The Earth Charter inspired musical "Our Blue Planet Will it Survive Till Tomorrow?", created by the Japan Classic Live for the United Nations group, was performed in New York at Hunter College Kay Playhouse Theatre on 1st November and at Stony Brook Southampton's Avram Theater on 3rd November 2009, followed by two other performances in Washington DC at the Japan Information & Culture Center on 4th November and at the Smithsonian's Freer Gallery on 5th November.
Presented in five acts, "Our Blue Planet" is featuring Jupiter melody of Gustav Holt's "Planets Suites" as the main chorus. The performance employs not only clasicc music but also rock music. It's fascinating stage were composed of dance, play and scenes of international conference (and over 50 performers plus 5 promintnent artists). "Our Blue Planet – Will It Survive Until Tomorrow?" is an eclectic theater piece with messages about environmental disaster that can be generated should we not take precautions today. It envisions in the year 2100 the people of Earth, living in the devastating aftermath of climate change, will look back and wonder how, when and where it all went wrong. This thought provoking production asks if the countries of the world can and will come together now to protect our planet and our future.
Produced and directed by Ms. Masayo Koike, Chair of the Japan Classic Live for the United Nations and by Professor Emeritus of Seikei University Ryokichi Hirono, this theatrical performance features violinist Kiyomitsu Obana, actor/choreographer Toshijiro Zenki, actor/singer Tekkan, and actor Hiroyuki Watanabe. Senator Wakako Hironaka, Chair of the Japan Earth Charter Committee, and Professor Ryokichi Hirono, the Vice-chair of the Japan Earth Charter Committee, played a major instrumental role on producing the play based on the Earth Charter. The play starts with an introduction to the Earth Charter, for these performances undertaken in early November in the USA it had the participation of Steven C. Rockefeller, Rick Clugston, and Peter Blaze Corcoran. In the play, the Earth Charter's key message of poverty reduction, human rights protection including gender and child rights, nonviolence to achieve world peace and global environment conservation and protection including global warming prevention are repeatedly conveyed to the audiences and the public and the United Nations are encouragedto join the actors to explore the way forward for realizing the goals and objectives of the Earth Charter .
UNCL is a non-profit organization based in Japan. This year's performance was co-sponsored by various government agences including the Prime Minister's office, the Ministry of Foreign Affairs, the Ministry of Environment and JICA. Activities of UNCL has been supported by national NGOs in addition to funding support from the government and and private foundations. Since its establishment 18 years ago, Classic Live has performend on the theme of environment throughout Japan, as well as Asia, Europe and the US, which include performances at the UN Headquarters in 2005 and in Geneva in 2007.
The next performance will take place (in Japanese language) on 12 December 2009 at Tokyo Women's Plaza Hall in Tokyo, Japan (adjacent to the United Nations House in Shibuya). If time permits, Ms. Wakako Hironaka, member of the International Earth Charter Council and Chair, Japan Earth Charter Committee and Ms Miyuki Hatoyama, the First Lady of Japan, will be one of the performers on the stage, as they have often done on this Environmental Musical in the past.


Leaders need to balance learning – which by definition means becoming vulnerable – with managing their image as a leader. Executive coaching allows you to learn about your dreams and your business challenges. Coaching allows you as a leader to further your own learning quickly, while getting a different picture of what's going on in your organization, especially with respect to how people experience you and your team. A coach will help someone change in areas that are not meeting expectations, and will help someone grow in areas that are of interest to the individual and their circle of influence.


The iconic red and yellow intersecting circles of Mastercard are one of the world's most recognized brands.
Exciting times! We're slowly releasing a new version of UpLabs, with simpler UI and major UX improvements! Let us present to you the team behind it: Flat_Studio! You might remember them from last month when we talked with the talented Bohdan and Slava, about their stunning redesign of Google Play.
Mondo is one of a growing group of fintech startups aiming to transform the way we bank. We talk to head of design Hugo Cornejo about working with customers and developers to create a digital banking service to rival existing apps.
Lauren's company, The Simply Co., sells cleaning products that are sustainable and toxin-free. And while Lauren's glad people are choosing to purchase products that don't hurt the earth, she would rather we all make them on our own.
With so many books out there, it's hard for my fellow bookworms to decide which to chew through next. Here's a collection of favorites I've read or heard about recently and have found useful.
Where Prototypes Fail — Hi, Five!
An increasing number of designers prototype on a regular basis, with a lot more interested in incorporating it in their design process. And rightly so — prototyping is very useful for exploring swift product solutions.
The word "process" appears 44 times in our roles doc — our reference for evaluating designers — and only increases its prevalence as a designer grows in seniority. So, why is having a unified process important?
For any app or web application, nothing will ever happen without some initial and ongoing input from the user. It is, therefore, critical that product designers, developer and product managers understand the best ways to allow them to do so.
This question comes up a lot. I coach and mentor a lot of students on product design: tutoring for the Academy of Art in San Francisco, reviewing for AIGA Portfolio Day, hosting interns at Facebook and so on.
Over the past few years, I have spent a considerable amount of time on side projects investigating contextual products. A contextual product uses hardware and software sensor inputs to create a better experience. Context goes beyond issuing commands to computers and waiting for a responses. Context seeks to codify computers with humanlike responses the product's user desires.
I've been designing Missive, the one app for email and chat, for the past two years as the only designer in a team of four co-founders.
Have you ever wondered why Netflix has such a great streaming experience? Do you want to learn how they completed their homepage plus other UI layout redesigns through A/B testing? If so, then this article is for you!
Pokémon Go is amazing. Everywhere in the world, millions of people go outside, explore their surroundings and meet like-minded monster hunters. It's the first time augmented reality has been applied to create a succesful, lasting and engaging experience.
These are the slides and speaker notes from a presentation I gave on July 21, 2016 at the Design & Content Conference in Vancouver, B.C..
Design Doesn't Scale is a statement that has bothered me for the last four-years. When I joined Spotify's design team in 2012, the level of inconsistency and fragmentation shocked me.
By now, you've probably heard about Netflix's latest cult show Stranger Things from your best friend or work buddy. And if you're like me, you innocently pushed play on a work night and by midnight realized the scene in your living room was looking a lot like that one Portlandia skit.
Sometime in the fall of last year I began to draw my calendar.
I talked about how design helps Airbnb's cross-culture business in my last article. As a Chinese person living in the US, I thought it would be interesting to go further and study the Airbnb users in the Chinese market.
If you had asked 22-year-old me what my "career aspirations" were, I would have looked at you blankly and then casually changed the subject to what programs you'd recommend to model cute 3D bunnies for a video game, or whether the writers of Alias would be so devious as to ship Sydney Bristow and Sark.
A handy guide to navigating what's coming up next in the design world.


Hey ! I would like to request a showing of 0 Mc Clellan Road. Let me know what times you are available. Thank you!
UNRESTRICTED Lot! Endless Possibilities! Land could be used as Commercial or Residential Use! GREAT Location! Frontage of 233 Ft on Sorters - McClellan Rd! 260 ft Frontage on Savell! 3.30 Acres of WOODED Land! Up and coming area!
This listing is courtesy of the listing agent Ruben Villarreal (#VILLAREA), with the office RE/MAX Integrity.
All data for this listing was last updated on January 17, 2019 at 12:24AM.


text:
Disgraced ex-pol Pedro Espada and his son to plead guilty
By KENNETH LOVETT , ROBERT GEARTY and John Marzulli
Pedro Espada Jr, right, and his son Pedro Gautier Espada, left, are expected to plead guilty Friday in Brooklyn Federal Court. (Seth Wenig/AP)
He's not going to be able to break out of this piggy bank.
Convicted former Bronx Sen. Pedro Espada and his son are scheduled to plead guilty Friday in Brooklyn Federal Court, after reaching a deal on the remaining criminal charges they face in connection with looting more than $400,000 from a low-income health care network, sources said.
Because of the brazenness of his looting, it's unlikely Espada will avoid prison time, sources said.
The son could escape with just probation because he will plead to much less serious misdemeanor charges, said the sources.
The elder Espada was convicted in May of stealing $448,000 between 2005 and 2009 from the Soundview Health Network — which he founded — to fund personal expenses like dinners, trips, home improvements and family parties. He faces 10 years in prison on each of the four theft convictions.
But after 11 days of deliberations, the jury deadlocked on four counts against the elder Espada and on all eight charges against Pedro Gautier Espada. They were expected to face a retrial.
There is no guarantee that Brooklyn Federal Judge Frederic Block will give anything more than probation. Both Espadas are expected to argue at sentencing that they should not go to prison because of their good works and that the Soundview clinic they stole from provided medical services to poor people in the Bronx for more than three decades.
But prosecutors proved Espada filled Soundview's board with cronies so he could use the nonprofit as his personal piggy bank. In recent years, the clinic missed payrolls, couldn't afford to replace aging medical equipment and was forced this year to stop seeing patients when it couldn't pay its malpractice insurance.
Both Espadas were scheduled to go on trial next month in Manhattan Federal Court on charges of not paying taxes on the money they stole, but the plea deal will cover that case as well, sources said.
"I expect to have a resolution of both matters Friday," Espada attorney Daniel Hochheiser said, declining to discuss the details of the plea.
"The senator is looking forward to moving on with his life and putting his legal problems behind him and his family," said Hochheiser.
The Daily News reported Thursday that lawyers for the disgraced former Democratic leader and his son were trying to hammer out a "package deal" for both defendants.
Robert Nardoza, a spokesman for U.S. Attorney Loretta Lynch, declined comment.
Sources said the father and son want to take their chances with the Brooklyn judge — who's seen as being more sympathetic to defendants — over hard-nosed Manhattan Federal Judge William Pauley, who is handling the tax case.
"He (Espada) realized that Judge Pauley meant business," the source said.
Prosecutors recently alleged that Espada and his relatives have continued to drain $144,000 from the proceeds of Soundview's sale, and unsuccessfully tried to revoke his bail.
Espada still has at least one other ongoing probe. Gov. Cuomo as attorney general launched a civil probe into Espada as part of a crackdown into public corruption.
Cuomo had no comment on the guilty plea, but his former chief of staff, Steven Cohen, said it was proof that aggressive enforcement works.
"I think this is an important case and a significant result because it shows a kind of corruption that in some circles had become almost accepted," Cohen said.
Word of Espada's pending plea brought little sympathy from his Albany colleagues on either side of the aisle.
"Hopefully this will be the end of the public chapter of Pedro Espada's life," said Sen. Diane Savino (D-Staten Island).
Sen. Martin Golden (R-Brooklyn) called the result "inevitable and just a matter of when."
With Edgar Sandoval
Jeffrey Epstein denied bail, will remain in jail while awaiting sex trafficking trial

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Linq2Sql: Manage DataContext In the following code doesn't work as
public void Foo()
{
   CompanyDataContext db = new CompanyDataContext();
   Client client = (select c from db.Clients ....).Single();
   Bar(client);
}

public void Bar(Client client)
{
   CompanyDataContext db = new CompanyDataContext();
   db.Client.Attach(client);
   client.SomeValue = "foo";
   db.SubmitChanges();
}

This doens't work, I get error msg. "An attempt has been made to Attach or Add an entity that is not new, perhaps having been loaded from another DataContext.  This is not supported."
How do you work with DataContexts throughout an application so you don't need to pass around a reference?
What

A: They really mean it with 'This is not supported.'. Attaching to an object fetched from another data context is not implemented.
There are a number of workarounds to the problem, the recommended way is by serializing objects, however this is not easy nor a clean approach.
The most simple approach I found is to use a readonly DataContext for fetching objects like this:
        MyDataContext dataContext = new MyDataContext()
        {
            DeferredLoadingEnabled = false,
            ObjectTrackingEnabled = false
        };

The objects obtained from this context can be attached to another context but only applies to some scenarios.

A: The PLINQO framework generates detach for all entities making it easy to detach and reattach objects without receiving that error.
public void Foo()
{
   CompanyDataContext db = new CompanyDataContext();
   Client client = (select c from db.Clients ....).Single();
   // makes it possible to call detach here
   client.Detach();
   Bar(client);
}

public void Bar(Client client)
{
   CompanyDataContext db = new CompanyDataContext();
   db.Client.Attach(client);
   client.SomeValue = "foo";
   db.SubmitChanges();
}

Here is the article that describing how the detach was implemented.
http://www.codeproject.com/KB/linq/linq-to-sql-detach.aspx

A: Yep.  That's how it works.
You have tagged this asp.net so I guess it's a web app.  Maybe you want one datacontext per request?
http://blogs.vertigo.com/personal/keithc/Blog/archive/2007/06/28/linq-to-sql-and-the-quote-request-scoped-datacontext-quote-pattern.aspx
(P.S.  It's a lot harder in WinForms!)

A: I've created data access classes that encapsulate all the communication with Linq2Sql.
These classes have their own datacontext that they use on their objects.
public class ClientDataLogic
{
    private DataContext _db = new DataContext();

    public Client GetClient(int id)
    {
        return _db.Clients.SingleOrDefault(c => c.Id == id);
    }

    public void SaveClient(Client c)
    {
        if (ChangeSetOnlyIncludesClient(c))
            _db.SubmitChanges();
    }
}

Ofcourse you will need to keep this object instantiated as long as you need the objects.
Checking if only the rigth object has been changed is altso somewhat bothersom, you could make methods like
void ChangeClientValue(int clientId, int value);

but that can become a lot of code.
Attaching and detaching is a somewhat missing feature from Linq2Sql, if you need to use that a lot, you sould probably use Linq2Entities.

A: You need to handle object versioning.
An entity can only be attached as modified without original state if it declares a version member or does not have an update check policy.
So, if there's no timestamp member or other 'versioning' mechanism provided there's no way for LINQ to determine whether that data has changed - hence the error you are seeing.
I resolved this issue by adding a timestamp column to my tables but there are other ways around it. Rick Strahl has written some decent articles about exactly this issue.
Also, see this and this for a bit more info.

A: I took a look at this and found that it appears to work fine as long as the original DataContext has been disposed.
Try wrapping the DataContext with using() and make sure your changes occur after you've attached to the second DataContext?  It worked for me..
        public static void CreateEntity()
        {
            User user = null;
            using (DataClassesDataContext dc = new DataClassesDataContext())
            {
                user = (from u in dc.Users
                        select u).FirstOrDefault();
            }
            UpdateObject(user);
        }

        public static void UpdateObject(User user)
        {
            using (DataClassesDataContext dc = new DataClassesDataContext())
            {
                dc.Users.Attach(user);
                user.LastName = "Test B";
                dc.SubmitChanges();
            }
        }

redpajama_set_name: RedPajamaStackExchange


Venture 5 Group Pty Ltd trading as CashnGo Australia (ABN 82 156 288 078) Australian Credit Licence Number 431627 (referred to as 'CashnGo Australia', 'we', 'our', 'us') is a short term and small amount loan credit provider for people who need a small amount of money for a short time. We recognise that our success in this business depends on us maintaining the utmost commitment to upholding your privacy rights when collecting, holding, using, or disclosing your personal information. We have established a number of procedures and protocols to help us keep personal information we hold secure, accurate, up to date, and complete.
This Policy outlines CashnGo Australia's obligations to manage and protect personal information and reflects the requirements of the Australian Privacy Principles (APPs'), the Credit Reporting Privacy Code ('the Code') and the Privacy Act 1988 (Cth) ("the Privacy Act"). This Policy is available free of charge from our website: www.cashngo.com.au.
This Policy also outlines CashnGo Australia's practices, procedures and systems that ensure compliance with the Privacy Act, APPs and the Code.
'Use' of information means use of information within CashnGo Australia.
CashnGo Australia does not give you the option of dealing with it anonymously, or under a pseudonym. This is because it is impractical, and in some circumstances illegal, for CashnGo Australia to deal with individuals who are not identified.
CashnGo Australia may receive unsolicited personal information about you. We destroy or de-identify all unsolicited personal information, unless it is relevant to CashnGo Australia's purposes, under this Policy, for collecting personal information. We may retain additional information we receive about you if it is combined with other information we are required or entitled to collect. If we do this, we will retain the information in the same way we hold your other personal information.
We may collect personal information from you electronically from our website :www.cashngo.com.au, when we receive emails and online account application forms. We may also use third parties to analyse traffic at that website, which may involve the use of a technology called 'cookies'.
e) and for security purposes.
CashnGo Australia does not collect Sensitive Information as defined in section 1 and as described in the Google AdWords sensitive category restrictions or sensitive interest information (which include personal hardship, identity and belief and sexual interests). The Google Analytics Advertising Features that we use include re-marketing, Google Display Network Impression Reporting and Google Analytics Demographics and Interest Reporting. These features require the collection of data via advertising cookies and identifiers. For more information about Google Analytics please refer to the Google Analytics link at : https://www.google.com.au/analytics. You can opt-out of Google Analytics Advertising Features by following the instructions in this link: https://tools.google.com/dlpage/gaoptout.
WHY DO WE COLLECT AND HOLD PERSONAL INFORMATION?
help us improve our products and services, and to enhance our overall business.
The main consequences of us not collecting your personal information are our inability or delay in being able to identify you, contact you or provide services to you.
other purposes authorised by the Privacy Act.
We use and disclose personal information for the purposes outlined in section 7 above. Sensitive Information will be used and disclosed only for the purpose for which it was provided or a directly related secondary purpose, unless the individual agrees otherwise, or if certain other limited circumstances apply (e.g., where required by law). Credit information will only be used and disclosed for the purposes outlined in section 10 below.
We engage other people to perform services for us ("Contractors"), which may involve them handling personal information we hold. In these situations, we prohibit Contractors from using personal information about you except for the specific purpose for which we supply it. We prohibit Contractors from using your information for the direct marketing of their products or services. CashnGo Australia will attempt to de-identify Sensitive Information held by us, wherever possible. We also undertake to delete all personal information about you when it is no longer needed or relevant.
an individual's financial institutions, referee(s), employer, co-account holder or authorised signatory; and anyone else to whom the individual authorises us to disclose it.
HOW MIGHT WE USE AND DISCLOSE CREDIT INFORMATION?
internal management purposes that are directly related to the provision or management of credit to you.
a CRB. If we intend to provide default information about an individual to a CRB, we will give you at least 14 days' written notice. If we disclose default information to a CRB, and you subsequently repay the amount owed, we will tell the CRB that you have repaid the amount owing. We will not disclose credit repayment history information to the CRB which is more than 2 years old or relates to an amount owing of less than $150.
personal information is overwritten to the extent possible when the information is no longer required. Where we no longer require personal information we will take reasonable steps to destroy or de-identify it.
you have not requested to opt out from receiving direct marketing from us. If you would not reasonably expect us to use or disclose the information for the purpose of direct marketing, we may only use or disclose that information for direct marketing if you have consented to the use or disclosure of the information for direct marketing or it is impracticable to obtain that consent. Individuals can opt out of direct marketing by contacting us, and we will give effect to the request within a reasonable period of time.
CashnGo Australia will provide you with the source of its information about you on request free of charge within a reasonable period of time. We will not use or disclose credit information for the purposes of direct marketing. CashnGo Australia may only use or disclose Sensitive Information about you for the purpose of direct marketing with your consent.
We will not use identifiers assigned by the Government, such as a tax file number, Medicare number or provider number, for our own file recording purposes, unless one of the exemptions in the Privacy Act applies. We may use government identifiers (as required or permitted by law) to verify your identity when you deal with us.
CashnGo Australia takes reasonable steps to ensure that the personal information, including credit information, it collects, uses and discloses is relevant, accurate, complete and up-to-date. We encourage you to contact us in order to update any personal information we hold about you. If we correct information that has previously been disclosed to another entity, we will notify the other entity within a reasonable period of the correction. If we are satisfied that personal information we hold is inaccurate, we will take reasonable steps to correct the information within 30 days, unless you agree otherwise. We do not charge you for correcting your information.
Subject to the exceptions set out in the Privacy Act, you may gain access to the personal information, including credit information, which CashnGo Australia holds about you by contacting the CashnGo Australia Privacy Officer. We will provide access within 30 days of the individual's request. If we refuse to provide access, we will provide reasons for the refusal. You can look at your personal information at the offices of CashnGo Australia. We will require you to verify your identity and specify what information is required. An administrative fee for search and photocopying costs may be charged for providing access.
This Policy will be reviewed from time to time to take account of new laws and technology, changes to our operations and the business environment. You will be notified if that happens.
Office of the Australian Information Commissioner by calling 1300 363 992, emailing enquiries@oaic.gov.au, or writing to Director of Complaints, Office of the Australian Information Commissioner, GPO Box 5218, SYDNEY NSW 2001.


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140 million pounds of nickel
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First Nickel Inc. Management
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& Directors
William J. Anderson
President, CEO, Director
Co-founder of First Nickel and Director since May 2004. William is an industry consultant with over 30 years of experience in mining and exploration. He was Exploration Manager for SELCO Mining and BP Canada from 1980 to 1992. President of MPH Consulting Limited ("MPH"), a private mining and exploration consulting firm (1995-present). His work has taken him to projects in Canada, the U.S., Brazil, Greenland and Africa.
Thomas F. Pugsley, P.Eng.
Chairman and Director
Chairman and Director of First Nickel since October 2004. A mining engineer, Thomas worked for Falconbridge Limited for 39 years. He began his career in 1964 as a junior engineer and moved into progressively senior positions, retiring in 2004 as Senior Vice President, Projects and Engineering.
C. David A. Comba, P.Geo.
Burlington, Ontario
A Director of First Nickel since May 2004. David is a professional geologist. From 1980 to 1986 he was employed by Texas Gulf Inc. as a field geologist and exploration manager for the region of Timmins, Ontario. From 1986 to 1993 he held increasingly senior positions with Falconbridge mineral and exploration companies. From 1994 to 1998, David was President and Chief Executive Officer of Pentland Firth Ventures Limited, a TSX-listed gold exploration company. From 1998 to 2005 David was Director, Issues Management, with the Prospectors and Developers Association of Canada.
Lyle R. Hepburn
A Director of First Nickel since October 2006. Mr. Hepburn is a Partner in the law firm of Beach, Hepburn LLP. Since co-founding Beach, Hepburn LLP in 1985, Mr. Hepburn's practice has been focused primarily on public mining and mineral exploration companies. Mr. Hepburn is a director of North Atlantic Resources Ltd., Gitennes Exploration Inc. and Fronteer Development Group Inc., mineral exploration companies listed on the TSX, the Corporate Secretary of Aber Diamond Corporation, a diamond mining company listed on the TSX, and the Corporate Secretary of Frontera Copper Corporation, a copper development company listed on the TSX.
Rob Whittall, CA, P.Eng
A Director of First Nickel since October 2006. Rob Whittall is a chartered accountant and a professional engineer (Queen's University, Mining) with over 20 years experience in the minerals industry including nine years in public accounting. He has worked in senior management positions for a variety of exploration and operating mining companies, recently with TVX Gold Inc. as Vice President, Finance until January 2003. Mr. Whittall is a founder and director of Goldcrest Resources Ltd. He is also a director of Andina Minerals Inc. and Viking Gold Exploration Inc.
Richard S. Hallisey, MBA
Appointed a Director of First Nickel in June, 2008. Mr. Hallisey is President and Director of Sullivan Holdings Limited, a position he has held full time since December, 2001. From January 1999 to December 2001, Mr. Hallisey was Vice-Chairman and Managing Director of National Bank Financial. Prior to his position with National Bank Financial, Mr. Hallisey was Co-founder, Vice-Chairman and Director of First Marathon Securities Limited. Mr. Hallisey holds a Bachelor of Applied Science (Civil-Geological Engineering) from the University of British Columbia and a Masters in Business Administration from the University of Western Ontario.
Joe Del Campo, CMA
Chief Financial Officer since June 2005. Joseph began his career with Falconbridge Limited and spent over 19 years working within the Falconbridge group of complanies at progressive financial positions, including Controller and Treasurer of Falconbridge Dominicana, a ferronickel operation in the Dominican Republic; and Falconbridge Gold Corporation, a gold mining company with operating mines in Africa and Timmins, Ontario. Over the past 13 years, Joseph has been a Director and Vice President, Finance and CFO of a number of junior exploration companies listed on the TSX and TSX Venture Exchange.
Paul Davis, P.Geo, M.Sc.
Vice President of Exploration
Vice President, Exploration since June 2005. Paul has over 16 years experience in nickel exploration. He has been directly involved in six new nickel sulphide discoveries in Ontario and has also worked in Finland and Australia. Prior to joining First Nickel, Paul worked on the Montcalm nickel mine outside of Timmins, Ontario for Outokumpu Mines Limited and managed the advanced exploration and production phases at the Alexo Nickel Mine, near Iroquois Falls, Ontario for Canadian Arrow Mines Limited.
Gerry Bilodeau
General Manager -- Sudbury Operations
General Manager -- Sudbury Operations since April 2007. Gerry has many years of senior operations management experience with Falconbridge/Noranda, most notably as Manager Mining at the Kidd Mine D Project in Timmins, and prior to that as Project Superintendent during development and construction at Falconbridge's remote Raglan Project in northern Québec. He is experienced in all phases of underground mine operations, and has a proven track record in development and construction management and in building and leading operating teams.
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The Maya takes its inspiration from the ethnic patterns of North African tiles and the azure blue waters of the Mediterranean. This combination of sky blue and jade green used on the pretty floral patterns and on the delicate handmade crochet edge create a design that is detailed and intricate. For a comfortable fit it is gently elasticated and features adjustable ties that are finished with delicate beaded tassels on the neck and back.
The design of these Maya lace-up pants influenced by the azure colours of the Mediterranean Sea combined with the intricate patterns of Moroccan tiles. The detailed pattern in light blue and soft jade on the simple white panel beautifully complements the handmade crochet edge for a look that is naturally stylish and relaxed. With soft adjustable side-ties they accentuate the hip and are extremely comfortable.


text:
Q: Find the Date range of week by current date in sql? I want to find record by this week just declare current date.
Example:
     select datename(dw,getdate())  -- Example today is Friday "27-04-2012"

so how can i get date range
     start on monday "23-04-2012" or sunday "22-04-2012"  As @dateStart to

     end on sunday "29-04-2012"  or saturday "28-04-2012" As @dateEnd

then i can select query by
     select * from table where date>=@dateStart  AND date<=@dateEnd

A: So you want only records from this week?
SELECT t.*
FROM table t
WHERE t.date >= DATEADD(DAY, DATEDIFF(DAY, 0, GETDATE()) / 7 * 7, 0)
AND   t.date <= DATEADD(DAY, DATEDIFF(DAY, -1, GETDATE()), 0)

A: Here are some helpful commands to get each day of the week
SELECT
    DATEADD(wk, DATEDIFF(wk,0,GETDATE()), -2) SatOfPreviousWeek,
    DATEADD(wk, DATEDIFF(wk,0,GETDATE()), -1) SunOfCurrentWeek,
    DATEADD(wk, DATEDIFF(wk,0,GETDATE()), 0) MondayOfCurrentWeek,
    DATEADD(wk, DATEDIFF(wk,0,GETDATE()), 1) TuesOfCurrentWeek,
    DATEADD(wk, DATEDIFF(wk,0,GETDATE()), 2) WedOfCurrentWeek,
    DATEADD(wk, DATEDIFF(wk,0,GETDATE()), 3) ThursOfCurrentWeek,
    DATEADD(wk, DATEDIFF(wk,0,GETDATE()), 4) FriOfCurrentWeek,
    DATEADD(wk, DATEDIFF(wk,0,GETDATE()), 5) SatOfCurrentWeek

you would then use these in your query to get the date range:
SELECT *
FROM yourTable
WHERE yourDate >= DATEADD(wk, DATEDIFF(wk,0,GETDATE()), -1) -- Sunday
AND yourDate <= DATEADD(wk, DATEDIFF(wk,0,GETDATE()), 5) -- Saturday

A: The queries that others have suggested may work, but you haven't defined what a "week" is for you. Depending on the country/region and the business reasons, a week could be Sun-Sat, Mon-Sun, Mon-Fri etc.
Therefore the best solution for finding the first and last days of the week is probably a calendar table where you pre-populate the first and last days of the week for every date that you'll need. Then you can use a simple query to get the correct start and end dates to use in your query:
select @StartDate = FirstDayOfWeek, @EndDate = LastDayOfWeek
from dbo.Calendar
where BaseDate = @SomeDate

This solution also has the advantage that you can easily work with different definitions of a week by adding new columns to your calendar table.


text:
Tag: St. Moritz
The Badrutt's Palace Hotel
15. October 2019 4. December 2019 Posted in Travel HighlightsTagged St. Moritz, Switzerland, Travel
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Badrutt's Palace Hotel, in the center of St. Moritz, has been synonymous with glitz and glamour since the resort opened as the Palace Hotel in 1896. This landmark luxury hotel overlooks Lake Saint Moritz and offers views of the surrounding Swiss Alps.
Every guest can feel it. The St. Moritz magic at this hotel. The feeling when you enter the Le Grand Hall is indescribable. Like a spell, far from the daily routine. The history of this luxury hotel in St. Moritz draws you in again and again into its enchantment. This is what St. Moritz looks and feels like!
It all started in 1856 when Johannes Badrutt took over the 12-bed Pension Faller in St. Moritz and upgraded it into a hotel with the name Engadiner Kulm (today's Kulm Hotel).
This was followed by the legendary bet: Caspar Badrutt (1848-1904), son of Johannes Badrutt, purchased the St. Moritz Hotel Beau Rivage, built in 1872 by C. Rungger. He charged the renowned Swiss architects Chiodera and Tschudi with the remodelling of the hotel. The hotel was also renamed Palace Hotel.
Johannes Badrutt won a wager and brought the first English tourists to St. Moritz for winter sports. He built curling rinks and the world's first toboggan run and, in doing so, invented alpine winter tourism. And that was exactly the time, when the magic began.
The official opening of the Palace Hotel was then on July 29th, 1896.
Alfred Hitchcock first came to St. Moritz in 1924, and returned here two years later for his December honeymoon with Alma Reville, staying at Badrutt's Palace Hotel (these days, locals just call it "the Palace").
Back in the day, Alfred Hitchcock was a regular here, staying in Badrutt's Palace Hotel annually for 50 years. In the picture above, you see the Hitchcock Suite at the Palace.
They have a total of 157 rooms, 37 of which are suites and junior suites. There are four room and seven suite categories ranging from CHF 490.00 to CHF 20'230.00.
I stayed in a Double Room Deluxe with lake view on the 5th floor. Spacious, individually designed, soothing colors. Only the best materials are used, such as Italian marble in the bathroom. My opinion: At the Palace, it is all about details. Very charming and your home away from home!
My friend Milos stayed in a Junior Suite Deluxe on the 2nd floor. The Junior Suite Deluxe meets the demands of a modern man or woman who knows exactly what he or she wants. Guaranteed lake view. Own balcony. Spacious and enough storage. Noble materials – and everything stylish.
My favorite suite is the Hans Badrutt Suite. This suite with lake view is like a catchy tune: it stays on your mind. A marble entrance hall. A cosy library. The princess-like bathroom with make up mirror. From the Jacuzzi the princess overlooks the mountains. The dressing room provides ample space for all treasures. Simply magical!
Restaurants, Bars and Night Club
IGNIV@Badrutt's Palace: A new restaurant concept never seen before in St. Moritz. IGNIV@Badrutt's Palace by Andreas Caminada opened on 21st December 2016 in the rooms of Le Relais. IGNIV means »nest« and for Andreas Caminada, the 3 Michelin starred Swiss chef, stands for sharing values, social exchange and comfort. Caminada's innovative finedining-sharing-experience focuses on time spent together, sharing menu components served on platters and in pans.
La Coupole/Matsuhisa@Badrutt's Palace: in the 2014/15 winter season the Japanesese star chef Nobuyuki Matsuhisa (»NOBU«) opened his premier brand Matsuhisa in the former tennis hall, which was once Europe's first. The Martin Brudnizki Design Studio in London designed the unique interior of this 108 seat restaurant where original classic elements are skilfully combined with modern style. One such example is the original studded steel girders of the former tennis hall which now support a glass dome. This affords guests a view of the legendary hotel tower and also acts as both the landmark and namesake of ›La Coupole‹. The restaurant incorporates a cocktail and sushi bar as well as a private dining room. Japanese Peruvian cuisine; only open in the winter season.
Le Restaurant: The Grande Dame of Badrutt's Palace Hotel's restaurants. Guests enjoy glamorous nights in a unique setting for a classic dinner, candlelight dinner or a cultural event. This venue seats 300 people and features International and French cuisine. During the winter a harpist entertains guests for breakfast. A set dinner is served daily throughout the summer and winter season. Dress code: From 07.30 pm jacket required, tie desired.
Le Relais: The Le Relais restaurant offers French cuisine for lunch daily (in winter). The restaurant offers a cosy atmosphere with its colourful décor in the Belle Epoque style and large windows with stunning views over Lake St. Moritz. It can be divided into two dining areas as well as a separate area for small to medium sized private events. In summer the breakfast buffet is served here.
Renaissance Bar – Vintage Cigar Lounge: Smoking allowed – in particular fine Cuban cigars! From 3rd December 2016 the Renaissance Bar will become Europe's first »Vintage Cigar Lounge«. Pure indulgence. The décor oozes comfort and encourages lounging. An exclusive choice of cigars. Paired with drinks and cocktails mixed by Andrea Delvo, Manager of the popular bar.
Le Grand Hall: The legendary lobby of the hotel with its stunning views, extravagant décor and fantastic architecture is known affectionately as the »living room of St. Moritz«. Guests can enjoy the hotel's glamorous atmosphere over High Tea, champagne and caviar with live piano accompaniment.
La Diala (Rhaeto-Romanic for »mountain fairy«): The latest of Badrutt's Palace Hotel's restaurants. Situated within Palace Wellness, the restaurant offers a light Mediterranean cuisine with a wide selection of salads and sandwiches. The family friendly restaurant with its terrace opens daily from 09.00 am to 08.00 pm.
Chesa Veglia: One of the oldest farmhouses of St. Moritz (built in 1658). Chesa Veglia is a hideaway for the rich and famous and its restaurants are among the favourites in St. Moritz. It features three restaurants and two bars: The Pizzeria Heuboden for original Italian pizza and pasta, the Grill Chadafö for elegant dining with classic French cuisine and the Patrizier Stuben for Swiss and International specialities. The Polo Bar and Carigiet Bar are the perfect place for a get-together, as well as for pre and after dinner drinks.
King's Club: All party animals and fans of sophisticated nightlife are on tenterhooks. The new King's Club has been revealed in its new outfit during winter season 2016/17. Tantalising afresh in shimmering red and glittering gold. Sizzling with life and energy, on fire. Mirrors, sparkle and light elements galore make the club and its future clubbers shine bright. The new King's Club celebrates the beautiful things in life: combining the joy of live music and famous DJ stars with an elegant, relaxed atmosphere and a tempting list of signature drinks and irresistible urban street food. Open only during the winter season.
Palace Wellness
Indoor swimming pool with access to heated outdoor pool, Jacuzzi
Treatment Centre with ten individual treatment rooms including two luxury Spa
Suites, private Hair Spa, Pedi Spa, Solarium, one room for facial treatments and four
rooms for body treatments, Wet Zone/ Palace Spa with two Saunas, Ice Room, Mist
Room, Aroma Therapy Room, Salt Steam Room, Massage Shower and Rain Shower
Fitness Centre with latest fitness and cardio facilities
Private sun terrace
Outdoor tennis courts managed by professional tennis coaches (summer only)
Natural outdoor ice-rink with instructor (winter only)
Kids' Club Palazzino with professional day care
Palace Galerie
Gallery with designer boutiques and elegant jewellers plus shopping guide: Bulgari,
Rebecca Ardessi, Church's, Embassy Jewel AG, Louis Vuitton, Cartier, De Grisogono, Les
Ambassadeurs, Trois Pommes, Miu Miu, de Nicola, Gübelin, Four Emotions, Santoni, Snow
Sports St. Moritz, Tom Ford, Gucci, Bottega Veneta, Giorgio Armani, Harry Winston, Lucia
Pieri, Fabio Caviglia and Galerie Gmurzynska
Service Spectrum
Palace Ski School in winter
In-house ski service, shop and rentals in winter
Ski pass included
Kids' Club Palazzino‹ with professional day care included
Free laundry service for children until 12 years
24-hour Concierge Service
Butler service for all rooms and suites
Free use of refreshment bar, movie channels, WiFi Internet access in all areas and free
Limousine service and car hire, including Rolls Royce transfers
Shuttle service to/from Zurich, Milan and Samedan airports on request
Free use of all fitness facilities
Free access to ice-rink
Events & Guest Relations Team
In-house fitness trainer
In-house bridge hostess
Baby sitting service
Coiffeur Hair Spa
To sum it all up: Tradition and quality endure. So it says daily in the ads. If the sales arguments are still the same almost 90 years later, it seems like tradition, quality and innovation were actually proven – and the St. Moritz glamour-factor is still there.


text:
\section{Introduction.}
\label{section 1}
\init

Consider the wave equation of the form
\begin{equation}                                               \label{eq:1.1}
\sum_{j,k=0}^n\frac{1}{\sqrt{(-1)^ng(x)}}\frac{\partial}{\partial x_j}\left(\sqrt{(-1)^ng(x)}g^{jk}(x)
\frac{\partial u(x_0,x)}{\partial x_k}\right)=0,
\end{equation}
where $x=(x_1,...,x_n)\in \R^n,\ x_0\in\R$  is the time variable,
the coefficients $g^{jk}(x)\in C^\infty$  and are independent of $x_0$,
 $g(x)=\det[g_{jk}(x)]_{j,k=0}^n,\ [g_{jk}(x)]_{j,k=0}^n$
is the inverse to the matrix $[g^{jk}(x)]_{j,k=0}^n$.
We assume  that  $[g_{jk}(x)]_{j,k=0}^n$ is a pseudo-Riemanian metric  with the Lorentz signature
$(1,-1,...,-1)$.
We also assume that
\begin{equation}                                               \label{eq:1.2}
g^{00}(x)>0,\ \ \forall x\in\R^n
\end{equation}
and
\begin{equation}                                               \label{eq:1.3}
g^{jk}(x)-\delta_{jk}=O\left(\frac{1}{|x|}\right)\ \ \mbox{when}\ \ \ |x|\rightarrow \infty.
\end{equation}
Equation (\ref{eq:1.1})  describes the wave propagation in a moving medium.
 As in [E1], [E2],  we consider two examples:
\\
\
\\
a) \underline{Propagation of light in a moving dielectric medium (cf. [G], [LP]).}
\\
\\
  In this case equation (\ref{eq:1.1}) is called the Gordon equation and it has the form:
\begin{equation}                                   \label{eq:1.4}
g^{jk}(x)=\eta^{jk}+(n^{2}(x)-1)u^ju^k,\ \ 0\leq j,k\leq n,\ \ n=3,
\end{equation}
 $\eta^{jk}=0$ when $j\neq k,\ \eta^{00}=1,\ \eta^{jj}=-1$ when $ 1\leq j\leq 3,
\ n(x)=\sqrt{\e(x)\mu(x)}$  is  the refraction index,
$x_0=ct$  where $c$ is the speed of light in the vacuum, $(u_0,u_1,u_2,u_3)$  is the four-velocity:
$u_0=\left(1-\frac{|w|^2}{c^2}\right)^{-\frac{1}{2}},\
u_j(x)=\frac{w_j(x)}{c}\left(1-\frac{|w_j|^2}{c^2}\right)^{-\frac{1}{2}},
\ 1\leq j\leq 3$.  Here   $w=(w_1(x),w_2(x),w_3(x))$  is the velocity of the flow,
 $|w|=\sqrt{w_1^2+w_2^2+w_3^2}$.
\\
\
\\
b) \underline{Acoustic waves in a moving fluid
(cf. [V1]).}
\\
\\
 In this case

\begin{eqnarray}                                     \label{eq:1.5}
g^{00}=\frac{1}{\rho c},\ \ g^{0j}=g^{j0}=\frac{1}{\rho c}v^j,\ 1\leq j\leq 3,
\\
\nonumber
g^{jk}=-\frac{1}{\rho c}(-c^2\delta_{ij}+v^jv^k),\ \ 1\leq j,k\leq 3,
\end{eqnarray}
where $\rho$  is the density,  $c$  is the sound speed, $v=(v^1,v^2,v^3)$  is the velocity.

Equations with metrics  (\ref{eq:1.4}), (\ref{eq:1.5})  may have black holes (see \S 2 below).
These black holes
are called optical and acoustic black holes,  respectively (cf. [V1], [NVV], [U]
and references there).  They are called often  artificial black holes since the metric in (\ref{eq:1.1})
not necessarily satisfies the Einstein equations.
Physicists hope to create artificial black holes in the laboratory. The artificial black holes play role
when one consider the perturbations of black holes of the general relativity such as the
Schwarzschield and the Kerr black holes.  We introduce the black holes in \S 2 and \S 3.  In \S 4
we shall study the existence and the stability of black holes in the case of two space dimensions.
In \S 5  we consider the axisymmetric case and in \S 6  we consider the inverse problems in
the presence of black holes.

\section{The black and  white holes.}
\label{section 2}
\init

Let $S_0(x)=0$  be a closed bounded smooth surface in $\R^n$.  Let $\Omega_{int}$  and $\Omega_{ext}$
be the interior and the exterior of $S_0(x)=0$,  respectively.
The domain $\Omega_{int}\times \R$ is called a black hole for  (\ref{eq:1.1})  if no signals (disturbances)
from $\Omega_{int}\times \R$  can reach the exterior domain $\Omega_{ext}\times\R$.  Analogously,
$\Omega_{int}\times \R$  is a white hole for (\ref{eq:1.1}) if no signals (disturbances)  from
$\Omega_{ext}\times\R$
can reach $\Omega_{int}\times\R$.  The surface $\{S_0(x)=0\}\times \R$  is called the event horizon
if $\Omega_{int}\times\R$  is either black or white hole.
In order to find the conditions when $\{S_0(x)=0\}\times \R$  is an event horizon we need the notion of
the forward domain of influence (cf. [CH]).

Consider the Cauchy problem for the equation (\ref{eq:1.1}) in half-space  $x_0>t_0$  with
 initial conditions
\begin{equation}                                       \label{eq:2.1}
u(t_0,x)=\varphi_0(x),\ \ u_{x_0}(t_0,x)=\varphi_1(x),
\end{equation}
where $\mbox{supp\ }\varphi_k(x)\subset\overline{X},\ k=0,1,\ x\in\R^n$.
Denote by $D_+(\varphi_0,\varphi_1)$  the support of $u(x_0,x)$  for $x_0\geq t_0$.
Let $D_+(X\times \{x_0=t_0\})$ be the closure of the union of $D_+(\varphi_0,\varphi_1)$  over
all $\varphi_0,\varphi_1$ with supports on $\overline{X}$.  Then $D_+(X\times\{x_0=t_0\})$  is
the forward domain of influence of $X\times\{x_0=t_0\}$.
Therefore $\Omega_{int}\times\R$  is a black hole if
$D_+(\Omega_{int}\times\{x_0=t_0\})\subset\overline{\Omega}_{int}\times \R$,  and
$\Omega_{int}\times\R$
is a white hole if
$D_+(\Omega_{ext}\times\{x_0=t_0\})\subset\overline{\Omega}_{ext}\times \R$
  for all $t_0\in \R$.

There is a geometric description of $D_+(X\times\{x_0=t_0\})$.

Let $[g_{jk}(x)]_{j,k=0}^n$  be the metric tensor corresponding to the operator $(1,1)$.
Consider a curve in $\R^{n+1}$:
\begin{equation}                                              \label{eq:2.2}
x_0=x_0(s),\  x=x(s),\ s\geq 0,\ x_0(0)=y_0,\ x(0)=y.
\end{equation}
The curve (\ref{eq:2.2})  is called a time-like ray if
\begin{equation}                                                  \label{eq:2.3}
\sum_{j,k=0}^ng_{jk}(x(s))\frac{dx_j(s)}{ds}\frac{dx_k(s)}{ds}>0,
\  \ \frac{dx_0}{ds}>0,
\ \ \mbox{for\ }\ \ s\geq 0.
\end{equation}
\begin{theorem}(cf., for example, [CH]).                        \label{theo:2.1}
The forward domain of influence $D_+(X\times\{x_0=t_0\})$  is the closure of the union
of all time-like rays
starting at $\overline X\times\{x_0=t_0\}$.
\end{theorem}
Let $\{S_0(x)=0\}\times\R$  be a characteristic surface for (\ref{eq:1.1}),  i.e.
\begin{equation}                                                \label{eq:2.4}
\sum_{j,k=1}^n g^{jk}(x)S_{0x_j}(x) S_{0x_k}=0 \ \ \mbox{when\ } S_0(x)=0.
\end{equation}
We assume that $S_{0x}(x)$ is the outward normal to $S_0(x)=0,
\ S_{0x}(x)\neq 0$  when  $S_0(x)=0$.

\begin{theorem}(cf. [E2]).                                    \label{theo:2.2}
The domain $\Omega_{int}\times\R$  is a black hole if (\ref{eq:2.4}) holds and
\begin{equation}                                                \label{eq:2.5}
\sum_{j=1}^n g^{j0}(x)S_{0x_j}(x)<0 \ \ \mbox{when\ } S_0(x)=0,
\end{equation}
and the domain $\Omega_{int}\times\R$  is a white hole if (\ref{eq:2.4}) holds
and if
\begin{equation}                                                \label{eq:2.6}
\sum_{j=1}^n g^{j0}(x)S_{0x_j}(x)>0 \ \ \mbox{when\ } S_0(x)=0.
\end{equation}
\end{theorem}

The proof of Theorem \ref{theo:2.2} based on the study of the time-like rays starting on $S_0(x)=0$
was given in [E2].

One can also prove Theorem \ref{theo:2.2}  using the energy-type estimates of the solutions of
the equation (\ref{eq:1.1})
in the  Sobolev spaces.
\begin{theorem}(cf., for example, [E4]).                               \label{theo:2.3}
Let (\ref{eq:2.4}) and (\ref{eq:2.5}) hold.   Then for any solution
$u(x_0,x)$  of (\ref{eq:1.1})  we have
\begin{equation}                                           \label{eq:2.7}
\|u(x_0,\cdot)\|_{1,\Omega_{ext}}^2 +
\|u_{x_0}(x_0,\cdot)\|_{0,\Omega_{ext}}^2
\leq
C_T(\|u(t_0,\cdot)\|_{1,\Omega_{ext}}^2 +
\|u_{x_0}(t_0,\cdot)\|_{0,\Omega_{ext}}^2),
\end{equation}
where  $T$  is arbitrary, $t_0\leq x_0\leq T,\ \|v\|_{p,\Omega_{ext}}$  is the norm
in the Sobolev space $H_p(\Omega_{ext})$.
\end{theorem}
Having the estimate (\ref{eq:2.7})  it is easy to see that  $\Omega_{int}\times\R$  is a black hole:

Consider the Cauchy problem (\ref{eq:1.1}), (\ref{eq:2.1}) in the half-space $x_0>t_0$,
where $\mbox{supp\ }\varphi_k(x)\subset\overline\Omega_{int},\ k=0,1$.  Then
$u(t_0,x)=u_{x_0}(t_0,x)=0$  when $x\in \Omega_{ext}$.  Applying the estimate (\ref{eq:2.7})
  we get that $u(x_0,x)=0$  in $\Omega_{ext}\times(t_0,+\infty)$.
Therefore $\mbox{supp\ }u(x_0,x)\subset \overline{\Omega}_{int}\times[t_0,+\infty)$,  i.e.
$D_+(\Omega_{int}\times\{x_0=t_0\})\subset\overline{\Omega}_{int}\times\R$  for any $t_0$,
i.e.  $\Omega_{int}\times\R$  is a black hole.

Analogous result holds for the white hole.
\begin{theorem}(cf., for example, [E4]).                               \label{theo:2.4}
Let (\ref{eq:2.4}) and (\ref{eq:2.6}) hold.   Then for any solution
$u(x_0,x)$  of (\ref{eq:1.1})  we have
\begin{equation}                                           \label{eq:2.8}
\|u(x_0,\cdot)\|_{1,\Omega_{int}}^2 +
\|u_{x_0}(x_0,\cdot)\|_{0,\Omega_{int}}^2
\leq
C_T(\|u(t_0,\cdot)\|_{1,\Omega_{int}}^2 +
\|u_{x_0}(t_0,\cdot)\|_{0,\Omega_{int}}^2),
\end{equation}
where  $T$  is arbitrary, $t_0\leq x_0\leq T$.
\end{theorem}
As in the case of Theorem \ref{theo:2.3}  the estimate (\ref{eq:2.8})  implies that
$D_+(\Omega_{ext}\times\{x_0=t_0\})\subset\overline{\Omega}_{ext}\times\R$,
i.e. $\Omega_{int}\times\R$  is a white hole.

\section{The ergosphere.}
\label{section 3}
\init

The ergosphere is the surface $S(x)=0$  where
\begin{equation}                                   \label{eq:3.1}
g_{00}(x)=0.
\end{equation}
We assume that $S(x)=0$  is a closed smooth surface,
$g_{00}(x)>0$  in the exterior of $S(x)=0$  and $g_{00}(x)<0$  in the interior
of $S(x)=0$  near $S(x)=0$.
We say  that $S(x)=0$  is a smooth  surface  if  $S_x(x)\neq 0$  when  $S(x)=0$.

Let $\Delta(x)=\det[g^{jk}(x)]_{j,k=1}^n$.
It is easy to show  (cf. [E1])
that $g_{00}(x)=0$  if and only if $\Delta(x)=0$.  In the case of the Gordon equation
(cf. (\ref{eq:1.4}))
the equation of the ergosphere
is
\begin{equation}                                       \label{eq:3.2}
|w(x)|^2=\frac{c^2}{n^2(x)}.
\end{equation}
Note that $(0,\xi)$  is not a characteristic direction for (\ref{eq:1.1})
for any $\xi\neq 0$  when $g_{00}(x)>0$.
It may happen that the ergosphere $S(x)=0$  is also a characteristic surface,  i.e.
$\{S(x)=0\}\times\R$  is an event horizon.  The celebrated example of such situation is
the Schwarzschield black hole.  The Schwarzchield  metric has the following form in
the Cartesian coordinates (cf. [V2]):
\begin{equation}                                        \label{eq:3.3}
ds^2=(1-\frac{2m}{R})dt^2-dx^2-dy^2-dz^2-\frac{4m}{R}dtdR-\frac{2m}{R}(dR)^2,
\end{equation}
where $R=\sqrt{x^2+y^2+z^2}$.  Therefore
\begin{equation}                                           \label{eq:3.4}
g_{00}=1-\frac{2m}{R}=0
\end{equation}
is the ergosphere.  Note that $R=2m$  is also  a characteristic surface and $\{R=2m\}\times\R$
is a black hole.  We shall call the black hole such that the ergosphere is also an event horizon
the Schwarzschield type black holes.

Note that Schwarzschield  type black holes is unstable with respect to the perturbations of
metrics (see \S 5 below).  If we perturb the metric the ergosphere persists since we assume
that the equation (\ref{eq:3.1}) is smooth,  i.e.  it has a non-vanishing normal at any point.
However the perturbed surface may cease to be a characteristic
surface and there is no characteristic surface near by (cf. \S 5).

It is easier to study the behavior of the solutions of (\ref{eq:1.1}) in the exterior of
the Schwarzschield type black hole
than in the case when the black hole is inside the ergosphere.  For example,
an important problem in the general relativity studied in [DR]  is the uniform boundedness
of solutions of (\ref{eq:1.1}) in the exterior of the black hole.  Using the ideas from
[DR]  one can prove the following theorem:
\begin{theorem}(cf. [E3])                                         \label{theo:3.1}
Let $\{S_0(x)=0\}\times\R$  be the ergosphere and the boundary of a black hole,
$S_{0x}(x)\neq 0$  when  $S_0(x)=0$.
Consider the Cauchy problem for (\ref{eq:1.1})  in the exterior $\Omega_{ext}\times(0,+\infty)$  of
the black hole with the initial conditions
$$
u(0,x)=\varphi_0,\ \ u_{x_0}(0,x)=\varphi_1(x),\ \ x\in\Omega_{ext},
$$
where $\varphi_0(x),\varphi_1(x)$  are smooth and rapidly
decaying when $|x|\rightarrow\infty$.
Then $u(x_0,x)$  is uniformly bounded in $\Omega_{ext}\times(0,+\infty)$:
\begin{equation}                                             \label{eq:3.5}
|u(x_0,x)|\leq C.
\end{equation}
\end{theorem}

 \section{The case of two space dimensions.}
\label{section 4}
\init

Let $S$  be an ergosphere,  i.e. $\Delta(x)=g^{11}(x)g^{22}(x)-(g^{12}(x))^2=0, \ x=(x_1,x_2)\in \R^2$.
We assume that $S$  is a smooth Jordan curve.  Let $S_1$  be another closed Jordan curve
inside $S$.  Denote by $\Omega$  the region between $S$  and $S_1$.  We assume that
$\Delta(x)<0$  in $\overline{\Omega}\setminus S$.  Let $K_+(y)$  be the half-cone of all forward
time-like
directions at $y\in S_1$,  i.e. $K_+(y)=\{(\dot{x}_0,\dot{x}_1,\dot{x}_2)\in \R^3:
\sum_{j,k=0}^2 g_{jk}(y)\dot{x}_j\dot{x}_k>0,\dot{x}_0>0\}$.  Let
$N(y)$  be the outward normal to $S_1$.  We assume that either
\begin{eqnarray}                               \label{eq:4.1}
(\dot{x}_0,\dot{x}_1,\dot{x}_2)\cdot (0,N(y))>0
\\
\mbox{or}
\nonumber
\\
\nonumber
(\dot{x}_0,\dot{x}_1,\dot{x}_2)\cdot (0,N(y))<0
\end{eqnarray}for all $y\in S_1$  and all $(\dot{x}_0,\dot{x}_1,\dot{x}_2)\in \overline K_+(y)$.

{\bf Remark 4.1}
The interior of $S_1$  is called a trapped region if \\
$(\dot{x}_0,\dot{x}_1,\dot{x}_2)\cdot(0,N(y))<0$
for all $y\in S_1$  and $(\dot{x}_0,\dot{x}_1,\dot{x}_2)\in \overline{K}_+(y)$.

The main result of [E2]  is the following theorem:
\begin{theorem}                                                \label{theo:4.1}
Suppose the ergosphere $S$  is not characteristic for any $x\in S$,  i.e.
\begin{equation}                                             \label{eq:4.2}
\sum_{j,k=1}^2g^{jk}(x)\nu_j(x)\nu_k(x)\neq 0,\ \ \forall x\in S,
\end{equation}
where $\nu(x)=(\nu_1(x),\nu_2(x))$  is the normal to $S$ at $x\in S$.
Suppose
the condition (\ref{eq:4.1})  is satisfied on $S_1$.  Then there exists a smooth Jordan curve
$S_0(x)=0$  between $S$  and $S_1$  such that $\{S_0(x)=0\}\times \R$  is a characteristic surface,
i.e. $\{S_0(x)=0\}\times R$  is an event horizon.
\end{theorem}

\underline{Sketch of the proof of Theorem \ref{theo:4.1}}.
\\
\\
Since $\Delta(x)<0$  in $\Omega$  there exist two families
$S^\pm(x)=\mbox{const} $
of characteristic curves
$$
\sum_{j,k=1}^2g^{jk}(x)S_{x_j}^\pm(x)S_{x_k}^\pm(x)=0.
$$
One can construct two vector fields $f^\pm(x)=(f_1^\pm(x),f_2^\pm(x))$  on $\overline{\Omega}$
such that $f^\pm(x)\neq (0,0)$  for all $x\in \overline{\Omega},\ f^+(x)\neq f^-(x)$
on $\overline{\Omega}\setminus S,\ f^+(x)= f^-(x)$  on $S$ and
\begin{equation}                               \label{eq:4.3}
f_1^\pm(x)S_{x_1}^\pm (x)+f_2^\pm(x)S_{x_2}^\pm(x)=0 \ \ \mbox{in}\ \ \overline{\Omega}.
\end{equation}
Consider two systems of differential equations:
\begin{equation}                                  \label{eq:4.4}
\frac{dx^\pm(\sigma)}{d\sigma}=f^\pm (x(\sigma)),\ \ \sigma\geq 0,\ \ x^\pm(0)=y\in S.
\end{equation}
Let
\begin{eqnarray}                                     \label{eq:4.5}
\frac{dx_j(s)}{ds}=2\sum_{k=0}^2 g^{jk}(x(s))\xi_k(s),\ \ x_j(0)=y_j,\ \ 0\leq j\leq 2,
\\
\nonumber
 \frac{d\xi_p(s)}{ds}=-\sum_{j,k=0}^2 g_{x_p}^{jk}(x(s))\xi_j(s)\xi_k(s),\ \ \xi_p(0)=\eta_p,
\ \ 0\leq p\leq 2,
\end{eqnarray}
be the equations of null-bicharacteristics for (\ref{eq:1.1}).
Note that $\frac{d\xi_0(s)}{ds}=0$,  i.e.  $\xi_0(s)=\eta_0$  for all $s\geq 0$
and we take $\eta_0=0$.
Therefore (\ref{eq:4.5})  is a null-bicharacteristic  if $\sum_{j,k=1}^2 g^{jk}(y)\eta_j\eta_k=0$.

It can be shown that the curves $x=x^\pm(\sigma)$  of (\ref{eq:4.4}) are the projections on
$(x_1,x_2)$-plane of some forward null-bicharacteristics.  Since $\frac{dx_0(s)}{ds}\neq 0$  on
these bicharacteristics we can use $x_0$  as a parameter instead of $\sigma$.  It appears that
for one family (say $x=x^+(\sigma)$)  $\sigma$ is decreasing when $x_0$  is increasing and
for another family ($x=x^-(\sigma)$)  $\sigma$  is increasing when $x_0$  is increasing.

The condition (\ref{eq:4.1})
is equivalent to the condition that the projections on
$(x_1,x_2)$-plane of all forward null-bicharacteristics are either leaving $\Omega$  when $x_0$ is
increasing or are entering $\Omega$ when $x_0$  is increasing.
Suppose for the definiteness that the projections of all null-bicharacteristics are leaving $\Omega$
when $x_0$  is increasing.  Then the trajectory $x=x^-(\sigma)$  starting on $S$ can not
 reach $S_1$ (cf. [E2]).
Therefore by the Poincare-Bendixson theorem there exists a limit cycle $S_0(x)=0$,  i.e.
a closed Jordan curve in $\Omega$  that is a characteristic curve.  Therefore
$\{S_0(x)=0\}\times\R$  is an event horizon,  i.e. a boundary of either black or white hole.

{\bf Remark 4.2}
Since conditions (\ref{eq:4.1}),  (\ref{eq:4.2})  hold  when we slightly perturb the metric
the black and white holes obtained by Theorem \ref{theo:4.1} are stable.

{\bf Example 4.1}  (cf.  [V1])  Consider the acoustic equation with
the metric (\ref{eq:1.5})
when $n=2,\ \rho=c=1$,
\begin{equation}                                   \label{eq:4.6}
v(x)=(v^1(x),v^2(x))=\frac{A}{r}\hat r+\frac{B}{r}\hat\theta,
\end{equation}
where $r=|x|=\sqrt{x_1^2+x_2^2},\ \hat r=\frac{x}{|x|},\ \hat\theta=(-\frac{x_2}{|x|},\ \frac{x_1}{|x|}),\
A>0,\ B>0$  are constants.  We assume that $\sqrt{A^2+B^2}\geq |x|>r_1$,  where $r_1<A$.
The ergosphere in this case is $r=\sqrt{A^2+B^2}$.  The differential equations (\ref{eq:4.4}) have
the following form in the polar coordinates $(r,\theta)$:
\begin{equation}                                          \label{eq:4.7}
\frac{dr}{ds}=A^2-r^2,\ \ \frac{d\theta}{ds}=\frac{AB}{r}+\sqrt{A^2+B^2-r^2},
\end{equation}
and
\begin{equation}                                          \label{eq:4.8}
\frac{dr}{ds}=-1,\ \ \frac{d\theta}{ds}=\frac{1-\frac{B^2}{r^2}}{\frac{AB}{r}+\sqrt{A^2+B^2-r^2}}.
\end{equation}
It follows from (\ref{eq:4.7}) that $r=A$  is a limit cycle and $\{r<A\}\times\R$  is a white hole.

{\bf Example 4.2}  Consider the same situation as in Example 4.1
with $B=0$  and the domain $r<A$.  Then $r=A$  is the ergosphere and $\{r=A\}\times\R$  is the event horizon.
Since $A>0$  we have that $\{r<A\}\times \R$ is a white hole.  Note that the equations (\ref{eq:4.4}) have
the following form in the polar coordinates:
\begin{equation}                                        \label{eq:4.9}
\frac{dr}{d\theta}=\pm\sqrt{A^2-r^2},\ \ r(\theta_0)=A.
\end{equation}
It has a solution $r=A$,  which is   the event horizon,  and it  also has other solutions
$r=A\cos(\theta-\theta_0)$  that touch the event horizon at $\theta=\theta_0$.  In
general situation when the
ergosphere coincides with the event
horizon  the solution of (\ref{eq:4.4}) are also tangent to the event horizon.

{\bf Remark 4.3}
When $B\neq 0$  is small
Example 4.1 can be viewed as a perturbation of Example 4.2.  Note that when $B$  is small
the stable event horizon $r=A$  will be close to the ergosphere $r=\sqrt{A^2+B^2}$.
 A similar situation will happen in the general case:

If the left hand side of the
condition (\ref{eq:4.2}) is small then the stable event horizon obtained in Theorem \ref{theo:4.1}
will be close to the ergosphere $S$.  If the left hand side of (\ref{eq:4.2}) changes sign on $S$
(for example, if $B$ in (\ref{eq:4.6}) depends on $\theta$  and changes sign when
$0\leq \theta\leq 2\pi$)  there will be no event horizon near $S$.

\section{Axisymmetric metrics and rotating black holes.}
\label{section 5}
\init

Let $(\rho,\varphi,z)$  be the cylindrical coordinates in $\R^3$:
\begin{equation}                                \label{eq:5.1}
x=\rho\cos\varphi,\ \ y=\rho\sin\varphi,\ \ z=z.
\end{equation}
A stationary axisymmetric metric in $\R^3\times\R$  is the metric that does not depend on
$t$  and $\varphi$.
For the convenience,  we shall use the following notations:
\begin{equation}                                  \label{eq:5.2}
y_0=t,\ \ y_1=\rho,\ \ y_2=z,\ \ y_3=\varphi.
\end{equation}
Then the stationary axisymmetric metric has the form:
\begin{equation}                                  \label{eq:5.3}
ds^2=\sum_{j,k=0}^3g_{jk}(\rho,z)dy_jdy_k,
\end{equation}
where $g_{jk}(\rho,z)$  are smooth and even in $\rho$.  Denote
$$
[g^{jk}(\rho,z)]_{j,k=0}^3=\left([g_{jk}(\rho,z)]_{j,k=0}^3\right)^{-1}.
$$
The ergosphere is given by the equation
\begin{equation}                                 \label{eq:5.4}
g_{00}(\rho,z)=0,
\end{equation}
or,  equivalently:
\begin{equation}                                     \label{eq:5.5}
\Delta(\rho,z)=\det [g^{jk}(\rho,z)]_{j,k=1}^3=0.
\end{equation}

We will be looking for the rotating black and white holes,  i.e.  when the event horizon
has the form:
\begin{equation}                                       \label{eq:5.6}
\{S(\rho,z)=0\}\times S^1\times\R,
\end{equation}
where  $S(\rho,z)=0$  is a closed smooth curve in the $(\rho,z)$-plane,  even in $\rho,
\ \varphi\in S^1,\ t\in \R,\ S^1$  is the unit circle.  More precisely,  we have to take
in (\ref{eq:5.5})  the restriction of the curve $S(\rho,z)=0$  to the half-plane $\rho\geq 0$
but we did not indicate this in (\ref{eq:5.6})  for the simplicity of notation.  Since
(\ref{eq:5.6})  is the event horizon it must be a characteristic surface,  i.e.
\begin{equation}                                     \label{eq:5.7}
\sum_{j,k=1}^2g^{jk}(\rho,z)S_{y_j}(\rho,z)S_{y_k}(\rho,z)=0\ \ \ \mbox{on}\ \ S(\rho,z)=0.
\end{equation}
Here $y_1=\rho,\ y_2=z$.  Therefore
$\{S(\rho,z)=0\}\times\R$  is  the event horizon for the tensor
$[g^{jk}(\rho,z)]_{j,k=0}^2$,  i.e.  for the case of two dimensions considered in the previous section.

Define
\begin{equation}                                         \label{eq:5.8}
\Delta_1(\rho,z)=\det [g^{jk}(\rho,z)]_{j,k=1}^2
=g^{11}(\rho,z)g^{22}(\rho,z)-(g^{12}(\rho,z))^2.
\end{equation}
We shall call the curve $\Delta_1(\rho,z)=0$  the restricted ergosphere since it is the ergosphere
of the two-dimensional
problem for $[g^{jk}(\rho,z)]_{j,k=0}^2$.  We can extend all results of \S 4 to the case of rotating
black and white holes.  For example,
let the curve $\Delta_1(\rho,z)=0$  be a Jordan curve  such that
$$
\sum_{j,k=1}^2 g^{jk}(\rho,z)\nu_j(\rho,z)\nu_k(\rho,z)\neq 0 \ \ \mbox{on}\ \ \Delta_1(\rho,z)=0,
$$
and let $S_1$  be a Jordan curve inside $\Delta_1(\rho,z)=0$.

Suppose  conditions (\ref{eq:4.1})  are satisfied where the matrix $[\tilde g_{jk}(\rho,z)]_{j,k=0}^2$
is the inverse to $[g^{jk}(\rho,z)]_{j,k=0}^2$.  Then there exists a Jordan curve $S_0(\rho,z)=0$
between $\Delta_1=0$  and $S_1$  such that $\{S_0(\rho,z)=0\}\times S^1\times \R$ is the event
horizon in $\R^3\times \R$.

Consider now the problem of the stability of the black and white holes with respect to
the perturbations of metrics.

The famous example of an axisymmetric metric is the Kerr metric.
The Kerr metric  in the Kerr-Schild coordinates has the  form (see [V2]):
\begin{eqnarray}                                          \label{eq:5.9}
ds^2=dt^2-dx^2-dy^2-dz^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\\
\nonumber
-\ \ \frac{2mr^3}{r^4+a^2z^2}
\left[dt+\frac{r(xdx+ydy)}{r^2+a^2}+
\frac{a(ydx-xdy)}{r^2+a^2}
+\frac{z}{r}dz\right]^2,
\end{eqnarray}
where
\begin{equation}                               \label{eq:5.10}
r(x,y,z)=\sqrt{\frac{(R^2-a^2)+\sqrt{(R^2-a^2)^2+4a^2z^2}}{2}},\ \ R^2=x^2+y^2+z^2.
\end{equation}
It follows from (\ref{eq:5.4})  and (\ref{eq:5.9}) that the ergosphere is
\begin{equation}                               \label{eq:5.11}
r^4+a^2z^2-2mr^3=0.
\end{equation}
One  can  show   that (\ref{eq:5.11}) consists of two curves  in $(\rho,z)$-plane
\begin{equation}                                \label{eq:5.12}
r-\left(m+\sqrt{m^2-\frac{a^2z^2}{r^2}}\right)=0,
\end{equation}
\begin{equation}                                \label{eq:5.13}
r-\left(m-\sqrt{m^2-\frac{a^2z^2}{r^2}}\right)=0,
\end{equation}
Equation (\ref{eq:5.12})  defines the outer ergosphere and (\ref{eq:5.13})  defines the inner
ergosphere  for the Kerr metric.

Compute the restricted ergosphere $\Delta_1(\rho,z)$ (cf. (\ref{eq:5.8})) for the Kerr metric.
The inverse to the Kerr metric tensor has the form:
\begin{equation}                              \label{eq:5.14}
\eta^{jk}+\frac{2mr^3}{r^4+a^2z^2}l^jl^k,
\end{equation}
where
$$
(l^0,l^1,l^2,l^3)=\left(-1,\frac{rx+ay}{r^2+a^2},\frac{ry-ax}{r^2+a^2},\frac{z}{r}\right).
$$
 In  the $(\rho,z,\varphi)$  coordinates we have
\begin{equation}                              \label{eq:5.15}
g^{jk}(\rho,z)=\xi^{jk}+\frac{2mr^3}{r^4+a^2z^2}m^jm^k,
\end{equation}
where  $(m^0,m^1,m^2,m^3)=\left(-1,\frac{r\rho}{r^2+a^2},\frac{z}{r},\frac{-a}{r^2+a^2}\right),\
\xi^{jk}$  is $\eta^{jk}$  in the cylindrical coordinates,
$\xi^{00}=1,\ \xi^{11}=\xi^{22}=-1,\ \xi^{33}=-\frac{1}{\rho^2},\
\xi^{jk}=0$  for $j\neq k$.
Therefore
\begin{equation}                                  \label{eq:5.16}
\Delta_1(\rho,z)=1-\frac{2mr^5\rho^2}{(r^4+a^2z^2)(r^2+a^2)^2}
-\frac{2mrz^2}{r^4+a^2z^2}.
\end{equation}
The equation $\Delta_1=0$  for the Kerr metric can be substantially simplified.

\begin{pro}(cf. [E3])                                       \label{prop:5.1}
The equation $\Delta_1(\rho,z)=0$  is equivalent
to two equations $r-r_+=0$ and $r-r_-=0$  where
$r_\pm=m\pm\sqrt{m^2-a^2}$.
\end{pro}
It happens that $r=r_\pm$  are two event horizons,  $r-r_+=0$  is called the outer event horizon and
$r-r_-=0$  is  the inner event horizon.  More exactly, $\{r=r_\pm\}\times S^1\times \R$
 are the event horizons.
Therefore $\Delta_1(\rho,z)=0$  relates explicitly the event horizons of the Kerr metric to
the metric tensor.

{\bf Definition 5.1}
Let $\{\psi=0\}\times S^1\times\R$  be the event horizon for the metric $[g_{jk}]_{j,k=0}^3$.
We say that this event horizon is stable in the class of axisymmetric metrics if any smooth
family $[g_{\e jk}]$  of axisymmetric metrics, $0\leq \e\leq\e_0,\ g_{0jk}=g_{jk}$,  has a smooth
family of event horizons $\{\psi_\e=0\}\times S^1\times\R$  such that
$\psi_0=\psi$.  Otherwise we say that $\{\psi=0\}\times S^1\times\R$  is
an unstable event horizon.

We restrict perturbations to a more narrow class of  axisymmetric metrics of the form:
\begin{equation}                                   \label{eq:5.17}
g_\e^{jk}=\xi^{jk}+v_\e^j(\rho,z)v_\e^k(\rho,z).
\end{equation}
Note that the Kerr metric and the metrics (\ref{eq:1.4}), (\ref{eq:1.5})
have the form (\ref{eq:5.17}).

\begin{pro}(cf. [E3])                                          \label{prop:5.2}
Let $\Delta_1=0$  be the restricted ergosphere,  and let $\Delta_1=0$
be a characteristic  curve, i.e.
$\{\Delta_1=0\}\times S^1\times \R$  is an event horizon.
Then this event horizon is unstable when we consider perturbations
in the class of the metrics of the form (\ref{eq:5.17}).
In particular,  the outer and the inner event horizons for the Kerr metric are unstable.
\end{pro}

\underline{Sketch of the proof of Proposition \ref{prop:5.2}.}
\\
\\
Denote $\Delta_1^\e=g_\e^{11}g_\e^{22}-(g_\e^{12})^2$.  Then $\Delta_1^\e =0$  is a smooth perturbation
of restricted ergosphere,  $\Delta_1^0=\Delta_1$.   We can choose perturbations of the form
 (\ref{eq:5.17})  such that $\Delta_1^\e=0$  will not be a characteristic curve  for $0< \e\leq \e_0$.
Moreover,  one
can choose $[g_{\e jk}]$  such that there is no characteristic curve near $\Delta_1^\e=0$ (cf. [E3]).

In the next proposition we shall prove that there  is a rich class of perturbations
$[g_{\e jk}],\ 0\leq\e\leq \e_0,$  of the Kerr metric that have a smooth family  of event horizons
$\{\Delta_1^\e=0\}\times S^1\times\R$  such that $\{\Delta_1^0=0\}\times S^1\times \R$  is the Kerr
event horizon.

\begin{pro}(cf. [E3])                                    \label{prop:5.3}
Let $\Delta_1=0$  be a restricted ergosphere and $\{\Delta_1=0\}\times S^1\times \R$  is an event horizon.
Let $\Delta_1^\e=0$  be arbitrary family of closed, even in $\rho$,  smooth curves,  $0\leq \e\leq \e_0$,
such  that $\Delta_1^0=\Delta_1$.
Then there exists a family of metrics $[g_{\e jk}],\ 0\leq \e\leq \e_0,\ [g_{0jk}]=[g_{jk}]$,
of the form  (\ref{eq:5.17})  such that $\Delta_1^\e=0$  are restricted ergospheres for $[g_{\e jk}]$  and
$\{\Delta_1^\e=0\}\times S^1\times\R$ are event horizons for $[g_{\e jk}]$.
\end{pro}

{\bf Remark 5.1}
We shall call the event horizons obtained in Theorem \ref{theo:4.1}  the stable event horizons and
the event horizons
that coincide with $\{\Delta_1=0\}\times S^1\times\R$  the Schwarzschield type event horizons.
According to this definition the Kerr event horizon is a Schwarzschield type event horizon.

Fix some axisymmetric
metric $[g_{jk}]$ that has a Schwarzschield type event horizon $\{\Delta_1= 0\}\times S^1\times\R$.
The proposition \ref{prop:5.3}  shows that in any neighborhood of $[g_{jk}]$  there are metrics having
Schwarzschield type event horizons close  to $\{\Delta_1=0\}\times S^1\times \R$.  Also it follows
from the Remark 4.3  that in any neighborhood of $[g_{jk}]$  (in particular,  in any neighborhood of
the Kerr metric)  there are stable event horizons close to $\{\Delta_1=0\}\times S^1\times \R$.

\section{Determination of the ergosphere by the boundary measurements.}
\label{section 6}
\init

Let $u(x_0,x)$  be the solution of (\ref{eq:1.1})  in a cylinder $\Omega\times \R$  satisfying
the zero initial
conditions
\begin{equation}                                              \label{eq:6.1}
u=0\ \ \ \mbox{for}\ \ x_0\ll 0,\ \ x\in \Omega,
\end{equation}
and the boundary condition
\begin{equation}                                            \label{eq:6.2}
u|_{\partial\Omega\times\R}=f.
\end{equation}
Here $\Omega$  is a smooth bounded domain in $\R^n, \ f$  is a smooth function with a compact
support in $\partial\Omega\times\R$.  The solution of the initial-boundary problem (\ref{eq:1.1}),
(\ref{eq:6.1}),  (\ref{eq:6.2})  exists and is unique assuming that $\partial\Omega\times\R$  is not
characteristic at any point  and $g^{00}(x)>0$  on $\overline{\Omega}$.

Denote by $\Lambda f$  the following operator (the DN operator):
\begin{equation}                                    \label{eq:6.3}
\Lambda f=\sum_{j,k=1}^ng^{jk}(x)\frac{\partial u}{\partial x_j}\nu_k(x)\left.\left(\sum_{p,r=1}^n
g^{pr}(x)\nu_p\nu_r\right)^{-\frac{1}{2}}\right|_{\partial\Omega\times\R},
\end{equation}
where
$(\nu_1(x),...,\nu_n(x))$
is the  outward unit normal to $\partial\Omega$.
Let $\Gamma$  be an open subset of $\partial\Omega$.  We say that boundary measurements on
$\Gamma\times(0,T)$  are taken if we know $\Lambda f$  on $\Gamma\times(0,T)$  for all
$f$ with support in  $\overline{\Gamma}\times[0,T]$.

The inverse boundary value problem is the determination of $[g^{jk}(x)]_{j,k=0}^n$  knowing
the boundary measurements on $\Gamma\times(0,T).$
Let
\begin{equation}                                          \label{eq:6.4}
\hat x=\varphi(x),\ \ \hat x_0=x_0+a(x),
\end{equation}
where  $\hat x=\varphi(x)$  is a diffeomorphism of $\overline\Omega$  onto a new domain $\overline\Omega,
\ a(x)\in C^\infty(\overline\Omega)$.  We assume that
\begin{equation}                                          \label{eq:6.5}
\varphi(x)=x \ \ \mbox{on}\ \ \overline\Gamma,\ \ a(x)=0 \ \ \mbox{on} \ \ \overline\Gamma.
\end{equation}
Note that (\ref{eq:6.4})  transform (\ref{eq:1.1})  to an equation of the same form with
a new tensor $[\hat g^{jk}(\hat x)]_{j,k=0}^n$  isometric to the old one.   It follows from
(\ref{eq:6.5})  that DN operator $\Lambda$  does not change under the change of variables
(\ref{eq:6.4}),  (\ref{eq:6.5}).  If there exists an event horizon inside $\Omega\times\R$  then
we can not determine the metric inside the event horizon  since any change of metric inside
the event horizon will not change boundary measurements. But we can try to recover the event
horizon itself (up to diffeomorphism (\ref{eq:6.4}),  (\ref{eq:6.5})).

This is an open problem.  We can prove only  that the boundary measurements allow to determine
the ergosphere.

\begin{theorem}(cf. [E3])                                               \label{theo:6.1}
Consider the wave equation (\ref{eq:1.1}).  Assume that $g^{00}(x)>0$  on
$\overline\Omega$  and the normal to $\partial\Omega$  is not characteristic
at any point of $\partial\Omega$.
Let $\Delta(x)=0$  be the ergosphere,  $\Delta(x)=0$  is a smooth closed surface,
$\Delta(x)>0$  in $\overline{\Omega}$  outside of $\Delta(x)=0$.  Let $\Gamma$  be
an open subset of $\partial\Omega$.  Then the boundary measurements on $\Gamma\times(0,+\infty)$
determine $\Delta(x)=0$ up to the change of variables (\ref{eq:6.4}),  (\ref{eq:6.5}).
\end{theorem}
Note that for the proof of Theorem \ref{theo:6.1} it does not matter
whether the ergosphere is an event horizon or not.  The proof
is an extension of the proof of Theorem 2.3 in [E1].

 We will determine the ergosphere  by determining
 the metric in
$\overline\Omega\cap\overline\Omega_{ext}$,   where $\overline\Omega_{ext}$ is
the exterior  of $\Delta(x)=0$.

We start with the determination of the metric in a small neighborhood of $\Gamma$ and
gradually continue to recover the metric deeper in $\Omega$.  As we progress the time interval
$(0,T)$  needed to reach the point $x\in\Omega$  increases when the point approaches the ergosphere.
One can show that $T\rightarrow +\infty$  when $x\rightarrow\{\Delta(x)=0\}$.  This is the reason why
one needs the unlimited time interval $(0,+\infty)$  to recover the ergosphere.

{\bf Remark 6.1}  Let $L(x,\frac{\partial}{\partial x},\frac{\partial}{\partial x_0})u(x_0,x)=0$
be the equation (\ref{eq:1.1})  in $\R^{n+1}$.  Making the Fourier transform in $x_0$  we get
\begin{equation}                                       \label{eq:6.6}
L(x,\frac{\partial}{\partial x},ik)\tilde u(k,x_0)=0,\ \ x\in \R^n.
\end{equation}
Suppose that
\begin{equation}                                       \label{eq:6.7}
L(x,\frac{\partial}{\partial x},ik)=-\Delta-k^2\ \ \ \mbox{for}\ \ |x|>R.
\end{equation}
Let $a(\theta,\omega,k)$  be the scattering
amplitude for the operator (\ref{eq:6.6}).  It is well known that the scattering amplitude given for all
$k>0,\ \theta\in S^{n-1},\ \omega\in S^{n-1},$
determines the DN operator on the $\{|x|=R\}\times[0,+\infty)$.  Therefore by the Theorem \ref{theo:6.1}
the scattering amplitude determines the ergosphere. Note that when (\ref{eq:6.7}) holds $a(\theta,\omega,k)$
is real analytic in $(\theta,\omega,k)$.  Therefore it is enough to know $a(\theta,\omega,k)$ in
an arbitrary neighborhood of some point $(\theta_0,\omega_0,k_0)$  to determine the ergosphere.

redpajama_set_name: RedPajamaArXiv


Listening to U.S. journalists demand to know what the Obama Administration is doing about Libya is growing tiresome.
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Palm Springs has underwhelmed me so far in my travels out to the desert. So many of the courses are unimaginative romps through housing developments. When I research courses on the internet, the best ones, to my eye, are the private ones nestled right up next to the mountains. Well, all things Palm Springs turned around for me in a big way playing La Quinta's Mountain course. The best course I have played in Palm Springs and one of the most scenic courses I have ever played is this one and one you have to play post haste.
The first hole starts you off in Dye land. Not too long but full of treachery either going left or going too long right into the humps.
To say that the course nestles up to the mountains for a long kiss and some scotch is an understatement. The mountains influence everything from putts to views and it is some of the most stunning scenery in Palm Springs or anywhere else.
but these aren't penal flourishes and in fact make for a really fun golf day.
The front 9 is wide open with no houses, fantastic conditioning and many holes run up against the mountains. It was super surprising how fun the front 9 is and each tee shot gives you a lot fo visually chew on.
Water is definitely a factor here and my advice is to steer well clear from it as the fairways and even the waste area bunkers are subtly sloped toward the water.
The less that is said about holes 10-13 the better. Forced to thread their way through the La Quinta housing development, the holes offer some of the claustrophobic ridiculousness that Palm Springs gives more times than not. There is a beautiful tree though so there's that.
With no sense of fairways and pot bunkers everywhere you are faced with an uncertain tee shot and definitely an uncertain second shot with a potential gully eating your ball.
All of this leads up to a green that is one of the most beautiful sights you have ever seen.
This is all prelude to the 15th, a long par 5 that parallels the mountains.
The real beauty of this hole comes into focus from above, in what is perhaps the most oft photographed hole in all of the La Quinta resort.
16 is a shorter par 3 that has a sea of green amidst a sea of rocks. Visually, there is nothing quite like it, at east in SoCal.
17 and 18 are really fun and challenging holes with a par 4 and a par 5 to close it out.
The only negative of the round was the pace of play. There were plenty of marshals but little marshaling. For a Saturday at high season, its not surprising but otherwise the round was fantastic.
Overall, this course was a surprise in all the best possible ways. I have always viewed Palm Springs with a lot of trepidation but now I am looking forward to going back and playing this course.


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Q: Creating Linux Virtual Machine in Azure from Image in Powershell I want to be able to create a new Azure Virtual Machine using Powershell with a custom image.  This custom image is in Azure Storage Account X and the new Virtual Machine will be created using Azure Storage Account Y.  When I run these commands to create the new Virtual Machine:
Set-AzureSubscription -CurrentStorageAccount $StorageAccount -SubscriptionName $SubscriptionName

New-AzureVMConfig -Name $MachineName -InstanceSize $InstanceSize -ImageName $Image |
    Add-AzureProvisioningConfig -Linux -LinuxUser $LinuxUser -Password $AdminPassword |
    Set-AzureSubnet $subNet |
    New-AzureVM -ServiceName $MachineName -VNetName $VNet -ErrorVariable errs

where $Image is the custom image in Storage Account X and CurrentStorageAccount set to Y for the Subscription, I get the following error:
The disk's VHD must be in the same account as the VHD of the source image

If the custom image is in Storage Account Y the commands to create the new Virtual Machine work correctly.
Can an Azure Virtual Machine be created when the image is in a different Storage Account?

A: Apparently not.  However, you could copy the image from storage account X to storage account Y before you create the new VM.  It would only add a few more lines to your script.
Here is an example:
http://michaelwasham.com/windows-azure-powershell-reference-guide/copying-vhds-blobs-between-storage-accounts/