In addition to the mentors listed below we bring in industry experts and phenomenal individuals on a case-by-case basis based on the specific cohort companies.
Born and raised in Oregon, Gary has passionately pursued this outdoor wonderland in every way he can. He grew up skating, surfing, waterskiing and riding motocross on the Oregon Coast, which inevitably led to a natural interest in snow sports as he explored the rest of the state.
Following his passion for business and entrepreneurship, Gary formed one of the first sales rep groups to serve the action sports industry and helped pioneer the new snowboard sports category. He later transitioned into sales management and consulting, assisting Morrow Snowboards in their purchase of an apparel brand and a transition to a public company. He also consulted with major brands looking to enter the lucrative action sports market, including Helly Hansen and Timex.
With experience and a knack for emerging categories, Gary became an early adopter of organic apparel usage in the outdoor industry, working with a privately-held company to introduce and develop apparel for brands such as Patagonia, Prana, LuLu Lemon, Marmot and many others. Not one to sit still, he also became involved in the fast-growing stand up paddle industry as Director of Global Sales at KIALOA Paddles.
Gary continues to have a passion for all outdoor activities and spending time with his family. He feels fortunate to live in Bend, Oregon where that balance is easily obtainable. BOW was born from his inspiration to help Bend become a hub of the outdoor industry and capitalize on its unique abundance of outdoor recreational activities. He saw a need to support local companies trying to make a mark in this industry and help support this growing economic category in Central Oregon.
Currently, Gary also oversees Sales for Homeschool Outerwear, sits on the board of directors for the Oregon Outdoor Alliance, and consults for outdoor industry businesses.
Will Blount grew up playing on the mountains and rivers of Colorado. He learned early that outdoor recreational pursuits, following his curiosity for the unknown, and learning by doing were his path to fulfillment. He was often humbled by nature, but discovered a talent for navigating and leading others through big water - both on the river and off. He believes that many of the skills that he uses to navigate the business landscape are things that he learned in his backcountry pursuits, maximizing each person's strengths to achieve a common goal. Will has worked in the outdoor industry as President of Ruffwear for over 13 years, manufacturing outdoor dog gear that is sold in 2,500 retail locations in the US and distributed in 50 countries internationally. He has experience in the development of efficient operations systems, sourcing in Asia, sales, and marketing. Will also serves as the President of Bend Paddle Trail Alliance, a non-profit focused on establishing a navigable paddle trail within Deschutes County and promoting water safety, education, and stewardship.
Justin was lucky to start his outdoor apprenticeship as a professional river guide working throughout most of the United States, Costa Rica, Ecuador, and South America for close to a decade. He inevitably stumbled upon full time employment and has been immersed in the start-up/entrepreneurship world since then. He was hooked after he sold his first business at the age of 24. When not working with his myriad of side projects he currently works with entrepreneurs and executives through his wealth management business at Northline Wealth Management. In addition, he is an active investor in private equity and angel investment deals throughout the country.
Fortunately he never let the river flow too far….he is an active partner in an international river business, ENRG Kayaking (www.enrgkayaking.com), and recently led an international expedition to the Grand Canyon of the Amazon in Peru. Believing in the power of community and outdoor recreation he has been instrumental in bringing the first whitewater park to the West Coast through his work with the Bend Paddle Trail Alliance.
Justin brings an active investor mentality to the group as well as an experienced successful entrepreneur mindset who has co-founded or founded a variety of companies from an outdoor ecommerce company, wealth management business, outdoor services company, and technology companies.
When not in the office, which is often, Justin is usually tooling around with his four kids somewhere around the Oregon outback.
Arriving in Bend, OR in 1994, armed with an architectural license and a passion for the outdoors, Eric Meade joined Entre Prises Climbing Walls and led it through its largest growth period in history. Eric and his team skyrocketed annual sales by achieving maximum marketplace penetration and made it the top climbing wall company in the world. EP USA dominated the climbing wall marketplace by exceeding customer expectations, developing innovative products, and pushing the boundaries while developing industry standards, which are still in place today. Eric supervised and grew the Company to 70+ employees, with annual revenues of $7M. Eric and his in-house investment partners, achieved a 3,000% return on their original investment through the sale of the company in 2008; by ensuring organized and strong financials, brand equity, a strong customer list, and setting achievable marketing/business plans.
Since Eric sold Entre-Prises in late 2008, he worked as the Membership Director for Opportunity Knocks, was an investor in two Bend Venture Conferences, co-founded Bend Outdoor Worx and opened his own consulting business, Eric Meade-Purposeful Consulting. His passion is to support and develop leaders of businesses to establish clear strategies, financial planning, implementation planning, and a sustainable profitability model. Eric is a subject matter expert in developing world-class infrastructure for newer companies while driving innovative product development. He is a big picture thinker with vision to break operations down into executable strategies. Eric is a leader who fosters and facilitates collaborative problem-solving to achieve Company objectives. Eric is financially focused and values long-term success.
Eric enjoys business, mountain biking, road biking, skiing, hiking, camping, backpacking, travel and his two kids and awesome wife.
Wes has been a practicing CPA (www.bendcpa.com) in Bend for over 30 years, providing business clients comprehensive tax, audit, accounting and management consulting services. He has a knack for helping business owners understand their finances and use the information to make their businesses more profitable. In addition to serving a wide variety of family businesses, Wes concentrates his practice in the manufacturing, utility and hospitality industries. He currently serves as Treasurer on EDCO board and as Business Oregon's finance committee chair. He is a past president of the Bend Chamber and has a long history of volunteering in central Oregon.
Scott has over two decades of experience in working with entrepreneurs and management teams of start-up and later-stage ventures across a broad spectrum of Pacific Northwest industry groups including consumer brands, apparel, footwear, entertainment and technology. Scott leads the White Summers (www.white-summers.com) consumer brands practice group and frequently works with clients on key strategic issues including angel, venture and private equity financings, debt financings and strategic partnerships. Additionally, Scott has extensive experience in corporate law, mergers and acquisitions, corporate finance, complex technology transfers and intellectual property matters.
In addition, Scott serves in a number of leadership roles with organizations that support entrepreneurs and emerging growth companies in Oregon and throughout the Pacific Northwest.


In 1986, Professor David Snowden started studying the onset of Alzheimer's among 678 nuns.
While the study is still in progress, his work has indicated that there are certain lifetime behaviors and/or tendencies that can influence the onset of Alzheimers later in life.
"Through brain donation, we can help unravel the mysteries of Alzheimer's disease"
The nun study might be creating More questions than it is answers, but it is building a strong case for keeping the brain active. It's good to know there there are behaviors to work towards that can better create longevity and overall mental capacity.
[Ethan Rozin]. (2006, Dec. 28). nun study video. [Video File]. Retrieved from https://www.youtube.com/watch?v=nw2lafKIEio.


What would be an adequate (or smallest) sump size for a 75g display with a 50g refugium ???
Sumps were meant to be bigger than the display.
I would go with atleast 50% of the tank volume. 40G breeder would work perfect.
My 80g tank has a 50G sump holding about 40G of water.
I would go with a mag 500 or 700. I'm a strong believer of low flow going through the sump. You end up with less problems in the end.
What heater size for 90 gal w/ 30 gal sump???


Crazy dude, I'd like him to participate in my affiliate program and be my referral. I would have been happy then.
He could have bought a few casinos with such money. Then go and gamble in your own house!
I see myself as and regular player on stake, and some would even say consistent , I myself have invested a long time taking the gradual pace to an unheard of level , yet the outcomes appear to be worth the exertion when you have a decent solid equalization.
Obviosly raising the wagered will bring down you balance twice as quick , add that to the reality your fortunes appears to have run dry and red is obviously your new most loved shading and you wind up falling at a disturbing rate.
Are you on indistinguishable ride from me ?
What number of lose in a fraction of the time it took to win ?


text:
Unrest In Tunisia
Protests in Tunisia
The United States regrets the loss of life, calls upon all parties exercise restraint, and urges all parties to work together toward a peaceful resolution.
Tunisia has been rocked by demonstrations throughout the country, some of which turned violent. According to the Tunisian government, 14 civilians were killed in three central Tunisian towns over the weekend. Protests that began in December continue as students, teachers, lawyers, journalists, human rights activists, trade unionists, and opposition politicians have taken to the street in criticism of the government's economic policies, limits on freedom of speech and association, and allegations of corruption.
The United States has also expressed its concern over reports that accounts of Tunisian users of American companies including Facebook, and providers of email such as Yahoo and Google, have been hacked and their passwords stolen. This kind of interference threatens the ability of civil society to realize the benefits of new technologies.
Cyber intrusions of all kinds, including reported attacks on government of Tunisia websites, disrupt the free flow of information and reduce overall confidence in reliability and security of vital information networks. The United States urges all parties to respect the freedom of expression that belongs to everyone and ensure the free flow of information. That includes the right of Tunisians to assemble and protest peacefully.
/dalet/Editorial_VO_215_016177_011411_Unrest_in_Tunisia.Mp3
Support For Democratic Tunisia
Obama Signs Press Freedom Act
Science And Technology Cooperation
Tunisian Activist Harrassed

redpajama_set_name: RedPajamaCommonCrawl


Hierarchical BS in fandom is going to happen. I'm troubled when our media preferences become more important to our tribal affiliation than the enduring sense of wonder that lifted us all up into fandom in the first place. Jealousy and envy are a part of life. Throw sexism, sizeism, publishing credits and perfect pitch into a small and vocal fandom and voila, ongoing eruptions.
Unless you're a tribble, you shouldn't hiss at Klingons. Or to rephrase, unless you have a physical problem with someone else's embodiment of fandom (eg., using peanut butter as part of your costume when so many fans are allergic is unacceptable) the correct response falls along a continuum. Privately giggle with your friends, whine to your BFF or SO, or work through the irritation or anger in some constructive fashion. And now I pass the talking stick to someone else.


Early scrutineering will be available for any competitors who are coming early. The scruiteneer will be in the village all day helping with set up.
0900-0930 - Driver/Rider and Marshal Safety Briefing at the start line.
Following the success of the Coleby downhill racing in June 2014 and 2016, where the course was described by racers as 'one of the best in the country' and reaching speeds in excess of 40 mph, 36 soapboxes, sidecars and gravity bikes have entered this year.
What is the Downhill Challenge?
Downhill soapbox racing is spectacular and breathtaking, and coupled with the quality of this year's competitors, the competition should be fierce and exciting.
Saturday 8 and 9 June.
Timed practice will take place on Saturday 9 June throughout the day, starting at 10 am.
Results and Presentations at 4 pm.
The 'Gravity Bike' class will be part of National Gravity Bike Championships.
Around 2,000 people are expected to attend the event this year which will see inventive adrenaline junkies shoot down the winding course in their own modified soapboxes.
It provides family entertainment all weekend plus ample parking facilities available in the village.
It is a charitable event hosted by Hykeham Lions and Coleby Village Hall Committee with all profits going to Lives (North Hykeham), Lincolnshire & Nottinghamshire Air Ambulance and other local charities.
In 2014, 12 soapboxes took part, 2016 20 soapboxes, 10 gravity bikes and 4 gravity sidecars went down the hill.
We have seen some great soapboxes, so this year we will be looking to see who provides the most spectacular soapbox.
The organisers of Coleby Downhill Challenge and the owners of the land do not accept any responsibility for any damage, loss or injury to the entrants/spectators or equipment.


A Bug's Life Blu-ray is reviewed as part of Disney presents its biggest and best 'buy one get one free' offer on over 30 DVD and Blu-ray titles - 26 September to 31 October 2011, so hurry while stocks last.
A Bug's Life Blu-ray is reviewed as part of Disney presents its biggest and best €˜buy one get one free€™ offer on over 30 DVD and Blu-ray titles - 26 September to 31 October 2011, so hurry while stocks last. €œThe difficult second album€ is a paradigm that has its parallel throughout the contemporary arts, not least in cinema. It is an expression used to illustrate the difficulty of the artist- or group of artists- emulating an initial overwhelming success. The very fact that this phenomenon exists in common critical parlance is enough to often profoundly affect those who may be subject to, thus making them apprehensive and creating a self-fulfilling prophecy. In the case of Pixar, however, the weight of expectation must have been crushing following the resounding critical and commercial success of Toy Story, the company€™s first feature film and the first full length CGI animation in history. The film chosen to follow the technologically revolutionary Toy Story was A Bug's Life, and far from succumbing to the inclination to produce a sequel or facsimile of their first feature length production, Pixar, through the writing and directing team of John Lasseter and Andrew Stanton, created a far more visually expansive, thematically and politically radical piece than Toy Story could have begun to hint at. Taking a strong lead from Kurosawa epic The Seven Samurai and the Aesop fable The Ant and The Grasshoper, the duo crafted a romantic but considered allegory for the strength of a democratic syndicalism as a means to enshrining the worth an integrity of the individual, whilst simultaneously using the collective strength of their unity to resist the coercion of foreign imperialism. The subject ant colony is presided over by a reasonably benevolent but demonstrably autocratic royal family and key advisors. The workers of said colony are highly organised, though lacking in self-confidence and determination, seeking authoritarian guidance and permission when faced with any situation that may depart from or impede strictly observed procedures. Flik (Dave Foley), the hero of the narrative, represents a free spirit, an inventor and innovator whose wilfulness and imagination are initially perceived to be at odds with the society€™s oligarchic nature. The ant society, under the leadership of an aging queen and a proud but incompetent Princess (Julia Louis-Dreyfus), are compelled by the stronger and more aggressive grasshoppers, who fly down like the green skinned helicopters of an invading army, to gather vast stocks of food for the winter. Flik€™s quest to find €œwarrior insects€ to defend the ant colony is what drives the film€™s drama, and, as such, he is easily the most complete character within A Bug€™s Life. A lack of confidence in his abilities, primarily due to the chastisements of Princess Atta and the colony elders, is what prevents him from taking advantage of his innate intellect and creativity, and his journey to and from the city and the menagerie of insects he accidentally hires from a failing fair that inspire him to provide the solution to the ants problems himself. The circus insects too, are perfectly crafted and it is their unfettered creativity that both inspire the protagonist Flick to be all that he can, as well as their unique physical and artistic skills, provide the engine for a great deal of the adroitly paced chases, battle and various cliff-hanger moments. If any of the characters disappoint it is Princess Atta to whom, in spite of the threats and challenges she undoubtedly faces, it is very difficult to warm. It seems that the Princess is spoiled and stubbornly domineering in such a way that she channels little audience empathy and, as a consequence, is a less than ideal love interest for the inherently likeable Flik. Aesthetically, it is clear that the animator€™s grasp of their technology€™s potential has grown exponentially, and the detailed rendering of images has allowed them to create a genuine sense of depth and tactility that can at times enrapture. Aside from such visual achievements however, it is the radical, political, thematic base- and the skill with which it is explored- that made A Bug€™s life such a unique achievement, especially given its target audience and commercial success. Its dénouement, in which the triumph of the ants rural collective over the powerful invaders through greater individual expression and democratic input in the governance of their community in place of the older, dictatorial order.
Ben Szwediuk hasn't written a bio just yet, but if they had... it would appear here.


text:
\section{Introduction}

A strongly pseudoconvex domain in $\C^n$ always admits a (strongly) plurisubharmonic defining function \cite{morrowrossi1975}. However weakly pseudoconvex domains do not generally satisfy an analogous property. Diederich and Fornaess \cite{DieFor77-1} and Fornaess \cite{Fornaess79} found examples of weakly pseudoconvex domains in $\C^2$ which do not admit plurisubharmonic defining functions.

A weaker notion than having a plurisubharmonic defining function was also introduced by Diederich and Fornaess \cite{DieFor77-2}. They showed that for any bounded pseudoconvex domain $\Omega$ in $\C^n$ with $C^2$ boundary, there exists a positive constant $\eta$ and a defining function $\rho$ such that $-(-\rho)^\eta$ is plurisubharmonic on $\Omega$. Such $\eta$ is called a Diederich-Fornaess exponent and the supremum of all Diederich-Fornaess exponents is the Diederich-Fornaess index. The existence of bounded plurisubharmonic functions have later been generalized to domains with $C^1$ boundary \cite{KerzmanRosay1981} and Lipschitz boundary \cite{Demailly1987}, \cite{Harrington07}.

If a domain admits a plurisubharmonic defining function then the Diederich-Fornaess index is $1$.
Furthermore, Fornaess and Herbig \cite{herbigfornaess07}, \cite{herbigfornaess08} showed that if a domain has a defining function plurisubharmonic on the boundary then the Diederich-Fornaess exponent is $1$. However the converse is not true: a domain with the Diederich-Fornaess index $1$ need not admit a plurisubharmonic defining function as shown by Behrens' example \cite{Behrens85}.
Examples with Diederich-Fornaess exponent strictly less than $1$ include worm domains; for explicit computations see \cite{Liu19-1}.

The focus of this paper is to identify obstructions to having a local plurisubharmonic defining function on the boundary.
In addition to Diederich and Fornaess examples, Behrens \cite{Behrens85}  constructed a pseudoconvex domain of D'Angelo type $6$ in $\C^2$ which does not admit a local plurisubharmonic defining function, not even on the boundary. The obstruction in their examples comes from the inability to construct a real-valued multiplier function $h$ that satisfies a specific partial differential equation on certain curves lying in the boundary.
We generalize this statement and make it precise by stating the explicit differential equation that needs to be solved. Namely:
\begin{theorem}
Suppose that $\rho=r\cdot h$ is a local plurisubharmonic defining function. Then
\[\frac{\partial}{\partial z} \log h = -\frac{\partial}{\partial z} \log r_{\bar w} +E , \] where $|E|^2\leq C(\sL_r+|r_z|^2)$.
\end{theorem}

The second obstruction involves the determinant of the complex Hessian $\sh$. We show that the Levi form generates ``free'' positivity for the determinant of the complex Hessian. This gives rise to a necessary and sufficient condition for having a plurisubharmonic defining function.
\begin{theorem}
A domain $\Omega=\{r<0\}\subset \C^2$ has a local plurisubharmonic defining function in a neighborhood of $p\in b\Omega$ if and only if there exists a function $T:\C^2\rightarrow \R$ and a positive constant $C>0$ such that $-\sh_{(1+T)r}\leq C \sL_r$ in a neighborhood of $p$.
\end{theorem}
Thus the Levi form is a threshold that a determinant of the complex Hessian of $h$ needs to achieve in order for $\rho=r\cdot h$ to be a local plurisubharmonic defining function on the boundary.
``Spreading'' of positivity of the Hessian and other intermediate positivity conditions have been studied in \cite{HerMcN09} and  \cite{HerMcN2012}.

The last possible obstruction is the $|r_z|^2$ term. It is unknown whether this is actually an obstacle for producing a local plurisubharmonic defining function on the boundary and if so, what a geometric interpretation should be.  The Example \ref{Ex:type4} shows that this term needs to be considered, but does not necessarily prevent the domain from having a local plurisubharmonic defining function on the boundary.

For domains in $\C^n$ the above conditions are still necessary as each $2\times2$ principal minor of the complex Hessian needs to be positive semidefinite on its own. However a few more obstructions arise. The same multiplier function must satisfy the corresponding differential equations for $z_1,...,z_{n-1}$ simultaneously. The necessary conditions imposed by positive semidefiniteness of higher order minors of the complex Hessian have not been studied.

Kohn \cite{Kohn99} showed that if the Diederich-Fornaess index is $1$ then the $\dbar$-Neumann operator is globally regular. For more general necessary condition needed for domains to have index $1$ see \cite{Liu19-2}. In general, plurisubharmonic defining functions are of importance in the study of the $\dbar$-Neumann operator as it is a sufficient condition for global regularity of $\dbar$-Neumann operator and the Bergman projection \cite{BoasStraube90}, \cite{BoaStr91}, \cite{BoasStraube1993}, \cite{BoasStraube99}. That is, the domains with plurisubharmonic defining function satisfy condition $R$.

This paper is a part of the authors PhD thesis. The author would like to thank his adviser Jeffery D. McNeal for bringing this problem to his attention and for many helpful discussions.

\section{Definitions and Notation}

We denote the partial derivatives with a subscript, e.g. $r_{z_j} =\frac{\partial r}{\partial z_j}$.

We say that $r$ is a defining function for a domain $\Omega\subset \C^2$ provided that  $\Omega=\{(z,w)\in \C^2 : r(z,w)<0\}\subset \C^2$ and $\nabla r\neq 0$ on the boundary.

Let $p\in b\Omega$.
By rotation and translation we may assume that $p=(0,0)$ is the origin. By the Implicit function theorem we may assume that  $r$ is of the form $$r(z,w)=\im w+ F(z,\bar z, \re w,\im w) \ ,$$ where the terms in $F$ are of degree at least $2$. The crucial property is that $r_w\neq0$ is non-vanishing in some neighborhood of the origin.

The complex tangent space $T^{1,0}_p b\Omega$  to $b\Omega$ at $p$ is defined to be
all $\xi=(\xi_1,\xi_2)\in\C^2$ satisfying $$\sum_{j=1}^2\frac{\partial r}{\partial z_j}(p)\xi_j=0.$$
$\Omega$ is pseudoconvex if

$$\sL_r(\xi)=\sum_{j,k=1}^2\frac{\partial^2 r}{\partial z_j\partial\bar z_k}(p)\xi_j\bar\xi_k\geq 0\qquad\text{ for all } \xi\in T^{1,0}_pb\Omega,$$
for all $p\in b\Omega$.
In $\C^2$ the tangent space is $1$-dimension and $\langle r_w , -r_z\rangle\in T^{1,0}_pb\Omega$, so define
$$\sL_r= \sL_r(\langle r_w , -r_z\rangle)=r_{z\bar z}|r_w|^2 +r_{w\bar w}|r_z|^2 -2\re[r_{z\bar w}r_w r_{\bar z} ] .$$

A function $r$ is plurisubharmonic if
$$\sum_{j,k=1}^2\frac{\partial^2 r}{\partial z_j\partial\bar z_k}(p)\xi_j\bar\xi_k\geq 0\qquad\text{ for all } \xi\in \C^2 .
$$
Alternative description of plurisubharmonic function $r$ is that a complex Hessian matrix $H_r$ is positive semidefinite. This is equivalent to the diagonal entries $r_{z\bar z},r_{w\bar w}\geq0$ and the determinant $\sh_r=det(H_r)=r_{z\bar z}r_{w\bar w}-|r_{z\bar w}|^2\geq0$.

We will consider the local versions of the above definitions, i.e. the above definitions only need to hold on a neighborhood of the origin inside the boundary.

Throughout, $r$ denotes the defining function of $\Omega$, and $\rho$ denotes a local plurisubharmonic defining function, provided one exists.
In that case we can write $\rho=r\cdot h$, for some real-valued, multiplier function $h$, which does not vanish in a neighborhood of the origin.

Finally, we use $\mathcal O$ and $\littleO$ as big O and little O notation respectively.

\section{Necessary Conditions}

Let $\Omega\subset \C^2$ be a domain with a defining function $r(z,w)= \im w +F(z,\bar z, \re w,\im w)$ where the terms in $F$ are of order at least $2$. Suppose that $\Omega$ admits a local plurisubharmonic defining function on the boundary $\rho=r\cdot h$. Write $h=1+Kr+T$ where $K\in \R$ and $T$ is a real-valued function.

We wish to analyze the properties of $\rho$, derivatives of $\rho$, and the complex Hessian of $\rho$ in terms of $r$ and the complex Hessian of $r$.

The first key proposition is
\begin{proposition}\label{Prop:Hessian}
\[\sh_\rho=\sh_{hr}=\sh_{(1+Kr+T)r}=2Kh\sL_r+\sh_{(1+T)r}\]
\end{proposition}

\begin{proof}
Let $h=1+Kr+T$ and $p=1+T$.
Note that on $b\Omega$, $h=p$.

\begin{align*}
\rho_{z\bar z} =& r_{z\bar z}h +2\re[r_{\bar z}h_z]= r_{z\bar z}h +2\re[r_{\bar z}(K r_z + T_z)] \\
=& r_{z\bar z}h + 2K|r_z|^2 + 2\re[r_{\bar z}T_z]\\
\\
\rho_{w\bar w} =& r_{w\bar w}h+2\re[r_wh_{\bar w}]=r_{w\bar w}h +2\re[r_w(K r_{\bar w}+T_{\bar w})]\\
=& r_{w\bar w}h +2K|r_w|^2 +2\re[r_wT_{\bar w}]\\
\\
\rho_{z\bar w}=& r_{z\bar w}h +r_zh_{\bar w}+r_{\bar w}h_z = r_{z\bar w}h +r_z(K r_{\bar w} +T_{\bar w}) + r_{\bar w}(K r_z +T_z)\\
=& r_{z\bar w}h +2K r_z r_{\bar w} + r_zT_{\bar w} + r_{\bar w}T_z \\
\end{align*}

Note that $\rho_{w\bar w}$ is non-vanishing and positive for $K>0$ big enough.

The determinant of the complex Hessian is:
\begin{align*}
\sh_\rho=&\rho_{z\bar z}\rho_{w\bar w} - |\rho_{z\bar w}|^2\\
=&( r_{z\bar z}h +  2\re[r_{\bar z}T_z]+2K|r_z|^2 )( r_{w\bar w}h +2\re[r_wT_{\bar w}]+ 2K|r_w|^2)
-|r_{z\bar w}h + r_zT_{\bar w} + r_{\bar w}T_z+2K r_z r_{\bar w}|^2\\
=& (r_{z\bar z}h+  2\re[r_{\bar z}T_z])(2K|r_w|^2) + ( r_{w\bar w}h +2\re[r_wT_{\bar w}])(2K|r_z|^2 )\\
 &+( r_{z\bar z}h +  2\re[r_{\bar z}T_z])( r_{w\bar w}h +2\re[r_wT_{\bar w}]) +\cancel{ 4K^2|r_z|^2|r_w|^2}\\
 &-|r_{z\bar w}h + r_zT_{\bar w} + r_{\bar w}T_z|^2 \cancel{- 4K^2|r_z|^2|r_w|^2} -2\re[(2K r_{\bar z}r_w)(r_{z\bar w}h + r_zT_{\bar w} + r_{\bar w}T_z)]\\
=& 2Khr_{z\bar z}|r_w|^2+ \cancel{4K\re[r_{\bar z}T_z r_w r_{\bar w}]} + 2Khr_{w\bar w}|r_z|^2+\cancel{4K\re[r_w T_{\bar w}r_zr_{\bar z}]} + (pr)_{z\bar z}(pr)_{w\bar w}\\
& - |(pr)_{z\bar w}|^2- 4Kh\re[r_{\bar z}r_wr_{z\bar w}] \cancel{-4K\re[r_{\bar z}r_w r_z T_{\bar w}]}
\cancel{- 4K\re[r_{\bar z}r_w r_{\bar w}T_z]}\\
=&2Kh \bigg[r_{z\bar z}|r_w|^2+r_{w\bar w}|r_z|^2 -2\re[r_{z\bar w}r_{\bar z}r_w]\bigg] +(pr)_{z\bar z}(pr)_{w\bar w}-|(pr)_{z\bar w}|^2\\
=& 2Kh\sL_r +\sh_{pr} \ .
\end{align*}
\end{proof}

\begin{remark}
If $A$ is the complex Hessian of $p\cdot r$ and $B$ is a complex Hessian of $r^2$, the proposition is equivalent to:
\\For $2\times2$ matrices $A$ and $B$,
\[det(A+B)= det A+det B +{det A}\cdot tr(A^{-1}B) \ ,\]
where  $det B=0$ and $det(A)tr(A^{-1}B)=h\sL_r$ when restricted to the boundary.
\end{remark}

Proposition \ref{Prop:Hessian} uncovers positivity of the Levi form that is ``hidden'' in the determinant of the complex Hessian. Thus the difficulty of producing a local plurisubharmonic defining function on the boundary lies in the construction of a real-valued function $T$ such that negativity of $\sh_{(1+T)r}$, the determinant of the Hessian of $(1+T)r$, can be controlled by the Levi form.
An immediate corollary to Proposition \ref{Prop:Hessian} is
\begin{theorem}\label{T:Hessiantresh}
$\Omega$ admits a local plurisubharmonic defining function on the boundary if and only if there exists a real-valued function $T$ and a constant $C>0$ such that $-\sh_{(1+T)r}\leq C\sL_r$.
\end{theorem}

\bigskip
The hardest term to control in the determinant of the complex Hessian $$\sh_r=r_{z\bar z}r_{w\bar w}-|r_{z\bar w}|^2$$ is the off-diagonal $-|r_{z\bar w}|^2$ term. Next, the necessary bounds, on the terms in the determinant of the complex Hessian, for the function to be plurisubharmonic are recorded.

\begin{lemma}\label{nece1}
Suppose $\rho$ is a local plurisubharmonic defining function. Then
\begin{enumerate}
\item $\frac{2h\sL_r}{|r_w|^2} +\frac{2\rho_{w\bar w}|r_z|^2}{|r_w|^2} \geq \rho_{z\bar z} $
\item $\rho_{z\bar z}\geq \frac{\rho_{w\bar w}|r_z|^2}{2|r_w|^2}-\frac{h\sL_r}{|r_w|^2}$
\item $\rho_{z\bar z}\geq \frac{h\sL_r}{2|r_w|^2} - \frac{\rho_{w\bar w}|r_z|^2}{|r_w|^2}$
\item $|\rho_{z\bar w}|^2\leq \frac{2\rho_{w\bar w}h\sL_r}{|r_w|^2} +\frac{2\rho_{w\bar w}^2|r_z|^2}{|r_w|^2}$
\end{enumerate}
As a consequence $\rho_{z\bar z},|\rho_{z\bar w}|^2 \leq C(\sL_r+|r_z|^2)$, or equivalently  $\rho_{z\bar z},|\rho_{z\bar w}|^2 =\mathcal O(\sL_r +|r_z|^2)$ in $U\cap b\Omega$ for some neighborhood $U$ of the origin.
\end{lemma}

\begin{proof}
Since $\rho$ is plurisubharmonic, the complex Hessian is positive  semidefinite for all vectors in $\C^2$. The complex Hessian for a vector
 $\langle 2^n r_w, -r_z\rangle$ is
\begin{align*}
0\leq\sh (\langle 2^n r_w, -r_z\rangle) =&  \rho_{z\bar z}2^{2n}|r_w|^2 +\rho_{w\bar w}|r_z|^2 -2\cdot 2^n \re[\rho_{z\bar w} r_w r_{\bar z}]\\
=&  2^{2n}\rho_{z\bar z}|r_w|^2 +\rho_{w\bar w}|r_z|^2  + 2^n (\sL_\rho - \rho_{z\bar z}|r_w|^2 - \rho_{w\bar w}|r_z|^2)\\
=& 2^n(2^n-1) \rho_{z\bar z}|r_w|^2 + (1-2^n)\rho_{w\bar w}|r_z|^2 - 2^n \sL_\rho\\
=& 2^n \left [ (2^n-1) \rho_{z\bar z}|r_w|^2 +\frac{(1-2^n)}{2^n}\rho_{w\bar w}|r_z|^2 + \sL_\rho \right]
\end{align*}
Therefore
\[(2^n-1) \rho_{z\bar z}|r_w|^2 +\frac{(1-2^n)}{2^n} \rho_{w\bar w}|r_z|^2+ \sL_\rho \geq0\]
For $n=1,-1$, using the fact that $\sL_\rho=h\sL_r$ on $b\Omega$, inequalities (2) and (1) are obtained:
\[\rho_{z\bar z} |r_w|^2 - \frac12 \rho_{w\bar w}|r_z|^2 + h\sL_r\geq 0\]
\[ -\frac12\rho_{z\bar z}|r_w|^2 + \rho_{w\bar w}|r_z|^2 +h\sL_r \geq0\]
For (3), apply the complex hessian to the vector $\langle r_w, r_z\rangle$:
\begin{align*}
0\leq \sh(\langle r_w,r_z\rangle) =& \rho_{z\bar z}|r_w|^2+\rho_{w\bar w}|r_z|^2 +2\re[\rho_{z\bar w}r_{\bar z}r_w]\\
=& \rho_{z\bar z}|r_w|^2 + \rho_{w\bar w}|r_z|^2 -\sL_\rho +\rho_{z\bar z}|r_w|^2+\rho_{w\bar w}|r_z|^2\\
=&2\rho_{z\bar z}|r_w|^2 + 2\rho_{w\bar w}|r_z|^2 -\sL_\rho
\end{align*}
To obtain inequality (4), use (1) and $|\rho_{z\bar w}|^2 \leq \rho_{w\bar w}\rho_{z\bar z}$.
\end{proof}

\begin{remark}
The Example \ref{Ex:type4}  shows that we cannot improve the inequality (4) to $|\rho_{z\bar w}|^2\leq C \sL_r$.
\end{remark}

Using the bounds above, we prove the second key proposition.
\begin{proposition}
Suppose that $\rho=r\cdot h$ is a local plurisubharmonic defining function on the boundary. Then
\begin{equation}
\frac{\partial}{\partial z} \log h = -\frac{\partial}{\partial z} \log r_{\bar w} +E \notag,
\end{equation} where $|E|^2\leq C(\sL_r+|r_z|^2)$.

If we write $h=1+Kr+T$, then
\begin{equation}
\frac{\partial}{\partial z} \log (1+T) = -\frac{\partial}{\partial z} \log r_{\bar w} +E \notag,
\end{equation}
 where $|E|^2\leq C(\sL_r+|r_z|^2)$.
\end{proposition}

\begin{proof}

We use the following fact in the subsequent calculations:
\[|A+B|^2=|A|^2+|B|^2+2\re[A\bar B] \geq \frac12|A|^2 - |B|^2 + \frac12|A|^2 +2|B|^2 - 2|A||B|\overset{\text{AM-GM}}{\geq}  \frac12|A|^2 - |B|^2\]

\[
C(\sL_r+|r_z|^2) \geq  |\rho_{z\bar w}|^2 = |r_{z\bar w}h + r_z h_{\bar w} + r_{\bar w}h_z|^2
\geq \frac12|r_{z\bar w}h+r_{\bar w}h_z|^2 - |r_z|^2|h_{\bar w}|^2
\]
\[
\tilde C(\sL_r+|r_z|^2) \geq|r_{z\bar w}h+r_{\bar w}h_z|^2 = |r_w||h|\left| \frac {h_z}{h}+ \frac{r_{z\bar w}}{r_{\bar w}}\right|^2
=|r_w||h|\left|\frac{\partial}{\partial z} \log h + \frac{\partial}{\partial z} \log r_{\bar w}\right|^2
\]
\[\hat C (\sL_r+|r_z|^2)\geq \left|\frac{\partial}{\partial z} \log h + \frac{\partial}{\partial z} \log r_{\bar w}\right|^2\]
Note that the logarithms are well defining in a small neighborhood of the origin, i.e. there is a branch cut consistent with $h$ and $r_{\bar w}$.

\bigskip
Write $h=1+Kr+T$, and notice that $h=1+T$ on $b\Omega$.
\[C(\sL_r +|r_z|^2)\geq  |r_{z\bar w}h +r_z h_{\bar w}+ r_{\bar w} (r_z+ T_z)|^2 \geq \frac12 |r_{z\bar w}(1+T)+r_{\bar w}T_z|^2 -|r_z|^2|r_{\bar w} +h_{\bar w}|^2\]
The conclusion follows from the calculation above.
\end{proof}

Therefore, we have obtained two necessary conditions on the multiplier $h=1+Kr+T$ to produce a local plurisubharmonic defining function on the boundary $\rho$. Namely:
\begin{theorem}\label{thm:nec}
Suppose that $\rho=r\cdot h$ is a local plurisubharmonic defining function on the boundary and $h=1+Kr+T$. Then
\begin{enumerate}
\item $\frac{\partial}{\partial z} \log (1+T) = -\frac{\partial}{\partial z} \log r_{\bar w} +E$ where $|E|^2\leq C(\sL_r+|r_z|^2)$ for some $C>0$.
\item $-\sh_{(1+T)r}\leq C\sL_r$ for some $C>0$.
\end{enumerate}
\end{theorem}

\section{Sufficient condition}
Suppose that there exists a real-valued function $T$ such that
 \begin{equation}\label{E:logder4}
 \frac{\partial}{\partial z} \log (1+T) = -\frac{\partial}{\partial z} \log r_{\bar w} +E
 \end{equation}
  where $|E|^2\leq C(\sL_r+|r_z|^2)$ for some $C>0$.

Let $p=1+T$.
The Equation \eqref{E:logder4} is equivalent to \[T_z= -\frac{p r_{z \bar w}}{r_{\bar w}}+pE\ . \]
Compute the second order derivatives:
\begin{align}\label{E:rhozz}
 (rp)_{z\bar z}&= pr_{z\bar z}+2\re[r_{\bar z}T_z]=pr_{z\bar z} +2\re[r_{\bar z}(-\frac{p r_{z \bar w}}{r_{\bar w}}+pE)] \notag\\
 &=p\left [r_{z\bar z}-2\re[r_{z\bar w}\frac{r_{\bar z}}{r_{\bar w}}]\right] +2p\re[r_{\bar z}E] \notag\\
 &= p\left[r_{z\bar z}-2\re[r_{z\bar w}\frac{r_{\bar z}}{r_{\bar w}}] +r_{w\bar w}\frac{|r_z|^2}{|r_w|^2}\right] - pr_{w\bar w}\frac{|r_z|^2}{|r_w|^2} +2p\re[r_{\bar z}E]\notag\\
 &= \frac{p}{|r_w|^2}\sL_r - pr_{w\bar w}\frac{|r_z|^2}{|r_w|^2} +2p\re[r_{\bar z}E]
\end{align}
and
\begin{align}\label{E:rhozw}
|(rp)_{z\bar w}|^2&= |pr_{z\bar w}+r_z T_{\bar w}+r_{\bar w}T_z|^2 =\left|pr_{z\bar w}+r_zT_{\bar w}+r_{\bar w}(-\frac{p r_{z \bar w}}{r_{\bar w}}+pE)\right|^2\notag\\
&=|r_zT_{\bar w} + pr_{\bar w}E|^2 = |r_z|^2|T_w|^2 + 2\re[pr_{\bar w}T_wr_{\bar z}E] +p^2|r_{\bar w}|^2|E|^2
\end{align}
In particular, both $|(rp)_{z\bar z}|,|(rp)_{z\bar w}|^2\leq K(\sL_r+|r_z|^2)$ for some $K$.
Therefore $-\sh_{pr}=-\sh_{(1+T)r}\leq \tilde K(\sL_r+|r_z|^2)$.

\begin{theorem}\label{T:Levidom}
Suppose that $|r_z|^2\leq C\sL_r$. Then there exists a local plurisubharmonic defining function on the boundary if and only if we can solve Equation \eqref{E:logder4}. Furthermore $\rho=(1+Kr+T)r$ is a local plurisubharmonic defining function on the boundary for some $K>0$.
\end{theorem}

\begin{proof}
We already showed that Equation \eqref{E:logder4} is a necessary condition. Under the additional assumption that there is a $T$ satisfying Equation \eqref{E:logder4}, $-\sh_{(1+T)r}\leq C(\sL_r+|r_z|^2) \leq \tilde C \sL_r$ for some $C,\tilde C>0$. Then by Theorem \ref{T:Hessiantresh} there exists $K>0$ such that $(1+Kr+T)r$ is a local plurisubharmonic defining function on the boundary.
\end{proof}

\subsection{$|r_z|^2\not\leq C\sL_r$ case}

If $|r_z|^2\not\leq C\sL_r$ for any $C>0$ in any neighborhood of the origin, then the terms involving $r_z$ and $E$ will play a significant role in determining if there is a local plurisubharmonic defining function on the boundary.
The terms we do not have a desired control of are $-\frac{p r_{w\bar w}}{|r_w|^2}|r_z|^2$ and $2p \re[r_{\bar z}E]$ in the Equation \eqref{E:rhozz}.
In the Equation \eqref{E:rhozw}, the problematic terms are $|r_z|^2|T_w|^2$, $2\re[pr_{\bar w}T_wr_{\bar z}E]$, and $p^2|r_{\bar w}|^2|E|^2$.

The terms involving $E$ can be improved by solving the Equation \eqref{E:logder4} to a higher order, for example, the $E$ terms satisfy $|E|^2\leq C\sL_r$ or even better. Secondly, if $\rho_{w\bar w}$ vanishes at the origin, the negativity of the determinant of the complex Hessian is easier to control.

On the other hand the terms involving just $|r_z|^2$ are harder to control. The lowest order terms of $T$, and therefore $T_w$, are forced by the Equation \eqref{E:logder4}. Thus there is no way of improving the bounds while still satisfying a necessary Equation \eqref{E:logder4}. However, $T_w$ and $r_{w\bar w}$ can be helpful. If $T_w$ and $r_{w\bar w}$ vanish to high order the determinant of the complex Hessian of $(1+T)r$ can still satisfy $-\sh_{(1+T)r}\leq C\sL_r$.

The Example \ref{Ex:type4} shows that $|r_z|^2\leq C\sL_r$ is not a necessary condition to having a local plurisubharmonic defining function on the boundary. Thus the following question remains open:
\begin{question}
Find a domain where $|r_z|^2$ is the obstruction to having a local plurisubharmonic defining function on the boundary.
\end{question}

\section{The Method}

\subsection{Basic strategy}
In this section we give an illustration of how to produce a local plurisubharmonic function on the boundary.
\\Given a defining function $r$, our goal is to construct a real-valued $T$ that satisfies
 \begin{equation}\label{E:logder5}
  \frac{\partial}{\partial z} \log (1+T) = -\frac{\partial}{\partial z} \log r_{\bar w} +E\ ,
  \end{equation} where  $|E|^2\leq C(\sL_r+|r_z|^2)$ for some $C>0$.

Write $r_w = \frac1{2i}+\tilde r_w$, where $\tilde r_w$ vanishes at the origin.
The Equation \eqref{E:logder5} is equivalent to
\begin{align}\label{E:de1}
T_z&= -(1+T)\frac{r_{z\bar w}}{r_{\bar w}} + (1+T)E \notag\\
&=-(1+T)\frac{r_{z\bar w}}{-\frac1{2i}+\tilde r_{\bar w}}+(1+T)E \notag\\
&=  -(1+T)\frac{r_{z\bar w}}{-\frac1{2i}(1 -2i\tilde r_{\bar w})} + (1+T)E \notag\\
&= 2i(1+T)r_{z\bar w}(1+2i \tilde r_{\bar w}+(2i\tilde r_{\bar w})^2+...) +(1+T)E \notag \\
&= 2i r_{z\bar w}(1+ \mathcal O(T, \tilde r_{\bar w})) + (1+T)E
\end{align}
We wish to solve the Equation \eqref{E:logder5} up to the error terms $E$, where $|E|^2\leq C(\sL_r+|r_z|^2)$.
Therefore, any terms in \eqref{E:de1} whose modulus squared is bounded above by $C(\sL_r+|r_z|^2)$ for some $C>0$ can be omitted when solving this differential equation. In order to take full advantage, split $r_{z\bar w}=S_r+E$, where $|E|^2\leq C(\sL_r+|r_z|)^2$ and $S$ are the remaining terms which do not satisfy this bound. Thus disregarding the error terms $E$, the differential equation \eqref{E:de1} reduces to:
\begin{equation}\label{E:de2}
T_z = 2i S_r  (1+\mathcal O(T,\tilde r_{\bar w}))\ .
\end{equation}
We may view the remaining terms as a telescoping series. Since $T$ and $\tilde r_{\bar w}$ vanish at the origin they will produce terms of higher order, which we may ignore at the first pass.
Therefore we may further reduce the differential equation \eqref{E:de2} to:
\begin{equation}\label{E:de3}
T_z=2i S_r \ .
\end{equation}
Suppose a real-valued function $T$ solving \eqref{E:de3} exists. Let $\rho_1=(1+T)r$. Then
\begin{align*}
(\rho_1)_{z\bar w}=& r_{z\bar w}+r_z h_{\bar w} +r_{\bar w}h_z\\
=& (S_r+E)(1+T)+ r_z T_w +r_{\bar w} (2i S_r)\\
=& S_r+ S_rT +E(1+T) +r_zT_w +(-\frac1{2i}+\tilde r_{\bar w})2i S_r\\
=& S_rT+ E(1+T) +r_zT_w +2i\tilde r_{\bar w}S_r
\end{align*}
Notice the cancellation of the $S_r$.
Therefore, \begin{align*}
|(\rho_1)_{z\bar w}|&\leq |S_r||T|+ |E|(1+|T|) +|r_z||T_w|+2|r_{\bar w}||S_r|\\
&= |S_r|\cdot\mathcal O(|T|,|\tilde r_{\bar w}|)+ |E|(1+|T|)+|r_z||T_w|\ . \end{align*}
Using Cauchy-Schwarz we obtain:
\begin{align*}
|(\rho_1)_{z\bar w}|^2&\leq 3|S_r|\cdot\mathcal O(|T|,|\tilde r_{\bar w}|)+ 3|E|^2(1+|T|)^2+3|T_w|^2|r_z|^2 \\
&=  3|S_r|\cdot\mathcal O(|T|,|\tilde r_{\bar w}|) +\mathcal O(\sL_r+|r_z|^2)
\end{align*}

The new defining function $\rho_1$ need not be plurisubharmonic, but a necessary condition $|\rho_{z\bar w}|^2\leq C(\sL_r+|r_z|^2)$ is ``closer'' to being satisfied. This is so because the relevant terms $S_{\rho_1}$ of $(\rho_1)_{z\bar w}$ satisfy
\begin{equation}
 |S_{\rho_1}|\leq 3|S_r|\cdot\mathcal O(|T|,|\tilde r_{\bar w}|)=|S_r|\cdot \littleO(1) < |S_r|\ .
 \end{equation}

We can repeat the above process to construct $\rho_2$, $\rho_3$,...
If at any point $\rho_n$ is plurisubharmonic, we achieved our goal. On the other hand, if one differential equation $T_z=2i S_{\rho_n}$ that comes up in the construction cannot be solved, the domain does not have a local plurisubharmonic defining function on the boundary.
This process may continue indefinitely, but we do not consider the question of convergence or plurisubharmonicity of the limit function in this paper.

\subsection{Strongly pseudoconvex domains}

Let $\Omega\subset\C^2$ be a strongly pseudoconvex domain. By the definition of strong pseudoconvexity, the Levi form $\sL_r>0$ for every point on the boundary. In particular, the Levi form at the origin, $\sL_r(0,0)=L>0$, is positive. By the continuity of the Levi form there is a neighborhood of the origin $U$ on which $\sL_r>\frac L2$. To produce a local plurisubharmonic defining function we need to solve the Equation \eqref{E:logder5}. However, we notice that on $U$, $|r_{z\bar w}|\leq C=\mathcal O(1)=\mathcal O(\sL)$. Therefore the Equation \eqref{E:logder5} reduces to
\[\frac{\partial}{\partial z} \log (1+T) = 0 +E \ ,\]
which is solved by $T=0$.

Also, on $U$,  $|r_z|^2\leq \tilde C=\mathcal O(1)=\mathcal O(\sL_r)$. Therefore by Theorem $\ref{T:Levidom}$, $(1+Kr)r$ is a local plurisubharmonic defining function on the boundary for some $K>0$.

\subsection{Example of D'Angelo type $4$}

\begin{example}\label{Ex:type4}
Let $r_A(z,w)= \im w +|z|^4+100|z|^6 +4\re z \re w - A(\re w)^2$.
\end{example}

\begin{lemma}
$\Omega_A=\{r_A<0\}$ is pseudoconvex in a (small) neighborhood of the origin if and only if $A\geq8$.
\end{lemma}

\begin{proof}
A direct computation shows that in a sufficiently small neighborhood of the origin
\begin{align*}
\sL_{r_A} \geq & \frac12(\im z)^2+ 100|z|^4 +(\re z)^2 +2A(\re w)^2 -8\re z\re w\\
=&  \frac12(\im z)^2+ 100|z|^4 + \epsilon(\re z)^2 + (2A-\frac{16}{1-\epsilon})(\re w)^2 + (\sqrt{1-\epsilon}\re z- \frac4{\sqrt{1-\epsilon}}\re w)^2\\
\geq& \frac12(\im z)^2 + \epsilon(\re z)^2 + (2A-\frac{16}{1-\epsilon})(\re w)^2 + 100|z|^4
\end{align*}
for any $1>\epsilon\geq0$. This shows that $\Omega_A$ is pseudoconvex if $A\geq 8$. (Actually, $\Omega_A$ is pseudoconvex if and only if $A\geq8$.)
\end{proof}

\begin{lemma}
Let $A\geq8$. The defining function $r_A$ is not plurisubharmonic in any neighborhood of the origin.
\end{lemma}

\begin{proof}
A necessary condition for $r_A$ being plurisubharmonic is $(r_A)_{w\bar w}\geq0$ in some neighborhood of the origin. However, $(r_A)_{w\bar w}=-\frac{A}{2}<0$.
\end{proof}

\begin{lemma}
Let $A>8$. Then $\rho_1=r(1-4\im z+Kr)$ is a local plurisubharmonic defining function on the boundary for some $K>0$.
\end{lemma}

\begin{proof}
Since $A>8$, we can pick $\epsilon>0$ small enough such that
\begin{equation}\label{E:Levi-rA}
\sL_{r_A}\geq \frac12(\im z)^2+ \epsilon (\re z)^2+ \epsilon (\re w)^2\geq \epsilon |z|^2 +\epsilon (\re w)^2 \ .
\end{equation}
Notice that
\begin{align*}
|(r_A)_z|^2=& \left| 2z|z|^2+300z|z|^4+2\re w\right|^2 \leq 2\left| 2z|z|^2+300z|z|^4\right|^2 +8(\re w)^2 \\
=&8(\re w)^2+\mathcal O(|z|^6)\leq \frac8\epsilon \sL_{r_A} \ .
\end{align*}
Thus by Theorem \ref{T:Levidom} $\rho=r(1+ T +Kr)$ is a local plurisubharmonic defining function for some $K>0$ if and only if $T$ solves the differential equation \eqref{E:logder5}. Furthermore, \eqref{E:Levi-rA} shows that any non-constant term in the equation \eqref{E:logder5} is an error term $E$.

The first differential equation we need to solve is \[T_z= 2i S_{r_A}=2i(1) \ . \]
It is easy to check that $T=-4\im z$ is a solution to $T_z=2i S_{r_A}$ and the differential equation \eqref{E:logder5} is satisfied up to error terms $E$.
Therefore $\rho=\rho_1=r(1-4\im z+Kr)$ is a local plurisubharmonic defining function on the boundary for some $K>0$.
\end{proof}

\begin{lemma}
Let $A=8$. Then $\rho_2=r(1-4\im z - 8(\re z)^2 + 8(\im z)^2 + Kr)$ is a local plurisubharmonic defining function on the boundary for some $K>0$.
\end{lemma}

\begin{proof}
The Levi form is given by
\[\sL_{r_8}\geq \frac12(\im z)^2 + (\re z-4\re w)^2 +|z|^4\ ,\]
and
\[|(r_8)_z|^2=4(\re w)^2+ 4\re w\re\left[2z|z|^2+300z|z|^4\right]+ \left|2z|z|^2+300z|z|^4\right|^2\ .\]
Notice that on $\{\im z=0, \re z= 4\re w\}$ the Levi form vanishes to order $4$, while $|(r_8)_z|^2$ vanishes to order $2$. Therefore $|(r_8)_z|^2\not\leq C\sL_{r_8}$ for any $C>0$ in any neighborhood of the origin. Thus Theorem \ref{T:Levidom} cannot be applied.

Moreover, direct computation shows that $\rho_1=r(1-4\im z+Kr)$ is not plurisubharmonic for any $K>0$. In this case we need to solve the differential equation \eqref{E:logder5} to higher order.
The second differential equation then becomes
\[(T_2)_z = 2i\left((\rho_1)_{z\bar w}\right) = 2i(-4\im z+4i\re z- 16i\re w) = -8i \im z - 8\re w +32\re w\ . \]
The solution is $T_2 = 8(\im z)^2 - 8(\re z)^2 +64\re z\re w$. However, notice that $64\re z\re w$ is a multiple of a term in the defining function $r$.
Thus, the contributions of this term already come from the $Kr$ term in the multipler function $h$.
Therefore we can omit $64\re z\re w$ from $T$ to produce a simpler multiplier function $h$. A direct computation shows that $\rho=\rho_2= r(1-4\im z +8(\im z)^2- 8(\re z)^2 +Kr)$ is a local plurisubharmonic defining function on the boundary for some $K>0$.

\end{proof}

\section{Domains in $\C^n$}

Let $\Omega={r(z_1,....,z_n)<0}\subset \C^n$.
The complex tangent space $T^{1,0}_p b\Omega$  to $b\Omega$ at $p$ is defined to be
all $\xi=(\xi_1,...,\xi_n)\in\C^n$ satisfying $$\sum_{j=1}^n\frac{\partial r}{\partial z_j}(q)\xi_j=0.$$
$\Omega$ is pseudoconvex if

$$\sL_r(\xi)=\sum_{j,k=1}^n\frac{\partial^2 r}{\partial z_j\partial\bar z_k}(q)\xi_j\bar\xi_k\geq 0\qquad\text{ for all } \xi\in T^{1,0}_pb\Omega,$$
Similarly, $r$ is plurisubharmonic if
$$\sL_r(\xi)=\sum_{j,k=1}^n\frac{\partial^2 r}{\partial z_j\partial\bar z_k}(q)\xi_j\bar\xi_k\geq 0\qquad\text{ for all } \xi\in \C^n$$

Choose a coordinate system such that the defining function $r$ is of the form \[r(z_1,...,z_{n-1}, w)=\im w +F(z_1,\bar z_1,...,z_{n-1},\bar z_{n-1}, \re w,\im w)\ , \] where terms of $F$ are of degree at least $2$.

Let $v_j=\langle 0,...,0, r_w, 0,...0, -r_{z_j}\rangle$, where $r_w$ is in the $j$-th coordinate for $j=1,...,n-1$. Notice that $v_1,...,v_{n-1}$ form a basis  for the tangent space $T^{1,0}_p b\Omega$ to $b\Omega$ at $p$. Let $$\sL_r(v_j)=r_{{z_j}\bar{z_j}}|r_w|^2+r_{w\bar w}|r_{z_j}|^2 -2\re[r_{{z_j}\bar w}r_wr_{\bar z_j}]$$ be the Levi form acting on $v_j$.
Let $\sh^j_f=det\begin{pmatrix}
f_{z_j\bar{z_j}} & f_{z_j \bar w}\\
f_{\bar{z_j} w} & f_{w\bar w}
\end{pmatrix}$ be the determinant of the corresponding $2\times2$ minor of the complex Hessian of $f$.

Similar proofs as in $\C^2$ case, by considering the appropriate $2\times 2$ minor of the complex Hessian matrix, give the following analogs:

\begin{proposition}\label{Prop:nHessian}
For $j=1,...,n-1$
\[\sh^j_{(1+Kr+T)r}=2Kh\sL_r(v_j)+\sh^j_{(1+T)r}\]
\end{proposition}

\begin{lemma}\label{nece1}
Suppose $\rho=r\cdot h$ is a local plurisubharmonic defining function on the boundary.
\begin{enumerate}
\item $\frac{2h\sL_r(v_j)}{|r_w|^2} +\frac{2\rho_{w\bar w}|r_{z_j}|^2}{|r_w|^2} \geq \rho_{z_j\bar z_j} $
\item $\rho_{z_j\bar z_j}\geq \frac{\rho_{w\bar w}|r_{z_j}|^2}{2|r_w|^2}-\frac{h\sL_r(v_j)}{|r_w|^2}$
\item $\rho_{z_j\bar z_j}\geq \frac{h\sL_r(v_j)}{2|r_w|^2} - \frac{\rho_{w\bar w}|r_{z_j}|^2}{|r_w|^2}$
\item $|\rho_{z_j\bar w}|^2\leq \frac{2\rho_{w\bar w}h\sL_r(v_j)}{|r_w|^2} +\frac{2\rho_{w\bar w}^2|r_{z_j}|^2}{|r_w|^2}$
\end{enumerate}

As a consequence $\rho_{z_j\bar {z_j}},|\rho_{z_j\bar w}|^2 \leq C(\sL_r(v_j)+|r_{z_j}|^2)$, or equivalently  $\rho_{z_j\bar {z_j}},|\rho_{z_j\bar w}|^2 = \mathcal O(\sL_r(v_j)+|r_{z_j}|^2)$ in $U\cap b\Omega$ for some neighborhood $U$ of the origin .
\end{lemma}

\begin{proposition}\label{Prop:nlogder}
Suppose that $\rho=r\cdot h$ is a local plurisubharmonic defining function on the boundary. Then for $j=1,...,n-1$
\begin{equation}\label{E:nlogder}
\frac{\partial}{\partial z_j} \log h = -\frac{\partial}{\partial z_j} \log r_{\bar w} +E_j , \end{equation}
where $|E_j|^2\leq C(\sL_r(v_j)+|r_{z_j}|^2)$.
\end{proposition}
The same mutiplier function $h$ needs to satisfy the differential equation \eqref{E:nlogder} for all $j=1,...,n-1$.

\section{Concluding remarks}

A similar problem is of interest in the real setting as well: can we find a convex defining function (real Hessian is positive semi-definite for all real vectors) for convex domains (real Hessian of a defining function is positive semi-definite for tangent vectors) in $\R^n$. The statements and proofs are completely analogous.
\begin{proposition}
Suppose that $\rho=r\cdot h$ is a convex defining function for $$\Omega=\{r(x_1,...,x_{n-1},y)<0\}\subset \R^n$$ with $r_y\neq0$. Then for $j=1,...,n-1$
\[\frac{\partial}{\partial x_j} \log h = -\frac{\partial}{\partial x_j} \log r_{y} +E_j , \] where $|E_j|^2\leq C(\tilde\sL_r(v_j)+|r_{x_j}|^2)$ and $\tilde \sL_r(v_j)$ is the ``real analog of the Levi form''.
\end{proposition}
However the real setting is ``easier'' in the following sense: since $r_y$ is real, we may take $h=1+Kr+r_y$ to be the multiplier function.

This recovers, from a different view-point, a result from \cite{HerMcN09} that every convex domain in $\R^n$ has a defining function whose Hessian is positive semi-definite in a neighborhood of the boundary of the domain.

A further question is considering extending the positivity of the Hessian past the boundary and inside the domain.
In a similar fashion to Proposition \ref{Prop:Hessian}, we obtain
\begin{align*}\sh_{rh}=& \sh_{rp} +4K^2r^2 \sh_r +4K^2 r\sL_r + 2K \sL_{rp} +2Kr \left[(rp)_{z\bar z}r_{w\bar w} +(rp)_{w\bar w}r_{z\bar z} -2\re[(rp)_{z\bar w}r_{\bar z w}]\right] \\
=&\sh_{rp} +4K^2r^2 \sh_r +4K^2 r\sL_r + 2K p \sL_r+2K r \sL_p \\
&+2Kr [(rp)_{z\bar z}r_{w\bar w} +(rp)_{w\bar w}r_{z\bar z} -2\re[(rp)_{z\bar w}r_{\bar z w}]]
\end{align*}
We plan to consider this in a future paper.

\bibliographystyle{acm}

redpajama_set_name: RedPajamaArXiv


In a recent blog post titled: Are You Measuring the Business Impact of Your Employee Training Programs? we identified a 4 step process for demonstrating the value of your employee training programs through measuring business impact. Defining the problem that your training initiative is expected to address is the first step in measuring business impact. The goal of this step is to build a better understanding of both the business problem and the expectations of your training solution.
Business problems are often defined as either workforce issues or operational issues. Workforce issues can include, for example, lack of skill sets, competencies or credentialing, or onboarding issues and even employee turnover costs. Operational issues might include improvements in productivity, safety, quality, or customer satisfaction. The best way to comprehend your business problem is to make sure that you have a good understanding of what's driving your business and what goals your leadership team is looking to achieve.
What are your key employee challenges? How would you like these to change?
Is there anything, in particular, driving this change?
What will be essential to your department's (division, region, etc.) success over the next few months/years?
How do you anticipate that training will help your department meet your goals?
Who is to receive the training?
What are your expected outcomes for the training?
How do these outcomes relate to the business problem at hand?
Once you have a clear understanding of the business, goals, challenges, and most of all, the problem at hand, you can develop measurable business objectives and training plans to address them. At a high level, in order for the business problem to be solved, employees will require training. This training will result in behavior change with business objectives and measurable business impact. Defining those business impact indicators is step 2 and coming soon!


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Bitcoin Cash has reached a new all-time high today, rising above $4,000 (pictured above) in a very first for the barely four months old digital currency.
Gaining a market cap of $70 billion, it is now just $7 billion away from overtaking ethereum, while trading volumes have spiked to $11 billion at the time of writing.
Much of that volume comes from South Korea's Bithumb, handling $2 billion, while Bitfinex's USD (USDT?) pair handles another $1 billion, followed by the BTC pair at around same levels.
Bitcoin Cash's top trading pairs by 24 hour volumes.
The currency has been on a bull run for the past few days, with BitPay surprising many after it announced it was to add it as an additional option for its merchants.
While Coinbase surprised many by announcing it was to instantly list it for buying and selling, opening America's main fiat pipeline to Bitcoin Cash.
That has seemingly turned BCH into a very bullish mode, gaining 25% of bitcoin's price, a recent high, but still quite below the near 50% it reached soon after bitcoin cash launched.
The two appear to be inversely correlated recently, with bitcoin's price down, although so is much else besides bch, including eth which is down around 5% today.
It's unclear why there is this inverse correlation, with a potential reason being btc-ers moving to bch, potentially even as a hedge.
That could be because bitcoin's fees have now risen to $30, an all-time high. Making the network very much unusable as even at these fee levels there are some 200,000 transactions waiting to move.
That's an entire town, and in some places it would even be called a city, waiting for their money to move so that they can get on with commerce or other actions.
Ethereum is also facing some problems on the fees and congestion side, with costs now rising to around 50 cent per eth transaction while around 25,000 transactions are stuck.
In contrast, Bitcoin Cash is operating smoothly without any congestion and fees at pennies, and while some have suggested litecoin as an alternative, even ltc's founder now no longer uses it, so selling all of his litecoins.
Does that leave BCH as the only alternative with a functioning network, at least temporarily? Perhaps, but unlike bitcoin where devs want fees to rise, ethereum developers are working hard to reduce fees.
And ultimately, all decentralized public blockchains may face the same problem at a certain point until the long term solutions, such as sharding, are deployed, but Bitcoin Cash has quite a way to go to reach that point at this stage.


A universal, low-foaming product for cleaning kitchen surfaces. It removes oil, sticky dirt, grease and everyday dirt. Ideal for cleaning and degreasing cabinets, tabletops, ovens as well as wall and floor tiles. It does not leave streaks nor water stains. You can use this product for cleaning enamel, ceramic, steel, laminate and stone surfaces.
The liquid has PZH (National Institute of Hygiene) certification, which means that it can be used to clean places that have direct contact with food.
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Mac Miller Dies – Today in Hip-Hop
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On this day, Sept. 7, in hip-hop history...
2018: One year ago today, the hip-hop community lost Mac Miller, a widely respected artist with top-tier craftsmanship, endless musical curiosity and plenty of positive energy.
On Sept. 7, 2018, the Pittsburgh, Pa. native, born Malcolm James McCormick, was found dead after an apparent drug overdose in his Studio City home in California. According to a toxicology report from the L.A. Coroner's Office, the late rapper died of an accidental overdose of fentanyl, cocaine and alcohol. He was only 26.
One year later, the U.S. Drug Enforcement Administration filed a charge of distribution of a controlled substance against Cameron James Pettit, a 23-year-old man whom they allege sold Miller counterfeit oxycodone pills that contained fentanyl, which they say is up to 50 times more potent than heroin. If convicted, Pettit could face 20 years in prison.
While Miller's death left a hole in the hip-hop community, his legacy continues to live on through his friends, family and music.
By the time of his tragic passing, Miller had earned the respect of many across the world of hip-hop. A self-taught drummer, guitarist and beat-maker, the rapper began rising to national prominence with his 2010 mixtape, K.I.D.S. (Kickin' Incredibly Dope Shit). With a penchant for dexterous rhyming, agile flows and a willingness to experiment musically, Miller was someone who couldn't be boxed into any one category. While much of his earlier work had been haphazardly labeled frat rap, projects like his experimental 2016 effort, The Divine Feminine—an album with funky instrumentals and soft Miller vocals that mirror vulnerability and warmth—proved he had some serious thematic and stylistic range.
In 2018, just over a month before he passed, Miller dropped off Swimming, a tranquil, introspective LP that earned rave reviews for Miller's lyricism and dream-like production. The album became his first to earn a Grammy Awards nomination.
R.I.P. to Mac Miller, a talented artist who passed far too soon.
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Sylvie Bodorová, née le , est une compositrice tchèque.

Liens externes

Naissance en décembre 1954
Compositrice tchèque de musique classique
Compositrice de musique classique de la période contemporaine

redpajama_set_name: RedPajamaWikipedia


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Latest News Afghan peace talks open in Doha, 19 years after...
Afghan peace talks open in Doha, 19 years after 9/11 triggered war
US Secretary of State Mike Pompeo and Qatar's Deputy Prime Minister and Minister of Foreign Affairs Sheikh Mohammed bin Abdulrahman al-Thani attend the signing of a US-Taliban agreement in the Qatari capital Doha on February 29, 2020. – Washington and the Taliban are set to sign a landmark deal in Doha that would see them agree to the withdrawal of thousands of US troops from Afghanistan in return for insurgent guarantees.
GIUSEPPE CACACE/AFP via Getty Images
The opening ceremony for talks between the Afghan government and Taliban insurgents began in Qatar's capital Doha on Saturday, marking the start of negotiations aimed at ending two decades of war that has killed tens of thousands of combatants and civilians.
The 19-year conflict is also the United States' longest overseas military action, vexing three successive presidents.
The ceremony began at 9 a.m. (0600 GMT) with a recitation from the Koran, followed by opening comments by Qatar's foreign minister.
Major players in the process, including Afghanistan's peace council chairman Abdullah Abdullah and Taliban leader Mullah Baradar Akhund, and U.S. Secretary of State Mike Pompeo are also scheduled to speak.
Officials, diplomats and analysts say that although getting both sides to the negotiating table was an achievement, this does not mean the path to peace will be easy.
READ MORE Covid-19 in Ireland: latest county-by-county data
"The negotiations will have to tackle a range of profound questions about the kind of country Afghans want," Deborah Lyons, the United Nations special representative for Afghanistan, told the U.N Security Council this month.
READ MORE Trump won't commit to peaceful transfer of power if he loses the election
The inauguration ceremony comes one day after the 19th anniversary of the 9/11 attacks on the United States that triggered its military involvement in Afghanistan.
U.S. forces intervened in Afghanistan on the orders of President George W. Bush a month after the attacks to hunt down their mastermind, Osama bin Laden, a Saudi who had been given sanctuary by the country's radical Islamist Taliban rulers. They initially offered mainly air support to the Taliban's local enemies.
Although the Taliban regime was quickly toppled, they regrouped and have since waged an insurgency that has sucked in Afghanistan's neighbours and troops from dozens of countries, including NATO forces.
Negotiations to broker a comprehensive peace deal were envisaged in a troop withdrawal pact signed between the United States and the Taliban in February in an attempt to find a political settlement to end the war.
After months of delay, a dispute over the Taliban's demand for the release of 5,000 prisoners was resolved this week.
Ahead of the U.S. presidential election in November, President Donald Trump is looking to show progress in his pledge to end the U.S. involvement and pull out most of the foreign forces stationed in Afghanistan.
READ MORE The coronavirus pandemic will intensify competition for white-collar jobs, says Singapore minister
The United States has reduced its troop levels and by November is expected to have fewer than 5,000 soldiers in Afghanistan, down from about 13,000 when the U.S.-Taliban deal was signed. More than 2,300 U.S. troops have been killed in Afghanistan since 2001, and about 450 British soldiers.
A European diplomat in Kabul said that a ceasefire — which the Taliban have so far rejected — should top the talk's agenda.
"The Taliban leaders will have to stop fighters from attacking Afghan forces and civilians, violence continues to degrade the atmosphere and potentially derail negotiations," the diplomat said.
How to include the Taliban, who reject the legitimacy of the Western-backed Afghan government, in any governing arrangement and how to safeguard the rights of women and minorities who suffered under Taliban rule are big challenges, experts said.
Nevertheless many diplomats, victims of violence and members of civil society say negotiations are the only realistic way to bring an end to a conflict that has killed more than 100,000 civilians and hampered Afghanistan's development, leaving millions in poverty.
"Solutions will not be found on the battlefield, we know this," Lyons said.
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Browse > Home / Featured Articles / Heading for the moon
Heading for the moon
February 12, 2019 by Yael Edelman
After an enterprise lasting nearly a decade, the Israeli unmanned moon mission "Beresheet" (Genesis) will soon take off from Earth, bound for the Moon's rocky surface.
Prof. Oded Aharonson
Prof. Oded Aharonson, of the Weizmann Institute of Science's Earth and Planetary Sciences Department, is the head of the international Science Team. He will be watching closely as the craft approaches the Moon and initiates the scientific part of the mission, which will start well before touch-down on the Moon's surface.
The cost of planning and building the spacecraft was 100 million dollars, most of it contributed by private donors, led by the president of SpaceIL, the philanthropist Morris Kahn.
If the Beresheet craft touches down successfully on the Moon, it will make Israel only the fourth country to land on the Moon, after the US, the former Soviet Union and China. The spacecraft will be launched on a Falcon 9 rocket made by SpaceX, from Cape Canaveral, Florida, and, after multiple orbits around the Earth, will arrive at its destination two months later.
Although the landing will be a historic achievement for Israel, the project is an independent initiative started by the three founders of SpaceIL, who had two main objectives in mind: firstly, to land the first Israeli space vehicle on the Moon and secondly, to inspire a new generation of students to study science and technology. The three, Yariv Bash, Kfir Damari and Yonatan Winetraub, had entered Israel into the Google LunarX Prize competition. Although the competition officially ended in March, 2018, with no winners, SpaceIL announced they would continue working toward the goal of landing on the Moon.
Since the establishment of SpaceIL in 2011, the mission of a lunar landing has become a national project, and it has received support from all quarters. Israel Aircraft Industries has been a full partner in the project from the beginning. Other supporters include government-owned companies and academia, as well as private donors. The most prominent among the former are the Weizmann Institute of Science, the Israel Space Agency, Israel's Ministry of Science, Bezek Communications and more. Among the private donors are Dr. Miri and Sheldon Adelson, Sylvan Adams, Sammy Segol, Lynn Schusterman and Stephen Grand.
The scientific instruments aboard the spacecraft will begin measuring even before landing. Aharonson, who leads the scientific investigation, explains that "the main scientific goal will be measuring the magnetic field of the Moon. This will help us understand its source." The Moon, today, has an iron core like that of the Earth, but it is small and cold. This core does not generate a global magnetic field, as ours does, but on the surface, various areas or rocks are magnetic at different levels. "If we can measure the magnetism of these rocks, we can begin to understand how and when this magnetism arose."
According to one widely-accepted theory, the Moon's iron core was once hotter and convecting, creating a dynamo that magnetized the rocks on the Moon. The instruments on the landing craft will thus be measuring the magnetic fields in ancient volcanic rocks (similar to basalts on Earth) to see if their intensity matches that suggested by the core-dynamo theory. Among other things, such measurements might frame the time in which the dynamo was active and reveal how long ago it ceased.
Other measurements – for example, of rocks in the Moon's craters – could uncover different sources of magnetization, possibly providing evidence that at least some of the Moon's magnetic field is due to the bombardment of asteroids, or even from magnetic material that originated in the asteroids, themselves.
Aharonson says that the instrument will first be calibrated by measuring the magnetic field of the craft, itself, while it is still cruising toward the Moon. Once it is in orbit around the Moon, the instrument will already be able to detect the lunar field. It will be the short 15 minutes in which the craft descends to surface of the Moon that will be critical. As it approaches the surface, the readings of the magnetic field will increase; measuring this increase, as well as the changes recorded as the craft passes over different areas, will be crucial to understanding its source.
As Head of the SpaceIL International Science Team, Aharonson helped select the landing site – one that will enable communication and ensure the safety of the mission, allowing the craft to land smoothly and in a suitable area for performing the scientific experiments.
The Beresheet craft will also carry a unique array of mirrors provided by NASA for reflecting a laser beam of light precisely back in the direction of its source. The source, in this case, will be a NASA Moon orbiter (LRO), and it will enable the team to locate the position of the Beresheet spacecraft on the Moon's surface.


Sierra Sentinel News- Serving The Sierra Nevada Communities: Guiliani: Truth isn't truth!!
During one of his many ridiculous interviews on Sunday, Guiliani stated many things about whether Trump would tell the truth to Mueller if he testified.
Guiliani said "Truth isn't truth!" to which Meet the Press' Chuck Todd was nearly speechless.


Mojo Barriers unveiled its new access control system, the Gatekeeper 2.0, at Belgium's Graspop Festival, combining a secure turnstile entrance with Playpass integrated scanning capabilities.
Eighteen Gatekeepers contained the ingress and egress of the 45,000 capacity crowd at Belgium's 'hardest rock festival', headlined by Twisted Sister, Iron Maiden and Slipknot.
Belgium-based Playpass, which provided RFID wristbands to festivalgoers, fitted scanners to the kit, offering complete entrance control and instant access to data on audience movement and interests across the three-day event.
"The organisers of this year's Graspop said that the crowd flow was one of the fastest of any year," David De Wever, CEO at Playpass, told this magazine.


Multitudes of citizens have filled the streets of the Sudanese capital, Khartoum, as the army said it had removed President Omar al-Bashir from power, after being in control of the country for 30 years. According to Sudanese First Vice President and Defense Minister Awad Mohamed Ahmed Ibn Auf, a military council was established following the removal of al-Bashir. Meanwhile, a three-month nationwide state of emergency has been declared in Sudan. Take a look at the best images of the events that are unfolding in Sudan's capital of Khartoum.


Welcome to the webpage of the Failure Trace Archive.
The Failure Trace Archive (FTA) is centralized public repository of availability traces of distributed systems, and tools for their analysis. The purpose of this archive is to facilitate the design, validation, and comparison of fault-tolerant models and algorithms.


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Edipo re (Oedipus Tyrannus) è una composizione musicale di Sir Charles Villiers Stanford, concepita per essere eseguita come musiche di scena per lEdipo re di Sofocle. La prima rappresentazione ebbe luogo nel 1887.

Come l'intera produzione musicale di Stanford anche quest'opera, classificata come opus 29 nella sua produzione, è al centro di osservazioni da parte dei critici per l'abitudine dell'autore di riutilizzare brani di sue opere precedenti in altri lavori, in una sorta di autoplagio.

Da questa opera sono, infatti, stati ripresi due pezzi nella sua "Quarta sinfonia" (opera 31) dell'anno successivo: in una prima versione dell'opera 31 era infatti inserito - nell'ambito del secondo movimento - un intermezzo ripreso dall'opera 29, ed inoltre, nell'esecuzione - risalente al 1889 - della prima di tale opera (da parte della Filarmonica di Berlino) era inserito anche il preludio dellOedipus Tyrannus.

La disputa fra i critici relativa al riutilizzo dei medesimi brani in opere diverse di Stanford verte su due ipotesi: da un lato la necessità di produrre per tempo le opere commissionate o, in antitesi, la visione dell'autore che considerava come un unicum la sua produzione musicale.

Musiche di scena


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← Home | Lim Dae-hyeong (임대형)'s News, Updates
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Merry Christmas Mr. Mo DVD (No En Sub)
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[Photos] New Stills Added for the Upcoming Korean Movie "Full Moon"
2019/03/12, Source
New stills added for the upcoming Korean movie "Full Moon",...More
[New Movie] "Full Moon" A Woman Receives a Letter from her First Love
Yuko Nakamura, Kim Hee-ae, Kim Sohye, director Lim Dae-hyeong and Sung Yoo-bin Added the upcoming Korean movie "Full Moon"'s page to HanCinema database,...More
55th Daejong Film Awards (Grand Bell Awards) 2018 Winners
55th Daejong Film Awards (Grand Bell Awards) 2018 winners during the ceremony presented by Shin Hyun-joon and Kim Gyu-ri,...More
[Video] 30 Seconds of Fun in Trailer for "Merry Christmas Mr. Mo"
There is such a feeling of joy and abandon in this trailer for "Merry Christmas Mr. Mo". It feels like a child exploring the world and breaks the boundaries of ageism. No matter how young or old, the world can always be explored anew,...More
[Video] Warm Music Video for ""Merry Christmas Mr. Mo"
Another of Ha Heon-jin's insightful tracks back the second music video for the currently screening "Merry Christmas Mr. Mo". Take a watch as the music paints a lovely picture of the events of the film,...More
[Photos + Video] New Posters and Stills for Winning film, "Merry Christmas Mr. Mo"
Ha Heon-jin worked on the music for "Merry Christmas Mr. Mo" and provides a lovely track for the music video that is just as quietly quirky as Mr. Mo. We also get a couple of new posters that juxtapose the characters, color, and black and white in an understated way also befitting the tone of the other trailers and the descriptions,...More
Korean Movies Opening Today 2017/12/14 in Korea
Korean movies opening today 2017/12/14 in Korea: "Vincent", "Love Of Star Island", "Intruder", "The Namesake", "Merry Christmas Mr. Mo", and "Steel Rain",...More
[Photos] "Merry Christmas Mr. Mo" Releases Charlie Chaplin-esque Stills
The newest stills for "Merry Christmas Mr. Mo" are just charming as they capture the humor of Mr. Mo and his passion for his project as he documents his life around his town,...More
[Photos] Main poster and stills for comedy "Merry Christmas Mr. Mo"
"Merry Christmas Mr. Mo" is looking to be as thoughtful as it says it is funny. Perhaps its an effect of the new poster, the black-and-white stills, and the previously released trailer, but while filming the story of his life, it seems as though Mr. Mo and the young film makers create a bond that is much more than the boring life Mr. Mo previously led,...More
[Video] Added main trailer for the upcoming Korean movie "Merry Christmas Mr. Mo"
Added main trailer for the upcoming Korean movie "Merry Christmas Mr. Mo",...More
[Photo] Added poster for the upcoming Korean movie "Merry Christmas Mr. Mo"
Added poster for the upcoming Korean movie "Merry Christmas Mr. Mo",...More
[Guest Film Review] "Merry Christmas Mr. Mo"
One of the biggest pleasures of watching and reviewing films is coming across hidden gems, surprisingly good movies that had no prior testament to their prowess. Lim Dae-hyeong's debut definitely falls under this category,...More
Upcoming Korean movie "Merry Christmas Mr. Mo"
Added the upcoming Korean movie "Merry Christmas Mr. Mo"'s page to HanCinema database,...More
[HanCinema's Film Review] "Sprout" and "The World of If" and "I am Joongsik"
In "Sprout", seven-year-old Bo-ri (played by Kim Su-an) goes on an epic quest to go find vegetables. Bo-ri isn't exactly mentally equipped for this journey, being only a small child who is easily distracted. Even so, Bo-ri makes a strike for independence and journeys on a miniature road trip guided only by her feet. "Sprout" is no thriller- Bo-ri's neighborhood is just, well, a typical Korean neighborhood. Or is it?,...More
Upcoming Korean short film "The World of If"
Added the upcoming Korean short film "The World of If"'s page to HanCinema database,...More
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After Reportedly Waiting 5+ Years for Kidney, 47-Year-Old Man Dies Just as Potential Match Is Found
By Loren Eaton
Published June 1, 2019 at 10:40am
One sad fact of life is that heroes don't always win. Sometimes all your striving just can't carry the day.
Sadly, that has proved true with a Canadian advocate for organ donation. However, his efforts may still have done some good in the end.
According to the Ottawa Citizen, Steve Dunn — a resident of Orléans in Ottawa, Ontario, Canada — suffered a stroke at the age of 35. Most of us are familiar with the neurological damage that such an injury can cause.
But in Dunn's case, it did something more: It caused his kidneys to stop functioning.
That caused him to land on dialysis. For three times a week, he had to sit for four-and-a-half hours while a machine cleaned his blood.
TRENDING: Five Guys Manager Gives Customer in Wheelchair Free Meal, Then Drops Everything To Help Him
There was only one treatment that stood a chance of aiding him: a kidney transplant. So Dunn found himself stuck in a holding pattern, waiting for an organ to become available.
It's a plight shared by plenty of Canadians. About 10 percent of the nation's people suffer from some kind of chronic kidney disease, according to the Ottawa Citizen.
What's more, 4,300 Canadians need a new kidney at any point in time. So Dunn decided that he wouldn't stoically wait, but would instead take action.
Have you considered being an organ donor?
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He had a message emblazoned on the back of his white GMC truck.
It read, "Asking for help. I need a kidney transplant. Many others like myself need your help. Don't take your organs to Heaven. Save a life instead."
Dunn had already tried to see if family and friends could help. But because he had O-positive blood, he could only receive an organ from someone that shared it.
Commenting on his vehicle-mounted message, Dunn told the Ottawa Citizen, "It's probably not going to help me — although it would be a miracle if it did — but maybe it will help people down the road. At least it might make people think about organ donation."
RELATED: Stevie Wonder Reveals Health Issues to Concert Crowd, Will Take Break for Life-Saving Surgery
Sadly, he was right. The Ottawa Citizen reported that he passed away on May 27 from a stroke or some kind of cardiac event.
The most tragic part was the fact that he had an organ donor ready to help him.
Family member Dave Dunn said, "He had a donor lined up, and she was undergoing the testing for the transplant, but unfortunately, it was too late."
However, his sad story had at least one good outcome. Physicians were able to harvest several of his organs so he could save someone else's life.
Submit your story here, and subscribe to our best uplifting stories here.
Loren Eaton
Contributor, Lifestyle
A graduate of Wheaton College with a degree in literature, Loren also adores language. He has served as assistant editor for Plugged In magazine and copy editor for Wildlife Photographic magazine.
A graduate of Wheaton College with a degree in literature, Loren also adores language. He has served as assistant editor for Plugged In magazine and copy editor for Wildlife Photographic magazine. Most days find him crafting copy for corporate and small-business clients, but he also occasionally indulges in creative writing. His short fiction has appeared in a number of anthologies and magazines. Loren currently lives in south Florida with his wife and three children.
Wheaton College
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Ramaker Brings Back 12 Days of Giving for 2021
Ready to spread some holiday cheer with Ramaker? Our 12 Days of Giving begin on December 9.
The holidays provide time to reflect on what we have—be it a full pantry, a place to stay, or some time with family. At Ramaker, we have a lot to be grateful for. A dedicated staff of employee-owners who have pulled together during a challenging couple of years. Strong partnerships with clients. Exciting projects in the works for 2022.
Taking stock of what we have and practicing gratitude are hallmarks of the holiday season. As we do so, we're also thinking about our responsibility to the communities in which we live and work. That's why we're making our 12 Days of Giving an annual end-of-year event.
About Ramaker's 12 Days of Giving
Ramaker's Corporate Social Responsibility (CSR) committee instituted the company's 12 Days of Giving in 2020. Over a 12-day span in December, the company will donate a total of $10,000 to organizations that our employee-owners hold close to their hearts. Through these contributions, the company aims to highlight local organizations with a variety of missions and investments—including addressing food insecurity, preventing homelessness, and restoring communities—and to make sure they have the resources they need for 2022.
"The pandemic put a lot of people in our communities in precarious positions. We started the 12 Days of Giving in response to that, and we're excited to make it an annual event," said CSR committee chair Joe Gallagher. "While last year's contributions primarily addressed food insecurity, this year we're excited to support local organizations with diverse visions and commitments."
Contributions for this year's 12 Days of Giving will be announced between December 9 and December 24 on this page.
2021 Donations
Sauk City, Wisconsin, is home for Ramaker and many of our employee-owners. For Day 1 of Ramaker's 12 Days of Giving, we're donating to an organization that fights food insecurity in the Sauk Prairie School District area: The Sauk Prairie Area Food Pantry.
Since 1983, the Sauk Prairie Area Food Pantry has provided access to emergency food resources for local community members. Want to get involved? Find information on their current campaigns and explore ways to support the pantry here.
For Day 2, we're giving gifts and clothes to children in the Sauk City and Madison areas as part of two community giving programs: The Sauk Prairie Caring Tree and Toys for Tots. Ramaker's CSR committee and employee-owners fulfilled 30 gift requests from local kids.
For Day 3, we're contributing to two organizations dedicated to providing essential community resources in South Central Wisconsin: Reach Out Lodi and People Helping People in Baraboo.
Through its community center and community outreach initiatives, Reach Out Lodi connects individuals and families in the Lodi School District with basic necessities like food, clothing, and personal products. Learn more about Reach Out Lodi and view the organization's current wish list here.
People Helping People is a community-building organization that serves low-income families and unemployed adults in Baraboo, Wisconsin. Learn more about the organization's 2021 outreach initiatives here.
For Day 4, we're giving to two organizations making a big difference near our Madison, Wisconsin, office: Madison Reading Project and NewBridge.
Madison Reading Project provides free books and literary programming that promote a passion for reading and academic success. Since 2014, the organization has distributed more than 200,000 free books to families and schools in Dane County and across Wisconsin. Learn how to get involved with its community book drive here.
NewBridge provides vital resources and community programming for older adults in Madison and Monona. Since 2019, the organization has connected aging community members with services and tools that promote safety, well-being, and independence. Learn more about how to get involved with NewBridge's outreach initiatives here.
For Day 5, we're highlighting two more organizations making an impact in Madison, Wisconsin: The River Food Pantry and the Goodman Community Center.
The River Food Pantry serves more than 1,000 South Central Wisconsin households every week. Since 2006, the food pantry has partnered with local organizations to provide free groceries and meals for low-income families in the Madison area. For our 12 Days of Giving, we're contributing to River Food Pantry's HOPE Holiday Food Drive. Learn how you can support the pantry's mission here.
Through educational support and academic enrichment programs, career training services, health and wellness programming, and the Fritz Food Pantry, the Goodman Community Center provides vital resources and classes that help members of the Madison community thrive. Today, we're supporting the center's Fritz Food Pantry. Find ways to donate and volunteer here.
For Day 6, we're directing our donations to two organizations fighting food insecurity in South Central Wisconsin: Middleton Outreach Ministry and the Deerfield Food Pantry.
Middleton Outreach Ministry strives to create food and housing security in West Madison, Middleton, and Cross Plains, Wisconsin. Today, we're donating to the organization's Winter Wishes program, which provides holiday gifts for community members in need. Learn more about Middleton Outreach Ministry's programs and services here.
The Deerfield Food Pantry at the Deerfield Community Center fights food insecurity in Deerfield, Wisconsin. The pantry distributes emergency food resources as well as holiday food baskets to families in need. Learn more about the pantry's current needs here.
Just days ago, severe storms and tornadoes devastated parts of the central and southern US. For Day 7, we're donating to organizations providing disaster relief in Kentucky and Tennessee: CARE and YAIPak Outreach.
Atlanta-based non-profit CARE is working with Louisville-based Change Today, Change Tomorrow to distribute supplies and cash vouchers to Kentucky families affected by the tornadoes. You can join us in donating to CARE's Kentucky Tornado Emergency Response fund here.
Ramaker employee-owner and Tennessee resident Adam Simon nominated YAIPak Outreach for our 12 Days of Giving. Based in Clarksville, Tennessee, YAIPak Outreach assists under-resourced communities around the world. Right now, the organization is providing emergency assistance in Adam's community. Learn more about how to get involved with YAIPak Outreach here.
For Day 8, we're donating to two organizations close to the hearts of our employee-owners: GameNight Productions and The Parenting Network.
Baraboo-based GameNight Productions seeks to enhance student achievement by teaching important skills and building community around athletics. Learn more about how the non-profit aims to increase student participation in co-curricular activities on its website.
The Parenting Network provides resources and programming that help anyone in a parenting role create safe and nurturing environments for children. The Milwaukee-based organization has worked to strengthen relationships and prevent child abuse since 1976. Find ways to support its mission here.
For Day 9, we're contributing to organizations and programs fighting hunger throughout Wisconsin: The Community Pantry of Spring Green, Feeding Friends, and the Green Cares Food Pantry.
The Community Food Pantry of Spring Green, Wisconsin, provides emergency food assistance and support for those living in the River Valley School District area. Learn more about the pantry's current needs on its website.
The Feeding Friends program at Dodgeville United Methodist Church in Dodgeville, Wisconsin, brings various churches and local organizations together to prepare an average of 200 hot, nutritious meals each week for community members in need.
The Green Cares Food Pantry in Monticello, Wisconsin, is a volunteer-run pantry that works in collaboration with the Southwest Community Action Program to serve frozen, fresh, and canned foods to low-income families in Green County, Wisconsin. Learn more about how you can help prevent food insecurity in Green County on the pantry's Facebook page.
As we planned this year's 12 Days Of Giving, one of our goals was to highlight organizations whose names and missions don't get much media attention despite the opportunities and support they provide for their communities. Today, we're donating to three organizations that make a huge impact in South Central Wisconsin: The Community Action Coalition for South Central Wisconsin (CAC), JustDane, and Mentoring Positives.
The CAC's goal is to transform local communities by fostering conditions that allow everyone to achieve social and economic security. The organizations provides services and resources that combat food and housing insecurity and improve quality of life across South Central Wisconsin. Find ways to get involved with CAC on its website.
JustDane provides support and opportunities for individuals and families whose lives have been affected by the criminal justice system. Since 1971, the organization has helped transform lives and advocate for more just and equitable communities. JustDane's Healing House is one of many programs created by the organization. It provides a place for families and children experiencing homelessness to recover after surgeries or medical incidents. Learn how you can support JustDane's initiatives on its website.
Mentoring Positives provides leadership, mentoring, and social entrepreneurship opportunities for the younger residents of Madison's Darbo-Worthington Park neighborhood. Join us in donating to Mentoring Positives on the organization's website.
For Day 11, we're donating to two causes close to the hearts of our employee-owners in New Jersey: the Tunnels to Towers Foundation and the Sky Mendoza Supplemental Needs Trust.
The Tunnels to Towers Foundation provides mortgage-free homes and smart homes to injured and fallen veterans, first responders, their families, and Gold Star families. Learn more about how you can help the organization give peace of mind to these families on its website.
The Sky Mendoza Supplemental Needs Trust was created to raise funds for a wheelchair accessible home for Sky Mendoza. "[Sky] is a local 'neighbor' of mine and needs our help so she can go home and be with her family," said Cassie O'Connor, Ramaker's Northeast Business Development Lead. Join us in donating to the fundraiser here.
For Day 12, we're contributing to three more organizations fighting hunger in South Central Wisconsin: 6:8, Beyond Blessed Pantry, and Little John's.
6:8 seeks to transform local communities through service. The organization's programming and outreach initiatives aim to reduce the poverty rate and eliminate food insecurity in the Sauk Prairie School District area. Learn more about 6:8 on the organization's website.
Beyond Blessed Pantry is a volunteer-powered organization addressing food scarcity in Baraboo, Lake Delton, Wisconsin Dells, and surrounding communities. Join us in donating to the pantry on its website.
Little John's works with partnering grocery stores to turn excess food into delicious meals for those in need. Learn how to get involved with the organization on its website.
About Ramaker CSR
Ramaker's CSR committee partners with organizations that positively impact the places where the company's employee-owners live and work. Since Ramaker is an employee-owned company, donations made by the CSR committee are not tax-deductible. Funds are distributed to benefit organizations in need, not to increase the company's bottom line.
Are you involved with a local organization? We'd love to hear more about how you're helping your community. Email csr@ramaker.com to get in touch with Ramaker's CSR committee.
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