text:
Well-Posedness in Hölder Spaces of Elliptic Differential and Difference Equations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9045)
Conference paper
First Online:
In the present paper the well-posedness of the elliptic differential equation
in an arbitrary Banach space E with the general positive operator in Hö lder spaces \(C^{\beta }(\mathbb {R},E_{\alpha })\) is established. The exact estimates in Hölder norms for the solution of the problem for elliptic equations are obtained. The high order of accuracy two-step difference schemes generated by an exact difference scheme or by Taylor's decomposition on three points for the approximate solutions of this differential equation are studied. The well-posedness of the these difference schemes in the difference analogy of Hölder spaces \(C^{\beta }(\mathbb {R}_{\tau }, E_{\alpha })\) are obtained. The almost coercive inequality for solutions in \(C(\mathbb {R}_{\tau },E)\) of these difference schemes is established.
$$\begin{aligned} -u^{\prime \prime }(t)+Au(t)=f(t)(-\infty <t<\infty ) \end{aligned}$$
KeywordsAbstract elliptic equation Banach spaces Exact estimates Fractional spaces Well-posedness
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|Qualification Type:
|Funding for:
|UK Students, EU Students
|Funding amount:
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|Full Time
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|12th June 2019
|30th June 2019
Over 70% of healthcare interventions in the UK are already based on one or more diagnostic tests, very often involving the determination of the concentration of proteins – or biomarkers – in a patient's blood. However, with the emergence of stratified and eventually personalised medicine, which requires the detection of very small numbers of proteins, eventually down to the single molecule levels, current diagnostic approaches have reached their limit.
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6-13 With 49ers mandatory mini-camp ending, Matt Barrows of the Athletic recaps OTAs, dives into particulars of the the Robbie Gould situation, and speaks on emerging story lines ahead of Training Camp that is less than a month away
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6-17 The Giants are on hot streak heading into LA, but all eyes are on Bumgarner. Henry Schulman of the SF Chronicle dives into what the Giants could get in a haul for 3 time WS winner


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As a Seeking Alpha reader, odds are you have already seen plenty of reports about the US hydrocarbon revolution and you are well aware of the booming oil and natural gas production taking place directly as a result of the advancements in Shale Fracking and Horizontal Drilling. We don't intend to write much if anything more about that topic other than to say, our independent studies strongly suggest it really is all true. America really is about to become the world's largest producer of oil and ng. America really is about to become one of the world's largest exporters of oil (light, sweet crude) as well as natural gas via LNG.
Here are two charts that show US oil exports are about to quadruple and LNG exports are about to rise 500%+ in the years to follow. It's exhausting to see these sorts of data points every time we click on a new pipeline article, so forgive me for my obligatory pair. If by chance you have not seen these two charts before, look them over and think about the implications. The rest of us can quickly scan forward to the analysis of ET's operating results.
In order for us to analyze what is happening inside Energy Transfer and why the next few years offer so much upside, we must first start with an understanding of the recent operating results as well the guidance management has provided in the past few conference calls. For those of you that do not listen to the quarterly conference calls nor read wall street brokerage firm research reports, it is important to understand that ET has been routinely smashing wall street estimates for more than a year. Analysts have been forced to repeatedly adjust upward their quarterly and annual expectations as prior projects such as Dakota Access Pipeline, Rover and Revolution have come on line and have begun to ramp up production. The whole industry has, in fact, been on a steady roll as oil and ng capacity has grown tighter with the booming shale production taking place in various basins. Business is strong across the board.
Meanwhile, management was required to issue year ahead guidance in their S-1 last Fall, as mandated by the SEC, when ET acquired ETP for a 10% premium. Guidance, once offered, often leads investors and analysts to ask for more. Given that ET is doing so well fundamentally, mgmt has enjoyed being more forthcoming and has, for the time being, continued to offer more insights into near term expectations along with moderate degrees of additional guidance. It is here that we begin our analytic effort.
Some Facts:
For the first quarter of 2019, ET earned $2.8 billion EBTIDA and $0.6313 per share DCF. Year end guidance continues to be roughly $10.8 billion EBITDA and $2.30 per share in DCF. The annual dividend continues to be $1.22 per share. There are roughly 2.6 billion shares and DCF guidance is on track to exceed the distribution payout by $1.08 a share ($2.30 - $1.22 = $1.08) or about $2.808 billion. Mgmt expects to spend roughly $5 billion on new projects in 2019, BUT mgmt suggests in the future the company will spend (invest) about $3 billion to $4 billion each year going forward. Mgmt also claims the environment is currently the best investment environment they have ever seen, suggesting that new projects can earn high teen returns (more than 16% - 18% ROI's).
Some Assumptions:
In order to calculate future numbers from the 2019 results we must make some assumptions. First, we ignore the risk that a recession may come along and slow down the Shale Revolution and possibly interfere with ET's operating results, Second, we assume ET will complete its projects on time and earn a 14% ROI (we hope for higher results but see no need to include 16%+ ROI's, let's just assume reasonable levels of success), Third, we assume expenditures on new projects remain at a steady $3.5 billion per year for four straight years (it's a reasonable guess that is helpful for this exercise) and last, we simply assume mgmt does not buy back any stock, does not pay down any debt and does not make any acquisitions. Oh, and for the record, we believe ET is overearning in 2019 with unsustainably high margins such that the $10.8 EBITDA currently expected for this year is about $300 million unsustainably too high, so for the purposes of this analysis, we use $10.5 billion as the year end operating basis.....(the truth is, we believe ET will likely raise guidance for 2019 in the Fall to about $10.9+ billion, but let's ignore I said that).
So let's pretend ET ends 2019 with an operating EBITDA of $10.5 billion and DCF of about $2.20 (both less than mgmt guidance and less than what I really think they will do). The $5 billion invested in 2019 ought to ramp next year's operating results much higher. Furthermore, it is very important to recognize that ET has invested many billions in prior years on projects that have been delayed, such as all the Mariner East pipelines and the Marcus Hook Terminal. This last point is significant as it means that many billions of dollars on top of the $5 billion newly invested this year will start to earn a return of some sort once these delayed projects are finished and come on line. For the record, we believe all the ME pipelines will be completed this Fall and all will begin ramping up by year end. As such, we loosely assume $2.0 billion or more previously invested but earning nearly nothing in 2019 will come on line in 2020 earning an ROI of say 9% (we recognize the ME system went over budget and the returns will be less than had been hoped for).
In order to avoid over stating our case, we are assuming that 50% of the $5 billion invested in 2019 comes on line during 2019 and is in fact already included in the numbers that allow ET to reach its 2019 goals. The other half of the $5 billion is then assumed to kick in and benefit 2020 and beyond.
Looking forward to 2020 we therefore are going to assume half or $2.5 billion of the investment spent in 2019 earns a 14% ROI and another $2.0 billion (money already invested and requiring no new debts) comes on line earning a 9% ROI. For purposes of calculating the cost of the new debt needed to complete the back half of 2019 projects, we are going to use mgmt's year end DCF guidance of $2.30, we subtract the distribution payout of $1.22 and we have about $1.08 x 2.6 billion shares and we see ET can invest $2.808 in 2019, and they borrow $2.2 billion to complete the $5 billion in new projects for the year.
Again, to figure out how much 2020 numbers might increase over 2019, we then take half of the $5 billion investment spent or $2.5 billion and we take half of the debt needed to support the back half of 2019 investments, so the back half of the year sees $2.5 billion in new investments and $1.1 billion in new debt. We can then calculate how much EBITDA and DCF the company will earn. Once that is done, we can simply add the 9% ROI earned on the $2 billion in delayed projects that seem likely to come on line by year end.
$2.5 billion x 14% = $350 million, less the cost of debt on the $1.1 billion borrowed. $1.1 billion x 5% = $55 million in interest. The $2 billion of newly finished projects starts earning $2 billion x 9% = $180 million. Add this all together and we see 2020 ought to see EBITDA rise $350 + $180 million = $530 million, then subtract the $55 million in interest and we more or less get DCF growth of about $475 million. Given that there are 2.6 billion shares, we can see that DCF might grow by $475/2600 = about 18 cents.
Now, remember we stated that ET is over earning in 2019 and conditions are simply too wonderful and too strong, so for extrapolating into the future, we decided to cut back our starting place and used $10.5 billion EBITDA and $2.20 DCF for year end 2019. From there, we can add the calculations directly above: EBITDA grows from $10.500 billion + $530 million = $11.300 billion for 2020 and DCF grows from $2.20 per share + 18 cents per share = $2.38 per share. If management elects to raise the dividend in 2020, and they elect to do so at about the same pace that DCF increases, then they could easily afford to take the distribution to about $1.37. Assuming such a rapid increase in dividends is aggressive but it also uses up a lot of free cash flow that otherwise could be used to reduce leverage even faster than this exercise portrays. If you think they may postpone a dividend raise another year, or increase the dividend at only half the pace I suggest here, then you must acknowledge the rate of deleveraging will take place faster than my numbers suggest. Either the dividend rises quickly or leverage declines more rapidly than my numbers show.
For this exercise, I demonstrate that ET can raise the dividend rapidly and also drop its leverage to 4.0, but I doubt they do them both in a straight line as shown here. They probably will continue to emphasize debt deleveraging for another year or two, but to demonstrate the power of the company, and for the ease of analysis, we show ET using a straight line focus on both deleveraging and dividend increases, thus, we raise the dividend each year by the amount that DCF rises each year, or about .17 per year.
The following years, then, become much easier to calculate (thank God) as we just use $3.5 billion in new projects earning 14% ROI's and a cost of debt of 5%, plus we raise the distribution payout by the same increase seen in DCF (again, about .17 cents per year).
$3.5 billion x 14% = $490 million EBITDA. Prior year's DCF of $2.38 - dividends of $1.37 = $1.01/share x 2.6 billion shares = $2.6 billion in retained free cash flow able to be invested in new projects. $3.5 in projects - $2.6 free cash flow = $900 in new debt needed for this year which costs $45 million in interest. $490 EBITDA - $45 interest = $445 million in additional DCF = 17.1 cents growth. EBITDA for 2021 thus grows from $11.3 + $490 = $11.790 and DCF per share grows from $2.38 + 17 cents = $2.55. We then also assume the dividend distribution grows the same amount to $1.54/share up from $1.37 in 2020.
Again, $3.5 billion x 14% = $490 million in additional EBITDA. Prior year's DCF of $2.55 - dividends of $1.54 = $1.01/share x 2.6 billion = $2.6 billion in retained free cash able to be invested in new projects. $3.5 billion in new projects - $2.6 billion of free cash flow = $900 in additional debt needed to complete this year's projects at a cost of $45 of additional interest. Same exercise as prior year, EBITDA grows in 2022 by $490 million less the $45 million in interest leaves about $445 additional DCF (of course the maintenance cap ex numbers would be climbing but the change in that rate is not known and we assume for this exercise it remains more or less stable). EBITDA ends the year at $11.79 + $.490 = $12.28 billion and DCF per share climbs to $2.55 + .17 = $2.72 per share. The dividend we assume rises to $1.71 per share.
Let's skip typing all the repetitive arithmetic and conclude that EBITDA rises $490 million and reaches $12.78 while DCF rises another .17 cents to $2.89. For fun, we assume the dividend rises to $1.88, in line with the rise in DCF.
Leverage Declines Significantly and the Dividend Rises 40%
To reasonably guess where Debt/EBITDA might end up by the end of 2023, we have to jump back in time to the present day. It's complicated and we are going to make guesses and assumptions, but from what we understand ET currently has an adjusted leverage ratio of 4.7 and it aims to finish 2019 at or near 4.5. If we multiply 4.5 x guidance of EBITDA of $10.8 billion, then we see that year end 2019 adjusted debt ought to be about $48.6 billion. Now we can add the $900 million of additional debt needed to complete the $3.5 billion of annual investment projects for each year going forward. Counting 2020, 2021, 2022 and 2023 we get 4 years x $900 = $3.6 billion of new debt, which we then add to the year end 2019 number of $48.6 billion and we end 2023 with total adjusted debt of about $52.2 billion. Take the EBITDA figure for 2023 of $12.78 and we see that D/EBITDA leverage has declined to 4.08 ($52.2 divided by $12.78 = 4.08). At the same time, our calculations assumed that DCF ends 2023 at $2.89 and the dividend rises to $1.88. If we assume this company is then seen as having successfully deleveraged to about 4.0 and it can trade up to 9 to 10 x DCF, then the stock rises to $26 to $29 a share and we collect about $7.11 in largely untaxed distributions along the 4 1/2 year journey. From today's $14.20 stock price that means we might make $19 to $22 per share or 134% to 155%. Sort of incredible, but we believe it is reasonable and fully possible if mgmt elects to focus on both leverage and dividends in a straight line.
Perhaps ET Elects NOT to Raise the Dividend so Quickly?
Before we end this exercise, let's consider the other very possible scenario, the one where ET mgmt decides to retain more cash flow while they raise the dividend at a slower pace than imagined above. We are not going to exhaust you any further with more mathematics as the conclusion is very easy to grasp. If ET does not raise the dividend as quickly as we have shown above, then obviously they will need to issue less debt and the debt to leverage ratio will fall all that much faster. It is currently anyone's guess, but if ET wants to drive the DEBT/EBITDA ratio below 4.08, say to 3.9 or less, they can easily do that as an alternative. No doubt, management will be holding many investor discussions as they grapple with this decision. Do they elect to drive the dividend to a lovely $1.88 as I have depicted, or do they decide to raise it to something more like $1.50 while they drive leverage well below 3.9? Enterprise Products Partners (EPD) currently carries a leverage ratio of about 3.6 and EPD trades between 11 to 13 x DCF on a regular basis. We believe EPD is also undervalued, although not nearly as much as ET is presently. Point being, if EPD ends up trading a bit higher to something like 12 to 14 x DCF in the future, then ET may elect to remain focused on quickly driving leverage down under 3.9 so it too can obtain a higher valuation more like 10 to 11 x DCF perhaps. If they pay smaller distributions per year then they borrow less debt and DCF rises faster than I portrayed. With smaller distributions, then 2023 DCF likely reaches $3.00 a share and Energy Transfer has a solid shot at rising to over $30-$33 a share, again, we make more than 100%.
A large dividend or super low leverage ratio, either way, it seems highly likely Energy Transfer is going to make us investors a great return in the next few years.
Disclosure: I am/we are long ET, EPD, KMI, MPLX. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.


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I am building a custom plugin to read a windows event log, and have been successfull enough in getting the monitor created, deployed in dynatrace and tested.
The monitor works perfectly fine, however i had created a metric group, which i would like to return a 0 in case of success or 1 in case of failure.
Currently the metric returns a null everytime the monitor is run.
Do i need to do anything specific in my code to set the monitor. Please suggest.
Thanks & Regards,
Answer by Jalpesh S. ·
Hi Team,
We have calculated some value (response time) in monitor plug-in and want to store that value as measure in Dynatrace.
Please suggest.
Hi Jalpesh
If you have a monitoring plugin that calculates that value and the plugin returns the value through the standard monitoring sdk interface the measure will be available in dynatrace and will automatically be stored in the performance warehouse
If you want to learn more about building monitoring plugins check out this youtube tutorial: https://www.youtube.com/watch?v=ZfdzCaSIdjk&list=P...
Answer by Rob V. ·
Hi Lester,
You do need to process your results and set the values in your metric group. Here's an example:
public Status execute(MonitorEnvironment env) throws Exception { Status result = super.execute(env); Collection measures; if ((measures = env.getMonitorMeasures(METRIC_GROUP, MSR_EXEC_SUCCESS)) != null) { for (MonitorMeasure measure : measures) measure.setValue(isMatchRuleSuccess() ? 1 : 0); } return result; }
Hope this helps,
Answer by Andreas G. ·
Hi Lester
Have you seen the Best Practices and Examples section in the doc? It gives an example on the actual code you need to place in your plugin that will report back the measure values for your metric groups
Let me know if this helps
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|WOW! Live on the Indian River waterfront. Minutes to restaurants, shops, Pubs and local events at Riverview Park. Fish off your own dock and enjoy glorious sunrises. Open up the front and back doors and let the river breeze cool your home. New roof 2018 More Info...
River Oaks Townhouse
732 Cleveland
Sebastian, FL 32958
3 Beds / 2 Baths
Courtesy of Dale Sorensen Real Estate Inc.
|Great Location! Large 3 story villa with poured concrete walls & Hardi board siding. River views from all floors. 3 bedrooms, 2.5 baths, living room with sliding glass doors to screened porch. NEW Metal Roof, County water/sewer, Day dock. Accordion shutte More Info...
Pelican Pointe-seb
9612 Riverside
Sebastian, FL 32958
2 Beds / 2 Baths
Courtesy of Alex MacWilliam, Inc.
|Stunning direct Riverfront views from all rooms of this second floor 2/2 condo at Pelican Pointe. Extensive enclosed porch for panoramic views. Private porch off master bedroom.Take the elevator from the underground parking to the 2nd floor.Extra storage More Info...
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June's digital wallpaper is ready for you to download!
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Tiësto, Eric Prydz, and Richie Hawtin to Headline EDC Las Vegas 2016
For the event's 20th anniversary, they'll be joined by everyone from Eric Prydz and Richie Hawtin to Zedd and Hardwell.
Photo by Doug Van Sant
International megafestival, Electric Daisy Carnival, just announced the lineup for its 2016 edition in Sin City, set to return to the Las Vegas Motor Speedway from June 17-19. Among the awe-inducing legion of huge artists to be featured on the event's 20th anniversary are Tiësto, Eric Prydz, Richie Hawtin, Zedd, Afrojack, Paul Oakenfold, and Hardwell.
They'll be joined by the likes of Loco Dice, Martin Garrix, Maya Jane Coles, The Chainsmokers, A-Trak, and Alesso.
EDC will take place between June 17-19 in Las Vegas. More information and tickets are available from EDC's website.
Last year's edition was the biggest ever, and it felt like an indicator of the post-EDM era to come.
Follow Alexander on Twitter.
- Tagged:
- Thump
- the chainsmokers
- Richie Hawtin
- tiesto
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- A-trak
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- EDC Las Vegas
- edc las vegas 2016


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@UofLSheriff50. Louisville native, University of Louisville Business School Grad c/o 2004. Co-Founder of TheCrunchZone.com
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Photo via: lonny.com
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Inheriting a problem: Deceased estates, expats and financial emigration
Thousands of elderly South Africans have children who are living overseas, which can become an administrative nightmare when the parents pass away and their expat children inherit the estate.
Inevitably, they run into issues with the payout of the estate and taking the money out of the country.
Tim Powell, director of forex at Sable International says the problem is arising more frequently: "Many South Africans who have emigrated, have been living overseas for a long time and often have lost their South African ID documents and have no local bank accounts, which makes it difficult for administrators to pay out an estate.
"We are working extensively with law firms and administrators liaising with estate beneficiaries, to establish what their status is in terms of exchange control and what their options are."
ID Book
According to Powell, the most common scenario is where the beneficiary has been living overseas for a long time, their parents pass away and they inherit in SA, but they've lost their ID book or didn't obtain the green barcoded ID book, and the only way they can access their money is to financially emigrate.
"Remember, when applying for a tax clearance at SARS, one of the things you have to do is submit a copy of your green barcoded ID, you cannot use a passport. If you cannot produce your green barcoded ID, you're going to be stumped."
"If they do have an ID book, then we can use the allowances - we can use the R1 million allowance or we can register you for tax if it's more than a million (up to R10 million). You would apply for tax clearance and then get permission to send the money overseas, which is quite a straight forward process," says Powell
Bank account
"If you have a green ID book but no South African bank account, you would need to open an account to receive the money in a FICA compliant manner," says Powell.
"If you don't have a South African ID you either have to financially emigrate or go through the schlepp of getting an ID. If you have the ID, but no longer have a South African bank account, you need to work with an entity like Sable or go through the mission yourself of opening a South African bank account so funds can be transferred in and then transferred out," says Powell.
According to Powell, if you are the beneficiary of a trust in a deceased estate there are sometimes further complications. "The problems often arise when the founder of the trust dies. Often in a family trust, one of the conditions of the trust is the trust will be terminated on the death of the founder and spouse, and this needs to be finalised," says Powell.
Isn't it easer just to financial emigrate?
"Taking the decision to move overseas permanently, is a complicated financial decision and emigrating South Africans have to consider whether or not they want to close all their bank accounts, leave certain assets and investments behind, and if they need to financially emigrate," explains Powell.
"Financial emigration, also known as formal emigration, is the process whereby a South African resident changes their status with the Reserve bank to that of a non-resident. It would require you to complete a form called an MP336 and to go to your bank and place your emigration on record with the South African Reserve Bank. You would receive a reference and a confirmation from SARB that your emigration is on record.
"The decision to financially emigrate can be taken at the outset, at a later stage or not at all. The death of a parent and the complications in winding up the estate, could be the impetus, but there are many other reasons to evaluate whether or not to financially emigrate."
Why do it?
Powell suggest that emigres look at the context and their wealth, before considering financial emigration: "South Africans and South Africans living abroad can move R10 million a year out of the country with a tax clearance certificate and another R1 million without tax clearance.
"If you're married, you can move R22 million, and if you have children over 18, you can extrapolate the R11 million per person per year for your children as well in some instances.
"The reason you financially emigrate is because it allows you take everything out in one go so if you want to take out more than the annual allowance at once you would need to financially emigrate. About several years ago, there used to be a levy on financial emigration - If you financially emigrated you would pay a 10% levy, but this is gone now.
"If you're living overseas and your only remaining asset is a retirement annuity policy, you may want to financially emigrate as the rules around retirement annuity policies require that the only way you can encash them, is to financially emigrate. A pension or provident fund, you can cash, pay the tax and take overseas, but cashing in a retirement annuity, requires financial emigration.
"Lastly, as I have mentioned, if you are already living overseas and inherit from an estate in South Africa, and you don't have a South African ID you probably need to financially emigrate."
"If you have trusts and property in South Africa, you might want to consider not financial emigrating. Banks will often say you need to financially emigrate, because they want to close your account, but it is not always the right solution for the client. They might be creating a headache for themselves. With the current laws, as long as you have your ID book, there's a lot you can do without financially emigrating," concludes Powell.
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