text:
Rockfish Program
Rockfish Program -
(1) General. The owners and operators of catcher vessels, catcher/processors, and shoreside processors authorized as participants in the Rockfish Program must comply with the applicable recordkeeping and reporting requirements of this section and must assign all catch to a rockfish cooperative or rockfish sideboard fishery, as applicable at the time of catch or receipt of groundfish. All owners of catcher vessels, catcher/processors, and shoreside processors authorized as participants in the Rockfish Program must ensure that their designated representatives or employees comply with all applicable recordkeeping and reporting requirements.
(2) Logbook -
(i) DFL. Operators of catcher vessels equal to or greater than 60 ft (18.3 m) LOA participating in a Rockfish Program fishery and using trawl gear must maintain a daily fishing logbook for trawl gear as described in paragraphs (a) and (c) of this section.
(ii) ELB. Operators of catcher/processors permitted in the Rockfish Program must use a combination of NMFS-approved catcher/processor trawl gear ELB and eLandings to record and report groundfish and PSC information as described in paragraph (f) of this section to record Rockfish Program landings and production.
(3) eLandings. Managers of shoreside processors that receive rockfish primary species or rockfish secondary species in the Rockfish Program must use eLandings or NMFS-approved software as described in paragraphs (e) and (f) of this section, instead of a logbook and WPR, to record Rockfish Program landings and production.
(4) Production reports. Operators of catcher/processors that are authorized as processors in the Rockfish Program must submit a production report as described in paragraphs (e)(9) and (10) of this section.
(5) Product transfer report (PTR), processors. Operators of catcher/processors and managers of shoreside processors that are authorized as processors in the Rockfish Program must submit a PTR as described in paragraph (g) of this section.
(6) [Reserved]
(7) Vessel monitoring system (VMS) requirements (see § 679.28(f)).
(8) Rockfish cooperative vessel check-in and check-out report -
(i) Applicability -
(A) Vessel check-in. The designated representative of a rockfish cooperative must designate any vessel that is authorized to fish under the rockfish cooperative's CQ permit before that vessel may fish under that CQ permit through a check-in procedure. The designated representative for a rockfish cooperative must submit to NMFS, in accordance with (8)(ii), a check-in designation for a vessel:
(1) At least 24 hours prior to the time the catcher vessel begins a fishing trip to fish under a CQ permit; or
(2) At least 1 hour prior to the time the catcher/processor begins a fishing trip to fish under a CQ permit; and
(3) A check-in designation is effective at the beginning of the first fishing trip after the designation has been submitted.
(B) Vessel check-out. The designated representative of a rockfish cooperative must designate any vessel that is no longer fishing under a CQ permit for that rockfish cooperative through a check-out procedure. A check-out report must be submitted to NMFS, in accordance with (8)(ii), within 6 hours after the effective date and time the rockfish cooperative ends the vessel's authority to fish under the CQ permit.
(1) If the vessel is fishing under a CQ permit for a catcher vessel cooperative, a check-out designation is effective at the end of a complete offload;
(2) If the vessel is fishing under a CQ permit for a catcher/processor cooperative, a check-out designation is effective upon submission to NMFS.
(ii) Submittal. The designated representative of the rockfish cooperative must submit a vessel check-in or check-out report electronically. The rockfish cooperative's designated representative must log into the online system and create a vessel check-in or vessel check-out request as indicated on the computer screen. By using the NMFS ID password and submitting the transfer request, the designated representative certifies that all information is true, correct, and complete.
(iii) Information required. The vessel check-in or check-out report must contain the following information:
(A) CQ permit number;
(B) ADF&G vessel registration number(s) of vessel(s) designated to fish under the CQ permit;
(C) USCG designation number(s) of vessel(s) designated to fish under the CQ permit; and
(D) Date and time when check-in or check-out begins.
(9) Rockfish CQ cost recovery fee submission (See § 679.85).
(10) Rockfish Ex-vessel Volume and Value Report -
(i) Applicability. A rockfish processor (as defined at § 679.2) that receives and purchases landings of rockfish CQ groundfish must submit annually to NMFS a complete Rockfish Ex-vessel Volume and Value Report, as described in this paragraph (r)(10), for each reporting period for which the rockfish processor receives rockfish CQ groundfish.
(ii) Reporting period. The reporting period of the Rockfish Ex-vessel Volume and Value Report shall extend from May 1 through November 15 of each year.
(iii) Due date. A complete Rockfish Ex-vessel Volume and Value Report must be received by the Regional Administrator not later than December 1 of the year in which the rockfish processor received the rockfish CQ groundfish.
(iv) Information required.
(A) The rockfish processor must log in using the rockfish processor's password and NMFS person ID to submit a Rockfish Ex-vessel Volume and Value Report. The NMFS software autofills the rockfish processor's name. The User must review the autofilled cells to ensure that they are accurate. A completed application must contain the information specified on the Rockfish Ex-vessel Volume and Value Report with all applicable fields accurately filled-in.
(B) Certification. By using the rockfish processor NMFS ID and password and submitting the report, the rockfish processor certifies that all information is true, correct, and complete to the best of his or her knowledge and belief.
(v) Submittal. The rockfish processor must complete and submit online by electronic submission to NMFS the Rockfish Ex-vessel Volume and Value Report available at https://alaskafisheries.noaa.gov.
(s) Amendment 80 Program -
(1) General. The owners and operators of Amendment 80 vessels must comply with the applicable recordkeeping and reporting requirements of this section. All owners of Amendment 80 vessels must ensure that their designated representatives or employees comply with all applicable recordkeeping and reporting requirements.
(2) Logbook-DCPL. Operators of Amendment 80 vessels must use a daily cumulative production logbook for trawl gear as described in paragraph (a) of this section to record Amendment 80 Program landings and production.
(3) Check-in/check-out report, processors. Operators or managers of an Amendment 80 vessel must submit check-in/check-out reports as described in paragraph (h) of this section.
(4) Production report. Operators of Amendment 80 vessels that use a DCPL must submit a production report as described in paragraph (e)(10) of this section.
(5) Product transfer report (PTR), processors. Operators of Amendment 80 vessels must submit a PTR as described in paragraph (g) of this section.
(6) Annual Amendment 80 cooperative report -
(i) Applicability. An Amendment 80 cooperative issued a CQ permit must submit annually to the Regional Administrator an Amendment 80 cooperative report detailing the use of the cooperative's CQ.
(ii) Time limits and submittal.
(A) The annual Amendment 80 cooperative report must be submitted to the Regional Administrator by an electronic data file in a NMFS-approved format; by fax: 907-586-7557; or by mail sent to the Regional Administrator, NMFS Alaska Region, P.O. Box 21668, Juneau, AK 99802-1668; and
(B) The annual Amendment 80 cooperative report for fishing activities under a CQ permit issued for the prior calendar year must be received by the Regional Administrator not later than 1700 hours A.l.t. on March 1 of each year.
(iii) Information required. The annual Amendment 80 cooperative report must include at a minimum:
(A) The cooperative's actual retained and discarded catch of CQ and GOA sideboard limited fisheries (if applicable) by statistical area and on a vessel-by-vessel basis;
(B) A description of the method used by the cooperative to monitor fisheries in which cooperative vessels participated; and
(C) A description of any actions taken by the cooperative against specific members in response to a member that exceeded the amount of CQ that the member was assigned to catch for the Amendment 80 cooperative.
(D) For each Amendment 80 cooperative, the percent of groundfish retained by that Amendment 80 cooperative of the aggregate groundfish retained by all Amendment 80 vessels assigned to that Amendment 80 cooperative using the following equations:
50 CFR § 679.5


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cd server
C:\Python34\python -m http.server 8080

redpajama_set_name: RedPajamaGithub


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Sergei Tcherepnin Aviary Clones 2018, installation view.
motion activated LEDs, motion activated sound, aviary netting, inkjet print dimensions variable.
Centred around Len Lye's noise-making kinetic sculpture and a set of audio recordings held in the Len Lye Foundation Archive, Sensory Agents focuses on the role sound plays in Lye's work, and links Lye to a younger generation of artists who share his interest in the capacity of sound and music to elicit sensory responses.
Sergei Tcherepnin Aviary Clones 2018, installation detail.
Work by Len Lye alongside installations and new commissions by Yuko Mohri (JP), Sergei Tcherepnin (US) and Danae Valenza (AU), three international artists working across sculpture, sound and musical composition.
Witnessing Lye's steel sculpture in motion is a highly physical experience, with the sounds produced by their movements – their force, energy, rhythm and resonance – vital to their sensory impact and appeal. Working with steel, Lye developed a range of techniques to heighten the potential sound-producing qualities of his sculptures, including the use of bells and percussive 'strikers'. This gave Lye the idea to record and make these new sounds available to musicians and composers as source material for their compositions, expanding their material for music.
In keeping with this idea, Sensory Agents also presents newly commissioned compositions by contemporary artists and composers using the sounds of Lye's sculpture alongside original recordings held in the Len Lye Foundation Archive. It opens a new evaluation of his work in terms of sound and music, to consider them, in Lye's own words, as 'musical instruments rather than visual kinetic works of art'.


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Fully blaming Marie Kondo for costing me $118. I still have a long way to go before mustering up the courage to put all my clothes in a single pile (spoiler alert: it would probably take up my entire living room). However, in recent months I've been trying to be more mindful of what I purchase and what I hang on to.
If you aren't staring at your feet are you even a blogger?
I went in to lulu a couple weeks ago for an "I'm home on a Saturday and why the hell not" epic Fitting Room Session (Part I & Part II), and the Round Trip Jacket was the number one piece that put an instant giddy smile on my face.
Note: I am 5'9″ and wearing size 10, one up from TTS.
The product description refers to this piece as 'body-skimming', and I don't disagree. I am usually an 8, but this jacket is pretty form-fitting even after sizing up to a 10. The sleeves are full length, but don't have any thumbholes. Because the fabric stretches, you don't lose any length in the sleeves when you have to do important things like fix your ponytail.
Overall length was a big selling point for me on how this jacket fits. My height is all in the torso, therefore some designs can fall in a weird spot on me. Not this time. Shorter women will find their backsides fully covered, but on taller women like me, it's going to hit you in a pretty flattering spot.
The Round Trip Jacket is meant for Office/Travel/Commute, so it features a headphone port and two zip pockets on the front. There's a tiny internal Gu pocket in one of them, but that's all you've got. No thumbholes, nothing else gimmicky.
The ribbing down the sides provides some nice flexibility, which is probably I love running around in this jacket so much. Even though it's a slim fit, I don't feel like my movement is restricted in any way.
Aesthetically, there's a ruched band across the waist for slimming effect. On the back, the ruched panel and slight flare in the design add a nice feminine touch.
I flubbed in the IGTV video and called it Glyde Ultra, but this piece's outer layer is Swift Ultra. (#badblogger) For those who don't spend too much time memorizing lululemon's textile lineup, this is the same fabric that their running shorts are made of. That means it's lightweight, 4-way stretch that moves in any direction you want to. It's lined with light luon, so there's a degree of coziness that comes with the slim fit.
I remember putting this jacket on and experiencing instantaneous giddiness, so you can say it's a win for me. My office is business casual, so I've already been able to sneak this one into the rotation with some black jeans & moto boots and call it an outfit. Many of the structured jackets I own have a certain degree of pulling when I start moving and stretching all around, but it doesn't happen with the Round Trip Jacket, which is probably why I'm so happy with my purchase.
The Round Trip Jacket is a keeper, and while I will sit here all day and try to convince myself I'm NOT going to go back and pick up a black one, that's probably a lie.
It's funny that you mention the Dance Studio Jacket. I have it in two colors and it feels so good on! I tried on the Round Trip Jacket last weekend and liked it, but didn't love it.
And with Lululemon's prices, I have to love it to spend the money.


text:
\section{Introduction}
In non-Hausdorff topology and domain theory, $d$-spaces, well-filtered spaces and sober spaces form three of the most important classes of $T_0$ spaces. In the past few years, some remarkable progresses have been achieved in the research of these three kinds of spaces(see, e.g., \cite{XSXZ,XXZ,XZ,XZ2,XYZ}). In order to reveal finer links between well-filtered spaces and $d$-spaces, X. Xu and D. Zhao introduced another class of $T_0$ spaces--\emph{strong $d$-spaces} which lie between $d$-spaces and $T_1$ spaces in \cite{XZ}. It is well-known that a $T_0$ space $X$ is a $d$-space iff $X$ is a \emph{directed complete poset} (\emph{dcpo}, for short) and the topology on $X$ is coarser than the Scott topology on $X$ with respect to its \emph{specialization order}. In order to obtain some characterizations of strong $d$-spaces (\cite[Proposition 3.22]{XZ}), the authors \cite{XZ} introduced the concept of \emph{strong Scott topology} and showed that for a $T_0$ space $X$,  if $X$ is a strong $d$-space, then $X$ is a $d$-space and the topology on $X$ is coarser than the strong Scott topology on $X$, and the converse is true if $X$ is a sup semilattice with the specialization order.

Strong Scott topology is a kind of new topology which is finer than the upper topology and coarser than the Scott topology. Inspired by the topological characterizations of continuous domains (resp., hypercontinuous domains) that a dcpo $P$ is a continuous domain (resp., a hypercontinuous domain) if and only if $P$ is a $C$-space with respect to the Scott topology (resp., upper topology), we introduce the concept of \emph{strongly continuous domains}. That is to say, a dcpo $P$ is called a strongly continuous domain if $P$ is a $C$-space with respect to the strong Scott topology. In this paper, we will investigate the properties of strongly continuous domains from the aspects of order structure and topology structure. In particular, we introduce the notion of \emph{strong way-below relation} and obtain a characterization of strongly continuous domains via this relation. We prove that the strong way-below relation on a strongly continuous domain satisfies the interpolation property and clarify the relationship between strongly continuous domains and continuous domains, and the relationship between strongly continuous domains and hypercontinuous domains. We prove that a strongly continuous domain $P$ endowed with the strong Scott topology is a locally compact sober space, and $P$ is a $T_{2}$ space with respect to the \emph{strong Lawson topology} which is the common refinement of the strong Scott topology and the lower topology.

\section{Preliminaries}

We now recall some basic definitions and notations needed in this paper. For further details, we refer the reader to \cite{GHK,GL}.
For a set $X$, the family of all finite sets in $X$ is denoted by $X^{(<\omega)}$. For a poset $L$, if $L$ has a greatest element (resp., smallest element), it is called the unit or top element (resp., zero or bottom element) of $L$ and is written as $1$ (resp., $0$). For any $x\in L$ and $A\subseteq L$, let $\downarrow x=\{y\in L: y\leq x\}$, $\downarrow \!A=\bigcup\{\downarrow \!x: x\in A\}$; $\uparrow \!x$ and $\uparrow \!A$ are defined dually. A subset $A$ is called a \emph{lower set} (resp., an \emph{upper set}) if $A=\ \downarrow \!A$ (resp., $A=\ \uparrow \!A$). A nonempty subset $D$ of $L$ is called \emph {directed} if every two elements in $D$ have an upper bound in $D$. $L$ is called a \emph{directed complete poset}, or \emph{dcpo} for short, if every directed subset of $L$ has the least upper bound in $L$. A subset $I\subseteq L$ is called an \emph{ideal} of $L$ if $I$ is a directed and a lower set. Dually, we define the concept of \emph{filters}. $L$ is called an (inf) \emph{semilattice} if any two elements $a, b$ have an inf, denoted by $a\wedge b$. Dually, $L$ is a \emph{sup semilattice} if any two elements $a,b$ have a sup, denoted by $a\vee b$. $L$ is called a \emph{complete semilattice} if $L$ is a dcpo and every nonempty subset of $L$ has an inf. $L$ is called a \emph{complete lattice} if every subset of $L$ has a sup and an inf. The \emph{upper topology} on $L$, generated by $\{L\}\cup\{L\setminus\!\downarrow \!x: x\in L\}$ (as a subbase), is denoted by $\upsilon(L)$. Dually, we define the \emph{lower topology} on $L$ and denote it by $\omega(L)$. A subset $U$ of $L$ is called \emph{Scott open} if $U$ is an upper set and for any directed subset $D$ for which $\bigvee D$ exists, $\bigvee D\in U$ implies $D\cap U\neq\emptyset$. All Scott open subsets of $L$ form a topology, and we call this topology the \emph{Scott topology} on $L$ and denote it by $\sigma(L)$. The complement of a Scott open set is called \emph{Scott closed}.

For a topological space $X$, let $\mathcal{O}(X)$ (resp., $\mathcal{C}(X)$) be the lattice of all open subsets (closed subsets) in $X$. For $A\subseteq X$, the \emph{closure} (resp., \emph{interior}) of $A$ in $X$ is denoted by cl$_XA$ (resp., int$_XA$). For a $T_0$ space $X$, we use $\leq_{X}$ to represent the \emph{specialization order} of $X$, that is , $x\leq_{X}y$ if and only if $x\in {\rm cl}_X(\{y\})$. Unless otherwise stated, throughout the paper, whenever an order-theoretic concept is mentioned, it is to be interpreted with respect to the specialization order.

\begin{definition}{\rm(\cite{GHK})} Let $L$ be a poset.
\begin{enumerate}
\item[\rm{(1)}] We say that $x$ is \emph{way below} $y$, in symbols $x\ll y$, iff for any directed subset $D\subseteq L$ for which ${\mbox{sup}}D$ exists, $y\leq {\mbox{sup}}D$ implies the existence of a $d\in D$ with $x\leq d$.
\item[\rm{(2)}] $L$ is called \emph{continuous}, if for any $x\in L, \Downarrow x=\{u\in L: u\ll x\}$ is directed and $x=\bigvee\Downarrow x$. A dcpo which is continuous is called a \emph{continuous domain}, or \emph{domain}. A domain which is a complete lattice is called a \emph{continuous lattice}.
\item[\rm{(3)}] We say that $x\prec y$ iff $y\in$ int$_{\upsilon(L)}\!\uparrow \!x$. And $L$ is called \emph{hypercontinuous} if for any $x\in L, \{y\in L: y\prec x\}$ is directed and $x=\bigvee\{y\in L: y\prec x\}$. A dcpo which is hypercontinuous is called a \emph{hypercontinuous domain}. A hypercontinuous domain which is a complete lattice is called a \emph{hypercontinuous lattice}.
\end{enumerate}
\end{definition}

\begin{definition}{\rm(\cite{VP})} Let $L$ be a complete lattice. A binary relation $\lhd$ on $L$ is defined as follows: $x\lhd y$ iff for any $S\subseteq L, y\leq\bigvee S$ implies that $x\in\ \!\downarrow \!S$. $L$ is called \emph{completely distributive lattice} if for all $x\in L, x=\bigvee\{y\in L: y\lhd x\}$.
\end{definition}

\begin{definition}{\rm(\cite{ZH})}
Let $X$ be a $T_{0}$ space. $X$ is called a $C$-space if for any $U\in\mathcal{O}(X)$ and $x\in U$, there exists $y\in U$ such that $x\in\!$ int$_{X}\!\uparrow \!y\subseteq\ \!\uparrow \!y\subseteq U$.
\end{definition}

\begin{proposition}{\rm(\cite{ZH})}\label{pro-2.4}
For a $T_{0}$ space $X$, $X$ is a $C$-space if and only if $(\mathcal{O}(X),\subseteq)$ is a completely distributive lattice.
\end{proposition}

\begin{theorem}{\rm(\cite{GHK})} Let $L$ be a dcpo.
\begin{enumerate}
\item[\rm{(1)}] $L$ is a domain iff $(L,\sigma(L))$ is a $C$-space.

\item[\rm{(2)}] $L$ is a hypercontinuous domain iff $(L,\upsilon(L))$ is a $C$-space.
\end{enumerate}
\end{theorem}

\begin{theorem}\label{the-2.6}{\rm(\cite{GHK})} Let $L$ be a complete lattice. The following conditions are equivalent:
\begin{enumerate}
\item[\rm{(1)}] $L$ is completely distributive;

\item[\rm{(2)}] $L$ is distributive, and both $L$ and $L^{\rm{op}}$ are continuous lattices;

\item[\rm{(3)}] $L$ is continuous and every element is the sup of co-primes.
\end{enumerate}
\end{theorem}

\begin{definition}{\rm(\cite{XZ})} Let $L$ be a dcpo. A subset $U\subseteq L$ is called \emph{strongly Scott open} if (i) $U=\ \uparrow \!U$, and (ii) for any directed subset $D$ of $L$ and $x\in L$, $\bigcap _{d\in D}\uparrow \!d~\cap \uparrow \!x\subseteq U$ (that is $\uparrow\bigvee D\ \cap\uparrow x\subseteq U$) implies $\uparrow \!d\ \cap \uparrow \!x\subseteq U$ for some $d\in D$. Let $\sigma^{s}(L)$ denote the set of all strongly Scott open subsets of $L$.

Clearly, if $U,V\in \sigma ^{s}(L)$, then $U\cap V\in \sigma ^{s}(L)$. The topology generated by $\sigma ^{s}(L)$ (as a base) is called the \emph{strong Scott topology} on $L$ and denote it by $\sigma _{s}(L)$. The space $(L,\sigma _{s}(L))$ is called the \emph{strong Scott space} of $L$, and will be denoted by $\sum _{s}L$.

In order not to cause ambiguity, the elements in $\sigma _{s}(L)$ will be called \emph{strong Scott topology open sets}.
\end{definition}

\begin{proposition}{\rm(\cite{XZ})}
Let $L$ be a poset, then $\upsilon(L)\subseteq \sigma^{s}(L)\subseteq \sigma_{s}(L)\subseteq \sigma(L)$.
\end{proposition}

\section{Strongly continuous domains}

In this section we introduce the notion of strongly continuous domains and give some characterizations of strongly continuous domains from the aspect of order structure.

\begin{definition} \label{def-3.1}Let $L$ be a dcpo. $L$ is called a \emph{strongly continuous domain} if $(L,\sigma_{s}(L))$ is a $C$-space, i.e., for any $U\in\sigma_s(L)$ and $x\in L$, $x\in U$ implies there exists a $u\in U$ such that $x\in{\rm{int}}_{\sigma_s(L)}\!\uparrow \!u\subseteq\ \! \uparrow \!u\subseteq U$.
\end{definition}

The reason we adopt the terminology ``strongly continuous'' in the paper is that we introduce the notion of strongly continuous domains via strong Scott topology. It should be pointed out that the terminology ``strongly continuous'' in this paper is completely different from that in \cite{XM}.

\begin{definition}(\cite{XM}) Let $P$ be a poset and $x, y\in P$. We write $x\ll_ly$, if for any directed set $D$ and any upper bound $z$ of $D$ with $y\leq\sup_zD$, there is a $d\in D$ such that $x\leq d$, where $\sup_zD$ denotes the supremum of $D$ in $\downarrow \!z$. $P$ is called a strongly continuous poset if for all $x\in P$, $\Downarrow_lx=\{y\in L: y\ll_lx\}$ is directed and $\sup\Downarrow_lx=x$.
\end{definition}

\begin{definition} Let $L$ be a poset. A binary relation $\ll_{s}$ on $L$ is defined as follows: $x\ll_{s}y$ if for any directed subset $D\subseteq L$ and $a\in L$, $\bigcap _{d\in D}\!\uparrow \!d\ \cap \uparrow \!a\subseteq\ \!\uparrow \!y$ implies $\uparrow \!d\ \cap \uparrow \!a\subseteq\ \!\uparrow \!x$ for some $d\in D$.
\end{definition}

\begin{remark} Let $L$ be a dcpo and $u, x, y, z\in L$. We have the following.\\
(1) $x\ll_{s}y$ implies $x\ll y$, and $x\ll_{s}y$ is equivalent to $x\ll y$ if $L$ is a sup semilattice.\\
(2) $u\leq x\ll_{s}y\leq z$ implies $u\ll_{s}z$.\\
(3) $x\ll_{s}z$, $y\ll_{s}z$ implies $x\vee y\ll_{s}z$ whenever $x\vee y$ exists in $L$.\\
(4) $0\ll_{s}x$ whenever $L$ has a smallest element $0$.\\
Hence $\ll_{s}$ is an auxiliary relation on $L$.
\end{remark}
For $x\in L$, we write $\Downarrow_sx=\{y\in L: y\ll_sx\}$ and $\Uparrow_sx=\{y\in L: x\ll_sy\}$.

\begin{proposition}
Let $L$ be a dcpo. Suppose that there exists a directed set $D\subseteq\ \Downarrow_{s}\!x$ such that $\sup D=x$, then we have the following conditions.
\begin{enumerate}
\item[\rm{(1)}] $\Downarrow_{s}\!x$ is directed and $\sup\Downarrow_{s}\!x=x$;
\item[\rm{(2)}] If $y\ll_{s}x$ in $\downarrow \!x$, then $y\ll_{s}x$ in $L$.
\end{enumerate}
\end{proposition}

\begin{proof}
(1): Let $y_{1},y_{2}\in\ \!\Downarrow_{s}\!\!x$, i.e., $y_{1}\ll_{s}x$ and $y_{2}\ll_{s}x$. Since $\ll_{s}\ \!\subseteq\ \!\ll$, then $y_{1}\ll x$ and $y_{2}\ll x$. Since $\textrm{sup}D=x$, then $y_{1}\leq d_{1}, y_{2}\leq d_{2}$ for some $d_{1},d_{2}\in D$. Since $D$ is directed, there exists $d_{3}\in D$ such that $y_{1}\leq d_{1}\leq d_{3}$, $y_{2}\leq d_{2}\leq d_{3}$, then $d_{3}\geq y_{1},y_{2}$. Thus $\Downarrow_{s}\!x$ is directed by $d_{3}\in D\subseteq\ \!\Downarrow_{s}\!x$. Since $x=\textrm{sup}D\leq \textrm{sup}\Downarrow_{s}\!x\leq \textrm{sup}\downarrow \!x=x$, we have $\textrm{sup}\Downarrow_{s}\!x=x$.\\
(2): Let $y\ll_{s}x$ in $\downarrow \!x$. Then $y\ll x$. Since directed set $D\subseteq\ \!\Downarrow_{s}\!x$ and $\textrm{sup}D=x$, $y\leq d$ for some $d\in D$. Therefore $y\ll_{s}x$ by $d\in\ \!\Downarrow_{s}\!x$.
\end{proof}

\begin{theorem}\label{The-3.5} Let $L$ be a dcpo. The following two conditions are equivalent:
\begin{enumerate}
\item[\rm{(1)}] $L$ is a strongly continuous domain;
\item[\rm{(2)}] For any $x\in L$, $\Downarrow_{s}\!x$ is directed, $x=\sup\Downarrow_{s}\!x$ and $\Uparrow_{s}\!x\in\sigma_{s}(L)$.
\end{enumerate}
\end{theorem}

\begin{proof}
$(1)\Rightarrow(2)$: Suppose that $L$ is a strongly continuous domain. Then $(L,\sigma_{s}(L))$ is a $C$-space. For any $a\in L$, let $H_{a}=\{x\in L:a\in \textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!x)\}$. Then since $(L,\sigma_{s}(L))$ is a $C$-space and $a\in L\in\sigma_{s}(L)$, there exists $x\in L$ such that $a\in \textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!x)\subseteq\ \!\uparrow \!\!x\subseteq L$. Hence $H_{a}\neq\emptyset$. For any $x_{1},x_{2}\in H_{a}$, since $(L,\sigma_{s}(L))$ is a $C$-space, there exists $x_{3}\in L$ such that $a\in\textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!x_{3})\subseteq\ \!\uparrow\!\! x_{3}\subseteq(\textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!x_{1}))\cap(\textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!x_{2}))$, hence $x_{3}\in H_{a}$ and $x_{1},x_{2}\leq x_{3}$, thus $H_{a}$ is directed. If $x\in H_{a}$ and $y\leq x$, then $a\in\textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!x)\subseteq\textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!y)$, thus $y\in H_{a}$, hence $H_{a}$ is a lower set. We now show that $\bigvee H_{a}=a$. Obviously, $a$ is an upper bound of $H_{a}$. Let $b$ be an other upper bound of $H_{a}$, i.e., $H_{a}\subseteq\ \!\downarrow \!b$. Assume that $a\nleq b$, then $a\in L\setminus\downarrow \!b\in\upsilon(L)\subseteq\sigma_{s}(L)$, since $(L,\sigma_{s}(L))$ is a $C$-space, there exists $x\in L\setminus\downarrow \!b$ such that $a\in\textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!x)\subseteq\ \!\uparrow\!\! x\subseteq L\setminus\downarrow \!b$. Hence $x\in H_{a}$ and $x\nleq b$, this is a contradiction. Thus $\bigvee H_{a}=a$. We now show that $H_{a}=\ \!\Downarrow_{s}\!a$. On the one hand, if $x\in H_{a}$, then there exists $U\in\sigma^{s}(L)$ such that $a\in U\subseteq\textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!x)$. For any directed subset $D\subseteq L$ and $z\in L$, if $\uparrow\!\bigvee D~\cap\uparrow \!z\subseteq\ \!\uparrow \!a$, then $\uparrow\!\bigvee D\ \!\cap\uparrow \!z\subseteq\ \!\uparrow \!a\subseteq U\in\sigma^{s}(L)$, hence $\uparrow \!d~\cap\uparrow \!z\subseteq U\subseteq\textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!x)\subseteq\ \!\uparrow \!x$ for some $d\in D$. Thus $x\ll_{s}a$. Therefore $H_{a}\subseteq\ \!\Downarrow_{s}\!a$. On the other hand, for any $y\in\ \!\Downarrow_{s}\!a$, i.e., $y\ll_{s}a=\bigvee H_{a}$, then $y\ll a=\bigvee H_{a}$. Since $H_{a}$ is an ideal, $y\in\ \!\downarrow \!H_{a}=H_{a}$. Now we prove that $\Uparrow_{s}\!\!a\in\sigma_{s}(L)$. Since $x\in\ \!\Uparrow_{s}\!\!a$ iff $a\in\ \!\Downarrow_{s}\!x=H_{x}$ iff $x\in\textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!a)$, we have $\Uparrow_{s}\!a=\textrm{int}_{\sigma_{s}(L)}(\uparrow \!a)\in\sigma_{s}(L)$.\\
$(2)\Rightarrow(1)$: Suppose $a,b\in L$ such that $a\ll_{s}b$. Since $\Uparrow_{s}\!\!a\in\sigma_{s}(L)$ and $\Uparrow_{s}\!\!a\subseteq\ \!\uparrow \!\!a$, then we have $b\in\ \!\Uparrow_{s}\!a\subseteq\textrm{int}_{\sigma_{s}(L)}(\uparrow \!\!a)$. We now show that $(L,\sigma_{s}(L))$ is a $C$-space. Suppose that $U\in\sigma_{s}(L)$ and $b\in U$, then $\bigvee\{x\in L:x\ll_{s}b\}=b\in U$. Since $\sigma_{s}(L)\subseteq\sigma(L)$, $\bigvee\{x\in L:x\ll_{s}b\}=b\in U\in\sigma_{s}(L)\subseteq\sigma(L)$, thus $\{x\in L:x\ll_{s}b\}\cap U\neq\emptyset$, hence $x\in U$ for some $x\in\ \!\Downarrow_{s}\!b$. Thus $b\in\textrm{int}_{\sigma_{s}(L)}(\uparrow \!x)$. Therefore $(L,\sigma_{s}(L))$ is a $C$-space.
\end{proof}

According to the Definition \ref{def-3.1} and Theorem \ref{The-3.5}, strongly continuous domains can be characterized by means of strong way-below relation.

\begin{proposition}
Let $L$ be a strongly continuous domain. If $x\ll_{s}z$ and $z\leq\bigvee D$ for a directed set in $L$, then $x\ll_{s}d$ for some $d\in D$.
\end{proposition}
\begin{proof}
Let $I=\bigcup\{\Downarrow_{s}\!d:d\in D\}$. Since $L$ is strongly continuous, $\bigvee I=\bigvee D$ and $I$ is an ideal. If $x\ll_{s}z$ and $z\leq\bigvee D$, then $x\ll z\leq\bigvee D=\bigvee I$. Since strongly continuous domains are continuous domains by definition, $x\in I$. Thus $x\ll_{s}d$ for some $d\in D$.
\end{proof}

\begin{proposition}\label{pro-3.7}
In a strongly continuous domain $L$, $\ll_{s}$ satisfies the interpolation property, i.e., for all $x, y\in L$, $x\ll_sy$ implies that there exists a $z\in L$ such that $x\ll_sz\ll_sy$.
\end{proposition}

\begin{proof}
Suppose $x,y\in L$ such that $x\ll_{s}y$, we now show that $x\ll_{s}z\ll_{s}y$ for some $z\in L$. Let $D=\bigcup_{a\in\Downarrow_{s}y}\Downarrow_{s}\!a=\{b\in L:$ there is an $a\in L$ with $b\ll_{s}a\ll_{s}y\}$. We claim that $D$ is directed. For any $b_{1},b_{2}\in D$, we have $b_{1}\ll_{s}a_{1}\ll_{s}y$ for some $a_{1}\in L$ and $b_{2}\ll_{s}a_{2}\ll_{s}y$ for some $a_{2}\in L$. Since $\Downarrow_{s}\!y$ is directed, there exists $a_{3}\in\ \!\Downarrow_{s}\!y$ such that $a_{1},a_{2}\leq a_{3}$. Hence $b_{1},b_{2}\ll_{s}a_{3}$. Since $\Downarrow_{s}\!a_{3}$ is directed, there exists $b_{3}\in\ \!\Downarrow_{s}\!a_{3}$ such that $b_{1},b_{2}\leq b_{3}\ll_{s}a_{3}\ll_{s}y$. Thus $b_{3}\in \!D$ and $b_{1},b_{2}\leq b_{3}$. Therefore $D$ is directed. Since $\bigvee D=\bigvee\{\bigvee\Downarrow_{s}\!a:a\in\ \!\Downarrow_{s}\!y\}=\bigvee\{a:a\in\ \!\Downarrow_{s}\!y\}=\bigvee\Downarrow_{s}\!y=y$, $\bigcap_{d\in D}\!\uparrow \!d\subseteq\ \!\uparrow \!y$. It follows from $x\ll_{s}y$ that $\uparrow \!d\subseteq\ \!\uparrow \!x$ for some $d\in \!D$. Thus there exists $a\in L$ such that $d\ll_{s}a\ll_{s}y$. Therefore $x\ll_{s}a\ll_{s}y$.
\end{proof}

Recall that hypercontinuous domains are continuous domains. Now we discuss the relationship between strongly continuous domains and hypercontinuous domains, and the relationship between strongly continuous domains and continuous domains.

\begin{lemma}{\rm(\cite{GHK})} \label{lem3.8}Let $L$ be a dcpo. Then the following conditions are equivalent:
\begin{enumerate}
\item[\rm{(1)}] $L$ is hypercontinuous;
\item[\rm{(2)}] $L$ is continuous and $\ll=\prec$;
\item[\rm{(3)}] $L$ is continuous and $\upsilon(L)=\sigma(L)$.
\end{enumerate}
\end{lemma}

\begin{theorem}\label{the3.9} Let $L$ be a dcpo. Then the following conditions are equivalent:
\begin{enumerate}
\item[\rm{(1)}] $L$ is hypercontinuous;
\item[\rm{(2)}] $L$ is strongly continuous and $\ll_{s}=\prec$;
\item[\rm{(3)}] $L$ is strongly continuous and $\upsilon(L)=\sigma_{s}(L)$.
\end{enumerate}
\end{theorem}
\begin{proof}
$(1)\Rightarrow(2)$: Let $L$ be a hypercontinuous domain, thus $\ll=\prec$ by Lemma \ref{lem3.8}. Since $\prec\subseteq\ll_{s}\subseteq\ll$, we have $\prec=\ll_{s}$. For any $x\in L$, $\Uparrow_{s}\!x=\{y\in L:x\prec y\}=\textrm{int}_{\upsilon(L)}\!\uparrow \!x\in\upsilon(L)\subseteq\sigma_{s}(L)$.\\
$(2)\Rightarrow(3)$: Obviously, $\upsilon(L)\subseteq\sigma_{s}(L)$. For each $U\in\sigma_{s}(L)$, we show that $U\in\upsilon(L)$. For any $x\in U$, $x=\bigvee^{\uparrow}\!\Downarrow_{s}\!x=\bigvee^{\uparrow}\{y\in L:y\prec x\}\in U\in\sigma_{s}(L)\subseteq\sigma(L)$, hence there is a $y\prec x$ with $y\in U$. Since $y\prec x$, $x\in \textrm{int}_{\upsilon(L)}\!\uparrow \!y$. Then $x\in \textrm{int}_{\upsilon(L)}\!\uparrow \!y\subseteq\ \!\uparrow \!y\subseteq U$. Thus $U\in\upsilon(L)$. Therefore $\upsilon(L)=\sigma_{s}(L)$.\\
$(3)\Rightarrow(1)$: $L$ is strongly continuous iff $(L,\sigma_{s}(L))$ is a $C$-space iff $(L,\upsilon(L))$ is a $C$-space iff $L$ is hypercontinuous.
\end{proof}

\begin{example}\label{example3.10} Let $L=\{0\}\cup\{a_{1},a_{2},\cdots,a_{n},\cdots\}$ with the order generated by
\begin{enumerate}
\item[\rm{(a)}] $a_{n}>0$ for all $n\in \mathbb{N}$;
\item[\rm{(b)}] There is no order relationship between $a_{i}$ and $a_{j}$ for all $i,j\in\mathbb{N}$ (Fig. \ref{Fig.1}).
\end{enumerate}
Then $L$ is a strongly continuous domain, but not a hypercontinuous domain.
\end{example}

\begin{figure}[H]
  \centering

  \includegraphics[width=0.45\textwidth]{01.png}\\
  \caption{The poset $L$.}
  \label{Fig.1}
\end{figure}

\begin{proof}
Since the directed subset in $L$ can only be a single point set or a binary set $\{0,a_{n}\}(n\in\mathbb{N})$, $L$ is a dcpo. It is easy to show that $L$ is not a hypercontinous domain. Now we prove that $L$ is a strongly continuous domain. Let $x\in L$, we now show that $\Downarrow_{s}\!x$ is directed. Obviously, $0\ll_{s}0$, then $\Downarrow_{s}\!0=\{0\}$. For each $n\in\mathbb{N}$, let directed set $D\subseteq L$ and $z\in L$ such that $\bigcap_{d\in D}\uparrow \!d\ \!\cap\uparrow \!z\subseteq\ \!\uparrow \!a_{n}=\{a_{n}\}$. Then there are only the following cases: (\textrm{i}) $D=\{0\}$, $z=\{a_{n}\}$; (ii) $D=\{a_{n}\}$, $z\in L$; (iii) $D=\{a_{m}\}(m\neq n)$, $z\neq\{0\}$ and $z\neq\{a_{m}\}$; (iv) $D=\{0,a_{n}\}$, $z\in L$; (v) $D=\{0,a_{m}\}(m\neq n)$, $z\neq\{0\}$ and $z\neq\{a_{m}\}$. Clearly, there exists $d\in D$ such that $\uparrow \!d\ \!\cap\uparrow \!z\subseteq\ \!\uparrow \!a_{n}=\{a_{n}\}$ in each case. Hence $a_{n}\ll_{s}a_{n}$. therefore $\Downarrow_{s}\!a_{n}=\{0,a_{n}\}$. Thus $\Downarrow_{s}\!x$ is directed and $x=\bigvee\!\Downarrow_{s}\!x$ for all $x\in L$. Now we prove that $\Uparrow_{s}\!x\in\sigma_{s}(L)$. Clearly, $\Uparrow_{s}\!0=L\in\sigma_{s}(L)$. For each $n\in\mathbb{N}$, $\Uparrow_{s}\!a_{n}=\{a_{n}\}$ and $\Uparrow_{s}\!a_{n}\in\sigma^{s}(L)\subseteq\sigma_{s}(L)$ according to the above proof. Therefore $L$ is a strongly continuous domain.
\end{proof}

According to the Theorem \ref{the3.9} and Example \ref{example3.10}, a hypercontinuous domain is a strongly continuous domain, but the converse is not true.

\begin{theorem}\label{the3.11} Let $L$ be a dcpo. Then the following conditions are equivalent:
\begin{enumerate}
\item[\rm{(1)}] $L$ is strongly continuous;
\item[\rm{(2)}] $L$ is continuous, $\ll_{s}=\ll$ and $\Uparrow_{s}\!x\in\sigma_{s}(L)$ for all $x\in L$;
\item[\rm{(3)}] $L$ is continuous and $\sigma_{s}(L)=\sigma(L)$.
\end{enumerate}
\end{theorem}
\begin{proof}
$(1)\Rightarrow(2)$: Since $L$ is strongly continuous and $\ll_{s}\subseteq\ll$, $L$ is continuous. If $x\ll y=\bigvee^{\uparrow}\{z\in L:z\ll_{s}y\}$, then there exists $z\in\ \!\Downarrow_{s}\!y$ such that $x\leq z$, hence $x\ll_{s}y$. Clearly, $\Uparrow_{s}\!x\in\sigma_{s}(L)$ for all $x\in L$.\\
$(2)\Rightarrow(3)$: We only need prove that $\sigma(L)\subseteq\sigma_{s}(L)$. Let $U\in\sigma(L)$, for each $x\in U$, $x=\bigvee^{\uparrow}\!\Downarrow \!x=\bigvee^{\uparrow}\!\Downarrow_{s}\!x\in U\in\sigma(L)$, then there exists $y\in\ \!\Downarrow_{s}\!x$ such that $y\in U$. Thus $x\in\ \!\Uparrow_{s}\!y\subseteq\ \!\uparrow \!y\subseteq U$. Since $\Uparrow_{s}\!y\in\sigma_{s}(L)$, $U\in\sigma_{s}(L)$.\\
$(3)\Rightarrow(1)$: $L$ is continuous iff $(L,\sigma(L))$ is a $C$-space iff $(L,\sigma_{s}(L))$ is a $C$-space iff $L$ is strongly continuous.
\end{proof}

The following example shows that a continuous domain need not be a strongly continuous domain.
\begin{example}\label{example3.12}(\cite{XZ}) Let $C=\{a_{1},a_{2},\cdots,a_{n},\cdots\}\cup\{\omega_{0}\}$ and $L=C\cup\{b\}\cup\{\omega_{1},\omega_{2},\cdots,\omega_{n},\cdots\}$ with the order generated by
\begin{enumerate}
\item[\rm{(a)}] $a_{1}<a_{2}<\cdots<a_{n}<a_{n+1}<\cdots$;
\item[\rm{(b)}] $a_{n}<\omega_{0}$ for all $n\in\mathbb{N}$;
\item[\rm{(c)}] $b<\omega_{n}$ and $a_{m}<\omega_{n}$ for all $n,m\in\mathbb{N}$ with $m\leq n$ (Fig. \ref{Fig.2}).
\end{enumerate}
\end{example}

\begin{figure}[H]
  \centering

  \includegraphics[width=0.5\textwidth]{02.png}\\
  \caption{The poset $L$.}
  \label{Fig.2}
\end{figure}

Then $L$ is a dcpo and $D$ is a directed set of $L$ iff $D\subseteq C$ or $D$ has a largest element, and hence $x\ll x$ for all $x\in L\setminus\{\omega_{0}\}$. Therefore $L$ is a continuous domain. However, $L$ is not a strongly continuous domain. In fact, choose $D=\{a_{n}:n\in\mathbb{N}\}$, then $\bigcap_{d\in D}\!\uparrow \!\!d\ \!\cap\!\uparrow \!\!b\subseteq\ \!\uparrow \!\!\omega_{1}=\{\omega_{1}\}$, but $\uparrow \!\!a_{n}~\cap\uparrow \!\!b=\{\omega_{n},\omega_{n+1},\cdots\}\nsubseteq\ \!\uparrow\!\!\omega_{1}$ for each $n\in\mathbb{N}$. Hence $\omega_{1}\notin\ \!\Downarrow_{s}\!\!\omega_{1}$. Since $\Downarrow_{s}\!\omega_{1}\subseteq\ \!\downarrow\!\omega_{1}=\{\omega_{1},a_{1},b\}$, $\Downarrow_{s}\!\omega_{1}\subseteq\{a_{1},b\}$, we have $\omega_{1}\neq\bigvee\Downarrow_{s}\!\omega_{1}$.\\

According to the Theorem \ref{the3.11} and Example \ref{example3.12}, a strongly continuous domain is a continuous domain, but the converse is not true. Therefore strongly continuous domains lie strictly between hypercontinuous domains and continuous domains.

\section{Topologies on strongly continuous domains}

In this section, we study some properties of strongly continuous domains endowed with strong Scott topology and strong Lawson topology.

\begin{proposition} \label{pro-4.1}Let $L$ be a dcpo. Then we have the following conditions.
\begin{enumerate}
\item[\rm(1)] $\textrm{cl}_{\sigma_{s}(L)}\{x\}=\ \downarrow \!x$ for all $x\in L$;
\item[\rm(2)] $\sigma_{s}(L)$ is a $T_{0}$-topology;
\item[\rm(3)] If $A=\ \uparrow \!A$, then $A=\bigcap\{U\in\sigma_{s}(L):A\subseteq U\}$.
\end{enumerate}
\end{proposition}

\begin{proposition} \label{pro-4.2}Let $L$ be a dcpo. Consider the following two conditions:
\begin{enumerate}
\item[\rm(1)] $y\in \textrm{int}_{\sigma_{s}(L)}\uparrow \!x$;
\item[\rm(2)] $x\ll_{s}y$.
\end{enumerate}
Then $(1)\Rightarrow(2)$; if $L$ is strongly continuous, then $(2)\Rightarrow(1)$, and $(1)$ and $(2)$ are equivalent.
\end{proposition}

\begin{proof}
$(1)\Rightarrow(2)$: By the proof of Theorem \ref{The-3.5}.\\
$(2)\Rightarrow(1)$: Let $x\ll_{s}y$, then $y\in\ \!\Uparrow_{s}\!\!x\subseteq\ \!\uparrow \!\!x$. Since $L$ is strongly continuous, $\Uparrow_{s}\!x\in\sigma_{s}(L)$. Hence $y\in\ \!\Uparrow_{s}\!x\subseteq\textrm{int}_{\sigma_{s}(L)}\uparrow \!x$.
\end{proof}

\begin{proposition} \label{pro-4.3}Let $L$ be a strongly continuous domain. Then we have the following conditions.
\begin{enumerate}
\item[\rm(1)] If $U=\ \!\uparrow \!U$, then $U\in\sigma_{s}(L)$ iff there is a $u\in U$ such that $x\in\ \!\Uparrow_{s}\!u$ for all $x\in U$;
\item[\rm(2)] $\{\Uparrow_{s}\!u:u\in L\}$ form a basis for the strong Scott topology;
\item[\rm(3)] $\textrm{int}_{\sigma_{s}(L)}\uparrow \!x=\ \!\Uparrow_{s}\!x$ for all $x\in L$;
\item[\rm(4)] For any subset $X\subseteq L$, $\textrm{int}_{\sigma_{s}(L)}X=\bigcup\{\Uparrow_{s}\!u:\Uparrow_{s}\!u\subseteq X\}$.
\end{enumerate}
\end{proposition}
\begin{proof}
(1) For each $x\in U$, since $L$ is strongly continuous, $\Downarrow_{s}\!\!x$ is directed and $x=\bigvee\Downarrow_{s}\!x$. And hence $x=\bigvee\Downarrow_{s}\!x \in\sigma_{s}(L)\subseteq\sigma(L)$, thus $\Downarrow_{s}\!x\cap U\neq\emptyset$. Therefore there exists $u\in U$ such that $x\in\ \!\Uparrow_{s}\!u$. On the other hand, it is trivial.\\
(2) It follows directly from (1).\\
(3) It follows from Proposition \ref{pro-4.2}.\\
(4) On the one hand, obviously, $\bigcup\{\Uparrow_{s}\!\!u:\ \!\Uparrow_{s}\!\!u\subseteq X\}\subseteq X$ and $\bigcup\{\Uparrow_{s}\!\!u:\ \!\Uparrow_{s}\!\!u\subseteq X\}\in\sigma_{s}(L)$, then $\bigcup\{\Uparrow_{s}\!\!u:\ \!\Uparrow_{s}\!\!u\subseteq X\}\subseteq\textrm{int}_{\sigma_{s}(L)}X$. On the other hand, for each $y\in\textrm{int}_{\sigma_{s}(L)}X$, there exists $u\in\textrm{int}_{\sigma_{s}(L)}X$ such that $y\in\ \!\Uparrow_{s}\!u\subseteq\textrm{int}_{\sigma_{s}(L)}X$. Thus $\Uparrow_{s}\!u=\textrm{int}_{\sigma_{s}(L)}\uparrow \!u\subseteq\ \!\uparrow \!u\subseteq\textrm{int}_{\sigma_{s}(L)}X\subseteq X$. Therefore $\textrm{int}_{\sigma_{s}(L)}X\subseteq\bigcup\{\Uparrow_{s}\!u:\Uparrow_{s}\!u\subseteq X\}$.
\end{proof}

Now we recall the definitions of \emph{prime elements}, \emph{sober spaces}. An element $p$ in a poset $L$ is called \emph{prime} iff $p=1$ or $L\setminus\downarrow p$ is a filter. An element is \emph{co-prime} iff it is prime of $L^{\textrm{op}}$. The sets of all prime and co-prime elements of $L$ are denoted by $\textrm{PRIME}(L)$ and $\textrm{COPRIME}(L)$, respectively. A nonempty subset $A$ of a $T_{0}$ space $X$ is said to be \emph{irreducible} if for any $\{B,C\}\subseteq \mathcal{C}(X)$, $A\subseteq B\cup C$ implies $A\subseteq B$ or $A\subseteq C$. Obviously, $\textrm{cl}\{x\}$ is a irreducible closed set for all $x\in X$. A space is called \emph{sober}, if for any irreducible closed set $C$, there is a unique point $x\in X$ such that $C=\textrm{cl}\{x\}$.

\begin{lemma}\label{lem4.4}{\rm(\cite{GHK})} Let $X$ be a space and $A$ a subset of $X$. Then the following conditions are equivalent:
\begin{enumerate}
\item[\rm{(1)}] $A$ is a irreducible closed set of $X$;
\item[\rm{(2)}] $A$ is a co-prime in lattice $\mathcal{C}(X)$;
\item[\rm{(3)}] $X\setminus A$ is a prime in lattice $\mathcal{O}(X)$;
\item[\rm{(4)}] For any $U,V\in\mathcal{O}(X)$, if $U\cap A\neq\emptyset$ and $V\cap A\neq\emptyset$, then $U\cap V\cap A\neq\emptyset$.
\end{enumerate}
\end{lemma}

\begin{definition}
Let $L$ be a dcpo. The set of all strong Scott topology open filters of $L$ is denoted by $\textrm{SOFilt}(L)$, i.e., $U\in \textrm{SOFilt}(L)$ iff $U\in\sigma_{s}(L)$ and $U$ is a filter.
\end{definition}

\begin{proposition} \label{pro-4.6}Let $L$ be a dcpo and $U\in\sigma_{s}(L)$.
\begin{enumerate}
\item[\rm(1)] $U$ is a co-prime in $\sigma_{s}(L)$ iff $U\in \textrm{SOFilt}(L)$;
\item[\rm(2)] $L\setminus \downarrow \!a\in\textrm{PRIME}(\sigma_{s}(L))$ for all $a\in L$; For each $U\in\textrm{PRIME}(\sigma_{s}(L)), U\neq L$, if $L$ is strongly continuous, then there exists $a\in L$ such that $U=L\setminus \downarrow \!a$.
\end{enumerate}
\end{proposition}
\begin{proof}
(1):  On the one hand, suppose that $U\in\textrm{COPRIME}(\sigma_{s}(L))$, we only need to show that $U$ is a filter. For any $x,y\in U$, assume that $U\ \!\cap \downarrow \!x\ \!\cap \downarrow \!y=\emptyset$, then $U\subseteq(L\setminus \downarrow x)\cup(L\setminus \downarrow y)$. Since $U\in\textrm{COPRIME}(\sigma_{s}(L))$, $U\subseteq L\setminus \downarrow x$ or $U\subseteq L\setminus \downarrow y$, which is in contradiction with $U$ is an upper set. Therefore there is a $z\in U$ such that $z\leq x$ and $z\leq y$. On the other hand, suppose that $U\in\textrm{SOFilt}(L)$, if $V,W\in\sigma_{s}(L)$ and $U\nsubseteq V,U\nsubseteq W$, we only need check $U\nsubseteq V\cup W$. Since $U\nsubseteq V$ and $U\nsubseteq W$, then there exists $v\in U\setminus V$ and $w\in U\setminus W$. Note that $U$ is a filter, hence there exists $u\in U$ such that $u\leq v,w$, then $u\in U\setminus(V\cup W)$. Therefore $U\nsubseteq V\cup W$.\\
(2): By Proposition \ref{pro-4.1} and Lemma \ref{lem4.4}, $L\setminus\downarrow \!a=L\setminus \textrm{cl}_{\sigma_{s}(L)}\{a\}\in\textrm{PRIME}(\sigma_{s}(L))$ for all $a\in L$. Conversely, for each $U\in\textrm{PRIME}(\sigma_{s}(L))$ and $U\neq L$, let $A=L\setminus U$, then $A$ is an irreducible closed set in $(L,\sigma_{s}(L))$. We have to show that $A$ has a largest element $e$; since $A$ is a lower set, this will show that $A=\ \!\downarrow \!e$ as desired. Let $A^{\ast}=\bigcup\{\Downarrow_{s}a:a\in A\}=\ \!\Downarrow_{s}\!A\subseteq\ \!\downarrow \!A=A$,  we claim that $A^{\ast}$ is directed. For each $b,c\in A^{\ast}$, there exists $a_{b},a_{c}\in A$ such that $b\ll_{s}a_{b}$ and $c\ll_{s}a_{c}$, respectively. We first show that $\Uparrow_{s}\!b\ \!\cap\Uparrow_{s}\!c\cap A\neq\emptyset$, if not, then $\Uparrow_{s}\!b\ \!\cap\Uparrow_{s}\!c\subseteq U$, but $\Uparrow_{s}\!b, \Uparrow_{s}\!c\in\sigma_{s}(L)$ and $U\in\textrm{PRIME}(\sigma_{s}(L))$, then $\Uparrow_{s}\!b\subseteq U$ or $\Uparrow_{s}\!c\subseteq U$. But $\Uparrow_{s}b$ contains an $a_{b}\in A=L\setminus U$ which is impossible, similarly $\Uparrow_{s}\!c\subseteq U$ is impossible. Pick $a\in\ \!\Uparrow_{s}\!b\ \!\cap\Uparrow_{s}\!c\cap A$, since $\Uparrow_{s}\!b\ \!\cap\Uparrow_{s}\!c\in \sigma_{s}(L)$, there exists $d\in\ \!\Uparrow_{s}\!b\ \!\cap\Uparrow_{s}\!c$ such that $a\in\ \!\Uparrow_{s}\!d\subseteq\ \!\Uparrow_{s}\!b\ \!\cap\Uparrow_{s}\!c$. Thus $d\in A^{\ast}$ and $b,c\leq d$. Hence $A^{\ast}$ is directed and $\bigvee A^{\ast}$ exists. Note that $A^{\ast}\subseteq A$ and $A$ is a strong Scott topology closed set, then $A$ is also a Scott closed set. Let $e=\bigvee A^{\ast}$, then $e=\bigvee A^{\ast}\in A$. Now we show that $e$ is the largest element in $A$. For any $x\in A$, since $\Downarrow_{s}\!x\subseteq A^{\ast}$, $x=\bigvee\Downarrow_{s}\!x\leq\bigvee A^{\ast}=e$.
\end{proof}

\begin{corollary}
Let $L$ be a strongly continuous domain. Then $(L,\sigma_{s}(L))$ is a sober space.
\end{corollary}

\begin{proof}
By Lemma \ref{lem4.4} and Proposition \ref{pro-4.6}.
\end{proof}

\begin{corollary}
Let $L$ be a strongly continuous domain. Then $(L,\sigma_{s}(L))$ is a locally compact sober space. If $L$ has a smallest element, then $(L,\sigma_{s}(L))$ is compact.
\end{corollary}

\begin{proof}
Suppose that $x\in U\in\sigma_{s}(L)$, by Proposition \ref{pro-4.3}, there exists $y\in U$ such that $x\in\ \!\Uparrow_{s}\!y\subseteq\ \!\uparrow \!y\subseteq U$. Note that $\uparrow \!y$ is compact with respect to any topology whose open sets are upper sets, thus the assertion is proved. If $L$ has a smallest element, let $\{U_{i}:i\in I\}\subseteq\sigma_{s}(L)$ and $L\subseteq\bigcup_{i\in I}U_{i}$, then there exists $i\in I$ such that $0\in U_{i}$, hence $L=\ \!\uparrow \!0\subseteq U_{i}$. Therefore $(L,\sigma_{s}(L))$ is compact.
\end{proof}

\begin{theorem}\label{the4.9} Let $L$ be a dcpo. Then the following conditions are equivalent:
\begin{enumerate}
\item[\rm{(1)}] $L$ is strongly continuous;
\item[\rm{(2)}] For each $x\in L$, $\Uparrow_{s}\!x\in\sigma_{s}(L)$ and if $U\in\sigma_{s}(L)$, then $U=\bigcup\{\Uparrow_{s}\!u:u\in U\}$;
\item[\rm{(3)}] $\textrm{SOFilt}(L)$ is a basis of $\sigma_{s}(L)$ and $\sigma_{s}(L)$ is a continuous lattice;
\item[\rm{(4)}] $\sigma_{s}(L)$ has enough co-primes and is a continuous lattice;
\item[\rm{(5)}] $\sigma_{s}(L)$ is completely distributive;
\item[\rm{(6)}] Both $\sigma_{s}(L)$ and $\sigma_{s}(L)^{\textrm{op}}$ are continuous.
\end{enumerate}
If $L$ is a complete semilattice, then these conditions are equivalent to
\begin{enumerate}
\item[\rm{(7)}] For each point $x\in L$, $\Uparrow_{s}\!x\in\sigma_{s}(L)$ and $x=\textrm{sup}\{\textrm{inf}\ \!U:x\in U\in\sigma_{s}(L)\}$.
\end{enumerate}
\end{theorem}

\begin{proof}
$(1)\Leftrightarrow(5)$: By Proposition \ref{pro-2.4} and Definition \ref{def-3.1}.\\
$(1)\Rightarrow(2)$: By Proposition \ref{pro-4.3} $(1)$.\\
$(2)\Rightarrow(1)$: Let $x\in L$. If $u\ll_{s}x$, $v\ll_{s}x$, then there exists $w\in\ \!\Uparrow_{s}\!u\ \!\cap\Uparrow_{s}\!v$ such that $x\in\ \!\Uparrow_{s}\!w$. Thus $\Downarrow_{s}\!x$ is directed. Set $y=\bigvee\Downarrow_{s}\!x\leq x$, if $y<x$, then $L\setminus\downarrow \!y$ is a strong Scott topology open neighborhood of $x$. Hence there exists $z\in L\setminus\downarrow \!y$ such that $x\in\ \!\Uparrow_{s}\!z$, then $z\ll_{s}x$, and thus $z\leq\bigvee\Downarrow_{s}\!x=y$, which is a contradiction.\\
$(3)\Leftrightarrow(4)$: By Proposition \ref{pro-4.6} $(1)$.\\
$(4)\Leftrightarrow(5)\Leftrightarrow(6)$: By Theorem \ref{the-2.6}.\\
$(3)\Rightarrow(7)$: Suppose that $L$ is a complete semilattice, then for each $U\in\sigma_{s}(L)$ and each $x\in U$, $\textrm{inf}\ \!U$ exists. Let $y=\textrm{sup}\{\textrm{inf}\ \!U:x\in U\in\sigma_{s}(L)\}$. Then $y\leq x$. Assume that $x\nleq y$, then $x\in L\setminus\downarrow y\in\sigma_{s}(L)$. Since $\sigma_{s}(L)$ is a continuous lattice, there exists $V\in\sigma_{s}(L)$ such that $x\in V\ll L\setminus\downarrow y$. And by the conditions, there exists $U\in\textrm{SOFilt}(L)$ such that $x\in U\subseteq V\ll L\setminus\downarrow y$. Note that $\textrm{inf}\ \!U\leq y$, hence $L\setminus\downarrow y\subseteq L\setminus\downarrow\textrm{inf}\ \!U=L\setminus\bigcap\{\downarrow u:u\in U\}=\bigcup\{L\setminus\downarrow u:u\in U\}$. Since $U$ is a filter, $\{L\setminus\downarrow u:u\in U\}$ form a directed family of strong Scott topology open sets. Since $U\ll L\setminus\downarrow y$, there is a $u\in U$ with $U\subseteq L\setminus\downarrow u$, which is a contradiction. Thus $x\leq y$. Since $(2)\Leftrightarrow(3)$, we have $\Uparrow_{s}\!x\in\sigma_{s}(L)$ for all $x\in L$.\\
$(7)\Rightarrow(1)$: We only need to show that for each $U\in\sigma_{s}(L)$ and each $x\in U$, $\textrm{inf}\ \!U\ll_{s}x$. For any directed set $D\subseteq L$ and $z\in L$, if $\uparrow\!\bigvee \!D\ \!\cap\uparrow \!z\subseteq\ \!\uparrow \!x$, since $x\in U\in\sigma_{s}(L)$, there exists $V\in\sigma^{s}(L)$ such that $x\in V\subseteq U$, and hence $\uparrow\!\bigvee \!D\ \!\cap\uparrow \!z\subseteq\ \!\uparrow \!x\subseteq V$. Thus there is a $d\in D$ with $\uparrow \!d\ \!\cap\uparrow \!z\subseteq V$, then $\uparrow \!d\ \!\cap\uparrow \!z\subseteq V\subseteq U\subseteq\ \!\uparrow\textrm{inf}\ \!U$. Therefore $\textrm{inf}~U\ll_{s}x$.
\end{proof}

\begin{corollary}
If $L$ is a complete semilattice, then $L$ is hypercontinuous iff $x=\textrm{sup}\{\textrm{inf}\ \!U:x\in U\in\upsilon(L)\}$ for all $x\in L$.
\end{corollary}
\begin{proof}
By Theorem \ref{the3.9} and Theorem \ref{the4.9}.
\end{proof}

Now we introduce the notation of strong Lawson topology and discuss the properties of strongly continuous domains endowed with the strong Lawson topology.

\begin{definition}
Let $L$ be a dcpo. The common refinement $\sigma_{s}(L)\vee\omega(L)$ of the strong Scott topology and the lower topology is called the \emph{strong Lawson topology} and is denoted by $\lambda_{s}(L)$.
\end{definition}

\begin{lemma}{\rm(\cite{GHK})}\label{lem4.12} Let $L$ be a complete semilattice. Then $\lambda(L)$ is a compact $T_{1}$ topology.
\end{lemma}

\begin{theorem}\label{the4.13} Let $L$ be a complete semilattice. Then $\lambda_{s}(L)$ is a compact $T_{1}$ topology.
\end{theorem}
\begin{proof}
By Lemma \ref{lem4.12}, $(L,\lambda_{s}(L))$ is compact. For each $x\in L$, $\{x\}=\ \!\downarrow \!x\ \!\cap\uparrow \!x$. Since $\downarrow \!x$ is a strong Scott topology closed set and $\uparrow \!x$ is a lower topology closed set, $\{x\}$ is a strong Lawson topology closed set. Thus $(L,\lambda_{s}(L))$ is a $T_{1}$ space.
\end{proof}

\begin{theorem}\label{the4.14} Let $L$ be a strongly continuous domain. Then $(L,\lambda_{s}(L))$ is a $T_{2}$ space.
\end{theorem}
\begin{proof}
Let $x,y\in L$, and $x\neq y$, assume that $x\nleq y$, then there exists $u\ll_{s}x$, such that $u\nleq y$. Thus $x\in\ \!\Uparrow_{s}\!u\in\sigma_{s}(L)$, $y\in L\setminus\uparrow \!u\in\omega(L)$, and $\Uparrow_{s}\!u\cap(L\setminus\uparrow \!u)=\emptyset$. Therefore $(L,\lambda_{s}(L))$ is a $T_{2}$ space.
\end{proof}

\begin{corollary}
Let $L$ is a strongly continuous complete semilattice. Then $\lambda_{s}(L)$ is compact and Hausdorff.
\end{corollary}
\begin{proof}
By Theorem \ref{the4.13} and Theorem \ref{the4.14}.
\end{proof}

Recall that the definition of Scott-continuous functions. For a function $f$ from a dcpo $P$ into a dcpo $Q$, if $f$ is continuous with respect to the Scott topologies, that is, $f^{-1}(U)\in\sigma(P)$ for all $U\in\sigma(Q)$, then $f$ is called a \emph{Scott-continuous function}.\\
\indent A function $f$ is called \emph{strong Scott-continuous} if it is continuous with respect to the strong Scott topologies. Next we discuss the properties of strong Scott-continuous functions.

\begin{proposition} Let $P$, $Q$ be dcpos and $f: P\rightarrow Q$. Consider the following conditions:
\begin{enumerate}
\item[\rm(1)] $f: (P,\sigma_{s}(P))\rightarrow (Q,\sigma_{s}(Q))$ is continuous;
\item[\rm(2)] $f^{-1}(U)\in\sigma_s(P)$ for all $U\in\sigma^{s}(Q)$;
\item[\rm(3)] $f^{-1}(U)\in\sigma^{s}(P)$ for all $U\in\sigma^{s}(Q)$;
\item[\rm(4)] For each directed set $D\subseteq P$ and $x\in P$, $\uparrow \!f(\bigcap_{d\in D}\uparrow \!d \ \!\cap\uparrow \!x)=\bigcap_{d\in D}\uparrow \!f(d) \ \!\cap\uparrow \!f(x)$.
\end{enumerate}
Then $(4)\Rightarrow (3)\Rightarrow (2)\Leftrightarrow (1)$; if both $P$ and $Q$ are sup semilattices and $f$ preserves finite sups, then $(1)\Rightarrow (4)$, and the four conditions are equivalent.
\end{proposition}
\begin{proof}
$(1)\Leftrightarrow (2)$: Trivial.\\
$(4)\Rightarrow (3)$: First we show that $f$ is order preserving. Suppose that $x\leq y$. Let $D=\{y\}$. Then $\uparrow \!f(\uparrow \!y\ \!\cap\uparrow \!x)=\ \!\uparrow \!f(y)\ \!\cap\uparrow \!f(x)$. Hence $\uparrow \!f(\uparrow \!y\ \!\cap\uparrow \!x)=\ \!\uparrow \!f(\uparrow \!y)$, then $f(y)\in\ \!\uparrow \!f(y)\ \!\cap\uparrow \!f(x)\subseteq\ \!\uparrow \!f(x)$. Thus $f(x)\leq f(y)$. For each $U\in\sigma^{s}(Q)$, since $f$ is order preserving, $f^{-1}(U)=\ \!\uparrow \!f^{-1}(U)$. Suppose directed set $D\subseteq P$ and $x\in P$ such that $\bigcap_{d\in D}\uparrow \!d\ \!\cap\uparrow \!x\subseteq f^{-1}(U)$, then $f(\bigcap_{d\in D}\uparrow \!d\ \!\cap\uparrow \!x)\subseteq U$, hence $\bigcap_{d\in D}\uparrow \!f(d)\ \!\cap\uparrow \!f(x)=\ \!\uparrow \!f(\bigcap_{d\in D}\uparrow \!d\ \!\cap\uparrow \!x)\subseteq U$. Since $U\in\sigma^{s}(Q)$, there is a $d\in D$ with $\uparrow \!f(d)\ \!\cap\uparrow \!f(x)\subseteq U$. Thus $\uparrow \!d\ \!\cap\uparrow \!x\subseteq f^{-1}(U)$. Therefore $f^{-1}(U)\in\sigma^{s}(P)$.\\
$(3)\Rightarrow (1)$: For each $U\in\sigma_{s}(Q)$, there exists $\{U_{i}:i\in I\}\subseteq\sigma^{s}(Q)$ such that $U=\bigcup_{i\in I}U_{i}$ by the definition of $\sigma_{s}(Q)$. Then $f^{-1}(U)=f^{-1}(\bigcup_{i\in I}U_{i})=\bigcup_{i\in I}f^{-1}(U_{i})$. By precondition $(2)$, $f^{-1}(U_{i})\in\sigma^{s}(P)$ for all $i\in I$. Thus $f^{-1}(U)\in\sigma_{s}(P)$.\\
$(1)\Rightarrow (4)$: Suppose that both $P$ and $Q$ are sup semilattices and $f$ preserves finite sups, then $\sigma_{s}(P)=\sigma(P), \sigma_{s}(Q)=\sigma(Q)$. For each directed set $D\subseteq P$ and $x\in P$, we have $\bigcap_{d\in D}\!\uparrow \!d\ \!\cap\uparrow \!x=\bigcap_{d\in D}\uparrow\!(d\vee x)=\ \!\uparrow\!\bigvee_{d\in D}(d\vee x)$, thus $\uparrow \!f(\bigcap_{d\in D}\!\uparrow \!d\ \!\cap\uparrow \!x)=\ \!\uparrow \!f(\bigvee_{d\in D}(d\vee x))=\ \!\uparrow \!\bigvee_{d\in D}f(d\vee x)=\ \!\uparrow \!\bigvee_{d\in D}f(d)\vee f(x)=\bigcap_{d\in D}\uparrow\!(f(d)\vee f(x))=\bigcap_{d\in D}\uparrow \!f(d)\ \!\cap\uparrow \!f(x)$.
\end{proof}

\begin{proposition}
Let $P$ be a strongly continuous domain. Both $f: (P,\sigma_{s}(P))\rightarrow (Q,\sigma_{s}(Q))$ and $g: (Q,\sigma_{s}(Q))\rightarrow (P,\sigma_{s}(P))$ are continuous functions, and $f\circ g=\mathbf{1}_{Q}$. Then $Q$ is a strongly continuous domain.
\end{proposition}

\begin{proof}
Let $U\in\sigma_{s}(Q)$ and $y\in U$. Then $g(y)\in f^{-1}(U)$. Since $f$ is continuous, $f^{-1}(U)\in\sigma_{s}(P)$. Since $P$ is a strongly continuous domain, there exists $u\in P$ such that $g(y)\in \textmd{int}_{\sigma_{s}(P)}\!\uparrow \!u\subseteq\ \uparrow \!u\subseteq f^{-1}(U)$, thus $y\in g^{-1}(\textmd{int}_{\sigma_{s}(P)}\!\uparrow \!u)\subseteq\ \uparrow \!f(u)\subseteq U$. Since $g$ is continuous, $g^{-1}(\textmd{int}_{\sigma_{s}(P)}\!\uparrow \!u)\in\sigma_{s}(Q)$. Hence $y\in \textmd{int}_{\sigma_{s}(Q)}\!\uparrow \!f(u)\subseteq\ \uparrow \!f(u)\subseteq U$. Therefore $Q$ is a strongly continuous domain.
\end{proof}

redpajama_set_name: RedPajamaArXiv


text:
Q: Version Control: multiple version hell, file synchronization I would like to know how you normally deal with this situation:
I have a set of utility functions. Say..5..10 files. And technically they are static library, cross-platform - SConscript/SConstruct plus Visual Studio project (not solution).
Those utility functions are used in multiple small projects (15+, number increases over time). Each project has a copy of a few files or of an entire library, not a link into one central place. Sometimes project uses one file, two files, some use everything. Normally, utility functions are included as a copy of every file and SConscript/SConstruct or Visual Studio Project (depending on the situation). Each project has a separate git repository. Sometimes one project is derived from other, sometimes it isn't.
You work on every one of them, in random order. There are no other people (to make things simpler)
The problem arises when while working on one project you modify those utility function files.
Because each project has a copy of file, this introduces new version, which leads to the mess when you try later (week later, for example) to guess which version has a most complete functionality (i.e. you added a function to a.cpp in one project, and added another function to a.cpp in another project, which created a version fork)
How would you handle this situation to avoid "version hell"?
One way I can think of is using symbolic links/hard links, but it isn't perfect - if you delete one central storage, it will all go to hell. And hard links won't work on dual-boot system (although symbolic links will).
It looks like what I need is something like advanced git repository, where code for the project is stored in one local repository, but is synchronized with multiple external repositories. But I'm not sure how to do it or if it is possible to do this with git.
So, what do you think?

A: The normal simple way would be to have the library as a project in your version control, and if there is a modification, to edit only this project.
Then, other projects that need the library can get the needed files from the library project.

A: It is not completely clear to me what you want but maybe git submodules might help : http://git-scm.com/docs/git-submodule

A: In Subversion you can use externals (it's not GIT I know, but these tips might still help).  This is how it works:

*

*Split the application specific code (\MYAPP) from the common code (\COMMON)

*Remove all duplicates from the applications; they should only use the common-code

*Bring in the common code in the applications by adding \COMMON as an external in \MYAPP

You will also probably have versions of your application.  Also introduce versions in the common code.  So your application will have the following folders in the repository:

*

*\MYAPP\TRUNK

*\MYAPP\V1

*\MYAPP\V2

Similarly, add versions to the common-code, either using version numbers, like this:

*

*\COMMON\TRUNK

*\COMMON\V1

*\COMMON\V2

Or using dates, like this:

*

*\COMMON\TRUNK

*\COMMON\2010JAN01

*\COMMON\2010MAR28

The externals of \MYAPP\TRUNK should point to \COMMON\TRUNK, that's obvious.
Try to synchronize the versions of the common-code with the versions of the applications, so every time an application version is fixed, also the common-code is fixed, and the application version will point to the relevant common-code external.
E.g. the externals of \MYAPP\V1 may point to \COMMON\2010JAN01.
The advantage of this approach is that every developer can now extend, improve, debug the common-code.  Disadvantage is that the compilation time of applications will increase as the common-code will increase.
The alternative (putting libraries in your version system) has the disadvantage that the management (extending, improving, debugging) of the common code is always done separately from the management of the applications, which may prevent developers from writing generic common code at all (and everyone starts to write their own versions of 'generic' classes).
On the other hand, if you have a clear and flexible team solely responsible for the common code, the common code will be under much better control in the last alternative.

A: In Configuration (general) terms, a solution is to have multiple trunks (branches):

*

*Release

*Integration

*Development
Release
This trunk / branch contains software that has passed Quality Assurance and can be released to a customer.  After release, all files are marked as "read-only".  The are given a label to identify the files with the release number.
Periodically or on demand the testing guru's will take the latest (tip) version from the Integration trunk and submit to grueling quality tests.  This is how an integration version is promoted to a release version.
Integration
This trunk contains the latest working code.  It contains bug fixes and new features.  The files should be labeled after each bug fix or new feature.
Code is moved into the integration branch after the bug has passed the quality testing or the new feature is fully developed (and tested).  A good idea here is to label the integration version with a temporary label before integrating developer's code.
Development
These are branches made by developers for fixing bugs or developing new features.  This can be a copy of all the files moved onto their local machine or only the files that need to be modified (with links to the Integration trunk for all other files).
When moving between trunks, the code must pass qualification testing, and there must be permission to move to the trunk.  For example, unwarranted new features should not be put into the integration branch without authorization.

In your case, the files need to be either checked back into the Integration trunk after they have been modified OR a whole new branch or trunk if the code is too different from the previous version (such as adding new features).
I've been studying GIT and SourceSafe trying to figure out how to implement this schema.  The schema is easy to implement in the bigger Configuration Management applications like PVCS and ClearCase.  Looks like for GIT, duplicated repositories are necessary (one repository for each trunk).  SourceSafe clearly states that it only allows one label per version, so files that have not changed will loose label information.

redpajama_set_name: RedPajamaStackExchange


SSR report: It will show you a list of all the SSR booked. You will be able to filter the information by flight and SSR.
Booking Transfers: It will show you a list of the booking transfer done. You will be able to filter by flight and user. Please notice that the log is available from today 10/06/18 and past transfer will not be shown.
SMS report: It will show you all the SMS sent from the system. You will be able to filter by Flight number, FF number, PNR and status.
Please notice that each System Administrator should activate these reports for the relevant groups in their airlines.
In order to activate them please go to Administrations > Permissions.
You need to select the relevant groups and assign the reports.


Florida's water supply is no longer sufficient to meet the future needs of the State's growing population based on current water use practices. Regional water supply plans developed by the five water management districts have identified areas where water supply shortages are projected to occur. As a result, recent legislative changes now require water supply concurrency, strengthening the link between local government agencies' land use planning and regional water supply planning.
The SMW GeoSciences consulting team can provide assistance with water supply concurrency including growth and water supply projections, water supply evaluation, 10 Year Water Facilities Work Plans and assistance with water supply related Comprehensive Plan updates.


The men's light heavyweight (81 kilograms) event at the 2006 Asian Games took place from 6 to 13 December 2006 at Aspire Hall 5, Doha, Qatar.
^ "15.Asian Games – Doha, Qatar – December 2–13 2006". amateur-boxing.strefa.pl. Retrieved 26 June 2014.
This page was last edited on 4 January 2019, at 04:43 (UTC).


text:
Brian S. Nageotte, President/CEO
Brian is a graduate of Penn State Behrend with a BS in Accounting and acquired his MBA from Case Western University. He is a Certified Public Accountant and a member of the American Institute of CPA's and the Pennsylvania Institute of CPA's. He worked in public accounting for 6 years before coming to Wesbury in 1999. Brian started at Wesbury as Controller and in 2005 became CFO. In 2010, Brian became Wesbury's Chief Operating Officer managing all aspects of Wesbury's operations. He is active in the local community serving as the Chairman of the Salvation Army Advisory Board. Brian has also been on the Meadville-Western Crawford County Board of Directors and the Board of Incorporators for Economic Progress Alliance. Brian became Wesbury's President and CEO in 2015.
Joe Palmiero, CFO
Joe Palmiero has been Wesbury's Controller since 2005 and has recently been promoted to Chief Financial Officer. After obtaining a BS in Accounting from Slippery Rock University, Joe worked in Public Accounting for eight years. He is a Certified Public Accountant and a member of the Institution of Management Accountants, American Institute of CPA's and the Pennsylvania Institute of CPA's.
Sheila Bundy, RN, NHA
Sheila Bundy is the Director of Healthcare and Community Based Services for Wesbury and the Administrator for Grace Rehabilitation and Health Center and the Memory Support Center. A graduate of St. Vincent School of Nursing, Sheila has more than 25 years of experience in Long Term Care as a Registered Nurse and Nursing Home Administrator. Her duties include the day to day operations of our Health Center, Memory Support Center and Wesbury at Home. Sheila is proud to serve as a member of VNA Alliance's Professional Advisory Committee and Meadville Rotary. Sheila also serves as a member of the United Methodist Association's Shared Learning Committee and most recently, she was nominated to serve on the EAGLE Accreditation Commission.
Larry D. Marsteller, NHA
Administrator of Cribbs Residential Center and Thoburn Village Larry is a graduate of Edinboro University of Pennsylvania with a B.S. in Business Administration and a certificate in secondary education. He also attended Community College of Allegheny County for the required courses to earn his NHA license. Larry's community involvement includes serving as Board of Director for ARC (Association for Retarded Citizens) and Greendale Cemetery. He has also served as Vice Chairman for the Crawford Area Transportation Authority. Larry has been with Wesbury since 1997 and is pleased to be part of a community minded organization that enriches the lives of seniors in the Meadville area. As Administrator of Cribbs Residential Center and Thoburn Village, Larry is responsible for all departments related to the services provided in these areas.
Melissa Porter, VP, Sales and Marketing
Melissa Porter joined the Wesbury team as VP of Sales and Marketing in 2009. She is responsible for all campus wide marketing efforts including the development of the annual marketing plan, analyzing performance measures, directing all advertising, overseeing the referral networking and all sales related activity to sustain a strong aggregate census. Prior experience includes a 10-year career with AAA West Penn West Virginia Travel Agency where Melissa was the largest regional producer. She was also the Director of Sales and Marketing at a nationally accredited continuing care retirement community in Erie, PA for 5 years.
Rick York, VP of Human Resources
Rick York graduated from Youngstown State University with a Bachelor of Science degree in Business Administration. He ran his own business, York Painting, for fifteen years then sold the business and entered the world of Manufacturing where he began his career in Human Resources. Rick joined Wesbury in December 2008 when he was hired as VP of Human Resources. Rick oversees all employee related issues for the community's 350+ employee workforce.
Pastor Sam Marchetta, Director of Pastoral Care
Pastor Samuel Marchetta comes to Wesbury after working as Spiritual Care Coordinator/Bereavement Coordinator at Heartland Hospice in Hermitage since 2008. Prior to working for Heartland Hospice, Samuel was the Lead Pastor at the Ridgewood Assembly of God Church in Pittsburgh and the Director of Student Ministries at South Hills Assembly of God in Bethel Park. Samuel received his Bachelor of Arts degree from Central Bible College in Springfield, Missouri and his Master of Arts from St. Bonaventure University in St. Bonaventure, New York. With a broad range of ministry experience, Samuel says he feels a strong connection to seniors and a passion to ensure their stories are heard, their dignity conserved and their contributions valued.
Rhonda Thomas, VP of Stewardship and Development for The Wesbury Foundation
Rhonda Thomas began working for The Wesbury Foundation as Event Coordinator in 2008. Prior to this, she worked as Wesbury's Director of Activities and Volunteer Services for ten years before taking a few years' off to raise her family. Before starting her career at Wesbury, Rhonda worked at Horizon Hospital System as the Manager of Development and Volunteer Services. She graduated from Slippery Rock University with a BA Degree in Communications/Public Relations and with a minor in Business Administration. Rhonda has been a long time supporter of Wesbury, greatly valuing its service and mission.
Alishia Stevenson, VP of Compliance, Risk, and Quality Management
Alishia is the Vice President of Compliance, Risk, and Quality Management for Wesbury. She is a graduate of Clarion University where she acquired her AS in Nursing and has more than 17 years of experience as a Registered Nurse in both acute and long-term care settings. After serving as Wesbury's Director of Nursing for six years, Alishia attended Penn State Beaver where she received her education to obtain her Nursing Home Administrator license and transitioned into her current role as the VP of Compliance, Risk, and Quality Management. Some of her responsibilities include the development, implementation, oversight, and monitoring of Wesbury's corporate compliance, risk, and quality management functions along with maintaining requirements for our EAGLE accreditation. She also serves as the organization's Corporate Compliance Officer.

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text:
Destiny 2 streamer UhMaayyze talks rapping, mindset, and Dragon Ball
Detrick 'UhMaayyze' Houchens wants to teach viewers about positivity through the power of Destiny and rapping
It's another day of Destiny 2 streaming for Detrick 'UhMaayyze' Houchens, and he and his team have zone advantage in The Dead Cliffs. Uhmaayyze is rocking a sniper rifle/hand cannon combo with a sword in his back pocket, and as he's pushing with his team toward point A, he's rapping the action on the screen, an old-school beat backing up his flow.
"'Maayyze, what's your favourite move?' I call it Dawnblade," he rhymes as he pops his Warlock super. "Hey, don't run from me, I'm too fast, I be moving like he's moving now, I'm too fabulous!" He slices an enemy who's fled around a doorway into the Depot area, and takes out another with a fiery Dawnblade swing for a double play.
The clips Houchens shares on Twitter of his live Destiny 2 freestyle sessions are almost frustrating to watch: it seems like it should be impossible to be an effective Crucible player while simultaneously composing and performing rhymes that describe exactly what's happening in the game. But he says that combining his love of freestyling with Destiny, which he's been playing since the 2014 beta, has resulted in getting better at both.
"That's what's scary," he tells us. "I tell chat that when I'm not rapping, I can't even play like that. You know what I mean? But when I rap, I play at this level that is very, very balanced."
UhMaayyze says he's been on Twitch for six years, but when he started out, he played Destiny and occasionally would break to rap for a while. Freestyling while he played seemed like a terrible idea.
I want people to enjoy themselves making games, so I want Bungie to clean it up
Detrick 'UhMaayyze' Houchens
"I was like, nah, I can't do anything like that," he says. "I have to be at a standstill when I'm doing rap. I have to be not moving, completely." But he said eventually the idea grew more appealing as a way to experiment with what he could do on Twitch. "Since it's my sixth year on the platform, I mean, why not? This is my career, I might as well go ahead and explore it and see what I can do."
After hitting a subscription goal he'd set for his viewers, UhMaayyze started playing Destiny 2 on stream, and he quickly discovered a comfortable groove as he added freestyle rhymes about the in-game action.
"When I'm freestyling, and I'm seeing what I'm doing, the other side of my mind is still at ease, and playing at that high-tier level that I wanted to play at," he explains. "It's like trying to control your words on the left side [of your brain], but trying to control the thumbsticks on the right side. So one side of your mind is telling a story. The other side of your mind is sort of producing the story you're telling."
Standing with two fellow fireteam members recently, UhMaayyze started up a beat, as the other Guardians in his group danced with emotes.
"Well I'm nasty when it comes to this game, I got a fever! 'What you kill that boss with Maayyze?' This is the Sleeper," he spat, hefting a very big gun called Sleeper Simulant in his Warlock's hands. "Crazy when you talk about games, I feelin' old / I've been strugglin' for streams right now for six years on."
Uhmaayyze's old-school style draws from his rap influences; Tupac, Biggie, Nipsey Hussle, and Dr Dre are his top four, with some Wu Tang Clan thrown in for good measure. "I'm an '80s guy, and when people hear my flow, they get '80s feelings."
UhMaayyze is also a big mindset guy, and he's keen to encourage his viewers to adopt a more positive attitude, which he sees as the key to success in streaming and in life in general. "It's a matter of not getting in your own way, and clearing distractions from your mind. It's like being Goku," he says.
"If you watch Dragon Ball Super, you see this animated form Goku goes into called Ultra Instinct. But he's not at the max form of the technique, he's sort of in his Bruce Lee stage, where he's using his mind, and his mind is doing more of the fighting than himself.
"He's literally fighting and his eyes are closed, but he's totally on point, he can't be hit, and he's hitting them in the critical spots without even looking at them," UhMaayyze explains. "That's what it feels like when you're cracking that mindset."
UhMaayyze has an encouraging, persuasive tone when he talks about getting his mindset right, and he's eager to share his insights with his viewers. It's clear that he's drawn to coaching and teaching roles, which was a big part of what made Destiny appeal to him in the first place.
Freestyling and gaming in destiny 2 pic.twitter.com/k99RxQ1Yys
— Uhmaayyze (@uhmaayyze) November 16, 2021
"What really drove me in a lot more was meeting communities, because I was just used to playing with my friends from work. I didn't really branch out to talk to a lot of other people," he says. His friends introduced him to raids, and something clicked – he wanted to learn the raid, and help others learn it, too. He found some Looking For Group communities and enthusiastically offered his services as a Destiny 'sherpa'.
One side of your mind is telling a story, the other side is producing it
"I was always the one coming in very, very hype, out of my mind," UhMaayyze recalls with a laugh. He says while fireteam members groused about which gear they needed, he would tell them, "you don't need that, man, you need your mindset!"
Once Destiny 2 came out, he says, he shifted away from the helper role he'd taken on in the first game. He played with groups and talked with people. "I've realised that I'm a very big talker," he says. "And I love getting to know people, whether they're new or old, as my main mission – trying to get to know you as a person."
That focus on others and their state of mind has made this year's revelations about toxic work environments at game development studios difficult for UhMaayyze, as someone trying to balance a developing streaming career with another full-time job. Recent reporting by IGN about Bungie's own struggles with toxic workplace culture were particularly disappointing.
I've realised that I'm a very big talker, and I love getting to know people
"When I saw the Bungie take, that one sort of hit," he says. The news arrived while he was streaming, and some of his fans and friends alerted him to it through direct messages and chat. UhMaayyze says he waited until his stream was over to read up on it, and while he was upset by the news, it wasn't a complete surprise.
"I want people to enjoy themselves making games," he says. "So I want Bungie to clean it up, stay powerful, and continue to create this amazing atmosphere that you're trying to build. And don't break it."
As for himself, UhMaayyze is going to keep grinding. He says consistency is what he's relied on when content creation starts to feel draining, or when growth hasn't come as quickly as he's wanted it to.
"You're going to feel hurt, you're going to feel pressure, you're going to feel jealousy, you're going to feel that you deserve more for what you're doing," he says. "I'm not gonna lie, man, I run into those walls all the time. But here's how I overcome it: I just keep doing what I'm doing. That's it. I do what I did yesterday, I'm doing it again today."
You can find UhMaayyze on Twitch and Twitter.
Ian Boudreau Senior news writer
A PC gamer since the 1980s, Ian enjoys strategy games, RPGs, and the FPS classics like Unreal and Quake. He began his writing career as a US army journalist, later working for a daily newspaper in New York while studying political science. Now he's happiest when he's moving large armies of orcs around in Total War: Warhammer or exploring dingy castle basements in Dark Souls.
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Destiny 2: Beyond Light review
Destiny 2 exotics


As the largest Asian American cultural center of its kind in North America, JACCC sustains a diverse program of cultural and community events throughout the year. Each event and program has always been made possible by the hard work and generosity of our volunteers.
We are indebted to our volunteers who have helped us with many of our community festivals and cultural events over the years. We are continually looking for volunteers who are willing to donate their time and hard work to many of these special events that wouldn't be possible without their support.
If you are interested in volunteering at JACCC, please email Kent at volunteer@jaccc.org.
The George J. Doizaki Gallery is the site for more than 13 exhibitions per year, from traditional to contemporary arts. JACCC is looking for volunteers to work as gallery monitors and also to help with the set-up of many of our unique exhibits.


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Steve is a Government Agent looking for the gang that stole the U.S. Mail. He goes undercover…
Director: Fred F. Sears
Actors: Anne James, Charles Starrett, Edgar Dearing, Frank Jenks, Harmonica Bill, Jock Mahoney, Smiley Burnette, Steve Darrell
Anna Sewell's classic 1877 novel beautifully comes to life in this family drama set in England. Told from the point of view of Black Beauty himself, the story sheds light…
Genre: Drama, Family, Western
After Drew Dixon, an upright young man, is sent west by his religious family to avoid being drafted into the Civil War, he drifts across the land with a loose…
Man from Del Rio
Mexican gunfighter Dave Robles outdraws the town's outlaw-turned-sheriff and is invited to fill the dead man's shoes. But a tin star doesn't bring automatic respectability and Robles is shunned by…
Comes a Horseman
Ella Connors is a single woman who gets pressured to sell her failing cattle farm to her corrupt ex suitor, Jacob Ewing. She asks for help from her neighbor, Frank…
Angel and the Badman
Notorious shootist and womanizer Quirt Evans' horse collapses as he passes a Quaker family's home. Quirt has been wounded, and the kindly family takes him in to nurse him back…
Genre: Romance, Western
The Lusty Men
Retired rodeo champion Jeff McCloud agrees to mentor novice rodeo contestant Wes Merritt against the wishes of Merritt's wife who fears the dangers of this rough sport.
Genre: Action, Drama, Western
Stagecoach: The Texas Jack Story
After retiring from his life as an outlaw, ranch owner Nathaniel Reed quietly leads an honest existence with his devoted wife, Laura Lee. But his gun-slinging past suddenly comes back…
Two Mules for Sister Sara
Hogan, on his way to do some reconnaissance for a future mission to capture a French fort, encounters Sister Sara, a nun in trouble. Before he knows it, Hogan is…
Gatling Gun
This dramatization of the origin of Dr. Gatling's self-named invention stands tall in the annals of the Old West. As cavalry transported the high-tech gun across the dangerous frontier, it…
Genre: Action, History, Western
William Munny is a retired, once-ruthless killer turned gentle widower and hog farmer. To help support his two motherless children, he accepts one last bounty-hunter mission to find the men…
The Yellow Mountain
A formula brawling-buddies western where one goes bad and then returns to the fold. Pete Menlo owns some gold claims in Nevada where he is joined by his old friend…
Big-city lawyer Casey McKay, is drawn to a small town by his ex-wife to defend her brother, accused of murdering a DA. He discovers a web of conspiracy that puts…
Genre: Action, Western


Looking for a meatless entree? Here's a SlimCado / Chickpea salad sent in by Nakita, sampled in the executive conference area last week.
An industry tradeshow where you see practically every retail and wholesale customer that you have. The sales force and marketing is all hands on deck.


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You are here: Home / Education / UW gets federal funds for flex program
UW gets federal funds for flex program
September 3, 2014 By Jackie Johnson
The University of Wisconsin System gets approval to give federal financial aid to some students in a competency-based flexible option degree program. Adults who started college but never finished have a new, affordable opportunity to earn a UW degree at their own pace — through the UW Colleges Flexible Option program.
UW System President Ray Cross explains, it's a result of a landmark financial aid option approved last week by the U.S. Department of Education. "There are in excess of 750,000 adults in Wisconsin that fit that criteria — somewhere between 750,000 and a million," and he says, "There are 31 million in the United States, so that's a pretty sizable number."
Cross says Wisconsin needs those individuals — workers — to obtain their degrees so they can help generate growth in the economy. He says there's a need to fill the so-called "talent gap." Cross says, "It isn't in every discipline; it's in select disciplines." He says, "The state is clearly short on talented workers in specific areas."
Aaron Brower, interim chancellor of UW Colleges and UW-Extension, says the highest demand is for workers is in the areas of healthcare, information technology (IT), and business. He says this is a big deal and others will look at the UW as a model. "We've now created a direct pathway for other institutions who wish to award aid for competency-based education."
This funding approval by the federal government allowing aid to students enrolled in competency-based education is the first of its kind for a public higher education system in the country, according to Cross. The flexible degree concept was introduced in June 2012. The first group of students started in January.
Filed Under: Education, News, Politics / Govt


The 2016 Mercury Dime Centennial Gold Coin has sold about 98% of its available mintage, according to official sales numbers posted today by the U.S. Mint.
The total puts sales of the Gold Mercury Dime at 122,510 units, just 2,490 away from the item's 125,000-piece mintage limit, giving collectors a general sense of how many more of the coins may, or may not, be released in the future.
As noted on Mint News Blog, there is currently no way to know for certain whether the Mint plans to sell more of this issue. It may declare a sellout soon, or it may release small batches of the coin in occasional morning sales, inching the total closer to 125,000 units over the next several weeks.
Coin Update will post the U.S. Mint's complete numismatic sales report tomorrow, April 27.
Update: this post has been updated to reflect new information published on April 26 in this week's U.S. Mint numismatic sales report.
Just don't buy from L&C coins. They sell the problem coins and keep the best for themselves. They have the worst customer service ever.


Give your outfit some life with a Cary pocket square. A solid orange and white center is traced by a yellow and orange edge to make for a refreshing, yet uncompli... read more Give your outfit some life with a Cary pocket square. A solid orange and white center is traced by a yellow and orange edge to make for a refreshing, yet uncomplicated design.


DanceKids offers a unique take on birthday parties for kids aged 3-6 and 7-10!
Our parties keep both age groups entertained for a whole hour with fun dances and sweet costumes. In all our themes we include environmental or cultural context, which gives the parties some educational depth on top of being heaps of fun.


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Perino reflects on tornadoes in Atlanta during 2008 SEC Tournament
By: Leigh Searcy
ATLANTA, Ga. (LEX 18) — Who remembers March 14th, 2008 inside the Georgia Dome?
Hey Kentucky's Mary Jo Perino was there getting ready for Kentucky to play in the next game when a tornado ripped through downtown Atlanta.
"There was a giant scoreboard that was hanging over bleachers full of fans swaying back and forth," Perino reflected. "We just kept watching that going, 'Oh my God.'"
It was 9:40 at night. Alabama and Mississippi went into overtime. Thousands of fans were packed inside the Dome as parts of the roof loosened and debris flew everywhere outside the complex.
"The streets were desolate except for debris, board, metal....everything, everywhere," Perino added. "It was a scary moment for sure."
Perino, like thousands of other fans, couldn't leave the Georgia Dome, but when they did they saw the destruction including a damaged LEX 18 live truck hit by flying debris.
The Kentucky game had to be postponed until the next day. It was moved to the campus of Georgia Tech where most fans could not attend the game.
Phil Coale/ASSOCIATED PRESS
Kim Hicks, of Lexington, Ky., holds up a sign up at the Georgia-Kentucky Southeastern Conference basketball game at Alexander Memorial Coliseum on the campus of Georgia Tech in Atlanta, Saturday, March 15, 2008. The tournament was forced to move to Georgia Tech after high winds damaged the Georgia Dome. Hicks was at the Georgia Dome on Friday night when it was damaged by a possible tornado. Georgia won 60-56 in overtime. (AP Photo/Phil Coale)
Like thousands of other Kentucky fans, Perino will head to Nashville next week for the SEC tournament at Bridgestone Arena, which was not damaged by Tuesday's tornado. Mary Jo says her heart goes out to everyone affected by the tornado.
"Feeling really sad for people who are waiting to show off their city and waiting for people to shop in their stores," Perino said. "You feel awful for them because they're dealing with life altering events, not preparing for what should be a fun amazing time."


Rinse the salmon under cold water to remove the brown sugar mixture. Pat dry with paper towels. Place the salmon on a large baking sheet. Brush the top of the salmon with 1 tablespoon of the oil and the remaining 1 tablespoon bourbon. Refrigerate the salmon�... Watch this video to learn how to make hot smoked salmon. Smoking fish isn't very difficult all you need are a grill, wet wood chips, and a pan made of aluminum foil.
Break the hot-smoked salmon into large chunks, then scatter over the top along with the spring onions. Finish by pouring remaining dressing over the top. Finish by pouring �... A hot-smoked fish will be preserved better than a fresh fish, but it will still spoil faster than a cold-smoked fish. That said, you still do not want high temperatures. Ideally, you should smoke your fish at around 140 degrees F.
Divide the broccolini, salmon, rice and cucumber among serving plates, or arrange on a large platter. Drizzle the dressing over the salad and toss to combine. Season well. Drizzle the dressing over the salad and toss to combine.
Watch this video to learn how to make hot smoked salmon. Smoking fish isn't very difficult all you need are a grill, wet wood chips, and a pan made of aluminum foil.


For thousands of years we have evolved to live in direct daily contact with the rest of nature. The forests, streams and savannahs were essential to our basic survival. But in the last few centuries, people in industrial societies have moved farther and farther away from that natural source of good health, with disastrous results.
Environmental well-being includes trying to live in harmony with the Earth by understanding the impact of your interaction with nature and your personal environment, and taking action to protect the world around you. By leading a lifestyle that is respectful to our environment and minimizes any harm done to it is a critical part of environmental wellness. It can protect you from environmental hazards and minimizing the negative impact of your behavior on the environment.
Ride your bike, walk or take public transportation instead of driving.
Plant and tend a garden.
Remove clutter from your home or office.
Volunteer time to a worthy cause.
Buzzell, Linda. "Have You Taken Your Vitamin 'N' Today?" The Huffington Post. TheHuffingtonPost.com, 23 Aug. 2010. Web. 02 Apr. 2014.
"Mind Body Wellness Challenge." Wellness Challenge: Environmental Wellness. N.p., n.d. Web. 01 Apr. 2014.
"University of California, Riverside." Wellness: Environmental Wellness. N.p., n.d. Web. 01 Apr. 2014.
April is here! In case you haven't heard it before… April's showers brings May's flowers! This is the perfect time to get re-acquainted with nature. Get outdoors, enjoy the fresh air, and do a little gardening — it's the best therapy on earth!
Now in some areas, April brings the first signs of winter's end; in others, it's the gateway to hot, summery weather. But in most climates, it's the magical month when gardens start to come to life. And if the weather cooperates, it's a time to plant, water everything and take care of the lawn.
Remember to adjust gardening tips to fit your own growing season — but most important of all, wait until the last frost to put tender plants in the ground. Step outside and soak in the sights of the season with our friendly reminders on how to get started!
Plan Ahead — Choose planting areas based on exposure to sun, shade, wind and distance from water source. Take a Soil Test and check soil pH with a home soil- test kit, taking several samples from different planting areas for an accurate reading. Enrich soil as necessary.
Watering — Don't let your garden dry out before it even hits full stride. Get into the rhythm of watering regularly early in the season to ensure happy, healthy plants.
Vegetables — In most areas, April is the real start of the outdoor vegetable garden, especially perennials such as asparagus, although it's probably still not warm enough to plant heat-loving crops such as tomatoes, cucumbers and squash.
Pests — Don't let pests enjoy the fruits — or vegetables for that matter — of your gardening labors. Take precautions early and throughout the growing season to keep your plants healthy and edible.
Weeds — Get the jump on weeds by applying a pre-emergent weed killer to beds and borders. Put it down in early April for best results. It works by preventing seeds from germinating, so don't apply anywhere you're planting seeds.
So, Spring doesn't just mean reorganizing your house, it means re-energizing your soul. Don't forget to stop and smell the roses today!
Anderson, Sally. "April Gardening Checklist." MSN Real Estate. N.p., n.d. Web. 01 Apr. 2014.
"Gardener's Check List for April." Organic Gardening. N.p., n.d. Web. 01 Apr. 2014.
"Spring Gardening Tips." Martha Stewart. N.p., n.d. Web. 01 Apr. 2014.


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Size 1 lb (454 g) 2 lbs (907 g) 5 lbs (2.27 kg)
Flavour Unflavoured & Unsweetened
Quantity 48 96 244 500
1 lb (454 g) / Unflavoured & Unsweetened / 48 1 lb (454 g) / Unflavoured & Unsweetened / 96 1 lb (454 g) / Unflavoured & Unsweetened / 244 1 lb (454 g) / Unflavoured & Unsweetened / 500 2 lbs (907 g) / Unflavoured & Unsweetened / 48 2 lbs (907 g) / Unflavoured & Unsweetened / 96 2 lbs (907 g) / Unflavoured & Unsweetened / 244 2 lbs (907 g) / Unflavoured & Unsweetened / 500 5 lbs (2.27 kg) / Unflavoured & Unsweetened / 48 5 lbs (2.27 kg) / Unflavoured & Unsweetened / 96 5 lbs (2.27 kg) / Unflavoured & Unsweetened / 244 5 lbs (2.27 kg) / Unflavoured & Unsweetened / 500
Pea protein isolate, ideal for vegans and vegetarians, is a 100% natural vegetable source of protein derived from golden peas and is free from dairy, lactose, cholesterol, sugar and other ingredients typically found in whey proteins.
Health Canada Recommended Dose (powder): Adults: 1 Scoop(s) 1 time(s) per day. Mix product well in 1-2 cups of liquid (water, juice, etc.) immediately before consumption. Store in a cool, dry place.
*Nutritional facts based on natural flavour. Other flavours may vary by 4-10%.
Pea Protein Isolate Ingredients
Per Scoop
Medicinal Ingredients (per scoop): Pea Protein (Pea Protein, Pisum sativum - Seed) .......................... 24.6 Grams (80 Percent Protein)
Non-Medicinal Ingredients: 100% Natural Pea Protein Isolate (non-GMO).
Potential side effects
Always speak to your doctor before using any new supplement, and discontinue use immediately, if you experience any adverse side effects. Pregnant and breastfeeding women should consult their doctor before using pea protein isolate. Although very healthy and safe, some mild side effects can include:
Mild stomach cramps
Cautions and Warnings
Ensure to drink enough fluid before, during, and after exercise. If you are pregnant or breastfeeding, consult a healthcare practitioner before using this product.
This product is made in a facility that handles milk products, gluten, shellfish, soy, peanuts and other tree nuts.
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