text:
Telestream Showcases Tools to Create, Repurpose, Distribute and Share Video Content at InfoComm 2017
By Highrez 07 June 2017
Nevada City, California, June 7, 2017 – At InfoComm 2017 (booth #387),Telestream, a leading provider of digital media tools and workflow solutions, will showcase a range of tools to help corporations, live event professionals, houses of worship and education institutions extend their AV strategy with effective video communication.
"Video is one the most effective ways for organizations to reach their audiences. AV and IT professionals need access to tools that allow them to create more video, stream it, repurpose their content, and quickly distribute it to a wide variety of platforms and destinations," explains Scott Murray, VP of Marketing at Telestream.
Visitors to the Telestream booth will be able to see how its Vantage® Media Processing Platform offers a powerful, scalable, software-enabled set of tools that manage and automate all media services from the camera to the point of distribution. Vantage allows users to quickly, easily, and cost-effectively ingest, edit, transcode, QC, package, caption, monetize, and distribute their media on the web, on social media platforms, and on any device.
Telestream will also be demonstrating its cloud service option. Telestream Cloud runs on a "pay-per-minute-created" basis, allowing users to leverage high-quality Telestream media processing in a SaaS model with no upfront investments. With Wirecast, a cross-platform, all-in-one live streaming production software that enables capture, live production, and encoding of live streams for broadcast to multiple servers and platforms simultaneously, will also be showcased at InfoComm. Wirecast is ideal for streaming or recording live internet shows, broadcasting breaking news and sports, streaming live concerts and games, transmitting church services, corporate meetings, lectures and more. Pro production features include multi-camera input, graphics/titling, live scoreboards, chroma-key support, advanced audio controls and more.
The latest version of Wirecast features intuitive, powerful production capabilities, GPU-accelerated encoding, NDI support, and a streamlined user interface that allows users to effortlessly create and stream high-quality live broadcasts from their computers to dozens of popular destinations such as Twitter, Facebook Live, YouTube and Vimeo as well as to proprietary streaming sites with just a few mouse clicks.
InfoComm attendees will also be able to see Wirecast Gear, a portable computer workstation fully configured for live event production and streaming. The easy-to-use system allows anyone to broadcast professional live productions in a matter of minutes with a fully configured system built for live event streaming. Wirecast Gear comes installed with Wirecast Pro live streaming production software. It is ideally suited for marketers, educators, corporate and online trainers, event producers, sports broadcasters, worship service staff, news gatherers and anyone who wants to deliver professional live streamed productions out of the box.
Delivering high production-value content helps keep viewers' attention and ultimately builds a loyal base of followers. "Studies show that user engagement directly correlates to the volume and timeliness of video content produced. With Telestream's media processing and live streaming tools, any organization can leverage the power of video to reach their internal and external constituencies --whether those are customers, employees, patients, congregations, students or families-- while simplifying the process and significantly accelerating the pace of their video social marketing programs," adds Murray.


text:
'Dexter': Why Does the Cast Keep Sleeping Around?
Posted on November 21, 2018 December 4, 2020 by
Dexter star Michael C Hall marries in surprise wedding
25 Ways "Dexter" Went Wrong
Dexter dating deb real life
Why Michael C. Hall was never the same after Dexter
'Dexter' recap, 'A Little Reflection'
20 Mind-Blowing Facts You Never Knew About Dexter
Jennifer Carpenter Tears Up Talking About Michael C. Hall Divorce at Dexter Event
'Dexter' Recap: 'Argentina' Brings Back Deb-Dexter Incest Storyline
Of all the behind-the-scenes couplings in the history of television, the Michael C. Hall and Jennifer Carpenter relationship may be one of the most well-known – especially because they played siblings on screen. As Dexter and Deb Morgan on Dexter , the two helped solve slayings in Miami, tracked down many bad guys, and witnessed tons of mayhem. Off screen, the two became a secret couple until they revealed their marriage to the public a few seasons into the show. Although the announcement surprised many fans, the actors' chemistry on screen was one of the show's highlights. Their very real relationship revealed what was behind it. Although the marriage didn't last to the end of the show, the actors didn't let their personal lives affect their performances. This was a testament to their friendship, as not many people would find it enjoyable to date, marry, and divorce their significant other while continuing to work with them the entire time.
Dexter 's fifth-season kickoff may have pulled in an impressive 2. Yes, Dexter is officially experiencing a veteran show's often-inevitable pitfall—the sometimes painfully contrived in-dating among cast regulars. Many mature shows suffer from such cast-cest. Maybe the problem develops two seasons in, maybe four. Given a fixed cast of characters, the trigger is simple enough.
But fear not, Dexter fans, the nuptials went down in real life, not on the hit Eve with Jennifer Carpenter, who plays Dexter's tough-talking sister Deb. 37, and Jennifer, 29, who have been secretly dating for about a year and.
I mean, I had to cover my eyes. And I may have even made retching sounds toward my television. We all know more about Michael C. How did we even get here? I thought this was a great relationship on so many levels. I was more than a little devastated when Lundy was killed. She even ended up living with Anton after she saved his life. He was ready to get more serious but she was not. Joey Quinn, her partner.
I never understood this relationship. It confused me until the day they broke up, although it was kinda of nice seeing Deb happy.
Take a quick look at the related searches for the Dexter character Debra Morgan. In prime real estate, you'll find something distinctly different from the usual "[Character Name] Married" and [Character Name] Actor" searches. According to Google, if you're looking for Deb, you might also be looking for "I hate Debra Morgan" as well. Sure, it's the result of an algorithm that probably doesn't understand the complexities of a premium cable series.
How could it understand what Deb has been through? It can't, but it does understand one thing: there's lots of hate for Debra Morgan out there.
Catch more honest [email protected]!ing truth from Deb in the new season of Dexter Deb's advice on dating Dexter. lol Deb Morgan, Dexter Morgan, Dexter Quotes.
Debra is living with him and Doakes follows him everywhere he goes, so he hasn't killed anyone since. When 13 dismembered bodies are found in Bay Harbor, the Miami Metro police department starts a massive manhunt for a man the media calls The Bay Harbor Butcher. Dexter is very involved in the case, considering the bodies they found were his. He doesn't like the name Bay Harbor Butcher and instead prefers The Dark Defender that some call him after it's revealed that the butcher only goes after criminals who had slipped through the law.
Dexter survives by framing Sergeant Doakes for the murders. Dexter's relationships deepen. He learns that his father didn't actually die from heart disease, but that he committed suicide after walking in on Dexter working with one of his kills. Dexter is shattered by this reveal but ends up having a closer relationship with Debra, who lives with him for several months because she can't sleep alone after discovering The Ice Truck Killer was her boyfriend.
Rita discovers that something is going on with Dexter and assumes drugs. She believes that he is a heroin addict and asks him to go to a step program.
Hi all, and welcome back to TV Tuesday! My first on Dexter is that it is a gruesomely interesting show. What I do like, among the fascinating plot is that the show takes us into the past, looking at Dexter and his sister and father when they were younger. It really gives the show that extra background that it needs to really telling its viewers who these characters are. So the show is about Dexter Morgan, obviously. His sister Debra also works with the police department, she starts out in Vice, which she hates.
Debra is living with him and Doakes follows him everywhere he goes, Dexter begins dating Lila, when he discovers that she can see the.
Debra's feelings and opinions were evident by her facial expressions. She was 5'9′" in height, slim with an athletic build. Deb was very fit and capable of running down a perp when necessary. On the right side of her stomach, she had a scar from when she was shot during " Dex Takes a Holiday. Her attire varied throughout the series.
While in Vice, she wore a police uniform or while undercover provocative outfits. After her transfer to Homicide, she sometimes wore long sleeve jackets, button-up shirts, and dress pants, often with boots. When she was promoted to Lieutenant, she adopted designer suits, but avoided high heels as she found them uncomfortable. During Season Eight , as a private investigator, she wore an assortment of tops and pants, depending on the circumstances.
At the gym, she wore workout clothes. Debra was not shy and could be headstrong at times. Despite the tough persona she presented, she was sensitive and caring inside although she didn't readily express it. Debra's ability to be "one of the guys" allowed her to be effective at her job. Suspects could anger her, especially when something violent happened to someone close to her.
Debra morgan: across was living a podcast devoted to humanity for dexter used to capture hannah, was – hundreds of! Through dexter's wife, jamie batista on the nuptials went from under? Lieutenant debra confessed to Is an interview to fake his real life. Ada miguel prado, at what we see that was attempting to team to humanity — a cafe in , does dexter and.
How many guys in fact, with.
Do We Still Care About Deb on 'Dexter'? After all, she was the detective unknowingly dating the infamous Ice Truck Killer while Dexter and.
It's her panel, and she can cry if she wants to. The actress, 33, teared up onstage when asked about what it was like to work with ex-husband and series star Michael C. Hall following their December divorce. It's an awkward thing to talk about your personal life in front of a bunch of strangers, but there's nothing but love and respect [between us]. Hall, for his part, said it was "gratifying" to be able to continue his professional relationship with his ex.
That said, the potential for awkward situations is high. At one point during the panel, the moderator prompted the cast to play "Kiss, Marry, Kill" — an idea that Carpenter did not take well to.
Spoiler warning: Don't read this if you don't want to know what happens in the "Dexter" season finale. So maybe fans shouldn't have been so surprised — to say nothing of shocked, baffled, and repulsed — by the so-called "incest" storyline between siblings Dexter and Deborah Morgan this season. The pair aren't blood relatives, after all: Show runner Scott Buck tells TheWrap that writers have considered the possibility that Deb Jennifer Carpenter might carry romantic feelings for Dexter Michael C.
Hall almost since the start of the show, even though it took her until Sunday's season six finale to truly realize it. Carpenter and Hall must have seen the possibilities; they were briefly married during the show's run. It's something we'd always talked about and it just felt like it was time to finally deal with that issue.
Aug 25, – This Pin was discovered by Cristela Flores. Discover (and save!) your own Pins on Pinterest.
Does deb and dexter hook up Also be upset over, i think of her. You want a bloody laguerta? Does and quinn up until season seven, drama, and do with your browser does, the worst. Will dexter book series, and breed little inbred babys. You think of the couple play brother would have. Jennifer carpenter: Dexter finds out.
Sometimes Dexter was Norman Bates. Sometimes he was John-Boy Walton. You might as soon have expected Hannibal Lecter to open a funeral home for the indigent, or the Talented Mr. Ripley to sculpt balloons into animals for nursing-home patients.
Jennifer Carpenter played Debra Morgan, Dexter's foster sister and a began dating in , and in May , they welcomed son Isaac.
Congratulations to Michael C Hall who has tied the knot for the third time. The former Dexter actor married his editor girlfriend Morgan Macgregor during a low-key ceremony at New York's City Hall on Monday morning, his rep has confirmed. The happy newlyweds have been dating since and made their first official appearance as a couple that same year at the Emmy Awards.
Michael C Hall has tied the knot with girlfriend Morgan Macgregor. Michael, 45, has been married twice before; he was previously wed to actress Amy Spanger from until , and then to his former Dexter co-star Jennifer Carpenter , from who he split in December Jennifer stood by his side while the star battled Hodgkin's lymphoma. He announced his cancer was fully in remission in April , and eight months later the couple confirmed their separation, finalising their divorce the following year.
The actor was previously married to his Dexter co-star Jennifer Carpenter. Through the production, Michael got the chance to meet David a number of times, and he has said that he felt the news of the rock star's death in January like " an internal fist clench". Speaking to the Guardian , Michael also revealed that on the show's opening night David sent him " a very, very amazing gift and note ".
We use our own and third-party cookies to improve our services and show you related advertising with your preferences by analyzing your browsing habits and generating the corresponding profiles. If you go on surfing, we will consider you accepting its use. You can change the configuration or get more information here. I Accept.
It's hard to believe but on Oct. The beloved Showtime crime series about a serial killer came to an end in , but its cast members have been up to a lot since then! The entire show revolved around his character, Dexter Morgan , a forensic blood spatter analyst at the Miami Metro Police Department by day — and a serial killer who targets other murderers by night. Keep reading to see what Michael and more of the cast are up to now…. After "Dexter" ended, Michael C.
Image may contain Human Person Dating Face Lighting Head and Duet Supposedly softening the blow is that Deb and Dexter aren't blood.
D eb – Dex Drama: Congratulations to whoever had Episode 8 in their "When will 'Dexter' drudge up the semi-incestuous Deb-is-in-love-with-Dexter storyline from last season" office pool. He already did her there last episode. When that revelation stirred up some jealous feelings, Deb finally confessed to Dexter that she's in love with him.
So we now have a brother-sister-serial-killer-cop-other-lady-serial-killer love triangle on our hands. To recap: Dexter was going to kill Hannah, then he decided to have sex with her instead. Dexter told her he couldn't because he's been sleeping with her. Deb told Dexter she was in love with him.
Debra Charlotte Morgan spelled Deborah in the novels is a fictional character created by Jeff Lindsay for his Dexter book series. She also appears in the television series , based on Lindsay's books, portrayed by Jennifer Carpenter. In Lindsay's novels, she first appeared in Darkly Dreaming Dexter and was featured in every novel in the series. A tough, foul-mouthed tomboy, she craved her father's attention and envied Dexter for the amount of time Harry spent with him, unaware that Harry was training him to be a vigilante serial killer.
When Debra was a teenager, her mother died of cancer.
So what happened to Michael C. Hall's Dexter Morgan, the Miami forensic Debra's death made Dexter see the folly of such dreams. Jensen Ackles Joins The Boys Season 3 as Supernatural Sets Series Finale Date.
Dexter finished its eight-season run tonight with a series finale that is certain to rankle. And how did the series end in general? Not well. Full-on spoilers after the jump. First: Deb dies. Sorry, Quinn. So Dexter did what Dexter does and pulled the plug himself. Then he wheeled her body out of the hospital, which no one seemed bothered by, since everyone was trying to evacuate due to the impending hurricane. Then he drove the Slice of Life right into the storm, apparently killing himself.
Muy malo. Fade to black. He survived the hurricane and is now a beardo working as a logger and looking very sad. In the final moments of the series, he sits at a table and looks down forlornly, and then stares right into the camera with his signature sinister stare.
Did derek and penelope dating on criminal minds
The Cast Of 'Gossip Girl': Where Are They Now?
Kaley Cuoco dating Ryan Sweeting?
'Real Housewives of Beverly Hills' star Taylor Armstrong engaged to lawyer boyfriend John Bluher
The Rules for Online Dating: Capturing the Heart of Mr. Right in Cyberspace
Him – Solitary Man 7″ Vinyl
PortuguêsSvenskaMagyarPolski中文(简体)EnglishSuomiالعربيةEspañol日本語DanskΕλληνικάTürkçeNorskEesti keelDeutschLëtzebuergeschNederlandsItalianoFrançaisČeština

redpajama_set_name: RedPajamaCommonCrawl


We recommend leaving space on each end or along the perimeter to allow for idiosyncrasies. But you can choose to cover as much of the surface you feel is necessary for your preferences.
The size, shape, and condition of the substrate may dictate the appropriate material of construction as will the preferred method of installation.
Which grit size is appropriate for your application? Consider the location, type of foot traffic (flat work shoe, high heels etc.) and the substance (mud, oil, water etc.) the cover will be subjected to when choosing the grade. Not sure? Just ask!
Safeguard has a number of standard, premium, and HiGlo colors. Custom color matching, safety messaging, PPE symbols, and logos are also available.
Finally, think about your preferred method of installation. Safeguard can provide the necessary hardware or adhesive as well as bare edges for tack welding (steel base covers only) or pre-drilled holes to aid in installation.
Looking for step covers in a hurry?
Check out Valu-Traction for standard sizes and colors available ASAP.
Call Safeguard with any questions or to place an order by phone at 1-800-989-1695 or submit a quote request online. Or simply send an email with your requirements and we will get back to you promptly.


4/11/19 - This is a post Great War era 1911 rework, with scarce Remington UMC frame. There were only ~21,000 pistols produced by Remington UMC, and this one falls in the last few hundred ever made. The left side frame shows Augusta Arsenal proofs, and the slide is a Colt production. The finish on the pistol rates at about 96-97%, with the majority of finish loss on the underside of the slide. Mint bore. C-S magazine. Excellent grips. Post-war Colt barrel.


text:
Huckleberry Hills Ranch protected forever
Huckleberry Hills Ranch, a 500-acre agricultural property in southwestern Pueblo County outside Rye, has been protected forever by a conservation easement held by San Isabel Land Protection Trust.
Protecting the ranch ensures that the property will remain open and in agricultural use, providing habitat for numerous wildlife species, maintaining the scenic beauty for travelers along Highway 165, part of the Frontier Pathways Scenic and Historic Byway, and providing a buffer to the adjacent San Isabel National Forest at the base of Greenhorn Mountain.
Laurie Sankey, president of Huckleberry Hills Ranch Inc., said, "The ranch is owned by five diverse families who don't always agree on everything associated with running a ranch. … But we have always agreed on one thing: We want to preserve the property as it is, including the resources, qualities and values that make the Mountain West unique.
"We feel blessed to own a slice of paradise and are honored to be able to preserve it," Sankey said. "San Isabel Land Protection Trust gave us the tools to do this, and we are grateful. Four of our five families inherited this land from our parents, most of whom have passed away. I think today they are smiling down on us in recognition of what this means to the future of the property they loved so dearly."
She added, "Native wisdom holds that we must treat the earth well, as it is not given to us by our parents, but loaned from our children. This sounds right to us!"
Great Outdoors Colorado and Frontier Pathways Scenic and Historic Byway provided funding for the project.
San Isabel's board president Larry Vickerman said, "All of us in the land trust community are grateful to the folks at Huckleberry Hills Ranch for committing to keep their gorgeous property open and protected into the future. This is no small achievement, and as landowners, they should be proud."
The Huckleberry Hills easement brings the total number of easements held by San Isabel to 133, protecting nearly 41,000 acres of working ranches, farm and forest lands, water resources, wildlife habitat and scenic spaces. San Isabel holds 13 easements on about 2,400 acres in Pueblo County.
San Isabel works with landowners to protect and care for land and water in Huerfano, Custer, Fremont and Pueblo counties. The land trust aims to ensure the region remains a beautiful and wild landscape with a strong agricultural foundation and a vibrant, healthy community.
Great Outdoors Colorado invests a portion of Colorado Lottery proceeds to help preserve and enhance the state's parks, trails, wildlife, rivers and open spaces. GOCO's independent board awards competitive grants to local governments and land trusts and makes investments through Colorado Parks and Wildlife. Created when voters approved a constitutional amendment in 1992, GOCO has since funded more than 5,000 projects in all 64 counties of Colorado without any tax dollar support. Visit GOCO.org for more information.


text:
\section{Introduction}
\noindent Connections between various forms of the Schwarz lemma and hyperbolicity in complex analysis,
i.e., negativity of curvature of a biholomorphically invariant metric, are too well known to need any
elaboration (a brief overview can be found in \cite{R}). Nevertheless, certain fundamental conjectures towards building
a {\it theory} of hyperbolicity pertinent to complex analysis in standard differential geometric terms,
still remain unsettled. The present article is
one of a two-part note, concerning the following conjecture of Kobayashi \cite{Ko}
and its modified form by Wu \cite{Wu}.
\medskip\\
\noindent \underline{Conjecture (K-W)}:
On every Kobayashi complete hyperbolic complex manifold, there exists a $C^k$-smooth (for some $k \geq 0$) complete
Hermitian metric with its holomorphic curvature \footnote{The term `holomorphic
curvature' stands precisely for the holomorphic {\it sectional} curvature and is said
to be strongly negative, if it is bounded above by a negative constant.} bounded above by a negative constant in the sense of currents.
 \medskip\\
\noindent Needless to say, for the above conjecture to contribute to complex analysis, the metric must transform in a `nice' manner
under holomorphic mappings. The Kobayashi metric is the largest pseudo-distance with the nice feature of being distance
decreasing under all holomorphic mappings. However, the Kobayashi metric fails to be Hermitian in general, obstructing applicability of
standard (Hermitian) differential geometric techniques.  A  method proposed by H. Wu in \cite{Wu}
to redress this problem is as follows. For an infinitesimal metric $\eta$, form a new metric whose unit ball about the origin, in each tangent space, is
the ellipsoid of minimal volume containing the unit ball with respect to $\eta$. By an ellipsoid, we mean the image of a ball in the
standard $l^2$-norm, under a linear automorphism of $\mathbb{C}^n$. As ellipsoids furnish the simplest compact convex sets with (quadratic) polynomial
boundary, Wu's methodology is perhaps the first best attempt at constructing Hermitian (invariant) metrics. In the present article, we work with $ \eta $ as the infinitesimal Kobayashi metric \footnote{We shall reserve the term `metric' for what was termed as a sub-metric in \cite{Wu} and
use the word `distance' for what is termed as a `metric' in general topology and metric geometry.} and refer the resultant metric as
the Wu metric.
\medskip\\
\noindent  An explicit description of the Wu metric on the Thullen domains \footnote{These are also referred to as `complex ellipsoids'
in the complex analysis literature. However, since the ellipsoid in Wu's construction is defined by a polynomial of degree two, we
adopt a different terminology.} in dimension $n=2$, namely $ \{ (z_1, z_2) \in \mathbb{C}^2:
|z_1|^{2m} + |z_2|^{2} < 1 \}$, where $ m > 0 $, was obtained by Cheung and Kim in \cite{CK1} and \cite{CK2}.
This is a natural example arising in the pursuit of well-adapted metrics in complex analysis, the background for which can be found in \cite{Wu} and \cite{Kim}.
 Let us make a few
remarks. Although the statement of the conjecture (KW) as it stands, had been affirmed for smoothly bounded Thullen domains way back in the 1980's
owing to the fact that the curvatures of the Bergman and the K\"ahler-Einstein metric do lie trapped between a pair of negative constants (\cite{AzSu}, \cite{Bl}),
these metrics are not functorial: the Hermitian metric sought for, in the conjecture (K-W) is desired to transform holomorphic
mappings into Lipschitz mappings with respect to the distance induced by the metric, {\it wherever such a metric is defined}. Being
functorial and the simplest modified (Hermitian) form of the Kobayashi metric, the Wu metric is the first natural candidate to be
investigated for (K-W). However, the Wu metric may fail to be upper semicontinuous \cite{Ju}, notwithstanding
the fact that the Kobayashi metric is always upper semicontinuous. But then again, the Wu metric seems to reflect the boundary
geometry {\it better} in special instances. For instance, the holomorphic curvature for the Kobayashi metric is well defined
\cite{JP} and for any bounded convex domain in $\mathbb{C}^n $, the holomorphic curvature of the Kobayashi metric is identically a negative
constant. On the other hand, for $C^2$-smooth convex Thullen domains in $ \mathbb{C}^2 $, the Wu metric is $C^1$-smooth Hermitian whose curvature
is a negative constant only on an appropriate neighbourhood of the strongly pseudoconvex portion of the boundary (see \cite{CK1}). The complement of
the closure of this neighbourhood forms a approach region for a thin subset of the boundary
consisting of weakly pseudoconvex points and the curvature of Wu metric is nowhere constant on this region.  Nevertheless, in all
cases, the Wu metric retains the strong negativity of curvature. \medskip\\
\noindent The purpose of this note and its counterpart \cite{BM2}, is to carry forward the case study of the
Wu metric in conjunction with (K-W) as in \cite{CK1} and \cite{CK2}, to egg domains of the form
\begin{equation} \label{Egg}
E_{2m} = \big\{ z \in \mathbb C^n : \abs{z_1}^{2m} + \abs{z_2}^2 + \ldots + \abs{z_{n-1}}^2 + \abs{z_n}^{2} <1  \big\}.
\end{equation}
More specifically, we reinstate the viewpoint of \cite{CK1}, \cite{CK2}: being functorial and {\it respecting Kobayashi hyperbolicity}, the Wu metric is conceivably the most natural answer to (K-W)
when restricted to a suitable class of domains -- the class for this article being the eggs $E_{2m}$ as above, with $m \geq 1/2$.
This condition on $m$ is precisely, to ensure the convexity of such $E_{2m}$. By Lempert's work \cite{Le}, all invariant metrics on convex bounded domains, which turn holomorphic maps into Lipschitz $1$-maps, coincide with the Kobayashi metric. Analysis of the non-convex eggs is dealt with in a separate article \cite{BM2}, for clarity.
\medskip\\
\noindent We now provide a description of our results.  First let $m>1$. Then $\partial E_{2m}$ is atleast $C^2$-smooth. Split up $E_{2m}$ as a disjoint union of the following subsets.
\begin{eqnarray*}
 Z & = & \{ f \big( (0, \hat{0} ) \big) | f \in \mbox{Aut} \; E_{2m} \}, \\
 M^{-} & = & \{ f \big( (p_1, \hat{0} ) \big) | f \in \mbox{Aut} \; E_{2m}, 0 < p_1 < 2^{-1/2m} \}, \\
 M^0 & = & \{ f \big( (2^{-1/2m}, \hat{0} ) \big) | f \in \mbox{Aut} \; E_{2m} \}, \; \mbox{and} \\
 M^+ & = & \{ f \big( (p_1, \hat{0} ) \big) | f \in \mbox{Aut} \; E_{2m}, 2^{-1/2m} < p_1 < 1 \},
\end{eqnarray*}
where $ \mbox{Aut} \; E_{2m} $ denotes the group of holomorphic automorphisms of $ E_{2m} $. Notice that each of the above sets
is a union of orbits under the action of $ \mbox{Aut} \; E_{2m} $. As orbits of distinct points either coincide or never
intersect, it follows that the above sets are disjoint. Further, observe that the subdomain $ M^+ $
is a `pinched' one-sided neighbourhood of the strongly pseudoconvex piece of the boundary, pinched along the weakly
pseudoconvex points of the boundary which form the real algebraic subvariety of
$\partial E_{2m}$ given by
\[
\omega = \{ (z_1, z_2, \ldots, z_n) : z_1=0, |z_2|^2 + \ldots + |z_n |^2 = 1 \}.
\]
The boundary of $M^+$ is the union of $\partial E_{2m}$ and $M^0$. The significance of these sets is that
the Wu metric is real analytic, K\"ahlerian of constant negative curvature on $M^+$. All these characteristics break
down on $M^0$ while just ensuring an overall $C^1$-smoothness of  the Wu metric therein. The real analyticity is
restored again on $M^{-}$, which lies `inside' $M^0$. Smoothness may be lost along the remaining seam inside $M^0$ namely, $Z$ which however
encodes some nuances about the smoothness of the boundary near $\omega$, laid down more precisely in the following

\begin{thm} \label{smoothconvexegg}
Let $m $ be any real number bigger than one. The Wu metric on $E_{2m}$ is a $C^1$-smooth Hermitian metric which is real analytic
on $E_{2m} \setminus (M^0 \cup Z)$. It is of class $C^1$ but not $C^2$ on $M^0$. At points of $Z$, the Wu metric is H\"older of
class $C^{[2m], 2m - [2m]}$ if $m$ is not an integer whereas it is real analytic in case $m$ is an integer. \\
On $M^+$, the Wu metric is K\"ahler of constant negative holomorphic curvature, whereas on $M^-$ it is a non-K\"ahler Hermitian
metric with its holomorphic curvature non-constant and bounded between a pair
of negative constants. Overall on $E_{2m}$, the Wu metric has a strongly negative holomorphic curvature in the sense of currents.
\end{thm}

\noindent Note that the set $Z$ is a complex hypersurface in $E_{2m}$ while $M^0$ is a real analytic hypersurface in $E_{2m}$. Indeed,
$M^0$ is described explicitly by
\[
\{ z \in E_{2m} \; : \;  2 \vert z_1 \vert^{2m} + \vert z_2 \vert^2 + \ldots + \vert z_n \vert^2 =1 \}
\]
while $Z$ is the intersection of $E_{2m}$ with the hyperplane $\{ z_1 =0 \}$. As the parameter $m$ drops below one, the order of
tangency of $E_{2m}$ with the normalized ellipsoid namely, the unit ball $ \mathbb{B}^n $, at the boundary orbit accumulation points (which precisely is
the set of weakly pseudoconvex points in $\partial E_{2m}$) drops below two. The `tangential approach' region $M^+$ to $\omega$, where
the Wu metric is K\"ahler of constant negative curvature, then disappears altogether.

\begin{thm}\label{convexegg}
Let $1/2 < m <1$. Then $\partial E_{2m}$ is $C^1$ but not $C^2$-smooth. The Wu metric on $E_{2m}$ is a $C^1$-smooth Hermitian metric which is real analytic on $E_{2m} \setminus Z$. At points of $Z$, the Wu metric is $C^{1,2m-1}$ but not of class $C^2$.\\
For $m=1/2$, the Wu metric on $E_{2m}$ is a continuous Hermitian metric, real analytic on $E_{2m} \setminus Z$.\\
For $ 1/2 \leq m < 1 $, the Wu metric on $E_{2m}$ is nowhere K\"ahler. Its holomorphic curvature is bounded above by a negative constant independent of $m$, in the sense of currents.
\end{thm}

\noindent {\it Acknowledgements:} We thank our advisor Kaushal Verma for suggesting this problem.
\section{Preliminaries}

\noindent Let $ \langle \cdot, \cdot \rangle $ denote the standard Hermitian inner product on $ \mathbb{C}^{n-1} $ which is conjugate-linear in the
second variable. Write $ z \in \mathbb{C}^n $ as $ z= (z_1, \hat{z})$, where $ \hat{z} = (z_2, \ldots, z_n) $. Any invariant metric, in particular
the Wu and the Kobayashi metric, can be written down explicitly on $E_{2m}$ once it is known at points of $S \cup \{0\}$ where
 $\{p \in \mathbb{C}^n \; :\; p=(p_1, \hat{0}), \; 0<p_1 < 1 \}$. Indeed, the automorphism
\begin{equation}\label{aut}
\Phi(z) = \Phi_p(z) = \Big( \frac{|p_1|}{p_1} \frac{s^{1/m}}{ (1-\langle\hat{z},\hat{p} \rangle )^{1/m} } z_1,  \Psi(\hat{z}) \Big)
\end{equation}
of $ E_{2m} $ takes $p=(p_1, \hat{p})$ to $(\tilde{p}_1, \hat{0})$, where $\tilde{p}_1 = |p_1|/s^{1/m}$ with $ s=\sqrt{1- |\hat{p}|^2}$ and
$\Psi$ is the automorphism of $\mathbb{B}^{n-1}$ taking $\hat{p}$ to the origin, given by
\[
\Psi(\hat{z}) = \frac{ \hat{p}I - P(\hat{z}) - sQ(\hat{z}) }{ 1 - \langle\hat{z},\hat{p} \rangle },
\]
where $P$ is the (linear) projection onto the one-dimensional complex subspace spanned by $\hat{p}$, i.e., $P(z) = \frac{\langle\hat{z},\hat{p} \rangle }
{|\hat{p}|^2}{\hat{p}}$ and $Q=I-P$ is the projection  ortho-complementary to $P$.

\begin{thm} (Theorem 1.6 of \cite{BMV}) \label{T1}
The Kobayashi metric for $E_{2m}$ at the point $(p_1, \hat{0})$ for $0<p_1<1$, is given by
\begin{alignat*}{4}
K \big( (p_1, 0, \ldots, 0), (v_1, \ldots, v_n) \big) =
   \left\{ \begin{array}{lrl}
\left( \frac{m^2 p_1^{2m-2} |v_1|^2}{(1-p_1^{2m})^2}
+ \frac{|v_2|^2}{1- p_1^{2m}} + \cdots + \frac{|v_n|^2}{1- p_1^{2m}} \right)^{1/2} & \mbox{for} & u \leq p_1, \\
\\
\frac{m \alpha (1-t) |v_1|}{p_1(1- {\alpha}^2) \left(m(1-t) + t \right) }
& \mbox{for} & u > p_1,
\end{array}
\right.
\end{alignat*}
where
\begin{eqnarray}
u & = & \left( \frac{m^2 |v_1|^2}{|v_2|^2 + \cdots + |v_n|^2} \right)^{1/2}, \label{E4} \\
t & = & \frac{2m^2 p_1^2}{u^2 + 2m(m-1) p_1^2 + u \big( u^2 + 4m(m-1) p_1^2 \big)^{1/2}} \label{E5}
\end{eqnarray}
and $ \alpha $ is the unique positive solution of
\begin{equation}
 \alpha^{2m} - t \alpha^{2m-2} - (1-t) p_1^{2m} = 0.
\end{equation}
Moreover, $ K $ is $ C^1$-smooth on $ E_{2m} \times \left( \mathbb{C}^n \setminus \{0\} \right) $ for $ m > 1/2 $.
\end{thm}

\noindent The Kobayashi metric at the origin is given by
$ K ( 0 ,v ) = q_{E_{2m}}(v)$ where $q_{E_{2m}}$ denotes the \textit{Minkowski functional}
of $E_{2m}$. Overall, the Kobayashi metric is $C^2$ but not $C^3$-smooth, as will be shown in section 6. The first step in investigating the smoothness of the Wu metric is to determine its unit sphere in tangent spaces. In terms of the Euclidean coordinates on the tangent bundle $ E_{2m} \times \mathbb{C}^n $, the unit
sphere of the Wu metric in $ T_p E_{2m} $ for $p \in S$, is given by
\[
 r_1 |v_1|^2 + r_2 \left( |v_2|^2 + \ldots + |v_n |^2 \right) = 1
\]
where $ r_1 $ and $ r_2 $ are positive real-valued continuous functions of $ p_1 $.  The main objective now is
\begin{enumerate}
\item[(*)] to find $ r_1, r_2 > 0 $ such that the ellipsoid
\[
\left\{ v \in \mathbb{C}^n:  r_1 |v_1|^2 + r_2 \left( |v_2|^2 + \ldots + |v_n |^2 \right) < 1 \right\}
\]
has the smallest volume while containing the set
\[
I \left( E_{2m}, (p_1, \hat{0}) \right) =
\left\{ v \in \mathbb{C}^n: K \left( ( p_1, \hat{0} ), v \right) < 1 \right\}.
\]
\end{enumerate}
To this end, first note that the expressions for the best fitting ellipsoid \footnote{The unit ball in any given tangent space with respect
to the Wu metric will be referred to as the `best fitting ellipsoid' or the Wu ellipsoid.}  at $ (p_1, \hat{0}) $ and the Kobayashi
indicatrix at $ (p_1, \hat{0}) $ involve terms of the form $ |v_1|^2$, $ |v_2|^2,
\ldots, |v_n|^2 $ only. Consequently, the problem reduces to finding $ r_1, r_2 > 0 $ such that the set
\[
\left\{ (v_1, \ldots, v_n) : v_1 \geq 0, \ldots, v_n \geq 0,
r_1 v_1^2 + r_2 \left( v_2^2 + \ldots + v_n^2 \right) = 1 \right\}
\]
encloses the smallest volume with the coordinate axes and contains the set
\[
\left\{ (v_1, \ldots, v_n) : v_1 \geq 0, \ldots, v_n \geq 0,
K \left( ( p_1, \hat{0} ), v \right) \leq 1 \right\}.
\]
\noindent We reformulate problem (*) using the concept of square-convexity from \cite{CK1}. Write
\begin{eqnarray*}
 x & = &  v_2^2 + \ldots + v_n^2 \; \mbox{and}\\
 y & = &  v_1^2,
\end{eqnarray*}
so that the problem of finding the best fitting ellipsoid at $ (p_1, \hat{0}) \in E_{2m} $ can be restated as:
\begin{enumerate}

\item[(**)] Find $ r_1, r_2 $ such that the line segment $ r_1 y + r_2 x = 1 $ in the first quadrant
bounds the smallest area with the coordinate axes and contains the set
\[
\left\{ ( x, y ) : v_1 \geq 0, \ldots, v_n \geq 0,
K \left( ( p_1, \hat{0} ), v \right) \leq 1 \right\}.
\]
\end{enumerate}
The boundary of this set is determined by the equation $ K ^2 \left( ( p_1, \hat{0} ), v \right) = 1 $, which splits into two parts, as is
evident from Theorem \ref{T1}. Henceforth, the portion of the curve $ K^2 \left( ( p_1, \hat{0} ), v \right) = 1 $ for
$ u \leq p_1 $ and $ u > p_1 $ will be referred to as the lower K-curve $ C_{low} $ and the upper K-curve $ C_{up} $ respectively.
In $ x$-$y $ coordinates, the lower K-curve $ C_{low} $ is given by
\begin{equation} \label{E10}
\frac{m^2 p_1^{2m-2} \; y }{(1-p_1^{2m})^2} + \frac{x}{1- p_1^{2m}} = 1,
\end{equation}
which represents a straight line. Denote by $ y = \left( f_{low} ( \sqrt{x}) \right)^2 $, the function representing the lower K-curve $ C_{low} $
in the first quadrant of $ \mathbb{R}^2 $. $C_{low}$ may also be parametrized as:
\begin{eqnarray}\label{E}
x(\alpha) & = & (1-p_1^{2m})^2\alpha, \\
y(\alpha) & =  & (1-p_1^{2m})^2\big( 1- \alpha (1-p_1^{2m})\big)/m^2 p_1^{2m-2} \nonumber
\end{eqnarray}
for $ 1 \leq \alpha < (1-p_1^{2m})^{-1} $. We shall only present the upper K-curve $ C_{up} $ in parametric form as:
\begin{alignat}{3} \label{E8}
x(\alpha) & =  \big( v_2 (\alpha)\big)^2 + \ldots +  \big( v_n (\alpha) \big) ^2 = \frac{ \alpha^{4m-2} + p_1^{4m} - p_1^{2m} \alpha^{2m-2}
- p_1^{2m} \alpha^{2m} } {\alpha^{4m-2}} \; \mbox{and} \\ \label{E9}
y(\alpha) & =  \big( v_1 (\alpha) \big) ^2 =  \left(\frac{ p_1 \big( m \alpha^{2m-2} - (m-1) \alpha^{2m} - p_1^{2m} \big)}
{m \alpha^{2m-1} } \right)^2,
\end{alignat}
for $ 0 < \alpha < 1 $ with $ {\alpha}^{2m-1} > p_1^{2m} $. Let $f_{up}$ denote the function representing the upper K-curve, so that $ y( \alpha) =
\left( f_{up} \big( \sqrt{x(\alpha)} \big) \right)^2 $ is the equation of the upper curve.

\begin{prop} \label{P1}
The function $ f_{low} $ is both square convex and square concave. The function $ f_{up} $ is strictly square convex for
$ 1/2 \leq m < 1 $ and strictly square concave for $ m > 1 $.
\end{prop}

\section{The Wu metric on $ E_{2m} $ for $ 1/2 \leq m < 1 $}
\noindent To find the best fitting ellipsoid for the Wu metric at $p \in S$, first note that
in $ x$-$y $ coordinates, the lower K-curve $ C_{low} $ and the upper K-curve $ C_{up} $ are both convex, by
Proposition \ref{P1}. Moreover, it follows from $ C^1$-smoothness of the Kobayashi metric on $ E_{2m} $ (refer Theorem \ref{T1}) that
the upper and the lower K-curve together yield a $C^1$-smooth convex curve in $x$-$y $ coordinates. This implies that the line segment
obtained by joining the $x$-intercept of the lower K-curve $ C_{low} $ and $y$-intercept of the upper K-curve $ C_{up} $ bounds
the smallest area with the coordinate axes while containing the set $ \left\{ K \left( ( p_1, \hat{0} ), v \right) \leq 1 \right\} $.
It is evident from (\ref{E10}) that the $x$-intercept of the lower K-curve is $ 1 - p_1^{2m} $ while the
$y$-intercept of the upper K-curve is $ \left( 1- p_1^2 \right)^2 $ since $K  \left( (p_1, \hat{0}), (v_1, \hat{0}) \right) = | v_1|/ \left( 1 - p_1^2 \right) $.
The line segment obtained by joining these two intercepts is given by
\[
\frac{x}{1 - p_1^{2m}} + \frac{y}{ \left( 1 - p_1^2 \right)^2 } = 1.
\]
Observe that the slope of this line segment is greater than the slope of the lower K-curve $ C_{low} $. To summarize,
$ r_1 = 1/\left( 1- p_1^2 \right)^2  $ and $ r_2 = 1/ \left( 1 - p_1^{2m} \right)$ provides, a solution to the extremal
problem (**)  and subsequently, the expression for the Wu metric $h_{E_{2m}}$ at reference points:
\begin{multline*}
h_{E_{2m}} (p_1, \hat{0}) = \frac{1} {\left( 1- p_1^2 \right)^2} d z_1 \otimes d \overline{z}_1 + \frac{1} {\left( 1 - p_1^{2m} \right) }
d z_2 \otimes d \overline{z}_2 + \ldots + \frac{1} {\left( 1 - p_1^{2m} \right) } d z_n \otimes d \overline{z}_n.
\end{multline*}
\noindent Explicit expression for the Wu metric at $ p \in E_{2m} $, with $ p_1 \neq 0 $
is obtained using the automorphisms $\Phi_p$. Continuity of the Wu metric allows its determination at $ ( 0, p_2, \ldots, p_n) \in E_{2m} $.
 \begin{thm} \label{explicit}
For $ 1/2 \leq m < 1 $, the Wu metric on $ E_{2m} $ at the point $ (z_1, \ldots, z_n) $ is given by
\begin{equation*}
 \sum_{i,j=1}^n h_{i\bar{j}} (z_1, \ldots, z_n) \; d z_i \otimes d \overline{z}_j,
\end{equation*}
where
\begin{alignat*}{3}
 h_{1\bar{1}}  & = \frac{ \left(1 - |\hat{z}|^2 \right)^{1/m} } {  \left( \left(1 - |\hat{z}|^2 \right)^{1/m} - |z_1|^2 \right)^2 }, \\
 %
 h_{1\bar{j}}  & =  \frac{  \left(1 - |\hat{z}|^2 \right)^{-1 + 1/m}  \overline{z}_1 z_j}
{ m  \left( \left(1 - |\hat{z}|^2 \right)^{1/m} - |z_1|^2 \right)^2 } \; \; \mbox{for} \; \; 2 \leq j \leq n \text{ and } h_{j\bar{1}} = \overline{h_{1\bar{j}}}, \\
h_{j\bar{j}}  & = \left( \frac{  \left(1 - |\hat{z}|^2 \right)^{-2 + 1/m} |z_1|^2 |z_j|^2 }
{ m^2  \left( \left(1 - |\hat{z}|^2 \right)^{1/m} - |z_1|^2 \right)^2 } + \frac{1 - |\hat{z}|^2 + |z_j|^2 }{ \left( 1 - | \hat{z}|^2 \right)
\left( 1 - |\hat{z}|^2 - |z_1|^{2m} \right) } \right) \; \mbox{for} \; 2 \leq j \leq n, \\
h_{i\bar{j}}  & = \left( \frac{  \left(1 - |\hat{z}|^2 \right)^{-2 + 1/m} |z_1|^2  \overline{z}_i z_j }
{ m^2  \left( \left(1 - |\hat{z}|^2 \right)^{1/m} - |z_1|^2 \right)^2 } + \frac{ \overline{z}_i z_j }{ \left( 1 - | \hat{z}|^2 \right)
\left( 1 - |\hat{z}|^2 - |z_1|^{2m} \right) } \right) \; \mbox{for} \; 2 \leq i, j \leq n \text{ and }  i \neq j .
\end{alignat*}
 \end{thm}
\noindent It follows that the Wu metric is real analytic  on the set $  \{ (z_1, \ldots, z_n ) \in E_{2m} : z_1 \neq 0 \} $. Verifying
$ \partial h_{1 \bar{2}} /\partial z_2 \neq  \partial h_{2 \bar{2}} / \partial z_1$ at points of $S$, by a direct calculation, we infer that the Wu metric is non-K\"ahler. Using Theorem \ref{explicit}, one can also verify that the holomorphic curvature of the Wu metric is bounded between a pair of
negative constants on the domain $U_Z = E_{2m} \setminus Z$. The strong negativity of the holomorphic curvature current
across the remaining thin set $Z$ (surrounded by $U_Z$) follows using arguments similar to those outlined in Section 5 (for $ 1/2 < m < 1 $)
and Section 3 of \cite{BM2} (when $ m =1/2 $).
\begin{rem} \label{degofsmoothness}
Explicit expression of the Wu metric as above, yields information about the overall-order of its smoothness, which relies
on the smoothness of the power function of one variable $t \to |t|^\alpha$,
where $\alpha$ is a positive real number. Such a function is infinitely differentiable if $\alpha$ is an integer $>1$, while
it is only $[\alpha]$-smooth if $\alpha$ is not an integer in which case, the $[\alpha]$th derivative lies in
the $C^{0, \alpha - [\alpha]}$-H\"older class. We are concerned about the regularity of such power functions
in a neighbourhood of the origin. Note that $(1-\vert\hat{z} \vert^2)^{1/m}$ is real analytic
on $E_{2m}$ as it never vanishes there. Barring $m=1/2$, note that the integral part of $2m$
is $1$, while its fractional part is $2m-1$. It follows from Theorem \ref{explicit} that the Wu metric
is \textbf{not} $C^2$-smooth at points of $Z$. However, it is $ C^{1,2m-1}$-smooth at $ Z $. So the
Wu metric is $C^1$-smooth overall, unless $m=1/2$.
\end{rem}
\section{The Wu metric on $ M^+ $ for $ m > 1 $}
\begin{thm}
The Wu metric tensor at $p=(p_1,p_2, \ldots,p_n) \in M^{+}$ is given by
\begin{multline*}
\frac{1}{(s^2-|p_1|^{2m})^2} \Big( m^2s^2|p_1|^{2m-2} dp_1 \otimes  d \overline{p}_1 + \sum\limits_{j=2}^{n}(s^2+|p_j|^2-|p_1|^{2m}) dp_j \otimes  d \overline{p}_j \\
+ 2 \Re \big( \sum\limits_{j=2}^{n} m|p_1|^{2m-2} p_1  \overline{p}_j dp_j \otimes  d \overline{p}_1 \big)
+ 2 \Re \big( \sum\limits_{\substack{{j,k=2}\\ {k<j}}}^{n} p_k \overline{p}_j dp_j \otimes d \overline{p}_k \big) \Big)
\end{multline*}
\end{thm}
\noindent The smooth function $\rho(z) = - \log\big( 1- (\vert z_1 \vert^{2m} + \vert z_2 \vert^2 + \ldots + \vert z_n \vert^2 ) \big)$ is a K\"ahler potential for the Wu metric on $M^{+}$. It is also straightforward to verify that the Wu metric is  K\"ahler  with constant holomorphic curvature $-2$ on $M^+$.
\section{The Wu metric on $ M^- $ for $ m > 1 $}
\begin{prop} \label{P4}
For $ 0 < p_1 < 2^{-1/2m} $, the unit sphere of the Wu metric in $ T_{(p_1, \hat{0})} E_{2m} $ does not intersect the
lower K-curve $ C_{low} $ and intersects the
upper K-curve $ C_{up} $ in a unique point $ (x^*, y^*) $ with $ x^* \neq 0 $.
\end{prop}
\noindent Real analytic dependence of $ (x^*, y^*) $ on the base point, can be deduced by the arguments involving  Fritz John's generalization of the Lagrange multiplier method to study the variation of the best fitting
ellipsoid (as we move from one tangent space to another), as in \cite{CK1}. The `Lagrangian' functional adapted to
study all the constraints and parameters jointly, is of the form
\begin{equation} \label{E0}
H=H(p, R_1(p), R_2(p), V_1(p), V_2(p), \Theta(p) \big) : \big( 0, 2^{-1/2m} \big) \times ( 0, \infty)^5 \rightarrow \mathbb{R}^5
\end{equation}
for our case as well. This will be useful for analyzing
the regularity of the Wu metric across the thin sets $M^0$ and $Z$ at the boundary of $M^{-}$. For the analysis of curvature, it is enough
to determine the curvature tensor at points of the form $(p_1 ,\hat{0})$ where the matrix representing the Wu metric is diagonal. This
requires knowledge about the metric tensor in a neighbourhood of points $(p_1 ,\hat{0})$ which we record below. First, let $\alpha^*$
be the value of the parameter $ \alpha $, where the upper $K$-curve meets the square transform
of the best fitting ellipsoid. Writing $X= (\alpha^*)^2$, we remark that $X$ may also be defined as the unique solution in the interval $(0,1)$ of the equation
\[
s^4 X^{2m-1} -(m+1)|p_1|^{2m}s^2X^{m-1} + (m-2)|p_1|^{2m}s^2X^m + 2|p_1|^{4m} =0.
\]

\begin{prop} \label{M-exp}
\noindent  The Wu metric at $p \in M^{-}$ is given by
\begin{multline*}
\frac{s^2X^{2m-1}}{2F_s^2} \Big( \frac{m^2s^2}{|p_1|^2}  dp_1 \otimes  d \overline{p}_1 + \sum\limits_{j=2}^{n} \big(\frac{F_{s_j}}{|p_1|^{2m}} -1 \big) dp_j \otimes  d \overline{p}_j
+2 \Re \sum\limits_{j=2}^{n}\frac{m\overline{p}_j}{\overline{p}_1} dp_j \otimes  d \overline{p}_1\\
+\frac{mX^{m-1}-(m-1)X^m}{|p_1|^{2m}}\sum\limits_{j,k=2, j\neq k}^{n} \overline{p}_j p_k dp_j \otimes  d \overline{p}_k \Big)
\end{multline*}
where $F_s = ms^2X^{m-1} - (m-1)s^2X^m - |p_1|^{2m}$, $s_j^2= s^2 + |p_j|^2 = 1- (|\hat{p}|^2 - |p_j|^2)$
and $F_{s_j}= ms_j^2X^{m-1} - (m-1)s_j^2X^m$. Moreover, the Wu metric is real analytic on the set $ M^- $.
\end{prop}
\noindent It turns out that on $M^{-}$, each component of the curvature tensor either vanishes identically or is a strictly negative
real valued function. We now list the components $R_{i \overline{j} k \overline{l}}$ of the curvature tensor, with
(standard) notations as in \cite{CK1}, which are negative. First, consider
the case where atmost two of the indices $(i,j,k,l)$ are distinct and one of them is $1$. Let $\gamma \in  \{2, 3, \ldots,n\}$. It follows from \cite{CK1}
that if $(i,j,k,l)$ is one of
\[
(\gamma, \gamma, \gamma,\gamma), (\gamma, \gamma, 1,1),(\gamma,1,1, \gamma), (1,\gamma, \gamma, 1), (1,1,\gamma, \gamma), (1,1,1,1)
\]
then $R_{i \overline{j} k \overline{l}}$ is strictly negative. For quadruples of $1, \gamma$ not listed above, the corresponding curvature component vanishes. It can
be checked that $R_{1 \overline{1} \gamma \overline{\gamma}} \neq R_{\gamma \overline{1} 1 \overline{\gamma}}$ at $(p_1, \hat{0})$ for all $p_1 \in (0, 2^{-1/2m})$, and
hence the Wu metric is nowhere K\"ahler on the orbit of the segment $(0, 2^{-1/2m})$, i.e. on $M^{-}$. Next, if $i=j>1$ and $k=l>1$, then
$ R_{i \overline{i} k \overline{k}}$ is negative. In case, both the indices $i,j$ are distinct and  $>1$, it turns out that  $R_{i \overline{j} k \overline{l}}$ is negative, iff  $(k,l)= (j,i)$. In \textbf{all} other cases, $R_{i \overline{j} k \overline{l}}=0$. It is then possible to establish
assertions about the curvature on $M^{-}$ as in Theorem 1.2.
\section{The Wu metric along and across the thin sets $Z$ and $M^0$}
\noindent Analysis of the Wu metric in the remaining thin subsets $Z$ and $M^0$ of $E_{2m}$, relies firstly on
the smoothness of elementary power functions, as mentioned in remark \ref{degofsmoothness}. We shall deal only with the case $m \not \in \mathbb{N}$, as
the complementary case is easier. Let us begin by analyzing the smoothness of the Wu metric {\it at} the origin. This entails studying the behaviour of how the Kobayashi metric is changing at the origin. We recall that
\[
K \big((0, 0, \ldots, 0), (v_1, \ldots,v_n) \big)= \frac{1}{\tilde{\alpha}},
\]
where $\tilde{\alpha}$ is the unique positive solution of the equation
\[
\vert v_1 \vert^{2m} \tilde{\alpha}^{2m} + \big( \vert v_2 \vert^2 + \ldots + \vert v_n \vert^2 \big) \tilde{\alpha}^2 =1.
\]
It follows that $\tilde{\alpha}$ is $C^{[2m]}$-smooth as a function of $\vert v_1 \vert$, and a real analytic function of the variables $ \vert v_2
\vert, \ldots, \vert v_n \vert$. Hence, $\tilde{\alpha}$ is $C^{[2m]}$-smooth function of the variables $ \vert v_1 \vert, \vert v_2 \vert, \ldots, \vert v_n \vert$. Indeed, these conclusions can be derived by consulting the assertions concerning the regularity
of the solution of $C^k$-smooth equations, in the implicit function theorem. We now examine the regularity of $K(p,v)$, when $p$ varies across $Z$. It suffices
to focus attention on the case when $p$ varies through $S^\epsilon = \{(p_1, \hat{0}):  p_1 \in [0,\epsilon)\}$ for some $\epsilon>0$. We shall
simultaneously deal with joint regularity in the variables $p,v$ as well, though we shall be terse; in this regard, observe that the
Kobayashi metric at a point $p$ in a small neighbourhood of the origin, is of the form $K(\Phi_p(p), D\Phi_p(v))$ with $\Phi_p(z)$ as in
(\ref{aut}). Note that $\Phi_p(z)$ is jointly real analytic in the variables $z$ and (the parameter) $p$. Consequently, the $C^{[2m]}$-smoothness of $K(\cdot,\cdot)$
in a neighbourhood of the origin follows, as soon as we verify that $K(p,v)$ is $C^{[2m]}$-smooth for $p$ varying in $S^\epsilon$. As
for $v$, it suffices to restrict attention in a neighbourhood of the set of points of contact of the Wu ellipsoid with the Kobayashi indicatrix
in $T_pE_{2m}$. Now, recall from Proposition \ref{P4} that, on $M^{-}$, the contact point of the square transforms of the Kobayashi indicatrix
and the Wu ellipsoid, lies on the upper K-curve, where the
Kobayashi metric is described as follows (cf. equation (7.29) of \cite{BMV}):
\begin{equation} \label{Kobalternate}
\Big(K \big( (p_1,\hat{0}), v \big) \Big)^2 = \frac{\tilde{\alpha}^2 \vert v_1 \vert^4}{\tilde{t}^2\Big(
\vert v_1\vert^2 \tilde{\alpha}^2 - p_1^2 \tilde{\alpha}^{2m} \vert v_1 \vert^{2m} \Big)^2 }.
\end{equation}
Here, $x = \tilde{\alpha}$ satisfies the equation $F(v,p,x)=0$ with $p=(p_1, \hat{0})$, where
\begin{equation} \label{eqnsol}
F(v,p,x) := \Big( 1- \tilde{t}^2 \frac{\vert \hat{v} \vert^2 p_1^2}{\vert v_1 \vert^2}\Big) \vert v_1 \vert^{2m} x^{2m}
+ \tilde{t}^2 \vert \hat{v} \vert^2 x^2 - 1,
\end{equation}
and
\begin{equation} \label{teqn}
\tilde{t}^2 = \frac{2 \vert v_1 \vert^2}{\vert v_1 \vert^2 + 2 \left(1-\frac{1}{m} \right) \vert \hat{v} \vert^2 p_1^2 + \vert v_1 \vert
\sqrt{\vert v_1 \vert^2 + 4 \left(1-\frac{1}{m} \right) p_1^2 \vert \hat{v} \vert^2}}.
\end{equation}
An application of the implicit function theorem to $F(v,p,x)$  will enable us to
write $\tilde{\alpha}$ as $ C^{[2m]} $-smooth function of $p$ and $v$, provided we verify
$
\frac{\partial F}{\partial x}(w,p, \tilde{\alpha}) \neq 0,
$
where $ w = (w_1, w_2, \ldots, w_n) $ is any of the points corresponding to the point $(x^*, y^*)$, obtained in Proposition \ref{P4}; so,
$ w_1^2 = y^*$ and $ w_2^2 + \ldots + w_n^2 = x^* $. To obtain a contradiction, assume that $\partial F/\partial x (w,p, \tilde{\alpha})=0$ i.e.,
\[
\frac{\partial F}{\partial x} (w,p, \tilde{\alpha}) = 2m \Big( 1-  \tilde{t}^2 \frac{\vert \hat{w} \vert^2 p_1^2}
{\vert w_1 \vert^2  } \Big) \vert w_1 \vert^{2m} x^{2m-1} + 2 \vert \hat{w} \vert^2 \tilde{t}^2 x = 0.
\]
 Since $ \tilde{\alpha} \neq 0$, it follows from the
above equation that
\begin{equation}\label{alphre}
\Big( 1-  \tilde{t}^2 \frac{ \vert \hat{w} \vert^2  p_1^2}{\vert w_1 \vert^2} \Big)\vert w_1 \vert^{2m} {\tilde{\alpha}}^{2m} = - \frac{ \vert \hat{w}
\vert^2 \tilde{t}^2 {\tilde{\alpha}}^2} {m},
\end{equation}
so that the defining equation for $\tilde{\alpha}$ can be rewritten as
$
\tilde{\alpha}^{2} = m(m-1)^{-1}\vert \tilde{t} \hat{w}\vert^{-2}.
$
Substituting the above expression for $ \tilde{\alpha} $ into (\ref{alphre}), dividing throughout by $ \tilde{t}^2 \vert \hat{w} \vert^2 p_1^2$ yields
\[
\Big( \frac{1}{p_1^2 \tilde{t}^2} \frac{\vert w_1 \vert^2}{\vert \hat{w} \vert^2 } - 1 \Big) \vert w_1 \vert^{2m-2} = -
\frac{(m-1)^{m-1}}{m^m}\frac{ \big( p_1^2\tilde{t}^2\vert \hat{w} \vert^2  \big)^{m-1} }{ p_1^2} \big( \frac{1}{p_1^2} \big)^{m-1}
\]
Define $
f(p_1,w) = \vert w_1 \vert^2/p_1^2\tilde{t}^2\vert \hat{w} \vert^2$,
so as to write the last equation as
\begin{equation} \label{freritten}
\big( f(p_1,w) - 1 \big) \big( f(p_1,w) \big)^{m-1} = - \frac{(m-1)^{m-1}}{m^m} \frac{1}{p_1^{2m}}.
\end{equation}
We claim that $f(p_1,w)>1$. To prove this claim, note that
\[
f(p_1,w) = \frac{R^2}{2 p_1^2} + \frac{R}{2 p_1} \Big( \frac{R^2}{p_1^2} + 4 \big(1- \frac{1}{m} \big) \Big)^{1/2}
+ 1- \frac{1}{m},
\]
where $R$ denotes the ratio $\vert w_1 \vert / \vert \hat{w} \vert$.
At this point, recall that we are in the case $u \geq p_1$ (where $u = m \vert w_1 \vert / \vert \hat{w} \vert$) or equivalently, $R/p_1 > 1/m$. Using
this in the above equation gives the claim. This is a contradiction since the right hand side of (\ref{freritten}) is
negative. Hence, we conclude that our assumption $\frac{\partial F}{\partial x}(w,p, \tilde{\alpha}) =0$  must be
wrong. This enables an application of the implicit function theorem to deduce that $\tilde{\alpha}$ is a $[2m]$-smooth function of $ (p, v) $. Next, (\ref{teqn})
shows that $\tilde{t}$ is a smooth function. Further, notice that the expression (\ref{Kobalternate}) of the Kobayashi metric is a rational function
(whose denominator is well-defined on $E_{2m}$) involving elementary power functions of $v, p, \alpha,\tilde{t}$. Hence, $ K^2 $ is $C^{[2m]}$-smooth
function of $(p, v) $ near the origin. Next, another application of the implicit function theorem, this time to the functional $H$,
mentioned at (\ref{E0}), one gets the desired smoothness of the Wu metric near $Z$. It may seem that, in doing so, there may be a loss of a degree of smoothness for the Wu metric as compared to the $C^{[2m]}$-smoothness of the Kobayashi metric. However, it is
possible to discern the optimal order of smoothness of the Wu metric to be $C^{[2m]}$ (as in Theorem 4.1 of \cite{Kim}), owing
to the fact that that the meeting point of the Wu ellipse with the $K$-curve in the tangent spaces near the origin, lies away from the
coordinate axes; this ensures the real analytic dependence of $K^2$ on the variables $v$. This together with an analysis of the explicit
expression of $K^2$ yields the $C^{[2m]}$-smoothness of the component functions of $H$; thereby the $C^{[2m]}$-smoothness of the Wu metric near the origin, subsequently, near $Z$. To remark now about the case $m \in \mathbb{N}$, similar analysis yields the conclusion that the Wu metric is real analytic near $Z$ in this case.
\medskip\\
\noindent In order to analyse the Wu metric on $M^0$, we do {\it not} need to assume that $m \not \in \mathbb{N}$ for convenience. We only
provide a couple of details to support the arguments in \cite{CK1}, for passing through to our present setting. Firstly, we claim that the Kobayashi
indicatrix is $C^2$-smooth but not $C^3$-smooth on $ E_{2m} $, for $m>1$. To establish this, it suffices to analyze the smoothness at the
joining point $ u = p_1 $ of the upper and lower K-curves. Note that the lower K-curve (as described by equation (\ref{E10})) is a straight line and hence
$ \partial^l y/\partial x^l \equiv 0$ for $l \geq 2$. We now show that, for the upper K-curve $ \big( x(\alpha), y(\alpha) \big)$, $\partial^l y/\partial x^l$
is zero for $l=1,2$ but not for $l=3$ at the joining point. To this end, note that the
joining point $u=p_1$ corresponds to the limiting value $1$ for the parameter $\alpha$.
\begin{equation}\label{2ndder}
\frac{\partial^2 y}{\partial x^2} =\frac{\dot{x}(\alpha)\ddot{y}(\alpha) - \dot{y}(\alpha) \ddot{x}(\alpha)}{\big(\dot{x}(\alpha) \big)^3}.
\end{equation}
A direct computation shows that the numerator of the right hand side above is given by
\[
-  8m(m-1)\alpha^{2m-3}(1- \alpha^2)p_1^{2m+2} \big( m \alpha^{2m-2} +(m-1)\alpha^{2m}-(2m-1)p_1^{2m} \big)^2/m^2\alpha^{8m-2},
\]
which as a function of $p_1$ vanishes identically when $ \alpha = 1 $.
This confirms that the values of $\partial^2 y/\partial x^2$ of the upper and lower K-curves
match at the ``joining point'' and leads to the $C^2$-smoothness of the Kobayashi indicatrix in $T_pE_{2m}$ with $p=(p_1, \hat{0})$.
Next, we evaluate $\partial^3 y/\partial x^3$  and show that the values fail to match up. Indeed, as the
numerator in (\ref{2ndder}) is zero at $\alpha =1$, it can be calculated that at the joining point, $\partial^3 y/\partial x^3$ is given by
\begin{equation}\label{3rdder}
\big( \dot{x}(1) \dddot{y}(1) - \dot{y}(1) \dddot{x}(1)  \big)/(\dot{x}(1))^4
\end{equation}
provided $\dot{x}(1) \neq 0$ -- it turns out that $\dot{x}(1) \neq 0$ precisely when $m=1/2$. The numerator of (\ref{3rdder}) is
$ 16p_1^{2m+2} (1-p_1^{2m})^2(2m-1)^2(m-1)/m$. As $1-p_1^{2m}$ never vanishes on $E_{2m}$ and we are in the case $m \neq 1$ and more importantly $m \neq 1/2$, this
proves that the Kobayashi metric is not $C^3$ smooth on $E_{2m}$ when $m>1$. For the case $m<1$, we only need to look at the indicatrix at
the origin, to conclude that the Kobayashi metric is not of class $C^2$. Getting back again to the case $m>1$, it remains to study how these indicatrices vary with respect to $ p $,
to establish $C^2$-smoothness of the Kobayashi metric. Indeed, first note the real analyticity in the expression for the `joining point' given by: $ \left((1-p_1^{2m})^2, p_1^2(1-p_1^{2m})^2/m^2 \right)$.
While this provides a clue about the $C^2$-smoothness, for a proof it remains to check that $\partial^2/\partial p_1^2$ and
the $\partial^2/\partial p_1 \partial x$ derivatives of $(f_{up}(\sqrt{x}))^2$ and $(f_{low}(\sqrt{x}))^2$ (which are actually functions of both $x$ and $p_1$)
agree when evaluated at the joining point. This indeed happens and involves several implicit differentiations. For this we note that (\ref{E}), (\ref{E8})  do {\it not} together form a parametrization of the $K$-curve, which is of desired smoothness at the joining point. Nevertheless, a  calculus with these parametrizations confirms that the $K$-curves do coalesce to form a regular surface in the $(x,y,p)$-space, which is $C^2$-smooth. More precisely, {\it all} second order partial derivatives
of $(f_{up}(\sqrt{x}),p_1)^2$ and $(f_{low}(\sqrt{x},p_1))^2$ match as required. This  leads to the $C^2$-smoothness of the the aggregate of the indicatrices, thereby yielding  $C^2$-smoothness of the Kobayashi metric, first at reference points of the form $(p_1, \hat{0})$ for $0<p_1<1$; thereafter, also on $E_{2m}\setminus Z$ which is the orbit of the segment $S$ under the real analytic action
of $\textrm{Aut}(E_{2m})$. Since we have already discussed the smoothness of the Kobayashi metric in
a neighbourhood of the origin, together with the foregoing observations,  this completes the verification that the optimal overall smoothness of the Kobayashi metric is indeed $C^2$, when $ m > 1 $. One may now proceed with  arguments employed in \cite{CK1} (past Proposition 7 therein) to conclude the regularity-analysis on $M^0$.\medskip\\
\noindent We now conclude the article with remarks, for completeness, on the curvature of the Wu metric on the critical sets $M^0$ and $Z$. It is enough to focus attention near the point $p=(2^{-1/2m},0)$ in $M^0$. As $M^0$ is a finite type hypersurface, it cannot contain any non-trivial germ of a complex analytic variety. In particular, any Riemann surface through $p$ can intersect $M^0$ only at $p$ or along a smooth curve. This together with the fact that
the holomorphic curvature is bounded above by a negative constant on either sides of $M^0$ namely, $M^-$ and $M^+$, paves the way for
applying the  lemma in Appendix B of \cite{CK1}, thereby rendering the negativity of the holomorphic curvature current on $M^0$. Recall that $ Z $ is
a complex hypersurface and consequently, $ Z $ intersects a embedded Riemann surface in $E_{2m}$ only in
a discrete set of points, unless it is contained in (as an open subset of) $Z$. In the former case, the required negativity of the
holomorphic curvature current follows from the arguments using the lemma in Appendix B of \cite{CK1}, as the holomorphic curvature
is strongly negative in any small (deleted) neighbourhood of $Z$ consisting of points of $M^-$. In the latter case, we may assume
that the Riemann surface is an open subset $U$ of $Z$ containing the origin. Pick any one-dimensional complex subspace $l$ in $Z$ -- recall
that $Z$ is in fact a complex hyperplane. So $ l_U =l \cap U $ is contained in $l$. We restrict attention to a small disc $ D $ about the origin
with $D \subset l_U$. Note that the holomorphic curvature in the direction of $l$ is realized by the Gaussian curvature of the Wu metric
restricted to $D$. As the Wu metric is an invariant metric, the desired negativity of the holomorphic curvature follows.

redpajama_set_name: RedPajamaArXiv


text:
<!--

    DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS HEADER.

    Copyright (c) 2012 Oracle and/or its affiliates. All rights reserved.

    Oracle licenses this file to You under the Apache License, Version 2.0
    (the "License"); you may not use this file except in compliance with
    the License.  You may obtain a copy of the License at

         http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.

-->

<project name="Build template">
    <property environment="env"/>

    <!--
	This is a template project that is designed to be imported into
        the subdirectories for executing Japex for Japex configuration
        files.
    -->
    <property name="project.dir" value="${basedir}/../../"/>

    <property name="FastInfoset.dir" value="${basedir}/../../FastInfoset"/>
    <property name="Japex.dir" value="${env.JAPEX_HOME}"/>

    <path id="class.path">
	<fileset dir="${Japex.dir}" includes="dist/lib/*.jar"/>
    </path>

    <path id="japex.class.path">
	<fileset dir="${FastInfoset.dir}" includes="dist/lib/*.jar"/>
	<fileset dir="${Japex.dir}" includes="dist/jdsl/*.jar"/>
    </path>

    <property name="japex.classPath" refid="japex.class.path"/>

    <!--
	This task is designed to be as follwing:

          ant -Dconfig=<Japex configuration file> run

    -->
    <target name="run">
        <java
                dir="."
                fork="true"
                classname="com.sun.japex.Japex">
            <jvmarg value="-server"/>
            <jvmarg value="-XX:+UseJumpTables"/>
            <jvmarg value="-Xms384m"/>
            <jvmarg value="-Xmx384m"/>
            <jvmarg value="-Djapex.classPath=${japex.classPath}"/>
            <classpath refid="class.path"/>
            <arg line="${config}"/>
        </java>
    </target>

</project>

redpajama_set_name: RedPajamaGithub


There are thousands of small businesses that sell wood products in the local community.
Here are a few for you to consider.. Be sure to check in your neck of the woods for others. Buy Local!
Other Timber Growers - Email your information to join.
* Create one full time well paying job for every 40 acres of timber.
* Local Manufacturing and Direct Marketing multiply the market value of standing timber 10 to 1,000 times.
* Keeping the money in the local community multiplies it again - 3 to 5 times.
* Trucking and shipping are minimized, saving lots & lots of fuel! Woodworking businesses can actually produce many types of energy from their scraps.
* Growers are encouraged to care for their timber for the future.
+ The forest owner is paid a couple of percent of the retail value of the timber. Distant big corporations take the wood and the value far away and make all of the profit. Most forest owners feel short-changed.
+ A few men in huge machines cut the timber in large volumes, creating major disturbance to the land. Forest owners feel they lose control of their land during the harvest.
+ Loads of fuel are used to haul the wood away, often half-way around the globe. 1/3 of the cost of retail wood products is trucking and shipping!
+ Local consumers buy highly manufactured wood products with a relatively short life-span, from distant lands at the Big Box Stores, again sending lots of money far away to subsidize the big corporations.
+ Growers are discouraged from managing their forest.
Who Loses from a change? Brokers, Big Equipment Dealers, Fuel Corporations, Foreign Countries, Shipping Corporations, Government Officials, Foreign Owned Timber Corporations, Big Box Stores.
Small timber management businesses are now selling natural wood products direct to their customers. There are thousands of small businesses scattered around the country, here is a listing of a few. Be sure to search your neck of the woods too, for others.
Our wood is different from what you might buy from the big store in the city. We own the land and trees, so our forest is our future. We grow each good tree as long as it is healthy and vigorous. Increasing the natural diversity of sizes and species is important to our sustainability. Our annual harvest averages about one tree per acre, this is the natural output of the forest. We start by taking the worst tree first, and work with the smallest possible equipment to minimize damage.
Thin kerf sawmills, solar and wood heated lumber dry kilns, modern woodworking equipment are used to efficiently manufacture our products, right here on our own properties.
We sell our wood direct to our customers. Products are hauled just one time, right into our customer's homes. We really know our wood, so customer service and satisfaction is guaranteed.
Along the way, we work to encourage other forest owners to join us. Buy Local!
Buying direct from the timber grower keeps all the money in the local community!
1. Encourage Common Sense Forest Management of privately owned small woodlots.
2. Practice Low Damage Logging with small equipment to protect our forest resources for our futures.
3. Promote Local Manufacturing of wood products on the farm and in the community.
4. Support Direct Sales of a large variety of agricultural producsts in the local marketplace.
6. Invite all Timber Growers to take an active role in the Businsess of Forestry.


I ALWAYS recommend to people (clients, etc.) that they take some time to look back on the previous year and reflect on what happened, in the hope that they can figure out what worked, what didn't work, and what needs to be changed for the future. While that recommendation is nice, and ideally, it is more efficient to do it all at once, I find that after an entire year, it is hard to remember what happened in any detail. This is complicated by the fact that we spend a lot of time suppressing/repressing the bad stuff. So, maybe write stuff down monthly and do a yearend review. Yeah, that might work.
If I had to quickly summarize 2018 as a year, and have a conversation with it, I'd probably shout "Go home, you're drunk!" to it. While this wasn't one of the worst years ever, I'd say that it was one of the weirdest I've experienced in some time.
I'd normally start in the winter time, since that is where the year technically starts (and ends) but some of the weirdest stuff happened in spring. Or was it summer? Or fall? It was hard to tell. We went from typically spring-ish weather directly into the deep, intense heat and dryness of mid-late summer, then back spring (minus the moisture), then into hot and dry. Winter arrived before fall did (unless you count the 3 hours of fall that preceded first winter) and hit hard and fast, along with the moisture that had been missing all summer in most areas. Heavy snows and definitely cold weather seemed like it was going to stick around permanently, but then things rebounded and we got late summer/fall in October. And now we are back to winter, just in time for … more winter. It was not impressive and was definitely challenging for producers to plant, grow and then harvest a crop.
This year, we avoided the brutal frosts that did a number on many of the crops a couple of years ago, but some of the weird winter weather was damaging for many of the orchard bush fruit crops, particularly in the south and south-central regions. Not a stellar Saskatoon berry and sour cherry crop this year, but hopefully next year will be better.
Similar to the last few winters, Winter 2017/2018 was a bit variable, with long, cold snaps, with a few mild stretches, just to keep us guessing. The dryness of the winter in a number of areas was suggested as being to blame for some of the orchard issues.
Stress was a pretty good descriptor of the growing season weather that we had, although that would be the first time I've used that word to describe weather. The hot temperatures of Springummer (spring/summer combo) was quite stressful on the newly awakening plants. I noticed that many of our street trees had thinner canopies this year, and produced a MASSIVE crop of seeds. In my town, the ground looked like it had snowed, the elm seeds were so thick. We also saw the impact of this early heat in some stunting and poor head development of some of the cool season crops, such as Cole crops like cabbage and broccoli. Later plantings were ok, but the early stuff never amounted to anything.
Depending on where you live, it was probably fairly dry, or it ended up that way. Southern and some central parts definitely started off pretty wet, and most areas finished the season overly wet (usually in the form of solid, frozen wetness). If you had irrigation, that made a dry year bearable. If you didn't, you would have seen sizing issues, and a yield hit.
Severe weather events seem to be a perennial challenge for producers most of the time now, although it wasn't something that seemed to come up as much this year (thankfully). Hail always hits, but things seemed quieter on that front this year.
A sneaky (while also obvious) issue this year was the wildfire smoke coming out of the west or the south. While a week or so of smoke isn't all that uncommon in recent years, this year was notable and certainly had an impact on the vigour and growth of crops, due to the reduced light and poor air quality. It was also hard on those working out in it. I tended to limit my efforts outside on really bad days to 1-2 pack-equivalent increments.
Insects seemed to be a bit quiet this season, which is fine. However, I did hear lots about spruce tree issues, which have been building for the past few years. In this case, the problems aren't insect-related, but it is tough to pin down a culprit (although Rhizosphaera is currently the culprit-elect), but there are issues, regardless. Other issues in forestry-type plants included the discovery of Mountain Pine Beetle in municipalities outside of the forested areas, which isn't great. Keep your eyes peeled in the future, as we're going to need to stay sharp to detect and deal with this and other pests.
We didn't see much in terms of disease issues this year, although there were reports of some soil-borne challenges in carrots, the causes of which are still not completely clear to me. As many (better than me) pathologists have resorted to (with good success), we can chalk it up to a combination of (unnamed) factors, any one of which might have resulted in the resulting damage. Fortunately, the generally dry conditions limited the development of most diseases.
Continuing some of the previous year's fun, there continues to be impacts from introduced or changed legislation and programs, with some sectors affected more than others. Things like minimum wage, Farm Safety Legislation and other things are taking some adjustment. There are some looming changes to federal legislation (Safe Food for Canadians Act) happening in the New Year, which will have impacts for many.
Growing Forward 2 programing (and associated funding) wrapped up at the end of March, and this has resulted in some noticeable changes in the amount of programing offered by Horticulture staff. With the newly launched Canadian Agricultural Partnership (CAP), there may be programs available for producers, associations and others to access, to get things done. While we wait for things to shake out, it might be a bit quieter. Reduced resources and staff in my area means I'll have to be creative to do more with less. But plans are underway, so stay tuned.
While there were a few less events this year, we continue to talk to many people on the phone or via email (and this won't change). It was a rewarding year and I hope that we were able to help out in a positive, impactful way.


text:
NFT Energy Use Info
Project FUERZA Energy Use Info
Let's get the confusion out of the way, it's not the actual NFT that uses energy. It is the transaction process associated with minting the NFT to the blockchain it will live on, which is known as proof-of-work (POW). And while the numbers may seem high, when you break it down and compare it to the energy we use every day, it puts things in a little bit of a different perspective. [8]
Let's start with a little comparison, say for instance, motor vehicles. Cars were invented around 1886 and even in 1927, 41 years later cars were still only getting 7-8mpg. Now in 2022, as technology has slowly advanced in this area, we have fully gas-powered vehicles that can get around 40 mpg on the highway. Not a large increase to be honest in nearly 100 years of improvements. [2],[3],[4]
In 2009, Bitcoin was made available to the public, and now in 2022, 13 years later, Ethereum plans to cut 99% of its energy use by the end of the year. They plan to do this by changing the transaction process to what is called proof-of-stake. We wanted to make this comparison first to show you how fast this new technology is advancing. The carbon footprint of Ethereum was on everyone's mind from the beginning and they have a plan and vision in place to reduce it. Now let's look at some other comparisons of NFT transactions specifically Ethereum (ETH) to everyday life. [5],[6],[9],[10]
CHECK OUT Ethereum's plan to switch to Proof-of-Stake HERE!
Doing so will cut 99% of their energy use.
A Single Ethereum Transaction = 129.43 kWh = 72.19 kgCO2
There are over 1 million Ethereum (ETH) transactions a day. This includes buying, selling, and trading ETH, using ETH to buy and sell other items, and using ETH to buy, sell, and trade NFTs. Out of that million, there are currently on average only 2,300 NFT transactions per day. Or around 16,000 per week, that is as of writing this in June 2022 from nonfungible.com. [1], [6]
2,300 x 129.43kWh = 299,000kWh per day.
How does that compare with something you probably use every day?
YouTube Stats:
YouTube's energy consumption is around 135kWh per 1000 views. It is estimated that there are 1.86 billion active users on YouTube, with 122+ million of them consuming more than a billion hours of video every day. From what The Fact Source put together in 2019, their math came out to 135kWh per 1000 views. This means that a single view is .135kWh. Multiplying that by 122 million users viewing one video a day, .135 x 122,000,000 and we get 16,470,000 kwh per day. Check out their article here where they breakdown the energy consumption from some of the most popular YouTube channels based on views. [14]
So, YouTube uses 55x (!) more energy PER DAY, than Ethereum NFT transactions.
YouTube 16,470,000kWh per day vs. ETH NFT Transactions 299,000kWh per day.[15]
In 2020 the International Energy Agency (IEA), reevaluated the numbers, and came up with one hour of Netflix streamed puts out about 0.08kWh [17]
It was reported back in 2009 that the total amount of Netflix hours watched PER DAY worldwide was 164 MILLION hours. [18]
Most recently it has been reported that their release of Stranger Things 4 has already been watched well over 1 BILLION hours in total. [19]
0.08kWh x 164 Million Hours Watched = 13,120,000kWh
0.08kWh x 1 Billion Hours Watched = 80,000,000kWh
On the low-end Netflix 13,120,000kWh PER DAY vs. ETH NFT Transactions 299,000kWh PER DAY!
Other Comparisons:
Air Conditioning and Heating: According to Direct Energy, the average central HVAC unit uses about 28-63kWh per day, resulting in 850-1,950 kWh per month, depending on the efficiency of your unit. 6% of ALL electricity in the United States is used by air conditioners. In 2020, the United States produced 4,007 billion kWh of electricity, which means that air conditioning systems alone used over 240 billion kWh of power, which accounts for roughly 117million metric tons of CO2 released into the air every year. [16]
Water Heating: The average household water heater will run about 3 hours a day using on average 13.5kWh per day, or 405kWh per month. [16]
If we compare these numbers to a single ETH NFT transaction, we see that at 129.43kWh per transaction is pretty miniscule compared to many of our everyday amenities.
https://nonfungible.com/market-tracker
https://www.cars.com/articles/what-are-the-most-fuel-efficient-cars-for-2022-447856/
https://www.fuelly.com/car/ford/model_t/1927#:~:text=Based%20on%20data%20from%203,0.81%20MPG%20margin%20of%20error.&text=Below%20you%20can%20see%20a,1%20outliers%20(4.55%25)%20removed.&text=Following%20shows%20the%20average%20MPG,3%20vehicles%20in%20the%20system
https://www.livescience.com/37538-who-invented-the-car.html
https://www.forbes.com/sites/bernardmarr/2017/12/06/a-short-history-of-bitcoin-and-crypto-currency-everyone-should-read/?sh=6f940313f279
https://www.cloudwards.net/nft-statistics/#Sources
https://blog.ethereum.org/2021/05/18/country-power-no-more/
https://ethereum.org/en/developers/docs/consensus-mechanisms/pow/
https://ethereum.org/en/upgrades/vision/
https://ethereum.org/en/upgrades/merge/
https://bitinfocharts.com/ethereum/
https://digiconomist.net/ethereum-energy-consumption
https://thefactsource.com/how-much-electricity-does-youtube-use/
https://www.omnicoreagency.com/youtube-statistics/#:~:text=YouTube%27s%20Usage%20Statistics,world%20(YouTube%2C%202021)
https://www.directenergy.com/learning-center/what-uses-most-electricity-in-my-
hhttps://www.iea.org/commentaries/the-carbon-footprint-of-streaming-video-fact-checking-the-headlinesome#:~:text=An%20average%20central%20HVAC%20unit,the%20efficiency%20of%20your%20unit
https://www.comparitech.com/blog/vpn-privacy/netflix-statistics-facts-figures/#:~:text=Netflix%20users%20spent%20a%20combined,hours%20per%20day%20of%20content.
https://www.cnet.com/culture/entertainment/stranger-things-4-crosses-1-billion-hours-watched-netflix-says/
GET THE LATEST FROM FUERZA.
Created by the FUERZA founder with special ♥ to our developer partners, our athletes, incredible artist around the world and the support from the cycling community.
For all press inquiries, please contact inquiry@projectfuerza.com
© 2023 BY FUERZA. PROUDLY DESIGNED BY ZENDA


text:
Your Sport
VIEW ATHLETES
Academic Tests
College Sports Divisions
SWIMMING SCHOLARSHIPS
Earning a swimming scholarship to a US university or college will allow you the opportunity to pursue both an academic and swimming career simultaneously. This means that you will be studying for a university degree whilst training and competing at an elite level, not dissimilar to that of professional sport.
Life as a college swimmer is extremely challenging and will involve being fully committed as both a full-time athlete whilst simultaneously pursuing a degree as a full-time student. It is an environment that produces most of America's professional and Olympic athletes.
Men's Swimming Scholarships
Coaches are looking for athletes who work just as hard in the classroom as they do in the pool. The recruiting process is about being able to show improvement over the course of your high school career with clear potential.
NCAA Division I: Colleges/Universities: 136, 9.9 scholarships for men per team, average roster size: 39
NCAA Division II: Colleges/Universities:77, 8.1 scholarships for men per team, average roster size: 36
NCAA Division III: Colleges/Universities: 415, they do not award sports scholarships only academic ones, average roster size: 34
NAIA: Colleges/Universities: 31, 8.0 scholarships for men per team, average roster size: 26
NJCAA: Colleges: 60, 15.0 scholarships for men per team, average roster size: 17
Women's Swimming Scholarships
Some of the top tier, elite women's swimming programs are Texas, Michigan, Stanford, California, Virginia and NC State. At the D2 level, Queens (NC), Drury, Indianapolis and UC San Diego top the list. The highest ranked NAIA programs are Keiser, SCAD, Cumberland and Lindenwood-Belleville.
NCAA Division I: Colleges/Universities: 199, 14.0 scholarships for women per team average roster size: 28
NCAA Division II: Colleges/Universities: 106, 8.1 scholarships for women per team, average roster size: 19
NAIA: Colleges/Universities: 36, 8.0 scholarships for women per team, average roster size: 11
NJCAA: Colleges: 65, 15.0 scholarships for women per team, average roster size: 14
Our successful athletes
Thea Simpson
Nationality: British
Committed to: St. Francis Brooklyn
Sophie Dix
Nationality: irish
Committed to: Northwestern University
Committed to: St. Andrew's University
Would you like to find out more?
Give us a call or fill in the form and we'll call you back when its convenient for you. We'll glady answer any of your questions related to scholarships and life in the USA.
Fill in you're details below and we'll be in touch to answer your questions and talk next steps.
What is your sport?Field HockeyGolfGymnasticsLacrosseRowingRugbySoccerSkiingSwimmingTennisTrack and FieldVolleyballWater Polo
Are you looking to go to university in the USA? Get in touch with us to find out how we can help you do it.
Title IX Consultancy
Title IX specialises in identifying and assisting young, talented athletes to pursue sports scholarships in the USA. A sports scholarship allows you to play full time sport whilst earning a degree at an American University
nicola@title9usa.com
Copyright © 2021 Atleta Consultancy Ltd trading as Title IX USA
ATHLETE ENQUIRY FORM


Whether by car or by public transport: Here are the directions to the headquarters of the DFL Deutsche Fußball Liga GmbH, Guiollettstraße 44-46 in Frankfurt.
From the central station take the city train lines S1 to S9 to the Taunusanlage. Exit at "Guiollettstraße". The headquarters are now just a three-minute walk away.
From the airport: Take the S8 or S9 train lines towards Hanau and exit at the Taunusanlage station. From there, it is approximately a four-minute walk to the headquarters.
Exit the A5 at junction Westkreuz Frankfurt towards Frankfurt-Stadtmitte. Continue on the street Westkreuz Frankfurt.
Exit the street Westkreuz Frankfurt. Continue on the motorway A648.
Exit the A648 at the junction (4) Frankfurt-Rebstock towards Stadtmitte. Continue on Wiesbadener Strasse (B8).
Continue straight ahead on the Theodor-Heuss-Allee (B8).
Leave the Theodor-Heuss-Allee (B44) and turn left into the Mainzer Landstraße.
Continue straight onto the Taunusanlage, then turn left into the Guiollettstraße.
Stay on the right on the A648 towards Frankfurt-Stadtmitte. Afterwards stay right at Westend-Süd and turn into the Friedrich-Ebert-Anlage (B44).
Afterwards turn left into the Mainzer Landstraße and straight onto the Taunusanlage, then turn left into the Guiollettstraße.
At the motorway junction Wiesbadener Kreuz drive onto the A66 towards Autobahndreieck Eschborner Dreieck, then towards Frankfurt. At the junction Eschborn drive onto the A648 towards Autobahndreieck Eschborner Dreieck.
At the Autobahndreieck Eschborner Dreieck stay on the A648 and continue towards Autobahnkreuz Westkreuz Frankfurt.
Keep to the right onto the B44/Friedrich-Ebert-Anlage. From there turn left into the Hohenstaufenstraße and continue onto the Rheinstraße. Then keep to the left, turn into the Beethovenstraße and into the roundabout.
Take the roundabout's second exit into the Mendelssohnstraße, then turn right into the Westendstraße, then turn left into the Arndtstraße, turn right into the Kettenhofweg, again right into the Lessingstraße. From there turn right into the Guiollettstraße.
Exit the motorway at the junction Offenbach (52) and continue on the B46 / B459 towards Frankfurt. Afterwards drive towards Frankfurt-Sachsenhausen / Offenbach-Süd.
Enter the roundabout towards Autobahnkreuz Offenbacher Kreuz.
At the Autobahnkreuz Offenbacher Kreuz, take the roundabout's second exit onto the B3/Babenhäuser Landstraße.
Then continue towards Frankfurt-Sachsenhausen. In Frankfurt, keep to the right onto B3/Darmstädter Landstraße. From there turn left onto B3/Dreieichstraße. Then turn right into the Martin-May-Straße. Continue on the Schifferstraße (left), from there turn left into the B43/Walter-Kolb-Straße. Then turn right into the Schweizer Straße.
Keep to the right and continue on the Neue Mainzer Straße. Turn left into the Junghofstraße. Turn left again into the Guiollettstraße.


Usually in the Windows remote desktop, if the session is full we have to wait for other user to logoff.
but sometimes we need to go to remote desktop immediately and can not wait because an important thing.
1. Open Run Command dialog by pressing Windows+R key.


Party A and Party B concluded deal via trading platform. Deal was reported and accepted by ACER in due time. During the contract's life cycle, due to force major event and/or some mistake one of the parties fails to deliver/accept the energy.
A force major event should not be considered a life cycle event per se. However, if the terms of the contract are amended, or the contract is cancelled, then a life cycle event should be reported.