text:
package com.client.vote;

import java.security.SecureRandom;
import java.util.ArrayList;
import java.util.Random;

import org.apache.http.NameValuePair;
import org.apache.http.message.BasicNameValuePair;
import org.json.JSONObject;

import android.app.Activity;
import android.app.AlertDialog;
import android.content.Context;
import android.content.DialogInterface;
import android.content.Intent;
import android.content.SharedPreferences;
import android.os.Bundle;
import android.preference.PreferenceManager;
import android.util.Log;
import android.view.LayoutInflater;
import android.view.View;
import android.widget.CheckBox;
import android.widget.EditText;
import android.widget.Toast;

import com.client.vote.common.SimpleHttpClient;

public class RegisterActivity extends Activity {
	private CheckBox agree;

	@Override
	public void onCreate(Bundle savedInstanceState) {
		super.onCreate(savedInstanceState);
		setContentView(R.layout.sign_up);
		SharedPreferences preferences = PreferenceManager.getDefaultSharedPreferences(this);
		preferences.edit().clear().commit();
	}

	public void regret(View view) {
		Intent intent = new Intent(this, RegretActivity.class);
		startActivity(intent);
	}

	public void verification(View view) {
		final EditText cid = (EditText) findViewById(R.id.signup_username);
		final EditText password = (EditText) findViewById(R.id.signup_password);
		final EditText email = (EditText) findViewById(R.id.register_email);
		agree = (CheckBox) findViewById(R.id.agree_terms);

		String chars = "0123456789";
		final int PW_LENGTH = 5;
		Random rnd = new SecureRandom();
		StringBuilder pass = new StringBuilder();
		for (int i = 0; i < PW_LENGTH; i++) {
			pass.append(chars.charAt(rnd.nextInt(chars.length())));
		}
		Log.i("otp password", pass.toString());
		final String otp = pass.toString();
		new LongRunningGetIO(email.getText().toString(), otp).execute();
		final Context context = this;
		LayoutInflater li = LayoutInflater.from(context);
		View promptsView = li.inflate(R.layout.prompts, null);
		AlertDialog.Builder alertDialogBuilder = new AlertDialog.Builder(context);
		// set prompts.xml to alert dialog builder
		alertDialogBuilder.setView(promptsView);
		final EditText userInput = (EditText) promptsView.findViewById(R.id.editTextDialogUserInput);
		// set dialog message
		alertDialogBuilder.setCancelable(false).setPositiveButton("OK",
				new DialogInterface.OnClickListener() {
			public void onClick(DialogInterface dialog, int id) {
				// get user input and set it to result edit text
				String aotp = userInput.getText().toString();
				if (aotp.equals(otp) && (agree.isChecked())) {
					try {
						final ArrayList<NameValuePair> postParameters = new ArrayList<NameValuePair>();
						postParameters.add(new BasicNameValuePair("clientId", cid.getText().toString()));
						postParameters.add(new BasicNameValuePair("password", password.getText().toString()));
						postParameters.add(new BasicNameValuePair("emailAddress", email.getText().toString()));
						String response = SimpleHttpClient.executeHttpPost("/registerClient", postParameters);
						JSONObject jsonobject = new JSONObject(response);
						SharedPreferences prefs = PreferenceManager.getDefaultSharedPreferences(context);
						SharedPreferences.Editor editor = prefs.edit();
						editor.putString("clientId", (String) jsonobject.get("client_id"));
						editor.putString("emailAddress", (String) jsonobject.get("email_address"));
						editor.commit();
						Intent intent = new Intent(context, SignTabActivity.class);
						startActivity(intent);
					} catch (Exception e) {
						Log.e("register", e.getMessage() + "");
						Toast.makeText(getApplicationContext(), "Login Failed, Please Retry !!!", Toast.LENGTH_LONG).show();
					}
				}
			}
		}).setNegativeButton("Cancel", new DialogInterface.OnClickListener() {
			public void onClick(DialogInterface dialog, int id) {
				dialog.cancel();
			}
		});
		// create alert dialog
		AlertDialog alertDialog = alertDialogBuilder.create();
		// show it
		alertDialog.show();
	}
}

redpajama_set_name: RedPajamaGithub


Click the button below to add the Oatmeal 2 Homespun Cotton Fabric to your wish list.
Oatmeal 2 - This soft 100% cotton yarn dyed homespun fabric is 44 to 45 inches wide and is the perfect fabric to use for the popular ragged style quilting. The colors in this fabric are a rich shade of taupe and a complimentary soft white. Use our Oatmeal neutral color fabrics in your rustic, primitive, or farmhouse decor. This homespun fabric is also available as a Fat Quarter.


As you know, at Sun Acupuncture we have always gone above and beyond to provide outstanding acupuncture and shiatsu massage services for you and your loved ones. We enjoy sharing our expertise with you and nothing makes us happier than seeing a satisfied smile on your face when you're done receiving a treatment. This is why we continue to work so diligently to be the best in our field and why we entered the healing arts to begin with.
We are very excited to offer you some new services in 2016! Pam will be adding Raindrop Therapy and a Healthy Ear Therapy to her already list of fabulous treatments! Look for details to be released very soon!
We will continue offering Tai Chi, Qigong, and Yoga classes in 2016 and will be expanding our classes as well. Watch for all the exciting opportunities we have coming in the New Year!
As of January 1st, 2016 we are raising the rates for some of our clinical services.
This is a GREAT time to utilize your (HSA) Health Savings Accounts and use the remaining balance of your insurance acupuncture treatments.
Insurance HMO Plans: If you have any questions regarding your insurance plan and how many visits you may have left for 2015, please feel free to call us so we can help you find this information.
HSA Accounts: Most HSA accounts are pretty straightforward and will allow you to use your account for Acupuncture and Shiatsu/Tuina Massage.
Most of all, we hope you Have a Happy Healthy Holiday Season!
A comprehensive study commissioned by the Department of Veterans Affairs found acupuncture to have a positive effect in the treatment chronic pain, migraine and tension headache.
The same study found a potentially positive effect in dysmenorrhea, cancer pain, labor pain, insomnia, post-operative nausea and vomit, depression, and smoking cessation.
Acupuncture outperforms placebo in relieving the most common types of chronic pain: headache, low back, neck, shoulder and knee pain.
Acupuncture significantly outperforms standard care in headache, low back, neck, and knee pain.
Acupuncture is superior to most forms of physical therapy in the treatment of knee osteoarthritis.
Acupuncture can reduce the risk of nausea and vomiting after surgery, with minimal side effects.
In a prospective study involving 229,230 patients, acupuncture was found to be a relatively safe treatment with a low risk of serious side effects.
The American College of Physicians and American Pain Society recommend acupuncture as a second-line therapy for chronic low back pain.
The American College of Chest Physicians recommends acupuncture for cancer patients when pain, nausea, vomiting, or other side effects of chemotherapy are poorly controlled.
The Joint Commission includes acupuncture as one of the non-pharmacological strategies that has a role in pain management in hospitals, nursing homes, and outpatient care.
Hempel S, Taylor SL, Solloway M, et al. Evidence Map of Acupuncgture. VAE-ESP Project #05-226; 2013.
Vickers AJ, Cronin AM, Mascino AC, et al. Acupuncture for Chronic Pain: Individual Patient Data Meta-analysis. Arch Intern Med. 2012 Sep 10:1-10.
Corbett MS, Rice SJC, Madurasinghe, et al. Acupuncture and Other Physical Treatments for the Relief of Pain Due to Osteoarthritis of the Knee: Network Meta-analysis. Osteoarthritis Cartilage. 2013 Sep;21(9):1290-8.
We sincerely thank each and everyone of you from the depths of our hearts for truly making our acupuncture, Chinese medicine, and shiatsu-tuina bodywork clinic a success.
We will keep striving with all of our heart and dedicated efforts to give each and every patient that walks through our door the best care we possibly can. Through our dedicated research, study, and training efforts, we will continuously improve our expertise and skills and bring even better healthcare to those who seek our services.
Here's our current patient incentives we are offering at Sun Acupuncture!


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ARE WE SAFER NOW? OR NOT?
Former senior level intelligence officials are disputing claims by the Bush Administration that the failure of Congress to pass a new foreign surveillance law is jeopardizing America's national security.
In a letter to Admiral Mike McConnell, the Director of National Intelligence, the officials say "the intelligence community currently has the tools it needs to acquire surveillance of new targets and methods of communication." Charging that the government's assertions to the contrary "have distorted rather than enhanced" public understanding, their letter says, "The sunset of the Protect America Act (PAA) does not put America at greater risk. Despite claims that have been made, surveillance currently occurring under the PAA is authorized for up to a year. New surveillance requests can be filed through current FISA law."
The letter was signed by two former officials at the National Security Council (NSC), Rand Beers, who was Senior Director for Combating Terrorism, and Richard A. Clarke, who served as head of counterterrorism; Lt. Gen. Don Kerrick, former Deputy National Security Advisor; and Susan Spaulding, former assistant general counsel at the Central Intelligence Agency (CIA).
The controversy has been triggered by disagreements focusing largely on a single provision of the PAA. Two weeks ago, a bipartisan coalition in the Senate overwhelmingly passed an extension of the PAA, which was due to expire unless renewed. The bill provides retroactive immunity from lawsuits to telecom companies that wiretapped U.S. phone and computer lines at the government's request after the Sept. 11, 2001 terrorist attacks, without court permission.
A similar bill passed by the House of Representatives but the House version did not provide such immunity.
Congress left Washington for their President's Day recess without agreeing on a single bill the president could sign – and Bush said he would veto a three-week extension of the current law. The result was the expiration of the PAA last Saturday.
Before and since that time, President Bush has been lobbying for Congressional action granting retroactive immunity. He has warned that terrorists are planning new attacks that could make the Sept. 11 attacks "pale by comparison" and that failure to pass the Protect America Act could have dire consequences. Democrats say they are trying to balance concerns about civil liberties against the government's spy powers.
Bush and DNI McConnell have claimed that the telecom companies were acting legally and acting patriotically at the request of their government, but noted that the companies are already the targets of class action lawsuits that are causing them to be less cooperative.
Bush has lobbied hard to persuade Congress to pass legislation immunizing the telecom companies. He said, "To put it bluntly, if the enemy is calling into America, we really need to know what they're saying, and we need to know what they're thinking, and we need to know who they're talking to."
He added, "Our government told them that their participation was necessary. And it was, and it still is, and that what we had asked them to do was legal. And now they're getting sued for billions of dollars. And it's not fair."
The Democrats have responded by accusing Bush of resorting to "scare tactics and political games."
The former national security officials who wrote to DNI McConnnell said, "It is wrong to make this one issue an immovable impediment to Congress passing strong legislation to protect the American people."
They took issue with President Bush's claim that, as a result of PAA not being extended by Congress, "the Attorney General and the Director of National Intelligence will be stripped of their power to authorize new surveillance against terrorist threats abroad."
They urged the President to abandon his claims that Congress' action makes the U.S. vulnerable to terrorist attacks. "It is the duty of the Executive Branch to inform this process. America's security cannot be captive to partisan bickering and distortions," they wrote.
They added, "It remains unclear - in light of the law - how the President believes surveillance capabilities have changed."
Their letter claimed that "The intelligence community currently has the tools it needs to acquire surveillance of new targets and methods of communication. As in the past, applications for new targets that are not already authorized by the broad orders already in place under the PAA can be filed through the FISA courts, including the ability to seek warrants up to 72 hours retroactively."
Passed by Congress in 1978, FISA, the Foreign Intelligence Surveillance Act, requires the government to obtain a warrant from a special court established under the law before it could conduct wiretaps or intercept the communications of Americans. The law FISA has been modernized nearly a dozen times since the terrorist attacks of September 11, 2001, to keep abreast new communications technologies.
Many legal experts and civil liberties advocates disagree with President Bush's claims that Congress' failure to extend the PAA has increased America's vulnerability to terrorist attacks.
Typical is Prof. Peter Shane of the University of Ohio law school, who told us, "Bush's position is senseless."
He said, "First, Congress has been willing to extend the PAA on a short-term basis in its current form. So any lapse in the availability of PAA authority cannot be attributed to Congress. Second, retroactive immunity has nothing to do with the authority of the executive branch going forward. It is simply an effort to make sure that lawsuits are not used to unearth the full scope of possible Bush Administration lawlessness in conducting its so-called terrorist surveillance program."
His view was echoed by Clayton Northouse, Information Policy Analyst for OMB Watch, a Washington-based open-government research group. Northouse told us, "Since day one, the administration has used the guise of national security to unilaterally increase the power of the Executive. This exposes the administration's position as a blatant power grab. The letter from senior intelligence officials shows us that the Bush administration isn't upset because the country is weakened by the House's decision not to reauthorize PAA and grant telecom immunity. Rather, the administration is upset because they may not be able to avoid the oversight and approval of the legislative and judicial branches."
Posted by Unknown at Wednesday, February 27, 2008 No comments:
Saudi Arabian "Justice"
By Mona Eltahawy
If justice really was a woman she would not survive long in Saudi Arabia.
Between the Kafkaesque-sounding Committee to Promote Virtue and Prevent Vice and its infamous morality police, and the hardline Wahhabi clerics who serve as judges with wide-ranging powers run amok in the absence of a written penal code, justice couldn't stand a chance in the royal kingdom.
More barbaric than Kafkaesque is the case of Fawzia Falih, a 51-year-old Saudi citizen of Jordanian origin who is awaiting public execution -- by beheading -- for "witchcraft." She had already been hospitalized from weeks of beatings by the morality police (the mutaween) prior to her conviction in April 2006.
Judges sentenced her to death based on a confession extracted during those beatings. Falih, who is illiterate, was made to fingerprint that confession although she could not read what it said. One witness against her was a man who claimed he had suddenly become impotent after Falih "bewitched" him.
In a rare moment of lucidity in September 2006, an appeals court threw out her capital conviction after Falih retracted the confession. But a lower court later ruled she should be executed in the "public interest."
It would be macabre to call Falih lucky, but at least she understood the proceedings against her. I doubt that Rizana Nafeek, a Sri Lankan maid who just turned 20, understood a word of her "trial" which sentenced her to be beheaded.
Nafeek was accused of murdering a baby -- who she says choked as she was feeding it. She was only 17 at the time. She had no access to lawyers during either her interrogation or her trial. Like Falih, Nafeek also retracted a "confession" extracted during police questioning.
A Saudi court is said to be considering Nafeek's appeal but human rights organizations are concerned because of Saudi Arabia's alarmingly high rates of execution. At least 26 people, including three women, have been executed since 8 January, and at least 158 people -- including three women -- were executed in Saudi Arabia in 2007.
As those groups point out, Nafeek's execution would be in contravention of the United Nations Convention on the Rights of the Child which prohibits the execution of offenders for crimes committed when they were under 18 years old.
In its complete mockery of justice, Saudi Arabia ignores these UN conventions -- even the ones it has signed. In 2000, it ratified an international bill of rights for women but stipulated that Islamic law (Sharia) would prevail if there were conflicts with its provisions.
A farce played out in Geneva earlier this year, when a Saudi delegation appeared for the first time before the UN women's rights panel. Finally an international body grilled the Saudis to explain why, in the 21st century, women have to have a male guardian's permission to do almost everything in the kingdom, and why women cannot drive.
It was absurd to hear the Saudis insist that women in their country faced no discrimination. But the most ludicrous claim came when the UN committee asked why Saudi men could marry up to four wives. With a straight face, a Saudi delegate -- a man of course -- explained that it was to ensure a man's sexual appetite was satisfied legally if one wife could not fulfill it.
Not surprisingly, the UN special rapporteur on violence against women, Yakin Erturk, soon went to Saudi Arabia on a 10-day fact-finding mission. She criticized the mutaween and the cleric-judges, mentioning two more cases of women whose treatment at the hands of those entities is nothing short of surreal.
Erturk met with Fatima Azzaz who was forced to separate from her husband Mansour al-Timani in 2006 after her brothers persuaded judges that Timani was from a lesser tribe. Azzaz is being held in a government home for orphans with a young son. She refuses to return to her family home as required by a court order divorcing her from her husband, who has custody of their daughter.
One of the latest atrocities of the mutaween was the arrest in early February of a businesswoman known only as Yara, a 40-year-old mother of three, for sitting in a Starbucks coffee shop in Riyadh with a male colleague. She told the English-language daily Arab News she was taken to a prison, strip-searched and forced to sign a confession of being caught alone with an unrelated man. Yara said the morality police released her several hours later after her husband intervened. The man with whom Yara had coffee, an unidentified Syrian financial analyst, had also been arrested and released the following day.
As these cases show, a grilling by a UN watchdog and a fact-finding mission to explore the miserable state of women's rights in Saudi Arabia were long overdue. But they are meaningless when Saudi Arabia daily abuses the very rights it has promised to uphold. It must choose -- either its Wahhabi 'justice' or international conventions.
By forcing it to choose, the civilized world supports Saudis who refuse to be intimidated by the morality police and the Wahhabi judges. Last year, several Saudis sued the mutaween for their abuses But my favorite story is of two young women out shopping last year who were chided by the mutaween apparently for wearing makeup. One of the young women pulled out a can of pepper spray and she emptied it into the face of the morality police as her friend filmed the incident with her mobile phone while calling the mutaween "terrorists."
You can't say Saudi women aren't fighting back.
Mona Eltahawy is an award-winning New York-based journalist and commentator, and an international lecturer on Arab and Muslim issues.
Posted by Unknown at Wednesday, February 27, 2008 1 comment:

redpajama_set_name: RedPajamaCommonCrawl


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OK, i'll try to explain. I have customized bootscript with uncommented tracker. When haiku starts it loads tracker which in turn open /boot/beos/apps. Now, if i start BitmapDrawing -> Alt+w -> Expander -> Alt+w i could see slowness of repainting background (about a second). I don't start any other apps before this to reproduce it.
Tested with rev16575 under vmware.
Correction. Don't need to go through those steps written above. There is an easy way. Just start Expander after tracker and close it and you'll see slow background repainting. Maybe Expander tries to wright settings to disk, but under vmware it takes to long? Need to test it under native installation.
I will retest it ASAP.
Specifically, the delay is caused by the MIME type being written.
Can't reproduce it anymore, it's been probably fixed in meantime.
This might have been fixed with hrev25719, please check.
So now both Expander and MediaPlayer should write their supported MIME types at first boot, regardless of whether you'll launch them of not, right?
Yes, it's seems "fixed". But I think hrev25309 could've been hide this bug and could potentially lead to boot time increase due to a slow MIME type write as stated above. What do you guys think?
That only happens once at the very first boot. I think the general idea behind that is ok. The other option would be to make the build system do this, but think the current solution is more fool proof.
+1 to the idea to make the build system take care of this as this will also speed up haiku start up in vmware and also potentially LiveCD boot time. Should I add a new ticket so we don't forget about it, Ingo?
Please don't; I don't think I'll implement it. The build system can't really prepare the MIME entries for optional packages, so the on-first-boot mechanism is needed anyway.


This entry was posted in 1 Blessing, A Hope for a Cure for Cancer, Amazing Grace, Cancer, Faith, Grace, Hope, Inspirational, Johnathan McCravy and Derek McCravy Facebook, Mercy, Peace, Pinterest, Prayer for, Strength, Uncategorized and tagged Christian Inspiration, Christianity, Encouragement, Faith, Faithfulness, Forgiveness, Friendship, Grief, Inspirational, Johnathan McCravy and Derek McCravy at http://www.dignitymemorial.com/AnthonyMcCravy, Johnathan McCravy and Derek McCravy Facebook, LinkedIn, Losing, Love, My good friend Sandi McCravy, Peace, Pinterest, Praise, Raleigh, Sandi McCravy Cancer, Sandi McCravy much to her credit Sandra Brooks McCravy applied for every scholarship for Derek that she could get her hands on and it paid off. Some of them were, Sandi McCravy Raleigh NC, Sandra Brooks McCravy Hope, Sandra Brooks McCravy Raleigh NC, Sandy McCravy, Scripture, Twitter, Uncategorized. Bookmark the permalink.


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SINGLES - Soundtrack Vinyl + CD
This newly expanded 2LP edition of the 'Singles: Original Motion Picture Soundtrack' features the album's original 13 tracks newly mastered and freshly pressed across four sides of collectible 12" vinyl with a bonus CD insert of rarities and unreleased tracks.
The bonus CD features previously unreleased recordings by Mudhoney, Paul Westerberg, Mike McCready and Chris Cornell in addition to rarities such as Cornell's 1992 EP 'Poncier' (debuting an early rendition of Spoonman") and tracks from the film not included on the original soundtrack album.
This expanded edition includes, for the first time on CD, "Touch Me I'm Dick," the signature track from "Singles" performed by Citizen Dick (a fictional band created for the film featuring frontman Matt Dillon backed by Pearl Jam's Eddie Vedder, Stone Gossard and Jeff Ament).
The film's soundtrack is produced by Danny Bramson and Cameron Crowe.


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Loan watch
by Jamie White
We take a look at the players out on loan and see how they have been doing in the past week.
Defender Charlie Goode played his 11th game for Northampton last Saturday, but the Cobblers were beaten 2-1 at home to Port Vale.
A yellow card was shown to Goode, as it left Northampton placed 15th in Sky Bet League Two.
Next up for Northampton is a trip to Notts County in the league.
Meanwhile, James Horsfield played in both of Dundee's latest two results, while Andy Dales featured in one of them.
Horsfield, who has been playing at right-back, played the entirety of their away defeat at St Mirren on Saturday, before also playing 64 minutes in the 2-0 loss against St Johnstone on Wednesday night.
Winger Dales replaced Horsfield in the second-half against St Johnstone.
In total, Horsfield has started nine games for the Scottish side since his loan move in January, whilst Dales has also started nine matches and has come off the bench three times.
Bottom of the league, Dundee's next clash is at home to Aberdeen.
Elsewhere, 19-year-old midfielder George Hornshaw was an unused sub for non-league side Gainsborough Trinity last Saturday.


Here are the pairings for the IHSAA girls basketball sectional which will be płayed on February 10, 13,14. Tickets are on sale in the high school office during regular school hours. Tickets are $10 per ticket. The Musketeers open up play on Tuesday night against Henryville. We have split with them during the regular season, so we need the "Musketeer Cheer Block to show up and support the team.


Christian HS Head Coach Matt Oliver has been with the Patriots since 1999 and is fired up to have the opportunity to play in the 2017 Honor Bowl. The Patriots will have returning QB Brad Jeremiah at the helm who compiled 2014 YDs with 21 TDs and only 6 INTs. The 2016 12-1 record is an indication of the dedication to believe in the coaching staff that strives to play with heart and soul on and off the field.
Boron High School is in the small desert community of Boron and is coached by Robert Kostopoulos. The Bobcats have recently been added to the Honor Bowl and are excited to be able to soak up the activities of the event as well as matchup against a great team that Christian HS will field in 2017. Boron typically fields a small roster but this first gamer of the 2017 Honor Bowl will definitely be a fun one to watch!


Abstract: Objective To investigate the protective effect of ω-6 soybean oil fat emulsion on folium sennae-induced diarrhea in mice. Methods Thirty-six Kunming mice were randomly divided into three groups,including control,diarrhea,ω-6 soybean oil fat emulsion group(12 mice in each group). Besides the mice in control group,other mice were administrated folium sennae by gavage for 15 days to establish the diarrhea model. Then mice in ω-6 soybean oil fat emulsion group received ω-6 soybean oil fat emulsion by intravenously administration at a dose of 15 mL/kg daily since 6th day after intragastric administration of folium sennae for 10 days. Animals in control group and diarrhea group were intravenously administered with same volume of saline. The body weight,general state and diarrhea index of the mice in each group were dynamically assessed. Ten days after intravenous injection,mice in every group were sacrificed and tissues were collected. Morphology of intestine mucosa was observed after HE staining. Albumin(ALB)level in plasma was evaluated by biochemical method. Proliferating cell nuclear antigen(PCNA)expression in intestine mucosa were assessed by immunohistochemical method. Results Compared with that in the diarrhea group,the general status,body weight and diarrhea index of mice in ω-6 soybean oil fat emulsion group were improved significantly. Ten days after intravenously administration,pathological change in intestine mucosa of mice in ω-6 soybean oil fat emulsion group was improved significantly,ALB level in plasma and PCNA expression in intestine mucosa were significantly increased(P < 0.05)compared with that in diarrhea group. Conclusion ω-6 soybean oil fat emulsion has a significant protective effect on the diarrhea of mice induced by folium sennae,which may be related to the up-regulated expression of PCNA by ω-6 soybean oil fat emulsion.
孙明立,赵海山,姚维范,魏敏杰. ω-6 大豆油脂肪乳对小鼠腹泻的保护作用[J]. 中国医科大学学报, 2016, 45(8): 742–745.
SUN Mingli,ZHAO Haishan,YAO Weifan,WEI Minjie. Protective Effect of ω-6 Soybean Oil Fat Emulsion on Folium Sennae-induced Diarrhea in Mice[J]. Journal of China Medical University, 2016, 45(8): 742–745.


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Clarence Thomas to attend Judicial Center dedication
Supreme Court justice will be second to visit Covington for courthouse milestone
Construction on an addition to the Newton County Judicial Building continues Wednesday, July 18, 2018. - photo by David Clemons
COVINGTON, Ga. — Supreme Court Justice Clarence Thomas will help dedicate the addition to the Newton County Judicial Center this fall.
Superior Court Judge Samuel D. Ozburn of the Alcovy Judicial Circuit announced Thomas' visit Wednesday morning.
"Newton County is honored to host this nationally esteemed jurist and scholar on this special occasion," Ozburn said.
Clarence Thomas was appointed as an associate justice of the U.S. Supreme Court in 1991.
Thomas, 70, is a Georgia native. President George H.W. Bush nominated him to the Supreme Court and he was confirmed in 1991.
With Justice Anthony Kennedy having announced his intentions to retire as an associate justice later this year, Thomas will be the longest-tenured member of the Supreme Court by the time of his visit to Covington in the fall.
Thomas receives appeals from the Atlanta-based 11th Circuit Court of Appeals. Ozburn said he has been working since 2015 to secure Thomas' visit.
A $12 million project to expand the Newton County Judicial Center is in its final months. Newton County has added thousands of residents since the Judicial Center opened in 1999, and the court system has added special courts for veterans, defendants with mental health concerns and defendants in a special drug program.
County voters approved the project in the 2011 special-purpose local option sales tax.
Details about Thomas' visit, including the date and time, will be released as the time approaches.
Kennedy attended the dedication ofthe Newton County Judicial Center in 1999 at Ozburn's invitation. At the time, it was the first new courthouse for Newton County in 115 years.
C-SPAN carried Kennedy's remarks to a national audience.
Thomas grew up in the Pin Point community near Savannah. He has degrees from Holy Cross College and Yale Law School.
Funeral arrangements set for Judge Horace Johnson Jr.
Ott, others in court system test positive for COVID-19
Covington woman killed in crash
Court emergency extends to Newton


IBC Section 159-After-acquired property of bankrupt.
(1) The bankruptcy trustee shall be entitled to claim for the estate of the bankrupt, any after-acquired property by giving a notice to the bankrupt.
(b) any property which is acquired by or devolves upon the bankrupt after a discharge order is passed under section 138.
(3) The notice under sub-section (2) shall be given within fifteen days from the day on which the acquisition or devolution of the after-acquired property comes to the knowledge of the bankruptcy trustee.
(b) anything which comes to the knowledge of a person before he is appointed as a bankruptcy trustee shall be deemed to have come to his knowledge on the date of his appointment as bankruptcy trustee.
(5) The bankruptcy trustee shall not be entitled, by virtue of this section, to claim from any person who has acquired any right over after-acquired property, in good faith, for value and without notice of the bankruptcy.
(6) A notice may be served after the expiry of the period under sub-section (3) only with the approval of the Adjudicating Authority.
Explanation.—For the purposes of this section, the term "after-acquired property" means any property which has been acquired by or has devolved upon the bankrupt after the bankruptcy commencement date.


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KAYA Mine Protected Vehicle
The KAYA is a 4x4 mine protected vehicle (MPV) developed by Otokar, a company based in Turkey.
Mine protected vehicle
KAYA mine protected vehicle can transport two crew and ten troops.
KAYA can be armed with a roof-mounted weapon station.
A rear view of the KAYA 4x4 mine protected vehicle.
KAYA 4x4 MPV demonstrates excellent cross country capabilities.
The KAYA Cargo Carrier variant is suitable for carrying cargo on all terrains in threat environments.
A KAYA Cargo Carrier exhibits its mobility during tests.
The KAYA is a 4×4 mine protected vehicle (MPV) developed by Otokar, a company based in Turkey. The vehicle is intended to provide mine and ballistic protection for armed forces operating in threat environments.
The development of the KAYA MPV began in 2006 and the first prototype was completed in 2007. The MPV was unveiled for the first time at the IDEX 2009 defence exhibition held in Abu Dhabi.
The KAYA has a length of 6.4m, a width of 2.5m and a height of 2.9m. It can carry two crew members and ten infantrymen. It has a combat weight of 12.5t.
KAYA variants
"The KAYA has a length of 6.4m, a width of 2.5m and a height of 2.9m."
KAYA MPV is available in two variants, the Armoured Personnel Carrier (APC)/Troop Carrier variant and Cargo Carrier variant. The APC variant features an armoured cabin and a dedicated troop compartment. It can be modified into an ambulance or a command post vehicle.
The Cargo Carrier variant is fitted with armoured cabin and an unprotected flat bed cargo section in place of troop compartment. The cargo compartment is equipped with drop sides and a tailgate.
KAYA design and crew protection features
KAYA is based on the Daimler Chrysler Unimog 5000 chassis. The MPV features an armoured cabin and a crew compartment. The two segments are mounted as separate units to achieve maximum cross country capability. The flexible design also allows the manufacturer to configure the vehicle for various mission requirements.
A large single-piece bullet proof wind shield in the front protects the driver and commander sitting inside the cabin. Either side of the crew cabin is provided with a forward opening door fitted with a bullet proof window.
The slightly raised troop section at the rear accommodates ten troops. The troops are seated on individual seats attached to the sides of the vehicle. The rear door provides entry and exit for the soldiers.
The troop compartment has six firing ports, 11 small bullet proof windows and three roof hatches. A Stepney is fitted to the right side of the troop section. The external stowage boxes on the lower part of the hull provide additional storage space. The standard equipment includes air conditioning system, additional heater, speed limiter, electrically controlled mirrors, and towing pintle and hook.
ARMA 6X6 Armoured Tactical Vehicle, Turkey
ARMA is a modular wheeled armoured tactical vehicle designed and developed by Otokar in Turkey.
The KAYA MPV can be armed with wide range of weapon stations such as open cupola and remotely controlled weapon station. The overhead station can be mounted with a 7.62mm/12.7mm machine gun or 40mm automatic grenade launcher.
KAYA is specifically developed to provide mine and ballistic protection for the occupants on all terrain conditions, while offering a high level of crew comfort. The engine compartment is provided with armour protection to withstand small arms fire and shell splinters. The V-shaped bottom of the troop section reduces the blast impact by deflecting the bomb fragments away from the vehicle.
The front and rear compartments are fitted with all-welded steel armour. The protection is further enhanced with an appliqué layer of armour. The armour protection around the wheel arches offers additional protection against mines.
The vehicle can be optionally fitted with an automatic fire extinguisher system.
"The propulsion system provides a maximum speed of 96km/h."
KAYA MPV engine and mobility
The KAYA MPV is powered by an OM 924 LA 4-cylinder diesel engine coupled to a UG-100 tiptronic, electro pneumatic transmission. The engine provides a power output of 218hp at 2,200rpm. The propulsion system provides a maximum speed of 96km/h.
KAYA is optionally equipped with Central Tyre Inflation System (CTIS) and run flat tyres for enhanced mobility.
The 200l tank capacity provides KAYA a range of 800km. The wheels are equipped with pneumatic hydraulic dual circuit disk brakes. The vehicle can negotiate a gradient of 60% and side slope of 30%. It can cross vertical obstacles of 480mm and ford 1,200mm deep waters.
The Global Armoured Vehicles and Counter-IED Vehicles Market 2011-2021
This project forms part of our recent analysis and forecasts of the global armoured vehicles and counter-IED vehicles market available from our business information platform Strategic Defence Intelligence. For more information click here or contact us: EMEA: +44 207936 6783; Americas: +1 415 439 4914; Asia Pacific: +61 2 9947 9709 or via email.
Otokar supplies modern armies with innovative tactical vehicle configurations from...


I approach a new sculpture in two very different ways depending on the result I am trying to achieve. The first is to go in with no idea in mind. I just start by removing stone and see where the piece wants to take me. This tends to be my approach with my abstract pieces. The second way is how I start in with realistic work. I have a specific piece in mind and to work towards that in a more methodical way. Both methods have their plusses and minuses, and they are very different ways of thinking and negotiating my way to a completed piece. As you will note, I said this is how I approach the start of a new sculpture. Once started, things don't always go as planned!
In my most recent sculpture, I started with the second approach. I had a very specific piece in mind. It was to be a realistic baboon face and was to be part of a show I did two years ago on all animal heads. (Yes, I started this piece over two years ago.) I quickly realized this would not work as the stone and I clearly had different agendas! The stone was a very odd shape that did not allow for as much depth for the eyes as I originally wanted. I stopped working on the piece and set the stone aside.
When I set a stone aside, I typically go back after a few months and look at it to see if I can solve the problems it has presented. Some times they continue to mock me and they go back on the shelf. Other times, we talk a little and a new idea comes up.
With "Baboon Mask" we agreed that I would drill all the way through the eyes and create an abstract piece that was totally unrelated to the original idea. So essentially, I took the approach that this was a new sculpture and had planned to complete a freeform piece now. I was pretty clear with the stone, that that was the direction I wanted to go and I thought it had agreed. It didn't.
I drilled all the way through the eyes and was surprised to see that I was really happy with the depth it created. It was no longer a realistic baboon, but it did not want to be a freeform piece wither, so we agreed that it would be more of a contemporary "mask" of a baboon. The stone and I were happy, and after over two years, I completed the piece last night. This was quite the journey to get to the completed piece, but carving stone is always a negotiation!


text:
SEOHow to use Google Trends for SEO
How to use Google Trends for SEO
Google Trends, first launched in 2006, provides marketers with invaluable insights into how people search on the world's most popular search engine. Over time, the power of this service has been tapped in new and enlightening ways. Here's how you can use it for SEO.
Clark Boyd
Date published December 11, 2017 Categories
Google Trends, first launched in 2006, provides marketers with invaluable insights into how people search on the world's most popular search engine.
In its earlier guises, Trends (or Insights for Search, as it was previously known) was a rather static resource, updated only on an infrequent basis with fresh data.
Over time, the power of this service has been tapped in new and enlightening ways.
For example, a study undertaken using Trends data by Seth Stephens-Davidowitz and written up in the New York Times in 2014 found, "Parents are two and a half times more likely to ask "Is my son gifted?" than "Is my daughter gifted?""
Such newsworthy incidents revealed the richness of Google Trends as a data source to the wider public. People's underlying attitudes, desires, and beliefs start to come to the fore when they communicate with a search engine.
As the megalomaniac founder of a fictional search engine puts it, while discussing the data at his disposal, in the 2015 science-fiction movie Ex Machina:
You see, my competitors, they were fixated on sucking it up and monetizing via shopping and social media. They thought that search engines were a map of what people were thinking. But actually they were a map of how people were thinking.
Both of these examples – one real, one imagined – highlight exactly why Google Trends is so valuable for search marketers.
It is the closest we have to a synthesis of market research and SEO data. With its ability to segment trends by geography, product category, content topic, and date, it allows us to go much broader in our analysis than traditional SEO tools ever could.
With Trends' recent expansion into News, Shopping, Images, and YouTube, it seems the perfect time to revisit and refresh the many ways in which this powerful tool can help your SEO efforts.
First, some housekeeping
If you are relatively new to Google Trends, there are a couple of things to bear in mind when you look at the data visualizations.
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First of all, Google Trends data is adjusted to make visual comparisons between different data sets easier for users. Google offers the following to explain for its methodology:
"Search results are proportionate to the time and location of a query:
Each data point is divided by the total searches of the geography and time range it represents, to compare relative popularity. Otherwise places with the most search volume would always be ranked highest.
The resulting numbers are then scaled on a range of 0 to 100 based on a topic's proportion to all searches on all topics.
Different regions that show the same number of searches for a term will not always have the same total search volumes."
In practice, this means that we end up with graphs like the below, showing trended data on a scale from 0 to 100:
Furthermore, a note is applied to all graphs that look back to before 2016, as Google made a significant update to the collection of data at this point. This can cause some unexpected jumps in graphs at the beginning of 2016, but the overall trends still provide a good guide to the historical demand for a topic.
Now, onto the tips.
How you can use Google Trends for SEO
Keyword research seems the most obvious SEO-based use for Trends, but it is often overlooked in favor of Keyword Planner and the other industry-standard tools.
In fact, it serves as the perfect complement to these platforms, bringing to light patterns that they cannot reveal.
Trends will suggest new keywords based on different criteria to those employed in Keyword Planner. For example, it highlights related search queries (using the example of "dogs" again) that have very recently risen in popularity, as we can see in the screenshot below:
Clearly, these will require a sense check before you add them straight to your keyword list. As stated before, we really can learn something about the human condition from Google Trends.
There will also be some outliers (in this case, the Watch Dogs video game), as Google groups together a lot of related sub-topics under the aegis of the main categories.
Nonetheless, these examples do show how frequently this tool can provide unexpected ideas.
It is also reflective of how the readily available nature of fresh data on Trends can add vital, new elements to a keyword list.
This is significant as we move beyond simple keyword matching and into an age of semantic relevance. Building out a keyword list that contains the spectrum of audience demand for your products is no longer a luxury; it is a pre-requisite for performing well.
Moreover, if SEOs can target trending queries before they peak, competition will be lower and potential rewards will be greater.
For those that would like to examine the data outside of the platform, there are numerous R and Python packages that can make calls via the Google Trends API.
This allows users to download queries in order to manipulate and visualize the data. One such package for R, (gtrendsR), is explained in more detail in this handy blog post.
Combined with a versatile plotting package like ggplot2, this approach opens up a new level of functionality to Google Trends data for SEO research.
Compare search trends across Google search engines
The addition of filters for News, Shopping, Images, and YouTube to Google Trends has opened up a wide range of new SEO research opportunities.
These can be accessed from a drop-down menu at the top of the results page.
Image search data in available from 2008 to the present day and it should prove a very valuable source of inspiration for SEOs.
Not only is image search responsible for a huge amount of queries already, but it is also an area of focus for Google as it aims to fend off threats from the likes of Facebook, Amazon, and Pinterest.
Once more, we can segment the data by sub-region or city and there are suggestions for related image search queries too:
It is also possible to compare these search trends across two different queries, due to the manner in which Google processes and displays the data. In the example below, I have set the filter to show the trends for "cats" in the US and for "dogs" in the UK:
We can therefore say that image searches for dogs in the UK are more popular than image searches for cats in the US, in relative terms, even though this would likely not be the case in absolute terms.
On YouTube, the eternal cats versus dogs battle lives up to its fiery reputation, with a much narrower gap between the two search topics:
Trending queries are highlighted here too, which should give us even more reason to keep visiting Google Trends for our research:
Assess and predict seasonal peaks
Perhaps the most common use of Google Trends for SEO is the analysis of peaks and troughs in consumer demand.
To cite a simple, but illustrative, example of how this works, we can look at the search query [olympics]:
We see significant worldwide peaks every four years for the summer Olympics, with the winter equivalent attracting another (if smaller) increase two years later each time.
In this example, history tells us that we are about to see another peak in demand for [olympics] very soon, but that insight alone does not translate into much.
Firstly, we don't know the size of the opportunity in absolute terms, as Trends provides only relative values.
However, if we cross-reference what we see in Trends with the data we have from Keyword Planner, we can start to understand what a value of 100 on this chart means in real terms.
Admittedly, Keyword Planner data is indicative at best, but we may also have data from AdWords campaigns. This can at least guide us towards a predicted search volume for the upcoming Olympics.
Of course, it seems very intuitive that a major event will lead to more searches for the event's name. Nonetheless, if we take this same approach and apply it to less predictable industries, such as fashion for example, Trends can help you to identify keywords before the competition does so.
This is supplemented by Trends' use of real-time data to suggest new topics.
Trending topics for reactive content
One of the most useful aspects of Google Trends is the access it provides to real-time search data. There are plenty of content marketing and SEO technologies out there, but none can provide data as reliable as the information Google serves from its own databases.
These can be accessed directly from the Google Trends homepage:
Clicking on a story will then lead to a selection of featured articles, plus a detailed breakdown of search interest and published articles over the past 24 hours:
The analysis goes further still by showing search interest by state, related queries, and related topics:
This should be a go-to resource for anyone that produces reactive content, whether for their website, social media, or elsewhere.
Another interesting way to work with this data is to take the URLs that are listed as featured articles and use an SEO tool like Ahrefs or SearchMetrics to source the keywords that the page ranks for.
This provides insight into how quickly a page can be indexed and ranked, along with the quantity of semantically related queries one page can rank for in a short period of time. More than anything, this can help us understand how Google processes and prioritizes fresh content.


text:
Home Costa Blanca Orihuela-Costa
Spanish News, Property for sale in Spain, Sport, and Information for the Orihuela-Costa, Province of Alicante, Community of Valencia, Spain.
Orihuela Costa is a hamlet of the municipality of Orihuela which is located in the province of Alicante and the community of Valencia in Spain. Orihuela Costa is located about 35 – 40 kilometers from the city of Orihuela. It covers the coastal area of the Southern Costa Blanca from Punta Prima to Mil Palmeras.
In 2018, the municipality of Orihuela had 76.778 inhabitants. The main urban population centers were the city of Orihuela and the coastal areas of the Orihuela-Costa. According to the census of the 2009, around 41% of the Oriolana population was of foreign nationality and 77% are of European origin. In the municipality of Orihuela, there were approximately 17.121 Britons and 9.545 citizens of other European countries. The non-Spanish population of European countries is mainly concentrated in the areas of Cabo Roig, Campoamor, Villamartin, Playa Flamenca, La Florida, Los Altos, and Punta Prima.
The Orihuela-Costa has enjoyed tremendous growth since the beginning of 2000 when there were barely 5,645 inhabitants. With the tourism and construction boom on the Costa Blanca the population of the Orihuela-Costa grew to 32,530 inhabitants in 2013, but following the housing crisis many foreigners living in Orihuela Costa decided to return to their countries of origin. In 2017 the population was just 20,000 inhabitants but that number increased slightly in 2018.
The data is based on the number of people registered on the coast, but there are many foreigners living in Orihuela Costa who are not registered. Some of those foreigners live there permanently and some of them own holiday homes there. Therefore, there is a disparity between the actual number of people living on the Orihuela-Costa and the number of people registered. In fact, it is thought that around 45.000 people actually live in the area.
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Out of nowhere I am having my first craving and the thought is lingering. I know I don't want to smoke and the addiction on my shoulder is telling me how good it would taste and smell. I am here and I know you all are here with me. I have to get thru this.
As is suggested around here, say "I don't do that anymore." Cravings are really annoying but each and everyone can be overcome. Hang in there. Yes you can.
You are so lucky for this to be your first crave! Although I'm having fewer and fewer, they're still there, rIGH..... Breath in through the nose, out through the mouth. When I breath out, I blow just like I did when I smoked. I do that as many times as it takes. We can do this! Good girl coming here for help!
You handled it brilliantly, MelodyEve!! We are here with you Always remember to breathe because it helps you think clearly and ease your fears but you are doing so very well!!
I had that problem too, my addiction talking to me. And I lost my quit about 3 or 4 times earlier this year. How good the cigarette would be, it never turned out to be that way, but I sure built it up in my mind about how good it would be, an d it never was and it left me all depressed and what a loser I am, kind of thing. It was horrible and depressing and then I had to face that day one over again. What a liar that addict is. Glad you didnt cave. See you tomorrow on the pledge page!
I don't think that craving fully disappeared yesterday but omg what a day. I found myself looking outside in the middle of a bad storm to see if I could see anyone out there smoking. I got up and got busy again. The dinner that would have taken 10 mins to cook took me 30 because I was cutting up all kinds of stuff to put into it. I washed dishes, I played a slots game the whole time thinking of smoking. I finally just got so tired I went to bed for the rest of the evening and night. Here I am at 3 a.m. but oh well I'm still smoke free and I feel like I'm doing much better this morning. I made my pledge and am refocusing. Have a good DOF everyone!
Think of it as a memory instead of a craving. See if that helps. You'll have lots of memories of smoking in different situations. Just let them come and go.
How's it going Melody? You stay tough now, ya hear?!
Remember that no crave ever killed ANYONE....NO ONE can say that about smoking. Smoking does nothing GOOD, it just causes damage and stops us from growing emotionally. I remember feeling like I would never stop thinking about cigarettes, i was CONSUMED with thoughts of them and I asked my husband what HE WOULD ADVISE...he is a recovering alcoholic and he quit smoking five years after he quit drinking...back in 1989. He told me that he remembered that feeling and he said that the ONLY thing that worked for him was to get down on his knees and ask God to remove the mental obsession...he said it worked, he also said I might have to repeat it but that it would work. I will admit that I did not have a lot of faith in that BUT I was willing to try ANYTHING. I got down on my knees, tears streaming down my face and I asked God to PLEASE remove the mental obsession. I knew that if I smoked again, it would kill me...I know that now. I did it...yes...more than once, but it ALWAYS worked. It put me in touch with my Higher Power and those spirits who have gone before me and who want me to succeed. I very, very rarely have craves now...once in a while, a weird memory emerges...I KNOW smoking wouldn't help me with anything and I also know how disappointed I would be and how disappointed my beloved family would be...the one HERE as well as the one I live with.
You can do this, my friend...LEAN ON US!


We're excited to be getting your updates again. We really loved our time with you this summer, and wish you the best winds and currents possible.
Thanks David and Kathy! We're glad to spend time with you both as well.
Will miss the early winter season in Park City...send photos of your fun in the snow!


text:
\section*{Abstract}
We consider the Euler equations of incompressible fluids \cite{AK,Li}
and attempt to solve the initial value problem with the help of a concave maximization problem.
We show that this problem, which shares a similar structure with the optimal transport problem
with quadratic cost, in its "Benamou-Brenier" formulation \cite{BB,AGS,Vi},
always admits a relaxed solution that can be interpreted
in terms of $sub-solution$ of the Euler equations in the sense of convex integration theory
\cite{DS}.
Moreover, any smooth solution of the Euler equations can be recovered
from this maximization problem, at least for short times.
\subsection*{Keywords}
Fluid mechanics, partial differential equations, calculus of variation, optimal transport,
Euler equations
\section*{Introduction}
Let us fix a time interval $[0,T]$
and denote by $D$ the periodic box $D=\mathbb{R}^d/\mathbb{Z}^d$.
The Euler model
\cite{AK,Li}
of an incompressible fluid of unit mass density,
moving in $D$ during the time interval $[0,T]$, without
external forces, assumes the existence of a square-integrable, divergence-free vector field $V$, over $[0,T]\times D$,
such that (written in coordinates,
with the usual implicit summation
over repeated lower and upper indices)
$
\partial_t V^i+\partial_j(V^i V^j)
$
is a gradient field. In weak form, this means
\begin{equation}
\label{weak0}
\int_{[0,T]\times D}
\partial_i\varphi(t,x)V^i(t,x)dxdt=0,
\end{equation}
for all smooth function $\varphi$ over $[0,T]\times D$,
which encodes that $V$ is divergence-free and
\begin{equation}
\label{weak}
\int_{[0,T]\times D}
\left(\partial_jA_iV^i V^j+\partial_t A_iV^i\right)(t,x)dxdt
+\int_D P_0^i(x)A_i(0,x)dx=0,
\end{equation}
for all smooth divergence-free vector fields $A$
on $[0,T]\times D$,
vanishing at $t=T$,
which includes (weakly) the initial condition that $V$ is $P_0$ at time $t=0$,
$P_0$ being a given $L^2$ divergence-free vector field on $D$.

Our goal is to solve, by a concave maximization method, the initial value problem for the Euler model with as initial condition a
fixed divergence-free vector field $P_0$, square integrable over $D$ and of zero spatial mean.
The idea is very simple: we try to find a divergence-free vector field $V$,
weak solution to the Euler equation with initial condition $P_0$, of minimal kinetic energy. This leads to the saddle-point problem

\begin{equation}
\label{ivp0}
\mathcal{I}[P_0]
=\inf_V \sup_{A,\varphi}
\;\int_{[0,T]\times D}
\frac{1}{2}{|V|}^2
+\partial_jA_iV^i V^j+(\partial_t A_i+\partial_i\varphi)V^i
+\int_D P_0^iA_i(0,\cdot)
\end{equation}
$$
$$
over all  $L^2$ vector fields $V$
on $[0,T]\times D$,
all smooth divergence-free vector fields $A$ vanishing
at $t=T$, and all smooth
real functions $\varphi$. We may interpret $(A,\varphi)$ as Lagrange multipliers
for the constraint that $V$ is a weak solution to the Euler equations with initial condition $P_0$,
in the sense of (\ref{weak0},\ref{weak}).
Investigating problem (\ref{ivp0}) looks silly since the Euler equation to be solved is already
included as a constraint! Furthermore, for
smooth solutions of the Euler equation on the periodic box,
the kinetic energy is constant in time and, therefore, depends only on the data $P_0$,
so that...there seems to be nothing to minimize! However, for a fixed initial condition,
weak solutions are not unique and the conservation of energy is generally not true
as well known since the celebrated results of Scheffer, Shnirelman,
De Lellis and Sz\'ekelyhidi \cite{Sc,Sh,DS}. Therefore, since, in addition, weak solutions always exist, following Wiedemann \cite{Wi}, the minimization problem is definitely not meaningless.
\\
\\
In this paper, we mostly investigate the dual problem obtained by
exchanging the infimum and
the supremum in (\ref{ivp0}), leading to a concave maximization problem which will be
shown to be solvable in section \ref{existence0}, after a suitable reformulation of the concept
of weak solutions established in section \ref{reformulation}.
The resulting maximization problem roughly reads
$$
\sup_{(E,B)}
\;\;-
\int_{[0,T]\times D}
E\cdot(\mathbb{I}_d+2B)^{-1}\cdot E+2P_0\cdot E
$$
where $\mathbb{I}_d$ denotes the $d\times d$ identity matrix, $E$ and $B$ are respectively valued  in $\mathbb{R}^d$ and in the space of $d\times d$ symmetric
matrices, and subject to
$$
\partial_t B=LE,\;\;\;B(t=T,\cdot)=0,
$$
$L$ being a suitable first-order constant coefficient (pseudo-)differential operator on $D$,
namely (in coordinates)
$$
L^k_{ij}E_k=
\frac{1}{2}(\partial_j E_i+\partial_i E_j)
+\partial_i\partial_j(-\bigtriangleup)^{-1}\partial^k E_k,\;{\rm{where}}\;\partial^k=\delta^{kj}\partial_j\;
{\rm{and}}\;\bigtriangleup=\delta^{ij}\partial_i\partial_j.
$$
Surprisingly enough, this problem looks very similar to the Monge optimal mass transport problem with quadratic cost in its "Benamou-Brenier"
formulation \cite{BB,AGS,Vi}, which would read
$$
\inf_{\rho,Q} \int_{[0,T]\times D}
Q\cdot\rho^{-1}\cdot Q,
$$
where $\rho$ and $Q$ are respectively valued in $\mathbb{R}_+$ and $\mathbb{R}^d$ and subject to $\partial_t\rho+\partial_i Q^i=0$, while $\rho$ is prescribed at $t=0$ and $t=T$. Presumably, the maximization problem can be treated by the same numerical method as the one used in \cite{BB}.
\\
\\
Next, in section \ref{consistency}, we will
establish the consistency result that any local smooth solution of the Euler equations can be recovered,
from the maximization problem, for short enough times $T$.
\\
\\
Finally, in section \ref{duality0}, we will make a connection
between the maximization problem and the theory of sub-solutions to the Euler equations
which has recently attracted a lot of interest after the celebrated work of De Lellis and
Sz\'ekelyhidi \cite{DS} in the framework of Convex Integration theory.
\subsection*{Acknowledgment}
This work has been partly supported by the grant ISOTACE
ANR-12-MONU-0013 (2012-2016). The author thanks Nassif Ghoussoub
for exciting discussions (held at the Erwin Schr\"odinger Institute in the
summer of 2016) about his new theory of "optimal ballistic transport"
\cite{Gh}, which were certainly influential for the present paper.
He is also grateful to the Schr\"odinger Institute and to the
CNRS-INRIA MOKAPLAN team for their help during the preparation of this work.
\section{Reformulation of the weak formulation of the Euler equations}
\label{reformulation}
We first revisit definition (\ref{weak0},\ref{weak}) of weak
solutions to the Euler equations by substituting for $(A,\varphi)$
the smooth fields $(E,B)$
respectively valued
in $\mathbb{R}^d$ and in the set of
symmetric $d\times d$ matrices,
defined (in coordinates) on $[0,T]\times D$ by
$$
E_i=\partial_t A_i+\partial_i\varphi\;,
\;\;\;B_{ij}=
\frac{1}{2}(\partial_jA_i+\partial_i A_j).
$$
We first observe that $B(T,\cdot)=0$, while
$(E,B)$ satisfy the compatibility condition:
$$
\partial_t B_{ij}=
\frac{1}{2}(
\partial_jE_i+\partial_i E_j)
-\partial_i\partial_j\varphi.
$$
Since $A$ is divergence free, $B$ is trace-less and, therefore,
$$
\bigtriangleup \varphi=\partial^k E_k,\;\;\;{\rm{with\;notations:}}\;\partial^k=\delta^{jk}\partial_j,\;\;\;
\bigtriangleup \varphi=\partial^k \partial_k.
$$
Thus, in short,
$(E,B)$ are just subject to
constraint
\begin{equation}
\label{constraint-B-E}
\partial_t B=LE,\;\;\;B(T,\cdot)=0.
\end{equation}
where $L$ is the constant (pseudo-)differential operator of order 1 defined by
\begin{equation}
\label{L}
L^k_{ij}E_k=
\frac{1}{2}(\partial_j E_i+\partial_i E_j)
+\partial_i\partial_j(-\bigtriangleup)^{-1}\partial^k E_k,\;{\rm{where}}\;\partial^k=\delta^{kj}\partial_j\;
{\rm{and}}\;\bigtriangleup=\delta^{ij}\partial_i\partial_j.
\end{equation}
Constraint (\ref{constraint-B-E}) can be, as well, written in weak form:
\begin{equation}
\label{constraint-B-E+}
\int_{(t,x)\in[0,T]\times D}
B_{ij}(t,x)\zeta'(t)\psi^{ij}(x)
-E_k(t,x)\zeta(t)
\left(\partial_j\psi^{kj}-\partial^k(-\bigtriangleup)^{-1}\partial_i\partial_j\psi^{ij}\right)(x)=0
\end{equation}
for all smooth functions $\zeta$ on $[0,T]$ vanishing at $t=0$ and all smooth functions $\psi$ on $D$
valued in the set of $d\times d$ symmetric matrices.
Notice that expression (\ref{constraint-B-E+}) still makes sense
as $(E,B)$ are just bounded Borel measures over $[0,T]\times D$.
Later on, we will use the class, denoted by $\mathcal{EB}$,
of such measures subject to (\ref{constraint-B-E+}).
\\
\\
Next, in order to reformulate (\ref{weak0},\ref{weak})
entirely in terms of $(E,B)$ instead of $(A,\varphi)$
we have to express the time-boundary term
$
\int_D P_0\cdot A(0)
$
in terms of $(B,E)$. We have
$$
A(0,x)=-\int_0^T \partial_t A(t,x)dt,
$$
since $A(T,\cdot)=0$. Thus
$$
\int_D P_0\cdot A(0)=-\int_{[0,T]\times D} P_0\cdot\partial_t A=-\int_{[0,T]\times D} P_0\cdot E
$$
(by definition of $E$, using that $P_0$ is divergence-free
with zero spatial mean).
Finally, using $(E,B)$ instead of $(A,\varphi)$, in definitions
(\ref{weak0},\ref{weak}), we conclude:
\begin{Proposition}
\label{weak-new}
Given a divergence-free zero-mean $L^2$-vector-field $P_0$ on $D$,
an $L^2$ vector-field  $V$ over $[0,T]\times D$ is a weak solution to the Euler equations with initial condition $P_0$, in the sense of
(\ref{weak0},\ref{weak}), if and only if
\begin{equation}
\label{weakbis}
\int_{[0,T]\times D} V^i V^j B_{ij}+(V^i-P_0^i)E_i=0,
\end{equation}
for all smooth fields $(E,B)$
respectively valued
in $\mathbb{R}^d$ and in the set of
symmetric $d\times d$, that are subject to constraint (\ref{constraint-B-E}),
namely
$$
B(T,\cdot)=0,\;\;\;\partial_t B_{ij}=
\frac{1}{2}(\partial_j E_i+\partial_i E_j)
+\partial_i\partial_j(-\bigtriangleup)^{-1}\partial^k E_k.
$$
In addition, in the new definition (\ref{weakbis}) of weak solutions,
we may extend the range of trial fields $(E,B)$ to the class
$\mathcal{EB}_{2,\infty}$ which is the intersection of $L^2\times L^\infty$
with the class $\mathcal{EB}$ of all bounded Borel measures  on $[0,T]\times D$
satisfying (\ref{constraint-B-E+}).
\end{Proposition}
The proof is straightforward: the first statement directly follows from the previous calculations,
while the second one follows from the rather obvious property that $\mathcal{EB}_{2,\infty}$ is just the $L^2\times L^\infty$ weak-*
closure of the class $\mathcal{EB}_{smooth}$ of its own smooth elements.
$[$Indeed, every $(E,B)$ in $\mathcal{EB}_{2,\infty}$ can be approximated, as closely as needed,
by $(\tilde E,\tilde B)\in\mathcal{EB}_{smooth}$ in two steps: we first,
mollify $E$ on $[0,T]\times D$ and get $\tilde E$; then, we just set $\tilde B(t,x)=-\int_t^T L\tilde E(s,x)ds$ so that
(\ref{constraint-B-E}), and therefore (\ref{constraint-B-E+}), is still satisfied by $(\tilde E,\tilde B)$, while $\tilde B$
stays close to $B$.$]$

\section{A concave maximization problem}
\label{existence0}
Using the new definition (\ref{weakbis}) of weak solutions we found in the previous section, we may formulate
the original minimization problem (\ref{ivp0}) just as
\begin{equation}
\label{ivp1}
\mathcal{I}[P_0]
=\inf_V \sup_{(E,B)\in\mathcal{EB}_{2,\infty}}
\;\;\int_{[0,T]\times D} \frac{1}{2}V^i V^j (\delta_{ij}+2B_{ij})+(V^i-P_0^i)E_i,
\end{equation}

Since $\inf\sup\ge \sup\inf$, we get the lower bound
$$
\mathcal{I}[P_0]\ge \mathcal{J}[P_0]
=\sup_{(E,B)\in\mathcal{EB}_{2,\infty}}\inf_V
\;\;\int_{[0,T]\times D} \frac{1}{2}V^i V^j (\delta_{ij}+2B_{ij})+(V^i-P_0^i)E_i.
$$
In this "dual" problem, the infimum over all $L^2$ vector fields $V$ on
${[0,T]\times D\times \mathbb{R}^d}$ is very easy to deal with. Indeed, it is certainly equal to
$-\infty$ unless
\begin{equation}\label{vp}
\mathbb{I}_d+2B\ge 0,\;\;\;a.e.\;\;{\rm{in}}\; [0,T]\times D,
\end{equation}
in the sense of symmetric matrices.
Next, we observe that, because $(E,B)$ belongs to $\mathcal{EB}_{2,\infty}$, $B$ must be trace-free.
Indeed, this follows from (\ref{constraint-B-E}), using definition (\ref{L}) of $L$. So, denoting by
$\lambda(\alpha)\in\mathbb{R}$ the eigenvalues of $B$,
for $\alpha\in\{1,\cdot\cdot\cdot,d\},$ we have (using (\ref{vp})):
$$
0\le 1+2\lambda(\alpha)\le \sum_{\beta=1}^{d}(1+2\lambda(\beta))=d,
$$
and, therefore,
\begin{equation}\label{vpbound0}
-\mathbb{I}_d \le 2B\le (d-1)\mathbb{I}_d,
\end{equation}
which provides an a priori $L^\infty$ bound for B (since $B$ is valued in the set of symmetric
matrices).
We also get
\begin{equation}\label{vpbound}
(\mathbb{I}_d+ 2B)^{-1}\ge d^{-1}\mathbb{I}_d.
\end{equation}
and, after minimization in $V$,
\begin{equation}\label{ivpdual0}
\mathcal{J}[P_0]
=\sup_{(E,B)\in\mathcal{EB}_{2,\infty}}
\;\;-K[E,B]-\int_{[0,T]\times D}
P_0\cdot E,
\end{equation}
where
\begin{equation}\label{K0}
K[E,B]=\frac{1}{2}\int_{[0,T]\times D}E\cdot(\mathbb{I}_d+2B)^{-1}\cdot E.
\end{equation}
This immediately implies $J[P_0]\ge 0$
(just by taking $E=B=0$).
\\
Here, we emphasize that (\ref{ivpdual0}) is a concave maximization problem in $(E,B)$.
Indeed, we can write, point-wise in $(t,x)$,
$$
E\cdot(\mathbb{I}_d+2B)^{-1}\cdot E
=\sup_{M,Z} \;\;2E_iZ^i-(\delta_{ij}+2B_{ij})M^{ij}
$$
where $M$ and $Z$ are respectively $d\times d$ symmetric
matrices and vectors in $\mathbb{R}^d$ subject to
\begin{equation}\label{matrineq}
Z\otimes Z\le M,
\end{equation}
in the sense of symmetric matrices. This allows us to give a more precise definition of $K$, namely
\begin{equation}\label{K}
K[E,B]=\sup_{M\ge Z\otimes Z} \;\;\frac{1}{2}\int_{[0,T]\times D}
2 E_iZ^i-(\delta_{ij}+2B_{ij})M^{ij}
\in [-\infty,0],
\end{equation}
where the infimum is performed over all pairs $(Z,M)$
of continuous functions on
$[0,T]\times D$, respectively valued
in $\mathbb{R}^d$ and in the set of
symmetric matrices $M$.
Notice that definition (\ref{K}) makes sense already as $(E,B)$ is just a pair of bounded Borel measures on $[0,T]\times D$, and a fortiori as $(E,B)$ belong to $L^2\times L^\infty$. In both cases,
$K$ is a lower semi-continuous convex function of $(E,B)$ valued in $[0,+\infty]$.
Next, because of the lower bound (\ref{vpbound}), we get an $L^2$ a priori bound for $E$. Indeed,
by definition (\ref{K0}) of $K$, we have:
$$
\frac{1}{2d}\int_{[0,T]\times D}|E|^2\le K[E,B].
$$
So, for any $\varepsilon-$maximizer $(E,B)\in \mathcal{EB}_{2,\infty}$ of (\ref{ivpdual0}), we get
$$
0\le \mathcal{J}[P_0]
\le \varepsilon-K[E,B]-\int_{[0,T]\times D}P_0\cdot E
\le \varepsilon-\frac{1}{4d}\int_{[0,T]\times D}(2|E|^2+4d P_0\cdot E)
$$
$$
= \varepsilon-\frac{1}{4d}\int_{[0,T]\times D}(|E|^2+|E+2dP_0|^2-4d^2|P_0|^2)
\le \varepsilon-\frac{1}{4d}\int_{[0,T]\times D}(|E|^2-4d^2|P_0|^2)
$$
which provides the a priori bound, for every $\varepsilon-$maximizer $(E,B)\in \mathcal{EB}_{2,\infty}$ of (\ref{ivpdual0}),
\begin{equation}\label{bound-E}
\int_{[0,T]\times D}|E|^2\le 4d\varepsilon+4d^2 T\int_{D}|P_0|^2.
\end{equation}
We also deduce
$$
0\le \mathcal{J}[P_0]\le Td\int_{[0,T]\times D}|P_0|^2.
$$
$$
[{\rm{Indeed}}\;\;\;
0\le \mathcal{J}[P_0]\le\varepsilon-\frac{1}{4d}\int_{[0,T]\times D}(|E|^2-4d^2|P_0|^2)
\le\varepsilon+Td\int_{D}|P_0|^2.]
$$
By definition (\ref{K}), $K$ is lower semi-continuous with respect to the weak-* topology of
$L^\infty \times L^2$, while
$$
E\rightarrow \int_{[0,T]\times D}P_0\cdot E,
$$
is continuous (since $P_0$ is given in $L^2$) and $\mathcal{EB}_{2,\infty}$ is weak-*
closed in $L^\infty \times L^2$.
Thus, we conclude that the maximization problem
(\ref{ivpdual0})
always has at least an optimal solution $(E,B)$ in class $\mathcal{EB}_{2,\infty}$, since its
$\varepsilon-$maximizers stay confined in a fixed ball (and therefore a
weak-* compact subset)
of $L^\infty \times L^2$, as $\varepsilon$ goes to zero.
\\
\\
In addition, let us observe that, for any $(E,B)$ in $\mathcal{EB}_{2,\infty}$,
$$
\int_{D} \left(B_{ij}(t_1,\cdot)-B_{ij}(t_0,\cdot)\right)\psi^{ij}\le
\sqrt{t_1-t_0\;}\;
||E||_{L^2([0,T]\times D)}||L^*\psi||_{L^\infty(D)}
$$
for all $t_0\le t_1$ in $[0,T]$ and or all smooth functions $\psi$ on $D$, valued in the set of $d\times d$ symmetric matrices, where
$$
(L^*)^k_{ij}\psi^{ij}
=\partial_j\psi^{kj}-\partial^k(-\bigtriangleup)^{-1}\partial_i\partial_j\psi^{ij}
$$
(because of (\ref{constraint-B-E}) and, more precisely,
(\ref{constraint-B-E+})). Thus
any maximizer $(E,B)$ must satisfy
$$
\int_{D} \left(B_{ij}(t_1,\cdot)-B_{ij}(t_0,\cdot)\right)\psi^{ij}
\le 2d\sqrt{T}
\sqrt{t_1-t_0\;}\;||P_0||_{L^2(D)}||L^*\psi||_{L^\infty(D)},
$$
because of (\ref{bound-E}).
This shows that $B$ belongs to $C^{1/2}([0,T],C^1(D)'_{w*})$.
\\
\\
So, we have finally obtained:
\begin{Theorem}
\label{existence}
Let $P_0\in L^2(D,\mathbb{R}^d)$ be
a divergence-free vector field
of zero spatial mean.
Let $\mathcal{EB}_{\infty,2}$ be the class of all $L^2\times L^\infty$ fields $(E,B)$ on
$[0,T]\times D$,
respectively valued
in $\mathbb{R}^d$ and in the set of
symmetric $d\times d$ matrices, that are subject to constraint
$$
B(T,\cdot)=0,\;\;\;\partial_t B_{ij}=
\frac{1}{2}(\partial_j E_i+\partial_i E_j)
+\partial_i\partial_j(-\bigtriangleup)^{-1}\partial^k E_k
$$
(or, more precisely, (\ref{constraint-B-E+})).
Then the maximization problem
$$
\mathcal{J}[P_0]
=\sup_{(E,B)\in\mathcal{EB}_{2,\infty}}
\;\;-
\int_{[0,T]\times D}\left(
\frac{1}{2}E\cdot(\mathbb{I}_d+2B)^{-1}\cdot E+P_0\cdot E\right)
$$
(or, more precisely, (\ref{ivpdual0},\ref{K})), always admits a solution $(E,B)$.
In addition,
$$
{\rm{spect}}(B)\subset[-1/2,(d-1)/2],\;\;
\int_{[0,T]\times D}|E|^2\le 4d^2 T\int_{D}|P_0|^2,\;\;
0\le\mathcal{J}[P_0]\le Td\int_{D}|P_0|^2,
$$
and $B$ belongs to $C^{1/2}([0,T],C^1(D)'_{w*})$.
\end{Theorem}
\rem
Notice that all the a priori bounds found for problem (\ref{ivpdual0})
are still valid when addressing the $relaxed$ maximization
problem
\begin{equation}\label{ivpdual}
\sup_{(E,B)\in\mathcal{EB}}
\;\;-K[E,B]-\int_{[0,T]\times D}
P_0\cdot E,
\end{equation}
where we only require $(E,B)$ to be plain bounded Borel measures and no longer in
the space $L^2\times L^\infty$, while $K$ should be understood
as in (\ref{K}) and $P_0$ is restricted to be in the class of continuous divergence-free vector fields,
with zero-mean, on $D$, so that
$$
E\rightarrow \int_{[0,T]\times D}P_0\cdot E,
$$
is still well defined and continuous.
Since the $\varepsilon-$maximizers of this relaxed problem
must satisfy the $same$
a priori bounds (\ref{vpbound0},\ref{bound-E}) as the ones of  (\ref{ivpdual0}),
they $necessarily$ belong to the subspace $L^2\times L^\infty$, which implies that
both problems (\ref{ivpdual0}) and (\ref{ivpdual})
admit the same optimal value $\mathcal{J}[P_0]$
and the same maximizers.
\\
In the last section of this paper, the relaxed problem (\ref{ivpdual})
will be reformulated and solved (at least in the case when $P_0$ is continuous)
by a duality method which will establish a link with the concept of
sub-solution used by De Lellis and Sz\'ekelyhidi in their approach of the Euler equations by
"Convex Integration" \cite{DS}.
\section{Recovery of smooth classical solutions to the Euler equations}
\label{consistency}
We want now to show that the optimization problem (\ref{ivpdual0}) addressed
in the previous section
is consistent with the classical theory of local smooth solutions of the initial value problem for the Euler equations. More precisely:
\begin{Theorem}
\label{smooth}
Let $V$ be a smooth solution to the Euler equations with initial condition $P_0$
and let $A$ be the unique solution of the linear final-value problem
\begin{equation}\label{fvp}
\partial_t A_i+(\delta_{ij}+\partial_j A_i+\partial_i A_j)V^j+\partial_i\varphi=0,
\;\;\;\partial^j A_j=0,\;\;\;A(T,\cdot)=0.
\end{equation}
If  $T$ is small enough the matrix-valued field $\delta_{ij}+\partial_j A_i+\partial_i A_j$
stays uniformly bounded away from zero in $[0,T]\times D$ and, then, the pair $(E,B)$
defined by
$$
E_i=\partial_t A_i+\partial_i\varphi\;,
\;\;\;B_{ij}=
\frac{1}{2}(\partial_jA_i+\partial_i A_j)
$$
is a a maximizer for the concave maximization problem (\ref{ivpdual0}),
while $V$ can be recovered as  $V=-(\mathbb{I}_d+2B)^{-1}E$.
\end{Theorem}
\subsection*{Proof of Theorem \ref{smooth}}

Let $V$ be a smooth solution to the Euler equations, which implies that $V$
is weak solution in the sense of Proposition \ref{weak-new}.
Let us solve the linear final-value problem (\ref{fvp}),
which means that $A$ is a time-dependent divergence-free vector of zero spatial mean,
vanishing at $t=T$ such that, in coordinates,
$$
\partial_t A_i+(\delta_{ij}+\partial_j A_i+\partial_i A_j)V^j+\partial_i \varphi=0,
\;\;{\rm{in}}\;[0,T]\times D,\;\;\int_D A_i(t,\cdot)=0,
\;\;\forall t\in [0,T],
$$
for some scalar field $\varphi$, which can be alternately written
$$
\partial_t A_i+V^j\partial_j A_i-A_j\partial_i V^j+\partial_i \psi+V_i=0,
\;\;\partial^j A_j=0,\;\;A(T,\cdot)=0,\;\;\int_D A_i(t,\cdot)=0,
$$
(where $\psi$ is just $\varphi+A_jV^j$).
Because $V$ is supposed to be smooth, this linear problem can be solved by standard methods
and admits
a unique smooth solution $A$ on $[0,T]\times D$.
In addition, there is a positive
time $T_0$ depending only on $V$, such that, as long as $0<T\le T_0$,
the field of symmetric matrices
$\delta_{ij}+\partial_j A_i+\partial_i A_j,$
which is just $\delta_{ij}$
at time $T$,
stays bounded away from $0$,
uniformly in $(t,x)\in [0,T]\times D$.
In this case, we deduce from (\ref{fvp})
\begin{equation}\label{V}
E=-(\mathbb{I}_d+2B)\cdot V,\;\;\;V=-(\mathbb{I}_d+2B)^{-1}\cdot E,
\end{equation}
where $B_{ij}=\partial_j A_i+\partial_i A_j$ and $E_i=\partial_ t A_i+\partial_i\varphi$.
Thus, using notation (\ref{K0}), namely
$$
K[E,B]=\frac{1}{2}\int_{[0,T]\times D}E\cdot(\mathbb{I}_d+2B)^{-1}\cdot E,
$$
we get
$$
2K[E,B]=-\int_{[0,T]\times D}V\cdot E=\int_{[0,T]\times D}V\cdot(\mathbb{I}_d+2B)\cdot V
=\int_{[0,T]\times D}2V\cdot B\cdot V+|V|^2.
$$
By definition, $(E,B)$ are smooth and satisfies constraint (\ref{constraint-B-E}), namely
$$
\partial_t B=LE,\;\;\;B(T,\cdot)=0.
$$
Using that $V$ is a weak solution of the Euler equations in the sense of Proposition (\ref{weak-new}),
we get (\ref{weakbis}), namely
$$
\int_{[0,T]\times D} V\cdot B\cdot V+(V-P_0)\cdot E=0.
$$
Thus
$$
2K[E,B]=\int_{[0,T]\times D}2P_0\cdot E-2V\cdot E+|V|^2
=4K[E,B]+\int_{[0,T]\times D}2P_0\cdot E+|V|^2,
$$
which shows
$$
-K[E,B]-\int_{[0,T]\times D}P_0\cdot E=
\frac{1}{2}\int_{[0,T]\times D}|V|^2.
$$
By definition of problems (\ref{ivp1}) and (\ref{ivpdual0}),
we have on one hand
\begin{equation}\label{euler-classic}
\int_{[0,T]\times D} \frac{1}{2}|V|^2\ge \mathcal{I}[P_0]\ge \mathcal{J}[P_0]
\end{equation}
and, on the other hand,
$$
\mathcal{J}[P_0]\ge -K[E,B]-\int_{[0,T]\times D}P_0\cdot E.
$$
So, we conclude that
$$
\int_{[0,T]\times D} \frac{1}{2}|V|^2=\mathcal{I}[P_0]=\mathcal{J}[P_0]=
-K[E,B]-\int_{[0,T]\times D}P_0\cdot E,
$$
which means that there is no duality gap and that $(E,B)$ is a maximizer of problem (\ref{ivpdual0}),
from which $V$ can be recovered as $V=-(\mathbb{I}_d+2B)^{-1}\cdot E$.
This completes the proof of Theorem \ref{smooth}.

\section{Convex duality and sub-solutions of the Euler equations}
\label{duality0}
Our last result establishes a link between the relaxed
concave maximization problem (\ref{ivpdual}) and the concept of sub-solution
for the Euler equations, as discussed in \cite{DS} in the context of "Convex Integration".
Here, we limit ourself to sub-solutions that are continuous on $[0,T]\times D$.
\begin{Definition}
\label{def}
We say that a pair of continuous functions $(Z,M)$
on $[0,T]\times D$, respectively valued in $\mathbb{R}^d$ and in the space of $d\times d$ symmetric matrices, is a sub-solution to
the Euler equations with initial condition $P_0$ if
\\
i) $M\ge Z\otimes Z$, holds true point-wise in $[0,T]\times D$, in the sense of symmetric matrices;
\\
ii) for every smooth divergence-free vector fields $A$ on $[0,T]\times D$,
of zero spatial mean, that vanishes
at $t=T$ and
each smooth functions $\varphi$ on $[0,T]\times D$, we have
\begin{equation}\label{diff20}
\int_{(t,x)\in[0,T]\times D} \partial_i\varphi(t,x)Z^i(t,x)=0,
\end{equation}
\begin{equation}\label{diff2}
\int_{(t,x)\in[0,T]\times D} \left(\partial_t A_i(t,x)Z^i(t,x)+\partial_i A_j(t,x)M^{ij}(t,x)\right)=-\int_D A_i(0,x)P^i_0(x)dx.
\end{equation}
\end{Definition}
Just as we did for weak solutions, we get:
\begin{Proposition}
\label{sub-new}
$(Z,M)$ is a continuous sub-solution of the Euler equations  with initial condition $P_0$
if and only if $M\ge Z\otimes Z$ and
\begin{equation}
\label{subbis}
\int_{[0,T]\times D} M^{ij}B_{ij}+(Z^i-P_0^i)E_i=0,
\end{equation}
for all smooth fields $(E,B)$
respectively valued
in $\mathbb{R}^d$ and in the set of
symmetric $d\times d$ matrices, that are subject to constraint (\ref{constraint-B-E}),
namely
$$
B(T,\cdot)=0,\;\;\;\partial_t B_{ij}=
\frac{1}{2}(\partial_j E_i+\partial_i E_j)
+\partial_i\partial_j(-\bigtriangleup)^{-1}\partial^k E_k.
$$
\end{Proposition}

Let us now state the main result of this last section:

\begin{Theorem}
\label{duality}
Let  $P_0$ be a continuous divergence-free vector-field, with zero spatial mean,  on $D$.
Then the infimum of
$$
\frac{1}{2}\int_{[0,T]\times D} \delta_{ij}M^{ij}
$$
over all continuous sub-solutions $(Z,M)$ of the Euler equations with initial condition $P_0$
(in the sense of Proposition \ref{sub-new}) is finite and just equal to the optimal value of
the relaxed problem (\ref{ivpdual}), namely
$$
\mathcal{J}[P_0]=\max_{(E,B)\in\mathcal{EB}}\;\; -\int_{[0,T]\times D}  P_0\cdot E+
\frac{1}{2}\;E\cdot (\mathbb{I}_d+2B)^{-1}
\cdot E,
$$
where $\mathcal{EB}$ is the class of all Borel measures subject to constraint
(\ref{constraint-B-E+}).
\end{Theorem}

\subsection*{Proof of Theorem \ref{duality}}

The infimum considered at the beginning of Theorem \ref{duality} can
be expressed exactly as
$$
\inf_{(Z,M)} K_1(Z,M)+K_2(Z,M)
$$
where $K_1$ and $K_2$ are
the following convex functions
\begin{equation}\label{K1}
K_1(Z,M)=
\int_{[0,T]\times D} \frac{1}{2}\delta_{ij}M^{ij}
\;\;{\rm{or}}\;\;+\infty
\end{equation}
whether or not $M\ge Z\otimes Z$ is satisfied point-wise, in the sense of symmetric matrices,
\begin{equation}\label{K2}
K_2(Z,M)=K_3(Z-P_0,M)
\end{equation}
\begin{equation}\label{K3}
K_3(Z,M)=
\sup\;\{\int_{[0,T]\times D} E_iZ^i+B_{ij}M^{ij},\;\;\;(E,B)\in \mathcal{EB}_{smooth}\},
\end{equation}
where
$\mathcal{EB}_{smooth}$ denotes the class
of all smooth pairs
$(E,B)$
defined on $[0,T]\times D$
with values respectively taken in $\mathbb{R}^d$ and in the set of $d\times d$
symmetric matrices, which satisfy constraint (\ref{constraint-B-E}), namely
$$
\partial_t B=LE,\;\;\;
B(T,\cdot)=0,
$$
where $L$ is the linear operator defined by (\ref{L}). Notice that $B$ is identically trace-free
(since $\delta^{ij}L^k_{ij}=0$ and $B(T,\cdot)=0$) which implies
$
K_3(Z,M)=0,
$
whenever $Z=0$ and $M$ is identically diagonal, a property that we will use in a moment.
\\
\\
There is a rather obvious point $(Z,M)$, namely
$$
Z(t,x)=P_0(x),\;\;M(t,x)=(1+|P_0(x)|^2)
\mathbb{I}_d,\;\;\forall (t,x)\in [0,T]\times D,
$$
at which $K_1$ is finite and continuous while $K_2$ is just finite.
\\
\\
$[$Indeed, on one hand,
$\xi\cdot(M-Z\otimes Z)\cdot\xi=(1+|P_0|^2)|\xi|^2-(P_0\cdot \xi)^2\ge |\xi|^2$,
for all $\xi\in\mathbb{R}^d$,
which implies that $M\ge Z\otimes Z$ holds true in a neighborhood (for the sup-norm) of $(Z,M)$
and, therefore, by definition (\ref{K1}),
$$
K_1(Z,M)=\int_{[0,T]\times D} \frac{1}{2}\delta_{ij}M^{ij}
$$
is finite and continuous in that neighborhood.
On the other hand,
$$
K_2(Z,M)=K_3(Z-P_0,M)=K_3(0,M)=0,
$$
since $M$ is diagonal, as just noticed above.$]$
\\
\\
 This is enough to apply Rockafellar's duality theorem (as stated in Chapter 1
of Brezis' book \cite{Brz}) and deduce
\begin{equation}
\label{rocka}
\inf_{(Z,M)} K_1(Z,M)+K_2(Z,M)
=\max_{(E,B)} -K^*_1(-E,-B)-K^*_2(E,B),
\end{equation}
where the minimization is performed over the Banach space of all pairs of continuous functions
$(Z,M)$ valued in $\mathbb{R}^d$ and in the space of $d\times d$ symmetric matrices, while
the maximization is performed over the dual Banach space of all pairs of bounded Borel
measures $(E,B)$, still valued
in $\mathbb{R}^d$ and in the space of $d\times d$ symmetric matrices.
In this relation,
$K^*_1$, $K^*_2$ denote the Legendre-Fenchel transform of $K_1$ and $K_2$, namely
$$
K^*_1(E,B)=\sup_{(Z,M)}-K_1(Z,M)+\int_{[0,T]\times D}  Z^iE_i+M^{ij}B_{ij}
$$
$$
K^*_2(E,B)=\sup_{(Z,M)}-K_2(Z,M)+\int_{[0,T]\times D}  Z^iE_i+M^{ij}B_{ij}.
$$
In the duality equality (\ref{rocka}),
the calculation of $K^*_1(-E,-B)$ is easy. Indeed,
$$
K^*_1(-E,-B)=\sup_{M\ge Z\otimes Z}\int_{[0,T]\times D}  -Z^iE_i-\frac{1}{2}M^{ij}
(\delta_{ij}+2B_{ij})
$$
is equal to $+\infty$, unless $\mathbb{I}_d+2B
\ge 0$ in the sense of symmetric matrices, in which case
$$
K^*_1(-E,-B)=\sup_{Z}\int_{[0,T]\times D}  -Z^iE_i-\frac{1}{2}(\delta_{ij}+2B_{ij})Z^i Z^j,
$$
which we can write in the more compact (but less precise) form:
$$
K^*_1(-E,-B)=\frac{1}{2}\int_{[0,T]\times D}  E\cdot (\mathbb{I}_d+2B)^{-1}\cdot E\;\;\in [0,+\infty].
$$
Let us now compute $K_2^*$. We find (by definition (\ref{K2})
$$
K^*_2(E,B)=\sup_{(Z,M)}\;-K_3(Z-P_0,M)+\int_{[0,T]\times D}  E_i Z^i+B_{ij}M^{ij}
$$
$$
=K_3^*(E,B)+\int_{[0,T]\times D}  E_i P_0^i.
$$
By definition of $K_3$ in (\ref{K3}), $K^*_3(E,B)$ is just zero or $+\infty$ whether or not
$(E,B)$ belongs to the weak-* closure
of class $\mathcal{EB}_{smooth}$.
This closure is nothing but the class $\mathcal{EB}$
of all bounded Borel measures $(E,B)$ valued
in $\mathbb{R}^d$ and in the space of $d\times d$ symmetric matrices that satisfy constraint
(\ref{constraint-B-E}), or, more precisely (\ref{constraint-B-E+}).
$[$The reason being the same as the one for which $\mathcal{EB}_{\infty,2}$ is the
weak-* closure of class $\mathcal{EB}_{smooth}$ in $L^2\times L^\infty$ as already explained
when proving Proposition \ref{weak-new} in section \ref{reformulation}.$]$
Therefore, the duality equality (\ref{rocka}) exactly gives the result stated in Theorem
\ref{duality} which completes the proof.

redpajama_set_name: RedPajamaArXiv


Orthogonality: Do the chapters cover distinct subjects of my work (good), or are there many overlaps in the subjects covered by the chapters (bad)?
Completeness: Do the chapters form a complete impression of my work (good) or do I miss some important issues (bad)?
Pertinence: Are all the chapters pertinent (they are about things that are used in the work, which is good), or do I have lots of text just to fill in pages (bad)?
Balance: Are the chapters balanced with respect to the amount of information (good), or do I have a couple of 'thin' chapters and one or two "thick' ones (bad)?
Consistency: Is your structure built according to a logical order of subjects, like, e.g., problem definition, approach, produced results and conclusions (good), or is the structure a collection of unrelated items (bad)?
Take care of the audience you are writing for.
Give preference to simple and short sentences.
Be precise. For example, use only one term to refer to some concept and keep the terminology consistent.
Give preference to the direct forms. For example, it is preferable to write 'The chapter discusses…' in place of 'In the chapter … is discussed'.
Give preference to the present tense. For example, it is preferable to write 'This chapter discusses…' in place of 'This chapter will discuss' or 'This chapter discussed'.
Try to make the layout of your text such that it is 'inviting to read'. For example, do not write too much text in a page without a break (e.g., section, sub-section, figures of tables), separate paragraphs with empty space or indentation, and do not emphasize too many words.
Emphasis should be homogenous throughout the text. We recommend the use of italics for emphasis.
A clear figure or table says more than 1000 words, but be careful: a bad figure says 1000 wrong words!
Be consistent with layout, captions, cross-references, etc. For example, place figures and captions always in the same place, use always the same font for similar things, etc.
Use chapters and sections to enforce the logical structure of your reasoning. This results in a thesis that appeals to the intuition of the reader.
Do not go too deep in the sub-sections. This normally indicates that the whole thesis is badly structured. For example, this manual has 20 to 30 pages and goes until level 2 (e.g., section 3.2); for an MSc thesis of around 100 to 150 pages it is reasonable to go until level 3.
Every time you have numbered sections in a chapter or numbered subsections in a section, you should have at least two. For example, a numbered section hanging alone in a chapter actually means that the chapter remains monolithic.
Avoid using footnotes, unless you have some remark that would ruin the line of reasoning if placed in the body of the text. These situations are very rare.


"Only a fool learns from his own mistakes. The wise man learns from the mistakes of others." ― Otto von Bismarck – Author of Gedanken und Erinnerungen. It makes logical sense to watch your competitors and learn from their marketing mistakes and their successes.
Marketing requires a lot of trial and error – why not skip as many lessons as you can by learning from your opposition, nothing nasty or sinister here, just not making the same mistakes they have. If you bumped into them at a function and asked them about their marketing lessons which they were happy enough to share with you, would you go and implement all the ones that were dismal failures for them – absolutely not, you will use the ones that worked.
We will speak mostly about digital marketing in this article, but on the physical marketing front, when you see their marketing gifts, or campaigns, ask your clients that have been exposed to the opposition marketing, whether their efforts are working – 9 times out of 10 they will give you the information you need and where to improve.
In the search results, look at the advertising Adwords – are the many firms advertising for that space – if not, there is an opportunity for you to grab an advert there that may not cost as much as you think.
If the top spots are made up of a law directory, make sure you are advertising with them and that your entry is as informative in the listing as the ones that appear above you in the rankings.
Once you visit the website of the opposition law firm, right click on the web page and "View Page Source" to see the meta data of that page.
See if any specific pages show up in the results and see what content they have that is catching the attention of the search engines.
Use Google Adwords Keyword Tool and use the opposition website to get new keyword ideas, this will tell you what keywords are prominent on their website – you may get some ideas on which will work for your site as well.
See if their website is secure and using SSL – if so the site address would start with "https" and not "http" – Google is rating sites higher if they are secure.
Use https://www.semrush.com or https://www.spyfu.com or http://www.keywordspy.com to analyse the Search Engine data – see the keywords, the backlink sites, their social media exposure etc.
Does the opposition website offer a blog, if so what topics seem to be grabbing attention?
Are the contact details easy enough to find and act on?
Is there a definite call to action on the website?
Visit their social media pages, look for the interaction they are getting, which topics and ideas are of interest to the clients?
Which business pages like their page, they may be interested in your firm as well?
See how quickly they respond to questions and input from their "friends".
What pages do they follow, see if there would be a mutual benefit between your firm and the business/person the opposition follow?
If they are using social links with counters, where you can easily share their content to social media sites, see which of their content is shared most often and to which social network.


Allan Goodwillie wrote: Ha John!
Serjt-Dave wrote: Whens the party?
Thanks Allan, the guys are certainly very keen to ensure that operation and signalling are correct. I've joined the group very late so these wagons are my first contribution to the layout.
Very sad news, Colin and I had swapped PMs in the past as well. Thoughts are with you and the family.
In the photo below, on the first wagon in the train, what would the significance of the yellow stripes on the body be?
Nice work so far Dave, I'm about 80% of the through the Penbits 45 bogies which are very similar.


text:
Critical Dems want Obama to chart own course on jobs
JIM KUHNHENN | THE ASSOCIATED PRESS
WASHINGTON — The tiff over the timing of President Barack Obama's jobs speech to Congress offers little hope that Republicans and the White House will now find common ground on how to reduce the nation's painfully high unemployment. In fact, some Democrats say it's time Obama stopped trying so hard to negotiate.
On matters large and small, Obama has yielded to House Speaker John Boehner in a string of concessions that have unnerved Democrats and emboldened Republicans. A chorus of Democratic voices is now demanding that the president abandon his attempts at being a compromiser and instead lay out an ideological vision that distinguishes him from Republicans and becomes a template for his re-election.
Obama had asked Congress to convene a joint session next Wednesday so he could announce his jobs agenda. Boehner objected, telling the president it would be better if he came the next night. Republicans were irritated that Obama wanted to speak at the same time Republican presidential candidates would be debating in California — and sharing TV time with him.
In the end, Obama accepted Boehner's invitation to speak at 5 p.m. MDT next Thursday, early enough to avoid yet another conflict — with the opening game of the National Football League season.
Obama must create a clear contrast between what he wants and what the Republicans want, Simon Rosenberg, president of the liberal-leaning think tank NDN, wrote this week. ''If the president is to win the election next year, he will have to first win the economic debate with the Republicans, something, to date, he has not done.''
Democratic strategist James Carville was even sharper, decrying the spectacle of the president being forced to change the day of his address to a joint session of Congress after Boehner took issue with Obama's initial request.
''The last thing that the White House needed was to appear to cave in to the speaker, and that's what happened,'' he said Thursday on ABC.
The pointed advice comes as Democrats are becoming increasingly anxious that joblessness and a weak economy are defining Obama's presidency and imperiling his re-election. His attempts to compromise with Republicans, they argue, have resulted in policies that have hurt him and the economy.
The critique goes to the heart of what Obama advisers say is the president's inclination to propose policies that have a chance of being accomplished. It also challenges the White House strategy of portraying the president as a sensible and pragmatic leader who is as frustrated with the ways of Washington as the public.
White House spokesman Jay Carney reiterated on Thursday that the president intends to offer proposals that ''are reasonable and . . . should receive bipartisan support.''
That strategy, these Democrats say, has not helped the president set a course for the economy.


Good morning, I hope your wind and rain has stopped. We have had 2 days with lots of showers after what has seemed like an endless summer. The sun is back today but the change of season is here. You have almost run out of road across Canada. What a feat! When you are ending your trip, 6 of us gals will be biking 200+km of the Kettle Valley. We plan to take a week, doing less than 50 km a day with stops to swim in the lakes and sip wine when we hit Naramata. Congratulations on your coast to coast ride!!!


text:
package network;

import com.google.gson.Gson;

/**
 * @author oguzb
 */
public class Message {
    protected P2PManager.MessageType type;
    protected Object content;

    public Message(P2PManager.MessageType type, String content) {
        this.type = type;
        this.content = content;
    }

    public Message(P2PManager.MessageType type, Object contentObject) {
        this.type = type;
        if(contentObject != null) {
//            this.content = new Gson().toJson(contentObject);
            this.content = contentObject;
        }
        else {
            this.content = "";
        }
    }

    public Message(P2PManager.MessageType type) {
        this.type = type;
        this.content = "";
    }

    public P2PManager.MessageType getType() {
        return type;
    }

    public void setType(P2PManager.MessageType type) {
        this.type = type;
    }

    public Object getContent() {
        return content;
    }

    public void setContent(Object content) {
        this.content = content;
    }

    public String makeJson() {
        return new Gson().toJson(this);
    }
}