projection for the respective nonconforming
and discontinuous elements, which fully takes advantage of the local feature of the element itself.
Both the approximations are element-wisely defined.
Thus, without the QMA, we are able to prove the robustness in both the
two- and three-dimension for the nonconforming and discontinuous elements.

The paper is organized as follows. Section~2 describes the nonconforming and the discontinuous Galerkin
finite element approximations and some preliminaries. Residual based a posteriori error estimators are described in
section~3, and local efficiency bounds are stated in section~4. Without the QMA, the robust reliability bounds are proved
for the nonconforming and the discontinuous Galerkin elements in both the two- and three-dimensions
in the section 5. \\

\section{Discontinuous Finite Element Approximations and Preliminaries}
\setcounter{equation}{0}

Assume that the triangulation ${\cal T}$ is regular
and that the physical interfaces $\{\partial\O_i\cap\partial\O_j\,:\, i,j=1,\,...,\,n\}$ do not cut
through any element $K\in{\cal T}$.
For the nonconforming finite element approximation, we only consider the Crouzeix-Raviart (CR)
linear element, and denote the  CR nonconforming linear finite element space by
$$
V^{cr} := \{ v \in L^2(\O) : v|_K \in P_1(K) \; \,\forall \, K\in{\cal T}\,
  \mbox{ and }\,\int_F \jump{v}\,ds =0 \; \forall  \,F\in{\cal E}\},
$$
where ${\cal E}$ is the set of all faces of the triangulation ${\cal T}$.
(A face in this paper means an edge or a face in the respective two- or three-dimension.)
Denote the discontinuous finite element space of degree $k\ge 0$ by
$$
D_k := \{ v \in L^2(\O) : v|_K \in P_k(K) \; \,\forall \, K\in{\cal T}\}.
$$

The corresponding variational formulation of problem (\ref{scalar}) with homogeneous boundary conditions
 is to find $u\in H_{0}^1(\O)$ such that
 \begin{eqnarray}\label{galerkin}
(\alpha \nabla u,\,\nabla v) &=& (f,v)\qquad \,\forall\,v\in H_{0}^1(\O).
\end{eqnarray}
The CR nonconforming finite element approximation is to find $u^{cr} \in V^{cr}$ such that
\begin{eqnarray} \label{problem_nc}
  ( \alpha\nabla_h u^{cr} ,\, \nabla_h v) &=& (f,v)  \qquad \,\forall\, v\in
  V^{cr}.
\end{eqnarray}
For any $K\in{\cal T}$ and some $\alpha>0$, let
 \[
 V^{1+\alpha}(K)=\{v\in H^{1+\alpha}(K)\,:\, \Delta\, v \in L^2(K)\}

 \]
and let
 \[
  V^{1+\alpha}({\cal T}) :=\{v\, :\, v|_K\in V^{1+\alpha}(K)\,\, \forall\, K\in{\cal T}\}.

  \]
In \cite{CaYeZh:09} we introduced the following variational formulation for the interface
problem in (\ref{scalar}): find $u\in V^{1+\epsilon}({\cal T})$ with $\epsilon >0$
 such that
 \begin{equation}\label{DGV}
 a_{dg}(u,\,v) = (f,\,v)\quad\forall\,\, v \in V^{1+\epsilon}({\cal T}),
\end{equation}
where the bilinear form $a_{dg}(\cdot,\,\cdot)$ is given by
\begin{eqnarray*}
a_{dg}(u,v)&=&(\alpha\nabla_h u,\nabla_h v)
 +\sum_{F\in{\cal E}}\int_F\gamma  \displaystyle\frac{{ \a_{\sF,_H}}}{h_F} \jump{u}
 \jump{v}\,ds \\[2mm] \nonumber
&&\quad -\sum_{F\in{\cal E}}\int_F\{\alpha\nabla
u\cdot{\bf n}_F\}_{w}^F \jump{v}ds -
\sum_{F\in{\cal E}}\int_F \{\alpha\nabla
v\cdot{\bf n}_F\}_{w}^F\jump{u}ds.
\end{eqnarray*}
Here, $\{\cdot\}_w^F$ is the weighted average,
${ \a_{\sF,_H}}$ is the harmonic average of $\alpha$ over $F$,
and $\gamma$ is a positive constant only depending on the shape of elements.
The discontinuous Galerkin finite element method  is then to
seek $u^{dg}_k \in D_k$ such that
\begin{equation}\label{problem_dg}
a_{dg}(u^{dg}_k,\, v) = (f,\,v)\quad \forall\, v\in D_k.
\end{equation}
Difference between (\ref{DGV}) and (\ref{problem_dg}) leads to the following error equation:
\begin{equation} \label{erroreq_dg}
a_{dg}(u-u^{dg}_k,\,v) = 0 \quad \forall \, v\in D_k.
\end{equation}
For simplicity, we consider only this symmetric version of the interior penalty discontinuous Galerkin finite element method
since its extension to other versions of discontinuous Galerkin approximations is straightforward.
Define the jump semi-norm and the DG norm by
$$
\|v\|_{J,F} = \sqrt{\displaystyle\frac{{ \a_{\sF,_H}}}{h_F}} \| \jump{v} \|_{0,F}
\quad\mbox{and}\quad
|\!|\!| v|\!|\!|_{dg} = \left(\|\alpha^{1/2}\nabla_h v\|_{0,\O}^2+\sum_{F\in {\cal E}}\|v\|_{J,F} ^2 \right)^{1/2},
$$
respectively, for all $v\in  H^1({\cal T})$.

In order to guarantee the robustness of the error estimate with respect to $\alpha$,
we choose harmonic weights in this paper:
$\omega_F^\pm = \displaystyle\frac{\alpha_F^\mp}{\alpha_F^-+\alpha_F^+}$.
It is easy to show that
\begin{equation} \label{weight1}
w_F^{\pm}\alpha_F^{\pm} \le \sqrt{\alpha^{\pm}{ \a_{\sF,_H}}}, \quad\,\,
 \frac{\omega_F^+}{\sqrt{\alpha_F^-}} \le \sqrt{\frac{1}{\alpha_{F,A}}},
	\,\quad \mbox{and} \quad\,
	\frac{\omega_F^-}{\sqrt{\alpha_F^+}} \le \sqrt{\frac{1}{\alpha_{F,A}}}.
\end{equation}
We shall use the following commonly used identity:
 \begin{equation}\label{jump-id}
 \jump{ u v}_F = \{v\}^w_F\, \jump{u}_F + \{u\}_w^F\, \jump{v}_F.
 \end{equation}

An inequality proved in \cite{CaZh:15apriori} plays an important role to bound the solution jump
in the reliability analysis for the nonconforming and discontinuous elements. For the convenience of readers,
we cite it here.

\begin{lem}
Let $F$ be a face of $K\in{\cal T}$, ${\bf n}_F$ the unit vector normal to $F$, and $s>0$.
Assume that $v$ is a given function in $V^{1+s}(K)$.
For any $w_h\in P_k(K)$, we have
 \begin{eqnarray}\label{tracecombined}
 \int_F \left(\nabla v\cdot{\bf n}_F\right)\, w_h \,ds
  &\leq & C\, h_F^{-1/2}\|w_h\|_{0,F}
 \left(\|\nabla v\|_{0,K} + h_K\|\Delta v\|_{0,K}\right),
\end{eqnarray}
with the constant $C$ independent of $h$ and $v$.
\end{lem}

\section{Residual-Based A Posteriori Error Estimators}
\setcounter{equation}{0}

This section describes local indicators and global estimators for nonconforming and discontinuous Galerkin finite element approximations.
The estimators for the nonconforming
elements introduced in \cite{CaHeZh:14} and  for the discontinuous elements in this paper are more accurate than the existing estimators
(see, e.g., \cite{Ain:05, CaYeZh:09})
and differ in replacing the face tangential
derivative jumps by the face solution jumps.

 \subsection{CR Nonconforming Elements}

For each $F\in{\cal E}$,
let ${\bf t}_F$ be the unit vector tangent to $F$ for $d=2$, and ${\bf n}_F$ be
the unit vector normal to $F$. Denote the tangential component of
a vector field $\mbox{\boldmath$\tau$}$ on $F$ by
 \[
 \gamma_F(\mbox{\boldmath$\tau$}) := \left\{ \begin{array}{llll} \mbox{\boldmath$\tau$}\cdot{\bf t}_F, & d=2,\\[2mm]
 \mbox{\boldmath$\tau$}\times {\bf n}_F, & d=3.
 \end{array}
 \right.
 \]
Denote the element residuals and the corresponding indicators by
 \[
  r^{cr}_K=f_0
  \quad \mbox{and} \quad
  \eta_{r,K}^{cr} = \displaystyle\frac{h_{_K}}{\sqrt{\alpha_{_K}}}\|r_K^{cr}\|_{0,K}, \quad \forall \; K\in {\cal T},
  \]

 respectively.
 Denote the respective face flux and tangential derivative jumps by
 \[
 j^{cr}_{n,F}=\jump{\alpha \nabla_h u^{cr}\cdot{\bf n}}_F, \quad\forall \,\, F \in {\cal E}_I
 \quad\mbox{and}\quad
  j^{cr}_{t,F}=\jump{\gamma_t(\nabla_h u^{cr})}_F, \quad\forall\,\, F\in{\cal E},
 \]
and the indicators corresponding to the face flux, tangential
 derivative, and solution jumps by
  \[
   \eta_{j,n,F}^{cr}=\sqrt{\displaystyle\frac{h_F}{{ \a_{\sF,_A}}}}\, \|j_{n,F}^{cr}\|_{0,F}, \quad
   \eta_{j,t,F}^{cr}=\sqrt{{ \a_{\sF,_H}} h_F} \,\|j_{t,F}^{cr}\|_{0,F},
  \quad\mbox{and}\quad
  \eta_{j,u,F}^{cr} = \sqrt{ \displaystyle\frac{{ \a_{\sF,_H}}}{h_F}}\, \| \jump{u^{cr}}\|_{0,F},
  \]
 respectively.
 Then the local indicator of the residual type for the nonconforming elements, introduced in
 \cite{CaHeZh:14} and to be studied in this paper, is given by
\[
	\eta_K^{cr} =
	\left(
	 	 \left({\eta^{cr}_{r,K}} \right)^2
	 	 + \sum_{F\in {\cal E}_K \cap {\cal E}_I }
		 	                \displaystyle\frac{1}{2} \left( \eta_{j,n,F}^{cr} \right)^2
			                 + \sum_{F\in  {\cal E}_K \cap {\cal E}_I}
		 	\displaystyle\frac{1}{2} \left( {\eta^{cr}_{j,u, F}}\right)^2
			  +\sum_{F\in  {\cal E}_K \cap {\cal E}_D}
		 	 \left( {\eta^{cr}_{j,u, F}}\right)^2
	 \right)^{1/2}.
\]
Now the global estimator for the nonconforming elements is given by
 \[
 \eta_{cr}=
 \left( \sum_{K \in {\cal T}}
  \left(\eta_K^{cr} \right)^2 \right)^{1/2}
 =  \left(  \sum_{K\in{\cal T}} \left( \eta_{r,K}^{cr} \right)^2
  + \sum_{F\in{\cal E}_I}   \left( \eta^{cr}_{j, n,F} \right)^2
  + \sum_{F\in{\cal E}}  \left(\eta^{cr}_{j,u, F}\right)^2
  \right)^{1/2}.
 \]

\begin{lem}\label{lem:svt}
Let $F\in{\cal E}_I$.
For any $v^{cr} \in V^{cr}$, we have
\begin{equation} \label{crjump}
 \|\jump{v^{cr}}\|_{0,F} \,\,
  \left\{\begin{array}{ll}
  =\displaystyle\frac{1}{\sqrt{12}}\,h_F\, \|\jump{\nabla v^{cr} \cdot {\bf t}_F}\|_{0,F}, & \mbox{if  } d=2,\\[6mm]
  \leq C\, h_F\, \|\jump{\nabla v^{cr}\times {\bf n}_F}\|_{0,F}, & \mbox{if  } d=3,
  \end{array}\right.
\end{equation}
where $C$ is a positive constant independent of $h_K$.
\end{lem}

Here and thereafter, we use $C$ with or without subscripts in this
paper to denote a generic positive constant, possibly different at
different occurrences, that is independent of the mesh parameter
$h_K$ and the ratio $a_{\max}/a_{\min}$ but may depend on the domain
$\O$.

\begin{proof}
The equality in (\ref{crjump}) is proved in \cite{CaHeZh:14} by a direct calculation.
To show the validity of the inequality in (\ref{crjump}), for any $v^{cr} \in V^{cr}$, note first that
its jump $\jump{v^{cr}}_F$ over $F\in{\cal E}_I$ is a linear function and that $\int_F \jump{v^{cr}}\,ds =0$.
If $\nabla \jump{v^{cr}}_F \times {\bf n}_F$ vanishes on $F$, then the jump $\jump{v^{cr}}_F$ on $F$ is constant and, hence, zero.
Now, the inequality in (\ref{crjump}) follows from the norms equivalence in a finite dimensional space
and the standard scaling argument.
\end{proof}

\begin{rem}
 Instead of the face solution jumps,
 existing residual based error estimators for the nonconforming elements
 use the face tangential derivative jumps. {\em Lemma~\ref{lem:svt}} indicates that
 our estimator $\eta_{cr}$ is less than the existing estimator and, hence, it is more accurate
 {\em (}see {\em Figure 6} in {\em \cite{CaHeZh:14})}.
 \end{rem}

\subsection{Discontinuous Elements}

Denote the element residuals and the corresponding indicators by
 \[
  r^{dg}_K=f_{k-1}+\nabla\cdot (\alpha\nabla u^{dg}_k)
  \quad \mbox{and} \quad
  \eta_{r,K}^{dg} = \displaystyle\frac{h_{_K}}{\sqrt{\alpha_{_K}}}\|r_K^{dg}\|_{0,K},
  \quad \forall \, K \in {\cal T}.
  \]

 respectively.
 Denote the respective face flux and solution jumps by
 \[
   j^{dg}_{n,F}=\jump{\alpha \nabla_h u^{dg}_k\cdot{\bf n}}_F, \,\;\forall \,\, F \in {\cal E}_I
   \quad\mbox{and}\quad
 j^{dg}_{u,F}=\jump{u_k^{dg}}, \,\, \forall \,\, F\in {\cal E},
 \]
and the indicators corresponding to the face flux and solution jumps by
  \[
   \eta_{j,n,F}^{dg}=\sqrt{\displaystyle\frac{h_F}{{ \a_{\sF,_A}}}}\, \|j_{n,F}^{dg}\|_{0,F}
   \quad\mbox{and}\quad
  \eta_{j,u,F}^{dg} = \sqrt{ \displaystyle\frac{{ \a_{\sF,_H}}}{h_F}}\, \| \jump{u^{dg}}\|_{0,F},
  \]
 respectively.
 Then the local indicator of the residual type for the discontinuous elements is given
\cite{CaYeZh:09} by
\[
	\eta_K^{dg} =
	\left(
	 	 \left({\eta^{dg}_{r,K}} \right)^2
	 	 + \sum_{F\in {\cal E}_K \cap {\cal E}_I }
		 	                 \displaystyle\frac{1}{2}\left( \eta_{j,n,F}^{dg} \right)^2
			                 + \sum_{F\in  {\cal E}_K\cap {\cal E}_I} \displaystyle\frac{1}{2}
		 	 \left( {\eta^{dg}_{j,u, F}}\right)^2
			 +\sum_{F\in  {\cal E}_K\cap {\cal E}_D}
		 	 \left( {\eta^{dg}_{j,u, F}}\right)^2
	 \right)^{1/2}.
\]
Now the global estimator for the nonconforming elements is given by
 \[
 \eta_{dg}= \left( \sum_{K \in {\cal T}} \left(\eta_K^{dg} \right)^2 \right)^{1/2}
 = \left(  \sum_{K \in {\cal T}}(\eta_{r,K}^{dg})^2
  + \sum_{F\in{\cal E}_I}  (\eta^{dg}_{j, n,F})^2 + \sum_{F\in{\cal E}}  (\eta^{dg}_{j,u, F})^2
  \right)^{1/2}.
 \]

\section{Efficiency Bounds}
\setcounter{equation}{0}

Let $f_{k}$ be the $L^2$ projection of $f$ onto $D_k$ for $k\geq 1$.
Denote local and global weighted oscillations by
$$
{\mbox{osc}}_\alpha(f,K) = \displaystyle\frac{h_K}{\sqrt{\alpha_K}}  \|f-f_{k-1}\|_{0,K} \quad\mbox{and}\quad
{\mbox{osc}}_\alpha(f,{\cal T}) = \left( \sum_{K\in{\cal T}} {\mbox{osc}}_\alpha(f,K)^2 \right)^{1/2},
$$
respectively.
The local efficiency bounds of all indicators described in the previous section have been established
without the QMA. For example, for the discontinuous Galerkin finite element approximation, it is proved in \cite{CaYeZh:09}
that for any $K\in {\cal T}$, there exists a positive constant $C$ independent of $\alpha$ and $h_K$ such that
 \begin{equation} \label{local efficiency}
 \eta_K^{dg} \le C\, \left(|\!|\!| u-u_{dg}^k |\!|\!|_{U\triangle_K} + {\rm osc \, }_\alpha(f, \triangle_K)\right),
 \end{equation}
where $\triangle_K$ is a local neighborhood of $K$.

The key idea of the proof is to use either element or edge bubble functions
in order to localize the error as well as to simplify the boundary conditions.
The proof of local efficiency bound similar to (\ref{local efficiency}) can be found in \cite{CaZh:10a, CaHeZh:14}
for the CR nonconforming element.

\section{Reliability Bounds for CR Nonconforming and Discontinuous Elements}
\setcounter{equation}{0}

In this section, we establish robust reliability bounds for the CR nonconforming and
discontinuous Galerkin approximations in both the two- and three-dimension.

\subsection{CR Nonconforming Elements}

Without the QMA, the robust reliability bound for the nonconforming elements was first established
in \cite{CaHeZh:14} for a slightly modification of the estimator $\eta_{cr}$ in the two-dimension.
The modification is due to the failure of bounding the solution jump term.
This difficulty may be overcome by using the trace
inequality introduced in \cite{CaZh:15apriori}.

Instead of using the modified Cl\'{e}ment-type interpolation \cite{CaHeZh:14} which may be extended
to the three-dimension in a straightforward manner, we use the standard nonconforming interpolation that can also be naturally extended to the three-dimension. Moreover, it is local
and, hence, has the approximation and stability properties needed for obtaining robust reliability bound
both without the QMA.
 To this end, let
 \begin{eqnarray*}
  W^{1,1}({\cal T}) &=&\{v\in L^2(\O)\, : \, v|_K\in W^{1,1}(K)\,\,\,\forall\, K\in {\cal T}\}\\[2mm]
 \mbox{and}\quad
 W ({\cal T}) &=& \{v\in W^{1,1}({\cal T})\, : \, \int_{F} \jump{v} ds =0\,\,\, \forall\, F\in {\cal E} \}.
 \end{eqnarray*}
Denote by $\theta_F ({\bf x})$ the nodal basis function of $V^{cr}_{\cal T}$ associated with the face
$F\in{\cal E}$, i.e.,
 \[
 \displaystyle\frac{1}{|F^\prime|} \int_{F^\prime} \theta_F ({\bf x})\, ds
 =\delta_{FF^\prime}
 \,\,\,\forall\, F^\prime\in{\cal E},
 \]
where $\delta_{FF^\prime}$ is the Kronecker delta. The local and global Crouzeix-Raviart interpolations are defined respectively by
 \[
  I^{cr}_K v = \sum_{F\in {\cal E}_K} \left(\displaystyle\frac{1}{|F|} \int_{F} v ds \right) \theta_F({\bf x})
 \quad\mbox{and}\quad
  I^{cr} v = \sum_{F\in {\cal E} } \left(\displaystyle\frac{1}{|F|} \int_{F} v ds \right) \theta_F({\bf x})
 \]
for the respective $v\in W^{1,1}(K)$ and $v\in W ({\cal T})$.
It was shown (see, e.g., Theorem 1.103 and Example 1.106 (ii) of \cite{ErGu:04}) that
for $v\in H^{1}(K)$
\begin{equation} \label{localcr}
\|v-I^{cr} v\|_{0,K} \leq C\, h_{K}\, \|\nabla v\|_{0,K} \quad\mbox{and}\quad
\| \nabla(v-I^{cr} v)\|_{0,K} \leq C\, \|\nabla v\|_{0,K}.
\end{equation}

 \begin{thm}\label{th:relcr}
Let $u$ and $u^{cr}$ be the solutions of {\em (\ref{galerkin})} and {\em (\ref{problem_nc})}, respectively.
Without the QMA in both the two- and three-dimension, the estimator $\eta_{cr}$ for the nonconforming elements satisfies
the following robust reliability bound:
 \begin{equation} \label{relcr}
 \|\alpha^{1/2}\nabla_h (u-u^{cr})\|_0
  \leq C\,\left(\eta_{cr} + {\mbox{osc}}_\alpha (f)\right),
 \end{equation}
 where $C$ is a positive constant independent of the $\alpha$.
\end{thm}

\begin{proof}
Let
 \[
 e^{cr}=u-u^{cr}
 \quad\mbox{and}\quad
 e_I^{cr} = I^{cr}u - u^{cr} = I^{cr} e^{cr}.
 \]
Then we have the following $L^2$ representation of the true error in the (broken) energy norm
(see Lemma 2.1 of {\cite{CaHeZh:14}}):
 \[
  \|\alpha^{1/2}\nabla_h e^{cr}\|_0^2
   = \sum_{K \in {\cal T}} (f, e^{cr}-
	e_I^{cr})_K -\sum_{F\in {\cal E}_I} \int_F j_{n,F}^{cr} \,\{e^{cr}-e_I^{cr}\}^w\,ds
	 -\sum_{F \in {\cal E}} \int_F \{ \alpha \nabla e^{cr} \cdot {\bf n} \}_w \, \jump{u^{cr}} \,ds.
	 \]
The first two terms of the above equality
may be bounded in a similar fashion as that in \cite{CaHeZh:14}.
That is, it follows from the Cauchy-Schwarz and triangle or trace inequalities, (\ref{localcr}),
and (\ref{weight1}) that
 \begin{equation}\label{CR-reliability 1}
  (f, \, e^{cr}-e_I^{cr})_K
	 \le  C\, \left( \eta^{cr}_{r,K} +{\rm osc \, }_\alpha(f,K)\right)\|\alpha^{1/2} \nabla_h e^{cr}\|_{0,K},
	\quad \forall \,\, K \in {\cal T},
\end{equation}
and
\begin{eqnarray}
	\int_F j_{n,F}^{cr} \{e- e_I^{cr} \}^w \,ds
	&\le&
		C\| j_{n,F}^{cr}\|_{0,F}
		\{\omega^+\|(e^{cr}-e_I^{cr})|_{K_F^-}\|_{0,F}
		+\omega^-\|(e^{cr}-e_I^{cr})_{K_F^+}\|_{0,F} \} \nonumber
	\\[2mm] \label{CR-reliability 2}
	&\le& C \sqrt{\frac{h_F}{{ \a_{\sF,_A}}}} \| j_{n,F}^{cr}\|_{0,F} \, \|\alpha^{1/2} \nabla e^{cr}\|
	_{K_F^+ \cup K_F^-},
	\quad \forall F \,\, \in {\cal E}_I.
\end{eqnarray}
To bound the third term on the solution jump, the key is the inequality in (\ref{tracecombined}), which
together with (\ref{weight1}) and the local efficiency bound of the element residual,
yields
\begin{eqnarray} \nonumber
		 && \int_F\{\alpha \nabla e^{cr} \cdot {\bf n}_F\}_w\, \jump{u^{cr}} \,ds \\[2mm] \nonumber
		&=&\int_F \jump{u^{cr}} \,\left(\o^+( \alpha^+ \nabla e^{cr}\cdot {\bf n})|_{K^+}
			+\o^- (\alpha^- \nabla e^{cr}\cdot {\bf n})|_{K^-} \right)\,ds\
		\nonumber \\[2mm]
		&\le &C\, \sqrt{\frac{ \alpha_{F,H}}{h_F}} \,\, \| \jump{u^{cr}}\|_{0,F} \,
			\sum_{K \in {\cal T}_F} \left(\|\alpha^{1/2} \nabla e^{cr}\|_{0,K}+
				h_K \alpha_K^{-1/2}\,\|f+\nabla \cdot (\alpha \nabla u^{cr})\|_{0,K}\right)
		\nonumber \\[2mm]  \label{CR-reliability 3}
		&\leq & C\, \eta^{cr}_{j,u,F} \,\sum_{K \in {\cal T}_F}\left(\|\alpha^{1/2} \nabla_h e^{cr}\|_{0,K}
		 +{\mbox{osc}}_{\alpha}(f,K) \right), \quad \forall \,\,F \in {\cal E}.
\end{eqnarray}
Summing (\ref{CR-reliability 1}) over $K\in {\cal T}$,  (\ref{CR-reliability 2}) over $F\in {\cal E}_I$,  and
(\ref{CR-reliability 3}) over $F\in {\cal E}$ implies the validity of (\ref{relcr}). This completes the proof of
the theorem.
\end{proof}

\subsection{Discontinuous Elements}

Without the QMA, the robust reliability bound for the discontinuous elements may be obtained in a similar
fashion as that for the nonconforming elements. Again, the key steps are the $L^2$ representation of
the true error and the inequality (\ref{tracecombined}) to bound the solution jump. Moreover, we simply use
the local constant average of the error instead of the modified Cl\'{e}ment interpolation due to the complete
local feature of the discontinuous elements.

Let $u$ and $u_k^{dg}$ be the solutions of (\ref{galerkin}) and (\ref{problem_dg}), respectively. Denote
the true error by
 \[
  e^{dg} = u-u^{dg}_k.
   \]
Let $\bar{e}^{dg}$ be piecewise constants on ${\cal T}$ with $\bar{e}^{dg}|_K$ being
the average of $e^{dg}$ on $K\in{\cal T}$. It is well known that
 \begin{equation} \label{localdg}
\|e^{dg} - \bar{e}^{dg}\|_{0,K} \leq C\, h_{K}\, \|\nabla\, e^{dg}\|_{0,K}, \quad \forall \,K\in {\cal T},
\end{equation}
where $C$ only depends on the regularity of ${\cal T}$.

\begin{lem}\label{5.6}
The true error of the discontinuous finite element approximation in the broken energy norm has the
following error representation:
\begin{eqnarray}  \nonumber
 \|\alpha^{1/2} \nabla_h \, e^{dg}\|_0^2
 &=& \sum_{K\in{\cal T}}  \left(f+\nabla \cdot (\alpha \nabla u_k^{dg}), \, e^{dg}-\bar{e}^{dg} \right)_K

  - \sum_{F\in{\cal E}} \int_F \{\alpha\nabla e^{dg}\cdot{\bf n} \}_w\, \jump{u_k^{dg}}\, ds \\ [2mm] \label{dg:5}
 &-&  \sum_{F\in{\cal E}_I} \int_F \jump{\alpha\nabla u^{dg}\cdot{\bf n}} \,\{ e^{dg} - \bar{e}^{dg}\}^w\, ds
   -\sum_{F\in{\cal E}} \int_F \gamma \displaystyle\frac{{ \a_{\sF,_H}}}{h_F}\, \jump{u_k^{dg}} \,\jump{\bar{e}^{dg}}\,ds. \,\,\,\,\,\,
\end{eqnarray}
\end{lem}

\begin{proof}
It follows from the error equation in (\ref{erroreq_dg}), integrations by parts, (\ref{jump-id}),
the continuities of the solution $u$ and the
normal component of the flux $-\alpha\nabla\,u$ across any face $F\in {\cal E}_I$, and the homogeneous
Dirichlet boundary condition that
\begin{eqnarray*}
  && \|\alpha^{1/2} \nabla_h \, e^{dg}\|^2_0
   = \left(\alpha \nabla_h e^{dg}, \,\nabla_h (e^{dg} -\bar{e}^{dg} )\right)  \\ [2mm]
 &=& \sum_{K\in{\cal T}} \left(f+\nabla\cdot (\alpha\nabla u^{dg}_k), \, e^{dg}-\bar{e}^{dg} \right)_K
   +\int_{\partial K} (\alpha\nabla e^{dg}\cdot{\bf n})(e^{dg} - \bar{e}^{dg}) \, ds \\ [2mm]
 &=&  \sum_{K\in{\cal T}} \left(f+\nabla\cdot (\alpha\nabla u^{dg}_k), \, e^{dg}-\bar{e}^{dg} \right)_K
   - \sum_{F\in{\cal E}_I} \int_F \{\alpha\nabla e^{dg}\cdot{\bf n} \}_w\, \jump{u_k^{dg} + \bar{e}^{dg}} \,ds \\[2mm]
 &&-\sum_{F\in{\cal E}_I} \int_F \jump{\alpha\nabla u^{dg}\cdot{\bf n}} \, \{ e^{dg} - \bar{e}^{dg}\}^w ds
  - \sum_{F\in{\cal E}_D} \int_F(\alpha\nabla e^{dg}\cdot{\bf n})(u_k^{dg} + \bar{e}^{dg}) \,ds.
\end{eqnarray*}
On the other hand, the fact that $a_{dg}(e^{dg}_k,\, \bar{e}^{dg}) = 0$ implies
 \[
 \sum_{F\in{\cal E}}\int_F\gamma  \displaystyle\frac{{ \a_{\sF,_H}}}{h_F} \,\jump{e^{dg}} \,\jump{\bar{e}^{dg}}\,ds
  -\sum_{F\in{\cal E}_I}\int_F\{\alpha\nabla e^{dg}\cdot{\bf n}\}_{w}\, \jump{\bar{e}^{dg}}\,ds
   -\sum_{F\in{\cal E}_D}\int_F(\alpha\nabla e^{dg}\cdot{\bf n} ) \,\bar{e}^{dg}\,ds
   =0.
 \]
Combining the above two equalities gives (\ref{dg:5}). This completes the proof of the lemma.
\end{proof}

\begin{thm}
Let $u$ and $u_k^{dg}$ be the solution of (\ref{galerkin}) and (\ref{problem_dg}), respectively.
Without the QMA in both the two- and three-dimension, the estimator $\eta_{dg}$ for the discontinuous
element approximation satisfies the following robust reliability bound:
\begin{equation} \label{reldg}
 |\!|\!| u-u^{dg}_k|\!|\!|_{dg}
 \leq C\,\left(\eta_{dg} + {\mbox{osc}}_\alpha(f,\,{\cal T})\right),
\end{equation}
where $C$ is a positive constant independent of the $\alpha$.
\end{thm}

\begin{proof}
By the definition of the DG norm $ |\!|\!| \cdot|\!|\!|_{dg} $, to prove the validity of (\ref{reldg}), it suffices to show that
 \begin{equation} \label{reldg1}
 \|\alpha^{1/2}\nabla_h\, (u-u^{dg}_k)\|_0
 \leq C\,\left(\eta_{dg} + {\mbox{osc}}_\alpha(f,\,{\cal T})\right).
\end{equation}
To this end, denote the estimators corresponding to the element residual, the face flux jump, and the
 solution jump by
  \[
   \eta^{dg}_r = \left(\sum_{K\in{\cal T}} \left(\eta^{dg}_{r,K}\right)^2 \right)^{1/2},
   \quad
   \eta^{dg}_{j,n} =\left(\sum_{F\in{\cal E}_I} \left(\eta_{j,n,F}^{dg} \right)^2\right)^{1/2},
   \quad\mbox{and}\quad
   \eta^{dg}_{j,u} = \left( \sum_{F\in{\cal E}} \left( \eta_{j,u,F}^{dg}\right)^2 \right)^{1/2}.
   \]
  respectively. Denote four terms in Lemma~\ref{5.6} by $I_1$, $I_2$, $I_3$, and $I_4$, respectively.
Hence,
 \[
  \|\alpha^{1/2} \nabla_h \, (u-u^{dg}_k)\|_0^2 = I_1+I_2+I_3+I_4.
  \]
 In a similar fashion as the proof of Theorem~\ref{th:relcr}, the $I_i$ for $i=1,\,2,\,3$
may be bounded as follows:
 \begin{eqnarray*} \label{dg1}
 I_1
  & \le & C\, \left( \eta^{dg}_r
   + {\rm osc \, }_{\alpha}(f,{\cal T}) \right)  \|\alpha^{1/2}\nabla_h \,e^{dg}\|_0, \quad
   I_2
	\leq  C\, \eta^{dg}_{j, u}
	\left( \|\alpha^{1/2} \nabla_h\, e^{dg} \|_0 +  {\rm osc \, }_{\alpha}(f, {\cal T})\right),

		\\[2mm] \label{dg3}
  \mbox{and}\quad  I_3
   & \le&   C\,  \eta^{dg}_{j,n}\,
    \|\alpha^{1/2}\nabla_h\, e^{dg}\|_0.

	\end{eqnarray*}

To bound $I_4$, for all $F\in{\cal E}$, it follows from the triangle and the Cauchy-Schwartz inequalities,
the continuity of the solution $u$, the trace inequality, and (\ref{localdg}) that
 \begin{eqnarray*}
   && \int_F \displaystyle\frac{{ \a_{\sF,_H}}}{h_F} \, \jump{u^{dg}_k}\, \jump{\bar{e}^{dg}} \, ds
   \leq \int_F \displaystyle\frac{{ \a_{\sF,_H}}}{h_F} \, \jump{u^{dg}_k}\,
      \left(\|\jump{e^{dg}}\|_{0,F} + \|\jump{e^{dg}-\bar{e}^{dg}}\|_{0,F}\right)\,ds

   \\ [2mm]
  &\leq  &

  \left(\eta_{j,u,F}^{dg}\right)^2
   + \eta_{j,u,F}^{dg}\,\sqrt{\displaystyle\frac{{ \a_{\sF,_H}}}{h_F}}\, \|\jump{e^{dg}-\bar{e}^{dg}}\|_{0,F}
   \leq \left(\eta_{j,u,F}^{dg}\right)^2
   + C\, \eta_{j,u,F}^{dg}\,  \sum_{K \in {\cal T}_F} \|\alpha^{1/2}\nabla_h e^{dg}\|_{0, K}.
\end{eqnarray*}
Summing over all faces $F \in {\cal E}$ and using the Cauchy-Schwarz inequality give
 \[
  I_4= \gamma\,\sum_{F \in {\cal E}} \int_F \displaystyle\frac{{ \a_{\sF,_H}}}{h_F}\, \jump{u^{dg}_k}\, \jump{\bar{e}^{dg}}\, ds
  \leq  C\, \left(  \left(\eta^{dg}_{j,u}\right)^2 +  \eta^{dg}_{j,u}\, \|\alpha^{1/2} \nabla_h\, e^{dg} \|_0 \right).
\]
Combining the bounds for all $I_i$ and using the Cauchy-Schwarz inequality, we have
 \[
 \|\alpha^{1/2} \nabla_h \, e^{dg}\|_0^2
 \leq C\, \left( \eta^{dg}_{r} + \eta_{j,n}^{dg}    +  \eta_{j,u}^{dg}
  + {\rm osc \, }_{\alpha}(f, {\cal T})\right) \, \|\alpha^{1/2} \nabla_h\, e^{dg} \|_0
  + C \left( \left( \eta_{j,u}^{dg} \right)^2 + {\rm osc \, }_{\alpha}(f,{\cal T})^2 \right),
 \]
which, together with the Cauchy-Schwarz inequality, implies
 \[
 \|\alpha^{1/2} \nabla_h \, e^{dg}\|_0 \leq C\,\left( \eta_{dg} + {\rm osc \, }_{\alpha}(f,{\cal T})\right).
 \]
This proves the validity of (\ref{reldg1}) and, hence, the theorem.
This completes the proof of the theorem.
\end{proof}

redpajama_set_name: RedPajamaArXiv


text:
Couple buys OKC Cafe
Sam RoykaAugust 31, 2022 2:44 pm
When the previous owner of Cafe Oasis, 1135 NW 25 St., could no longer open the door, two employees had a choice to make.
When the cafe, adjacent to Super Cao Nguyen supermarket, was up for sale, business and life partners Norman Haase and Emily Shan were the only interested buyers.
They took over last year because they wanted to "keep the doors open for the Cafe Oasis legend," Haase said.
As the cafe celebrates its 20th anniversary, the pair reminiscences on their time working at the Taiwanese cafe.
Haase said the previous owner had been running "all cylinders" of the restaurant and "it just eventually got to the point where she couldn't deal with the physical nature of the job and the work."
"It was time to go ahead and move on, in her case, and that's when the opportunity came up," he said.
The couple needed more help running the business without their former boss.
Though Haase and Shan officially acquired ownership of the cafe last October, the transition was a cooperative effort with the previous owner, lasting a few months.
It took a lot of communication to make a smooth transition.
"The restaurant business over the last couple of years is a very contrarian business to move into," Hasse said, mentioning the restaurant below them had just gone out of business.
In business, Haase said, "first and foremost, there's always uncertainty. It kind of all worked out, you know, in an odd sort of way," he said, calling Oasis, "part of the fabric" of Oklahoma City as one of the first boba tea shops to open in the Asian District.
"The whole time that the restaurant's open, six days a week, she and I are there doing something or picking something up or, you know, doing something business related," Haase said. "Which is well over 70 hours a week. But we're busy. We're busy people."
"Everything that we use in our drink space is imported so you get a traditional Taiwanese boba tea experience when you come to Cafe Oasis, which is something that maybe even some of the long standing customers don't even realize," Haase said.
Emily Shan highlighted large bags of their real tea in two varieties: black and jasmine green. She said they use real tea instead of instant tea powder.
Even when the tea got expensive, "25, 26 dollars per pound," Shan said, they still bought it because they did not want to change companies.
"They know us, we know them," Shan said. "A customer says 'Hey, your tea is really good. [We] taste the difference. So that's why I keep using it," she said.
Haase agreed.
"Everything's got a secret recipe," he said. "It's not easily duplicated, people come there for the taste, they come there for the drink, you know, the atmosphere, it's kind of got everything you'd want to have in a small cafe type environment in the heart of a big city. Every day brings something different,"
When asked what his favorite part was about the cafe, Haase said it was "the fact that you can talk to a customer that's been coming there for 18 years and loved every single bit of their experience."
While the owner may change, Shan said, the food and the experience will never change.
With ingredients too, Shan said, quality matters.
"Bubble Tea, food, meat, veggie, everything – we buy the quality," she said.

redpajama_set_name: RedPajamaCommonCrawl


text:
[#]: subject: (Making portable functions across serverless platforms)
[#]: via: (https://opensource.com/article/21/6/quarkus-funqy)
[#]: author: (Daniel Oh https://opensource.com/users/daniel-oh)
[#]: collector: (lujun9972)
[#]: translator: ( )
[#]: reviewer: ( )
[#]: publisher: ( )
[#]: url: ( )

Making portable functions across serverless platforms
======
Quarkus Funqy brings portability to serverless functions.
![Parts, modules, containers for software][1]

The rising popularity of serverless development alongside the increased adoption of multi- and hybrid-cloud architectures has created a lot of competition among platforms. This gives developers many choices about where they can run functions on serverless platforms—from public managed services to on-premises [Kubernetes][2].

If you've read my previous articles about [Java serverless][3], you learned how to get started [developing Java serverless functions][4] with Quarkus and how those serverless functions can be [optimized][5] to run on Kubernetes. So what should you do next to make your serverless functions fit better with the many choices available to you?

As a clue, think about why the Linux container (Docker, [LXC][6], cri-o) has become so popular: Portability. It's what made containers the de facto packaging technology for moving things from a developer's local machine to Kubernetes environments at scale. It means developers and operators don't need to worry about incompatibility and inconsistency between development and production environments.

For adopting multi- and hybrid cloud architectures, these container portability benefits should also be considered for serverless function development. Without portability, developers would likely have to learn and use different APIs, command-line interface (CLI) tools, and software development kits (SDKs) for each serverless platform when developing and deploying the same serverless functions across multiple serverless runtimes. Developers, who have limited resources (e.g., time, effort, cost, and human resources), would be so overwhelmed by the options that they would find it difficult to choose the best one.

![Many serverless runtime options][7]

(Daniel Oh, [CC BY-SA 4.0][8])

### Get Funqy the next time you hit a serverless dance floor

The [Quarkus Funqy][9] extension supports a portable Java API for developers to write serverless functions and deploy them to heterogeneous serverless runtimes, including AWS Lambda, Azure Functions, Google Cloud, and Knative. It is also usable as a standalone service. Funqy helps developers dance on the serverless floor without making code changes.

Here is a quick example of how to build a portable serverless function with Quarkus Funqy.

### 1\. Create a Quarkus Funqy Maven project

Generate a Quarkus project (`quarkus-serverless-func`) to create a simple function with Funqy extensions:

```
$ mvn io.quarkus:quarkus-maven-plugin:1.13.6.Final:create \
       -DprojectGroupId=org.acme \
       -DprojectArtifactId=quarkus-serverless-func \
       -Dextensions="funqy-http" \
       -DclassName="org.acme.getting.started.GreetingResource"
```

### 2\. Run the serverless function locally

Open the `Funqy.java` file in the `src/main/java/org/acme/getting/started` directory:

```
public class Funqy {

    private static final [String][10] CHARM_QUARK_SYMBOL = "c";

    @Funq (1)
    public [String][10] charm(Answer answer) { (2)
        return CHARM_QUARK_SYMBOL.equalsIgnoreCase(answer.value) ? "You Quark!" : "👻 Wrong answer";
    }

    public static class Answer {
        public [String][10] value; (3)
    }
}
```

In the code above:

(1) Annotation makes the method an exposable function based on the Funqy API. The function name is equivalent to the method name (`charm`) by default.
(2) Indicates a Java class (`Answer`) as an input parameter and `String` type for the output.
(3) `value` should be parameterized when the function is invoked.

**Note**: Funqy does type introspection at build time to speed boot time, so the Funqy marshaling layer won't notice any derived types at runtime.

Run the function via Quarkus Dev Mode:

```
`$ ./mvnw quarkus:dev`
```

The output should look like:

```
__  ____  __  _____   ___  __ ____  ______
 --/ __ \/ / / / _ | / _ \/ //_/ / / / __/
 -/ /_/ / /_/ / __ |/ , _/ ,< / /_/ /\ \
\--\\___\\_\\____/_/ |_/_/|_/_/|_|\\____/___/
INFO  [io.quarkus] (Quarkus Main Thread) quarkus-serverless-func 1.0.0-SNAPSHOT on JVM (powered by Quarkus x.x.x.) started in 2.908s. Listening on: <http://localhost:8080>
INFO  [io.quarkus] (Quarkus Main Thread) Profile dev activated. Live Coding activated.
INFO  [io.quarkus] (Quarkus Main Thread) Installed features: [cdi, funqy-http, kubernetes]
```

Now the function is running in your local development environment. Access the function with a RESTful API:

```
`$ http://localhost:8080/charm?value=s`
```

The output should be:

```
`👻 Wrong answer`
```

If you pass `value=c` down as a parameter, you will see:

```
`You Quark!`
```

### 3\. Choose a serverless platform to deploy the Funqy function

Now you can deploy the portable function to your preferred serverless platform when you add one of the Quarkus Funqy extensions in the figure below. The advantage is that you will not need to change the code; you should need only to adjust a few configurations, such as function export and target serverless platform.

![Quarkus Funqy Extensions][11]

(Daniel Oh, [CC BY-SA 4.0][8])

Try to deploy the function using [Knative Serving][12] (if you have installed it in your Kubernetes cluster). Add the following extensions to the Quarkus Funqy project:

```
`$ ./mvnw quarkus:add-extension -Dextensions="kubernetes,container-image-docker"`
```

Open the `application.properties` file in the `src/main/resources/` directory. Then add the following variables to configure Knative and Kubernetes resources—make sure to replace `changeit` with your container registry's group name (username in DockerHub):

```
quarkus.container-image.build=true
quarkus.container-image.group=changeit
quarkus.container-image.push=true
quarkus.container-image.builder=docker
quarkus.kubernetes.deployment-target=knative
```

Containerize the function, then push it to the external container registry:

```
`$ ./mvnw clean package`
```

The output should end with `BUILD SUCCESS`. Then a `knative.yml` file will be generated in the `target/kubernetes` directory. Now you should be ready to create a Knative service with the function using the following command (be sure to log into the Kubernetes cluster and change the namespace where you want to create the Knative service):

```
`$ kubectl create -f target/kubernetes/knative.yml`
```

The output should be like this:

```
`service.serving.knative.dev/quarkus-serverless-func created`
```

### 4\. Test the Funqy function in Kubernetes

Get the function's REST API and note its output:

```
$ kubectl get rt
NAME URL READY REASON
quarkus-serverless-func  <http://quarkus-serverless-func-YOUR\_HOST\_DOMAIN>   True
```

Access the function quickly using a `curl` command:

```
`$ http://http://quarkus-serverless-func-YOUR_HOST_DOMAIN/charm?value=c`
```

You see the same output as you saw locally:

```
`You Quark!`
```

**Note**: The function will scale down to zero in 30 seconds because of Knative Serving's default behavior. In this case, the pod will scale up automatically when the REST API is invoked.

### What's next?

You've learned how developers can make portable Java serverless functions with Quarkus and deploy them across serverless platforms (e.g., Knative with Kubernetes). Quarkus enables developers to avoid redundancy when creating the same function and deploying it to multiple serverless platforms. My next article in this series will explain how to enable CloudEvents Bind with Java and Knative.

--------------------------------------------------------------------------------

via: https://opensource.com/article/21/6/quarkus-funqy

作者:[Daniel Oh][a]
选题:[lujun9972][b]
译者:[译者ID](https://github.com/译者ID)
校对:[校对者ID](https://github.com/校对者ID)

本文由 [LCTT](https://github.com/LCTT/TranslateProject) 原创编译,[Linux中国](https://linux.cn/) 荣誉推出

[a]: https://opensource.com/users/daniel-oh
[b]: https://github.com/lujun9972
[1]: https://opensource.com/sites/default/files/styles/image-full-size/public/lead-images/containers_modules_networking_hardware_parts.png?itok=rPpVj92- (Parts, modules, containers for software)
[2]: https://opensource.com/article/19/6/reasons-kubernetes
[3]: https://opensource.com/article/21/5/what-serverless-java
[4]: https://opensource.com/article/21/6/java-serverless-functions
[5]: https://opensource.com/article/21/6/java-serverless-functions-kubernetes
[6]: https://www.redhat.com/sysadmin/exploring-containers-lxc
[7]: https://opensource.com/sites/default/files/uploads/choices.png (Many serverless runtime options)
[8]: https://creativecommons.org/licenses/by-sa/4.0/
[9]: https://quarkus.io/guides/funqy
[10]: http://www.google.com/search?hl=en&q=allinurl%3Adocs.oracle.com+javase+docs+api+string
[11]: https://opensource.com/sites/default/files/uploads/funqyextensions.png (Quarkus Funqy Extensions)
[12]: https://knative.dev/docs/serving/

redpajama_set_name: RedPajamaGithub


text:
The D.C. Blacks is an African-American prison gang in the United States whose members are from Washington D.C. They are allied with the Black Guerrilla Family and some other black prison gangs. The Aryan Brotherhood is one of their main rivals. Although the D.C. Blacks are one of the largest prison gangs within penitentiaries, they are small compared to the gangs outside of the prison system, such as the Bloods and the Crips.

History
The D.C. Blacks prison gang is said to have originated in the late 1960s or the early 1970s. From being in prison, the D.C. Blacks became enemies with another prison gang called the Aryan Brotherhood, which is a group consisting of only convicted white men. The race wars against the D.C. Blacks raged across the federal prison system in the early 1980s and again in the 1990s when two of the high-ranking officers within the D.C. Blacks were stabbed and killed at the United States Penitentiary in Lewisburg, Pennsylvania by Aryan Brotherhood members. The race war in the federal system between the Aryan Brotherhood and the D.C. Blacks started on November 22, 1981 when a member of the Aryan Brotherhood, Thomas Silverstein, murdered a member of the D.C. Blacks, Robert M. Chappelle. An FBI investigation was sparked when Chappelle's body was found dead in his cell at the United States Penitentiary in Marion, Illinois. The race war continued when Silverstein killed the national leader of the D.C. Blacks, Raymond "Cadillac" Smith, on September 27, 1982. The violent campaign against the D.C. Blacks was at the center of the government's 2002 indictment against the Aryan Brotherhood when one of the leaders from the Aryan Brotherhood allegedly ordered the 1997 killing of two D.C. Blacks at Lewisburg with an invisible ink message written in urine. This message was sent to Lewisburg to warn their other members that the D.C. Blacks called hits on two of their members. Messages began to be going back and forth between the two penitentiaries calling hits on both gangs.

Individuals from both the D.C. Blacks and the Aryan Brotherhood have testified in court, giving the public a general idea of what life at USP Marion looked like.

References

Prison gangs in the United States
African-American gangs
Gangs in Washington, D.C.
African-American history of Washington, D.C.

redpajama_set_name: RedPajamaWikipedia


Those control-freaks at the Olympics once again are banning the participants from blogging.
Posted on Monday, January 30th, 2006 at 1:00 pm. Subscribe to the comments feed. Both comments and pings are currently closed. Post on your own blog.
The Canadian Olympic Committee has ruled that athlete blogs — as long as they report on the athletes' own experiences — are not included in the IOC ban.
There is an interesting issue here, for sure.
What's with the phrases "professionalism" and "lack of professionalism?" Did I miss something? I thought the olympics were "amateur" events. Hello? Thank God for the mute button. The former Olympian NBC commentators are bitter that they're too old to compete. Pikabo Street(among others) really has something against Julia Mancuso. I'm REALLY psyched that Julia won the Gold, not only because she's deserving of it, but also because her detractors will be eating crow.
I always tend to go with the definition of amateur as someone who "does it for love" as opposed to a "professional" who is typically someone who does it for money. I prefer amateurs.


Did you want to save your wedding bouquet,forever?
Yet it never looks as good as on that special day.
Send me a photo of your bouquet and I will paint you a beautiful painting that can be placed anywhere in your home.
It will not duplicate of your bouquet, but rather a watercolor painting created with the flowers that bring back loving memories.
Art Size 11 X 14 $ 250.
Art Size 18 x 24 $ 350.
Art work will arrived unframed.
four legged best friend. Pastel creates a nice texture and must be framed behind glass.
For all the cat lovers this is the purr-fect gift for yourself or a friend . Pastels are best preserved behind glass. Name tag included upon request.


HOW many of you have heard of MILLIONAIRE MIND INTENSIVE (MMI)?
T Harv Eker, the author of the best selling book - Secrets of The Millionaire Mind, has designed a series of programs and training.
One of the most famous programs or the beginner program is the MILLIONAIRE MIND INTENSIVE (MMI). It is a three days program from early morning till evening.
1. Worthy to attend Millionaire Mind Intensive?
2. Is Millionaire MindIntensive useful?
3. Can I be a Millionaire after attending Millionaire Mind Intensive???
I have the same questions! But his book (Secrets of The Millionaire Mind) is really convincing and powerful. It stirs a lot of thoughts in my mind. So I am fully motivated to attend the Millionaire Mind Intensive Singapore.
Sadly I paid for the tickets, while others got free tickets from somewhere else.
Anyway, the ~ S$ 100/pax is utterly well spent for this three days course.
I will briefly describe the highlights of the event.
As you can see, few hundreds of people are in a hall with excitement and anticipation.
Even though I do hope to see T Harv Eker in the training, that is only a dream. Instead of Harv, Mac Attram is the lead trainer for this Millionaire Mind Intensive Singapore.
He is undeniable a good speaker and trainer. He can engage the audience easily and possess wonderful skills in storytelling. Needless to say, he is confident, humorous, entertaining and knowledgeable. But he can be quite particular and fierce on certain things such as video recording (prohibited throughout the event) or undesired interruption of the activities led by him.
But no worry, he is considered an excellent speaker, which mean you are in good hand when you see him.
A three days event is really intensive and could be tiring. So Success Resource always keep the energy of their events, including this one, at very high level. So you will expect some dancing, clapping and high-five throughout the event. These are what make the event fun and enjoyable.
Ok, I think I talk too much on the trainer and how the event is conducted.
The main purpose is to change your mindset towards money and money management.
Firstly everyone will be given a workbook. Mostly are fill-in-the-blanks and plenty space for participants to take note. This is GOOD!
Then at the beginning of the MMI, they lead you to think about your mindset toward money. There is a series of questions to help us getting the answers from our inner hearts. E.g. Money is root of all evil? Money isn't important?
Once you have a rough idea what money and being rich mean to you. Then they slowly instill the correct mindset in you.
They talk about financial freedom (passive income > Expenses), passive income, money management and etc.
One of the most important take-away is the JAR SYSTEM.
The JAR System is basically the money allocation system. There are 6 accounts under the JAR Sysmte. E.g. 55% of your income spent on necessity; 10% put in investment (Financial Freedom Account); 10% put in Education account and others.
This is a viable system to me. Even though they recommend certain percentages on each account, I will prefer to set the percentage for myself. Generally we always spill our accounts into Expenses and Saving (possibly investment as well). This doesn't include some plans for self improvement.
A lot time, we are stingy on education (That's me). So this jar system suggests that we spare some money to be spent on educations, be it a short term course, training and talks, to learn something new.
Once you allocate a budget for certain thing (education for this case), you are mentally prepared to spend the money on it. Agree? PAY YOURSELF FIRST.
At least, I feel that way. Some money allocated to join Toastmasters, I pay the membership fee with the money without feeling "pain" in the heart.
They talk about Money Blueprint and Beliefs.
The roots of a tree produce the fruits of the tree. In short, the roots produce the fruits.
It makes sense! So our mind is like the root, what we think and feel will lead to the results.
T Harv Eker well known saying: Thoughts lead to Feelings, Feelings lead to Action, Action brings Results.
During this part, the speaker shared some stories from the book (exactly the same) to prove that it has to do with out mind. However they don't really emphasize on setting our Money Blueprint (throughout the seminar) that aggressively like the book does. I suppose this is an important part as Money Blueprint determines the value we set for ourselves. They do talk about the golden goose story and ask us to set a value. However they should put on a bit weight on this part, in my opinion.
Then here comes the interesting and useful part. Identify how we get the belief about money and remove it. E.g. your parents show certain attitudes towards money and this leaves an impact on you. You tend to follow your model (parents in this case) unconsciously.
NOTE: I do not work for Success Resources or MMI.
One way they think can change our mind is by doing declarations. Reading our some positive sentences + some actions to let these thoughts settle in our mind.
Identify your purpose. As motivator always say, your life purpose or purpose of bring rich must be greater than yourself. if we focus on traveling around the world, buying big houses and etc, we cannot go far and will not be Happy.
So they ask us to think and write down our purposes of being wealthy.
If we wake up every morning knowing our life purposes, will we feel bored or demotivating? Instead we will know how to get the stage we want.
There are other parts like money personality (Spender, Saver, Monk and Avoider), acknowledging successes (Success Breeds Success) and others.
They are trying to remove our negative emotions towards money and re-frame the past.
Call To Action! Encouragement like "Act in spite of fear". Our brain naturally protects us and warns us of danger. A lot of "what if" will pop out in our mind especially when we do something new and adventurous.
So here is the interesting thing, MMI tells us that the secret of freedom is to realize that you don't have to believe your mind! (WHAT so is our soul the one tells our brain, "I DON'T BELIEVE YOU"??? Haha, Sorry I am confused) Anyway, we need to have awareness about our thoughts and say "Thank you for sharing" to the negative ones.
ACT IN SPITE OF FEAR!
Mac said: "If you want to get rich, the first step is to start a BUSINESS!"
*You will expect an interesting "Arrow Breaking" Activity as described in the book too.
Do you notice I put a lot of Minion High Five photo in there? That's exactly what they love to ask us to do! Give high five to your neighbours and shout "You! Have a millionaire mind!"
All in all, as I said, it is worthy to attend this mindset changing program.
My biggest take-away is - There is nothing wrong to be wealthy, instead with the wealth we have, we can bless more people. The negative thoughts about money shall be removed and we shall take actions to get rich!
You must be OPEN and PARTICIPATE to fully experience their programs. Just remove the skeptical mind and go to have FUN. It is a great place to know more people too, just beware of aggressive MLM people :) And please train your stamina as three days are quite tiring too.
P/S: Don't waste your money to buy the over-priced and thin book "SpeedWealth".
Oh ya, the best part is, they give us a 90-days wealth conditioning program workbook too! This workbook can help us to retain the lessons during MMI and root the lessons in mind. NICE!!!
Guys, Enjoy the Millionaire Mind Intensive and Be a Millionaire!!!
Toastmasters Club - A non-profit organization which provides a platform for members to practice public speaking.
Now I actively involve in the world largest professional club - Toastmasters Club of Singapore.
Toastmasters Club organizes International Speech contest annually. It is the Olympics of Public Speaking and a highly regarded competition. The contestants will first compete at Club level before moving on to Area, Division, National, Regional, Semi-Final and Final. The most exciting part is, the Semi-Final and Final are organized in Vancouver, Canada.
This is my dream, and I take action by participating in the contest. Honestly, I have never been so serious in preparing a speech. I wrote my draft one month before the contest date, sought mentor-ship, practiced more than 50 times. I even practiced in my mind before I shut myself down on bed.
It took quite some efforts I would say, but not torturing.
I really didn't expect I could win anything after knowing all the finest speakers in our club signing up the contest. The contestants included the previous World 2nd Runner Up. But still, I hoped miracle to happen. So I just tried my best.
Do you want to know what is my speech content and how is my performance that evening?
I talked about "Never Try, Never Know". This is a topic which resonates with me a lot because I am about going to try something new and shocking to the others.
Anyway, Thanks God everything was smooth and I had delivered what I could just as I expected. I thought I was fine as my delivery was at my 100%.
That's before I listened to others.
After listening to a few, I knew I stand no chance.
Firstly, I was the first to present, nobody's going to remember me unless others were way too lousy.
Secondly, other speakers were 300% more humorous and speech contents were 300% better than mine.
Thirdly, I just knew I was at the losing edge.
Well, after the final speaker who was the previous World Second Runner-Up, I knew I would bring back nothing.
Hahaha. Ok I wrote in a too negative and sad way.
Humor is an important element in a speech as it can engage, enchant and entertain the audience including the judges. The harder the audience laugh, the more the audience enjoy. Humor can arouse audience attention too, at least they won't look at their hand phones.
I did include humor in my speech, more to actions and vocal variety types, e.g. funny actions. But the others created humor through the structure, content and language.
For example, "My wife asked me to bring my kids to Disneyland, but I was scared of roller coaster. At the end, my kids happily followed me because I scared my wife more "
"Inspirational speaker loves to say if you follow your dream, anything is possible. So I am inspired and decide to follow my dream. Since young, I dream to get pregnant"
These speakers are so humorous until they can make the audience laugh throughout at least 80% of their speeches. The most important thing is - they manage to convey their speech message at the same time. This is definitely not EASY!
Perhaps I should watch more comedies so that I can learn how to crack better and damn funny jokes in English. Choices of words, twisting of sentences, cheeky expressions and so on.
Yup, I believe sense of humor can be nurtured, it just needs practices!
So I will continue my humorous speech projects in Toastmasters. Hopefully I will be able to craft a humorous yet meaningful speech very soon.
Normal business presentation is not an issue at all. But when come to storytelling, I believe I need a boost! The structure, the choice of words and etc. I need to improve myself on these so that I can be more inspiring,convincing, engaging and entertaining. Ah! Creativity is one important element too. But good language is needed to ensure the creativity is well presented.
OK. Lots of things to improve.
The approaches to improve, undeniably, are to listen more and read much more. Perhaps story books or novels. So that I get used to writing stories and being able to narrate in better ways.
To me, others are more natural in their delivery. Perhaps they speak English most of the time, unlike a mandarin speaker here (⟶ me). They crack jokes so naturally, I suppose they master the rhythm. Every language has its rhythm when it comes to speaking, like a melody of a song.
Pronunciation, enunciation and intonation come along closely if we want to deliver a good speech. Mistakes in these can confuse the audience and disconnect them from following the speakers.
I am glad that my 50 times practices and my mentors help a lot on this.
Still I find my delivery a little bit not natural. Do you feel so?
I don't know la. I just feel such way.
So the only way, again, is practice! I should give more speeches in the club then. LOL!
But I shouldn't feel so negative, after all this is my first time.
I am satisfied that everything goes smoothly, good body language, no nervousness at all, good audience engagement despite being the first speaker.
Thanks all those good and encouraging words from some members too.
True enough, there are huge gaps between me and the giants.
But I shall not give up and one day, I will be one of the giants too!
Finally the days of memorizing script are temporary OVER! hahaha.
Today must be a wonderful and blissful day!
In the first dream, I was standing in front of a big crowd. There were a few primary schools kids sitting behind me looking very nervous. I looked around and Ah! I was in a debate competition (looked like one). I was the tallest among them, perhaps I failed to reminisce my "child form". As a toastmasters trained person, I immediately turned to my neighbors and shared with them some skills to do a proper self introduction (Don't ask me why we need to give self intro, I do not understand either). Of course I was the first speaker to establish a role model to the others. I remembered I exaggerated my intonation, enunciation and pronunciation during my introduction. I was so confident without any nervousness as if I was dominating the stage and crowd.
Triumph like a kid below, not Triumph like D Trump.
The happiness was damn real! I could feel it, people congratulated me and the event continued with a cocktail session as if celebrating my victory.
I still remembered vividly, I talked to myself: "I can't believe I can win a debate in English, when I can speak like a pro!? LOL"; "Perhaps may be I am extremely confident, that's why I can speak so well"
HAHAHA. OK done with the stupid monologue part.
The most interesting part was, I was required to give 2 minutes victory speech! What a nonsense dream!
I slid the cake and tasted it. The cake was so delicious, creamy and satisfying sweet (I am a sweet stuff lover anyway). Then I saw a lot of kids coming towards me. Most of them are Caucasian kids. I was so happy to see them and played with them joyfully. The exhilaration was so beyond description. We hold hands and ran around. We laughed and cared nothing. It was just like going back to the innocent childhood.
There was a kid telling me that there were a lot more cakes waiting for us. So all of us rushed there and started eating more cakes. The variety of cakes was impressive, they had different layers with different colors. I kept eating like no tomorrow, my unlimited appetite could be compared to a black hole! Some kids even told me, next time they would bring their special cakes from their countries for me. Yes Yes Yes, I couldn't wait for that!
Later on, all of us started dancing. You would not believe that, everyone was doing Indian dance! HAHAHA. (Since when I am a fan of Indian Dance?! LOL) I even saw Indian uncles and aunties demonstrating the Indian dances to us! What a hilarious and enjoyable moment.
In a few minutes, I was literally "transferred" back to my house (Pooooffff~~~) meeting my brother and the uncle, they asked me where I got all those cakes.
blu... blu... blu... I opened my eyes.
Two neighbors in a flat; one with a kid but poor, one without any kid but rich. The poor looks happy but the rich looks sad. Because there is a baby smiling to the poor but the money doesn't smile to the rich.
Undeniable, one day I also want to have my own family and kids, if that's God's will and blessing.
Anyway, happiness can be as simple as having a sweet dream.
In fact, reading truly teaches me a lot of things and motivates me in different aspects.
Recently I am reading/listening to an audio book (for the first time) called OUTWITTING THE DEVIL, by Napoleon Hill. I am a fan of Napoleon. I strongly recommend everyone to read THINK AND GROW RICH, a motivational book that can boost your spirit.
The purpose of writing this blog post is to record down the methods protecting us against drifting.
1. Do your own thinking on all occasions. The fact that human beings are given complete control over nothing save the power to think their own thoughts is laden with significance.
I have to confess, I am one lazy bug to think on my own. Some time, I opt to listening to others' ideas and seek solutions/recommendations from others. This number 1 is already a big slap on my face to wake me up. I need to have my own thinking, or else who am I? For example, when customer asks me some technical questions, I will do little thinking and dial my boss's number to seek opinions. Perhaps I have no confidence on my answer OR I choose not to think about it myself.
Thus, say "No" to this and start thinking independently. Don't be lazy to come out with our own thoughts.
2. Decide definitely what you want from life: then create a plan for attaining it and be willing to sacrifice everything else, if necessary, rather than accept permanent defeat.
We are brought up by systematic education, most part of the world is practicing this. Study hard, get good grade and get an excellent job. But the question is, is it what we want from life? Most of the people including me do not know our life purposes at some points of time. Fortunately, some do know their purposes in life. Unfortunately, most do not dare to take the leap in faith. Imagine a manager with $ 100,000 annual income is deciding whether to quit his job and start his/her dream business or keep the status quo. What will be your advice? If he/she decides to quit, he/she has to sacrifice the steady paycheck and takes a risk to venture into new adventure.
Even though the sacrifices are/might be humongous, the fulfillment, gratification and achievement will absolutely satisfy our deepest desires.
A definite goal is necessary and crucial in everyone's life. If we know our definite goal in life, we shall waste time no more and work hard to move towards that striking goal.
3. Analyze temporary defect, no matter of what nature or cause, and extract from it the seed of an equivalent advantage.
Chinese famous saying goes, "Failure is the mother of success". It is not about how hard we fall, but how much we learn from the failure. Temporary failures contribute to future successes. To say this, it is pretty easy. However, the fear of failure has deterred a lot of people from even trying.
We need to know, failure is not scary, it is an educational lesson. I love what Thomas Edison had said, "I haven't failed. I have just found 10,000 ways that won't work". A little positive thinking is required here. In short, don't be defeated by failure; transform temporary failures to be weapons to conquer our future.
4. Be willing to render useful service equivalent to the value of all material things you demand of life, and render the service first.
From personal interpretation, it talks about the art of giving. We always love to take rather to give. Little example, I love lunch treats from others, but I am not really willing to treat them back (for those not so closed one). I have to confess, this is bad. A peaceful world needs to be in balance of give and take. Imagine everyone in this world only takes, then who gives?
We are familiar with the well known teaching "Give First". I believe if we are willing to give sincerely, people will recognize and be willing to render back. Imagine providing services is like a circle, at the end, the first to offer help will get help from others too.
Note: the highest level of rendering is, provide without expecting any return.
5. Recognize that your brain is a receiving set that can be attuned to receive communications from the universal storehouse of infinite intelligence, to help you transmute your desires into their physical equivalent.
I notice a lot of books love to cite "Infinite intelligence". This is how they fill the spiritual needs in human. It is very true, human can't live without faith. That's why the world has a lot of different religions. For me, Lord Jesus Christ is the infinite intelligence. All wisdom comes from Him, the creator of this world. Through prayer, I commit my desires and dreams to Him. I pray for wisdom to identify my life purposes, I pray for courage to take actions, I pray for guidance to keep me in check.
The prayers are the communications with God.
6. Recognize that your greatest asset is time, the only thing except the power of thought which you own outright, and the one thing which can be shaped into whatever material things you want. Budget your time so none of it is wasted.
This is the biggest slap to wake me up. Time is limited and precious; it is our greatest asset. However I love to waste it in my games, hangout and entertainment. I admire those who are willing to sacrifice sleeping time, hanging out time and fun time to work relentlessly towards their aims. Many successful people sleep less (like 4-6 hours), for instances, Barack Obama and Elon Musk. I am fond of this quote from Donald Trump, "How does somebody that's sleeping 12 and 14 hours a day compete with someone that's sleeping 3 or 4?". Note: Sleep is important!
Besides saving time from cutting sleeping time, the wise management of time in the day is imperative. If you have decided to manage your time wisely, I suggest to work on the habits; Reduce slowly the time-wasting activities; Pick up some beneficial habits like reading during leisure time; Occupy free time with some courses to upgrade yourselves.
7. Recognize the truth that fear generally is a filler with which the devil occupies the unused portion of your mind. That it is only a state of mind which you can control by filling the space it occupies with faith in your ability to make life provide you with whatever you demand of it.
Fear, the number one tool used by the devil, is truly dominating our lives. To name a few, the fear of failure, the fear of losing and the fear of criticism. However, we need to know we are in control of our lives. Fear is not our master. Fear is inevitable, so we need to recognize it and think of ways to overcome it. Let's say we are afraid to start a business due to a lot of uncertainties. What we can do to overcome our fear is to do research and study to clear all doubts and uncertainties.
Fear is manageable if you are willing to do so. As the writer explained, we can control by countering our fear with faith. Having faith on ourselves is the key. Be optimistic.
8. When you pray, do not BEG! Demand what you want and insist upon getting exactly that, with no substitutes.
This point has two parts; Pray but not Beg and insist exact demand.
Insisting exact demand is valid when we know what we want. A very firm desire which is unchangeable over time and unshakable over influence of others. Once we know that demand is the best for us, how could we be satisfied with any substitute?
Again, knowing what we want in life is extremely important.
9. Recognize that life is an cruel taskmaster and that either you master it or it masters you. There is no half-way or compromising point. Never Accept from life anything you do not want. IF that which you do not want is temporarily forced upon you, you can refuse. In your own mind, to accept it and it will make way for the thing you do want.
Life is indeed about choices. Choice to be mastered or choice to master. If we didn't want to do any decision or action, we would be mastered by others. On the contrary, if we will to take charge of our lives, we can make a difference. Take myself as an example, I have graduated with good results, followed the norm to get a job and perhaps along this path, I will get incremental pay check. This typical life, I would say, is mastered by others. My bosses and the companies are deciding my future; I am not taking charge of my life. So I always have the ambition to start on my own and take back the decision making rights. Napoleon is right about "Accept it and it will make way for the thing you do want". Perhaps we can refer to law of attraction, power of subconscious mind and etc, I do believe if we desire something so desperately, we will take actions to acquire, achieve and accomplish it.
10. Lastly, remember that your dominating thoughts attract, through a definite law of nature, by the shortest and most convenient route, their physical counterpart, be careful what thoughts you dwell upon.
Have you ever experienced, you mind cannot control your thoughts? Simple example, you are sleeping in a dark + creepy room, a lot of scary imaginations and thoughts pop out, and you simply cannot stop them. Perhaps we should do some mind exercises to control our thoughts. One exercise I can think of is; be conscious on your thinking. Once some undesired thoughts come out, stop them immediately through your conscious mind. Soon, we can control our mind better and positive thoughts can emerge well. So our dominating thoughts attract their physical counterpart. As I share in previous point, the stronger the desire, the faster the actions taken, the earlier the physical fruits can be reaped.
Be definite in everything you do and never leave unfinished thoughts in the mind. From the habit of reaching definite decisions on all subjects.
All in all, in order to prevent drifting in life, we need a clear and precise direction. Whatever we are doing, they should contribute to our ultimate goals. Focus on what we want and eliminate unnecessary thoughts. Remember that we are in control of our mind.
"With the tongue we praise our Lord and Father, and with it we curse human beings, who have been made in God's likeness. Out of the same mouth come praise and cursing. My brothers and sisters, this should not be."
"Look at her, so ugly still dare to carry LV bag. The bag 100% is counterfeit!". "Go to hell, you stupid idiot". "He will never ever succeed in life, if he did, the Sun would rise from the west!".
These sentences are so common in our daily lives. Judging, accusing and cursing people are what we do best. It is so natural for us to say those words which can hurt and break others' hearts. Often we forget they are made in God's image as well. Cursing them is equivalent to humiliating God. The most interesting fact in James 3:9-10 is, we use the same tongue to praise our Lord.
Personally, I used to indulge in gossiping about people. Whenever I detected some fresh news, my radar automatically activated its reception. Sometime I shared the gossip I have in order to exchange some other news. However at one point of time, I felt so guilty because I discovered my news were false after sharing with my friends. Gossiping is as bad as cursing because some time we don't even know whether what we share is true fact. Imagine, we praise God with our foul mouths, will God be pleased?
Thus, we need to be conscious about the words coming our from our mouths. Our mouths are meant to communicate with one another and worship God. We cannot curse and praise God with the same mouth. It is easy to come out with this conclusion, however, it takes a lot of efforts and determination to eliminate our habit of judging, gossiping and cursing. I believe step by step, we can make a change. May God's strength and wisdom be with us.
"But He said to me, "My grace is sufficient for you, for my power is made perfect in weakness." Therefore I will boast all the more gladly about my weaknesses, so that Christ's power may rest on me."
Verse of the day! 2 Corinthians 12:9. This carries an important lesson which impacts me a lot. We always boast about our strengths and glories during interview, chit chatting and writing. However, we (at least I) never thought of boasting about our weaknesses. God tells us that His power is made perfect in weakness. I strongly believe no one except Jesus is perfect, we all have different weaknesses. For example, I always have a serious problem of 3 minutes fever. I was so excited about selling phone casings on Carousell in May this year. Successful example of a friend doing this inspired me to venture in this business. Booking some stocks and listing the items on Carousell were fun and interesting at the beginning. 3 months down the road, I was bored with the tedious buy and sell process. The excitement was gone. Eventually, I put up my white flag and left my Carousell account aside.
I seldom talked about this little business in front of my friends because it was a shame to me. This experience amplified my weakness. So instead of feeling shameful, I should humbly commit this weakness of mine to Lord Jesus. I believe as long as we willingly confess our weaknesses to God, He will hear our voices and lend a hand to us. Just like what 2 Corinthians 12:9 tells us; we should boast about our weaknesses and Christ's power may rest on us. With the wisdom and strength from God, we take actions and eliminate our weaknesses. As people know about our weaknesses and witness our changes, by then, we can be good testimonial of God and share this to encourage others. Every weakness we have is an opportunity for God to show His power in our lives.
Moreover, God teaches us the attitude of humble too. God loves humble people who are not arrogant and not boastful of themselves. Even we have great successful achievements in life, we should not boast about it. Praises from others' mouths are always better and truthful than coming from own mouth.
I am a Dreamer: Oversea Robbing Mission!
Body felt exhausted and brain juice was running real low, I switched off my brain and rested comfortably on my bed.
Yawn, I woke up at home. There, I saw my cousin (阿颜) and remembered I wanted to go his house to have a festive feast (Perhaps is ghost month). But it was too far from my house, I couldn't go without a car. I was so desperate to go, probably my stomach complaint too hard. Then I asked my cousin whether he was going back. And he said yes, but when stepping out of my house, I saw my aunts and other cousins came, they brought down all the food and set them up like catering. I was so happy until I forgot what food there was. I remember... Curry?
When I turned to my back, out of sudden I physically appeared in another place. This time is a flower garden.
I saw a gang of strangers but I felt like I knew them. They walked towards me. We had a little chat, and know what the topic was about? Robbing somebody oversea. I remembered vaguely the excitement when we decided on this mission. "He deserved it! He was so rich and we should target him", circulating in my mind. The excitement and the sensation was so real. Then we somehow came to a consensus and a plan which I had forgotten. What I remembered was I happily left the garden and turned my head back, I saw vivid and colourful sea of flowers, purple, yellow and etc. They were so lively and dancing gracefully. I could sense the joy from them.
Story seemed to fast forward when I suddenly appeared in an airport! That's it, it made sense because it was an oversea Mission! Wohoo, my brain told me the airline was EMIRATES! In real life I took once, it gave me Super good impression.
This made me even more excited! I bought a big backpack and hold some stuffs on my hand. I saw a little cute plant (something like Money Plant) in its flower pot. I somehow knew the purpose of plant, it was to distract the officer on my Mission to rob people! "Hahaha". So they would ask a lot about the plant and forgot about my big backpack (Super naive!!!).
The airport was so huge and looked sophisticated. I remembered how impressed I was at there. The spacious lobby, the cool air-cond, the exciting Mission, my adrenaline level was so high! I also couldn't wait to hop onto the Emirates airplane!
When I approached the airport scanner gantry, I saw a guy in his uniform with Super Black Face! He was not in a good mood man! Then I put my stuffs down on the scanner belt and ready for them to get scanned, including my little cute flower pot. Out of sudden, the officer was mad and raged, he flipped my stuffs downside up just like flipping a table! He showed his poker face! But I felt INFURIATED. I quickly attended to my stuffs on the floor and my little cute flower pot was broken into pieces and the soil was everywhere. I was sad and mad at the same time. But wait! I was rushing to meet my friends, they all passed the scanner already. I was so nervous and needed to hurry up! I quickly ran toward another lanes and suddenly something strange popped out in my mind. I saw some lady officers were handling the other lanes, they were Japanese! And they are wearing big earphones. My mind told me they were listening to some training because they got no free time to attend physically a training. "Omg! Out of story".
I ran to the scanner and wanted to take out my passport.
But wait, I couldn't FIND IT!!! WALAO! Not this time! Where was my damn passport! I took out all the cards in my backpack pocket. I saw my EzLink card only, NO SIGN OF PASSPORT!
The image of airplane taking off was flashing in my mind again. I was so so so MAD and ANGRY, shouted loudly, "WHY WHY WHYYYYY!!!"
Haha. I had a weird dream again. That was a failed mission! But I think I would never rob someone in real life. LOL!!!
Love these funny dreams lah!
Before it faded away, I hold the pieces of memory and wrote them down.
I am going to write down all my weird dreams here in my blog! A DREAM Blogger! wohoo. Haha.
And my dreams got colors! Do you? Haha.