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SME eNews - View Past Issue
A: MiningEngineeringMagazine.com. Daily news updates, 24-hour metal prices, special web-only features, plus all the high-quality magazine content you’re used to getting from Mining Engineering—all as part of your regular membership. Log in with your member number and access the Mining Engineering web experience today!
SME thanks AngloGold and MMSA
Thank you to AngloGold and MMSA for their continued generous support of the SME Foundation and its programs. AngloGold once again showed its support for our educational programs with a contribution of $10,000 and MMSA has provided $40,000 for the new Minerals Education Coalition (MEC) program.
We appreciate and are very grateful to everyone who supports our programs, no matter the size of the contribution. Everything adds up and, as the saying goes, "you get to a million dollars one penny at a time."
Thank you everyone for your continued support of the SME Foundation and its programs!
All participants will receive a 2012 online-only subscription to Minerals & Metallurgical Processing; winners will receive two copies of the May 2012 Student Poster Contest issue, in which the winners are announced.
Stay tuned for the May 2012 issue of M&MP, in which selected abstracts of the winning student posters will be presented, along with an introduction by editorial board member Jon Kellar. For more information about the 2013 MPD Student Poster contest, click here or contact Emily Wortman-Wunder at wunder@smenet.org or Tessa Baxter at Baxter@smenet.org.
Don’t forget! Time is running out to take advantage of M&MP’s new subscriber Annual Meeting sale: subscribe for the first time between now and March 31, 2012, and get M&MP for the fantastic low price of $50 for Online Only or $75 for Print & Online (sorry, U.S. addresses only).
Washington Updates
House passes bipartisan bill protecting coal mining
On February 29, the House Natural Resources Committee passed H.R. 3409, the "Coal Miner Employment and Domestic Energy Infrastructure Protection Act" with a bipartisan vote of 26-18. The legislation, sponsored by Rep. Bill Johnson (R-OH), would prohibit the Secretary of the Interior from approving any new rules or regulations that could adversely impact employment in coal mines, cause a reduction in federal, state or tribal revenue from coal mining, or diminish the ability of the American people to produce coal. Specifically, this legislation opposes the Administration’s reconsideration of the Stream Buffer Zone Rule for coal mining that took five years of environmental analysis and scientific consideration to complete. An Associated Press story revealed that the new regulation could cost up to 7,000 coal mining jobs and have a negative economic impact on 22 states. A more recent study by ENVIRON (PDF) shows similar or higher job losses as a result of the implementation of this proposed rule.
SME board member to testify at House USGS budget hearing
On March 22, SME Board member and Nevada state geologist Jon Price will testify on behalf of SME before the House Natural Resource’s Subcommittee on Energy and Mineral Resources. The subcommittee is holding an oversight hearing titled, "Effects of the President’s FY 2013 Budget for the U.S. Geological Survey on Private Sector Job Creation, Hazard Protection, Mineral Resources Deficit Reduction." The proposed FY 2013 budget for the USGS is $34.5 million above the 2012 enacted level for a total 2013 budget request of $1.1 billion. The budget includes $97.1 million for energy, minerals and environmental health, a $914,000 increase over this year's budget. Nevertheless, it includes program reductions of $5.3 million in the Minerals Resource Program. The mission of the USGS National Minerals Information Center is to collect, analyze and disseminate information on the domestic and international supply of and demand for minerals and mineral materials essential to the U.S. economy and national security.
MSHA responds to congressional inquiry on technical support documents
U.S. House Committee on Education and the Workforce Chairman John Kline (R-MN) commended the Mine Safety and Health Administration (MSHA) for addressing a flaw in its internal operations that withheld important safety information from mine operators. In a November 2011 letter (PDF) to Assistant Secretary of Labor for Mine Safety and Health Joe Main, Chairman Kline raised concerns about MSHA’s numerous failures to transmit technical support documents to mine operators. The support documents contain recommendations that could improve mine safety. Mines that failed to receive technical reports include Upper Big Branch Mine in Montcoal, WV and the Lucky Friday Mine in Mullan, ID.
In response (PDF) to Chairman Kline’s request for a review of agency policy, Assistant Secretary Main stated revised procedures now in place “will ensure that Technical Support investigation findings are timely transmitted to mine operators.”
"Safety reports should never fall through the cracks of a federal bureaucracy," said Chairman Kline. "Instead, they must be placed in the hands of mine operators who have a responsibility to address any concerns. I hope this represents a new chapter at MSHA in which important safety and health information is always relayed to our nation’s mine operators. The committee will keep a close eye on MSHA’s enforcement of this new internal policy."
SEC to phase in conflict minerals rule
On March 7, the SEC revealed that it will phase in compliance by public companies of new disclosure regulations whose products contain certain so-called African "conflict minerals." Companies will not be forced to immediately start complying with the new disclosure regulations set to be adopted this year, the top U.S. securities regulator revealed on Tuesday.
During a hearing on the SEC’s FY 2013 budget, the commission said they are working to finalize the rule in the next couple of months that will include a phase-in compliance period to give sufficient time for some of the supply chain due diligence mechanisms to be developed and put in place.
The conflict-minerals rule stems from a provision tucked into the 2010 Dodd-Frank financial oversight law at the last minute. The provision requires the SEC to establish new rules forcing companies to disclose whether they use tantalum, tin, gold or tungsten from the war-torn Democratic Republic of the Congo.
As proposed, companies would need to identify if any conflict minerals are used in their products. If the minerals are present, they would then need to conduct a due diligence check to track them through the supply chain to their origins. An audited conflict minerals disclosure would also need to be filed as an exhibit to a company's annual report.
But the SEC has been bogged down with delays after it became clear the rule was much more complex to implement than it appeared on paper. The law also gives the SEC little wiggle room to be flexible, frustrating U.S. companies and regulators alike.
On March 6, the Northwest Mining Association filed a lawsuit (PDF) in Arizona federal district court against the Obama Administration for blocking access to hundreds of millions of pounds of the high-grade uranium ore in Arizona. NWMA asserts (PDF) in its complaint that U.S. Department of the Interior Secretary Ken Salazar’s January 2012 order withdrawing more than 1 million acres of federal land in northern Arizona from location and entry under the 1872 Mining Law violates the Federal Land Policy and Management Act, the National Forest Management Act and the National Environmental Policy Act. NWMA is represented in the suit by the Mountain States Legal Foundation.
Canada seeks 100K new miners in next decade
Canada’s mining sector is entering a period of "significant and sustained growth," according to a recent report (29.66MB PDF) from the Mining Association of Canada, which will translate into the need to hire more than 100,000 additional workers in the next decade.
The association estimates that Canada’s mining industry plans to invest a further $139-billion in new projects nationwide in the next 10 years. Demand for commodities in countries such as China and India are driving part of the overall appetite for investment in Canada’s mining industry. Among the top-paying and most highly sought-after workers are geologists and other highly skilled geosciences professionals, but the need for more talent is being felt at every level of the industry including mineral extraction, smelting, fabrication and manufacturing, among other areas. In addition to the mining firms there are 3,215 companies supply engineering, geotechnical, environmental, financial and other services to mining operations.
SME’s related report, "Emerging Workforce Trends in the U.S. Mining Industry," demonstrates an equal need for mine workers in the US and other mining boom countries, such as Canada. SME’s report found that a dramatic 52% outflow of senior mining labor in the U.S. by 2029 will put significant pressure on the industry to backfill those positions with qualified, skilled and trained miners.
On March 6, MSHA released the results of its internal review of the agency's actions prior to the April 5, 2010, explosion that killed 29 miners at the Upper Big Branch Mine in Raleigh County, WV. The internal review team, comprised of MSHA employees outside the district where the accident occurred, was charged with evaluating agency actions relative to the explosion and making recommendations to improve the agency's performance in order to better protect the nation's miners. The internal review team identified a number of shortcomings in MSHA’s inspection and mine plan approval processes. A number of factors led to these shortcomings that included lack of resources, inspector experience, management turnover, supervisory and managerial oversight.
International guide to quarry rehabilitation now available
The World Business Council for Sustainable Development has issued guidelines (PDF) on quarry rehabilitation that provide practical guidance for managing the impacts of aggregate and cement quarrying activities around the world and ensuring that local environments are properly revitalized. The international guidelines reflect the principles of quarry rehabilitation and outline the conditions and milestones for developing rehabilitation plans. These include defining context and assessing baseline conditions; setting technically and financially sustainable objectives; planning finances; developing and implementing plans and monitoring, adjustments and post-closure land-use management. The Guidelines also feature 30 operational case studies, covering a wide range of quarry types and local habitats around the world.
Behre Dolbear rankings released
Global mining consultant Behre Dolbear has issued their 2012 ranking of countries for mining investment, Where Not To Invest (PDF). According to the report, the competition for mineral resources will make those countries perceived to have the lowest political risk, all other things being equal, able to attract a significant portion of the global mineral investment, as well as receive a premium for their resources over countries where perceived instability exists. Rankings are based on a set of criteria that include political systems, social issues, permitting delays, economic systems, corruption, currency stability and tax regimes. The top five countries for investment potential are Australia, Canada, Chile, Brazil and Mexico. The U.S. position remained unchanged from the 2011 ranking at number six. The bottom three countries are the Democratic Republic of Congo, Bolivia and Russia. |
Age estimation from the teeth using a modified Demirjian system.
The estimation of age at time of death is often an important step in the identification of human remains. The purpose of this study was to test the applicability of the Demirjian system on a sample of the Sydney child population and to develop and test age-prediction models using a large sample of Sydney children (1624 girls, 1637 boys). The use of the Demirjian standards resulted in consistent overestimates of chronological age in children under the age of 14 by as much as a mean of 0.99 years. Of the alternative predictive models derived from the Sydney sample, those that provided the most accurate age estimates are applicable for the age ranges 2-14 years, with R-square = 0.94 and a 95% confidence interval of ±1.8 years. The Sydney-based standards provided significantly different and more accurate estimates of age for that sample when compared to the published standards of Demirjian. |
735 S.W.2d 404 (1987)
Lloyd J. COLLINS and Betty O. Collins, Plaintiffs-Appellants,
v.
WEST PLAINS MEMORIAL HOSPITAL, Defendant-Respondent.
No. 14882.
Missouri Court of Appeals, Southern District, Division Two.
July 23, 1987.
Motion for Rehearing and/or Transfer to Denied August 13, 1987.
Application to Transfer Denied September 15, 1987.
*405 John S. Pratt, Pratt & Fossard, Springfield, for plaintiffs-appellants.
Gail L. Fredrick, Freeman, Fredrick, Bennett and Rogers, P.C., Springfield, for defendant-respondent.
Motion for Rehearing and/or Transfer to Supreme Court Denied August 13, 1987.
PREWITT, Presiding Judge.
Plaintiffs sought damages for the wrongful death of their son, Terry Collins. They contended that he died as a result of defendant's negligence after he was taken to defendant's emergency room for treatment of a gunshot wound to his abdomen. Following a jury verdict in favor of defendant, judgment was entered accordingly. Plaintiffs appeal.
For their first point plaintiffs contend that the trial court erred in failing to strike for cause four veniremen. The potential jurors each indicated they believed they could fairly hear the matter in an impartial manner.
One of the veniremen, Wilma Puckett, stated that she was employed at Travenol Labs in West Plains as an assembler of hospital products and that defendant purchased items from Travenol Labs. Earlier the week of trial her son was treated by Dr. Terryl Mackey, a potential witness for defendant, who was not called to testify, and she had talked with her. Mrs. Puckett stated that she, her husband, her mother-in-law and her daughter-in-law had been treated at defendant hospital.
Venireman Gary Carter also was employed at Travenol Labs and he was acquainted with Dr. Michael Moore, an expert witness who testified for defendant. He stated that Dr. Moore had treated him, his wife, and their children. Venireman Barry Randolf had taken his son to Dr. Moore for minor illnesses. Venireman Robert Whittington had been treated at the emergency room by Dr. Terryl Mackey and a child of his was born in defendant hospital.
Plaintiff does not contend that any statutory challenge to these veniremen existed. The trial judge is vested with broad discretion in ruling on nonstatutory challenges and that decision is not overturned unless there is a clear abuse of that discretion; any doubts are resolved in favor of the trial judge's decision. State v. Reynolds, 619 S.W.2d 741, 749 (Mo.1981).
Even though a juror has some business or personal relationship with a party, the trial court has broad discretion in determining the qualifications of such veniremen to sit as jurors and its rulings are not disturbed on appeal unless they are clearly and manifestly wrong. Golden v. Chipman, 536 S.W.2d 761, 765 (Mo.App.1976) (upholding refusal to dismiss for cause venireman whose son was employed by defendant's counsel).
The cases which plaintiff cites contending that the relationship of these veniremen to defendant was such that they should have been stricken for cause are distinguishable. In Murphy v. Cole, 338 Mo. 13, 88 S.W.2d 1023 (1935), the venireman was a local agent of defendant's liability insurance carrier. That carrier, of course, would have a substantial interest in the outcome of the case. Here, none of the veniremen were agents or employees of a *406 party with an interest in the case. In McFall v. St. Louis & S.F.R. Co., 185 S.W. 1157 (Mo.App.1916), the juror excused was a local freight agent who had to deal with the same questions as were at issue in the case. No one here professed to be an expert in any of the matters in controversy. In Edmonds v. Modern Woodmen of America, 125 Mo.App. 214, 102 S.W. 601 (1907), the trial court properly excluded members of a fraternal benefit society whose assessments could be effected by the result. Here, there is no indication that any of the veniremen would be financially affected by the outcome.
Numerous cases have indicated that some business connection with a party is not a ground requiring disqualification to serve on a jury. In Joyce v. Metropolitan St. Ry. Co., 219 Mo. 344, 118 S.W. 21, (1909), the court said that it was error to excuse for cause a juror who was a "contracting freight agent" for a railroad who solicited business from street railroads including the defendant.
In Kennedy v. Holladay, 105 Mo. 24, 16 S.W. 688 (1891), a new trial was held properly refused although defendant consummated a mule trade with a juror during the trial and treated two jurors with oysters during a recess in the trial. In Murphy v. Fidelity Nat. Bank & Trust Co., 226 Mo. App. 1181, 49 S.W.2d 668 (1932), a prospective juror was employed in a meat market which occasionally sold meat to the wife of one of plaintiff's attorneys and to a person who had "some connection" with that attorney's office. The court held that it was not error to refuse to strike him.
The relationship that the challenged veniremen had to defendant was not so direct that their disqualification was required. The trial court's action in not striking them was not a clear abuse of discretion. Point one is denied.
Plaintiffs state in their second point that the trial court erred "in reassigning the case to the 37th Judicial Circuit on March 28, 1983, and in each and every ruling and action after March 28, 1983," because the matter was assigned to Judge "John Brackman to preside and said order was never vacated, amended, or modified by the Supreme Court, therefore making a nullity the actions of the presiding judge of the 37th Judicial Circuit" who presided over the trial. Defendant's brief treats that point as having been abandoned by plaintiffs but there is no direct expression of abandonment in this court's files.
In the supplemental legal file filed by plaintiffs after they filed their brief, is a certified copy of an order of the Missouri Supreme Court entered on the 25th day of March 1983, assigning the handling of this case from Judge Brackman to Judge Holstein. As this order appears valid and is not challenged, it appears that Judge Holstein properly proceeded to preside over this matter. The point is denied.
Plaintiffs assert for their third point that the trial court erred in refusing to permit them to read into evidence certain portions of defendant hospital's records without first offering them into evidence. Plaintiffs say this was erroneous as it "improperly permitted the jury to infer and conclude that plaintiffs were vouching for the accuracy and veracity of defendant's records, when, in fact, plaintiffs' case against defendant was based upon being able to prove that portions of the records were false as they related to the time when decedent was brought to the defendant hospital and the timeliness of care and treatment." At the commencement of plaintiffs presenting evidence, the following occurred:
MR. PRATT [plaintiffs' attorney]: Your Honor, I would like to read from the emergency room records consisting of Plaintiff's Exhibits 1 and 2.
THE COURT: Are you offering those at this time?
MR. PRATT: No. I'm asking to read these as admissions, Your Honor.
THE COURT: Objections to him reading from Exhibits 1 and 2?
MR. FREEMAN [defendant's attorney]: Just a moment, Judge. Let me look them over.
I don't think they are into evidence and I would object until they are placed into *407 evidence of any reading from them but let mewhat do you show as Exhibits 1 and 2?
MR. PRATT: One is the outpatient emergency room record and two is the x-ray report.
THE COURT: You're going to have to offer them before you may read from them.
We doubt that the jury was sophisticated enough in legal proceedings that it or any member might "infer and conclude" that plaintiffs were vouching for the accuracy of defendant's records. However, we proceed to analyze this point further. It appears that the trial court was requiring that the records be authenticated and in evidence before anything be read from them. This was a proper requirement. The authenticity of a document cannot be assumed, what it purports to be must be established by proof. United Factories v. Brigham, 117 S.W.2d 662, 665 (Mo.App. 1938); Missouri Evidence, Third Edition, The Missouri Bar (1980), § 10.1; McCormick on Evidence, § 218, pp. 684-687 (3d ed. 1984). See also Davison v. Farr, 273 S.W.2d 500, 504 (Mo.App.1954) ("general rule is that execution of a private writing must be established before it may be admitted in evidence"). Of course, the authenticity can be agreed upon and certain documents can be admissible if properly certified or otherwise proved, see ch. 490, RSMo 1986.
Plaintiffs assert that "had Plaintiffs not been required to offer into evidence the medical records, Plaintiffs would have read only those portions of the record which benefited Plaintiffs' case". Plaintiffs say they could not do so because it would look to the jurors "that Plaintiffs were only disclosing a part of the record" (emphasis by plaintiffs). Plaintiffs also state in their brief that "the procedural hamstring placed upon Plaintiffs by the trial court made the risk of partial reading of the medical records too great."
We fail to see how the trial court's ruling prejudiced plaintiffs. If plaintiffs obviously only read a part of a document, that could be apparent to the jury whether or not the document was introduced into evidence. Plaintiffs concluded their argument under this point in their brief by stating that the "Court should have permitted the Plaintiffs to read such portions of the medical records as Plaintiffs desired in Plaintiffs' case and then permitted Defendant to read such portions as it desired in Defendant's case" (emphasis by plaintiffs). We find no indication in the record that the trial court prevented the plaintiffs from reading whatever portion of the records that they wished.
The trial court's procedure was correct in requiring that the records be in evidence before plaintiffs read from them and no prejudice to plaintiffs is shown in its ruling. This point is denied.
For their fourth point plaintiffs state that the trial court erred in permitting defendant's counsel to ask during cross-examination of decedent's mother, plaintiff Betty Collins, if decedent had been convicted of a crime. They contend "that such evidence was vague, remote, irrelevant, and immaterial ... and was highly prejudicial in that it portrayed the decedent to the jury as a heinous criminal."
Prior to trial the trial court sustained plaintiffs' motion in limine seeking to prevent defendant from inquiring or making comments as to the criminal conviction of the decedent. During cross-examination of Mrs. Collins the transcript shows the following:
MR. FREDERICK: [sic] [Defendant's attorney] In the Court's [sic] motion in limine, the Court had indicated that we could not get into the criminal record of Terry Collins. It's our belief that that issue has been opened.
THE COURT: I think that's correct. She testified as to the areas of good character and conduct such as he volunteered for Vietnam and he had special talents and he sang at church and at funerals and never back talked his parents. I think you've gone into character and I'm going to let you into the others.
MR. FREDERICK: [sic] Thank you, Your Honor.
[The following proceedings were had in open court.]
Q. Ma'am, was Terry Collins, your deceased son, ever convicted of a crime?
*408 MR. PRATT: [Plaintiffs' attorney] Your Honor, at this time I object on the basis that it's immaterial and irrelevant to any issue in this case.
THE COURT: Overruled.
Q. Tell the jury, please, was Terry Collins ever convicted of a crime?
A. Yes, he was.
Q. And what crime was that?
A. He was accessory to a robbery.
Earlier plaintiffs had presented evidence as to decedent's military and educational background and his employment after he "came back from the Army". His mother testified that he helped with their farming operation, paid some of the grocery and utility bills, bought feed for their cows and "never back talked" his parents. She testified that their family quartet, of which decedent was a member, sang at funerals and revivals[1].
Neither party cites any authority dealing with evidence of criminal convictions, character, or damages, in wrongful death cases. Plaintiffs cite only Wood v. St. Louis Public Service Co., 362 Mo. 1103, 246 S.W.2d 807 (banc 1952), a personal injury action, and Missouri Evidence, Third Edition, The Missouri Bar (1980), § 12.1. Chapter 12 of Missouri Evidence deals with "Relevancy In General" and the cited section "Test of Relevancy". Defendant cites only State v. Wolfe, 343 S.W.2d 10 (Mo. banc 1961), cert. denied, 366 U.S. 953, 81 S.Ct. 1912, 6 L.Ed.2d 1246; 368 U.S. 907, 82 S.Ct. 188, 7 L.Ed.2d 101 (1961), where defendant was charged with statutory rape, and Weller v. Provow, 220 Mo.App. 1283, 290 S.W. 1017 (1927), a slander action for calling plaintiff "a mean woman".
In measuring pecuniary loss in a wrongful death action the trier of fact may consider the character of the deceased. Dowell v. City of Hannibal, 200 S.W.2d 546, 559 (Mo.App.1947), rev'd on other grounds, 357 Mo. 525, 210 S.W.2d 4 (1948); Chambers v. Kupper-Benson Hotel Co., 154 Mo.App. 249, 134 S.W. 45, 49 (1911), Pamela S. Wright, Damages under the Missouri Wrongful Death Act, 37 J.Mo.B. 92, 95-96 (1981); Joseph J. Russell, Measure of Damages under Missouri Wrongful Death Act, 15 Mo.L.Rev. 31, 37, 43 (1950); 22 Am.Jur.2d Death § 140, p. 708 (1965). See also Grothe v. St. Louis-San Francisco Railway Co., 460 S.W.2d 711, 718 (Mo. 1970) ("In a death claim it is proper to show conditions such as health, earning capacity, age, and habits of the deceased."); Ransom v. Adams Dairy Co., 684 S.W.2d 915, 917 (Mo.App.1985) (evidence of deceased's acts of violence not erroneous in wrongful death action).
As evidence of decedent's character was relevant, at least if it was not too remote, and plaintiffs make no claim of remoteness, a criminal conviction could bear on his character and be admissible. The trial court did not err in allowing evidence of decedent's conviction. This point is denied.
Plaintiffs assert in their remaining point that the trial court erred in sustaining defendant's motion in limine which prevented plaintiffs from disclosing to the jury the existence of a minor child who was born to decedent following his death "for the reason that the obligation of the decedent for the support of the minor child is relevant and material on the issue of damages."
Plaintiffs claim that decedent was the father of a child born after his death to a woman to whom decedent was not married. Plaintiffs contend that since he owed the child a duty to support, its existence would be relevant to damages and to decedent's "family circumstances". It is not necessary to decide whether plaintiffs could recover damages that the child, who has not been a party to this action, might be entitled to recover. See § 537.095, RSMo 1986 (not cited by either party).[2]
Plaintiffs contend that evidence of the child was relevant on the issue of damages. Plaintiffs' submission instruction did not require the jury to find that they were damaged before deciding liability in their favor. Damages were to be considered pursuant to another instruction. As the *409 liability question was found in favor of defendant, the jury did not reach the issue of damages. Error is harmless if it relates solely to the issue of damages and the jury never reaches that issue. Guthrie v. Missouri Methodist Hospital, 706 S.W.2d 938, 943 (Mo.App.1986). If any error existed as claimed in this point, a question not necessary to decide, it was harmless. Only error "materially affecting the merits" calls for reversal. Rule 84.13(b). This point is denied.
The judgment is affirmed.
HOGAN, FLANIGAN and MAUS, JJ., concur.
NOTES
[1] Evidence that an eight-year-old girl had blond hair, big eyes, rosy cheeks and a fair, natural complexion; that she had a good voice and could sing well was held admissible in an action for wrongful death. Smiley v. Reid Ice Cream Corp., 5 N.J.Misc. 82, 135 A. 504 (1927).
[2] Subsections 1 and 2 of § 537.095, RSMo 1986 state:
1. Except as provided in subsection 2 of this section, if two or more persons are entitled to sue for and recover damages as herein allowed, then any one or more of them may compromise or settle the claim for damages with approval of any circuit court, or may maintain such suit and recover such damages without joinder therein by any other person, provided that the claimant or petitioner shall satisfy the court that he has diligently attempted to notify all parties having a cause of action under section 537.080. Any settlement or recovery by suit shall be for the use and benefit of those who sue or join, or who are entitled to sue or join, and of whom the court has actual written notice.
2. When any settlement is made, or recovery had, by any plaintiff ad litem, the persons entitled to share in the proceeds thereof shall be determined according to the laws of descent, and any settlement or recovery by such plaintiff ad litem shall likewise be distributed according to the laws of descent unless special circumstances indicate that such a distribution would be inequitable, in which case the court shall apportion the settlement or recovery in proportion to the losses suffered by each person or party entitled to share in the proceeds and, provided, that any person entitled to share in the proceeds shall have the right to intervene at any time before any judgment is entered or settlement approved under this section.
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Low Blood Pressure (Hypotension) treatment
Description
Hypotension, also known as low blood pressure, is a condition in which the blood pressure during and after each heart beat is too low. Blood pressure measures the force of blood pumping inside arterial walls, and normal blood pressure falls between 90/60 mmHg and 120/80 mmHg. The top number is the systolic pressure (when blood vessels contract) and the bottom number is diastole pressure (resting heartbeat). When arteries dilate and there is not enough blood flow, it results in a decrease of pressure. The 3 different types of hypotension are: (1) Orthostatic hypotension - which occurs right after standing up from a sitting or lying down position (2) Neurally Mediated Hypotension (NMH) - resulting from a miscommunication between the brain and heart (3) Shock - severe drop in blood pressure brought on by a sudden drop in blood flow. Shock is an emergency condition where blood pressure cannot return to normal on its own. View more...
Causes
Two common causes of orthostatic hypotension are dehydration and old age. Other causes include anemia, severe infections, disorders of the central nervous system, pulmonary embolism, and certain medicines used to treat high blood pressure (hypertension), such as diuretics. Neurally mediated hypotension occurs after standing for a long period of time. Blood begins to pool in the legs, so the brain tells the heart that blood pressure is too high, and in turn blood pressure is decreased even more. Septic shock results from severe infections entering the bloodstream; hypovolemic shock occurs as a result of a major loss in body fluids, and cardiogenic shock is caused by a drastic decrease in the body's ability to pump blood (i.e. heart attack, pulmonary embolism, arrhythmia). View more...
Prevention
Avoiding alcohol, avoiding standing for a long time (if you have NMH), drinking plenty of fluids, getting up slowly after sitting or lying down, or using compression stockings to increase blood pressure in the legs.
Common Symptoms
If someone suffers from hypotension, their heart, lungs, brain, and other organs are not receiving an adequate amount of blood flow and oxygen. Common symptoms include dizziness, feeling light headed, blurry vision, confusion, weakness, nausea, and chest pain. A person with severe hypotension as a result of shock brought upon by heart failure or major blood loss will exhibit cold, clammy skin that is often blue or pale in color, weak and rapid pulses, and rapid, shallow breathing. Vasovagal syncope is brought upon by a severe drop in blood pressure and is the most common cause of fainting. View more...
Rare Symptoms
Less common symptoms are described as "an electric shock running through the body," or even "burning in one extremity." Other rare symptoms include constipation, diarrhea, myofascial pain, noise and light sensitivity, and weight loss and gain. Since blood flows to every minute part of the body, hypotension can affect literally any part of the body. Thus, the symptoms are innumerable and it is difficult to pinpoint exactly what rare symptoms of hypotension a person may exhibit. View more...
Traditional Treatment
Treatment for hypotension is determined by the cause of the low blood pressure. Low blood pressure without signs or symptoms is usually not unhealthy, and the body can usually correct itself. Treatment for those suffering from orthostatic hypotension is to increase fluid and electrolyte intake with IVs or to take medications that increase blood pressure. Your doctor can adjust your prescriptions if you are taking medications that cause NMH. Ibuprofen or indomethacin are helpful in treating postprandial hypotension (a drop in blood pressure after eating a meal). Vasovagal syncope can be treated with beta blockers, selective serotonin reuptake inhibitors, or fludrocortisone to prevent dehydration. View more...
Alternative Treatment
Herbs such as bayberry, ginger, hawthorn berry, ginseng, capsicum, mate, and vervain; Other alternative treatments include yoga therapy, acupressure, and healing through reflexology.
Choose a condition to compare treatments based on user feedback. You can sort by Effectiveness, Holistic Benefits or Side Effects RateADrug user scores, or the number of Ratings. Scores gain significance with the number of ratings, so please share your experiences - rate your drug!
A catheter based procedure that disrupts nerves around the kidneys to dramatically reduce high blood pressure is being tested in Australia. Additionally, herbal therapies are being studied including Rauwolfia, Stephania, Crataegus, and Panax. |
Michigan Tech News
Students Reach Out to India and Its Poor
Last Modified 9:14 AM on Fri Dec 9, 2016
April 30, 2012—
Two teams of undergraduate engineering students at Michigan Technological University have developed two low-cost, workable prostheses—one a knee, one a foot—and brought them to India, the first step in an effort to make them available to that nation's many poor.
Kelsy Ryskamp was on the knee team that traveled to Jaipur and New Delhi to meet orthopedic surgeons over spring break. “They were impressed with our work,” she says. “It’s amazing we had this opportunity, and it’s crazy to think that a group of six students could do something this big—potentially change the way people live in a developing country.”
As part of International Senior Capstone Design, a program based in the Department of Mechanical Engineering-Engineering Mechanics, the two teams have been working on their projects since fall 2011. Both teams were to develop a device that is affordable and lightweight; made with local materials and by local labor; easy to assemble, adjust and repair; and allows a natural gait.
Teams also had to consider the Indian culture and design devices that would accommodate common practices, such as sitting cross-legged and squatting, and suit people who often wear sandals or go barefoot.
Ryskamp is from Grand Ledge and has a dual major in mechanical engineering and biomedical engineering. “We started with basically nothing,” she says. “We had creative license to do what we wanted. It was very exciting. We were passionate about it.”
Although there are many artificial knees on the market, they can cost up to $5,000, a prohibitive price for the poor of India. Ryskamp says the students’ model would cost $510 and is designed to be more sturdy. Their device joins an amputee’s real upper leg to an artificial lower leg and is the same size as a human knee; details are a secret because the students have applied for a patent. Students tested stresses; creep and deformation; and aesthetics. The knee comes in three sizes, all for adults.
The prototype was completed in March, and refinements were made after the 10-day spring break trip to India. It is now being tested at the All India Institute of Medical Science in New Delhi.
“This experience means just about everything to me,” Ryskamp says. “It reflects what I want to do and where I want to go.”
Before she came to Tech, she never envisioned such opportunities. “I love it here. Tech has been everything I thought and more.” She says the faculty gave her inspiration as well as confidence.
Marcel Kerkove, a senior in mechanical engineering from Ironwood, worked on a prosthetic foot with five other students. They, too, trekked to India in March to present their artificial foot—an adaptation of the famous Jaipur foot, in use throughout India—to surgeons at the Santokba Durlabhji Memorial Hospital in Jaipur.
Their charge was to design a prosthesis that is lightweight and costs less than $50 to build. They realized both: the device weighs less than an actual foot, and it can be built for $18 (this in a country where a laborer earns $5 a day). Kerkove says the foot is reliable and has a life cycle of three years. “There’s nothing on it that will stop working,” he says. It is meant to affix to a prosthetic leg with a single bolt.
“As we kept going,” Kerkove adds, “there were more and more things to work on and improve. It was easy for us to get inspired and work hard. The expectations were high. Everyone was motivated to try and help people over there. We didn’t want to let them down. ”
Associate Professor Gregory Odegard was the advisor for both teams.
“These students are very talented,” he says. “I’m impressed at what they accomplished. They’ve gone the extra mile by doing more than what was asked of them. Their heart was in this. I love working with them. It’s a lot of fun because they are so enthusiastic.”
The students on these teams graduated this spring, but Odegard has already envisioned the task for next year’s seniors: an inexpensive new brace for scoliosis—a deformed spine—designed for children and adolescents. They will work with doctors at the Council for Child Welfare in New Delhi. As well, Tech seniors might tackle another project: modifying the artificial knee and foot for children.
This project was made possible in part by financial support from the Texas-based Jiv Daya Foundation and its Amputee Assistance-India team.
Michigan Technological University (www.mtu.edu) is a leading public research university developing new technologies and preparing students to create the future for a prosperous and sustainable world. Michigan Tech offers more than 120 undergraduate and graduate degree programs in engineering; forest resources; computing; technology; business; economics; natural, physical and environmental sciences; arts; humanities; and social sciences. |
The present invention relates generally to magnetic bearings which may be used, for example, to bear the rotor of a blood pump which is implanted into the human body to assist the heart. Magnetic bearings are ideally suited for a blood pump since they allow the rotor to be suspended relative to the stator and therefore allow free flow of blood without obstructions so that it does not stagnate and thus coagulate and allow the blood to flow along a path large enough that individual blood cells are not damaged due to shear.
Bearings for blood pumps as well as other pumps and motors must not only bear the rotor radially (journal bearing) but must also bear the rotor axially (thrust bearing). Reliable axial control of the rotor is particularly important in blood pumps since too much movement of the rotor axially may narrow a blood pathway thereby restricting blood passage so much that individual blood cells may become damaged due to shear and the blood may coagulate. In addition, it is important that the power consumption in blood pumps be low since the heat resulting from high power consumption may damage or destroy blood cells, and low power consumption is also desirable to reduce the operating costs.
Patents (in addition to those cited hereinafter) which may be of interest in the development of magnetic bearings include U.S. Pat. Nos. 5,084,643; 5,133,527; 5,202,824; 5,666,014; 5,175,457; and 5,521,448, which above patents are hereby incorporated herein by reference.
An example of radial and axial magnetic bearings for blood pumps is found in U.S. Pat. No. 6,201,329 which is assigned to the assignee of the present invention and which is hereby incorporated herein by reference. This application discloses a blood pump wherein permanent magnetic rings are provided in attraction on opposite sides of each of two axially spaced radial gaps to levitate the rotor, and an actively controlled magnetic means is provided across radial gaps to bear thrust.
While the above blood pump bearings are considered to work well, it is nevertheless considered desirable to simplify the magnetic bearing arrangement so as to provide a more compact blood pump as well as to reduce manufacturing cost. It is also considered desirable to reduce the bearing operating cost.
U.S. Pat. Nos. 4,944,748; 5,078,741; and 5,385,581 to Bramm et al disclose a magnetically suspended and rotated rotor having an axially polarized cylindrical permanent magnet at each end of the rotor. An axially polarized permanent magnet ring is provided at each end of the stator to magnetically interact therewith respectively to levitate the rotor. The stator magnet rings are offset axially outwardly of the rotor magnets respectively. An Electromagnet exerts a control force on the rotor magnets to keep the impeller at the null position, in the absence of additional static axial forces on the impeller. The electromagnet receives feed-back of rotor position (see col. 14, last paragraph, of the ""581 patent) to maintain the null position. As seen in FIG. 4 of the ""581 patent, it appears that one pole of the rotor magnet is used to levitate the rotor and the electromagnet flux interacts with the other pole to act as a thrust bearing. It is believed that this does not allow an arrangement of magnets to achieve a desired radial and angular stiffness to suitably support the rotor, with the result that the specific gravity of the fluid determines the rotor design (see the paragraph which spans cols. 26 and 27 of the ""581 patent) so that the rotor may not be able to levitate and spin without the presence of fluid.
When additional static axial forces are applied to the impeller of the above pump, as detected by the electronic circuitry, a different equilibrium position is thereafter maintained, instead of the null or previous equilibrium position (see the paragraph which spans cols. 11 and 12 of the ""581 patent). As discussed in the paragraph which spans cols. 22 and 23 of the ""581 patent, if an additional axial force is exerted on the impeller, this is detected by signals, provided to a difference amplifier by the position sensors, having a direct current component which is said to arise from a persistent small shift in the impeller position as opposed to random variations in impeller position about the null position. Thus, a new equilibrium position is established in response to these direct current component signals. Not only is such a system which uses displacement as feedback for establishing a new equilibrium position complex but it is also unreliable (prone to error) since there may be instances in which it may be difficult for the circuitry to xe2x80x9ctellxe2x80x9d whether there is an outside axial force or just instability causing a change in impeller position.
It is accordingly an object of the present invention to provide a simplified, compact, and reliable magnet assembly for the radial and thrust bearings for a rotor.
It is a further object of the present invention to provide low power consumption for such a magnet assembly.
In order to provide a simplified, compact, and reliable magnet assembly for the radial and thrust bearings for a rotor, in accordance with the present invention, first and second axially spaced combinations are provided each including at least one permanent magnet disposed on each of the rotor and stator and polarized to levitate the rotor, and there is further provided an electrically energizable coil for modulating flux between the respective stator and rotor magnets, and the rotor magnets are offset axially both inwardly or both outwardly of the stator magnets respectively.
In order to provide low power consumption for such a magnet assembly, in accordance with a preferred embodiment of the present invention, an electrical circuit responsive to feed-back of electrical energy to at least one of the coils is provided for comparing thereof with a reference electrical energy and integrating the differences therebetween to provide a signal to modify a reference position of the rotor, whereby to attain a zero force balance position wherein the current to the coils may be reduced to near zero.
The above and other objects, features, and advantages of the present invention will be apparent in the following detailed description of the preferred embodiment thereof when read in conjunction with the accompanying drawings wherein the same reference numerals denote the same or similar parts throughout the several views. |
Q:
Plupload file error 5 mb
I am using the plupload queue widget but it won't work.
Everytime i tries to upload a file larger than 5 mb it went to 100% and gives me a http Error.
When i upload a file from 3 mb this wil work perfectly and after 100% he gives me a green ok sign.
$(function () {
$("#uploader").pluploadQueue({
runtimes: 'html5,html4,flash,gears,silverlight,browserplus',
url: '/Upload/Upload',
max_file_size: '10mb',
post_max_size: '10mb',
upload_max_filesize: '10mb',
chunk_size: '10mb',
unique_names: true,
urlstream_upload:true,
multipart: true,
multiple_queues: false,
filters: [
{title: "Foto's", extensions: "jpg,gif,png"},
{title: "Video's", extensions: "wmv,avi" },
{ title: "Microsoft Office", extensions: "docx,xslx" },
{ title: "Zip files", extensions: "zip" },
],
preinit: {
FileUploaded: function (up, file, response) {
var data = response.response; //$.parseJSON(response.response);
$('<input>').attr({
type: 'hidden',
name: 'fileId' + data,
value: data
}).appendTo('#uploadFinishedForm');
if (data.error == 1) {
uploader.trigger("Error", { message: "'" + data.message + "'", file: file });
console.log('[Error] ' + file.id + ' : ' + data.message);
return false;
}
},
UploadComplete: function (up, files) {
window.setTimeout(function (form) {
// $('#uploadFinishedForm').submit();
$('.nextButton').append('<input type="submit" class="btn btn-large btn-success submit-btn" value="Transfer" />');
}, 2000)
},
Init: function (up, info) {
$('#uploader_container').removeAttr("title");
}
}
});
$('#uploadForm').submit(function (e) {
var uploader = $('#uploader').pluploadQueue();
if (uploader.files.length > 0) {
uploader.bind('StateChanged', function () {
if (uploader.files.length === (uploader.total.uploaded + uploader.total.failed)) {
$('#uploadForm').submit();
}
});
uploader.start();
} else {
$('#uploadInfo').html('Zonder foto\'s valt er niets te uploaden!');
}
return false;
});
A:
Try to decrease the value of the chunk_size (1mb instead of 10mb by example):
chunk_size: '1mb'
|
Q:
No shadow-root found in Polymer component but works, why?
Polymer uses a Shadow DOM for its components as found at docs.
Im investigating a very basic example of Hello-World in github:
https://github.com/webcomponents/hello-world-polymer
Im inspecting the demo and I cant find any shadow-root.
I have worked with Polymer and I have used the shadow-root before, but why theres no shadow-root for this component? Because of some optimizations?
A:
There is no shadow-root because they use the polyfilled Shadow DOM for v0 spec and not the current one supported by the browsers (v1).
The demo you provided was built with Polymer 1 (according to hello-world.html source code since it uses Polymer() function and the deprecated HTML imports). Polymer 1 was built on top of Web Components v0 specs (Custom Elements v0, Shadow DOM v0 and HTML Imports) which are now deprecated and replaced by Shadow DOM v1 and Custom Elements v1.
|
Kal ka nawaab
KAL KA NAWAAB is a film about four Hyderabadi boys with lower-middle-class background. The hero, Hafeez, is a fruit vendor, his friends Kabza, Khayyum, all are street vendors at Charminar. The fourth one, Jeelani, is an auto driver. They want to make good fortune and become big for which they plan to go to Dubai to earn money. The effort fails and they are duped to lose the money that was borrowed from Shakeel Pahelwan, a notorious rowdy. To pay back the amount taken, Hafiz tries to trap a wealthy girl.
Category:Indian comedy films
Category:Indian films |
1. Field of Use
The present invention relates to flying prober systems and more particularly to systems for enabling reliable testing of printed circuit assemblies (PCA's).
2. Prior Art
Modern Flying Probers are a class of In-Circuit Test (ICT) equipment which use a plurality of moving probes in lieu of a standard bed of nails fixture to provide all or most connections between the PCA undergoing test and the test unit. Generally, flying prober tests are a subset of the tests that might have been performed by an ICT unit, because of the limited number of simultaneous connections possible between the PCA and tester. However, in present day test operations, such contact requirements have diminished compared with the recent past.
The principal benefit of flying probers is cost avoidance, in eliminating standard ICT bed of nails fixtures sometimes costing tens of thousands of dollars and having a short useful lifespan and little residual value. Another benefit is avoiding the delay associated with constructing such a fixture. Most flying prober models have four moving probes, mechanically positionable to any board location by a relatively high speed mechanism. The list of board locations to be used in testing a given PCA type is generally derived from computer aided design (CAD) files provided as part of nearly all modern PCA designs. The same files are similarly used to define nail location points in a bed of nails fixture in non-flying prober testing. Alignment of the PCA on the flying prober is accomplished using electro-optical methods, whereby registration holes of the PCA that would be engaged when mounted on a bed of nails are, instead, found by image recognition methods and their precise locations recorded. Then, instead of mechanically aligning the PCA to the tester, the list of probing locations is recalculated to take into account the actual positions of the registration holes, essentially aligning the tester to the PCA.
The electro-optical system usually is or is the equivalent of a miniature television camera connected through a digitizer to the computer used to control the tester in its execution of a test program. In addition to its usefulness in PCA to tester alignment, the electro-optical system is used for other purposes related to testing. For example, the probing points may be sighted one by one for the benefit of the test programmer in verifying that the CAD data, upon which the test program is based, indeed matches the PCA for which a test program is being developed. Usually, the television camera used for this purpose is mounted on the carrier that also holds one of the probes. It is mounted in a position that is a predetermined offset from the probe itself. Thus, while the television camera system may not be able to display the probe as it touches the PCA, it can be placed directly over the point where the probe would touch the PCA had not the offset been applied. The camera's optics are aligned perpendicularly to the ideal plane of the PCA, and allow cross hairs or similar positional markings to be added to the image, creating a bombsight effect and allowing confirmation of theoretical probe positioning to a very high degree of precision. For purposes of this explanation the term “ideal plane” is used to describe the plane of the flat surface of the etched printed circuit board upon which the various components of the PCA are mounted, assuming board fabrication exactly as designed, with no imperfections and somehow held in place for flying prober testing without affecting its perfect planarity. The display attached to the camera may also be used to verify the lack of probing obstacles in the vicinity of probing targets or that targets are otherwise suitable for probing. One or more additional cameras are sometimes employed to further aide in test programming and/or execution, showing, for example a larger area of the PCA, and at an angle that provides an overview of some probes as they are extended to contact test target points. The electro-optical system employed is sometimes sufficiently complex to allow Automated Optical Inspection (AOI) testing to be performed in conjunction with electrical flying prober tests.
While the nails of a standard ICT bed of nails fixture are mounted perpendicularly to the plane of the PCA while in its test position, flying prober system probing is performed at angles somewhat off perpendicular (Z-axis). Angles of between five and sixteen degrees to the Z-axis (“height axis”) have been noted in some modern flying prober specifications. In some systems, the probe angle may be altered by test program commands. The angles are necessary to allow probing a series of closely spaced points by probes which are, by necessity, attached to relatively large drive mechanisms which allow speedy extension and withdrawal. Those mechanisms are in turn mounted to a carrier driven by an X-Y positioning mechanism. Two types of X-Y mechanisms used are linear motor and lead screw. Furthermore, the probes may be at angles to the X-axis or Y-axis as well as the Z-axis. A single X-Y table of probe points suffices, regardless of the number of probes, variety of angles, or designed thickness of the particular PCA type being tested, by applying appropriate offsets as compensation for these effects in determining the precise point at which the PCA will be contacted.
However, the compensation discussed above is based upon the assumption that the probing points of the PCA exist in an ideal plane, or at predetermined distances from an ideal plane. Warpage of the PCA is both non-planar and unpredictable. Hence, planarity variations result in probing variations. In some cases, the intended test probing target may be probed slightly askew from the intended point of contact, usually the center of a circular target. In other cases, the probe may miss the target altogether. For example, consider the case of a probe which is fifteen degrees from perpendicular attempting to probe a target point which is 35 mils in diameter. The required probing accuracy would be +/−17 mils, assuming the probe will not slide once one physical contact is made (not a safe assumption). At an angle of fifteen degrees, a 17 mil error occurs when the height of the intended target is approximately 1/16″ (0.017″/0.268, the tangent of 15 degrees). The actual safe region for contacting a 35 mil target with a 15 degree probe is a matter of opinion. If, however, half the error were considered safe (about 8 mils), the height would have to be predictable to within approximately 1/32″. Maintaining a planarity tolerance of +/− 1/16″ is generally not possible in a manufacturing environment with PCA's measuring 16″ by 16″ or more. Even with larger test target points, the planarity requirements are often impractical to maintain. However, some test target points of modern PCA's may be less than 20 mils.
In the art of PCA testing using flying probers, planarity variations that cause a misprobe are a known problem, but there is a paucity of detailed data as to its significance. One result of a misprobe is a false error (e.g., when testing for resistance and getting an open indication) or a missed error (e.g., when a short is present but not detected). But, there are so many possible reasons for such errors, such a large quantity of such errors and so little engineering time to devote to making exact determination of error causes (real vs. false), that the effectiveness of available attempted solutions to the planarity problem has never been fully tested. Such attempted solutions are, e.g., standoff posts used to support a concave PCA from the underside during probing (but which may have no effect on convex PCA's) and standoff posts which attempt to apply either an upward or downward force, as needed, by means of vacuum applied over so small an area as to effect only relatively flexible PCA's. In all such cases, the required planarity cannot be guaranteed in a production environment.
In addition to the problems incurred in attempting to force a PCA to become sufficiently flat for flying prober testing is the issue of whether it is advisable to do so at all. Connections of devices soldered to the surface of a PCA (e.g., surface mount or ball grid array-BGA-devices) may be mechanically stressed by forcing the PCA to become flatter than it is when not being tested. Furthermore, it sometimes may occur that the means of applying pressure is applied at the wrong point (e.g., through operator error) or to points which are not at the intended level in relation to the PCA surface (e.g., through PCA assembly errors). Stresses to PCA connections may result in cracking and cause intermittent contacts which later cause errors in system operation of the PCA. Such errors are difficult or impossible to diagnose on a practical basis.
Misprobes may also occur when the probing target is large enough that it will not be missed despite skewed probing caused by height differences. In such cases, the force applied by the probe may be inadequate, causing a lack of contact between the probe and PCA, or too great, causing marking of the contact area. The marking may be in the form of a pit or a scored line, the latter resulting when the probe is pushed by excessive force. The marking occurs because probe contact depends upon spring force. In normal operation, contact force is achieved by attempting to drive the probe perhaps 50 to 100 mils further than would be required for the tip to make contact with the PCA probing point. At contact, the probe will stop moving and its internal spring will compress to take up the distance, providing contact pressure. Should the PCA contact point be significantly closer to the probing mechanism, early contact would be made and the probe might be driven 100 mils before the 100 mils previously referenced, for a total of 200 mils. In some cases, the spring might even fully compress, causing the probe to be driven against the PCA with the maximum force the probe extension motor can produce. In certain applications, significant marking of PCA targets is not tolerated and the PCA has to be reworked or scrapped.
In addition to PCA warpage issues, another problem confronting flying prober users is that of devices erroneously mounted on the PCA during the assembly process. Similarly, a test program for a PCA where optional components should not be mounted may be mistakenly applied to a similar PCA where these components are mounted. The occurrence of either situation may result in damage to the PCA and or the flying prober system. In some cases, the flying prober damage or misalignment may interrupt the production process for a long period of time and at great expense.
The cross-referenced patent is of primary benefit in dealing with PCA's exhibiting warpage when integrated with the software which controls the flying prober. That is, it enables sensing of and compensation for warpage conditions. However, there exist certain applications where there is no opportunity to modify the software controlling the flying prober.
Accordingly, it is a primary objective of the present invention to provide a method and apparatus for overcoming variations in PCA planarity of PCA's mounted for testing in a flying prober system.
It is a further objective of the present invention to utilize extensively hardware typically found on existing flying prober systems, making practical the retrofitting of such systems to incorporate the present invention.
It is an even further objective of the present invention to provide an improved method and apparatus for overcoming variations in PCA planarity of PCA's mounted for testing in a flying prober system when alteration of or integration with the software which controls the flying prober system is not practical.
It is a still even further objective of the present invention to provide a method and apparatus suitable for efficiently detecting components erroneously mounted on a PCA before damage can occur. |
Q:
How to return grades and custom values from LTI (learning tools interoperability) Tool Provider to Moodle
I am developing Tool Provider (TP) of Learning Tools Interoperability (LTI) version 1.1.1 using PHP.
I want to pass grades and custom values from TP back to Moodle LMS (ie. the Tool Consumer).
Knowing that lis_result_sourcedid and lis_outcome_service_url should be used, but I don't know how to make use of these parameters in the TP programs.
A:
You need make a POST request from the TP to the TC using the lis_outcome_service_url as destination URI. The format of the body needs to conform the one defined in the LTI 1.1 standard (see here) which, among others, uses the lis_result_sourcedid parameter as a way to identify the item you are grading in the TC gradebook.
|
Saks to be acquired by Hudson's Bay Co.
By
NEW YORK — Hudson’s Bay Company has reached a deal to buy Saks Inc. The Canadian retail conglomerate, which operates Lord & Taylor in the United States and Hudson Bay in Canada, will purchase Saks and its 41 stores for a total of about $2.9 billion. Purchase price includes $16 per share of Saks as well as the assumption of Saks’ debt.
"This exciting portfolio of three iconic brands creates one of North America's premier fashion retailers," stated Richard Baker, HBC's chairman and CEO. "I've had a long connection with Saks throughout the years, and am thrilled to bring one of the world's most recognized luxury retailers into the HBC family. This acquisition will increase our growth potential both in the U.S. and Canada, generate significant efficiencies of scale, add to our powerful real estate portfolio and deliver substantial value to our shareholders."
According to a joint press release, the acquisition will benefit HBC by introducing Saks as a full-line retail brand in Canada, which is currently the largest international market for saks.com. HBC will also continue expanding the Off 5th Saks outlet brand in the United States and expects to realize about $97 million in synergies in three years as a result of the acquisition.
Saks will operate separately under the HBC umbrella, including its own merchandising, marketing and store operations teams, and will remain headquartered in New York City. It is also expected that Saks will continue to be led by key members of its existing management team. HBC will leverage top talent across both organizations and optimize a multi-banner shared services organization to drive additional benefits and reduce expenses. HBC plans to bring Saks department stores and outlet stores into Canada by converting some of its own locations, according to Reuters.
"We believe this transaction delivers compelling value to our shareholders and that Saks Fifth Avenue is an excellent fit within the HBC organization,” said Steve Sadove, chairman and CEO of Saks. “We also believe that HBC recognizes the tremendous value of our people, our real estate, our customer and vendor relationships, and most importantly the power and potential of our iconic brand. The $16 per share price represents an approximate 30% premium to the May 20, 2013 closing price, the day before media speculation began. We have made significant progress over the past few years to position Saks for future growth and to evolve into an omni-channel retailer. We are excited about what this opportunity and being part of a much larger enterprise can mean for the future of the Saks Fifth Avenue brand."
There is a 40-day "go-shop" period when Saks can seek better bids, but the company said it did not expect to get any. The transaction has been approved by each company's board of directors and is expected to close before the end of the calendar year, subject to approval by Saks shareholders, regulatory approvals and other customary closing conditions.
Previous reports indicated that Starwood Capital Group LLC, the investment firm headed by real estate developer Barry Sternlicht, had bid around $2.5 billion to purchase Saks and an unidentified third bidder, reportedly a sovereign wealth fund from the Middle Eastern nation of Qatar, was also said to be in the running to buy Saks. |
[Study advance on haloacetic acids in drinking water].
Haloacetic acids (HAAs) in drinking water have attracted more and more attention of researchers due to their higher potential combination of chlorine, their carcinogenic and mutagenic effects and higher carcinogenic. The formation mechanism, analytical methods, the effects of many factors on HAAs formation such as precursor types, chlorine doses, pH, temperature, bromide, reaction time and seasonal change, toxicological character and the minimizing technology of HAAs in resent studies about HAAs are discussed in details in this paper. Further researches are still needed to clarify the formation mechanism of HAAs and find a feasible minimizing technology. New concerns including toxicological characters that correlate with human and other HAAs exposure routes besides oral ingestion (i.e., inhalation and dermal adsorption) should be put forward. |
The German federal anti-monopoly office, the Bundeskartellamt, on Thursday agreed to the takeover of the German airline Condor by the Polish Aviation Group (PGL), the parent company of Polish national airline PLL LOT.
Bundeskartellamt said in justification of its decision that Condor and PGL do not compete with each other but, on the contrary, they run complementary services.
PGL, a state-owned company, said in a press release in late January that the takeover should be completed by the end of April.
"The Condor takeover offer presented by PGL was recognised as the most beneficial to the company, its workers, partners, suppliers and customers," the release stated.
"The PGL investment will enable Condor to pay off its obligations regarding German development bank KfW in full and on time," the press release added.
PGL President Rafal Milczarski said in late January that together with Condor Air, PGL will develop dynamically and work together with scheduled airlines as well as charter lines. "From my point of view, there is no better partner for LOT than Condor," he said.
Condor Air has a 22-percent share of the German charter market.
According to unofficial information from sources "among those conducting negotiations," acquired by German press agency dpa, LOT beat several other investors bidding for Condor, including US fund Apollo and the UK's Greybull.
The Frankfurt-registered Condor, which belonged to Thomas Cook since 2009, survived the travel agency's bankruptcy thanks to financial support from the German state to the tune of EUR 380 million. An important partner to German travel agencies, Condor employs around 5,000 people and operates about 60 aircraft.
PGL is 100-percent owned by the Polish State Treasury and is supervised by the prime minister. It is made up of LOT, LOT AMS, and LS Airport Services. |
Figures
Abstract
Background
Production of proteins as therapeutic agents, research reagents and molecular tools frequently depends on expression in heterologous hosts. Synthetic genes are increasingly used for protein production because sequence information is easier to obtain than the corresponding physical DNA. Protein-coding sequences are commonly re-designed to enhance expression, but there are no experimentally supported design principles.
Principal Findings
To identify sequence features that affect protein expression we synthesized and expressed in E. coli two sets of 40 genes encoding two commercially valuable proteins, a DNA polymerase and a single chain antibody. Genes differing only in synonymous codon usage expressed protein at levels ranging from undetectable to 30% of cellular protein. Using partial least squares regression we tested the correlation of protein production levels with parameters that have been reported to affect expression. We found that the amount of protein produced in E. coli was strongly dependent on the codons used to encode a subset of amino acids. Favorable codons were predominantly those read by tRNAs that are most highly charged during amino acid starvation, not codons that are most abundant in highly expressed E. coli proteins. Finally we confirmed the validity of our models by designing, synthesizing and testing new genes using codon biases predicted to perform well.
Conclusion
The systematic analysis of gene design parameters shown in this study has allowed us to identify codon usage within a gene as a critical determinant of achievable protein expression levels in E. coli. We propose a biochemical basis for this, as well as design algorithms to ensure high protein production from synthetic genes. Replication of this methodology should allow similar design algorithms to be empirically derived for any expression system.
Funding: The project was financially supported by NSF SBIR grant no. 0638333. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors declare competing financial interests: DNA2.0 performs gene design optimization as a free service with the genes that it sells. The authors also declare competing interests in the form of two pending relevant US patent applications, nos. 12/184,240 and 12/184,234. Austin Gurney declares no competing interests.
Introduction
Protein expression is important at many different levels of biological research. The cost of production for biopharmaceuticals and recombinant research reagents depends in large part upon the protein expression levels that can be achieved; construction of metabolic pathways requires that genes moved from one organism express protein in another; even biochemical studies of fundamental processes are frequently hampered or made impossible because sufficient amounts of protein cannot be obtained.
Genetic constructs for the expression of proteins now frequently use synthetic DNA. This is because sequence information from genome and metagenome sequencing projects has increased exponentially over the last decade [1], but most of these sequences are not available as physical DNA. The increase in speed and decrease in cost of synthetic DNA provides a convenient route to obtain genes encoding these virtual proteins [2]. Modifications of the natural DNA sequences are often introduced into the synthetic genes with the aim of enhancing expression, particularly in heterologous hosts.
Designing a gene to express a protein requires choosing from an enormous number of possible DNA sequences [3]. Most current synthetic gene design strategies are guided by mimicry of natural gene characteristics thought to be relevant for increased expression [4]. A variation on this approach is to copy the codon bias of a subset of highly-expressed native host genes [5] or even to exclusively use the codons most common in highly expressed genes [6]. The codon bias of a gene toward common codons is reflected in the Codon Adaptation Index (CAI) [7]. While genes designed to match host bias or maximizing CAI have expressed successfully in many instances [8], [9], clear relationships between these practices and expression are lacking. Most reported “codon optimization” successes describe only two genes: one natural and one synthetic [8]. Since only successful optimization experiments are published, and published examples generally differ in many respects, one cannot draw reliable conclusions on how best to design synthetic genes [3], [9], [10].
A recent study of expression of a diverse library of GFP genes in E. coli concluded that expression was limited primarily at initiation of translation [11]. Impaired expression correlated with a strong mRNA secondary structure near the translational start site, but no dependence on CAI or overall GC content was observed. However, a significant body of literature suggests that synonymous codon usage beyond the initiation region can impact expression [3], [8], [9]; for example E. coli strains over-expressing rare tRNAs can significantly improve gene expression [12]–[14].
In this work we have examined the relationship between protein expression and gene sequence characteristics, using two different proteins of commercial value for which expression levels were limiting. We designed and independently synthesized about 40 genes encoding each of these proteins; synonymous codon variation caused more than 40-fold variation in expression. We identified sequence properties that correlated with expression by combining partial least squares regression [15], [16] with genetic algorithms [17]. Variation among both gene sets was highly correlated to the codon biases for 10 amino acids. We tested the predictive value of these correlations by designing and testing several new genes; expression levels of these genes were high and well predicted. Finally, we discuss a possible biochemical basis for the codon preferences we observe.
Results
Synonymous substitutions cause expression differences
Two genes were chosen as targets for systematic exploration of the effect of synonymous codon usage on expression; one encoding the DNA polymerase of Bacillus phage Φ29 [18], the second encoding a synthetic single-chain antibody fragment (scFv) developed by OncoMed, Redwood City, CA. These genes were selected because they encode evolutionarily, structurally and functionally different proteins. There was also immediate commercial value in improving their expression as well as expression of the general classes they represent.
Two initial variant sets were designed: 21 variants of the polymerase gene and 24 of the scFv. Only synonymous codon usage within the open reading frame was varied. Gene variants were designed by back-translating the protein sequence using a Monte Carlo repeated random sampling algorithm to select codons probabilistically from codon frequency lookup tables [19]. Different sequences were obtained from different lookup tables, and by independently controlling predicted mRNA structures and GC bias in the first 15 codons (see Supplementary Material). The average pairwise DNA sequence identity was 79% and 82% within the scFv and polymerase variants, respectively.
Gene variants were synthesized, sequence-verified and cloned under control of the T7 promoter (Materials & Methods). Expression of full-length protein was directly measured by polyacrylamide gel electrophoresis for a minimum of three clones for each gene variant (see Fig. 1). Sequences and expression levels for all genes in this study are provided in Table S1. Protein yields varied from undetectable (<5 µg/ml of culture at A600 = 3.0) to ~68 µg/ml (estimated to be ~10% of total cell protein) for the polymerase, and to ~200 µg/ml (~30% of total cell protein) for the scFv. Synonymous codon changes thus caused more than 40-fold differences in expression.
Expression variation is caused by distributed sequence differences
Sequence characteristics affecting expression could be local (e.g. mRNA structures and rare codon clusters) or global (e.g. codon usage and GC content). To distinguish between localized or distributed effects, four sets of chimeras were constructed. For each set, a well-expressed gene and a poorly-expressed gene were divided into three segments (5′, middle and 3′), chimeras were synthesized and their expression determined (Table 1).
Chimeras between polymerase genes P19 (high expresser) and P15 (low expresser) showed highly distributed effects. The 5′ or 3′ segments of P19 when individually substituted into P15 increased expression over that seen for P15 alone, with the strongest effect contributed by the 3′ segment. Conversely, any one segment of P15 was deleterious when substituted into P19, with the strongest effect again seen for the 3′ segment. In contrast, expression of chimeras of P7 (low expresser) and P20 (high expresser) showed a strong dependence on the parental origin of the middle segment with relatively little contribution from the 5′ and 3′ segments. Chimeras between scFv genes A1(high expresser) and A17 (low expresser) correlated strongly with the parent of the 3′ segment, while chimeras between scFv genes A1 and A11 (low expresser) expressed protein at comparable levels to the parent of the 5′ segment (first 43 codons).
These results show that protein expression levels can depend on elements distributed throughout the gene and are not confined to any specific region. Each of A11, A17 and P7 appeared to have a dominant “poisoning” segment; replacement of that segment with the corresponding segment from a good expresser boosted expression close to the level seen in the good expresser. However the position of the deleterious segment was different in each of these chimera sets, while in the P15/P19 set each segment contributed similarly.
We analyzed all gene variants, attempting to correlate expression levels with properties that have been suggested to affect expression (see Table S1). We could not find correlation with previously suggested deleterious motifs, such as predicted 5′ or internal mRNA secondary structures, GC bias in the first 15 codons, content, runs of C or G, transcriptional terminator motifs [20], [21], internal Shine-Dalgarno-like motifs [22], RNaseE cleavage sites [23], or over- or under represented codon pairs [24], [25]. This suggested that expression level differences were either determined by several unidentifiable elements or were influenced by a distributed sequence property such as codon usage.
Synonymous codon choice correlates with expression
Models to predict expression as a function of codon usage were constructed using Partial Least Squares (PLS) regression [15]. Models were calculated from the polymerase and scFv variant sets separately and in combination. Initial regression analysis with all sense codons suggested that frequencies of only a subset of codons could explain most expression variation. A genetic algorithm was used to evolve 888 highly-predictive unique PLS models, each with a reduced set of codons (average of 14.2 codons per model). The predictions of the best models are shown in Figure 2.
For each variant the measured expression level was plotted against the expression predicted from a PLS model using genetic algorithm-selected codons. (A) Model fit for polymerase variant expression data. Blue diamonds indicate the 34 gene training set used to create the model. (B) Model fit for scFv expression data. Blue diamonds indicate the 24 gene training set used to create the model. Green triangles are variants from the initial set with undetectable expression, and which were not used for model building. (C) Combined model constructed from polymerase variants (34 red squares) and scFv variants (27 blue diamonds). Expression in each set was normalized to the highest expression level in that set ( = 3). R2(CV) indicates the correlation coefficient for the fit of the model in cross-validation (see Materials and Methods). Variants used to provide datapoints for construction of the models are indicated in Table S1.
doi:10.1371/journal.pone.0007002.g002
Using on average 80% of the 34 datapoints in the polymerase set, the model predicted expression from the remaining 20% of sequences with a correlation coefficient of 0.69 (Figure 2A). Genetic algorithm selection identified 6 codons representing biases for 6 different amino acids (Gly, Leu, Asp, Glu,Tyr, and Ala) as most critical for modeling. Five of these 6 codons (all but Ala) encode the 5 most utilized amino acids in the polymerase and 5 of 6 (all but Leu) encode amino acids that are utilized at levels above that of average genes in E. coli.
Initial modeling of scFv expression gave results similar to the polymerase. However, 9 scFv gene variants showing no or barely detectable expression were difficult to explain along with the remainder of the set. When these 9 variants were not included in the model, a strongly predictive model was obtained (R2 = 0.86, Cross-Val R2 = 0.68; Fig. 2B). Genetic algorithm selection identified 5 codons representing 4 amino acids (Ser, Thr, Ala, and Val) as most significant.
The two datasets were combined by normalizing expression of each gene to the highest expressing gene in its set. A PLS model of the combined data is shown in Figure 2C (R2 = 0.77, Cross-Val R2 = 0.65). Fitting statistics for this model are shown in Table S3. As a further validation of low sensitivity to over-fitting of our method and significance of the correlations observed, the genetic algorithm was applied to datasets where the association of expression levels to variants was randomized. No predictive model based on codon frequency could be obtained after randomization for either the polymerase dataset (Best model: R2 = 0.037, Cross-Val R2 = 0.004), the reduced scFv dataset (Best model: R2 = 0.44, Cross-Val R2 = 0.30) or the combined dataset (Best Cross-Val R2 = 0.11). We conclude that variation in expression within our dataset is highly correlated to codon usage.
Preferred codons are not those used most frequently by E coli
Ten amino acids were consistently represented in all 888 evolved models (Table 2), suggesting they are critical for optimal prediction. All other amino acids were represented in fewer than 30% of the models. Summary codon usage data for the 10 highly-represented amino acids is shown in Table 2. The codon bias observed for highly expressed genes of the dataset is different from codons used at highest frequency in naturally highly expressed E. coli genes [5], [7]. We also see no correlation between codon bias of highly expressed native E. coli genes and the codon regression vectors obtained from PLS regression of our data (Table S3). For example, although Ser-UCU is preferred in highly expressed E. coli genes, our model indicates that Ser-AGC is preferred: it is used 7 times more often than UCU in our most highly expressing genes. For threonine, highly-expressed E. coli genes use ACC 4 times as often as ACG; our model suggests that ACG should be used more often than this, and our most highly expressed variants use ACG at over half the frequency of ACC.
Bias towards codons that are most used in highly expressed native E. coli genes (increasing the CAI [7]) is widely used as the basis of gene optimization [26]. The discrepancy between these codons and those that our PLS model indicates are important is therefore significant. Plotting the CAI score against the expression obtained for each gene in our study confirmed that CAI has no value in predicting gene expression for either gene set (Fig. 3A).
Figure 3. Expression is not predicted by Codon Adaptation Index or mRNA structure.
The codon adaptation index [7] (part A) and the strength of mRNA secondary structure from position −4 to +38 relative to the initiating AUG (part B) were calculated for each variant synthesized in this study and plotted against the expression level measured for that variant. Blue diamonds indicate scFv variants. Red squares indicate polymerase variants. Expression levels are normalized to highest expressing variant for each set (equal to 3).
doi:10.1371/journal.pone.0007002.g003
Another factor that has recently been shown to be important for expression of green fluorescent protein is the structure of the mRNA around the initiating AUG [11]. For the most part, we see no correlation between the energy of RNA structure in this region and expression (Fig. 3B), although a few of the most structured scFv genes show very poor expression that was not predicted by our codon usage model.
5′ mRNA affects expression in some scFv variants
From the analysis expression levels of the variant chimeras, we observed that the 5′ segment of A11 appeared highly deleterious for expression (Table 1). This poorly expressing variant is predicted to express highly based on our codon usage model. Several reports have implicated the 5′ coding region as especially important in modulating translation initiation [3], [11], [27]–[33]. A recent study implicated mRNA structure formed in the region from −4 to +38 relative to the start of the ORF (starting A identified as position 1) as particularly deleterious for green fluorescent protein expression [11]. The 5′ regions of variants A11, A14, A16, and A19, all of which expressed at levels below those predicted by our codon usage model also showed stronger than average predicted mRNA secondary structure around the site of translational initiation (Table S1). We therefore tested whether replacing the 5′ segment of 6 other antibody genes would increase protein expression levels as it had for A11. Three of 6 of the non-expressing antibody genes were clearly improved when their 5′ segments (the first 15 codons) were replaced by that of A1. An A1_14 chimera expressed at similar levels to A1. Chimeras A1_19 and A1_24 showed improved but lower expression than A1_14. Barely detectable expression was seen for the A1_7 and A1_16 chimeras and no expression was seen for chimera A1_8, indicating that something other than the 5′ leader is limiting expression of these gene variants. Four of these 6 gene variants (all that show significantly improved expression and A1_8) are well predicted from their codon usage by the PLS model, as shown in Figure 4.
Figure 4. Modification of 5′ sequence improves the performance of some scFv variants.
For each scFv variant the measured expression level was plotted against the expression predicted from a PLS model using genetic algorithm-selected codons. Blue diamonds indicate the 24 gene training set used to create the model, Green triangles are variants from the initial set with undetectable expression. Red squares are new variants created by combining the first segment (the first 15 codons) of variant A1 with the remainder of these 6 poorly-expressed variants. Arrows indicate changes in predicted and measured expression upon 5′ codon exchange. Variants represented as green triangles or red squares were not included in the training set from which the model was built. Variant A1_11_11, in which a larger 43 codon portion of the 5′ section of the A11 gene was replaced with that of A1, is also indicated for comparison.
doi:10.1371/journal.pone.0007002.g004
None of three weakly expressing polymerase variants (P2, P11, and P16) were detectably improved by exchange of the first 15 codons with those of the highly expressed P19 (data not shown). Clearly, these genes are poor due to downstream elements or global features. All three were predicted to be low expressed based on codon usage by the PLS model.
Variation among gene chimeras is largely explained by codon usage
The variation in the distribution of critical sequence determinants among variant gene chimeras is described in Table 1. Chimeras between polymerase variants P15 and P19 showed that expression levels resulted from sequence properties that were distributed throughout the gene, whereas other chimera sets showed different emphasis on particular gene fragments. With the exception of the chimeras made with one parent showing undetectable expression, indicating a deleterious 5′ mRNA leader, the variation among the chimeras is largely explained by the codon usage based PLS model, as shown in Figure 5.
Expression predicted by the combined model shown in Figure 2C for the subset of chimeric variants. Each chimera series is indicated by different symbols as shown in the legend.
doi:10.1371/journal.pone.0007002.g005
We interpret these results to mean that codon usage is a strong determinant of the overall expression level that can be obtained from a gene, but that this level can be reduced if deleterious sequence elements are present, for example those that form mRNA structures that may interfere with the initiation of translation.
Codon usage models supported by design and testing of new gene variants
Although the PLS model uses codon usage to predict gene expression for two different gene sets, it does not directly provide an optimal codon usage. Rather it indicates which codons should be used more and less often than their average use in the dataset (see Table 2). An optimal solution from this kind of experiment typically requires several iterations of modeling and testing [34], but this is unnecessary to demonstrate that expression depends upon the frequencies of particular codons. Instead, we tested this hypothesis by designing a set of new genes using new codon bias tables, measuring their expression and comparing with that predicted by the model.
We tested three different codon biases, none of which we expected to be optimal, but all predicted to give better than average expression in the dataset. These frequencies are shown in Table S2. The expression of 2 scFv variants (A_FreqA and A_FreqB) and 2 polymerase variants (P_FreqB and P_FreqC) synthesized using these tables are shown in Figure 6, and their expression levels are also given in Table S1. All of these genes expressed extremely well, and as predicted by the PLS model. In contrast, an additional scFv variant, A_HiCAI, was designed using codons that occur frequently in highly expressed native E. coli genes. This gene also used identical coding to the highest expressed variant A1 for the first 15 codons to avoid possible deleterious mRNA structure near the translational initiation site. Known toxic motifs were avoided in the design. A_HiCAI's expression, accurately predicted by the PLS model, was only 15% of the levels obtained for A_FreqA or A_FreqB. This data supports the conclusion that controlling gene codon frequencies, but not maximizing CAI, is critical for optimal protein expression.
Figure 6. New gene variants express as predicted by the combined PLS model.
For each variant the measured expression level was plotted against the expression predicted from a PLS model using genetic algorithm-selected codons. Polymerase variants (34 red squares) and scFv variants (27 blue diamonds) were included in the training set, expression in each set was normalized to the highest expression level in that set ( = 3). Green triangles show measured and predicted expression of 5 new genes not included in the training set. Correlation coefficients represent fits of the entire training set.
doi:10.1371/journal.pone.0007002.g006
Discussion
By designing and synthesizing 81 individual genes encoding two different proteins, we have found that sequence differences entirely confined to non-coding changes within the open reading frame caused at least 40-fold differences in protein expression. We were able to create predictive sequence-expression models based on a strong correlation between expression and the codon bias of a subset of amino acids. The model correctly predicted the expression of variants not included in the model-building, and of new variants designed using improved codon bias tables.
Most of the codons that were identified as influential for expression encode amino acids that are highly represented in one or both proteins studied (Table 2). However, the most favorable biases for expression clearly do not correspond to those found in highly expressed native E coli genes [5], [7]. This contradicts a widespread gene design principle that mimicking the codon bias of the host or of a selected group of host genes will ensure protein expression [6], [26]. The rationale for this approach has been that tRNA availability could limit translational elongation. However, translation is not limited directly by tRNA levels, but by the availability of amino-acylated (charged) tRNA [35].
In 2003, Elf et al[36] predicted that charging of some tRNA isoacceptors would be much more sensitive than others to perturbations of the recharging rate. These are tRNAs used at high frequency relative to their level in the cell. Subsequently, these predictions were experimentally confirmed for a subset of tRNAs [37]. Furthermore, heterologous overexpression is predicted to deplete intracellular amino acid and charged tRNA concentrations depending on the amino acid composition of the overexpressed protein [38], [39]. This may have a direct impact on translation rate and may also induce metabolic responses deleterious for expression yield [38].
PLS modeling suggests that most of the variation in our dataset can be explained by codons for serine (AGC favored and UCU disfavored), threonine (ACG favored), and leucine (UUG favored). These results fit well with the predicted sensitivities to amino acid starvation of the isoacceptor tRNAs that recognize these codons [36]. The tRNA pools for all three favored codons (AGC, ACG and UUG) are the least sensitive to starvation for their respective amino acids (Table 2). The relative tRNA charging levels during starvation have been measured for threonine and leucine [37]. From this data and from the tRNA abundance [40] we can estimate the number of copies of each charged and uncharged tRNA per cell (Table 3). Considering either absolute numbers of charged tRNAs or the ratio of charged to uncharged tRNAs, UUG becomes a more attractive codon for encoding leucine relative to CUG as recharging is limited by starvation. Likewise ACG improves greatly relative to ACC for encoding threonine. Both trends are consistent with the codon preferences identified by our PLS model.
From this data it is tempting to speculate that much of the variation we see in expression is influenced by charged tRNA depletion and/or induction of a metabolic response from the host organism. High translation rates deplete the translational machinery [41]. As amino acid charging of tRNA becomes limiting, only those tRNAs that can maintain charge can support high translation levels. The optimal codon bias for a gene probably depends both on maintaining high levels of charged tRNAs and minimizing the levels of uncharged tRNAs which may inhibit translation and/or cause a deleterious metabolic response [38], [39], [41].
In contrast with a recent study of GFP variants [11], we saw relatively little influence of mRNA structure near the initiation site. In three scFv genes weak expression, poorly predicted by the model, correlated with stronger than average mRNA structure in this region. Replacing the first 15 codons with a less-structured synonymous equivalent restored expression to levels predicted by the model, suggesting that mRNA structure may limit expression of these genes. In reconciling our results with those of Kudla et al, we note that the predicted 5′ mRNA structures of almost all of our genes are significantly weaker than those found to have a significant effect in the GFP study: only one of our gene variants had a free energy less than −9 kcal/mol in this region (Table S1). Indeed, little correlation was observed in the GFP study between 5′ mRNA structure and expression for genes with structure strength >−9 kcal/mol despite greater than 20-fold variation in expression among these genes [11]. Inhibition of initiation by especially strong mRNA structure would obscure effects resulting from factors that influence elongation, such as codon usage, which dominates our results.
Although we were unable to find any predictive correlations between expression and any parameter other than codon frequency, other sequence elements may contribute to some variation observed and could be important in optimal gene design. Differences in mRNA stability could also cause at least some expression variation observed. The translation rate itself can influence mRNA degradation rate making cause and effect in this case difficult to disentangle [42]–[44].
As direct synthesis replaces classic cloning as the preferred path for constructing functional genetic elements, it is critical to develop gene design algorithms for reliable heterologous expression. Here we have shown that sequences beyond the translational initiation region are critical and that codon usage is a key determinant of expression yield. Regardless of the mechanism by which codon bias affects expression, systematic analysis of the relationship between gene sequences and expression will be a powerful tool to refine our design algorithms, both for E. coli and other expression hosts.
Materials and Methods
Gene synthesis and protein expression
Synthetic gene variants and chimeras were all made by standard in-house procedures essentially as previously described [45] and cloned into a pET24a expression vector (EMD, Madison, WI) under control of the T7 promoter, between the XbaI and EcoRI restriction sites. Each construct was completely sequenced in both directions to ensure consistency with the designed sequence. Each variant plasmid was transformed into E. coli expression host strain BL21(DE3) pLysS (Invitrogen, Carlsbad, CA). BL21(DE3) pLysS was chosen as the host for all expression studies described. The low-level expression in this host of T7 lysozyme, an inhibitor of T7 RNA polymerase, gives tight repression of heterologous expression prior to induction to minimize potential gene toxicity which could affect data quality.
Prior to protein expression analysis of the variants, expression was analyzed for multiple variants showing a range of expression levels to determine appropriate expression time and temperature. Strong, consistent expression was achieved at 30°C, a commonly used temperature for heterologous expression in E. coli. Time courses at 30°C showed expressed protein levels increasing to a maximum after approximately two hours, as the cells entered stationary phase growth, and expression remained steady for at least five hours. Relative protein expression levels between these variants were consistent as protein accumulated during growth phase and were maintained in stationary phase (data not shown). For our variant analysis we chose to express for four hours at 30°C.
At least three independent isolates for each gene were picked and cultured overnight in 2 ml Luria Broth (LB) containing 25 µg/ml kanamycin and 25 µg/ml chloramphenicol. Overnight cultures were diluted 50-fold in fresh media and incubated at 37°C until the cells were in mid-log growth (OD at 600 nm = 0.6). Expression was induced by addition of IPTG to 1 mM and incubation for four hours at 30°C. Final optical densities of cultures were measured and equivalent amounts of culture were analyzed by polyacrylamide gel electrophoresis. Gels were stained with Sypro Ruby (Pierce), visualized by fluorescence imaging, and protein band intensities quantified using TotalLab100 image analysis software (Nonlinear, Inc). Each gel contained protein concentration standards to calibrate band intensity. In each experiment, a consistent reference variant was co-expressed in triplicate. For analysis of polymerase expression, the reference was a phi29 DNA polymerase variant identical to variant 21 but containing two differences in the 5′ untranslated region. For analysis of the scFv variants, Variant A13 was used as the reference. Reference variants were used to correct for experiment to experiment variation in yield. Measured expression levels are all relative to these references. Reported values in µg/ml are normalized to the average expression level of the references over the sum of experiments. The detection limit of the assay was approximately 5 µg protein per ml culture at an A600 = 3. The standard error of measured expression for variant repeats was generally <20% of the mean.
Design of initial gene variant sets
Gene variants were designed by back-translating the protein sequence using a Monte Carlo repeated random sampling algorithm [19]. This algorithm selects a codon for each position at a probability defined in a codon frequency lookup table. A variety of different lookup tables and constraints were applied to create variant designs that differed in a number of parameters that have been associated with expression effects in the literature. Global codon usage was primarily varied in bias toward or away from codons used preferentially in either highly expressed or average native E. coli genes and inclusion or exclusion of naturally rare codons. We also specifically varied the first 15 codons toward higher or lower GC content. Design of Experiments methodology was used to minimize co-variation of these constraints and thus maximize diversity among the variants and improve our ability to distinguish independent contributions. We also analyzed and edited mRNA structure to minimize co-variation of structure, internally or near the translational initiation site, with codon usage constraints. We also minimized co-variation of codon bias with G/C islands, which might promote frame-shifting, by selectively avoiding runs of consecutive G and/or C greater than 6 nucleotides for half of the variants. Due to the use of Monte-Carlo sampling in the gene design, all of these variants were highly divergent in sequence identity from each other. The average pairwise DNA sequence identity was 79% within the 24 member scFv dataset and 82% within the 21 member polymerase dataset. This broadly distributed dataset ensures that most global sequence variables are sampled, either as a direct consequence of the design, or as an indirect consequence of the varied dataset. Except where restriction sites were fixed in the scFv genes, no contiguous string of nucleotides longer than five nucleotides was conserved throughout either set. With the exception of codons used extremely infrequently in E. coli, the frequency use of all individual sense codons showed high variability across the sets. The complete sequence alignment of both gene variant datasets is available in Table S1.
PLS analysis and genetic algorithm variable selection
The frequency of occurrence of each codon was calculated for each gene variant and compiled for all variants that gave detectable protein expression. Stop codons were not varied in frequency and thus were not included in the modeling. For individual phi29 polymerase and scFv gene models, sense codons with no or redundant information content were excluded from the dataset. These included ATG for Met, and TGG for Trp and one codon for each two-codon amino acid, as, for such amino acids, the frequencies of the two codons are perfectly inversely correlated. For modeling of the combined dataset, all sense codons were included.
We used the PLS Toolbox 5.2 software (Eigenvector Research Inc., Wenatchee, WA) run in the MATLAB environment (Mathworks, Inc.) to model the relationship between sequence variables and protein expression data. For all modeling, independent (e.g., codon frequency) and dependent (expression) variables were pre-processed by mean centering and scaling to the standard deviation of variation among the samples included. For cross-validation, the dataset was randomly split into 5 subsets of variants and each subset was predicted by PLS models trained on the remaining 4 subsets. This process was repeated for ten iterations with different random data splits. The error in prediction of left-out data was monitored as a function of the number of latent variables used. In each case described, the number of latent variables used was limited to the number that minimized error in cross-validation models to avoid over-fitting. As an additional check of sensitivity to over-fitting, we randomly re-assigned expression data to the samples, such that original and randomized data were not correlated, and assessed the ability of PLS to construct a model. For all modeling described, such randomization prevented construction of any predictive model.
For variable selection a genetic algorithm was used to determine codon subsets that were most predictive of expression (those that minimized cross-validation error). For typical codon based modeling, 256 random codon subsets, each consisting of approximately 30% of the total codon pool, were chosen. PLS models were created for random cross-validation subsets of the samples as described above. Codon sets were then ranked in fitness according to their cross-validation error in prediction of expression. Variable sets that showed better than median error in prediction were chosen as parents and randomly pair-wise recombined to create new progeny subsets. Along with their parents, these were then evaluated for prediction and best subsets again selected. At each generation a low level of mutation (random substitution of variables at a frequency of 0.01) was allowed to avoid trapping in local optima. This process was continued until convergence, defined here as fewer than half of the subsets in the population being unique (i.e., ≤128 unique subsets in a population of 256). The entire evolutionary process was repeated 20 times to further avoid bias from local optima trapping, creating a population of codon subsets improved in prediction of expression. The same selection process was also run after random assignment of expression data as described above. In each case, randomization prevented the algorithm from identifying a predictive model. Results were used in to identify codons most enriched in the evolution, and thus most critical for explaining expression. The best evolved subsets were used to create working PLS models.
Gene Sequence Analyses
All RNA structure strengths are optimal predicted structures calculated using the Vienna RNAfold software package using parameters from Mathews, et al [46]. CAI estimates were calculated as the geometric mean for test gene codons of the ratio of the codon frequency in highly expressed E. coli genes divided by that of the highest frequency codon for each amino acid in those genes [7]. Codon frequencies in highly expressed E. coli genes were taken from EMBOSS [47].
Supporting Information
Expression data, sequences, and selected sequence characteristics of all polymerase and scFv variants. Variants beginning with “A” are scFv genes. Those beginning with “P” are polymerase genes. Column 2 shows the calculated average expression level relative to the highest expressing variant for the same gene set (set to 3). Columns 3 & 4 show the calculated absolute expression level and standard error (minimum of 3 independent determinations). Columns 5–7 indicate which variants were included in datasets used for PLS modeling for the figures indicated. Columns 8 & 9 show the calculated GC content and codon adaptation index (CAI) [7], respectively, for each variant. Columns 10 & 11 show the number of occurrences of codons used at <10% per amino acid in naturally highly-expressed and all E. coli genes [5], [47], respectively. Column 12 shows the number of occurrences of contiguous runs of G and/or C of 7 or more nucleotides. Columns 13 & 14 show the strongest and average RNA structure strength for all 50 nucleotide frames along the mRNA open reading frame region. Columns 15 & 16 show calculated mRNA structure strengths for two 5′ mRNA windows, one including sequence from 5′ to the ribosome binding site to 50 nucleotides into the open reading frame (−42 to +50) and one identical to that shown to correlate best with expression of GFP variants [11]. All RNA structure strengths are optimal predicted structures calculated using the Vienna RNAfold software package using parameters from Mathews, et al [46]. Column 17 includes the complete DNA sequences of the variant open reading frames and those for the 5′ and 3′ untranslated regions listed in the bottom three columns of the table.
Codon Frequency Bias Tables. Two codon frequency tables were constructed as averages of the frequencies found in the best variants: FreqA from the 4 genes comprised of the 2 most highly expressing variants of each set (A1, A21, P19, and P20); FreqB from 10 of the most highly expressing variants (P19, P20, A1, A21, A1_14, A17_17_1, A17_1_1, A1_17_1, A1_11_11, and A_FreqA) and FreqC approximates the bias used to create polymerase variant P19. A fourth set of frequencies, “HiCAI” used codons that are most common in highly expressed native E. coli genes.
PLS model statistics for combined gene sets Statistics for the PLS model depicted in Figures 2C, 5, & 6 of the manuscript. Codons listed are those selected by genetic algorithm to provide minimal error in cross-validation for prediction of the dataset (see Materials and Methods). The particular model includes 5 latent variables, which were determined to yield minimal error in cross-validation. Mathematical descriptions of model statistics have been published by Eriksson, et al [15]. Statistics shown apply to the datatset preprocessed as described in Materials and Methods.
doi:10.1371/journal.pone.0007002.s003
(0.03 MB XLS)
Acknowledgments
We thank all members of the DNA2.0 production team for synthesizing all genes described here. |
Effect of radiotherapy and other treatment-related factors on mid-term to long-term cognitive sequelae in low-grade gliomas: a comparative study.
Because survival benefits of treatment with radiotherapy are questionable and such treatment can cause substantial damage to the brain over time, the optimum management strategy for low-grade gliomas remains controversial. We aimed to identify the specific effects of radiotherapy on objective and self-reported cognitive function, and on cognitive deterioration over time, in patients with low-grade gliomas treated with early radiotherapy. 195 patients with low-grade glioma (of whom 104 had received radiotherapy 1-22 years previously) were compared with 100 low-grade haematological patients and 195 healthy controls. Our analyses aimed to differentiate between the effects of the tumour (eg, disease duration, lateralisation) and treatment effects (neurosurgery, radiotherapy, antiepileptic drugs) on cognitive function and on relative risk of cognitive disability. Low-grade glioma patients had lower ability in all cognitive domains than did low-grade haematological patients, and did even less well by comparison with healthy controls. Use of radiotherapy was associated with poorer cognitive function; however, cognitive disability in the memory domain was found only in radiotherapy patients who received fraction doses exceeding 2 Gy. Antiepileptic drug use was strongly associated with disability in attentional and executive function. Our findings suggest that the tumour itself has the most deleterious effect on cognitive function and that radiotherapy mainly results in additional long-term cognitive disability when high fraction doses are used. Additionally, the effects of other medical factors, especially antiepileptic drug use, on cognitive function in glioma patients deserve attention. |
Schumacher an F1 great, if not the greatest
LONDON (Reuters) - Michael Schumacher enjoyed more wins, more titles and more success than any driver in the history of Formula One but where he ranks in the pantheon of greats will be debated for decades to come.
To his fervent fans the seven times world champion will always be simply the best - a giant whose fame transcends the sport and whose name is familiar even to those with scant passion for motor racing.
'Schumi', 'Schuey', 'The Red Baron', 'Der Weltmeister' (world champion): The German won an unprecedented 91 races and set record after record including five titles in a row with glamour team Ferrari between 2000 and 2004.
In 2002, Schumacher finished every race on the podium and statistically, stands in a class of his own.
The prayers and tide of goodwill messages as the 44-year-old lies in critical condition in hospital in Grenoble after a skiing accident in the French Alps testify to his status and esteem in the sport and beyond.
It seems almost churlish at such a time to point out an alternative view, that his greatness was flawed by favoritism over team mates and a questionable sense of fair play with too many controversies.
The late triple champion Ayrton Senna remains revered, despite the Brazilian's own suspect behavior on the track, and was mourned like no other driver after his death at the 1994 San Marino Grand Prix.
Although Schumacher's popularity in his native Germany was always unquestionable, bringing out the fans in droves even in his unsuccessful comeback years with Mercedes, it was far from universal.
"I think he is the greatest racing driver of this century," his former Mercedes team principal Ross Brawn said when the German announced his definitive retirement last year, an accolade that neatly sidestepped the sport's first 50 years.
Even that assessment may be questioned sooner than anyone expected, with compatriot Sebastian Vettel this year chalking up his fourth successive title to become Formula One's youngest ever quadruple champion.
With Ferrari in 2004, Schumacher had chalked up a record 13 wins including seven in a row. Vettel, still only 26, matched that total this year and also racked up nine successive victories.
TWO PARTS
In truth, Schumacher's career stands as a drama in two acts with a three-year intermission.
The Schumacher Mark II drove a gleaming silver Mercedes but was still a scuffed shadow of the shiny Mark I model, who dominated racetracks around the world in the colors of Benetton and then Ferrari.
In 2006, when he told the world at an Italian Grand Prix news conference that he had decided to retire as a Ferrari driver, it seemed like the end of an era.
In some ways it was. His Mercedes comeback produced just one podium finish even if he looked as fit as ever, positively glowing with health and far more mellow in his attitude.
When he called time for good in Japan last year, looking forward to a new life with his wife and two children in Switzerland, there was more a sense of relief that he was getting out intact. The Formula One world had already moved on.
"I have had my doubts for quite a while," he acknowledged. "It's time for freedom again."
Self doubt was never a big part of the old Michael Schumacher's make-up, even from the early days when his bricklayer father Rolf took him to the Kerpen Kart track near Cologne where his mother Elisabeth worked in the canteen.
He entered Formula One in 1991 with Jordan as a late replacement for jailed Belgian Bertrand Gachot after a payment from Mercedes, who had contracted him for their sportscar team, eased his passage.
Schumacher had only ever ridden around the Spa circuit on a bicycle but his debut made everyone sit up and take notice when he qualified seventh. He was immediately snapped up by Benetton and the rest was history. By the end of 1994, he was a champion.
Schumacher II was softer, more prepared to admit mistakes. He became much more approachable than in the Ferrari days when his life seemed divided into compartments and nothing was allowed to interrupt his focus.
He even practiced his Italian - something he rarely managed at Ferrari whose loyal 'tifosi' worshipped his success but often wished he would be a little less German.
"In my first career, as I entered into Formula One (with Jordan in 1991), immediately I had a lot of focus on me. So there was a constant demand and pressure on me that was difficult to cope with over the years," he said last year.
"In that absence (from 2007 to 2010), I was more free and recharged myself... when I was back, I noticed it is possible to be open, to enjoy, but not lose the focus. And that is something I was not doing in the first part.
"(In the second part) I had a bigger picture, I had more experience, it was much more easy to handle things."
CONTROVERSIAL PAST
The controversies of the past continue to hang over his reputation like the mists that shroud his favorite Spa circuit in the Belgian forests and always will.
There was the collision with Damon Hill in the 1994 title decider, the notorious attempt in 1997 to run Jacques Villeneuve off the road and the global scorn and outrage that followed Austria 2002 when Ferrari ordered Brazilian Rubens Barrichello to gift him an undeserved win.
On his day, and particularly in the wet, he was breathtaking. His mind-management, and ability to gel a team around him and give swift and incisive feedback, set him apart from the rest.
But his achievements were countered by the feeling that he benefited from the best car and a subservient team mate throughout his Ferrari years, even if others argue that only happened because he was the best.
The 2006 Monaco Grand Prix saw him branded a cheat after a blatant attempt to block rivals in qualifying by stopping his car at the penultimate corner in the final seconds.
"I was very privileged to work with Michael from the very beginning," Brawn said last year. "We had some fantastic times, tough times but also very successful times.
"I think Michael brought a lot to the team in his second period that people don't see, a huge contribution behind the scenes... when we do achieve in the future, Michael will have made a contribution to it."
Mercedes finished the 2013 season as runners-up to Red Bull, with Schumacher's reputation already going through a reappraisal.
So much so that when Lotus needed a replacement for Kimi Raikkonen at short notice late in the year, they even sounded out the 44-year-old.
"Michael's performance against Nico and Nico's performance against Lewis (Hamilton, the 2008 champion who replaced Schumacher) made a lot of people aware of how good Michael still was," said his spokeswoman Sabine Kehm. |
Source: Couple Yelling at Each Other, by Vic/Flickr
When young children are denied what they want, or when they feel criticized, misunderstood, or not empathized with, what they experience emotionally is hurt. And in such instances, their impulse is either to dissolve into tears, and possibly retreat to their room, or stay engaged by puffing themselves up with self-righteous .
Very few of us have any difficulty recognizing that crying conveys hurt. But far fewer of us realize that getting mad—as a reaction to some perceived threat, insult, or injustice—is a desperate attempt to cover up that hurt. And in kids that inflamed emotional state is far less likely to be rationally articulated than exaggeratedly “acted out.” And, guess what? It’s pretty much the same with adults, too.
But let’s first center on the dynamics of anger in children. It’s fairly obvious that kids haven’t yet developed adequate emotional resources to cope effectively with whatever psychological pain they may be feeling. So, given their limited capacity not only to comprehend their emotions, but also to communicate them, they’re pretty much compelled to act them out. And that’s why, whether they begin to whimper, wail, shout or scream, the only way they know how to express their feelings is through visually putting them on display.
As adults, however, we’ve typically learned to restrain ourselves from physically demonstrating our emotions. Still, when our buttons get pushed, when another person makes us feel threatened—especially someone we’re intimately connected to and so emotionally depend on, like our partner—we betray a strong tendency to instantly regress into our reactive child self. Sure, we may do so with somewhat more reserve and sophistication. But we’re hardly dissimilar from children when we sulk, withdraw, rush to defend ourself—or raise our voice and fervently go into blaming (or perhaps counter-blaming) mode.
However unconsciously, most of us have discovered that our most potent defense is a strong offense. Consequently, when we feel denied or accused, we’re likely to block off our lurking fears, insecurities, and self-doubts by turning them back on our adversary. Which is the reason so many of us get mad—or even “lose it”—when our partner begins to make us question ourselves.
So when we’re distraught, when we let our emotions get the better of us, we really haven’t evolved much beyond . Just like kids unable to count the cost of their acting out behaviors, our own pained reactions prompt us to respond to the one who hurt us in ways likely only to further harm the relationship. In a word, our incited reactions are counter-productive. For in the moment we’re driven by a deeply felt need to hurt the other back.
It only makes sense that once flooded with distress, we’re incapable of (re-)focusing our on better understanding the other person's point of view, or on making the situation better. Rather (and frequently without much justification), we assume that they deliberately meant to hurt us. After all, we do feel hurt. So our efforts are geared toward fighting back, to safeguard ourselves from any additional pain they might inflict on us.
Source: Scream and Shout, by Mdanys/Flickr
To be sure, this is understandable enough—but, irrefutably, it’s kid stuff, too. Our behavior is coming from raw emotion, not our rational mind. And what’s most unfortunate here is that rarely is the , , or shame just beneath our anger even apparent to us. So we’re generally not in any position to repair the relational damage being done by our reactive (i.e., childlike) anger.
I’ll repeat about anger what I’ve already underscored in many of my Psychology Today writings on this crucial subject (see end of post for titles and links). When in our gut we feel “assaulted” by another—and it hardly matters whether such a felt attack is verbal or physical—our emotional distress derives from such feelings as being disregarded, devalued, distrusted, guilty, rejected, or unloved. But of all the possible reactions here, perhaps the deepest, most survival-related emotion is feeling powerless. For when someone says or does something hurtful to our feelings, at the most primal level it revivifies ancient fears of helplessness and hopelessness.
So our reacting with self-righteous anger (and what anger isn’t self-righteous?!) immediately sticks a band-aid over our hurt. And furthermore, the emotion has the effect of negating the other person’s “rightful” authority to judge us.
Think about it. Expressing our anger toward another has a condescending quality to it. It’s demeaning (mostly in reaction to our feeling demeaned ourselves). Moreover, it enables us to experience not only a certain moral superiority over the other, but a renewed sense of power over them as well. Quite literally, our “fight” (vs. “flight”) reaction toward them pumps up our adrenaline supplies. Our organism now “fortified,” we’re able to feel back in control of the situation—though the reality of our actually getting back in the driver’s seat is far more illusory than real.
Returning specifically to angry reactions in children, when kids are hurt by parental reprimand or restriction, unless they’re so scared of their that they cower and recoil, they’re likely to turn the negative evaluation right back on the parent. By protesting the “terrible unfairness” of it all, their self-justifying righteousness enables them to feel less bad about themselves. Their anger transmits the message that they deserved what they’d been refused—or don’t deserve the criticism or they’re receiving.
Cycling from hurt or disappointment to indignant anger also reduces the child's sense of vulnerability. For in refusing to accept the parent’s critical assessment of them, their retaliatory anger rescues them from any troublesome feelings of guilt and shame they’d otherwise have to bear.
A Most Challenging—but Powerful—Solution
So what’s to be done about all of this? After all, whether defensive (though seemingly offensive) anger occurs with a child or adult, such an aggressive reaction rarely solves anything. Blaming or shaming another may help you feel back in control, but typically it doesn’t diminish conflict. It escalates it.
In this post, I’ll offer only a single suggestion on how to forestall or move beyond the impasses created by this so-fiery emotion (though, collectively, my many posts on the subject suggest a broad array of solutions). Admittedly, this particular remedy isn’t at all easy to implement. But if you can get yourself “up” for it—and execute it with genuine warmth, sensitivity and caring—it can be extraordinarily powerful.
It all starts with the realization that beneath your vulnerability-protecting anger (as well as your partner’s) are such emotions as fear, sadness, helplessness, and . For it’s these core hurts and anxieties that “sourced” your anger in the first place. And because anger conveniently masks these much more disturbing emotions, unless you can accurately identify and work through them, the felt provocations that cause your upset will compel you to return to your anger again—and again—and again. Since your ego-defensive reactions may have become habitual, until you lay to rest these old self-doubts, you’ll feel obliged to continue to “exploit” your anger to safeguard these still-fragile feelings.
But beware. In such instances, understanding by itself is just the booby prize. It won’t finally resolve anything. What’s needed is to share with the person who (however accidentally) hurt your feelings, and so prompted your anger, that their actions or words stirred up old insecurities in you. The reason that admitting this can be so difficult is that it requires you to own up to your susceptibilities in the relationship (which is precisely what, till now, your "empowering" anger has been protecting you from!). And for most of us, such a confession would immediately increase our feelings of vulnerability, by betraying to them their substantial influence over us. So—frankly—it takes a very strong ego to “go there.
If, on the other hand, you were on the receiving end of the emotional eruption, your approach will be complementary—and every bit as difficult. For here, too, you’ll need to divulge your vulnerability, willing to let yourself be “one down” and admit to the person that their shaming or blaming hurt your feelings.
You might suggest to them—tentatively, since you don’t want to further provoke them by making them feel “psychoanalyzed”—that maybe, in addition to their anger, they felt bad because they felt misunderstood by you, or that you weren’t really listening to them. Or that what you said made them feel , or abandoned—maybe because lately you hadn’t been paying much attention to them. Or that your criticism brought up old fears of inadequacy—of not being good enough, or sufficiently worthy, to be cared about. Or that their raising their voice may have been a desperate plea for you to be more encouraging, sympathetic or supportive. In short, you’re trying to help them identify the soft underbelly of their anger by asking them what might lie behind it.
What do you know about their childhood wounds? (And, rest assured that, to whatever degree, we’re all among the ranks of the walking wounded!) Hopefully, they’ve already shared some of their old hurts with you, which definitely would give you a head start in talking with them. For you can begin to reflect aloud about what your behavior might have reminded them of, what they'd become particularly sensitive to. How in the past, say, might they have degraded, disregarded, disrespected, or even “dis-owned,” whenever they asserted their needs, made a mistake, or misbehaved?
If, nonetheless, you have little idea of what so yanked their anger chain, then ask them. But be sure to make it clear that you’re not challenging their anger or requesting that they justify or defend it. You just need help in better understanding it. For only then can you offer them the caring and compassion that, alone, can restore their lost sense of relational security.
More than anything else, we all need to feel safe in our relationships. So you can comfortably assume that whatever you said or did must have threatened this crucial feeling. If the person you’re having problems with is to develop the courage to look at, and work through, their past hurts and fears—and ultimately become “desensitized” to them—they really do need you to play the role of nurturing parent to them.
And finally, it can’t just be a role. So, beyond your words, can you truly accept them—despite whatever limitations or shortcomings they might have? And more, can you love that “wounded child” trembling just beneath their “falsely fortifying” (and doubtless, irksome) anger? And regardless of the fact that this anger may feel exaggerated, unjustified—or even abusive?
If you can be sufficiently and “high-minded” to really care about your having hurt them (despite their anger’s having hurt you back!), then such heartfelt compassion can be a potent healing force in their life.
And actually, that’s what, over time, will enable both of you to heal whatever emotional wounds remain from your past. For nothing removes the stinging venom from your—or your partner’s—defensive anger more than lovingly approaching what lies beneath it.
For those who’d like to explore this crucial topic further, here are some titles—and accompanying links—for other posts I’ve done on anger:
© 2016 Leon F. Seltzer, Ph.D. All Rights Reserved. |
Q:
What is the origin of "beziehungsweise"?
I can't understand "beziehungsweise" in the context of its two parts, "beziehen" and "weise".
What is the logic behind its meaning?
A:
The trick that leads us to understand the logic of "beziehungsweise" is knowing that the first part is not derived from the verb "beziehen" (to refer to) but from the noun "Beziehung".
If we translate "Beziehung" with "respect" then building an adverb with the suffix "-weise" follows a similar logic in English, and in German:
English: Respect -> respectively
German: Beziehung -> beziehungsweise
|
Brain-savvy Business™
The brain and change
Published byJan HillsApril 17, 2015
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What we often hear from leaders is that the resistance is not direct. At an intellectual level people agree with the proposition.
Is there a leader today who is not involved in a change situation? Most leaders have some form of change project or programme going on. With the amount of uncertainty and the challenging economic climate getting projects to work is crucial and yet the statistics on the success of change in business are dire. Something like 70% of change programmes fail or only partially succeed. For leaders that is high risk. In a recent Economist report a lack of buy-in from people was the cause sited as the reason for the failure. Does this have to be the case? The latest research from neuroscience, the science of how the brain works is beginning to show us why change is painful, why it is resisted, and what leaders can do to make change easier and to institute new ways of working.
What we often hear from leaders is that the resistance is not direct. At an intellectual level people agree with the proposition. Leaders tell us time and again that people revert back to their old ways of working or even fail from the outset to make the shift to the new role and work methods. Incentives and threats drive resistance underground.
In other words there is no logical reason for people to continue working in the old way. But before we make judgments, reflect on when you personally may have resisted change. We have all done this at some time, even when logically we know the direction is right.
This resistance begins to make sense when we look at the results of neuroscientific research into how the brain works. Developments in technology have allowed scientists to literally see how the brain deals with change.
Change creates a painful experience in the brain. Much like being punched or breaking a bone.
The research shows that people’s response to change is common, at a biological level. Change creates a painful experience in the brain. Much like being punched or breaking a bone.
Our brain responds to and encourages us to create patterns, regular ways of doing things. This reduces uncertainty and saves energy. These patterns act as a short cut; you don’t have to work out how to do something like open a door every time. These types of routine or regular activities are run by the basal ganglia which is much more efficient in terms of energy usage. After a period of time, our job becomes one of these regular actions. We get comfortable doing the ‘old’ process and routine. The role is predictable. Doing something different to the norm, is the equivalent of telling the brain something is wrong. This activates the emotional centre, the amygdale which controls our flight or fight response. The new behaviour is registered as an error and as a potential threat in the brain. Whilst the prefrontal cortex can override the more primitive emotional centre this takes a lot of energy and it soon becomes fatigued.
Unfortunately traditional change management approaches are not compatible with this new understanding of the brain’s functioning. Bonuses and incentives or threats of job loss will not overcome the biological reaction to change.
The way to get past the threat response is to help people to decide for themselves that the new approach is what they want.
One reason for this is that traditional change management relies on selling the change and, in the extreme, simply telling people to adopt the new behaviour. This approach creates warning messages in the prefrontal cortex. The way to get past the threat response is to help people to decide for themselves that the new approach is what they want.
At Head Heart +Brain we have been working with leaders in organisations to adopt a brain -savvy approach to change. This uses the findings of neuroscience and applies them to change.
We created the CORE model; it stands for Certainty, Options, Reputation and Equity. Neuroscience has found that these are the areas which are most likely create a threat or reward response in social situations, like work. The model helps leaders understand that a threat in any of these elements will impact people by creating sub-optimal brain functioning, poor motivation and resistance to change, just at the time employees need to be functioning at their maximum capacity. We have created tools so that leaders can analysis how their leadership style helps or hinders others to accept the change in each of the CORE elements, and if their style is creating threat adapting to a more brain-savvy approach. Using the CORE model and our tools helps leaders activate more reward responses in the brain and less threat responses. Thus helping people accept and work in the change environment.
So for change projects to succeed act on the neuroscientific understanding of change and the brain. |
Tuesday, March 11, 2014
Good Together Super Book Blast
GOOD TOGETHER
by CJ
Carmichael
~~~~~~~~~~~~~
BLURB:
Mattie,
the eldest of Marietta’s Carrigan girls, married rodeo cowboy, Wes Bishop,
right out of high school and raised twin daughters. A happy life, she thought,
but now that she’s in her late thirties and their daughters have left for
college, her husband has become strangely distant.
Then one night Wes
comes home late from a rodeo—with a stranger’s key in his pocket. He won’t
talk, but she knows something is wrong.
When her worst fears
are confirmed, the hits keep coming. It seems her husband is determined to
destroy everything she loves in this world. Thankfully she still has her
sisters, and her home on The Circle C Ranch. But more and more she thinks, not
of her roots in Marietta, but of her kind, dependable neighbour, Nat Diamond.
Over the years Nat has been a constant in her life, but only as a friend. Is it
possible the two of them could become more? But if Nat really does have
romantic feelings for her—as she suspects—why does he keep pulling away?
Is there something he
needs to tell her?
~~~~~~~~~~~~~
Excerpt
Three:
“Parents have to step back when their kids are grown. That’s
just how it is.”
He’d never talked like this before. “Our roles change,” she
agreed, talking slowly, trying to figure out who this man was. She’d always
felt that their parenting styles blended perfectly. But looking back now she
could see that Wes had connected better with the girls when they were younger.
Their adolescent stage had confused him. And maybe he’d pulled back more than
she realized. “But they still need us.”
“Portia and Wren haven’t needed me since I taught them to
drive.”
“Why are you being so literal? You know being part of a
family is more than doing jobs for one another. Family provides our emotional
bedrock. None of us ever grow out of the need to be loved.”
The implication of his words hit her with another ferocious
stab of pain.
He’d never stop loving their daughters.
But he had stopped loving her.
~~~~~~~~~~~~~
AUTHOR Bio and Links:
CJ
Carmichael has published over 35 novels and has twice been nominated for a RITA
award. She likes to write stories about romance, family and intrigue, usually
in small town or rural settings. When it’s time to take a break from the
computer, she heads to the Rocky Mountains near her home in Calgary where she
lives with her partner Michael and their cat, Penny. If you’d like to learn
more about her books, check out her website: http://cjcarmichael.com.
Knit something for someone special today!
This book had projects for everyone. From felting, to regular knitting and crochet, this book has many different styles to inspire you.
Gifted is based on the premise of small, quick gift items and I can think of no other book for some fast holiday knitting or crocheting. The Felted Heart Milagros project on the cover is one of my favorites! The instructions are easy to understand for an intermediate knitter such as myself.
The projects are arranged in two groups. Gifts for the Body focuses on wearable projects. There are scarves, earmuffs, hats and more. Gifts for the Soul has scissor sleeves,a pincushion and adorable crochet flowers.
If you are trying to learn a new technique, this book is for you. The projects are small and portable and work out quickly.
There are recipes from author Mags Kandis and great photographs to inspire you while you knit one of a kind gifts that are sure to delight someone special. |
Role of intermolecular interactions on the electronic and geometric structure of a large pi-conjugated molecule adsorbed on a metal surface.
The organic semiconductor molecule 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) exhibits two adsorption states on the Ag(111) surface: one in a metastable disordered phase, prepared at low temperatures, the other in the long-range ordered monolayer phase obtained at room temperature. Notably, the two states differ substantial in their vertical bonding distances, intramolecular distortions, and electronic structures. The difference is explained by intermolecular interactions, which are particularly relevant for the long-range ordered phase, and which hence require attention. |
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Combinatorial RNA interference indicates GLH-4 can compensate for GLH-1; these two P granule components are critical for fertility in C. elegans.
We report that four putative germline RNA helicases, GLHs, are components of the germline-specific P granules in Caenorhabditis elegans. GLH-3 and GLH-4, newly discovered, belong to a multi-gene glh family. Although GLHs are homologous to Drosophila VASA, a polar granule component necessary for oogenesis and embryonic pattern formation, the GLHs are distinguished by containing multiple CCHC zinc fingers. RNA-mediated interference (RNAi) reveals the GLHs are critical for oogenesis. By RNAi at 20 degrees C, when either loss of GLH-1 or GLH-4 alone has no effect, loss of both GLH-1 and GLH-4 results in 97% sterility in the glh-1/4(RNAi) offspring of injected hermaphrodites. glh-1/4(RNAi) germlines are under-proliferated and are without oocytes. glh-1/4(RNAi) animals produce sperm; however, spermatogenesis is delayed and the sperm are defective. P granules are still present in glh-1/4(RNAi) sterile worms as revealed with antibodies against the remaining GLH-2 and GLH-3 proteins, indicating the GLHs function independently in P granule assembly. These studies reveal that C.elegans can use GLH-1 or GLH-4 to promote germline development. |
When Big Ronnie and his son Brayden meet lone female tourist Janet on Big Ronnie’s Disco Walking Tour—the best and only disco walking tour in the city—a fight for Janet’s heart erupts between father and son, and the infamous Greasy Strangler is unleashed. With singularity of vision that could only exist in a post-Tim-and-Eric mediascape, first-time filmmaker Jim Hosking (with the support of the boundary-pushing SpectreVision) has concocted a complete and contained, triumphantly grotesque, idiosyncratic cinematic universe all his own. Proving there is indeed space on this planet for the endangered species that is the Trash Auteur, Hosking’s reverence for repetition, especially of the drippingly raunchy variety, doesn’t allow you a single moment to gaze away from the absurdity that is this sick, nihilistic, and oddly sweet, little world. |
As the partial shutdown of the federal government stands poised to enter its fourth week, many organizations are using their platforms to call for a resolution.
The shutdown becomes more painful today as many federal workers miss their first paycheck, and many are speaking out against having to work without pay, including tweets using the hashtag #ShutdownStory.
Federal workers and their supporters rallied for their jobs near the White House on Thursday as the partial government shutdown rolled through its third week with no end in sight.
Almost half of the 800,000 civilian federal employees are not working, and even those who are won’t be paid until the stalemate is settled. For most, the furlough becomes real Friday when they miss their first payday.
Hundreds of protesters marched near the White House on a sunny but cold and windy day with signs saying, “Let me work for the people,” “We want to work” and “Trump: End the shutdown.”
Some organizations have tried to talk about it officially, too:
USA Today continued:
The U.S. Coast Guard posted a tip sheet with a list of suggestions such as holding garage sales, baby-sitting or tutoring to make ends meet. One last option: declaring bankruptcy. The tip sheet was later removed from the agency’s website.
The union that represents the FBI wrote a letter, which read in part:
We, the undersigned, are proud FBI Special Agents. Today, we write in our capacity as the volunteer leadership and chapter representatives of the FBI Agents Association (“FBIAA”), a professional organization representing nearly all active duty Special Agents. FBIAA members elected us, and we represent all FBI field offices. We are the only dedicated voice for the nearly 13,000 active FBI Special Agents, the vast majority of whom are members of the FBIAA.
[…]The men and women of the FBI proudly serve this nation and are honored to protect our country and Constitution from all threats, foreign and domestic. We are confident that our leaders share this commitment to protecting our country and will find a path forward to fund the DOJ and the FBI. As those on the frontlines in the fight against criminals and terrorists, we urge expediency before financial insecurity compromises national security.
Airlines and airports have been compelled to respond, as the shutdown has led to TSA agent shortages.
Closing of the security checkpoint at Terminal G is set to begin at 1 p.m. Saturday, in what would be the 22nd day of a partial shutdown of the federal government. Federal screeners are calling in sick at double the normal rate for Miami, and TSA managers aren’t confident they will have enough workers to operate all 11 checkpoints at normal hours throughout the airport, said MIA spokesman Greg Chin.
“We felt we had to make a decision before the weekend,” Chin said. “They’re erring on the side of caution.”
“Without a fully functioning F.A.A., a layer of safety is missing,” said Mike Perrone, the national president of the Professional Aviation Safety Specialists, which represents safety inspectors who are furloughed.
At a rally outside the Capitol, where a crowd of air traffic controllers and other aviation workers gathered on a blustery afternoon to call for an end to the shutdown, Mr. Perrone warned of the risk of sidelining F.A.A. workers who could be inspecting planes and pilots.
[…]“Every day that goes by that the government is shut down, safety is going to be compromised,” Mr. Perrone said. “Every day that goes by, something could occur that causes a crack in the system.”
Airline spokespeople have promised to not let shortages disrupt service.
The Belleville News-Democrat continued:
Thursday night, a United spokeswoman issued a statement predicting passengers won’t be impacted by the logistical scramble.
“We will work to ensure we do everything we can for our customers, and we do not expect any operational impact,” the airline said.
Other companies, including craft beer breweries, are telling their customers how the government shutdown is affecting their business.
As of Dec. 21, the TTB had received 192,279 label applications since the start of 2018. That breaks down to over 3,000 applications coming in every week.
But since the government shut down, labels aren’t getting approved right now. That’s a problem for beermakers like Joe Katchever, owner and brewmaster of Pearl Street Brewery in La Crosse, Wis.
Pearl Street is celebrating its 20th anniversary in February, and Katchever’s team brewed something special for the big anniversary party. Called Deux Decadence (a nod to two decades), the stout has been aging in bourbon barrels from Kentucky for a year.
But Katchever can’t bottle the more than 500 cases of beer until his label gets approved by the bureau.
“We can still roll out the beer in draft form,” Katchever said. “We’re all hoping they figure out what they need to figure out and open the government back up.”
Associations that represent the big beer companies also voiced concerns.
NPR continued:
Craig Purser, president of the National Beer Wholesalers Association, said large alcohol companies and their distributors rely on the same services from TTB that craft producers use. “[It] doesn’t matter what the size of the company is; when nobody’s answering the phone, the work stops and it really puts the beer industry at a disadvantage,” Purser said.
Purser said breweries big and small worry that disadvantage could start to affect their bottom line if the government shutdown continues to keep them from bottling and selling their beers.
During the federal government shutdown, we will not monitor or update social media. Some NPS areas are accessible, however access may change without notice, and there are no NPS-provided services. For more information, visit the park’s website at https://t.co/OfxpwHOf5G
During a federal government shutdown, we will not monitor or update social media. Some Yellowstone areas are accessible: however, access may change without notice and there are no NPS-provided services. For more information go to https://t.co/5Msp3OK8Sa.
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Nancy and Chuck can end the shutdown anytime they want. The price is $5 billion added to border security. 1/3 of the 2 houses and the presidency doea not give Democrats a free pass from negotiating with the President. |
A Novel Role for RNA Methylation (m6A) in the DNA Damage Response
Every day our cells undergo substantial amounts of DNA damage from exogenous and endogenous sources. UV light, in particular, can cause an estimated 100,000 lesions per cell every day. Left unrepaired, these DNA lesions could lead to induction of senescence, cell death or mutations, which could be responsible for the development of cancer, neurodegeneration and several other diseases. However, our organisms have developed a mechanism to recognize the DNA damage caused by UV light and other damaging agents, in the DNA-damage response (DDR) pathway. This pathway is mediated by members of the phosphatidylinositol 3-kinase-related protein kinase (PIKK) family and members of the poly (ADP-ribose) polymerase (PARP) family, and allows the cells to recognize the DNA damage and facilitate recruitment and activation of DNA repair proteins.
RNA methylation specifically at position 6 of adenosine, 6-methyladenosine (m6A), is the most abundant internal modification in messenger RNA (mRNA), and is also present in transfer RNA (tRNA), ribosomal RNA (rRNA) and other non-coding RNAs. m6A has several roles in RNA metabolism, including regulating splicing, translation, and stability of mRNA.
Recently, Yang Xiang and colleagues have reported a novel role for RNA methylation (m6A) in the ultraviolet-induced DNA damage response. Here we’ll summarize how this RNA epigenetic mark serves as a signal in the DDR.
Post translational modifications often coordinate the DNA damage response early on, by allowing chromatin access and mediating recruitment of repair factors to DNA damage sites. Therefore, to investigate the modifications involved in the DNA damage response, this group screened for modifications localized to DNA damage sites in several cancer cell lines, including U2OS osteosarcoma, A375 melanoma, and HeLa cervical cancer cells.
They found that an antibody to m6A stained intensely at sites of UV-induced DNA damage. The induction of m6A was specific to UV irradiation, as other types of DNA damage did not induce accumulation of m6A. Treatment of cells with RNAse A abolished accumulation of m6A at damaged sites, indicating that RNA was the subject of methylation, and not DNA, and the signal derived mostly from Poly(A)+ transcripts.
Methyltransferase like-3 (METTL3) and METTL14 are two enzymatic components of the methyltransferase complex responsible for adenosine methylation (m6A). The researchers confirmed that the catalytic activity of METTL3 and METTL14 were necessary for m6A accumulation, which was rapidly detected just 2 minutes after UV irradiation. The m6A mark was transient and dissipated quickly suggesting demethylation shortly thereafter, which was shown to be catalyzed by the RNA demethylase FTO (fat mass and obesity-associated protein). In the UV-irradiated cells, PARP was necessary for m6A accumulation, indicating that PARP may mediate recruitment of METTL3 to damaged sites, with subsequent RNA methylation. The METTL3 knock-out cells had delayed removal of the DNA lesions and reduced survival, indicating that METTL3 and RNA methylation were important for repair of the lesions and cellular resistance.
Next they assessed which DNA polymerases could be acting downstream. They found that polymerase κ, an enzyme involved in several DNA repair pathways, co-localized with m6A at damaged sites and mediated the removal of cyclobutane pyrimidine dimers (CPDs), the principal lesions observed upon UV irradiation. METTL3 and METTL14 were necessary for pol κ localization to damaged sites, altogether suggesting that m6A may be important for recruitment of pol k to DNA damage sites and for pol κ-induced DNA repair.
The authors propose a DNA repair model in which upon UV irradiation, PARP mediates the accumulation of m6A at DNA damaged sites, possibly by recruiting METTL3, and m6A mediates the recruitment of pol κ, promoting DNA repair and cellular survival. Factors responsible for pol κ recruitment still need to be further elucidated, as direct binding of pol κ to m6A was not detected in this study. However, these findings suggest a novel role for RNA methylation as a signal mediating the recruitment of pol κ to UV-induced damage sites, thus facilitating DNA repair and cellular resistance to UV-induced DNA damage.
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Blanca Valle received her Ph.D. in Biochemistry from the University of Puerto Rico, Medical Sciences Campus. She completed postdoctoral training at NIH and Johns Hopkins University in Baltimore, where she studied cancer chemo-preventive agents and tumor progression using ovarian cancer cells and mouse models, and performed epigenetic studies to identify biomarkers in body fluids of ovarian and cervical cancer patients. Besides her passion for the cancer and epigenetic research fields, she also loves to dance, jog, and read.
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Tragedy: Lauren Patterson, 24, was murdered in Qatar in October last year
The mother of a British school teacher murdered in Qatar sobbed as her killer was sentenced to death by a court in Qatar today.
Lauren Patterson, 24, from Kent, was sexually assaulted and stabbed before her burnt remains were left smouldering in a remote desert location by a local 'casual acquaintance' in October last year.
Badr Hashim Khamis Abdallah al-Jabr and an accomplice maintained Miss Patterson's death was accidental, but were today found guilty of the brutal killing.
Miss Patterson's grief-stricken mother Alison was in court in Doha to hear the verdict and dropped her head into her hands and let out a brief sob upon hearing the sentence.
She was supported by more than a dozen friends and family in the courtroom.
Another man, Mohamed Abdallah Hassan Abdul Aziz, was jailed for three years for helping the killer to dispose of Miss Patterson's body by burning it, as well as damaging and getting rid of other evidence.
Both men were arrested after Miss Patterson's remains were found in a remote desert spot outside the Qatari capital city of Doha in October last year, shortly after she went missing after a night out.
Her mother said Al-Jabar's sentence meant ‘justice has been served’ for the killing of ‘my beautiful daughter’.
In a statement issued by the Foreign Office, she described Ms Patterson as ‘my closest friend and confidant’ who helped raise her siblings after the sudden death of her father.
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She said: ‘Nothing will ever bring my daughter back. As a family we will never be able to replace the times we were looking forward to: Lauren getting married, having children - all of those things and more have been taken away from us by these two individuals.
‘Even though this trial is now over, we will never forget Lauren, nor the horrific way she was murdered.
‘Because of the truly heinous and brutal way in which Badr Hashim Khamis Abdullah Al-Jabar and Muhammad Abdullah Hassan Abdul Aziz tried to dispose of Lauren's body, we were not able to say a final goodbye.
Unbearable loss: Alison Patterson, pictured with Lauren's uncle Brian Roke, was in court in Doha to hear the verdict and sobbed upon hearing the death sentence for her daughter's killer
'Excited to be back': Lauren Patterson, right, was clubbing with best friend Lea Monet, left, before she was killed. Two Qatari men are on trial and the prosecutor has called for one of them to be given the death penalty
‘This will be etched in my memory till
the day I die. Nothing will ever make the pain and grief that we have
all suffered go away. It is something none of us will forget. ‘
At a hearing earlier this year, Lea Monet
testified how she, Miss Patterson and the two men, who she said they were
'casually acquainted with', had left a nightclub at La Cigale Hotel in Doha
around 3.30am on October 12 last year.
She
said Miss Patterson, who had just returned from attending her
grandmother's funeral in England, was not drunk and was 'aware of her
surroundings'.
She said the men dropped her home with the promise they would also drop off her friend shortly afterwards at her house.
The Miss Monet told the court when she tried to call Miss Patterson the following morning her phone was off.
She said when she asked one of the two men about this, he said he could have dropped off Miss Patterson at the wrong building.
Miss Monet said the next day
she noticed he had a cut on his lower lip and it was swollen, which were
not there when she last saw him.
At the earlier hearing, the prosecutor said one of the defendants took Miss
Patterson to a residence he used for sexual trysts with women, 'conquered her
body', and killed her by stabbing her twice.
Link: Miss Patterson was identified by DNA which was matched to her mother Alison (right), a reflexologist
School: The 24-year-old was working as a teacher at The Newton International School in Doha for several months before she was killed
Favourite: Lauren enjoyed an evening at Club 7, pictured, before she was killed
He
said with the help of the second defendant, he put Miss Patterson's
body in the boot of his car and drove her out of the city of Doha to
Al-Kharrara, where they burned her remains.
He
said Miss Patterson, who worked at a primary school in Doha, had been
sexually assaulted but forensic tests could not prove this because the
remains were too badly burned.
He also petitioned the court for
monetary compensation, saying that Miss Patterson's mother had requested
20 million Qatar Riyal (approximately £3.6 million pounds) be paid by
the defendants - 15 million Qatar Riyal for the pain Miss Patterson must
have endured before her death, and five million Qatar Riyal for the
emotional damage felt by her mother.
Qatari
journalists say MIss Patterson's murder has drawn significant
international attention, and the trial has proceeded quickly through the
country's often slow court system.
The court was told this morning the death penalty would be carried out by either hanging or shooting.
However,
the death sentence has not actually been carried out in Qatar for more
than 10 years despite courts giving out such a punishment for crimes.
The two convicted men did not appear to show any emotion when the verdict and their sentences were announced in court.
They were led out out of court by guards immediately afterwards.
Outside court, Lauren's mum Alison walked along a line of supporters, many of whom were in tears, giving each one a hug.
She declined to comment to the media.
It is not yet known if the convicted men plan to appeal their sentences. |
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Hematuria and clinical findings as indications for intravenous pyelography in pediatric blunt renal trauma.
The essential aids in the evaluation of suspected blunt urinary tract injury are urinalysis and IVP. In 78 consecutive children who had IVPs because of trauma from January 1982 to March 1986, the following were evaluated: (1) the yield of IVP; (2) the correlations between IVP and hematuria, mechanism of injury, and associated clinical findings; and (3) the effect of IVP on patient management. Of the 26 children (33%) with abnormal IVP findings, 13 had congenital urinary tract anomalies only and 13 had urinary tract injuries (eight renal contusions, four renal lacerations with extravasation, and one bladder rupture). The number of RBCs per high-power field correlated with IVP evidence of injury (P less than .05). If only those patients with greater than or equal to 20 RBCs per high-power field had received IVPs, 42% of IVPs would have been avoided and no injuries or surgically correctable anomalies would have been overlooked. Urinary tract injury occurred significantly more often in patients with extremity fractures (P less than .05) and pelvic fractures (P less than .05). Mechanism of injury, admission to the hospital, and flank tenderness or hematoma were not associated with IVP evidence of trauma (P greater than .05), however. In four patients with trauma, results of IVP led to lengthened hospitalization or further diagnostic studies but did not result in surgery. Two patients in whom ureteropelvic junction obstruction was discovered incidentally had delayed corrective surgery.(ABSTRACT TRUNCATED AT 250 WORDS) |
Two celebrated Neil Gaiman (and Terry Pratchett) novels to get the adaptations they justly deserve
Neil Gaiman and Terry Pratchett stand with Dirk Maggs (centre) to confirm the good news.
It really has been a good few years for Neil Gaiman. From the enormously successful film adaptations of Stardust (2007) and Coraline (2009), to the acclaim received by his most recent novel The Ocean at the End of the Lane, to penning two now fan-favourite Doctor Who episodes (one of which, The Doctor’s Wife, was voted best Matt Smith era episode), the cult sci-fi/fantasy author must surely have one of the most enviable CVs in the literary industry. Last year saw his 1996 novel Neverwherebroadcast for radio, with James McAvoy, Natalie Dormer, and Benedict Cumberbatch among the dazzlingly distinguished cast; 2014, staggeringly, has seen the proposals for at least three more adaptations of his works.
While there has been little further word on the reported Sandmanand The Ocean at the End of the Lane films in development, Gaiman fans have two altogether more tangible reasons to start haemorrhaging with excitement, and those are: American Gods and Good Omens.
It’s true. Finally, more than ten and twenty years since their original publication dates; after several aborted film scripts and many more dashed hopes; after years of fan-hypothesised casts, and hundreds of works of fan art, and thousands of words of fan fiction written just to see more of those beloved characters beyond their limited canon, it is confirmed. American Gods and Good Omens, two obsessively adored and utterly inimitable classics, are coming soon to a television and radio near you.
To those who are unfamiliar, Good Omens, co-written by the likewise legendary Terry Pratchett, follows the demon Crowley and angel Aziraphale, to be voiced by Peter Serafinowicz and Mark Heap, who after several millennia of meddling in the affairs of mankind decide that they are rather fond of the world, and would rather Armageddon came another day, thank you very much. The only problem is, they seem to have misplaced the Antichrist, who has his own ideas. Good Omens is the kind of novel you pick up for its intriguing synopsis (the most accurate I’ve come across being ‘six billion people almost die, and it is funny’), and find yourself still reading in the bookshop an hour later, shop attendants casting pointed looks; it’s a book you’ll snort maniacally over in public places, and be so engrossed you won’t realise you’re making a sound; a book you’ll want all your friends to know about, but won’t lend because no one would return it; a book you’ll flick to a random page of to make you smile, and next thing you know it’s three in the morning and the words are swimming and wow, weren’t you going to be a productive member of society today? In short, it is hilarious, and touching, and disturbing, and you will reassess your whole universe with each subsequent reread (and there will be rereads. Many, many.) As with Neverwhere, the adaptation is to be directed by Dirk Maggs (of The Hitchhiker’s Guide to the Galaxy radio drama) with a voice cast including BBC Merlin’s Colin Morgan and Sherlock’s Louise Brealey, and is set to be released in time for Christmas on BBC Radio 4.
Thousands of fans (this writer included) have waited years for news of these adaptations.
American Gods, meanwhile, has been taken up for television by director and writer Bryan Fuller, of Hannibal and Pushing Daisies fame — and if you are at all familiar with these shows, you’ll know the book is in safe hands. Since the adaptation was first announced in July, subsequent interviews have resulted in increasingly fabulous headlines such as ‘A vagina will eat a man on your television screen’, ‘Bryan Fuller promises to keep “orgasm of death” scene’ and ‘Bryan Fuller: casting a white man to play Shadow [the novel’s protagonist, of non-white ethnicity] would make us TV’s biggest assholes’. In a novel that deals with the collected deities of multiple continents, from Egyptian to Norse to the ‘new’ gods of America (including the gods of media and the stock market), a director set on an appropriately racially diverse cast is most relieving to hear, with Fuller and co-writer Michael Green adamant on keeping true to the novel and its characters. The novel’s drama centres around a brewing war between the traditional ‘old’ gods of religion, and the increasingly powerful ‘new’ gods that reflect modern society’s loyalty to the likes of technology, the internet, and money. Protagonist Shadow Moon, an ex-con turned bodyguard to the mysterious Mr Wednesday, finds himself aiding this ancient deity as they gather forces in preparation for battle. While no casting decisions have been released of yet, Fuller revealed in a recent interview his desire to bring writer and actor Mark Gatiss in as Mr Ibis, one of the ancient Egypian gods. No doubt there will be further information on these eagerly-awaited decisions over the next few months as the show’s plans unfurl.
Believe me, no amount of work load is worth coming between you and these books. Consider your degree in one hand, and the emotional and intellectual ride of your life in the other, and reassess your life choices if you opt for the former. While there is some time before American Gods will be gracing — and no doubt traumatising — our TV screens, strangers to Good Omens have but until December to acquaint themselves with this paperbacked perfection, and must not waste a moment longer before acquiring a copy. I would lend you my own, but I fear I’d never get it back…
You can follow further progress on these adaptations by visiting Neil Gaiman and Terry Pratchett’s websites, and if you require any further (and perhaps less biased) opinions on the novels, have a look at the independent review site Good Reads’ pages for American Gods and Good Omens. |
This invention relates to sol-gel processes for making large sol-gel bodies. It is especially applicable to techniques for preparing optical fiber preforms prior to fiber draw.
A variety of methods have been suggested for the manufacture of high-silica content glass articles, such as the single and double dispersion processes described by D. W. Johnson, et al. in Fabrication Of Sintered High-Silica Glasses, U.S. Pat. No. 4,419,115, and the process described by D. W. Johnson, et al in Sintered High-Silica Glass And Articles Comprising Same, U.S. Pat. No. 4,605,428. Uses of high-silica content include the fabrication of glass rods for use as preforms in the manufacture of optical fibers as suggested by F. Kirkbir, et alii, U.S. Pat. No. 5,254,508 for a Sol-gel Process For Forming A Germania-doped Silica Glass Rod, and the fabrication of secondary cladding tubes for use during fabrication of an optical fiber by a solgel process. Although sol-gel processes enable fabrication of glass objects at lower cost than other processes, N. Matsuo, et alii, in U.S. Pat. No. 4,680,046 for a Method Of Preparing Preforms For Optical Fibers, among others, has noted that it is difficult to provide a glass article that is large enough to be used as a preform for optical fibers.
Considering that the functioning part of an optical fiber (the core and inner cladding carrying 99+% of the optical energy) typically consists of but 5% of the mass, a significant part of this effort has concerned structures providing for overcladding of such inner portion. State of the art manufacture often makes use of an inner portion constituting core and inner clad region as fabricated by Modified Chemical Vapor Deposition, or, alternatively, by soot deposition in Outside Vapor Deposition or Vapor Axial Deposition. This core rod may be overclad by material of less demanding properties, and, consequently, may be produced by less costly processing. Overcladding may entail direct deposition on the core rod, or may result from collapsing an encircling tube. Such xe2x80x9covercladdingxe2x80x9d tubes have been produced from soot or fused quartz. Making very large bodies of soot require extensive processing, and large bodies of fused quartz are expensive.
It has been recognized that significant economies may be realized by fabricating overcladding tubes by sol-gel techniques. This well-known procedure is described, for example, in J. Zarzycki, xe2x80x9cThe Gel-Glass Processxe2x80x9d, pp. 203-31 in Glass: Current Issues, A. F. Wright and J. Dupois, eds., Martinus Nijoff, Boston, Mass. (1985). Sol-gel techniques are regarded as potentially less costly than other known preform fabrication procedures. While sol-gel fabrication of overcladding tubes, and other optical glass components, has met with considerable success, improvements are continually sought.
A persistent problem in making very large sol-gel bodies, e.g. greater than 5 Kg, for state of the art optical fiber drawing is cracking of the gelled body. Cracking may occur during drying or handling of the gelled body prior to consolidation. See for example, T. Mori, et al, xe2x80x9cSilica Glass Tubes By New Sol-Gel Methodxe2x80x9d, J. Non-Crystalline Solids, 100, pp. 523-525 (1988), who describe the cracking problem, and recommend modification of the starting mixture and of the gel forming process, both of which are involved and expensive. The cracking problem is explained in a paper by Katagiri and Maekawa, J. Non-Crystalline Solids, 134, pp. 183-90, (1991) which states, xe2x80x9cOne of the most important problems in the sol-gel preparation method for monolithic gels is avoidance of crack formation which occurs during dryingxe2x80x9d. A 1992 paper published in the Journal of Material Science, vol. 27, pp. 520-526 (1992) is even more explicit: xe2x80x9cAlthough the sol-gel method is very attractive, many problems still exist, as pointed out in Zarzycki. Of these problems, the most serious one is thought to be the occurrence of cracks during drying of monolithic gelxe2x80x9d. The reference then reviews remedies, e.g. hypercritical drying procedures and use of chemical additives such as N,N dimethylformamide, collectively referred to as Drying Control Chemical Additives. Both methods are regarded as expensive and, therefore, undesirable in routine glass production. An extensive description of a suitable sol-gel process, and of additives useful for improving the strength of sol-gel bodies, is contained in U.S. Pat. No. 5,240,488, which is incorporated herein in its entirety.
The cracking problem becomes more severe as the size of preforms in commercial fiber production increases. State of the art optical fiber manufacture typically involves drawing hundreds of kilometers of fiber from a single preform. These preforms typically exceed 5 Kg in size. Although improvements in techniques for making large sol-gel bodies have been made, strength continues to be an issue and any process modification that results in improvement in the strength of intermediate products during the sol-gel process will constitute a valuable contribution to the technology.
We have developed a modified colloidal sol-gel process for making large sol-gel bodies of silica, and silica-containing, glasses. The modification takes advantage of a surprising discovery that the starting material in the sol-gel process, silica particulates, may be much larger than previously thought. We formulated sol-gel bodies using colloidal suspensions of silica particles in the size range defined by 5-25 m2 per gram. These particles are substantially larger than those typically recommended, i.e. 50 m2 per gram. Contrary to expectation, colloids formed with these large particles did not result in premature settling, as would have been expected.
Also contrary to expectation, wet sol bodies with very high solids loading, i.e. 65-78%, may be obtained using large particulate starting materials and proper processing. These large loading quantities are found to improve wet strength without impairing sol stability and rheology. Due to the large loading, shaped sol bodies in the xe2x80x9cgreenxe2x80x9d state more closely match the dimensions of the final desired form and thus allow for more complex shapes and greater dimensional control.
It was also found that particle morphology contributes significantly to the improved results. Particles with essentially spherical shapes are necessary for the results obtained. Conventional silica particle mixtures contain both spherical and non-spherical particles, the latter in quantities of 30% or more. We have achieved the improved results reported here using particle mixtures with less than 15% and preferably less than 10% non-spherical.
Sol-gel bodies formulated using these starting colloids result in strength improvements of 100%, and in some cases, 300%. The enhanced strength as well as higher loading allows faster drying of the sol, thus reducing overall processing time. The reduced surface area per gram also allows additives to be included in smaller amounts. This lowers the cost of materials and also decreases the process time required for burn-off of additives. These processing efficiencies translate into lower production cost, especially for very large bodies. |
Well, the day has come and gone. Conservative commentator Ben Shapiro delivered his speech at Berkeley after doling out thousands of dollars in security fees, which has been viewed as a mechanism from which liberal institutions can silence conservatives from speaking. Who has $15K lying around? That was the rough estimate of the bill Shapiro paid to just give a speech in the belly of the liberal beast.
The school has recently been at the center of free speech controversy, especially when progressive thugs rioted after shutting down a speaking engagement by Milo Yiannopoulos in February. Shapiro did thank the UC Berkeley administration, despite the hurdles, for allowing him to speak and, as he said, unshackling the police so that a repeat of what had occurred on campus doesn’t happen again. Shapiro also noted the oddity of having to spend this much money and have this much controversy surrounding this speech when he said the exact same thing in 2016. The exceptions being there were only a couple of security guards and zero controversy. Shapiro’s event, called “campus thuggery,” wasted no time going after the stupidity of progressives, specifically Antifa, who tried to shut his lecture down. The speech began at 10 p.m. EST, 7 p.m. PST. It was slated to be a two-hour event. It's featured below (via The Hill):
"Thanks to antifa and the supposed anti-fascist brigade for exposing what the radical left truly is," Shapiro said in his speech, referring to anti-fascist or "antifa" activists. "All of America is watching because you guys are so stupid. It's horrifying, I am grateful, and you can all go to hell, you pathetic, lying, stupid jackasses," he said. […] These are the folks that stand between civilization and lawlessness," Shapiro said of the police, saying they are "the only people who are standing between those ATMs and the antifa are the police, and all they get is from the left is a bunch of crap."
He also played on the Left’s antics regarding lobbying accusations of white supremacy on him, in which he pointed to his yarmulke, noting that the alt-right doesn’t like him either. Yet, in the context of leftist attacks, if you disagree with them on anything, you’re racist, a white supremacist, a Nazi, or a fascist. Therefore, you deserve to be beaten up. It’s part of the insane notion that speech can be violent.
Here is a map of the cordoned off buildings for the @benshapiro talk at @UCBerkeley pic.twitter.com/mOh4H18ney — Frances Dinkelspiel (@Frannydink) September 14, 2017
Blessedly, this event saw no fires or riots. Four people were arrested for carrying weapons. One of the methods of crowd control that was permitted by police was the use of pepper spray, which apparently was banned back in 1997. The city itself doled out $600,000 to ensure law and order was maintained. Parts of campus were cordoned off with concrete barricades (via LA Times):
Hundreds of protesters swarmed UC Berkeley on Thursday evening as conservative writer Ben Shapiro spoke on campus, with law enforcement out in force to prevent a repeat of recent violent clashes between far-left and far-right agitators. At least four people were arrested for carrying banned weapons. One was also held on suspicion of battery on a police officer. Hundreds of law enforcement officers, many in riot gear, prepared for violence and seized potential weapons. But as of 10 p.m., no major skirmishes had been reported. Several shouting matches erupted but ended peacefully. A campus spokesman said there is a “sense of relief” that the preparations worked and Shapiro’s speech went smoothly. The intense security for the evening came with a $600,000 price tag, and involved shutting down and clearing out large swaths of the campus. Days earlier, Berkeley Police Chief Andrew Greenwood successfully lobbied the City Council to adjust a 1997 ban on the use of pepper spray as a crowd-control technique. Officers Thursday were free to use pepper spray on individual protesters deemed violent.
The Mercury News also added that this was a test run for the school, which did not want a repeat of the chaos that has engulfed the city in recent months:
This event is a test run for the campus. Later in the month, from Sept. 24 to Sept. 27, a number of controversial speakers, including Milo Yiannopoulos and former White House chief strategist Steve Bannon, are expected to descend on campus for what the student group Berkeley Patriot is dubbing a “Free Speech Week.” When Yiannopoulos last tried to speak on campus in February, demonstrators turned violent, smashing windows and throwing objects, and the school canceled the event. Conservative student groups, backed by national conservative organizations, accused the school of limiting conservative free speech and even filed a lawsuit against the university alleging as much. Former Chancellor Nicholas Dirks was criticized for his handling of the situation, and new Chancellor Carol Christ has made a point of pledging to support free speech this year. Earlier this month, she hosted a faculty forum on the topic, with both liberal and conservative faculty weighing in on how the school should handle such events.
One last note, God bless the Young America’s Foundation and all that they do to protect free speech, give conservative students a place to voice their views and engage in activism, and add some conservative flavor to the putrid rot of progressivism that’s infested America’s colleges. Well done, YAF. Keep fighting. |
Timecracker Cosmos
Timecracker Cosmos
Timecracker Cosmos
Description: You must see this clock to believe it. On the hour, this clock's face that features planet Earth splits in two to reveal even more splendor beneath. Add to this harmony - a renowned sound system of 30 melodies, and you too will experience the peace and tranquility of Timecracker Cosmos. Clock is battery quartz operated, has a auto night shut-off, demonstration button, volume control, and on/off switch.
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#ifndef _STR_LIST_SET_H
#define _STR_LIST_SET_H
#include <event.h>
#include <simplehttp/uthash.h>
struct SetItem {
const char *value;
UT_hash_handle hh;
};
struct ListInfo {
char sep;
char sepstr[2];
char *saveptr;
char **buf;
size_t buflen;
};
void prepare_token_list(struct ListInfo *list_info, char **db_data, size_t db_data_len, char sep);
char *reverse_tokenize(struct ListInfo *list_info);
void reserialize_list(struct evbuffer *output, struct json_object *array, char **db_data, size_t db_data_len, char sep);
void deserialize_alloc_set(struct SetItem **set, char **db_data, size_t db_data_len, char sep);
void serialize_free_set(struct evbuffer *output, struct json_object *array, struct SetItem **set, char sep);
static inline void serialize_list_item(struct evbuffer *output, const char *item, char sep)
{
if (EVBUFFER_LENGTH(output) > 0) {
evbuffer_add_printf(output, "%c", sep);
}
evbuffer_add_printf(output, "%s", item);
}
static inline void add_new_set_item(struct SetItem **set, const char *value_ptr)
{
struct SetItem *set_item;
set_item = calloc(1, sizeof(struct SetItem));
set_item->value = value_ptr;
HASH_ADD_KEYPTR(hh, *set, value_ptr, strlen(value_ptr), set_item);
}
#define TOKEN_LIST_FOREACH(item, list_info) \
for (item = strtok_r(*(list_info)->buf, \
(list_info)->sepstr, \
&(list_info)->saveptr); \
item != NULL; \
item = strtok_r(NULL, \
(list_info)->sepstr, \
&(list_info)->saveptr) )\
#define TOKEN_LIST_FOREACH_REVERSE(item, list_info) \
while ((item = reverse_tokenize(list_info)) != NULL) \
#endif
|
Two pills are better than one: Israeli Prof. Ada Yonath and her researchers have discovered that a combination of two antibiotics can fight antibiotic resistant diseases.
Researchers from Israel and the US have discovered that two marginally useful antibiotics working together could be more effective in fighting off today’s deadly antibiotic-resistant superbugs than either drug working alone.
In Israel, the researchers were led by Prof. Ada Yonath, who won the Nobel Prize in Chemistry in 2009 for her pioneering work in ribosome crystallography. They found that when used together, the two antibiotics lankacidin and lankamycin (which are produced naturally by the microbe streptomyces) are much more successful in inhibiting growth of pathogens such as MRSA (methicillin-resistant Staphylococcus aureus), a dangerous staph infection that is resistant to certain antibiotics.
MRSA was discovered in the UK in 1961, and made its first major appearance in the US 20 years later, sounding alarm bells throughout the medical community. The infection was soon labeled a superbug because of its resistance to traditional antibiotic treatment.
In 2007, a report by the Centers for Disease Control and Prevention (CDC), estimated that the number of MRSA infections in US hospitals had doubled since 1999. In another report later that year the CDC estimated that 95,000 people in the US had suffered an MRSA infection that year alone, and that the infections were responsible for more deaths in the US than AIDS.
Epidemic proportions
Especially common in hospitals, the deadly infection is nearing epidemic proportions. Patients with open wounds or weakened immune systems are considered to be at greater risk of infection than the general public.
Antibiotics work in two ways. Some stave off an infection by preventing the ribosome – the protein-synethizing factories of the cell – from assembling proteins, while others bind in a tunnel through the ribosome body and block the passage of newly made proteins.
Under the leadership of Yonath, the Israeli researchers from the Weizmann Institute of Science in Rehovot used X-ray crystallography, which determines the arrangement of atoms in biological molecules, to discover the exact binding site of lankacidin in the ribosome.
The scientists in the US, led by Alexander Mankin, professor and associate director of the Center for Pharmaceutical Biotechnology at the University of Illinois, Chicago, then showed that lankacidin prevents the ribosome from assembling new proteins.
When the researchers realized that streptomyces also manufacture lankamycin, they became curious as to whether the two drugs might help each other. Biochemical analysis and molecular modeling showed that lankamycin binds in the ribosomal tunnel right next to lankacidin.
Combining drugs for better treatment
“What we found most amazing is that the two antibiotics appeared to help each other in stopping pathogens from making new proteins and in inhibiting bacterial growth,” says Mankin.
With the increase of new superbugs like MRSA, many drug companies are seeking ways to improve existing drugs. The researchers believe the study suggests that drug companies should start exploring how combinations of drugs work together.
It is a “much better strategy not to improve individual drugs, but the combinations of drugs that can act together,” Mankin explains.
The research results were published in the online edition of the Proceedings of the National Academy of Sciences of the USA in January.
Yonath, the director of the Center for Biomolecular Structure and Assembly at the Weizmann Institute, has revealed the modes of action of over 20 different antibiotics that target bacterial ribosomes. Through this work she has been able to identify how bacteria become resistant to antibiotics and has helped lay the groundwork for scientists to start developing new bacteria-resistant antibiotics that better target the ribosomes of pathogens to avoid the problem of resistance.
Related Articles
About Nicky Blackburn
Editor and Israel Director,
Nicky Blackburn has worked extensively as a journalist and editor both in Britain and Israel for a range of national and international publications including The Cambridge Evening News, London News, Travel Weekly, Israel High Tech Investor, and The Times of London.
She was the Associate Editor at LINK Israel’s Business and Technology Magazine, and the High-Tech Correspondent for The Jerusalem Post. |
1. Technical Field
This invention relates generally to memory devices, and more particularly, to a memory device with improved switching speed and data retention.
2. Background Art
The volume, use and complexity of computers and electronic devices are continually increasing. Computers consistently become more powerful, new and improved electronic devices are continually developed (e.g., digital audio players, video players). Additionally, the growth and use of digital media (e.g., digital audio, video, images, and the like) have further pushed development of these devices. Such growth and development has vastly increased the amount of information desired/required to be stored and maintained for computer and electronic devices.
Generally, information is stored and maintained in one or more of a number of types of storage devices. Storage devices include long term storage mediums such as, for example, hard disk drives, compact disk drives and corresponding media, digital video disk (DVD) drives, and the like. The long term storage mediums typically store larger amounts of information at a lower cost, but are slower than other types of storage devices. Storage devices also include memory devices, which are often, but not always, short term storage mediums. Memory devices tend to be substantially faster than long term storage mediums. Such memory devices include, for example, dynamic random access memory (DRAM), static random access memory (SRAM), double data rate memory (DDR), flash memory, read only memory (ROM), and the like. Memory devices are subdivided into volatile and non-volatile types. Volatile memory devices generally lose their information if they lose power and typically require periodic refresh cycles to maintain their information. Volatile memory devices include, for example, random access memory (RAM), DRAM, SRAM and the like. Non-volatile memory devices maintain their information whether or not power is maintained to the devices. Non-volatile memory devices include, but are not limited to, ROM, programmable read only memory (PROM), erasable programmable read only memory (EPROM), flash memory and the like. Volatile memory devices generally provide faster operation at a lower cost as compared to non-volatile memory devices.
Memory devices generally include arrays of memory devices. Each memory device can be accessed or “read”, “written”, and “erased” with information. The memory devices maintain information in an “off” or an “on” state, also referred to as “0” and “1”. Typically, a memory device is addressed to retrieve a specified number of byte(s) (e.g. 8 memory devices per byte). For volatile memory devices, the memory devices must be periodically “refreshed” in order to maintain their state. Such memory devices are usually fabricated from semiconductor devices that perform these various functions and are capable of switching and maintaining the two states. The devices are often fabricated with inorganic solid state technology, such as, crystalline silicon devices. A common semiconductor device employed in memory devices is the metal oxide semiconductor field effect transistor (MOSFET).
The use of portable computer and electronic devices has greatly increased demand for non-volatile memory devices. Digital cameras, digital audio players, personal digital assistants, and the like generally seek to employ large capacity non-volatile memory devices (e.g., flash memory, smart media, compact flash, and the like).
Because of the increasing demand for information storage, memory device developers and manufacturers are constantly attempting to increase storage capacity for memory devices (e.g., increase storage per die or chip). A postage-stamp-sized piece of silicon may contain tens of millions of transistors, each transistor as small as a few hundred nanometers. However, silicon-based devices are approaching their fundamental physical size limits. Inorganic solid state devices are generally encumbered with a complex architecture which leads to high cost and a loss of data storage density. The volatile semiconductor memories based on inorganic semiconductor material must constantly be supplied with electric current with a resulting heating and high electric power consumption in order to maintain stored information. Non-volatile semiconductor devices have a reduced data rate and relatively high power consumption and large degree of complexity. Typically, fabrication processes for such cells are also not reliable.
Therefore, there is a need to overcome the aforementioned deficiencies.
FIG. 1 illustrates a type of memory device 30 which includes advantageous characteristics for meeting these needs. The memory device 30 includes a Cu electrode 32, a copper sulfide passive layer 34 on the electrode 32, an active layer 36 such as Cu2O or various polymers on the layer 34, and a Ti electrode 38 on the active layer 36. Initially, assuming that the memory device 30 is unprogrammed, in order to program the memory device 30, an increasingly negative voltage is applied to the electrode 38, while the electrode 32 is held at ground, so that an increasing electrical potential is applied across the memory device 30 from a higher to a lower potential in the direction from electrode 32 to electrode 38, until electrical potential Vpg (the “programming” electrical potential) is reached (see FIG. 2, a plot of memory device current vs. electrical potential applied across the memory device 30). This potential Vpg is sufficient to cause copper ions to be attracted from the superionic layer 34 toward the electrode 38 and into the active layer 36, causing the active layer 36 (and the overall memory device 30) to switch to a low-resistance or conductive state (A). Upon removal of such potential (B), the copper ions drawn into the active layer 36 during the programming step remain therein, so that the active layer 36 (and memory device 30) remain in a conductive or low-resistance state, as indicated by the resistance characteristic (B).
In order to erase the memory device (FIG. 2), an increasingly positive voltage is applied to the electrode 38, while the electrode 32 is held at ground, so that an increasing electrical potential is applied until electrical potential Ver (the “erase” electrical potential) is applied across the memory device 30 from a higher to a lower electrical potential in the reverse direction. This potential Ver is sufficient to cause copper ions to be repelled from the active layer 36 toward the electrode 32 and into the superionic layer 34, in turn causing the active layer 36 (and the overall memory device 30) to be in a high-resistance or substantially non-conductive state. This state remains upon removal of such potential from the memory device 30.
FIG. 2 also illustrates the read step of the memory device 30 in its programmed (conductive) state and in its erased (nonconductive) state. An electrical potential Vr (the “read” electrical potential) is applied across the memory device 30 from a higher to a lower electrical potential in the same direction as the electrical potential Vpg. This electrical potential is less than the electrical potential Vpg applied across the memory device 30 for programming (see above). In this situation, if the memory device 30 is programmed, the memory device 30 will readily conduct current (level L1), indicating that the memory device 30 is in its programmed state. If the memory device 30 is erased, the memory device 30 will not conduct current (level L2), indicating that the memory device 30 is in its erased state.
Upon application of the electrical potential Vpg to switch the memory device 32 from an erased state to a low-resistance or conductive state (low-resistance state indicated by the on-resistance line B), the current vs. voltage path A in this environment includes two identifiable connected portions, a first, or initial (in time) portion A1 and a second, or later (in time) portion A2. Typically, upon the programming voltage Vpg being applied to the memory device 30, an initial rapid movement of ions into the active layer 34 takes place (A1), followed by a slower transfer of ions thereinto (A2). Thus, it has been found that the first portion A1 of the switching operation takes place relatively rapidly (i.e., consumes relatively little time), while on the other hand, the second portion A2 of the switching operation takes place relatively slowly (i.e., consumes appreciably more time). It will be understood that high switching speed is desirable, and that this second, slower portion slows down the pace of the switching operation, i.e., causes the overall switching operation to take more time than is desirable.
Therefore, what is needed is an approach which decreases switching operation time in the present environment. |
89/416934.
2084670
What is the common denominator of -33/6097 and 46/9919?
664573
What is the smallest common multiple of 1301544 and 4989252?
29935512
Calculate the smallest common multiple of 404 and 7789524.
7789524
What is the common denominator of 28/3 and 91/116575545?
116575545
What is the smallest common multiple of 238660 and 4415210?
8830420
Calculate the least common multiple of 1916616 and 1586.
116913576
What is the common denominator of -109/560 and 69/3241616?
16208080
What is the common denominator of -103/5755782 and 37/3?
5755782
Calculate the smallest common multiple of 408171 and 39.
5306223
What is the common denominator of 79/314526 and -47/5456?
27678288
Calculate the smallest common multiple of 1800 and 8275590.
165511800
What is the lowest common multiple of 1020601 and 3081?
39803439
What is the least common multiple of 24400992 and 66020?
122004960
Calculate the least common multiple of 127371312 and 1116.
127371312
What is the smallest common multiple of 152558980 and 22?
1678148780
What is the least common multiple of 8770 and 2452969?
24529690
Calculate the smallest common multiple of 59646490 and 15018.
178939470
Calculate the smallest common multiple of 2856168 and 2856168.
2856168
Calculate the lowest common multiple of 18 and 47775430.
429978870
What is the common denominator of 119/45372 and -85/33882?
256215684
What is the common denominator of -38/1641093 and 7/14769837?
14769837
Calculate the common denominator of 181/2604 and 32/22077.
19162836
What is the common denominator of -79/123296 and -27/254?
15658592
What is the common denominator of -73/288 and -55/260976?
1565856
Calculate the lowest common multiple of 61876 and 680.
10518920
Calculate the lowest common multiple of 1984 and 4459200.
138235200
What is the least common multiple of 2020452 and 12627825?
50511300
Calculate the smallest common multiple of 145044270 and 63.
145044270
What is the smallest common multiple of 260 and 49586758?
495867580
What is the least common multiple of 45595 and 159940?
132590260
Calculate the lowest common multiple of 2847208 and 187728.
17083248
What is the lowest common multiple of 23256 and 829464?
2488392
What is the common denominator of -91/64160 and 71/1640090?
26241440
Calculate the common denominator of -31/377 and -25/156032.
58824064
Find the common denominator of 13/16971480 and -28/51.
288515160
Find the common denominator of 37/12 and -25/29941012.
89823036
Find the common denominator of -49/47280 and 45/13396.
803760
Find the common denominator of 16/18151 and -89/68009204.
476064428
Find the common denominator of -11/5049108 and -41/3927084.
35343756
Find the common denominator of -17/1123008 and -41/24.
1123008
What is the smallest common multiple of 13185352 and 138446196?
276892392
Calculate the smallest common multiple of 38096 and 2180996.
8723984
Calculate the common denominator of 71/12188 and -73/205162.
1250257228
Calculate the common denominator of 31/418476 and -69/2494.
12135804
Find the common denominator of -28/1806097 and -65/637446.
10836582
What is the least common multiple of 90965388 and 33744?
363861552
Calculate the common denominator of 93/1355804 and -29/324214.
14913844
Calculate the lowest common multiple of 12946010 and 1012.
25892020
Calculate the common denominator of 71/22794 and -73/564.
2142636
What is the smallest common multiple of 91609 and 101108?
57530452
What is the smallest common multiple of 2246896 and 128?
17975168
Calculate the common denominator of 71/147000 and -93/53704.
20139000
Find the common denominator of -119/2592 and 151/1464048.
8784288
What is the lowest common multiple of 18085773 and 2703?
18085773
What is the least common multiple of 310481766 and 266127228?
1862890596
Calculate the common denominator of -33/10748410 and -87/20.
21496820
What is the least common multiple of 31176 and 31542318?
126169272
Calculate the common denominator of -64/36207 and 179/3240.
1448280
Find the common denominator of 53/405 and -113/159462.
2391930
What is the lowest common multiple of 4248 and 48528090?
194112360
Find the common denominator of -103/4576202 and 13/584196.
27457212
What is the smallest common multiple of 276 and 242170082?
1453020492
What is the common denominator of -91/1062435 and 46/293865?
13811655
Calculate the lowest common multiple of 18900470 and 11340282.
56701410
Calculate the common denominator of 42/23 and -29/1067398.
24550154
What is the least common multiple of 6019038 and 9?
6019038
What is the least common multiple of 48 and 125935758?
1007486064
Calculate the lowest common multiple of 100848 and 4170.
70089360
What is the least common multiple of 47875 and 350?
670250
Calculate the common denominator of -89/34515 and 98/2925.
172575
What is the common denominator of -47/583439110 and 89/270570?
1750317330
Find the common denominator of -22/6651991 and -5/86475883.
86475883
What is the smallest common multiple of 1745568 and 526176?
109970784
Calculate the smallest common multiple of 222332 and 6138.
2000988
What is the lowest common multiple of 3070 and 1531440?
470152080
What is the least common multiple of 12 and 557957756?
1673873268
What is the common denominator of 179/10920 and -107/1310400?
1310400
What is the lowest common multiple of 30258 and 2952?
121032
What is the lowest common multiple of 3965775 and 286235?
519516525
What is the common denominator of -1/11009866 and 59/49?
77069062
What is the smallest common multiple of 2351010 and 16457070?
16457070
What is the common denominator of -107/138 and -107/882?
20286
Calculate the lowest common multiple of 30105308 and 1552.
120421232
What is the smallest common multiple of 85002372 and 8657649?
935026092
What is the lowest common multiple of 767475 and 682200?
6139800
Find the common denominator of 62/2782821 and -94/156723.
331155699
Calculate the least common multiple of 152005 and 121260.
85730820
Calculate the smallest common multiple of 20129869 and 8.
161038952
Calculate the common denominator of 77/30 and 83/1715703.
17157030
What is the smallest common multiple of 42240 and 864?
380160
Find the common denominator of 3/2912168 and 113/170240.
465946880
Calculate the lowest common multiple of 910 and 23210278.
116051390
Calculate the smallest common multiple of 56044 and 22529688.
22529688
What is the least common multiple of 5815061 and 287904?
558245856
Calculate the smallest common multiple of 1481087 and 1911080.
59243480
What is the common denominator of -73/2257080 and 9/37618?
2257080
What is the common denominator of -19/223808 and 19/4432?
61994816
Find the common denominator of 59/24400 and -149/120048.
3001200
Calculate the least common multiple of 10540972 and 564.
31622916
What is the common denominator of -13/85 and 167/1999746?
169978410
Find the common denominator of 67/189560 and 53/980.
1326920
Calculate the smallest common multiple of 8120872 and 53.
8120872
What is the smallest common multiple of 2590128 and 359740?
12950640
What is the smallest common multiple of 3860 and 90795692?
453978460
Calculate the lowest common multiple of 25338272 and 368.
25338272
What is the common denominator of -61/169470 and -91/1803645?
25251030
What is the common denominator of 79/1140258 and -49/663?
14823354
What is the common denominator of -45 and -70/10435521?
10435521
Find the common denominator of -83/44330220 and -22/255.
44330220
Calculate the lowest common multiple of 18 and 12709677.
76258062
Calculate the common denominator of 71/578984 and 101/98.
578984
Find the common denominator of -21/174260 and 57/1237246.
12372460
Calculate the common denominator of 73/41600 and 27/363520.
23628800
Calculate the lowest common multiple of 1257 and 8657797.
25973391
Calculate the least common multiple of 11910910 and 18430566.
1750903770
Calculate the smallest common multiple of 5791172 and 124.
5791172
What is the least common multiple of 6 and 19911183?
39822366
Calculate the smallest common multiple of 59966208 and 768.
59966208
What is the smallest common multiple of 341 and 62395932?
686355252
What is the smallest common multiple of 312657304 and 16?
625314608
Calculate the common denominator of -69/232 and 32/24049207.
192393656
What is the co |
Welcome screen + Null state CTAs. Our first principle was giving developers space to own the experience. Think of the message thread as your app. We're giving you the real estate and the tools to customize your experience. This starts with the welcome screen. People discover our featured bots and enter the conversation. Then, they see your brand, your Messenger greeting, and a call to action to “Get Started”.
There are lots of free chatbot building tools such as the one I run that offer the ability to setup a bot and connect it to facebook. You won’t require any coding knowledge, and you can sign up using your Facebook account. Once you’ve set up a free account you can start creating your chatbot. Make sure you keep these tips in mind when building your bot:
Streamchat is one of the most basic chatbot tools out there. It’s meant to be used for simple automations and autoresponders, like out-of-office replies or “We’ll get back to you as soon as we can!” messages, rather than for managing a broader workflow. It’s quick to implement and easy to start with if you’re just dipping your toes into the chatbot waters.
However, as irresistible as this story was to news outlets, Facebook’s engineers didn’t pull the plug on the experiment out of fear the bots were somehow secretly colluding to usurp their meatbag overlords and usher in a new age of machine dominance. They ended the experiment due to the fact that, once the bots had deviated far enough from acceptable English language parameters, the data gleaned by the conversational aspects of the test was of limited value.
The process of building, testing and deploying chatbots can be done on cloud-based chatbot development platforms[49] offered by cloud Platform as a Service (PaaS) providers such as Oracle Cloud Platform [50][30] and IBM Watson.[51][52][53] These cloud platforms provide Natural Language Processing, Artificial Intelligence and Mobile Backend as a Service for chatbot development.
Chatbots talk in almost every major language. Their language (Natural Language Processing, NLP) skills vary from extremely poor to very clever intelligent, helpful and funny. The same counts for their graphic design, sometimes it feels like a cartoonish character drawn by a child, and on the other hand there are photo-realistic 3D animated characters available, which are hard to distinguish from humans. And they are all referred to as ‘chatbots’. If you have a look at our chatbot gallery, you will immediately notice the difference.
However, as irresistible as this story was to news outlets, Facebook’s engineers didn’t pull the plug on the experiment out of fear the bots were somehow secretly colluding to usurp their meatbag overlords and usher in a new age of machine dominance. They ended the experiment due to the fact that, once the bots had deviated far enough from acceptable English language parameters, the data gleaned by the conversational aspects of the test was of limited value.
One of the key advantages of Roof Ai is that it allows real-estate agents to respond to user queries immediately, regardless of whether a customer service rep or sales agent is available to help. This can have a dramatic impact on conversion rates. It also eliminates potential leads slipping through an agent’s fingers due to missing a Facebook message or failing to respond quickly enough.
A toolkit can be integral to getting started in building chatbots, so insert, BotKit. It gives a helping hand to developers making bots for Facebook Messenger, Slack, Twilio, and more. This BotKit can be used to create clever, conversational applications which map out the way that real humans speak. This essential detail differentiates from some of its other chatbot toolkit counterparts.
In the early 90’s, the Turing test, which allows determining the possibility of thinking by computers, was developed. It consists in the following. A person talks to both the person and the computer. The goal is to find out who his interlocutor is — a person or a machine. This test is carried out in our days and many conversational programs have coped with it successfully.
The first formal instantiation of a Turing Test for machine intelligence is a Loebner Prize and has been organized since 1991. In a typical setup, there are three areas: the computer area with typically 3-5 computers, each running a stand-alone version (i.e. not connected with the internet) of the participating chatbot, an area for the human judges, typically four persons, and another area for the ‘confederates’, typically 3-5 voluntary humans, dependent on the number of chatbot participants. The human judges, working on their own terminal separated from one another, engage in a conversation with a human or a computer through the terminal, not knowing whether they are connected to a computer or a human. Then, they simply start to interact. The organizing committee requires that conversations are restricted to a single topic. The task for the human judges is to recognize chatbot responses and distinguish them from conversations with humans. If the judges cannot reliably distinguish the chatbot from the human, the chatbot is said to have passed the test.
At Facebook’s F8 Developers Conference, Messenger Bots were announced. These bots are being developed by media corporations and retailers alike and very quickly so which raises the question as to what a Messenger bot is and how it’s useful to so many different types of companies. Even more important to know is what these bots mean for the average user, whether or not they will always be safe or can they present a potential threat if they are developed by anyone with malicious intent. Here’s a the answer to all that and more. |
---
abstract: 'The Euler-Poisson equations model rotating gaseous stars. Numerous efforts have been made to establish existence and properties of the rotating star solutions. Recent interests in extrasolar planet structures require extension of the model to include a inner rocky core together with its own gravitational potential. In this paper, we discuss various extensions of the classical rotating star results to incorporate a solid core.'
address: 'Department of Mathematics, University of Michigan, Ann Arbor, MI 48109'
author:
- Yilun Wu
bibliography:
- 'biblio.bib'
title: 'Existence of rotating planet solutions to the Euler-Poisson equations with an inner hard core'
---
Introduction
============
The motion of a rotating Newtonian gaseous star is described by the following compressible Euler-Poisson equations: $$\label{intro: eq: Euler-Poisson system primal}
\begin{cases}
\rho_t + \nabla\cdot(\rho\mathbf{v}) = 0 \\
(\rho\mathbf{v})_t + \nabla\cdot(\rho\mathbf{v}\otimes\mathbf{v}) + \nabla p = -\rho\nabla\phi\\
\Delta \phi = 4\pi \rho
\end{cases}$$ Here $\rho$, $p$, $\phi$ and $\mathbf{v}$ are respectively density, pressure, gravitational potential and velocity vector field of the gas comprising a star. The solution to the Poisson equation is not unique. One picks the decaying solution at infinity $$-\phi = B\rho = \rho * \frac{1}{|\mathbf{x}|} = \int \frac{\rho(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}~d\mathbf{y}$$ according to Newton’s law of gravitation, where $*$ defines a convolution. In order to model a rotating star in dynamical equilibrium, one further makes the assumptions that the solution is axisymmetric and time independent. Under these assumptions the first equation in is indentically satisfied, whereas the second equation is reduced to $$\label{intro: eq: vector rotating star}
\frac{\nabla p}{\rho} = -\nabla \phi + r\Omega^2 \mathbf{e}_r.$$ Here we are assuming that the velocity vector field $\mathbf{v}$ is given by $\mathbf{v}=r\Omega(r)\mathbf{e}_{\theta}$, where the cylindrical coordinates $(r,\theta,z)$ and orthogonal frame field $\{\mathbf{e}_r, \mathbf{e}_{\theta}, \mathbf{e}_z\}$ are used. To close the system one imposes an equation of state $p=p(\rho)$, sets up the velocity field $\mathbf{v}$, and prescribes the total mass $\int_{{\mathbb{R}}^3}\rho ~d\mathbf{x}$. We seek a non-negative axisymmetric solution $\rho$ to . The existence and properties of rotating star solutions to were attained by Auchmuty and Beals [@auchmuty1971variational], Auchmuty [@auchmuty1991global], Caffarelli and Friedman [@caffarelli1980shape], Friedman and Turkington [@friedman1980asymptotic; @friedman1981existence; @friedman1980oblateness], Li [@li1991uniformly], Chanillo and Li [@chanillo1994diameters], Luo and Smoller [@luo2004rotating], and Luo and Smoller [@luo2009existence].
Recent observations on extrasolar giant gaseous planets have raised fundamental questions about their interior structure and origin. Many of the extrasolar gaseous planets possess unexpectedly small radii, suggesting high metallicity in their composition and possibly the existence of a solid core in the center (Anderson and Adams [@anderson2012effects]). Efforts have been made to simulate the evolution of these planets, and evidence for the existence of a solid core has been found (Militzer et al. [@militzer2008massive]). Models involving high metallicity and center core have been constructed and examined (Miller et al. [@miller2011heavy], Burrows et al. [@burrows2007possible]). As a first model from a mathematical perspective, one could modify the Euler-Poisson equations for rotating stars to include a solid core and its gravitational potential. Let $K$ be an axisymmetric bounded domain in $\mathbb{R}^3$, and $\rho_K$ be a given axisymmetric non-negative function on $K$, indicating the density of the solid core. Let $\phi_K = -\rho_K * \frac{1}{|\mathbf{x}|}$ denote the gravitational potential of $\rho_K$. Then by the $-\phi_K$-modified Euler-Poisson system we mean the following $$\label{intro: eq: phi_K modified Euler-Poisson system primal}
\begin{cases}
\rho_t + \nabla\cdot(\rho\mathbf{v}) = 0 \\
(\rho\mathbf{v})_t + \nabla\cdot(\rho\mathbf{v}\otimes\mathbf{v}) + \nabla p = -\rho\nabla(\phi + \phi_K) \\
\Delta \phi = 4\pi \rho
\end{cases}$$ As is in the case of rotating star solutions, we assume axisymmetry and time independence to reduce the equations as follows. $$\label{intro: eq: vector rotating planet}
\frac{\nabla p}{\rho} = -\nabla (\phi + \phi_K) + r\Omega^2 \mathbf{e}_r.$$ The goal of the present paper is to discuss existence and non-existence of solutions to .
The idea that led to existence results for is to regard it as a gradient: $$\label{eq: gradient Bernoulli}
\nabla \big( a(\rho) \big)= - \nabla \phi + \nabla J,$$ where $$a(s) = \int_0^s \frac{p'(t)}{t}dt, \text{ and }J(r) = \int_0^r s\Omega^2(s) ds.$$ From , we get $$\label{intro: eq: Bernoulli relation}
a(\rho)= -\phi + J(r) + \lambda$$ for some constant $\lambda$. With prescribed equation of state and angular velocity profile $\Omega(r)$, is a single equation for the unknown function $\rho$, although we still don’t know the value of $\lambda$ at this stage.
Now the key idea to solve relation is to regard it as the Euler-Lagrange equation of the following energy functional $$E(\rho) = \int_{{\mathbb{R}}^3} \bigg( A(\rho) - \frac{1}{2}\rho B\rho - \rho J \bigg)~d\mathbf{x}$$ subject to the constraint $$\int_{{\mathbb{R}}^3} \rho ~d\mathbf{x}= M.$$ Here $$A(s) = \int_0^s a(t)dt$$ and $$B\rho(\mathbf{x}) = \rho * \frac{1}{|\mathbf{x}|} = \int \frac{\rho(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}~d\mathbf{y}.$$ Under this formulation the unknown constant $\lambda$ in is naturally realized as a Lagrange multiplier.
Auchmuty and Beals [@auchmuty1971variational] imposed some non-trival decay conditions on $J$ and got the first existence results for rotating stars. However, these conditions excluded constant $\Omega$ and therefore ruled out a large family of physically interesting solutions. Li [@li1991uniformly] removed this restriction and was able to obtain an existence result for $J$ with small $L^{\infty}$ norm. This enabled him to prove existence for small constant $\Omega$. The smallness of $\|J\|_{\infty}$ is essential in Li’s proof. He also substantiated the smallness requirement by proving a non-existence result for with large constant $\Omega$.
Following a similar route, one can write down a scalar equation for the modified Euler-Poisson equations: $$\label{intro: eq: Bernoulli relation rotating planets}
a(\rho)= -\phi -\phi_K + J(r) + \lambda.$$ The corresponding Euler-Lagrange energy is $$E(\rho) = \int_{\mathbb{R} ^3 \setminus K} \bigg( A(\rho) - \frac{1}{2}\rho B\rho - \rho J - B\rho_K \bigg)~d\mathbf{x}.$$ Recall that $\rho_K$ is the density of the axisymmetric solid core and is positive. The minus sign in front of the $B\rho_K$ term is slightly surprising. One would expect that the gravitation of an extra center core should somehow cancel out the effect of centrifugal force due to the appearance of $J$, but at least on the energy level, they are of the same sign. In particular, without a smallness assumption on $\rho_K$, Li’s proof no longer works. It is physically reasonable to assume slow rotation in order for a solution to exist, but unreasonable to assume smallness of solid core density.
Furthermore, with a given rotation profile that is not necessarily small, a solution may still exist if the core gravitational pull is sufficiently large. The potential existence of a fast rotating planet with heavy core is a unique phenomenon that is not present in the classical rotating star case.
On the other hand, with a given core density and total mass, there should still be no solution if the rotation is sufficiently large. One may want to look for a non-existence result like the one in [@li1991uniformly]. However, the proof in [@li1991uniformly] involves a subtle argument based on integral identities, and fails to apply to the case with a solid core. We thus employ a different argument to show non-existence.
Statement of Results
====================
Let us consider the following axisymmetric equilibrium $\Phi_K$-modified Euler-Poisson equations in $\mathbb{R}^3\setminus K$, for a bounded axisymmetric domain $K$: $$\label{chap3: eq: Euler-Poisson}
\frac{\nabla p}{\rho} = \nabla \big(B\rho+ J + \Phi_K \big),$$ which is the gradient of the following equilibrium relation $$\label{chap3: eq: equilibrium eq}
A'(\rho)- B\rho - J -\Phi_K = \lambda.$$ Here $$B\rho(\mathbf{x})=\int_{\mathbb{R}^3\setminus K}\frac{\rho(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}~d\mathbf{y}$$ is the Newtonian potential of $\rho$, $$J(r)=\int_0^r s\Omega ^2(s)~ ds,$$ where $r=\sqrt{x_1^2 + x_2^2}$, is the potential of centrifugal force, and $\Phi_K$ is the potential generated by the core. We assume $$\label{chap3: cond: J}
s\Omega^2(s) \text{ is a given non-negative function in } L^1[0,\infty)\cap C[0, \infty).$$ If gravity is the only effect of the core, $\Phi_K$ is given by $$\label{chap3: eq: Phi_K by gravity}
\Phi_K(\mathbf{x})=B\rho_K(\mathbf{x})=\int_K \frac{\rho_K(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}~d\mathbf{y}$$ where $\rho_K \in L^q(K)$ for some $q>3$ is a given axisymmetric non-negative function on $K$. More generally, $\Phi_K$ is a function satisfying $$\label{chap3: cond: Phi_K}
\Phi_K \in C^1(\mathbb{R}^3)\text{ is positive, axisymmetric, and }\lim_{\textbf{x} \to \infty}\Phi_K(\textbf{x}) = 0,$$ and $$\begin{aligned}
\label{chap3: cond: Phi_K 2}
&\text{there is a }z_0>0 \text{ such that if } |x_3|>z_0, ~\Phi_K\text{ is non-increasing as }\\ &|x_3|\text{ increases}. \notag\end{aligned}$$ The equation of state is given by $p = f(\rho)$, where $f$ is a function satisfying $$\label{chap3: cond: f 1}
f(s) \text{ is non-negative, continuous, and strictly increasing for } s>0.$$ $$\label{chap3: cond: f 2}
\lim_{s\to 0} f(s)s^{-\frac{4}{3}} = 0, \quad \lim_{s\to \infty}f(s)s^{-\frac{4}{3}}=\infty .$$ A typical example of such an $f$ would be $f(s)=s^{\gamma}$ for some $\gamma>\frac{4}{3}$. The internal energy potential $A$ in is related to $f$ by $$\label{chap3: eq: define A}
A(s)=s\int_ 0^s \frac{f(t)}{t^2}dt.$$
We then have the following
\[chap3: thm: existence of solution with small J\] Given $M>0$, $\Phi_K$ satisfying , and $f$ satisfying and , there is an $\epsilon_1 >0$, such that if $\|J\|_{\infty} < \epsilon_1$, there exists a compactly supported axisymmetric continuous function $\rho: \mathbb{R}^3\setminus K\to [0,\infty)$, such that
1. $\rho$ is differentiable where it is positive, and satisfies the $\Phi_K$-modified Euler-Poisson equation there.\
2. $\int_{\mathbb{R}^3\setminus K}\rho(\mathbf{x})~d\mathbf{x}=M$.
\[chap3: thm: existence of solution with small Omega\] Given $M>0$, $\Phi_K$ satisfying , and $f$ satisfying and , there is an $\epsilon_2 >0$, such that if $\Omega(s)\equiv \Omega < \epsilon_2$, there exists a compactly supported axisymmetric continuous function $\rho: \mathbb{R}^3\setminus K\to [0,\infty)$, such that
1. $\rho$ is differentiable where it is positive, and satisfies the $\Phi_K$-modified Euler-Poisson equation there.\
2. $\int_{\mathbb{R}^3\setminus K}\rho(\mathbf{x})~d\mathbf{x}=M$.
Theorem \[chap3: thm: existence of solution with small J\] and Theorem \[chap3: thm: existence of solution with small Omega\] establish existence of rotating planet solutions with given mass and core potential for sufficiently small angular velocity profile.
Furthermore, we have the following
\[chap3: thm: existence of solution with large core gravity, variable angular velocity\] Given $M>0$, $J$ satisfying , $f$ satisfying and , and $\Phi_K$ satisfying , there is a $\mu_0 >0$, such that if $\mu > \mu_0$, there exists a compactly supported axisymmetric continuous function $\rho: \mathbb{R}^3\setminus C\to [0,\infty)$, such that
1. $\rho$ is differentiable where it is positive, and satisfies the $\mu \Phi_K$-modified Euler-Poisson equations there.\
2. $\int_{\mathbb{R}^3\setminus K}\rho(\mathbf{x})~d\mathbf{x}=M$.
\[chap3: thm: existence of solution with large core gravity, constant angular velocity\] Given $M>0$, $\Omega(r)\equiv \Omega\geq 0$, $f$ satisfying and , and $\Phi_K$ satisfying , there is an $\mu_0 >0$, such that if $\mu > \mu_0$, there exists a compactly supported axisymmetric continuous function $\rho: \mathbb{R}^3\setminus C\to [0,\infty)$, such that
1. $\rho$ is differentiable where it is positive, and satisfies the $\mu \Phi_K$-modified Euler-Poisson equations there.\
2. $\int_{\mathbb{R}^3\setminus K}\rho(\mathbf{x})~d\mathbf{x}=M$.
Theorem \[chap3: thm: existence of solution with large core gravity, variable angular velocity\] and Theorem \[chap3: thm: existence of solution with large core gravity, constant angular velocity\] establish existence of rotating planet solutions with given mass and angular velocity profile for sufficiently large core potential.
Finally, in order to describe a non-existence theorem for fast constant rotation, we need some further assumptions on the equation of state $f$. $$\label{chap3: cond: f cond nonexistence}
\liminf_{s \to \infty}f(s)s^{-\gamma}>0, \text{ for some }\gamma>\frac{4}{3}.$$ $f(s)$ is continuously differentiable for $s>0$ and $$\label{chap3: cond: f continuous differentiability}
\liminf_{s\to 0}f'(s)s^{-\mu}>0$$ for some $\mu>0$. A typical example of such an $f$ is again given by $f(s)=s^{\gamma}$ for some $\gamma >\frac{4}{3}$.
\[chap3: thm: nonexistence of solution\] Suppose $f$ satisfies , , and . Let $\Phi_K$ be given by , and let $M>0$ be given. Also assume that $K$ satisfies the “no trapping” condition:
- If $(x,y,z)\in \mathbb{R}^3 \setminus K$, then the half line $(x,y,z)+t(x,y,0)$, ($t\geq 0$) also belongs to $\mathbb{R}^3 \setminus K$.
Then there exists an $\Omega_0>0$ such that for $\Omega(r)\equiv \Omega > \Omega_0$, there does not exist a bounded continuous function $\rho: \mathbb{R}^3\setminus C\to [0,\infty)$, such that
1. $\rho$ satisfies where positive.
2. $\int_{\mathbb{R}^3\setminus K}\rho(\mathbf{x})~d\mathbf{x}=M$.
Theorems \[chap3: thm: existence of solution with small J\] and \[chap3: thm: existence of solution with small Omega\] are proved in section \[chap3: slow rotation\]. Theorems \[chap3: thm: existence of solution with large core gravity, variable angular velocity\] and \[chap3: thm: existence of solution with large core gravity, constant angular velocity\] are proved in section \[chap3: dense core\]. Theorem \[chap3: thm: nonexistence of solution\] is proved in section \[chap3: non-existence\].
Variational Formulation {#chap3: variational}
=======================
We first need a few convolution inequalities. These lemmas turn out to be quite useful for the rotating star existence theory. Their proofs can be found in [@auchmuty1971variational].
\[chap2: lem: L r bound on B rho\] Suppose $\rho\in L^1(\mathbb{R}^3) \cap L^p(\mathbb{R}^3)$, and $1<p\leq \frac{3}{2}$. Then $B\rho \in L^r(\mathbb{R}^3)$ for all $3<r<\frac{3p}{3-2p}$, and $$\label{chap2: ineq: convolution}
\| B \rho \| _r \leq C(\| \rho \|_1 ^b\| \rho \|_p ^{1-b} + \| \rho \|_1 ^c \| \rho \|_p^{1-c})$$ for some constant $C$ and $0<b,c<1$ depending on $p$ and $r$. If $p>\frac{3}{2}$, then $B\rho $ is bounded and continuous and satisfies with $r=\infty$.
\[chap2: lem: bound on gravity potential\] If $\rho \in L^1(\mathbb{R}^3) \cap L^{4/3}(\mathbb{R}^3)$, then $$\bigg|\int_{\mathbb{R}^3} \rho B\rho ~d\mathbf{x} \bigg|\leq C \bigg( \int_{\mathbb{R}^3}|\rho|^{4/3} ~d\mathbf{x}\bigg) \bigg(\int_{\mathbb{R}^3}|\rho| ~d\mathbf{x}\bigg)^{2/3}.$$
\[chap2: lem: continuous diff of B rho\] If $\rho\in L^1(\mathbb{R}^3) \cap L^p(\mathbb{R}^3)$ for some $p>3$, then $B\rho$ is continuously differentiable.
As [@auchmuty1971variational] and [@li1991uniformly], we will solve this problem via a variational approach. Let us consider the energy functional $$\label{chap3: energy functional}
E(\rho)=\int_{\mathbb{R}^3\setminus K}\bigg( A(\rho)(\mathbf{x}) -\frac{1}{2}\rho(\mathbf{x}) B\rho(\mathbf{x}) -\rho(\mathbf{x}) J(\mathbf{x}) -\rho(\mathbf{x})\Phi_K(\mathbf{x})\bigg) ~d\mathbf{x},$$ where $A$ is given by , on the space of admissible functions $$W=\bigg\{\rho: \mathbb{R}^3\setminus K \to \mathbb{R}, ~\rho \text{ is axisymmetric}, ~\rho \geq 0 \text{ a.e.}, ~\int_{\mathbb{R}^3\setminus K }A(\rho) < \infty, \int_{\mathbb{R}^3\setminus K }\rho = M \bigg\}.$$ We first verify that $E$ is well-defined on $W$. From , it follows easily that $$\label{chap3: cond: A}
\lim_{s\to 0} A(s)s^{-\frac{4}{3}} = 0, \quad \lim_{s\to \infty}A(s)s^{-\frac{4}{3}}=\infty .$$ and imply the existence of a $c>0$ such that $$A(s)\geq c s^{4/3}$$ for $s>1$. Hence $$\begin{aligned}
\int \rho^{4/3} &\leq \frac{1}{c} \int A(\rho) + \int_{\rho<1}\rho^{4/3} \notag \\
& \leq \frac{1}{c} \int A(\rho) + M. \label{chap3: ineq: bound on 4/3 norm}\end{aligned}$$ and lemma \[chap2: lem: bound on gravity potential\] give the finiteness of the second term in . The last two terms in are finite because $J$ and $\Phi_K$ are bounded functions. We have shown that $E$ is well-defined on $W$.
The basic assertion is the following:
\[chap3: prop: variational principle\] If $\rho$ is a local minimum for $E$ in $W$, then $\rho$ is continuous and is differentiable where it is positive, and satisfies there.
The proof is standard. See [@auchmuty1971variational].
Existence for Slow Rotation with Fixed Core Density {#chap3: slow rotation}
===================================================
In the following proof, we will construct a number of bounds $R_{n}$ on the size of the support of the density functions. Without further mentioning, we always assume that $R_{n+1}$ is no less than $R_{n}$. All constants in the following may depend on $M$, $f$, $\|J\|_{\infty}$ and $\Phi_K$. Cartesian coordinates $\textbf{x} = (x_1,x_2,x_3)$ and cylindrical coordinates $(r,\theta,z)$ are used interchangeably. To look for a minimizer of $E$ in $W$, let us first show that $E$ is bounded from below.
There is a $C>0$ such that $E(\rho)\geq -C$ for all $\rho \in W$.
By lemma \[chap2: lem: bound on gravity potential\], we have $$E(\rho)\geq \int A(\rho) ~d\textbf{x}- M\|J+\Phi_K\|_{\infty} -\frac{1}{2}cM^{2/3}\int\rho^{4/3}~d\textbf{x}.$$ By , there is an $s>0$ such that for $\rho>s$, $A(\rho)>\frac{1}{2}cM^{2/3}\rho^{4/3}$. Therefore $$\begin{aligned}
E(\rho)&\geq \int_{\rho >s} A(\rho)~d\textbf{x} - M\|J+\Phi_K\|_{\infty} -\frac{1}{2}cM^{2/3}\int_{\rho> s}\rho^{4/3}- \frac{1}{2}cM^{2/3}s^{1/3}\int_{\rho < s}\rho ~d\textbf{x} \\
& \geq - M\|J+\Phi_K\|_{\infty}- \frac{1}{2}cM^{5/3}s^{1/3}.\end{aligned}$$
Now that we know $E$ is bounded from below, it makes sense to talk about the infimum of $E$. Let $$I=\inf_{\rho \in W}E(\rho).$$ We will take a sequence of minimizers in bounded balls as a minimizing sequence for $I$. For that purpose, we need to define $$\label{chap3: eq: define W_R}
W_R=\bigg\{\rho \in W ~\big|~ \textbf{Supp}\rho \in S_R, ~0\leq \rho \leq R \text{ a.e.}\bigg\}.$$ Here $S_R$ is the ball centered at the origin with radius $R>R_0$ so large that $K$ is contained in $S_R$. As usual we will extend functions in $W_R$ by zero values outside $S_R$, and treat them as functions defined on the whole space if necessary. The next assertion is the starting point of this existence method.
There is an $R_0>0$ such that for $R>R_0$, there exists some $\rho_R\in W_R$ which minimizes E: $$I_R=E(\rho_R)=\inf_{\rho\in W_R}E(\rho).$$
The proof is standard. See [@auchmuty1971variational] or [@li1991uniformly].
As in [@li1991uniformly], we can give a uniform $L^{\infty}$ bound on $\rho_R$.
\[chap3: lem: L infty bound on rho\_R\] There is a $C>0$, such that $$\|\rho_R\|_{\infty}\leq C$$ for all $R\geq R_0$.
Notice that $\Phi_K\in L^{\infty}(\mathbb{R}^3)$. The proof in this case is basically the same as that in [@li1991uniformly].
The $L^{\infty}$ bound frees the restriction on $\rho_R$ from above, and therefore implies a variational inequality in one direction:
There is an $R_1>0$, such that for all $R>R_1$, there exists a $\lambda_R$ such that $$\begin{aligned}
A'(\rho_R)- B\rho_R -J -\Phi_K \geq \lambda_R, &\quad \text{ in }B_R,\label{chap3: ineq: Euler Lagrange rho_R}\\
A'(\rho_R)- B\rho_R -J -\Phi_K = \lambda_R, &\quad \text{ where }\rho_R > 0.\label{chap3: eq: Euler Lagrange rho_R}\end{aligned}$$
See [@auchmuty1971variational].
There is an $R_2>0$ and $e_1>0$, such that $I_R\leq -e_1$ for all $R>R_2$.
Let $$F(\rho)=\int_{\mathbb{R}^3\setminus K}\bigg( A(\rho)(\mathbf{x}) -\frac{1}{2}\rho(\mathbf{x}) B\rho(\mathbf{x}) \bigg) d\mathbf{x}.$$ This is the corresponding energy functional for an Euler-Poisson system with no rotation and a zero density core. The method in [@auchmuty1971variational] is fully applicable to this case. We therefore get a compactly supported minimizer $\sigma \in W$ of $F$. Let $$e_1=-F(\sigma)=-\inf_{\rho \in W}F(\rho).$$ $e_1$ is seen to be positive by the following scaling argument: pick a non zero $\rho \in W$ that is bounded and compactly supported in $\mathbb{R}^3\setminus S_{\tilde{R}}$ for some $S_{\tilde{R}}\supset K$. Let $$\rho_t(\mathbf{x})=t^{-3}\rho(t^{-1}\mathbf{x})$$ for $t>1$. We see easily that $\rho_t$ is supported in $\mathbb{R}^3\setminus tB_{\tilde{R}}$, and therefore belongs to $W$. $$\begin{aligned}
F(\rho_t)& =\int_{\mathbb{R}^3\setminus tB_{\tilde{R}}}A(\rho_t)-\frac{1}{2}\rho_t B\rho_t \\
& = \int_{\mathbb{R}^3\setminus B_{\tilde{R}}}(t^3A(t^{-3}\rho)-\frac{1}{2}t^{-1}\rho B\rho)\\
& = \int_{\mathbf{Supp} \rho}o(t^{-4}\|\rho\|_{\infty})t^3-t^{-1}\frac{1}{2}\int\rho B\rho\\
& = o(t^{-1})-\Theta(t^{-1}).\end{aligned}$$ The penultimate step follows from . This shows that the minimum of $F$ must be negative. Now let $R_2$ be large enough to contain the support of $\sigma$, then $\sigma \in W_R$ for $R>R_2$, and $$\begin{aligned}
E(\rho_R)& \leq E(\sigma) \\
& = \int(A(\sigma)-\frac{1}{2}\sigma B\sigma - J\sigma -\Phi_K\sigma)\\
& \leq \int(A(\sigma)-\frac{1}{2}\sigma B\sigma)\\
& =F(\sigma)\\
& =-e_1.\end{aligned}$$
\[chap3: lem: lower bound on mass in unit ball\] Suppose $\|J\|_{\infty}<\frac{e_1}{2M}$. There is an $\epsilon_0>0$ and an $R_2>0$ such that for all $R>R_2$, $\epsilon_R := \sup_{\mathbf{x}\in \mathbb{R}^3}\int_{|\mathbf{x}-\mathbf{y}|<1}\rho_R(\mathbf{y})d\mathbf{y}\geq \epsilon_0$.
Under the assumption on $\|J\|_{\infty}$ $$\begin{aligned}
& \int \frac{1}{2}\rho_R B\rho_R + \rho_R \Phi_K \\
=& -E(\rho_R)+\int A(\rho_R)-\rho_R J \\
\geq & \quad e_1 - \|J\|_{\infty}M \\
\geq & \quad \frac{e_1}{2}.\end{aligned}$$ Therefore either $$\label{chap3: ineq: case 1}
\int \frac{1}{2}\rho_R B\rho_R \geq \frac{e_1}{4},$$ or $$\label{chap3: ineq: case 2}
\int \rho_R \Phi_K \geq \frac{e_1}{4}.$$ If happens, then $$\label{chap3: ineq: lower bound on B rho_R}
\frac{e_1}{2}\leq \int \rho_R B\rho_R \leq M \|B \rho_R\|_{\infty}.$$ Now $$\begin{aligned}
B\rho_R(\mathbf{x}) & = \int_{\mathbb{R}^3}\frac{\rho_R(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}d\mathbf{y} \\
& = \int_{|\mathbf{y}-\mathbf{x}|<1}\frac{\rho_R(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}d\mathbf{y} + \int_{1<|\mathbf{y}-\mathbf{x}|<\tilde{R}}\frac{\rho_R(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}d\mathbf{y} + \int_{|\mathbf{y}-\mathbf{x}|>\tilde{R}}\frac{\rho_R(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}d\mathbf{y} \\
& := B_1 + B_2 + B_3.\end{aligned}$$ By lemma \[chap3: lem: L infty bound on rho\_R\] and lemma \[chap2: lem: L r bound on B rho\], we have $$B_1 \leq C(\epsilon_R ^b + \epsilon_R ^c)$$ for some $0<b,c<1$. The annulus $1<|\mathbf{y}-\mathbf{x}|<\tilde{R}$ can be covered by $C\tilde{R}^3$ balls of radius one, hence $$B_2 \leq C\tilde{R}^3 \epsilon_R.$$ One clearly has $$B_3 \leq \frac{M}{\tilde{R}}.$$ Hence $$\label{chap3: ineq: upper bound on B rho_R}
\|B \rho_R\|_{\infty} \leq C(\epsilon_R ^b + \epsilon_R ^c) + C\tilde{R}^3 \epsilon_R + \frac{M}{\tilde{R}}.$$ Choosing $\tilde{R}$ sufficiently large and comparing with , we see that there must be an $\epsilon_0 >0$ such that $\epsilon_R> \epsilon_0$. Now let us assume that happens. We have $$\begin{aligned}
& \int \rho_R \Phi_K \\
= & \int_{|\mathbf{x}|>\tilde{R}}\rho_R(\mathbf{x}) \Phi_K(\mathbf{x})d\mathbf{x} + \int_{|\mathbf{x}|<\tilde{R}}\rho_R(\mathbf{x}) \Phi_K(\mathbf{x})d\mathbf{x} \\
:= & B_1 + B_2.\end{aligned}$$ By , we can choose $\tilde{R}$ so large that $\Phi_K(\mathbf{x})\leq \frac{e_1}{8M}$ when $|\mathbf{x}|>\tilde{R}$. Then $$B_1\leq \frac{e_1}{8}.$$ The ball $|\mathbf{x}|<\tilde{R}$ can be covered by $C\tilde{R}^3$ balls of radius one, hence $$B_2 \leq C\tilde{R}^3 \epsilon_R.$$ Therefore $$\label{chap3: ineq: upper bound on int rho Phi}
\int \rho_R \Phi_K \leq \frac{e_1}{8} + C\tilde{R}^3 \epsilon_R.$$ Comparing with , we again see that such an $\epsilon_0$ exists.
\[chap3: lem: upper bound on R\_a\] There is an $R_a>0$ such that if $$\int_{|\mathbf{y}-\mathbf{x}|<1}\rho_R(\mathbf{y})d\mathbf{y}\geq \frac{\epsilon_0}{2},$$ then $r(\mathbf{x})\leq R_a$. Here $r(\mathbf{x})=\sqrt{x_1^2 +x_2^2}$.
Assume $|r(\mathbf{x})|>\tilde{R}+1$ where $S_{\tilde{R}}\supset K$. By the axisymmetry of $\rho_R$, $$\begin{aligned}
Cr(\mathbf{x})\frac{\epsilon_0}{2} & \leq \int_{T}\rho_R \leq M, \\
r(\mathbf{x}) &\leq \frac{2M}{C\epsilon_0}.\end{aligned}$$ Here $T$ is the torus obtained from rotating the the ball $|\mathbf{y}-\mathbf{x}|<1$ around the $z$-axis.
\[chap3: lem: uniform negative upper bound on lambda\_R\] Suppose $\|J\|_{\infty}\leq \frac{e_1}{2M}$. There is an $R_3>R_a$ and an $e_2>0$ such that $\lambda_R\leq -e_2$ for all $R>R_2$.
By lemma \[chap3: lem: lower bound on mass in unit ball\], for $R>R_2$ there is an $\mathbf{x}_R$ such that $$\int_{|\mathbf{y}-\mathbf{x}_R|<1}\rho_R(\mathbf{y})d\mathbf{y}\geq \frac{\epsilon_0}{2}.$$ By lemma \[chap3: lem: upper bound on R\_a\], $r(\mathbf{x}_R)<R_a$. Let $\mathbf{x}_0$ be on the $z$-axis such that $z(\mathbf{x}_0)=z(\mathbf{x}_R)$. Let $B(\mathbf{x}_0,R_3)$ be the ball centered at $\mathbf{x}_0$ with radius $R_3>R_a$ to be determined. When $R>R_3$, the volume of the set $B(\mathbf{x}_0,R_3) \cap B_R$ is of order $R_3^3$. There must exist a point $\mathbf{x}\in B(\mathbf{x}_0,R_3)\cap B_R$ such that $$\rho_R(\mathbf{x})\leq \frac{CM}{R_3^3}$$ for some constant $C>0$. Clearly $$|\mathbf{x}-\mathbf{x}_R|\leq |\mathbf{x}-\mathbf{x}_0|+|\mathbf{x}_R-\mathbf{x}_0|\leq 2R_3.$$ Hence $$B\rho_R(\mathbf{x})\geq \int_{|\mathbf{y}-\mathbf{x}_R|<1}\frac{\rho_R(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}d\mathbf{y}\geq \frac{1}{2R_3+1}\frac{\epsilon_0}{2}.$$ By , $$\begin{aligned}
\label{chap3: ineq: upper bound on lambda_R}
\lambda_R\leq A'(\frac{CM}{R_3^3})-\frac{1}{2R_3+1}\frac{\epsilon_0}{2}\end{aligned}$$ Notice that implies $$\lim_{s\to 0}\frac{A'(s)}{s^{1/3}}=0.$$ Hence implies $$\begin{aligned}
\label{chap3: ineq: upper bound on lambda_R final}
\lambda_R \leq o(R_3^{-1})-\Theta(R_3^{-1}).\end{aligned}$$ Pick $R_3$ so large that the right hand side of becomes negative, and call that $-e_2$.
Suppose $\|J\|_{\infty}\leq \min\bigg\{\frac{e_1}{2M},\frac{e_2}{2}\bigg\}$, then $$\label{chap3: ineq: lower bound on B rho_R + Phi_K}
B\rho_R + \Phi_K \geq \frac{e_2}{2} \quad \text{where }\rho_R>0$$ for $R>R_3$.
By and lemma \[chap3: lem: uniform negative upper bound on lambda\_R\], we have $$A'(\rho_R)-B\rho_R-J-\Phi_K = \lambda_R\leq -e_2$$ when $\rho_R>0$.
\[chap3: lem: r bound on the support of rho\] Suppose $\|J\|_{\infty}\leq \min\bigg\{\frac{e_1}{2M},\frac{e_2}{2}\bigg\}$. There exists an $R_4>0$ such that $\rho_R(\mathbf{x})=0$ if $R>r(\mathbf{x})>R_4$.
We have $$\begin{aligned}
B\rho_R(\mathbf{x})& =\int \frac{\rho_R(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}d\mathbf{y}\\
& = \int_{|\mathbf{x}-\mathbf{y}|<1} \frac{\rho_R(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}d\mathbf{y} + \int_{1<|\mathbf{x}-\mathbf{y}|<\tilde{R}} \frac{\rho_R(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}d\mathbf{y} + \int_{|\mathbf{x}-\mathbf{y}|>\tilde{R}} \frac{\rho_R(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}d\mathbf{y} \\
& := B_1 + B_2 + B_3.\end{aligned}$$ Clearly $$B_3\leq \frac{M}{\tilde{R}}.$$ We choose $\tilde{R}>\frac{12M}{e_2}$, so that $$B_3 < \frac{e_2}{12}.$$ By lemma \[chap2: lem: L r bound on B rho\], $$\begin{aligned}
B_1\leq c_0 \bigg( \bigg(\int_{|\mathbf{x}-\mathbf{y}|<1} \rho_R(\mathbf{y})d\mathbf{y}\bigg)^b + \bigg(\int_{|\mathbf{x}-\mathbf{y}|<1} \rho_R(\mathbf{y})d\mathbf{y} \bigg)^c \bigg)\end{aligned}$$ for some $0<b,c<1$. By requiring $R>r(\mathbf{x})>R_4$ to be large enough, we have $$B_1 \leq c_0\bigg( \bigg(\frac{CM}{R_4} \bigg)^b + \bigg(\frac{CM}{R_4} \bigg)^c\bigg) < \frac{e_2}{12}$$ by axisymmetry, just like in lemma \[chap3: lem: upper bound on R\_a\]. The annulus $1<|\mathbf{x}-\mathbf{y}|<\tilde{R}$ can be covered by $C\tilde{R}^3$ balls of radius 1. Again by axisymmetry, we have $$B_2\leq \frac{C\tilde{R}^3M}{R_4-\tilde{R}}<\frac{e_2}{12},$$ provided $R_4$ is chosen to be sufficiently large. Therefore $$B\rho_R(\mathbf{x})= B_1 + B_2 + B_3 < \frac{e_2}{4}$$ if $R>r(\mathbf{x})>R_4$. Enlarge $R_4$ if necessary so that $\Phi_K(\mathbf{x})<\frac{e_2}{4}$ when $r(\mathbf{x})>R_4$. We get $$\label{chap3: ineq: upper bound on B rho_R + Phi_K}
B\rho_R(\mathbf{x}) + \Phi_K(\mathbf{x}) < \frac{e_2}{4} + \frac{e_2}{4} =\frac{e_2}{2}$$ when $R>r(\mathbf{x})>R_4$. Comparing with , we see that the assertion is true.
\[chap3: lem: pre z bound on the support of rho\] Suppose $\|J\|_{\infty}\leq \min\bigg\{\frac{e_1}{2M},\frac{e_2}{2}\bigg\}$. There exist $R_5>0$, $\delta>0$ and $r>0$ such that if $R>z(\mathbf{x})>R_5$, and if $$\int_{|z(\mathbf{x})-z_0|<r}\rho_R(\mathbf{x})d\mathbf{x}<\delta,$$ then $\rho(\mathbf{x})=0$ for $|z(\mathbf{x})-z_0|<1$.
Suppose $r>2$. If $|z(\mathbf{x})-z_0|<1$, $\text{dist}\big(\mathbf{x},\{\mathbf{y} ~\big|~ |z(\mathbf{y})-z_0|>r\}\big) > r-1$. Just like in lemma \[chap3: lem: r bound on the support of rho\], we have $$\begin{aligned}
B\rho_R(\mathbf{x}) & = \int_{|z(\mathbf{y})-z_0|<r} \frac{\rho_R(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}d\mathbf{y} + \int_{|z(\mathbf{y})-z_0|>r} \frac{\rho_R(\mathbf{y})}{|\mathbf{x}-\mathbf{y}|}d\mathbf{y} \\
& \leq C(\delta^b +\delta ^c)+\frac{M}{r-1} \\
& < \frac{e_2}{4}\end{aligned}$$ by choosing $\delta$ small and $r$ large. Furthermore $\Phi_K(\mathbf{x})<\frac{e_2}{4}$ if $z(\mathbf{x})>R_5$ is sufficiently large. These imply $$B\rho_R(\mathbf{x}) + \Phi_K(\mathbf{x}) < \frac{e_2}{2}.$$ The assertion follows again from a comparison with .
\[chap3: lem: z bound on the support of rho\] Suppose $\|J\|_{\infty}\leq \min\bigg\{\frac{e_1}{2M},\frac{e_2}{2}\bigg\}$. There is an $R_6>0$ such that $\rho_R(\mathbf{x})=0$ if $R>z(\mathbf{x})>R_6$.
Let $Z_n=\{x : |z(x)-2n|<1\}$, $n=\pm ([R_5]+1), \pm ([R_5]+2), \dots$, and let $Z_n'=\big\{x ~\big|~ |z(x)-2n|<r\big\}$. By lemma \[chap3: lem: pre z bound on the support of rho\], if $\rho_R$ is not identically zero on a $Z_n$, then $\int_{Z_n'}\rho_R\geq \delta$. Let $m$ be the number of such $n$’s. Since each point in $\mathbb{R}^3$ is covered by at most $r$ different $Z_n'$’s, $m\delta \leq rM$. Also such $Z_n$’s must be contiguous, if they lie in the region $|z|>z_0+2$ for $z_0$ given in . Otherwise there would be an “empty” $Z_n$ below a “non-empty” half space. If one slides the whole “non-empty” half space down by two units to create a new $\rho_R'$, $\int A(\rho_R)-J \rho_R = \int A(\rho_R') - J\rho_R'$, but $\int -\frac{1}{2}\rho_R B\rho_R- \rho_R \Phi_K > \int -\frac{1}{2}\rho_R' B\rho_R'- \rho_R' \Phi_K $. This implies $E(\rho_R)>E(\rho_R')$, but $\rho_R'\in W_R$, a contradiction. Now pick $R_6 > 2\bigg( [R_5]+\frac{rM}{\delta}\bigg)+z_0 +3$. The proof is complete.
We are now in a position to prove theorem \[chap3: thm: existence of solution with small J\] and theorem \[chap3: thm: existence of solution with small Omega\].
Let $\epsilon_1=\min\bigg\{\frac{e_1}{2M},\frac{e_2}{2}\bigg\}$. From lemma \[chap3: lem: r bound on the support of rho\] and lemma \[chap3: lem: z bound on the support of rho\], we see that $\rho_R=\rho_{R_7}$ when $R>R_7 := \sqrt{2}R_6$. Since $\Phi_K \in L^{\infty}(\mathbb{R}^3)$, a similar argument as in [@auchmuty1971variational] shows that $\rho=\rho_{R_7}$ minimizes $E$ in $W$. By proposition \[chap3: prop: variational principle\], $\rho$ solves and has the stated properties.
Let $\epsilon_2=\frac{\sqrt{\epsilon_1}}{R_7}$, and let $\tilde{J}(r)\in C^{\infty}(0,\infty)$ be an increasing function such that $$\tilde{J}(r)=
\begin{cases}
\frac{1}{2}\Omega^2r^2 &\quad \text{if }r \leq R_7, \\
\Omega^2 R_7^2 &\quad \text{if } r \geq 2R_7.
\end{cases}$$ If $\Omega < \epsilon_2$, we have $\|\tilde{J}\|< \epsilon_1$, hence by theorem \[chap3: thm: existence of solution with small J\], there is a solution $\rho$ to where $J$ is replaced by $\tilde{J}$, supported in $S_{R_7}$. Clearly such a $\rho$ also solves with the original $J$, and has the stated properties.
Existence for Fast Rotation with Heavy Core Density {#chap3: dense core}
===================================================
In this section, we give proofs to theorem \[chap3: thm: existence of solution with large core gravity, variable angular velocity\] and theorem \[chap3: thm: existence of solution with large core gravity, constant angular velocity\]. That corresponds to establishing existence of minimizer of $$E_{\mu}(\rho)=\int_{\mathbb{R}^3\setminus C}\bigg( A(\rho)(\mathbf{x}) -\frac{1}{2}\rho(\mathbf{x}) B\rho(\mathbf{x}) -\rho(\mathbf{x}) J(\mathbf{x}) -\mu \rho(\mathbf{x})\Phi_K(\mathbf{x})\bigg) d\mathbf{x}$$ for large enough $\mu$. We will omit an argument in the proof if it runs parallel to the proof in the previous section.
As before, $E_{\mu}$ is bounded from below on $W$ and has an infimum which we denote by $I_{\mu}$. If we pick $$\label{chap3: eq: defining W_R without upper bound}
W_R=\bigg\{\rho \in W ~\big|~ \textbf{Supp}\rho \in S_R, ~\rho \geq 0 \text{ a.e.}\bigg\}.$$ $E_{\mu}$ will also attain its infimum $I_{\mu, R}$ on each $W_R$. We still denote the minimizers by $\rho_R$. It is understood that $\rho_R$ implicitly depends on $\mu$. Comparing with , we see that the $L^{\infty}$ bound on $W_R$ (namely, the $\leq R$ constraint) is removed. This is to allow large $\rho_R$ on $B_R$. As we will see later, the $L^{\infty}$ bound of $\rho_R$ depends on $\mu$ and $J$. For that purpose, we start by modifying the bound on $\|\rho\|_{4/3}$.
\[chap3: lem: upper bound on rho\^4/3\] Let $\rho_R$ be a minimizer of $E_{\mu}$ in $W_R$, and assume that $B_{R_0}$ contains the core $K$. There is a constant $C$ depending only on $f$, $M$, $J$ and $\Phi_K$ such that $$\int \rho_R^{\frac{4}{3}}~d\mathbf{x} \leq C( 1+ \mu )$$ for all $R>R_0$.
Let $\rho_0$ be some fixed function in $W_{R_0}$. For $R>R_0$, $$\begin{aligned}
& \int \bigg( A(\rho_0) - \rho_0 J-\frac{1}{2}\rho_0 B\rho_0 -\mu \rho_0 \Phi_K \bigg)~d\textbf{x}\\
\geq & \int \bigg( A(\rho_R) - \rho_R J-\frac{1}{2}\rho_{R}B\rho_{R}-\mu \rho_{R}\Phi_K \bigg) ~d\textbf{x}\\
\geq & \int \bigg( A(\rho_R) - \rho_R(J+\mu \Phi_K) \bigg) ~d\textbf{x}-CM^{\frac{2}{3}}\int \rho_R^{\frac{4}{3}}~d\textbf{x}.\end{aligned}$$ The last step follows from lemma \[chap2: lem: bound on gravity potential\]. By condition , there is an $s_1>0$ such that $$A(s)s^{-\frac{4}{3}}>2CM^{\frac{2}{3}}$$ for $s>s_1$. Therefore $$\begin{aligned}
\tilde{C} &= \int \bigg( A(\rho_0) - \rho_0 J-\frac{1}{2}\rho_0 B\rho_0 -\mu \rho_0 \Phi_K \bigg)~d\textbf{x} \\
& \geq \int_{\rho_R \leq s_1}A(\rho_R) ~d\textbf{x}+\int_{\rho_R> s_1}A(\rho_R) ~d\textbf{x} -M(\|J\|_{\infty} +\mu \|\Phi_K\|_{\infty}) \\
& \quad \quad \quad -CM^{\frac{2}{3}} s_1^{\frac{1}{3}}M -\int_{\rho_R>s_1}\frac{1}{2}A(\rho_R) ~d\textbf{x}\\
& \geq \frac{1}{2} \int A(\rho_R)~d\textbf{x}- C' (1+ \mu). \end{aligned}$$ Or, $$\int A(\rho_R) ~d\textbf{x}\leq C(M,s_1) (1+\mu ).$$ Notice that we have $$\begin{aligned}
\int \rho_R^{\frac{4}{3}} ~d\textbf{x}& = \int_{\rho_R \leq s_1} \rho_R^{\frac{4}{3}}~d\textbf{x}+\int_{\rho_R > s_1} \rho_R^{\frac{4}{3}}~d\textbf{x} \\
& \leq s_1^{\frac{1}{3}}M + \frac{1}{2CM^{\frac{2}{3}}}\int_{\rho_R >s_1}A(\rho_R)~d\textbf{x}\\
& \leq C(M,s_1) \bigg(1 + \int A(\rho_R)~d\textbf{x}\bigg).\end{aligned}$$ The assertion is now apparent.
Now let us give an $L^{\infty}$ bound on $\rho_R$. It is crucial to make the power of $\mu$ as low as possible.
\[chap3: lem: l infty bound on rho\_R for heavy core\] There is an $R_1>0$ and a constant $C$ depending on $f$, $M$, $J$ and $\Phi_K$ such that $$\|\rho_R\|_{\infty}\leq C(1+\mu)$$ for $R>R_1$.
Let $E_R=\big\{\mathbf{x}\in \mathbb{R}^3 \setminus K ~\big| ~ \rho_R(\mathbf{x})>10M\big\}$, $F_n=\big\{\mathbf{x}\in \mathbb{R}^3 \setminus K ~\big| ~ 10M< \rho_R(\mathbf{x})<n\}$ for $n$ large. It is easy to see that the Lebesgue measure $|E_R|<\frac{1}{10}$. Choose $D\subset B_R \setminus E_R$ such that $|D|=1$. This is possible if we choose some $R_1>\max\{R_0,10\}$. Now let $\gamma_1=\frac{4}{3}$ and $\alpha_1=\frac{5\gamma_1-6}{3}-\epsilon=\frac{2}{9}-\epsilon$ for some very small $\epsilon>0$ to be determined later. Now define $$v_1=\begin{cases}
-\rho_R^{1+\alpha_1} \quad & \text{on } F_n \\
\int_{F_n}\rho_R^{1+\alpha_1} \quad & \text{on } D\\
0 \quad & \text{otherwise}
\end{cases}$$ One sees that $\rho_R+tv_1 \in W_R$ for $t>0$ sufficiently small. Since $\rho_R$ is a minimizer of $E_{\mu}$ in $W_R$, we have $\lim_{t\to 0^+}\frac{E_{\mu}(\rho_R + tv_1)-E_{\mu}(\rho_R)}{t}\geq 0$. Calculating the limit, we get $$\int (A'(\rho_R)-J-B\rho_R -\mu \Phi_K )v_1 \geq 0,$$ from which it follows that $$-\int_{F_n} v_1 A'(\rho_R)\leq \int_{D}v_1 A'(\rho_R) - \int_{F_n}v_1(J+\mu \Phi_K) -\int_{F_n} v_1 B\rho_R.$$ Condition on $f$ implies that $A'(s)\geq C_1 \rho^{\frac{1}{3}}$ for $s> 10M$. Therefore $$-\int_{F_n}v_1 A'(\rho_R) \geq \frac{1}{C_1}\int_{F_n} \rho_R^{\frac{4}{3}+\alpha_1}.$$ Furthermore, $$\begin{aligned}
\int_{D}v_1 A'(\rho_R) & \leq A'(10 M)\int_{F_n} \rho_R^{1+\alpha_1}, \\
-\int_{F_n}v_1(J+\mu \Phi_K) & \leq (\|J\|_{\infty} +\mu \|\Phi_K\|_{\infty})\int_{F_n}\rho_R^{1+\alpha_1}, \\
-\int_{F_n}v_1 B\rho_R & \leq \|\rho_R^{1+\alpha_1}\|_{\frac{3\gamma_1}{5\gamma_1- 3- 3\epsilon}} \|B\rho_R\|_{(\frac{1}{\gamma_1}-\frac{2}{3}+\frac{\epsilon}{\gamma_1})^{-1}} \\
& = \|\rho_R\|_{(1+\alpha_1)\frac{3\gamma_1}{5\gamma_1- 3- 3\epsilon}}^{1+\alpha_1} \|B\rho_R\|_{(\frac{1}{\gamma_1}-\frac{2}{3}+\frac{\epsilon}{\gamma_1})^{-1}} \\
& = \|\rho_R\|_{\gamma_1}^{1+\alpha_1} \|B\rho_R\|_{(\frac{1}{\gamma_1}-\frac{2}{3}+\frac{\epsilon}{\gamma_1})^{-1}} \\
& \leq C \|\rho_R\|_{\gamma_1}^{2+\alpha_1}.\end{aligned}$$ Here the last step follows from lemma \[chap2: lem: L r bound on B rho\]. Now $$\begin{aligned}
& \int_{F_n} \rho_R^{\frac{4}{3}+\alpha_1} \\
\leq & C_1(A'(10M)+\|J\|_{\infty} +\mu \|\Phi_K\|_{\infty})\int_{F_n}\rho_R^{1+\alpha_1} + C \|\rho_R\|_{\gamma_1}^{2+\alpha_1} \\
\leq & C_2(1+\mu)\|\rho_R\|_{1+\alpha_1}^{1+\alpha_1}+ C \|\rho_R\|_{\gamma_1}^{2+\alpha_1} .\end{aligned}$$ Since $1+\alpha_1<\gamma_1$, by the interpolation inequality for $L^p$ spaces, $$\|\rho_R\|_{1+\alpha_1}\leq C(M)\|\rho_R\|_{\gamma_1}^{\frac{4\alpha_1}{1+\alpha_1}}.$$ Hence $$\begin{aligned}
& \int_{F_n} \rho_R^{\frac{4}{3}+\alpha_1} \\
\leq & C_3(1+\mu)\|\rho_R\|_{\gamma_1}^{4\alpha_1}+ C \|\rho_R\|_{\gamma_1}^{2+\alpha_1} \\
\leq & C_3(1+\mu)\bigg(\int \rho_R^{\frac{4}{3}}\bigg)^{3\alpha_1} + C\bigg(\int \rho_R^{\frac{4}{3}}\bigg)^{\frac{3}{4}(2+\alpha_1)}\\
\leq & C_4(1+\mu)^{1+3\alpha_1}+C_4(1+\mu)^{\frac{3}{4}(2+\alpha_1)} \\
\leq & 2C_4(1+\mu)^{\frac{5}{3}}.\end{aligned}$$ Lemma \[chap3: lem: upper bound on rho\^4/3\] is needed for the penultimate step, and the last step follows from the choice of $\alpha_1$. Now let $n$ tend to infinity. Since the $F_n$’s increase to $E_R$, one gets $$\int_{E_R} \rho_R^{\frac{4}{3}+\alpha_1} \leq 2C_4(1+\mu)^{\frac{5}{3}}.$$ $$\begin{aligned}
\int \rho_R^{\frac{4}{3}+\alpha_1} & = \int_{E_R} \rho_R^{\frac{4}{3}+\alpha_1} + \int_{\rho_R\leq 10M} \rho_R^{\frac{4}{3}+\alpha_1} \\
& \leq 2C_4(1+\mu)^{\frac{5}{3}} + (10M)^{\frac{4}{3}+\alpha_1-1}M \\
& \leq C_5(1+\mu)^{\frac{5}{3}}.\end{aligned}$$ Or, $$\label{chap3: ineq: bound on 4/3 + alpha_1 norm}
\|\rho_R\|_{\frac{4}{3}+\alpha_1}\leq C_5(1+\mu)^{\frac{5}{4+3\alpha_1}}.$$ Here we assumed that we had chosen $\epsilon$ so small that $$\label{chap3: ineq: alpha_1,1}
\frac{4}{3}+\alpha_1 = \frac{14}{9}-\epsilon > \frac{3}{2}.$$ Let $b_1(\mathbf{x})=\frac{1}{|\mathbf{x}|}\chi_{S_1}(\mathbf{x})$ and $b_2(\mathbf{x})=\frac{1}{|\mathbf{x}|}-b_1(\mathbf{x})$. We have $B\rho_R=\rho_R*b_1 + \rho_R * b_2$. $$\label{chap3: ineq: bound on b2 part}
\|\rho_R * b_2\|_{\infty}\leq \|b_2\|_{\infty}\|\rho_R\|_{1}\leq C.$$ Now let us pick some $p$ between $1$ and $2$. Assume that we have chosen $\epsilon$ so small that the following is true $$\label{chap3: ineq: alpha_1,2}
\frac{1}{1-\frac{p}{5}(1+3\alpha_1)}>\frac{3}{2}.$$ Notice that since $\alpha_1=\frac{2}{9}-\epsilon<\frac{2}{9}$, $1-\frac{p}{5}(1+3\alpha_1)>1-\frac{p}{3}>0$. is equivalent to $\alpha_1>\frac{1}{3}(\frac{5}{3p}-1)$. Since the right hand side is less than $\frac{1}{3}(\frac{5}{3}-1)=\frac{2}{9}$, this is possible. Now choose $q$ satisfying $q>\frac{3}{2}$, $q<\frac{4}{3}+\alpha_1$, $q<\frac{1}{1-\frac{p}{5}(1+3\alpha_1)}$. That this is possible follows from and . Since $b_1\in L^{q'}$ for $1\leq q' < 3$, $$\begin{aligned}
\|\rho_R * b_1\|_{\infty} &\leq \|b_1\|_{q'}\|\rho_R\|_{q} \\
& \leq C(M)\|\rho_R\|_{\frac{4}{3}+\alpha_1}^a\end{aligned}$$ where $a=\frac{1-\frac{1}{q}}{1-\frac{1}{\frac{4}{3}+\alpha_1}}$, by the interpolation inequality for $L^p$ spaces. Now it follows from that $$\|\rho_R * b_1\|_{\infty} \leq C_6(1+\mu)^{\frac{5a}{4+3\alpha_1}}.$$ Combining this with , we get $$\|B\rho_R\|_{\infty}\leq C_7(1+\mu)^{\frac{5a}{4+3\alpha_1}}.$$ Let us calculate the exponent: $$\begin{aligned}
& \frac{5a}{4+3\alpha_1} \\
= & \frac{1-\frac{1}{q}}{1-\frac{1}{\frac{4}{3}+\alpha_1}} \frac{5}{4+3\alpha_1} \\
= & \frac{5(1-\frac{1}{q})}{1+3\alpha_1} < p\end{aligned}$$ by the choice of $q$. Therefore $$\label{chap3: ineq: power p bound on Brho}
\|B\rho_R\|_{\infty}\leq C_7(1+\mu)^p.$$ Now if $p\geq 3$, the same inequality is obviously true since it is already true for smaller exponents. Now let $\alpha_{l+1}=\alpha_{l}+\frac{1}{3}$. Define $$v_l=\begin{cases}
-\rho_R^{1+\alpha_l} \quad & \text{on } F_n \\
\int_{F_n}\rho_R^{1+\alpha_l} \quad & \text{on } D\\
0 \quad & \text{otherwise}
\end{cases}$$ and repeat the previous argment, only this time using the better estimate . That gives us $$\int \rho_R^{\frac{4}{3}+\alpha_l}\leq C_8(1+\mu)^p\int \rho_R^{1+\alpha_l},$$ or, $$\begin{aligned}
\int \rho_R^{1+\alpha_{l+1}} & \leq C_8(1+\mu)^p\int \rho_R^{1+\alpha_l} \\
& \leq (C_8(1+\mu)^p)^l \int \rho_R^{1+\alpha_1} \\
& \leq (C_9(1+\mu)^p)^l \int \rho_R^{\frac{4}{3}} \\
& \leq (C_9(1+\mu)^p)^l C (1+\mu).\end{aligned}$$ Therefore $$\begin{aligned}
\|\rho_R\|_{\infty} &= \lim_{l \to \infty} \|\rho_R\|_{1+\alpha_{l+1}}\\
& \leq \lim_{l\to \infty} (C_9(1+\mu)^p)^{\frac{l}{l+1}} (C (1+\mu))^{\frac{1}{l+1}}\\
& \leq C_9(1+\mu)^p.\end{aligned}$$ We now use this better bound on $\rho_R$ to estimate $$\begin{aligned}
\|\rho_R*b_1\|_{\infty} & \leq \|b_1\|_{2}\|\rho_R\|_2 \\
& \leq C(M)\|\rho_R\|_{\infty}^{\frac{1}{2}} \\
& \leq C_{10}(1+\mu)^{\frac{p}{2}}.\end{aligned}$$ Hence $$\label{chap3: ineq: heavy core sublinear growth in mu of Brho_R}
\|B\rho_R\|_{\infty}\leq C_{11}(1+\mu)^{\frac{p}{2}}.$$ Since we have chosen $p<2$, this grows at most linearly in $\mu$. We can now repeat the previous bootstrap argument with this better estimate on $\|B\rho_R\|_{\infty}$. One gets $$\int \rho_R^{\frac{4}{3}+\alpha_l}\leq C_{12}(1+\mu)\int \rho_R^{1+\alpha_l},$$ and the assertion of the lemma follows.
$\rho_R$ still satisfies variational equations like and for $R>R_1$. From here on, we will construct a series of bounds $R_n$ on the support of $\rho_R$, and a series of lower bounds $\mu_n$ for $\mu$. Let us emphasize from the beginning that although the $\mu_n$’s depend on $f$, $M$, $\Phi_K$ and $J$, the $R_n$’s are independent of $J$ and $\mu$. Also we always take $R_{n+1}\geq R_n$ and $\mu_{n+1}\geq \mu_n$.
\[chap3: lem: heavey core bound on lambda\_R\] There is an $R_2>0$ and a $\tilde{K}>0$ such that $\lambda_R\leq 1-\mu \tilde{K}$ for $R>R_2$.
One first observes that if $R>R_2>R_1$, there must be a point $\mathbf{x}\in S_{R_2}$ such that $$\rho_R(\mathbf{x})\leq \frac{M}{\frac{4}{3}\pi R_2^3}.$$ By , $$\label{chap3: ineq: heavy core bound on lambda_R}
\lambda_R \leq A'\bigg(\frac{M}{\frac{4}{3}\pi R_2^3}\bigg)-\mu \Phi_K(\mathbf{x}).$$ implies that $$\lim_{s\to 0}\frac{A'(s)}{s^{1/3}}=0.$$ Hence $$A'\bigg(\frac{M}{\frac{4}{3}\pi R_2^3}\bigg)=o(R_2^{-1}).$$ Pick $R_2$ large enough to make $A'\bigg(\frac{M}{\frac{4}{3}\pi R_2^3}\bigg)<1$, and let $\tilde{K}=\inf_{B_{R_2}}\Phi_K>0$. By , $$\lambda_R \leq 1-\mu \tilde{K}.$$
There is a $\mu_2>0$ such that if $\mu>\mu_2$ and $R>R_2$, $$\label{chap3: ineq: extra bound}
B\rho_R + \mu \Phi_K \geq \frac{\mu \tilde{K}}{2} \text{ where } \rho_R>0.$$
By and lemma \[chap3: lem: heavey core bound on lambda\_R\], $$A'(\rho_R)-B\rho_R - J -\mu \Phi_K = \lambda_R \leq 1-\mu \tilde{K}$$ where $\rho_R>0$. Hence $$B\rho_R +\mu \Phi_K \geq \mu \tilde{K}-1-J.$$ Pick $\mu_2>\frac{2(1+\|J\|_{\infty})}{\tilde{K}}$ to get the result.
\[chap3: lem: heavy core bound on support rho\_R\] There is a $\mu_3>0$ and an $R_3>0$ such that $\rho_R(\mathbf{x})=0$ if $R>|\mathbf{x}|>R_3$ and $\mu>\mu_3$.
We only need to prove $B\rho_R + \mu \Phi_K < \frac{\mu \tilde{K}}{2}$ in view of . By , $\|B\rho_R\|_{\infty}\leq C(1+\mu)^a$ for some $0<a<1$. We may choose $\mu_3$ so large that $\frac{C(1+\mu)^a}{\mu}<\frac{\tilde{K}}{4}$ when $\mu>\mu_3$, and $R_3$ so large that $\Phi_K(\mathbf{x})<\frac{\tilde{K}}{4}$ when $|\mathbf{x}|>R_3$. The lemma then follows.
The argument goes exactly as before. For the constant angular velocity case just notice that the $R_3$ in lemma \[chap3: lem: heavy core bound on support rho\_R\] only depends on $f$, $M$, $\Phi_K$ and not on $J$ and $\mu$, so we can construct a smooth increasing function $$J(r)=
\begin{cases}
\frac{1}{2}\Omega^2 r^2 \quad &\text{if }r<R_3, \\
\Omega^2 R_3^2 \quad & \text{if } r>2R_3,
\end{cases}$$ and find a $\mu_0$ such that a solution exists and is supported in $S_{R_3}$ if $\mu>\mu_0$.
Non-existence for Fast Rotation with Fixed Core Density {#chap3: non-existence}
=======================================================
We now show that a solution does not exist for large enough constant rotation if the core potential $\Phi_K$ is given by the gravity of a density function $\rho_K$. Let us start with a few estimates.
\[chap3: lem: nonexist L infty bound on B rho\] Let $\rho\in L^{\infty}(\mathbb{R}^3)$ be a non-negative function such that $\int \rho=M$, then there is a $C>0$ such that $$\|B\rho\|_{\infty}\leq C M^{\frac{2}{3}}\|\rho\|_{\infty}^{\frac{1}{3}}.$$
See [@friedman2010variational].
\[chap3: lem: nonexist L infty bound on B rho\_r\] Let $\rho\in L^{\infty}$ be a nonnegative function supported in the infinite cylinder $x_1^2+x_2^2\leq d^2$. Then there is a $C>0$, such that for $x_1^2+x_2^2 \leq d^2$, $$\label{chap3: ineq: upper bound on the r derivative of B rho}
|(B\rho) _r(\mathbf{x})|\leq C\|\rho\|_{\infty} \bigg(d+\sqrt{x_1^2+x_2^2}\bigg).$$ Here the subscript $r$ denotes directional derivative in the cylindrical radial direction, even if the function under consideration is not axisymmetric.
Without loss of generality, we may assume $x_1\geq 0,x_2=0,x_3=0$. $$\begin{aligned}
|(B\rho)_r(x_1,0,0)| &\leq \bigg| \int_{\textbf{supp}\rho}\frac{\rho(x_1',x_2',x_3')(x_1-x_1')}{\sqrt{(x_1'-x_1)^2+x_2'^2+x_3'^2}^3}dx_1'dx_2'dx_3' \bigg| \notag \\
& \leq \int_{\textbf{supp} \rho \cap \{x_1'<x_1\}}\frac{\|\rho\|_{\infty}(x_1-x_1')}{\sqrt{(x_1'-x_1)^2+x_2'^2+x_3'^2}^3}dx_1'dx_2'dx_3' \notag \\
& \leq \|\rho\|_{\infty} \int_{-d<x_1'<x_1}\frac{x_1-x_1'}{\sqrt{(x_1'-x_1)^2+x_2'^2+x_3'^2}^3}dx_1'dx_2'dx_3' \notag \\
& = C\|\rho\|_{\infty} (d+x_1). \notag\end{aligned}$$ The last equality follows either from a direct calculation or a simple application of the divergence theorem.
\[chap3: lem: Holder and Lip continuity of Phi\_K\] Let $l=\sup \big\{|x_3|~\big| ~ (x_1,x_2,x_3)\in K\big\}+1$, $Z=\big\{(x_1,x_2,x_3)~\big|~ |x_3|\leq l\big\}$. Then $\Phi_K|_Z=B\rho_K|_Z \in C^{1,\frac{3}{q}}(\bar{Z})$, $\Phi_K|_{\mathbb{R}^3\setminus Z}=B\rho_c|_{\mathbb{R}^3 \setminus Z} \in C^{1,1}(\overline{ \mathbb{R}^3 \setminus Z})$.
We first estimate $\Phi_K|_{\mathbb{R}^3\setminus Z}$: $$\Phi_K(x_1,x_2,x_3)=\int_{\textbf{Supp}\rho_K}\frac{\rho_K(x_1',x_2',x_3')}{\sqrt{(x_1-x_1')^2+(x_2-x_2')^2+(x_3-x_3')^2}}dx_1'dx_2'dx_3'.$$ Since $(x_1,x_2,x_3)$ is bounded away from $\textbf{Supp}\rho_K$, we can differentiate under the integral sign and see that $$\begin{aligned}
|D\Phi_K(x,y,z)|&\leq C \int_{\textbf{Supp}\rho_K}\frac{\rho_K(x_1',x_2',x_3')}{\sqrt{(x_1-x_1')^2+(x_2-x_2')^2+(x_3 - x_3')^2}^2}dx_1'dx_2'dx_3' \\
&\leq C\int_{\textbf{Supp}\rho_K}\rho_K(x_1',x_2',x_3')dx_1'dx_2'dx_3' \\
&\leq C\|\rho_K\|_1\\
&\leq \tilde{C}\|\rho_K\|_{q}^q.\end{aligned}$$ In the above inequalities, the second line is because $|x_3-x_3'|\geq 1$, the last line is because $\textbf{Supp}\rho_K$ is compact. We can give a similar estimate for $D^2\Phi_K$, therefore $\Phi_K|_{\mathbb{R}^3\setminus Z} \in C^{1,1}(\mathbb{R}^3\setminus Z)$. As for $\Phi_K|_Z$, the Lipschitz continuity of the first derivative in a neighborhood of $\infty$ follows in the same way as above, whereas the Hölder continuity of the first derivative in a neighborhood of $\textbf{Supp}~\rho_K$ follows from the standard Calderon-Zygmund inequality and the Sobolev embedding theorem.
From now on, we assume $\Omega$ is at least $1$ and use cylindrical coordinates $(r,\theta,z)$. Let us suppose, contrary to the assertion of theorem \[chap3: thm: nonexistence of solution\], that there is such a $\rho$ satisfying all the properties stated.
\[chap3: lem: bound on d\] $d=\sup\big\{r~\big|~(r,\theta,z)\in \bf{Supp} \rho\big\}<\infty$.
By , $$\frac{1}{2}r^2\leq \frac{1}{2}\Omega^2 r^2 \leq A'(\rho)-B\rho - \Phi_K -\lambda \leq A'(\rho)-\lambda.$$ We know that $A'(s)=\int_0^s \frac{f(t)}{t^2}dt+\frac{f(s)}{s}$. It follows from and that $A'(\rho)\in L^{\infty}$ if $\rho$ is.
By the expression of $A'(s)$ in the proof, we see that $A'(\rho)>0$ iff $\rho>0$.
\[chap3: lem: size of lambda\] $\lambda \leq -\frac{1}{2}\Omega^2 d^2$.
Pick a sequence $(r_n,\theta_n,z_n)$ such that $\rho(r_n,\theta_n,z_n)>0$, and $r_n\to d$. We claim that $A'(\rho)(r_n,\theta_n,z_n)\to 0$. If not, a subsequence will be bounded away from zero. Without loss of generality, we still call that subsequence $A'(\rho)(r_n,\theta_n, z_n)$. By the no trapping condition, $A'(\rho)(r,\theta_n,z_n)$ is defined for all $r>r_n$, in particular we have $A'(\rho)(d,\theta_n,z_n)=0$. By Rolle’s theorem there is an $r_n^*$ between $r_n$ and $d$ such that $A'(\rho)(r_n^*,\theta_n, z_n)>0$ and $(A'(\rho))_r(r_n^*,\theta_n, z_n) \to -\infty$. By and the smoothing effect of $B$, $A'(\rho)$ is differentiable when positive. Differentiating , we get $$\label{chap3: eq: force balance in the r direction}
(A'(\rho))_r-\Omega^2 r -(B\rho)_r-(\Phi_c)_r=0.$$ We see a contradiction if we evaluate this expression at $(r_n^*,\theta_n, z_n)$: the first term goes to $-\infty$ while the last three terms are bounded by lemma \[chap3: lem: bound on d\], lemma \[chap3: lem: nonexist L infty bound on B rho\_r\] and lemma \[chap3: lem: Holder and Lip continuity of Phi\_K\] respectively. Now evaluate at $(r_n,\theta_n,z_n)$. By the limit of $A'(\rho)(r_n,\theta_n,z_n)$ and the positivity of $B\rho$ and $\Phi_K$, we get the desired result.
\[chap3: lem: nonexistence l infinity bound on rho\] There is a constant $C_1>0$, depending on $\Phi_K$, $f$ and $M$, such that $\|\rho\|_{\infty}\leq C_1$.
By lemma \[chap3: lem: size of lambda\], $$A'(\rho)\leq B\rho +\Phi_K.$$ By , there is a $C>0$ such that if $s>C$, $$Cs ^{\gamma-1}\leq A'(s).$$ Hence either $\rho<C$ or $C\rho^{\gamma -1}\leq B\rho +\Phi_K$. Therefore $$C\|\rho\|_{\infty}^{\gamma -1}\leq C^{\gamma}+\|\Phi_K\|_{\infty}+CM^{\frac{2}{3}}\|\rho\|_{\infty}^{\frac{1}{3}}.$$ The last term follows from lemma \[chap3: lem: nonexist L infty bound on B rho\]. Here we have taken the liberty of using the same constant $C$. Now take $\epsilon>0$ so small that $\epsilon M^{\frac{2}{3}}<\frac{1}{2}$. Since $\gamma-1>\frac{1}{3}$, we have $$\|\rho\|_{\infty}^{\frac{1}{3}}\leq \epsilon \|\rho\|_{\infty}^{\gamma -1} + C(\epsilon).$$ It follows that $$\begin{aligned}
C\|\rho\|_{\infty}^{\gamma -1} &\leq C^{\gamma}+\|\Phi_K\|_{\infty}+\frac{1}{2}C\|\rho\|_{\infty}^{\gamma -1} + C(M)\\
\frac{1}{2}C\|\rho\|_{\infty}^{\gamma -1} &\leq C^{\gamma}+\|\Phi_K\|_{\infty} + C(M).\end{aligned}$$ The assertion now follows from the fact that $\Phi_K \in L^{\infty}(\mathbb{R}^3)$.
\[chap3: lem: nonexist uniform bound on d\] There is an $\Omega_1>0$ and $0<d_0<\frac{1}{4}$ such that if $\Omega>\Omega_1$, then $d<d_0$.
Pick an $(r,\theta,z)$ such that $\rho(r,\theta,z)>0$, $r>\frac{d}{2}$. Then there is an $r^*$ between $r$ and $d$ such that $(A'(\rho))_r(r^*, \theta, z)\leq 0$. Evaluating at this point, we have $$\begin{aligned}
& \Omega^2\frac{d}{2}\leq \Omega^2 r^* \notag \\
\leq &(B\rho)_r(r^*,\theta,z) + (\Phi_K)_r(r^*,\theta,z).\notag\end{aligned}$$ The first term above is bounded by $2CC_1d$ by lemma \[chap3: lem: nonexist L infty bound on B rho\_r\] and \[chap3: lem: nonexistence l infinity bound on rho\]. Noticing $(\Phi_K)_r(0,\theta,z)=0$ by axisymmetry, the second term above is therefore bounded by $Cd^{\frac{3}{q}}$ by lemma \[chap3: lem: Holder and Lip continuity of Phi\_K\]. Now we have $$\begin{aligned}
\Omega^2 \frac{d}{2} \leq \tilde{C}(d+d^{\frac{3}{q}})\notag \\
(\frac{\Omega^2}{2}-\tilde{C})d^{1-\frac{3}{q}} \leq \tilde{C}, \label{chap3: ineq: nonexist crucial ineq}\end{aligned}$$ and the assertion follows.
\[chap3: lem: nonexist Holder continuity of rho on B\] $\rho\in C^{0,\alpha}(\bar{S})$ for some $0<\alpha<1$, where $S$ is any ball of radius $\frac{1}{2}$ whose center is on $(\mathbb{R}^3\setminus Z) \cap x_3$-axis, and we have $\|\rho\|_{C^{0,\alpha}(\bar{S})}\leq C_2$. Here $C_2$ is a constant depending on $\Phi_K$ $f$ and $M$, and $Z$ is the region given in lemma \[chap3: lem: Holder and Lip continuity of Phi\_K\].
We first observe that since $A''(s)=\frac{f'(s)}{s}$, $A'(s)$ is strictly increasing. Also notice that $A'(0)=0$. By , $A'(\rho)$ is uniformly Lipschitz continuous on $S\cap \{\rho>0\}$ and continuous on $S$, hence is uniformly Lipschitz continuous on $S$. It is sufficient to prove $$|\rho(\mathbf{x})-\rho(\mathbf{y})|\leq \tilde{C_2}|A'(\rho(\mathbf{x}))-A'(\rho(\mathbf{y}))|^{\alpha},$$ or $$A'(t)-A'(s)\geq \tilde{C_2}(t-s)^{\frac{1}{\alpha}}$$ for $0\leq s<t \leq \|\rho\|_{\infty}\leq C_1$. By there exists a $C>0$ such that $f'(s)\geq Cs^{\mu}$ for $0\leq s \leq \|\rho\|_{\infty}\leq C_1$. Now let $u=t-s$, $$\begin{aligned}
& (A'(t)-A'(s))(t-s)^{-\frac{1}{\alpha}} \notag \\
= & (A'(s+u)-A'(s))u^{-\frac{1}{\alpha}} \notag \\
= & u^{-\frac{1}{\alpha}} \int_s^{s+u}A''(\xi)d\xi \notag \\
= & u^{-\frac{1}{\alpha}} \int_s^{s+u}\frac{f'(\xi)}{\xi}d\xi \notag \\
\geq & u^{-\frac{1}{\alpha}} \int_s^{s+u}\frac{C\xi ^{\mu}}{\xi}d\xi \notag \\
= &\tilde{C}u^{-\frac{1}{\alpha}}((s+u)^{\mu}-s^{\mu}) \label{chap3: eq: lower bound on (A'(s+u)-A'(s))u^ 1/alpha imdt step}\end{aligned}$$ If $\mu \geq 1$, is equal to $$\begin{aligned}
& \tilde{C} \bigg[\bigg(1+\frac{s}{u}\bigg)^{\mu}-\bigg(\frac{s}{u}\bigg)^{\mu}\bigg]u^{\mu-\frac{1}{\alpha}} \notag \\
\geq &\tilde{C} u^{\mu-\frac{1}{\alpha}} \notag \\
\geq &\tilde{C} C_1^{\mu-\frac{1}{\alpha}}\geq \tilde{C_2}>0. \notag\end{aligned}$$ The last step is correct if we choose $\alpha < \frac{1}{\mu}$. On the other hand if $0<\mu<1$, is equal to $\tilde{C}\mu \xi ^{\mu-1} u^{1-\frac{1}{\alpha}}$, where $\xi$ is between $s$ and $s+u$. This in turn is greater than or equal to $$\begin{aligned}
\tilde{C}\mu C_1^{\mu -1} u^{1-\frac{1}{\alpha}} \geq \tilde{C}\mu C_1^{\mu -1} C_1^{1-\frac{1}{\alpha}} \geq \tilde{C_2}>0\notag \end{aligned}$$ if we choose an $\alpha<1$.
\[chap3: lem: nonexist bound on supp rho in z direction\] There is an $\Omega_2>0$ such that if $\Omega>\Omega_2$, $\rho_{\mathbb{R}^3\setminus Z} \equiv 0$. Here $Z$ is the region given in lemma \[chap3: lem: Holder and Lip continuity of Phi\_K\].
We first show that $\|B\rho\|_{C^{1,1}(\bar{S_1})}$ is uniformly bounded, where $S_1$ is any ball of radius $\frac{1}{4}$ whose center is on $(\mathbb{R}^3\setminus Z) \cap x_3$-axis. Let $S$ be a ball concentric with $S_1$ of radius $\frac{1}{2}$, then $B\rho= B(\rho\chi_{S})+B(\rho\chi_{\mathbb{R}^3 \setminus S})$. The first term is bounded in $C^{2,\alpha}(\bar{S_1})$ by lemma \[chap3: lem: nonexist Holder continuity of rho on B\] and elliptic Schauder estimates. The second term is bounded in $C^2(\bar{S_1})$ by a direct differentiation under the integral sign argument since $\mathbb{R}^3 \setminus S$ is bounded away from $S_1$.
We first pick $\Omega>\Omega_1$ so that $d<d_0<\frac{1}{4}$. Now suppose $\rho(r,\theta,z)>0$ for some $(r,\theta,z)$ in $\mathbb{R}^3 \setminus Z$. Let us switch to Cartesian coordinates for the moment and, without loss of generality, denote this point $(x,0,z)$ with $x\geq 0$. Let $x^*=\sup\big\{x~\big|~ \rho(x,0,z)>0\big\}$. There must be a sequence $x_n\to x^*$ such that $\rho(x_n,0,z)>0$ and $(A'(\rho))_x(x_n,0,z)\leq 0$, differentiating with respect to $x$ and evaluating at $(x_n,0,z)$, we have $$\Omega^2 x_n\leq -(B\rho)_x(x_n,0,z) - (\Phi_K)_x(x_n,0,z).$$ Taking limit as $n \to \infty$, we get $$\label{chap3: ineq: local 1}
\Omega^2 x^*\leq -(B\rho)_x(x^*,0,z) - (\Phi_K)_x(x^*,0,z).$$ If there was an $x_0 \in [0,x^*)$ such that $\rho(x_0,0,z)>0$ and $(A'(\rho))_x(x_0,0,z)\geq 0$, we would have $$\label{chap3: ineq: local 2}
\Omega^2 x_0\geq -(B\rho)_x(x_0,0,z) - (\Phi_K)_x(x_0,0,z).$$ Subtracting from , we get $$\begin{aligned}
\label{chap3: ineq: local 3}
\Omega^2 (x^*-x_0) \leq \big((B\rho)_x(x_0,0,z)-(B\rho)_x(x^*,0,z)\big) \notag \\
+\big((\Phi_K)_x(x_0,0,z)- (\Phi_K)_x(x^*,0,z)\big).\end{aligned}$$ The first term on the right hand side is bounded by $C(x^*-x_0)$ because $B\rho$ is uniformly bounded in $C^{1,1}(\bar{S_1})$ as indicated above, while the second term is bounded by $C(x^*-x_0)$ because of lemma \[chap3: lem: Holder and Lip continuity of Phi\_K\]. Hence becomes $$\Omega^2 (x^*-x_0) \leq 2C(x^*-x_0),$$ which is impossible if we choose $\Omega_2 > \max\{\Omega_1, 2C\}$. Therefore such an $x_0$ does not exist. This in particular implies that there is no $x\in [0,x^*)$ for which $\rho(x,0,z)=0$, which then implies that $\rho(0,0,z)>0$ and $(A'(\rho))_x(0,0,z)<0$. But exactly the same argument in the $-x$ direction would imply $(A'(\rho))_x(0,0,z)>0$. This contradiction indicates that there is no such $(r,\theta,z)$ in the first place, and the assertion is therefore true.
We are now ready to give
By lemma \[chap3: lem: nonexist bound on supp rho in z direction\], $\bf{Supp}\rho$ is uniformly bounded in the $z$ direction. Recall from lemma \[chap3: lem: Holder and Lip continuity of Phi\_K\] that this bound is given by $l$, $$\begin{aligned}
M& =\int_{\bf{Supp} \rho}\rho \notag \\
& = \int_{|z|\leq l, r\leq d}\rho \notag\\
& \leq \|\rho\|_{\infty}2\pi d^2 l \notag\\
& \leq 2C_1\pi d^2 l.\end{aligned}$$ Therefore $$d\geq \sqrt{\frac{M}{2C_1\pi l}}.$$ Compare this with , we get $$(\frac{\Omega^2}{2}-\tilde{C})\sqrt{\frac{M}{2C_1\pi l}}^{1-\frac{3}{q}} \leq \tilde{C},$$ which is clearly false if we choose $\Omega_0>\Omega_2$ sufficiently large. This contradiction indicates that such a solution $\rho$ does not exist.
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What Is the Equivalent of 1 Liter in Gallons?
One liter is the equivalent of approximately 0.2642 gallons. As both terms are measurements of volume, one can convert between the two by utilizing the fact that there are about 3.785 liters per gallon.
To convert liters to gallons, one can either divide the number of liters by 3.785 or multiply it by 0.2642. In order to convert from gallons to liters, one must do the opposite, either multiplying by 3.785 or dividing by 0.2642. Though not exact, these calculations result in a close approximation, especially when the volumes used are relatively small. On very large scales, however, it would be more accurate to use the United States' officially recognized conversion rate of exactly 3.785411784 liters per gallon. When referring to the Imperial Gallon, the conversion rate is 4.54609 liters per gallon. |
I'm not sure if they will move in the future but jemimah is welcome to leave them on my site.
Smokey01.com will remain the primary mirror but I think I've figured out how to automatically sync the repo at saluki-linux.com. This should only download the changed packages - not the whole repo every time.
Smokey01, just in case you ever want to mirror something, here's what I've learned so far.
It is possible to get ssh access at Hostgator, but you may need to open a ticket. Once you can login with ssh it's pretty easy to test commands like the one above. Plus you can do things you can't do with ftp, like create symlinks.
Once the syncing command is perfected, it should be possible to schedule it to run periodically with cron._________________http://saluki-linux.com
Saluki runs very well. any way of getting pulseaudio working on it? pulseaudio doesn't appear to be of high importance in puppy world.
is there a better or equal way of using a bluetooth stereo headset on linux...without all the commandline song and dance?
Last time I tried, bluetooth audio was possible, but still quite a hassle. When I get back to my desk on Thursday, I'll get out my bluetooth speaker and see if I can get it to work and write a tutorial._________________http://saluki-linux.com
You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot vote in polls in this forumYou cannot attach files in this forumYou can download files in this forum |
Q:
SQL query with count() from another table
I got the following tables:
pictures
------------------------------------
id
name
views
votes
------------------------------------
id
user_id
pic_id
I want to get a result from a query that will give me each picture id, with the views of the picture, and the total votes from the table votes for the specific pic_id
example:
pictures.id, pictures.views, total votes
1 ------------ 78------------------ 123
2 ------------ 23------------------- 69
and so on...
The code I tried:
SELECT `pictures`.`id`,`pictures`.`views`, COUNT(`votes`.`pic_id`) as votes
FROM `pictures`
JOIN `votes`
ON `pictures`.`id` = `votes`.`pic_id`
But it doesn't give me the reuslt I desire.
A:
You need to have GROUP BY clause.
The use of LEFT JOIN will display all records on table pictures with or without matching record on table votes.
SELECT a.id, a.name, a.views,
COUNT(b.pic_id) TotalVotes
FROM pictures a
LEFT JOIN votes b
ON a.id = b.pic_id
GROUP BY a.id, a.name, a.views
|
Q:
Units in Dense layer in Keras
I am trying to understand a concept of ANN architecture in Keras. Number of input neurons in any NN should be equal to the number of features/attributes/columns. So, in the case of having matrix of (20000,100), my input shape should have 100 neurons. In the example on the Keras page, I saw a code:
model = Sequential([Dense(32, input_shape=(784,)),
, which pretty much means that input shape has 784 columns and 32 is the dimensionality of output space, which pretty means that the second layer will have an input of 32. My understanding is that such a significant drop happens because some of the units are not activated due to an activation function. Is my understanding correct?
At the same time, another piece of code, shows that number of input neurons is higher than number of features:
model = Sequential()
model.add(Dense(64, activation='relu', input_dim=20))
model.add(Dropout(0.5))
model.add(Dense(64, activation='relu'))
model.add(Dropout(0.5))
model.add(Dense(10, activation='softmax'))
This example is not clear to me. How can it be that the size of units is larger that number of input dimensions?
A:
Neural Networks are basicly matrix multiplications, the drop you are talking about in the first part is not due to an Activation function, it's only happen because of the nature of matrix multiplication :
The calcul here is : input * weights = output
so -> [BATCHSIZE, 784] * [784, 32] = [BATCHSIZE, 32] -> output dimension
With that logic we can easily explain how we can have an input shape << size of units, it will give this calcul :
-> [BATCHSIZE, 20] * [20, 64] = [BATCHSIZE, 64] -> output dimension
Hope that helped you !
To learn more :
https://en.wikipedia.org/wiki/Matrix_multiplication
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HOW TO REMOVE UP TO 20 POUNDS OF WASTE FROM YOUR COLON BY 2PM
It’s almost hard to believe that 10-20 pounds of waste could be stuck in your colon, but it turns out that the colon is a pretty big place. And from time to time it may need a little help getting out all of those toxins built up over time.
These supposed toxins are rarely described by cleansers in detail, but generally referred to as “poisons” or “pollutants.” In the medical field, toxins can refer to just about anything, from alcohol, to foods, to medicines, to asbestos.
“Detoxing” can also refer to treatment for drug addiction, but that’s very different—here, we’re specifically discussing these food-and-drink cleanses. Your liver eliminates toxins from the body, but its function depends on the condition of your colon. The same applies to every cell in the body.
THE WASTE FROM YOUR LIVER, BLOOD, LYMPH, THROAT, LUNGS, AND SINUSES ENDS UP IN THE COLON.
Nutrient leftovers also end in the colon. If your colon is “blocked,” none of these functions will give proper results. Toxic buildups cause severe health problems, meaning that you have to clean your colon more often.
The digestion of food lasts for 22-24 hours. The food you eat has plenty of time to travel through your digestive tract and the colon. Once your body is done digesting it, food leftovers are eliminated in the form of a toxic waste.
It takes 70 hours for the body to digest nutrient-deficient food. The waste accumulates in your colon, and you end up dealing with severe constipation and irregular bowel movement.
Dona Gates, the founder of Body Ecology, says that a healthy digestive system is important for the overall health.
Here are the most common symptoms of colon toxicity:
Diarrhea, stomachache, gas, bloating, indigestion, constipation
Joint and muscle pain
Vaginal infections, poor immunity, skin rashes, bladder problems
Anxiety, memory loss, depression, fatigue, mood swings, brain fog
Have you ever done a colon cleanse? It’s extremely effective, and you will never ever deal with a “clogged” colon again. We have a couple of nice suggestions, and it’s up to you to decide what works best for your body.
DON’T STARVE YOURSELF
Be sure to eat a slow-carb diet with any cleanse despite what common juicing trends suggest.
If you drink nothing but juice/colon cleanse for a week, you’ll lose weight, but it’s because you’re not eating, not because your body is “detoxing”. Water is stored in your muscles with glycogen. When you eat a low-calorie diet, you use up those glycogen stores, and lose the water weight with it.
You’ll gain that water weight right back when you return to your normal diet. You’re also missing out on all those other vital nutrients like fat, fiber, and protein. In fact, some cleanses suggest that you avoid exercise when you’re on them because your caloric intake is so low—which leads to fatigue and dizziness. |
Point-of-care testing. Impact on medical outcomes.
There is now clear evidence that POCT has a positive benefit on morbidity and mortality. In addition, there are other tangible benefits that may themselves influence morbidity and mortality, e.g., reduced blood sample requirement in pediatrics, reduced length of stay, and greater doctor and patient satisfaction. These benefits accrue from the ability to make decisions and implement the appropriate intervention more quickly. It has also been demonstrated that POCT can facilitate improved patient motivation and satisfaction and thereby compliance with a prescribed disease management strategy. Improvement in health outcome, morbidity, and mortality can only be achieved, however, when the diagnostic and therapeutic interventions operate in concert. A review of the literature on medical outcomes of POCT has demonstrated the complexity of establishing evidence and the paucity of robust literature that exists at the present time. It is hoped, however, that the reader will appreciate how important it is to stress the role of a diagnostic test in decision making, to ensure that decisions are made and that benefits will be achieved. From a more pragmatic standpoint, however, it is hoped the reader will see the potential value of the arguments put forward in favor of implementing POCT when submitting a business case to a funding authority; the fact that the cost of POCT may be greater should not be a deterrent. |
Q:
How to identify AudioStreamer isBuffering state or As_Waiting_for_queue_to_start state?
Continue from previous question
I found that when I am having slow streaming from internet and I click next and Previous buttons then two or more song starts because when a new instance of AudioStreamer is created and State of AudioStreamer is neither of isPause, isIdle or isStop.
But actually a new Thread starts inside AudioStreamer class and has isBuffering or As_WAITING_FOR_QUEUE_TO_START state.
My question is how can i identify this states so that when I click Next button twice then only 1 song starts and other request is rejected?
Please help in this regards.. thanx
A:
Actual problem i was having is when my song is being stream and i click next then 2 songs started toghther.
So I found that this is a bug in AudioStreamer Class and the solution to this could be something as link given on gitHub
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Free Panel to Make 16-bit Luminosity Masks
Lately I’ve been experimenting with several features that could make Photoshop extension panels easier to install and use. To test some of these new elements, I’ve created a mini-panel (image below) focused on just making 16-bit luminosity masks, like the downloadable actions that were available in the previous blog posts. With the new custom panel these same actions can now be run with a click of a button instead of having to play them from Photoshop’s regular Actions panel. The new panel can be downloaded free at this website.
It’s a very simple panel overall and provides the easiest way yet to quickly generate the Lights, Darks, and Midtones series of luminosity masks using the new 16-bit process. The luminosity masks generated are placed on the Channels panel, so check there for the results after clicking one of the buttons. Luminosity masks can do many things, and it’s up to the user to determine which mask they want to use and how to use it for their image. Techniques for using luminosity masks are described in the tutorials section of my website.
The CC and CS6 versions look slightly different, but do the same thing. They also have slightly different installation procedures. The complete Instructions PDF describes how to install the panel, how to use it, and also has some trouble-shooting tips. Please take a few minutes to read it before installing the panel to help insure that the process goes smoothly.
Once installation is complete on any compatible version of Photoshop, open Photoshop and click through the menu commands Window > Extensions > TK. The panel should appear. Once available, it can be opened, closed, and docked to a panels bar just like over Photoshop panels. An image needs to be open for most of the buttons to work.
This is my first experience with the new features and distribution method. If there are problems, please let me know. We can try and work them out together.
Thanks Tony, for your continuing development of your actions. Like someone before me said, everyone is jumping on the bandwagon but few are crediting you with your work. They installed flawlesly. Will there be a 16 bit Triple Play down the road?
Hi Tony,Thank you so much for the new ‘TK-mini Panel’ !! Installed flawlessly, and while I’ve just barely got my feet wet with it, I like it’s compactness.The idea of being able to add/subtract each group separately leaves a less cluttered working area. Thanks again, Tony, stay well, Emerson E Liley Jr
Hello Tony, I hope all is well with you. Thank you for the mini-panel. I hope it is a portent of another great iteration of the full version, which I still use on every processed image. The panel installed exactly as it was supposed to install. I added it to cc 2014 and CS6. Really looking forward to easy 16 bit renditions. My best always, Guy |
FUCT Fall/Winter 2010 Releases
The latest release from FUCT features a few carefully curated pieces that span a more formal monogrammed Oxford shirt, to the camouflage down vest pictured above. Overall, it’s a nice collection of basic items that would round out any sartorialists wardrobe. Available here. |
?
-20, 1, 134
Factor p**2/6 + 77183*p/3 + 5957215489/6.
(p + 77183)**2/6
Solve -38*t**2/9 - 2754*t - 6520/9 = 0 for t.
-652, -5/19
Factor 3*g**4/2 - 29163*g**3/2 + 46838610*g**2 - 48363582984*g - 4345257271584.
3*(g - 3268)**3*(g + 83)/2
Factor -2*x**2/13 - 42580*x/13 - 226632050/13.
-2*(x + 10645)**2/13
Let -16*r**5 - 109176*r**4 + 273063*r**3 + 156938*r**2 - 409596*r - 245736 = 0. Calculate r.
-6826, -3/4, 2
Factor d**4 + 15*d**3 + 8*d**2 - 84*d.
d*(d - 2)*(d + 3)*(d + 14)
Factor n**2/4 - 7913*n/4 - 5937.
(n - 7916)*(n + 3)/4
Suppose x**5/5 - 118*x**4/5 - 1256*x**3/5 - 3082*x**2/5 + 251*x + 640 = 0. What is x?
-5, -1, 1, 128
Factor d**2 - 154*d + 3528.
(d - 126)*(d - 28)
Factor 2*r**4 - 9482*r**3 + 11252750*r**2 - 33672966*r.
2*r*(r - 2369)**2*(r - 3)
Find v such that -5*v**2/2 + 430*v - 855/2 = 0.
1, 171
Let 2*m**3/3 + 22664*m**2/3 + 64568200*m/3 + 2043040000/3 = 0. What is m?
-5650, -32
Factor -4*c**2 - 944*c - 12432.
-4*(c + 14)*(c + 222)
Factor -3*l**3/2 + 42*l**2 + 3*l/2 - 42.
-3*(l - 28)*(l - 1)*(l + 1)/2
Let -2*w**5/9 - 128*w**4/9 + 692*w**3/9 + 128*w**2/9 - 230*w/3 = 0. What is w?
-69, -1, 0, 1, 5
Factor 21*b**3 + 73919*b**2 - 77470*b - 28168.
(b + 3521)*(3*b - 4)*(7*b + 2)
Determine q, given that q**2/3 + 551*q/3 + 548 = 0.
-548, -3
Let 72*d**5/7 + 3302*d**4/7 + 30714*d**3/7 - 38982*d**2/7 + 562*d + 960/7 = 0. What is d?
-32, -15, -1/9, 1/4, 1
What is o in 5*o**3 + 48355*o**2 + 117079360*o + 817187840 = 0?
-4832, -7
Factor -2*n**2/13 - 275176*n/13 - 9465228872/13.
-2*(n + 68794)**2/13
Solve 1534523929*u**2/4 - 195865*u/2 + 25/4 = 0.
5/39173
What is a in 13*a**2/2 - 26142*a - 4022 = 0?
-2/13, 4022
Determine w so that -5*w**5/4 + 847*w**4/4 - 7557*w**3/4 + 5873*w**2/4 + 3781*w/2 - 1680 = 0.
-1, 1, 42/5, 160
Factor -3*x**3 - 537*x**2 + 5598*x - 13608.
-3*(x - 6)*(x - 4)*(x + 189)
Factor 2*v**4/17 - 164*v**3 - 154440*v**2/17 - 2803248*v/17 - 16889472/17.
2*(v - 1448)*(v + 18)**3/17
Suppose 3*s**5/2 - 84*s**4 - 1170*s**3 - 3720*s**2 + 2976*s + 19584 = 0. What is s?
-6, -4, 2, 68
Suppose 4*l**2 + 1361348*l = 0. Calculate l.
-340337, 0
Factor -6141330075*y**3 - 12282388680*y**2 + 542937*y - 6.
-3*(y + 2)*(45245*y - 1)**2
Determine b so that -b**4 + 1399*b**3 + 7014*b**2 + 8424*b = 0.
-3, -2, 0, 1404
Let 11*s**3 - 279090*s**2 + 228337*s + 50742 = 0. What is s?
-2/11, 1, 25371
Find a such that -a**2 + 742919*a = 0.
0, 742919
Determine d so that -36*d**3/7 + 12144*d**2/7 - 5740*d + 33400/7 = 0.
5/3, 334
Determine w so that -w**4/2 - 27*w**3/2 - 83*w**2/2 + 243*w/2 + 414 = 0.
-23, -4, -3, 3
Let -3*w**5 + 2730*w**4 - 581454*w**3 - 18136644*w**2 - 79457511*w - 91063854 = 0. Calculate w.
-23, -3, -2, 469
What is v in -2*v**4/13 - 176*v**3/13 + 926*v**2/13 - 388*v/13 - 1488/13 = 0?
-93, -1, 2, 4
Factor -2*z**4/11 + 1152*z**3/11.
-2*z**3*(z - 576)/11
Determine n so that -20*n**3 - 1952*n**2 + 53584*n - 21120 = 0.
-120, 2/5, 22
Factor 3*w**2/7 + 204*w/7.
3*w*(w + 68)/7
Factor 273207841*k**2/3 + 66116*k/3 + 4/3.
(16529*k + 2)**2/3
Factor -2*l**5/5 - 8*l**4/5 - 8*l**3/5.
-2*l**3*(l + 2)**2/5
Let 5*u**5 - 1335*u**4 + 87090*u**3 + 269330*u**2 + 272025*u + 91125 = 0. Calculate u.
-1, 135
Let 2*a**3/7 - 6088*a**2/7 + 36474*a/7 - 7812 = 0. What is a?
3, 3038
Solve -m**3 - 26*m**2 - 215*m - 550 = 0.
-11, -10, -5
Let 11*v**4/4 + 2235*v**3/4 + 181*v**2/2 - 2235*v - 406 = 0. What is v?
-203, -2, -2/11, 2
Factor 4*d**4/3 - 1936*d**3/3 + 11292*d**2 - 50328*d.
4*d*(d - 466)*(d - 9)**2/3
Factor -2*p**2/7 - 2152*p/7 - 36006/7.
-2*(p + 17)*(p + 1059)/7
Solve l**2/3 + 20732*l/3 + 20731/3 = 0 for l.
-20731, -1
Factor 5*t**2 - 9350*t + 4371125.
5*(t - 935)**2
Let -y**2 + 186678*y - 8712168921 = 0. Calculate y.
93339
Find m, given that m**5/4 - 58*m**4 - 1897*m**3/4 - 1373*m**2 - 1677*m - 720 = 0.
-3, -2, -1, 240
Find m, given that 2*m**5/5 - 224*m**4 - 3374*m**3/5 - 2252*m**2/5 = 0.
-2, -1, 0, 563
Find d, given that -14*d**5 - 1242*d**4 - 8898*d**3 - 12182*d**2 - 2568*d + 1944 = 0.
-81, -6, -1, 2/7
Let -c**2 + 96294*c - 2318133609 = 0. What is c?
48147
Solve s**2 - 75*s - 8100 = 0 for s.
-60, 135
Factor 3*l**5 + 678*l**4 + 5232*l**3.
3*l**3*(l + 8)*(l + 218)
Factor 2*p**2 + 67432*p - 67434.
2*(p - 1)*(p + 33717)
Factor 3*z**3 + 61710*z**2 + 123411*z + 61704.
3*(z + 1)**2*(z + 20568)
Let t**2 - 228766*t + 13083470689 = 0. What is t?
114383
Let -y**5 + 523*y**4 - 2081*y**3 + 2597*y**2 - 1038*y = 0. Calculate y.
0, 1, 2, 519
Factor -5*u**3 + 219460*u**2 - 877780*u + 877760.
-5*(u - 43888)*(u - 2)**2
Solve 5*k**3 - 15830*k**2 - 63385*k - 47550 = 0.
-3, -1, 3170
Solve -140*k**4/3 + 194*k**3/3 + 1622*k**2/3 - 644*k/3 + 16 = 0 for k.
-3, 1/10, 2/7, 4
Factor -2*w**2/21 + 34*w/7 + 12644/21.
-2*(w - 109)*(w + 58)/21
Factor -t**4/2 - 69*t**3 + 139*t**2/2.
-t**2*(t - 1)*(t + 139)/2
Let 5*v**3 + 205*v**2 - 605*v - 7525 = 0. Calculate v.
-43, -5, 7
Determine s, given that -126*s**4 - 7701*s**3 + 14895*s**2 - 2268*s = 0.
-63, 0, 1/6, 12/7
Suppose 8*a**4/3 - 986*a**3/3 + 7342*a**2/3 + 28586*a/3 - 2530 = 0. Calculate a.
-3, 1/4, 11, 115
Factor 3*k**3 - 1923*k**2 + 297312*k + 3507108.
3*(k - 326)**2*(k + 11)
Let 2*n**5/5 - 63*n**4/5 - 173*n**3/5 + 13918*n**2/5 - 4092*n + 6776/5 = 0. What is n?
-14, 1/2, 1, 22
Factor 2*f**3/13 + 122*f**2 - 1592*f/13 - 3176/13.
2*(f - 2)*(f + 1)*(f + 794)/13
Suppose -3*l**2 + 77256*l - 386205 = 0. What is l?
5, 25747
Find s, given that 3*s**2 - 1284552*s + 1284549 = 0.
1, 428183
Let -2*h**3/13 + 15320*h**2/13 - 29414250*h/13 + 292612500/13 = 0. What is h?
10, 3825
Find z such that -3*z**2 - 28152*z - 66044592 = 0.
-4692
Factor -5*k**3 + 1655*k**2 - 1650*k.
-5*k*(k - 330)*(k - 1)
Find q such that -10*q**3 + 2369575*q**2 - 140371549620*q - 70186367205 = 0.
-1/2, 118479
Factor -2*x**2/5 + 7236*x/5.
-2*x*(x - 3618)/5
Factor 5*a**2 + 33330*a + 66640.
5*(a + 2)*(a + 6664)
Determine a, given that -778*a**5 + 3116*a**4 - 1572*a**3 - 3104*a**2 + 2350*a - 12 = 0.
-1, 2/389, 1, 3
Let -3*n**4 + 39*n**3 + 309*n**2 + 609*n + 342 = 0. Calculate n.
-3, -2, -1, 19
Factor -s**4/3 - 9*s**3 + 58*s**2/3.
-s**2*(s - 2)*(s + 29)/3
Factor -2045*q**3 - 6155*q**2 + 8120*q + 80.
-5*(q - 1)*(q + 4)*(409*q + 4)
Solve 2*y**5 - 72*y**4 - 558*y**3 + 5588*y**2 + 19680*y = 0 for y.
-10, -3, 0, 8, 41
Factor -u**3/5 - 943*u**2/5 - 942*u/5.
-u*(u + 1)*(u + 942)/5
Determine q so that -60*q**5 - 11456*q**4 + 350852*q**3 - 691224*q**2 + 439088*q - 87200 = 0.
-218, 2/5, 2/3, 1, 25
What is a in 15*a**5 - 26770*a**4 + 12190835*a**3 - 220114800*a**2 + 796271740*a - 436625840 = 0?
2/3, 4, 14, 883
Factor 5*j**2 - 481780*j + 11605598420.
5*(j - 48178)**2
Solve 6*l**3/5 + 264*l**2/5 + 768*l/5 - 1536 = 0 for l.
-40, -8, 4
Factor 17*m**3/7 + 3*m**2/7 - 425*m/7 - 75/7.
(m - 5)*(m + 5)*(17*m + 3)/7
Factor 3*v**5 - 39*v**4 + 72*v**3 + 264*v**2 - 912*v + 720.
3*(v - 10)*(v - 2)**3*(v + 3)
Suppose 3*y**4/7 - 197*y**3/7 + 531*y**2 - 23127*y/7 + 19604/7 = 0. Calculate y.
1, 13, 116/3
Determine m, given that -2*m**4/11 + 182*m**3/11 - 3846*m**2/11 + 25298*m/11 - 21632/11 = 0.
1, 13, 64
Solve b**3/3 - 1461*b**2 + 4380*b = 0.
0, 3, 4380
Suppose -500*b**4 + 1897300*b**3 + 759255*b**2 - 967770*b + 170775 = 0. Calculate b.
-1, 3/10, 3795
Factor 4*k**2/3 + 1852*k + 471744.
4*(k + 336)*(k + 1053)/3
Factor 2*h**3/5 + 57034*h**2/5 + 81327632*h + 406581128/5.
2*(h + 1)*(h + 14258)**2/5
Factor 67*b**2/6 - 947*b - 1105/6.
(b - 85)*(67*b + 13)/6
Factor -4*i**3 + 2294*i**2 + 58604*i.
-2*i*(i - 598)*(2*i + 49)
Find d such that 4*d**5/3 - 10336*d**4/3 - 8*d**3/3 + 20672*d**2/3 + 4*d/3 - 10336/3 = 0.
-1, 1, 2584
Solve 27*x**2 + 26157*x - 5814 = 0.
-969, 2/9
Suppose -5*i**4 + 219470*i**3 - 2405938665*i**2 - 53010344860*i - 291703027220 = 0. What is i?
-11, 21958
Factor -5*y**3 + 50345*y**2 - 50310*y - 302040.
-5*(y - 10068)*(y - 3)*(y + 2)
Determine b, given that b**2/6 + 229*b/3 - 4780/3 = 0.
-478, 20
Factor 2*a**2/5 - 102*a - 81252/5.
2*(a - 366)*(a + 111)/5
Let -3*k**5/2 - 33*k**4 - 291*k**3/2 + 396*k**2 + 1134*k = 0. What is k?
-14, -9, -2, 0, 3
Solve 18*h**5 + 2526*h**4 + 104660*h**3 + 1114012*h**2 + 2887290*h + 2182950 = 0 for h.
-63, -11, -5/3
Find b, given that 2*b**5/11 - 78*b**4/11 + 942*b**3/11 - 1586*b**2/11 - 36504*b/11 + 158184/11 = 0.
-6, 6, 13
Factor i**5/5 - 892*i**4/5 + 108813*i**3/5 - 3589794*i**2/5.
i**2* |
The inaugural Grand Prix of Indianapolis, which will be held on at Indianapolis Motor Speedway’s newly configured infield road course, edges closer with the green flag set to drop at 3:30 p.m. ET Saturday.
Graham Rahal was towards the bottom of the timing sheet’s after this morning’s wet final practice, but has provided us with some magnificent views of the circuit this weekend with Google Glass strapped on in his car.
Sebastian Vettel’s day ended with the four-time defending Formula One champion hitching a ride on a scooter after his Red Bull puttered out.
Lewis Hamilton finished Friday’s opening day of practice at the Spanish Grand Prix with the top times from both training sessions. The British driver is looking to add to his three poles positions and hat trick of wins after four races this season.
Mercedes teammate and F1 leader Nico Rosberg set the afternoon’s second best time after his crew fixed a cooling issue. |
The purpose of this project is to determine the reliability and validity of an instrument designed to assess functional ability of patients with Alzheimer's Disease (AD) enrolled in clinical treatment trials. At present functional scales measuring activities of daily living (ADLs) are often used as secondary but rarely as primary outcome measures either in trials of antidementia drugs or in trials of drugs for the treatment of ancillary symptoms such as agitation. Existing instruments are limited first because there is no consensus that they measure all of the major functional limitations found in AD patients and more importantly, that no existing instrument has been shown to be suitable for assessing functional change over a broad spectrum of dementia severity. Previously we have conducted reliability and longitudinal validity studies of the two most widely used instruments for assessing activities of daily living (ADLs) in AD patients, the Physical and Self-Maintenance Scale (PSMS) and Instrumental Activities of Daily Living Scale (IADLS) of Lawton and Brodie (1969). These studies have determined that many but not all of the items on these two scales have adequate reliability and longitudinal validity. We propose to modify some of the PSMS items to enhance reliability and to modify or replace several IADLS items so that they are less gender and location specific. Then we propose to assess the inter-rater, test-retest and alternate source reliability of each item; those with poor reliability will be eliminated or modified. Then a group of at least 50 AD patients with a wide range of baseline severity will be evaluated every six months for a minimum of 12 months. The ability of each item to measure longitudinal change for each level of dementia severity will be determined, and the reliability and sensitivity of the scale will be compared with other clinician rating scales used in clinical trials. The ultimate aim of the project is to produce an instrument for measuring activities of daily living (ADLs) in AD patients that can be used to evaluate the efficacy of drug treatments or other interventions. |
At 11.15 a.m. this morning, Justin Bieber discovered an amazing new use for Instagram:
The long-form social media rant.
The tactic takes advantage of Twitter's famous limit on tweet-length.
For years, angry celebrities (and anyone else with thoughts more complicated than 140 characters) have been frustrated by the central flaw in Twitter's publishing architecture: Everything you say is published most-recent first.
This is fine for one-off, short messages. But it's lousy if you need to express a concept that requires two or more tweets — the sentences appear "backwards" when seen by your readers, with the last tweet appearing as the first tweet at the top of your feed.
Bieber has now fixed this for all of us.
"Everyone in my team has been telling me, 'keep the press happy' but I'm tired of all the countless lies in the press right now," he told his fans in a 315-word essay decrying his critics, "Saying I'm going to rehab and how my family is disappointed in me."
The link to his cri de coeur — "I honestly don't care if you don't believe in me because I believe in me, my friends believe, my family believe, my fans believe, and look where that's gotten me so far" — was posted on Twitter as an Instagram photo link:
Followers who clicked on it were taken through to Instagram, where they saw a black-and-white picture of the back of Bieber's head (above) and his screed against the media, which was 1,266 characters long.
Here it is:
Justin Bieber / Twitter
Twitter should take this seriously: Although a tweet was used to publicize the statement, the actual scoop was delivered on Instagram, owned by Twitter's arch-rival, Facebook.
Long-form writing has taken a beating in social media over the last five years. In addition to Twitter's letter-limit, Facebook hides longer status updates (requiring users to click for more) and advertisers have deliberately targeted dollars at so-called "snackable media" — the kind of content short enough to be satisfying on a cell phone.
To show you how different the Bieber Instagram proclamation is, compare it to Bieber's previous Manifesto Against The Haters, published March 6:
As a piece of writing, it's a disaster. Something about rumors, God and a 19-year-old going to a nightclub? What? Who can tell.
It's not a soliloquy, it's a grammar puzzle.
So, thank you Justin Bieber. History has yet to judge your existential philosophy — "i know who i am and i know who i'm not" — or, indeed, your punctuation. But as Marshall McLuhan once noted, the medium is the message: And you have delivered a new one.
Now Watch: Why Instagram Is Such A Huge Success
|
Signals
=======
django-crudbuilder comes with built-in signals to perform/execute specific actions after post create and post update views.
You can able to access ``request`` and ``instance`` in your own handlers.
Usage of these signals you can view in `handlers of example project`_ on Github.
Following are the list of supported signals.::
post_create_signal --> runs after modelform.save() in CreateView
post_update_signal --> runs after modelform.save() in UpdateView
post_inline_create_signal --> runs after inlineformset.save() in CreateView
post_inline_update_signal --> runs after inlineformset.save() in UpdateView
post_create_signal
------------------
This signal will loaded/executed soon after the object gets created for specific model. In otherwords this will fires right after the ``modelform.save()`` method gets called during the CreateView.::
# tutorial/handlers.py
from django.dispatch import receiver
from crudbuilder.signals import post_create_signal
from example.models import Person
@receiver(post_create_signal, sender=Person)
def post_create_signal_handler(sender, **kwargs):
# print "execute after create action"
request = kwargs['request']
instance = kwargs['instance']
instance.created_by = request.user
instance.save()
post_update_signal
------------------
This signal will loaded/executed soon after the object gets updated for specific model. In otherwords this will fires right after the ``modelform.save()`` method gets called during the UpdateView.::
# tutorial/handlers.py
from django.dispatch import receiver
from crudbuilder.signals import post_update_signal
from example.models import Person
@receiver(post_update_signal, sender=Person)
def post_update_signal_handler(sender, **kwargs):
# print "execute after update action"
request = kwargs['request']
instance = kwargs['instance']
instance.updated_by = request.user
instance.save()
post_inline_create_signal
-------------------------
This signal will get executed soon after the inline formset gets saved which means this get fires right after the ``inlineformset.save()`` method gets called in CreateView.::
# tutorial/handlers.py
from django.dispatch import receiver
from crudbuilder.signals import post_inline_create_signal
@receiver(post_inline_create_signal, sender=Person)
def post_inline_create_handler(sender, **kwargs):
request = kwargs['request']
parent = kwargs['parent']
children = kwargs['children']
parent.created_by = request.user
parent.save()
for child in children:
child.created_by = request.user
child.save()
post_inline_update_signal
-------------------------
This signal will get executed soon after the inline formset gets updated which means this get fires right after the ``inlineformset.save()`` method gets called in UpdateView.::
# tutorial/handlers.py
from django.dispatch import receiver
from crudbuilder.signals import post_inline_update_signal
@receiver(post_inline_update_signal, sender=Person)
def post_inline_update_handler(sender, **kwargs):
request = kwargs['request']
parent = kwargs['parent']
children = kwargs['children']
parent.updated_by = request.user
parent.save()
for child in children:
child.updated_by = request.user
child.save()
.. _handlers of example project: https://github.com/asifpy/django-crudbuilder/blob/master/example/example/handlers.py |
Mangkunegara IX
Mangkunegara IX (born 1951) is the current traditional ruler of the former state of Mangkunegaran, located in Java, Indonesia. He succeeded his father, Mangkunegara VIII, as Prince of Mangkunegaran on 3 September 1987. His full royal name is Kanjeng Gusti Pangeran Adipati Arya Mangku Negara.
Prior to his accession he was named Gusti Pangeran Hadiningrat Sujiwakusuma. In the meantime Sujiwakusuma became viceroy in Mangkunegaran.
His accession was controversial because for the first time in Indonesian history, Mangkunegaran involved relatives outside the core to participate in the decision.
Early life
He was born in Surakarta the son of Mangkunegara VIII with brothers KPA. Prabu Kusumo, B.R.Aj. Retno Satuti. Rahadiyan Yamin, B.R.Aj. Retno Rosati Hudiono Kadarisman, B.R.M. Susaktyo, B.R.M. Herwasto, B.R.M. Kumiyakto and B.R.Aj. Retno Astrini.
His maternal grandfather and father were their brother and sister's son Mangkunegara V. His maternal grandfather was Prince Suryakusuma descended from the father whose grandfather was Mangkunegara VII.
Personal life
Sujiwa Kusuma was previously married to Sukmawati Sukarnoputri, the third daughter of Indonesia’s founding president Sukarno and his wife Fatmawati.
They had three children, and are now divorced.
Crown Prince
Sujiwakusuma became the crown prince, replacing his brother King Kusumo KPA-BRM Radityo who died. He was the fourth son of Mangkunegara VIII.
Existence dilemma
The King is no longer the head of government of his nominal territory. The monarchy was originally supplanted when the area was colonized by the Netherlands. Following the end of colonial rule, it retained its ceremonial role.
References
Category:Princes of Mangkunegaran
Category:1951 births
Category:Living people |
Aspects of the mammalian visual system such as retinotopy \[point-to-point topographic connections between the retina, lateral geniculate nucleus (LGN), and cortical visual area 1 (V1)\], and cortical maps for ocular dominance (OD), orientation (OR) and directional selectivity (DS) have all been well studied experimentally. In some species (such as ferrets, cats, and primates) cortical maps for OR and DS possess a distinct patchy structure with features such as pinwheels, saddle points and discontinuities[@b1][@b2][@b3]. In these species, DS appears to arise first in visual cortex and depends on cortical developmental plasticity after eye-opening (EO)[@b4], but exactly how this occurs and the importance of pre-EO structures are poorly understood.
Earlier studies showed that significant OR maps were already present at EO, but that DS maps developed post-EO with visual experience[@b5][@b6]. However, a weak DS bias has been recently reported at EO in ferret, which then develops rapidly with visual experience during the first few weeks[@b7][@b8]. The implication is that DS may be present prior to visual experience[@b9]. However, whether this precocious DS is activity dependent is unclear. There is some experimental evidence to suggest that pre-EO neural activity (retinal waves) may be responsible[@b4][@b7], and this has also been investigated in several computational studies[@b10][@b11][@b12][@b13]. It is also possible that merely testing for DS is sufficient to develop DS in an incipient network. A third possibility is that DS exists independent of neural activity and is laid down by physical growth of a neural 'proto-architecture' in the form of retino-LGN-V1 network connections. Such a proto-architecture could potentiate rapid learning once visual experience becomes available.
In a recent modelling study, we proposed an artificial spiking neural network model to investigate how its structure and connectivity could provide an initial DS capability prior to visual experience[@b14] ([Fig. 1](#f1){ref-type="fig"}). The advantage of a modelling approach is that we could switch off the network's learning ability to examine DS which is not possible *in-vivo*. We found that a basic cortical structure with 'Mexican hat' connectivity, distance-dependent delays, and afferent input layer with 'receptive fields' produced DS and OR maps similar to those seen experimentally (and in previous modelling studies).
We concluded that this 'innate' structure was sufficient to produce DS prior to any visual experience. Experimental findings from ferret have shown that DS at EO was stronger in layer 4 of V1 than layer 2/3, and that layer 4 DS developed more rapidly up to post-natal day (PND) 35[@b8]. Therefore, as it seems likely that our prospective proto-architecture for DS resides in layer 4 of V1, in the current work we specifically compare our results with learning to those found for layer 4.
Given this functionally plausible model, we now ask two fundamental questions. First, does this proto-architecture learn from visual experience in the same way that real networks do? That is, is there refinement of the patchy DS map with training, or is the patchiness lost? To test this, we employed spike timing dependent plasticity (STDP) as a biologically plausible learning rule. We show that the major features of the natural developmental time course of DS and OR are reproduced and we investigate how this plasticity operates to cause refinement of DS.
Second, does a proto-architecture provide any selective advantage to the organism, such as facilitating learning after EO? We show that 'lesioning' the model disrupts the ability to learn from visual experience, and that an initial structure is essential for rapid learning. In conclusion, we propose that for mammals that develop patchy cortical DS and OR maps, a proto-architecture is likely to be an essential component.
Results
=======
Visual experience sharpens DS and OR selectivity
------------------------------------------------
We used Spike-Timing Dependent Plasticity (STDP) (see Learning subsection in Methods) on all the connections in the model. We generated ten randomly initialised networks and trained them with 50 random presentations of a bar object moving in one of eight different directions (replicating the 'visual experience' of real animals after EO). Before switching on learning, the initial DS preference map was patchy ([Fig. 2a](#f2){ref-type="fig"}). After switching learning on, the patchiness was not lost but became more delineated with sharper boundaries ([Fig. 2b,c](#f2){ref-type="fig"}). As training progressed the maps developed characteristics seen in experimentally derived maps such as areas of smoothly changing preference, fracture lines and saddle points[@b1][@b2]. To quantify the strength of preference, we employed a 'selectivity index' (SI) for neurons in the networks at various stages of training using a vector average method (see [Supplementary Methods](#S1){ref-type="supplementary-material"}). SI takes on values between 0.0 (no preference) and 1.0 (exclusive preference for one direction or orientation). The average DS SI increased with training from 0.1 to 0.32, and compares favourably with experimental measurements of average DS SI in ferret of 0.12 at EO to 0.30 at postnatal day (PND) ≥ 35[@b8]. OR preference maps showed a similar pattern of development. Average OR SI increased with training from 0.21 to 0.36 compared with experimental measurements in ferret of 0.24 at EO to 0.48 at PND ≥ 35[@b8]. [Figure 3a,b](#f3){ref-type="fig"}) (top) shows cumulative percentage curves of SI calculated for all neurons over all runs for the initial (EO) condition (grey dashed line) and the trained condition (solid black line). [Figure 3c,d](#f3){ref-type="fig"}) (bottom) shows the experimental curves[@b8] for layer 4.
Our computationally derived curves are similar to the experimental ones. The initial curves show distinct 'corner' shapes (in particular DS) shifted to the left reflecting the low average SIs. Training increased the selectivity strength for both DS and OR considerably causing a distinctive rightwards shift and a more S shaped curve exactly as seen in[@b8] (Mann-Whitney test, α = 0.05, n = 36000, p \< 2.2e-16).
We also investigated how responses to the preferred and null directions and orthogonal orientation changed over time compared to experimental data[@b8]. The preferred direction is the direction for which the neuron has the largest response (number of spikes generated during a pattern presentation), the null direction is the opposite direction to the preferred and the orthogonal orientation is at 90 degrees to the preferred/null directions. We collected responses to all directions for all neurons in one run, and to enable comparisons for all neurons we shifted the data so that the preferred direction response was always aligned at 0 degrees for all neurons and therefore the null direction and orthogonal orientation responses also aligned at 90 and 180 degrees respectively. Any neurons which did not respond to any direction were discarded. We performed Mann-Whitney tests for three specific comparisons (with adjusted alpha of 0.0167 for 95% confidence level after a Bonferroni correction): comparing changes in response to preferred direction in the initial and midway cases (n = 3285, 3319, average response increased from 0.23 to 0.34, p \< 2.2e-16) ; to the null direction in the midway and final cases (n = 3285, 3352, average response decreased from 0.16 to 0.12, p \< 2.2e-16) and to the orthogonal orientation in the midway and final cases (n = 3285,3352, average response decreased from 0.08 to 0.07, p \< 2.2e-16). [Figure 4](#f4){ref-type="fig"} shows the average responses to all directions for the initial, midway and final cases. To compare with[@b8], we fitted the three cases separately with a double Gaussian function, with the preferred mean set at 0 degrees, and the null mean at 180 degrees. The standard deviations of the preferred and null Gaussians were constrained to be the same, and found using the least-squares method. As training progressed, the responses to preferred and null directions change from being roughly equal to a situation where the preferred response was much larger, indicating that the neurons had developed DS. These results are in agreement with those of[@b8] who found that the response to the preferred direction increased in the first half of training (EO to PND \< 35) and the responses to the null direction and orthogonal orientation decreased in the second half of training (PND \< 35 to PND \>= 35). Our [Fig. 4](#f4){ref-type="fig"} closely resembles the experimentally derived tuning curves in [Fig. 2](#f2){ref-type="fig"} from[@b8].
Disruption of initial afferent and lateral connectivity prevents training from refining OR and DS
-------------------------------------------------------------------------------------------------
In order to further investigate the importance of the network structure in delivering an early DS capability, we examined the effect of disruptions to the initial structure on the ability to develop mature DS. In our previous work we examined how changing afferent and lateral connectivity from the default case affected the proto-architecture's innate ability to represent DS and OR in the 'EO' condition[@b14]. We found that the worst disruption occurred when there was no receptive field structure in the afferent connections (i.e. the LGN and Cortical layers were fully connected) and when the extent of lateral inhibition in the Cortical layer was reduced. In the current work we investigated whether the same connectivity disruptions affected the network's ability to refine with visual experience or in fact capability is restored by training. We performed learning experiments with both full LGN-Cortical connectivity and the spatial range of lateral inhibition drastically reduced. This was done by forcing the lateral inhibition to zero at distances greater than eight units, effectively reducing the range from approximately five times the excitatory range down to only two times. All other network parameters (e.g. starting weights) were kept the same.
Five randomly initialised networks were generated with disrupted afferent and lateral inhibitory connectivity and trained in the same way as for the intact case. Initially, selectivity was so low it was impossible to assign strong preferences to neurons hence the complete lack of features ([Fig. 2d](#f2){ref-type="fig"}). As training progressed through mid-training ([Fig. 2e](#f2){ref-type="fig"}) to the final state ([Fig. 2f](#f2){ref-type="fig"}), individual neurons did acquire preferences but no coherent map emerged. Average SI strength increased for DS from 0.02 to 0.12 and for OR from 0.09 to 0.11, but final values were much weaker compared to the intact case. The impact of connectivity disruption on training was very clear in the cumulative percentage curves ([Fig. 5](#f5){ref-type="fig"}). The initial distributions (grey dashed line) comprised of only very low SI values, and the trained curves (solid black line) showed some shift to higher Sis but only for low strengths. The cumulative percentage distributions seen in the intact connectivity case and in the experimental data ([Fig. 3a--d](#f3){ref-type="fig"}) were absent.
Uni and bi -- directional training alter initial DS biases in favour of the trained directions
----------------------------------------------------------------------------------------------
Experimental studies have examined the extent to which the initial DS bias in ferret could be overridden by visual experience with either training in only one direction[@b7], or with two directions only (same orientation)[@b6]. For comparison, we performed the same training with our network. For the uni-directional case, we trained only with stimuli moving left to right (direction E) and found that the number of neurons that acquired a preference for this direction (with a tolerance of +/−5°) increased (n = 154) compared to the case when trained with all eight directions (n = 133). We also found that the average DS selectivity index (SI) after training was larger for the neurons which had a preference for the trained direction (SI = 0.45) compared to all other neurons (SI = 0.23) (Mann-Whitney, p \< 2.2e-16). It should be noted, however, that all neurons increased their DS SI significantly from the initial untrained case where average SI was 0.09. These results mainly agree with experiment, except that we found that training was very effective in changing neurons' initial preference regardless of the strength or direction of that bias, whereas[@b7] observed that neurons with an initial strong bias opposite the trained direction did not change their bias.
For bi-directional training we used stimuli moving rightward (direction E) and leftward (direction W) and ensured there was approximately an equal number of presentations of each direction. The number of neurons that acquired a preference for the E direction (+/−5°) increased (n = 141) compared to the case when trained with all eight directions (n = 133). The number of neurons that acquired a preference for the W direction (+/−5°) decreased (n = 113) compared to the case when trained with all eight directions (n = 149). We also found that the average DS selectivity index (SI) after training was larger for the neurons which had a preference for one of the trained directions. For direction E, SI = 0.22 compared to non-trained directions SI = 0.21 (Mann Whitney, p = 0.01657). For direction W, SI = 0.28 compared to non-trained directions SI = 0.21 (Mann Whitney, p = 0.000655).
Weight increases on Cortico-Cortical connections are the primary driver for refinement of DS
--------------------------------------------------------------------------------------------
To investigate in more detail how the plasticity method we used caused refinement of DS with visual experience we firstly examined weight changes on the afferent (LGN-Cortical) and lateral (Cortico-Cortical) connections after uni-directional training. We selected neurons which acquired a preference for the trained direction (moving left to right) with low, medium and high SI values and measured the change in connection weights. [Figure 6a](#f6){ref-type="fig"} (left) shows plots of LGN-Cortical weight (initial-final) for three example neurons. We saw a clear asymmetry in the weight changes related to the training direction - generally there are weight increases on the left and decreases on the right on all three plots in [Fig. 6a](#f6){ref-type="fig"}. We also found that the asymmetry was more pronounced as SI increased. [Figure 6b](#f6){ref-type="fig"} (right) gives an example of lateral excitatory and inhibitory weight changes typical for all neurons examined. Excitatory and inhibitory lateral weights strengthened during the course of training but we saw no asymmetry related to the training direction, however, larger weight increases occurred on synapses to neurons with larger SI values. These results implied that plasticity on both afferent and cortical connections contributed to the development of DS.
To further clarify the relative roles of afferent and lateral weight changes we firstly repeated the uni-directional training experiment, disabling afferent and lateral plasticity in turn. Secondly, to examine the impacts on SI distribution and DS map structure we performed experiments training with all eight patterns with plasticity disabled on the afferent and lateral connections in turn. We found that with cortical plasticity disabled, there was no significant refinement of DS. For the uni-directional training, average SI for the neurons which had a preference for the trained direction increased slightly (SI = 0.11) compared to other neurons (SI = 0.09), but this was not statistically significant (Mann-Whitney, p = 0.5921). Examples of afferent weight changes without cortical plasticity are given in [Fig. 7a](#f7){ref-type="fig"}. These weights show asymmetry in parts but are not as smoothly varying and do not show the relationship to the training direction or SI as seen in [Fig. 6a](#f6){ref-type="fig"}. [Figure 8a,b](#f8){ref-type="fig"} show the cumulative percentage graph and DS map extract for training with all patterns with cortical plasticity disabled. The average SI, distribution of SI and the DS map are very similar to those from the untrained state (see [Fig. 2a](#f2){ref-type="fig"} and [Fig. 3a](#f3){ref-type="fig"}, grey dashed line for comparison). With only afferent plasticity disabled, refinement of DS occurred normally. For the uni-directional training, average SI for neurons that acquired a preference for the trained direction increased (SI = 0.45) compared to other neurons (SI = 0.23) and was statistically significant (Mann-Whitney, p \< 2.2e-16), so a very similar result to training with both afferent and cortical plasticity enabled. [Figure 7b](#f7){ref-type="fig"} shows an example of typical excitatory and inhibitory cortical weight changes. Weights increased on both excitatory and inhibitory connections in a similar manner to when both afferent and lateral plasticity were enabled. Again we saw no asymmetry particularly related to the training direction. [Figure 8c,d](#f8){ref-type="fig"} show the cumulative percentage graph and DS map extract for training with all patterns with afferent plasticity disabled. The average SI, distribution of SI and the DS map were very similar to the trained state (see [Fig. 2c](#f2){ref-type="fig"} and [Fig. 3a](#f3){ref-type="fig"}, solid line for comparison). These results imply that, in our model, cortical plasticity is in fact the main driver for refinement of DS. Cortical plasticity seems to contribute somewhat to weight changes on the afferent connections as the asymmetry related to the training direction was more pronounced when cortical plasticity was enabled.
Discussion
==========
Our simple computational model ([Fig. 1](#f1){ref-type="fig"}) generates patchy preference maps of directional selectivity prior to any training ([Fig. 2a](#f2){ref-type="fig"}). This was observed by switching off any weight updating (learning) during testing, which is not possible in natural experiments. Our data closely match the experimental distributions for DS and OR in layer 4 of ferret V1 at EO[@b8], implying that the model is sufficient to capture important features of the connectivity in layer 4 of V1. It also shows that the initial DS bias observed experimentally at EO[@b8] may indeed arise from the structure of the network prior to any visual experience, rather than an artefact of rapid learning during testing.
For these initial maps to emerge, afferent receptive fields and lateral cortical connections (excitatory and inhibitory) were necessary. We found that lateral cortical inhibition was crucial, which is in agreement with experimental evidence that cortical inhibition plays an important part in the development of OR and DS[@b15][@b16][@b17].
After switching on learning, we observed that exposure to visual input increased the degree of selectivity in DS and OR maps with sharper delineation among patches, but also with a distinctive spread of selectivity indicating that many neurons increased their selectivity, such that a distribution of neurons with low and high selectivity emerged as in[@b8]. This learning was remarkably rapid needing only 25--50 presentations of a moving object, which is a very small amount of training compared to typical computational studies (for example, 6000 presentations in[@b10] and 20,000 image presentations in[@b12]). In the ferret, training has also been observed to be very rapid after EO[@b8] -- so much so that the experimental procedure for measuring the DS and OR of neurons needed to account for any training effect caused during measurement.
We previously disrupted the initial connectivity in various ways to explore which key features contributed to innate DS (structured afferent receptive fields and sufficient lateral inhibition in the Cortical layer) and in the current work have assessed the impact of these same disruptions on learning. We found that initial DS/OR selectivity was much weaker than with intact connectivity, and with learning switched on, recovery did not occur. We gave one of our disrupted networks double the amount of training and still saw no improvement, showing that a permanent impairment was caused by the disrupted connectivity. In particular the distributions of DS/OR selectivity were markedly different and we did not see the formation of patchy cortical maps.
In order to explore the plasticity mechanism further we performed experiments training with uni- and bi-directional stimulus motion and disabling either afferent or cortical plasticity. For uni-directional training, DS SI increased more for neurons with a preference for the training direction, as seen experimentally[@b7]. More neurons were converted to the training direction than when trained with all eight directions, as also seen experimentally[@b7]. We also found that training was able to completely override the initial DS biases of neurons, which contrasts with experimental data[@b7] where neurons with an initial bias opposite to the training direction were less likely to be converted. For the bi-directional training we found that DS SI increased for both directions, as seen experimentally[@b6] but the numbers of neurons converted only increased for one of the directions. A possible reason for these discrepancies is that only layer 2/3 neurons were examined experimentally[@b6][@b7] and it is possible that the time-course or mechanism of plasticity may be different in layer 4. Following the uni-directional training experiment, we analysed the weight changes on both afferent and lateral connections for neurons which acquired a preference for the trained direction. For the afferent connections, asymmetric receptive fields developed after training with one direction of motion and also the asymmetry increased with DS SI. Increases in both lateral excitatory and inhibitory connections were observed, and were larger for neurons with larger SI but they were not asymmetric. From further experiments disabling either afferent or lateral plasticity we found that cortical plasticity alone was necessary and sufficient to explain the refinement of DS in our network (in terms of average SI, distribution of SI and changes in map structure). These results imply that initial weak DS in V1 could arise purely from the cortical connectivity and become stronger through strengthening of weights on only the cortico-cortical connections. The role of afferent connections in DS is unclear. From our previous work it appears they contribute something to the initial capability for DS[@b14] but the current work we did not find that plasticity on afferent connections was required to replicate the refinement of DS seen in experiments.
Our model appears to be a minimal model inasmuch as it contains necessary and sufficient connectivity to replicate the observed experimental distributions of OR and DS at EO. With training, selectivity refined and distinctive maps with a smoothly varying patchy structure emerged, and various 'lesions' of the initial connectivity led to failure. We have not modelled how this proto-architecture itself grows. Presumably it results from a complex process of cellular replication and migration, steering of axonal and dendritic growth, and excitatory and inhibitory synaptogenesis that is ultimately genetically controlled. Such processes have been explored in computational studies[@b18][@b19][@b20]. Clearly, the output of this pre-EO process greatly influences the post-EO plastic development of DS and OR maps, and hence the long-term phenotype. How variation in this growth impacts on post EO function remains to be explored. We also have not yet considered the role of structural plasticity (synaptogenesis and pruning) and critical periods but intend to do so in future work.
As we have shown here, computational modelling of biological neural networks can be an important tool to complement and supplement experiments in developmental plasticity. With computational models, it is possible to do things that cannot be done experimentally -- for example run many more trials, sample more neurons, experiment with different stimulation, investigate alternative learning paradigms, and switching off learning entirely. Such models can help us understand the relative roles of prenatal structural development and postnatal developmental plasticity.
Methods
=======
Our system architecture is predominantly the same as described in Adams & Harris[@b14]. More details of the network construction, initial parameters and neuron models are given in the [Supplementary Methods](#S1){ref-type="supplementary-material"}. Here we restrict ourselves to summarising only the main features and new additions relevant to the current work.
The Visual Map Architecture
---------------------------
[Figure 1](#f1){ref-type="fig"} shows the network architecture. The Input layer consists of 128 × 128 neurons and relays spike data into the network at the same resolution as the DVS camera we use to capture the moving input. The Input layer is connected to the 32 × 32 LGN layer with feed-forward excitatory connections with fixed weights of value 1.0. These connections are set up such that a 4 × 4 connection field (CF) from the Input layer is connected topologically to 1 neuron in the LGN layer (Box 1 in [Fig. 1](#f1){ref-type="fig"}) and effects a down-sampling from 128 × 128 to 32 × 32. The 'Cortical' layer consists of 60 × 60 neurons of which 20% are randomly assigned as inhibitory and 80% as excitatory. The LGN and Cortical layers are not fully connected: each cortical neuron only 'sees' neurons from the LGN layer within a feed-forward connection field. See Box 2 in [Fig. 1](#f1){ref-type="fig"}. The connection fields from each Cortical neuron overlap. The Cortical layer is also recurrently connected: there are sparse lateral connections and these follow a 'mexican hat' profile of short-range excitation and long-range inhibition. Input, LGN and Cortical neurons are modelled as spiking neurons using a simple Leaky Integrate and Fire (LIF) model.
Input Patterns
--------------
Simplified but naturalistic visual stimulation is provided using data captured with a DVS-128 Silicon Retina Camera. The DVS camera is a specialised neuromorphic device that generates spike events in response to luminance changes in the individual pixels in the camera's 128 × 128 array and the spikes can be directly injected to the network with minimal processing (apart from the down-sampling mentioned above). An extended bar object (as shown in [Fig. 1](#f1){ref-type="fig"}) was moved across the camera lens in eight different directions (N, NE, E, SE, S, SW, W and NW) and the data logged in a file. Ten repeats of each direction were captured to provide variability. For more details of the DVS-128 camera and the information extraction and processing of the data it generates see References [@b21], [@b22], [@b23].
Learning
--------
Previous experimental and modelling studies have shown that Spike-Timing Dependent Plasticity (STDP) is a plausible mechanism in real neurons[@b24][@b25][@b26]. The relative firing times of pre- and post-synaptic neurons influence the strengthening or weakening of connections. When a pre-synaptic spike is emitted *before* a post-synaptic spike within a specified time window, there may have been a causal effect and the synaptic connection between the neurons is strengthened (Long Term Potentiation or LTP). In contrast, when the post-synaptic spike occurs first then it cannot have had a causal effect on presynaptic firing and the connection is weakened (Long Term Depression or LTD). The computational modelling study of[@b12] showed how robust cortical directional selectivity could arise using STDP with an asymmetric time window combined with distance dependent delays between cortical neurons. We have adopted this method on both LGN-Cortical afferent and Cortical-Cortical lateral connections. The STDP weight change rules for the LTP and LTD elements are given as [equations (1](#eq1){ref-type="disp-formula"}) and ([2](#eq2){ref-type="disp-formula"}).
where:
Δ*w*~*ltp*~, Δ*w*~*ltd*~ are the magnitudes of the weight changes
Δ*t* is (firing time of the pre-synaptic neuron -- firing time of the post-synaptic neuron)
*τ*~*ltp*~, *τ*~*ltd*~ are the LTP and LTD time constants.
*A*~*ltp*~, *A*~*ltd*~ are the LTP and LTD learning rates for STDP.
In most formulations of STDP the LTD rate (*A*~*ltd*~) is set slightly higher than the LTP rate to ensure stability[@b25] and we have adopted this approach. See [Table 1](#t1){ref-type="table"} for details of the parameter values we used in our learning experiments. [Equations (1](#eq1){ref-type="disp-formula"}) and ([2](#eq2){ref-type="disp-formula"}) result in an STDP window where the LTP part is an exponential curve as in regular STDP[@b25] but the LTD part is represented by an alpha function as introduced in[@b12]. The effect of this asymmetric window is that LTD is deeper and persists over a longer timescale than LTP.
STDP is a form of Hebbian learning and in its standard form weights will continue to increase or decrease unbounded. Most computational studies therefore include some form of mechanism to counteract this such as global normalisation or hard limiting of synaptic weights. To avoid the need for such artificial measures we employed weight dependant updates[@b27]:
[Equations (3](#eq3){ref-type="disp-formula"}) and ([4](#eq4){ref-type="disp-formula"}) are the update rules for LTP. In (3), the proposed weight change for a synapse between presynaptic neuron *i* and postsynaptic neuron *j* (Δ*w*~*ij*~) takes the value Δ*w*~*ltp*~ directly from [equation (1)](#eq1){ref-type="disp-formula"}. In (4) the new weight of the synapse is calculated by adding the value from (3) to the existing weight. In (5) (LTD), (Δ*w*~*ij*~) is calculated as 1+ the value Δ*w*~*ltd*~ (from [equation (2)](#eq2){ref-type="disp-formula"}) and in (6) the new weight of the synapse is calculated by multiplying the value from (5) by the existing weight. The effect for LTD is that Δ*w*~*ij*~ is a value less than 1.0 (as Δ*w*~*ltd*~ is always negative) and when multiplied by the existing weight results in a decrease.
Experimental Procedure
----------------------
For each experiment randomly initialised networks were generated with either the intact or disrupted connectivity and trained as follows:One of the eight directions (N, NE, E, SE, S, SW, W and NW) was randomly selectedOne of 10 different instances of pre-recorded data for that direction was selectedThe corresponding data file was loaded and the spike events processed to lists of x,y coordinates and timestampsSpike events were applied to the Input layer (128 × 128)Neural processing startedSpikes were down-sampled and processed through the LGN layer (32 × 32) and propagated into the Cortical layerAfferent and Lateral learning (as per [equations 1](#eq1){ref-type="disp-formula"}, [2](#eq2){ref-type="disp-formula"}, [3](#eq3){ref-type="disp-formula"}, [4](#eq4){ref-type="disp-formula"}) was applied continuouslyOnce all spikes in the sequence had been processed, the network was reset for the next pattern (i.e. there is no interaction between successive presentations).
Additional Information
======================
**How to cite this article**: Adams, S. V. and Harris, C. M. A Computational Model of Innate Directional Selectivity Refined by Visual Experience. *Sci. Rep.* **5**, 12553; doi: 10.1038/srep12553 (2015).
Supplementary Material {#S1}
======================
###### Supplementary Information
The authors would like to thank Stephen D. Van Hooser for kindly supplying the experimental data for Figure 3c) and d).
**Author Contributions** S.V.A. and C.M.H. designed the experiments, S.V.A. ran the experiments and analysis, S.V.A. and C.M.H. wrote the manuscript.
{#f1}
{ref-type="supplementary-material"}) and extracted the same rectangular area for each. Numbers indicate the average selectivity (SI). (**a**) shows how in the intact connectivity case the initial map is patchy and there are some areas of smoothly varying preference but the map is immature and does not have all the features seen in mature maps. (**b**,**c**) show the effects of training to refine the selectivity and the arrangement of preferences to form a smoothly varying map. In (**d**) the initial case for disrupted connectivity, there is no evident map structure and selectivity is so low that distinct preferences cannot be detected. (**e**,**f**) with training, many neurons acquire a preference for one of the directions as shown by the speckling in the map. However, there is no true map structure with patches of similar preference smoothly varying across the cortical area as in (**b**) and (**c**).](srep12553-f2){#f2}
![Intact connectivity: cumulative % curves of selectivity (SI) for (**a**) DS and (**b**) OR generated from our computational model and (**c**) DS and (**d**) OR generated from experimental data for layer 4 (same data as shown in Figs 3c and 4c from[@b8]). In (**a**) and (**b**) the Selectivity Index (SI) for both DS and OR has been calculated for all neurons from ten randomly initialised networks both before and after training and cumulative percentage curves calculated to show the distributions. (**a**) distributions for DS for the initial (grey dashed line) and trained (solid black line) cases. (**b**) distributions for OR for the initial (grey dashed line) and trained (solid black line) cases. In both cases the effect of training is to shift the curve rightwards and increase the average selectivity. (**c**) DS for layer 4 neurons at EO (grey dashed line) and at PND ≥ 35 (solid black line). (**d**) OR for layer 4 neurons at EO (grey dashed line) and at PND ≥ 35 (solid black line). With visual experience the average selectivity for both DS and OR increases. The distribution curves shift to the right maintaining a proportion of low and high responders.](srep12553-f3){#f3}
![Changes in response to null and preferred direction and orthogonal orientation during training.\
Responses (y axis) are normalised rate. Raw data points are overlaid with fitted double Gaussians with the preferred response fixed at 0. (**a**) Initial case before training, (**b**) midpoint of training and (**c**) at the end of training. As training progressed the responses to preferred and null directions change from being roughly equal to a situation where the preferred response is much larger indicating the development of DS. In agreement with the experimental results of[@b8], the response to the preferred direction (pref) increases greatly in the first half of training. The responses to the null direction (null) and orthogonal orientation (orth) decrease during the second half of training. \*indicates differences across conditions that were significant with Mann-Whitney pairwise tests.](srep12553-f4){#f4}
{ref-type="fig"} and training does not shift the curves rightwards or increase selectivity by a large amount.](srep12553-f5){#f5}
{#f6}
{#f7}
{ref-type="fig"} (grey dashed line). The DS map in (**b**) looks similar to that of [Fig. 2a](#f2){ref-type="fig"}. When afferent plasticity was disabled, refinement of the DS map and increase in SI proceeded normally. The cumulative percentage curve in (**c**) looks similar to the trained case shown in [Fig. 3a](#f3){ref-type="fig"} (solid line). The DS map in (**d**) looks similar to that of [Fig. 2c](#f2){ref-type="fig"}.](srep12553-f8){#f8}
###### Summary of STDP parameters.
**Learning Rule Parameters** **Value**
------------------------------- --------------
A~pa~, Afferent LTP rate 0.02
A~ma~, Afferent LTD rate −1.05 · A~p~
A~pl~, Lateral LTP rate 0.01
A~ml~, Lateral LTD rate −1.05 · A~p~
*τ*~*ltp*~, LTP time constant 11 ms
*τ*~*ltd*~, LTD time constant 20 ms
|
BERKLEY — Travelers on Route 24 heading underneath the newly built Padelford Street overpass bridge can expect intermittent nighttime delays and detours during the next few weeks.
Although officials held a press conference Monday to celebrate the completion of the new Hollis E. Jennings Memorial Bridge, residual work for the foreseeable future will continue to cause traffic slowdowns on the highway.
“The bridge is done, but the ribbon-cutting might have been a bit premature,” said Michael Socci, whose MAS Construction and Bridge Inc. of Franklin won the $5.6 million bid to build the new overpass structure.
On Thursday, Socci said paving work is now underway on a section of state highway beneath the bridge.
Depending on weather conditions, he said it should take two to three weeks to repave and mill a small section of Route 24, as well as to paint striping and install a new stretch of steel guardrail.
Cyr said one night next week will be devoted to milling and the next for repaving. Both nights will require the closure of Route 24 at Exit 11 and a detour for vehicles.
Cyr and Socci said there is also some ongoing utility relocation work and minor landscaping that needs to be finished.
Socci said his crew has no control over that work, which involves telephone and power lines.
He noted that installing new above-ground lines will temporarily constrict movement on the bridge but will not affect traffic below.
Socci said either milling or paving could begin Sunday night. He said he is required, by contract, to detour traffic in either direction on alternate nights.
On nights that southbound Route 24 traffic is affected, vehicles, from 9 p.m. to 5 a.m., are diverted onto Padelford, then Porter and South Main streets, until finally reconnecting with the highway in Freetown.
A detour in the northbound lane of 24 diverts traffic onto Myricks Street to Route 140 and finally Route 24.
Monday’s ribbon-cutting celebrated the fact that the project came in on time and within budget. Socci said his contract gives him until November to finish the job.
“We have plenty of time, but I don’t expect to shut down and leave to do another job,” he said.
The DOT budgeted an additional $800,000 to cover “built-in contingency expenses” and traffic-control considerations, including Berkley and state police detail officers, according to DOT spokesman Michael Verseckes.
Socci praised MassHighway’s District 5 for its help in coordinating the effort with his company and local law enforcement.
“Very few jobs are easy, but every member of the team worked very well together,” he said.
Page 2 of 2 - Built in the 1950s, the Berkley overpass was renamed in 1966 in honor of Hollis E. Jennings, who was killed in action in World War II. |
## 虚拟机存储
TVM作为一种运行于tron协议上的虚拟机，需要能够和链上的数据做交互，为智能合约提供访问链的状态的能力。
智能合约能够访问到的链上数据可以分为两类：
1. 区块链的数据，比如账户数据，投票数据，资产发行等
2. 智能合约数据：storage
### 链上数据访问
在虚拟机的运行时，常常也需要访问到链已有的数据，如果账户数据，资产发行数据等。在tron的实现中，为了避免频繁对磁盘上的数据进行访问，每一个智能合约启动都会创建相应链数据库的cache。一次合约的执行，同一个key最多只会在LevelDB上访问两次，首次读取和更新数据(包括删除key)
#### Storage
Storage是为了保存智能合约的状态。每一份合约都拥有一份自己的Storage(可能为空)，在Solidity中，主要通过`SLOAD`和`STORE`对Storage数据进行访问和持久化。
Storage所存放的数据为多个KV对，storage-key和storage-value，KV均为一个word(在solidity中，为32byte)
在Solidity中，不同的数据类型的有相应的规则确定其结构，具体可见[文档](https://solidity.readthedocs.io/en/v0.4.24/miscellaneous.html#layout-of-state-variables-in-storage)，Storage的Key的逻辑结构由Solidity语言所决定，对于不同的合约可能出现一样的storage-key，故无法将storage直接按照其逻辑结构存放在我们现有的数据库(LevelDB)当中，也为了能够更加有效与链进行结合，Storage在链上的物理存储必须进行相应的设计。
由于在智能合约中对storage的访问常常只是访问其中一部分的storage-key，故并不需要将每次将一个合约中的所有Storage全部载入内存，只需要按需访问即可。为了达到这种细粒度的访问，需要将每个合约中storage-key具有全局唯一性才能够将其存放在同一个数据库中。
storage-key的逻辑结构决定其后16字节可以确保在同一个合约当中storage-key的唯一性。所以可以采用将合约地址的hash和storage-key的后16字节拼接组成全局唯一的key。组成逻辑如下：
```
input: 32-byte addrress hash, 32-byte storage-key
output: [前 16-bytes of address hash : 后 16-bytes of storage-key]
example1
input:
address base58: TGtZHTi4FZHjoNzcLcD36BnAX6FMSpLaKq
address hex : 414BE7BB5E1D250BEAF39ADB69F73527071E303375
address hash : a59e620dbf248894f097d9a6e5bcb6a2e72ab51b3d0ec19219c45be0dfc0b47d
storage-key : bbbbbb5be78dbadf6c4e817c6d170bbb47e9916f8f6cc4607c5f3819ce98497b
output:
最终组合的key为 : a59e620dbf248894f097d9a6e5bcb6a247e9916f8f6cc4607c5f3819ce98497b
example2
input:
address base58: TGtZHTi4FZHjoNzcLcD36BnAX6FMSpLaKq
address hex : 414BE7BB5E1D250BEAF39ADB69F73527071E303375
address hash : a59e620dbf248894f097d9a6e5bcb6a2e72ab51b3d0ec19219c45be0dfc0b47d
storage-key : 0000000000000000000000000000000000000000000000000000000000000001
output:
最终组合的key为 : a59e620dbf248894f097d9a6e5bcb6a200000000000000000000000000000001
```
|
Background {#Sec1}
==========
Various studies conducted show that unintended pregnancies and related consequences such as abortion are as a result of reasons such as low availability and non-use of contraceptives \[[@CR1]--[@CR3]\]. Sub-Saharan African (SSA) countries are the most affected as they have persistent high rates of unmet need for family planning and low contraceptive use \[[@CR4]--[@CR6]\]. Countries such as Tanzania and Nigeria record high unmet needs and low contraceptive use \[[@CR7], [@CR8]\].
In Ghana, the modern contraceptive prevalence as reported by the Ghana Health Demographic Survey \[[@CR9]\] was as low as 17 % with unmet need of family planning for women between 15 and 49 years at 35 % and total fertility rate (TFR) at 4.0. Ghana was one of the first African countries to adopt and formulate a National Population Policy in 1969 which was revised in 1994. The revised national policy states the aims of the family planning component in the reproductive health policy and these include: provision of information to individuals as well as making available a full range of safe and effective contraceptive methods \[[@CR10]\].
The Ghana Demographic and Health Survey \[[@CR9]\] has awareness of modern contraceptives amongst women of reproductive age at 98 %. The use of these methods varied according to the commodity, with injectables and pills as the most preferred methods. Information on the availability of these family planning commodities in health facilities in Ghana is however limited \[[@CR9]\]. The importance of making available family planning commodities in order to improve contraceptive use and family planning coverage in Ghana is emphasized in a recently released Ghana Millennium Development Goals Acceleration Frame work and Country Action Plan \[[@CR11]\].
The Ghana Millennium Development Goals framework states "making available family planning commodities in health facilities" one of the major bottlenecks that needs to be addressed in order to improve maternal health in Ghana \[[@CR11]\]. Making available family planning commodities is also linked with improved accessibility to family planning, increased family planning coverage as well as acceptability of these methods; all these lead to improved maternal and neonatal health \[[@CR11]\].
Ghana is known for operating a pluralistic health system which is guided by policies and legislations such as the Ghana Health Service and Teaching Act 525 amongst others \[[@CR12]\]. Health care in the country is obtained primarily from two main providers: the private and the public. Private providers in Ghana usually include 'not for profit' organizations and private practitioners who operate private health facilities such as clinics, pharmacies and licensed chemical shops \[[@CR12], [@CR13]\]. Private health facilities in Ghana such as pharmacies obtain their medical supplies and other required logistics primarily from registered private organizations such as pharmaceutical companies \[[@CR13]\]. Public providers on the other hand are associated with government institutions such as public hospitals, health centres and the community-based health planning and services (CHPS) \[[@CR13]\]. Public health facilities in Ghana obtain their medical supplies and other required logistics primarily from the Ghana medical stores \[[@CR14], [@CR15]\]. Health care from private providers is perceived to be better than public health care \[[@CR13]\]. It is estimated that more than fifty percent (50 %) of Ghanaians obtain their health care including contraceptives from private providers \[[@CR15]\].
This study sought to assess the availability of modern contraceptive methods in public and private health facilities and factors affecting this as perceived by facility managers in the Ga East municipality. A comparative analytical approach was used to measure this outcome.
Methods {#Sec2}
=======
Study design {#Sec3}
------------
A cross-sectional design was used allowing for a comparative analytical approach. A mixed-methods approach involving quantitative and qualitative data collection techniques was used.
Study area {#Sec4}
----------
Ghana is divided into districts, municipalities and metropolis Data for the study was collected in the Ga East municipality, a predominantly peri-urban community located in the Greater Accra region of Ghana \[[@CR16]\]. The rapidly developing population makes it ideal to study. The municipality is made up of four sub-municipalities with a total population of 320,853 and over 100 health facilities ranging from hospitals and clinics to pharmacies and licensed chemical shops \[[@CR16]\].
Sampling methods and data collection {#Sec5}
------------------------------------
The health facilities in the municipality served as the sampling frame for the study. For the purposes of the comparative analytical approach, the health facilities were first divided into two broad arms: private and public health institutions. These two broad arms were made up of four major types of health facilities depending on the level of care each facility provided. These four types of health facilities were the only available health facilities where clients could obtain family planning commodities in the district. The four types were: hospitals, clinics//maternity homes/health care centres, pharmacies and licensed chemical shops. A sample of 51 facilities from an estimated 150 health facilities were used. These were made up of 43 private and 8 public health facilities.
The municipality had only eight public health facilities where family planning services were rendered and all were used for this study. For the private institutions, a total of three different lists covering all the private health facilities in the municipality was employed to select the final sample. The first list comprising all maternity homes/clinics/ health centres and hospitals in the municipality where family planning services were provided was obtained from the municipality's health directorate in Abokobi, the capital of the municipality. Health facilities where family planning services were not provided were excluded from the list.
The municipality's health directorate could not provide a clear cut list for pharmacies and chemical shops. However, they were instrumental in the acquisition of two representative lists covering all pharmacies and chemical shops. These were obtained from the government facilities in the four sub-municipalities under the municipality.
The three different lists showed that pharmacies provided the most number of private health facilities with hospitals providing the least. The forty three (43) private facilities used were distributed as follows: pharmacies 20 (45 %), chemical shops 13 (35 %), clinics/polyclinics/health centres/maternity homes 7 (15 %) and hospitals 3 (5 %). This was in accordance with the proportion each category of health facility contributed.
Simple random sampling was employed to select from each of the three lists the required number of facility under each category. With the help of the community health nurses in the respective sub-municipalities, each of the randomly selected facilities under the various categories was located and the availability of modern contraceptives in that facility determined using a checklist. We adopted and adapted a previously used checklist in a related study \[[@CR17]\]. The current study's checklist, which was pre-tested in a few selected health facilities outside the study area, had four main sections with corresponding questions ranging from the age and sex of the respondent to the name and location of the health facility. The checklist defined availability of a contraceptive as follows:
For a contraceptive to be available, the facility manager first of all indicated that the facility had that contraceptive in stock as in Bowen *et al.* \[[@CR17]\]. Additionally, the current study impressed upon facility managers to provide evidence; and this was observed by the trained data collection personnel. Finally, for each type of contraceptive, the trained personnel ensured that the quantity in stock met the minimum contraceptive stock level for that facility.
The facility manager present in each selected facility was also interviewed by a trained personnel and the interview recorded. The in-depth interview guide used by the trained personnel also had four main sections covering key indicators such as factors affecting availability and cost of modern contraceptives in the facility. A total of 51 in-depth interviews (IDIS) were conducted amongst the facility managers.
Power calculations {#Sec6}
------------------
A descriptive study by Bowen *et al.* \[[@CR17]\] provided information on the availability of male condoms and IUDs in the municipality and this was used in the calculating the sample size. The availability of male condoms in the government health facilities was 71 % whilst that of the private health facilities was 25 %. Given the lack of data on the other modern contraceptives, this was used as a proxy. Using a 95 % confidence level and a statistical power of 80 %, the minimum sample size of 48 was obtained \[[@CR18]\] as illustrated below. At the end of the study however, 51 facilities participated.
***Sample size calculations (illustration)***Key outcome of interestExpected frequency of outcome in public health facilityExpected frequency of outcome in private health farcicalityConfidence levelStatistical powerMinimum Sample sizeAvailability of modern contraceptives (male condom used as a proxy)71 %25 %95 %80 %48
Data analysis and management {#Sec7}
----------------------------
A comparative assessment of the two groups, private and public health facilities was done after data entry and cleaning. We used univariate analysis to generate descriptive tabulations for key variables. Statistical tools such as frequency distribution tables and cross tabulation were used to compare the availability of modern contraceptives in public and primary health facilities. Analysis looking at the associations between certain attributes of the facilities (type, place, and average number of clients per day) and the main outcome variable, availability of each category of contraceptive identified, was tested using logistic regression. Associations were assessed using multiple logistic regression techniques, where odds ratios (ORs) and their 95 % confidence intervals (CI) were computed. We employed a standard logistic regression modelling in SPSS (the "Enter" method) in our analysis. With this method, all the variables previously reported to be associated with the outcome variable or found to be associated with the outcome during the bivariate analysis were entered and a full model generated in a single step. A key attribute of each model (R^2^) are included in Table [2](#Tab2){ref-type="table"}. *P* value \<0.05 was used to denote statistical significance. All analyses were performed using IBM SPSS Statistics for Windows, Version 20.0.
The key outcome variables assessed in this study was fertility intentions/childbearing desires (the desire to a child or children in the near future), awareness and use of contraceptives (being aware of and usage of various contraceptive options available to HIV-positive women).
For the qualitative aspect, the running notes from the in-depth-interviews were written into expanded notes. The audio recordings were also transcribed and read several times to clean the data. The information collected was listed in Microsoft word 2010 and then categorized manually into emerging themes. The themes were not determined prior to the start of the study.
Ethical approval and informed consent {#Sec8}
-------------------------------------
Ethical clearance was obtained from the Ghana Health ervice Ethical Review Committee of the Research and Development Division of the Ghana Health Service. In addition to the ethical clearance, permission was also sought from the Municipal director of the Ga East municipal health directorate, as well as the facility managers of the various private and public health facilities.
Informed consent was sought from the facility managers of the various health facilities and it included: the purpose of the study, the risks and benefits, privacy and confidentiality as well as conflict of interest.
Results {#Sec9}
=======
Background characteristics {#Sec10}
--------------------------
The health facilities in Ga East where contraceptives are sold were identified and categorized into two broad groups: public and private health facilities. The public health facilities were eight (8) in number and they included one (1) hospital, seven (7) health centres/clinics/polyclinics. The private health facilities used were 43 in number and these were: 13 chemical shops, 20 pharmacies, 3 hospitals and 7 health centres/maternity homes/clinics.
Range and brand of contraceptives {#Sec11}
---------------------------------
Eleven different categories of contraceptives in the municipality were identified and distributed in the health facilities as follows: combined oral contraceptives (82 %), progestin only pills (18 %), emergency contraceptives (49 %), progestin only injectable (35 %), monthly injectable (22 %), spermicides (39 %), female condoms (4 %), male condoms (78 %), copper intra-uterine devices (14 %), implants (14 %) and the ovulation predictor (2.3 %). The common brands under each category of contraceptives available in the facilities include: *Microgynon, Secure, Depo Provera, Postinor 2, Champion condom* and *Norigynon*. These brands were available in more than one of the health facilities visited (Table [1](#Tab1){ref-type="table"}). Male condoms had the most brands available (37) but they were specific to certain facilities. The long acting reversible contraceptives (LARC) such as implants and IUDs had as well as the female condoms had only one brand available (Table [1](#Tab1){ref-type="table"}).Table 1Brand of contraceptives in private and public health facilitiesType of contraceptivePrivate health facilitiesPublic health facilitiesHospitalPharmacyLC SClinic/H.C/M. HHospital Clinic/H.C/M.H/P. CCombined oral contraceptivesFrequency (*n* = 43)Frequency (*n* = 8) Microgynon--1--215 Secure119121----Emergency contraceptive WhitePostinor2--118----1 GreenPostinor2--81------Long term contraceptives Jadelle1----3--3 Copper IUD2----3--3Injectables Depo Provera21--717 Norigynon1----217Condoms Female condoms------1--1 Be Safe--95114 Protector plus--1471---- Lubricated152----2
Availability of contraceptives in public and private health facilities {#Sec12}
----------------------------------------------------------------------
The most available modern contraceptive in the health facilities was the combined oral contraceptives. Eighty four (84 %) of private facilities had oral contraceptives compared to (75 %) of public facilities (Fig. [1](#Fig1){ref-type="fig"}). The public hospital available in the municipality (100 %) and (71 %) of the public clinic/maternity had these oral contraceptives. Comparatively, all the pharmacies in the municipality (100 %) and 92 % of the LCS also had these oral contraceptives. Only 33 % of the private hospitals and 43 % of the private clinics/maternity in the municipality had these oral contraceptives. There was no statistically significant relationship between availability of combined oral contraceptives and the type of health facility (private/public) (Table [2](#Tab2){ref-type="table"}).Fig. 1Contraceptives available in private and public health facilities
The male condom was another of the modern contraceptives that was highly available in the Ga East municipality. Seventy nine (79 %) of private facilities had male condoms compared to (75 %) of public facilities (Fig. [1](#Fig1){ref-type="fig"}, Table [1](#Tab1){ref-type="table"}). The male condoms were mostly available in pharmacies (95 %) and LCS (92 %). Only 33 % of the private hospitals and 28 % of private clinics/maternity in the municipality had these male condoms. Comparatively, (71 %) of the public clinic/maternity homes and the public hospital (100 %) had the male condoms. From the multiple regression analysis, there was no association between availability of male condoms and type of health facility (private /public).
The perceived reasons for the high availability of condoms in pharmacies and LCS was summed up by one of the facility managers as follows:"*"People are learning and they want to protect themselves so most of these men go for condoms" (chemical shop assistant).*"
All (100 %) public health facilities (both hospitals and clinics/maternity homes) had both the 3-month injectable and the monthly injectable available. The 3-months injectables was also available in all (100 %) of private clinic/maternity and 75 % of private hospitals. None of the LCS visited had the 3-months injectables whilst (5 %) of pharmacies had them available. The monthly injectables was not available in any of the LCS and pharmacies whilst 28 % of clinics/maternity homes and 33 % private hospitals had them in stock. The facility managers at the chemical shops and pharmacies offered reasonable explanations for not having injectables."*"We do not give injections here. When clients come we tell them to go to the hospital or clinic. Those are the places where injections are given." (pharmacy assistant)"The injectables belong to the hospitals and clinics. We refer anyone who comes asking for some to those places." (chemical assistant)*"
The emergency contraceptives was available primarily in private health facilities such as pharmacies (75 %) and LCS (69 %). At the bivariate level, emergency contraceptives were less likely to be found in public health facilities (OR = 0.11, *p* = 0.05) (Table [2](#Tab2){ref-type="table"}).Table 2Comparison of availability of modern contraceptives in public and private health facilities: Univariable and Multiple Logistic RegressionContraceptive type availableOR^1^ \[95 % CI\]OR^2^ \[95 % CI\]Combined oral contraceptive Private1 Public0.58 \[0.10--3.50\]0.63 \[0.33--11.84\]Progestin only Private1 Public7.60\* \[1.43--40.39\]0.30 \[0.02--4.71\]Male condoms Private1 Public0.80 \[0.14--4.62\]0.30 \[0.01--7.46\]Implants Private1 Public5.85\* \[1.01--34.10\]3.24 \[0.11--93.07\]Copper IUD Private1 Public5.85\* \[1.01--34.10\]3.24 \[0.11--93.07\]For the multiple regression the following categories of contraceptives: the combined oral contraceptives, the male condoms, the implants and the copper IUD contained three predictor variables namely, the type of facility (eg LCS, pharmacy) under each health institution, the last time the facility was stocked with contraceptives and the average number of clients. The progestin only contraceptive contained two predictor variables namely the type of facility (eg LCS, pharmacy) under each health institution and the average number of clients per day*OR* ^*1*^ Odds Ratio for univariable logistic regression, *OR* ^*2*^ Odds Ratio for multiple logistic regression analysis, *CI* ^*1*^ &*CI* ^*2*^ 95 % Confidence Interval for OR^1^ & OR^2^\**P* value significant at 0.05
The increase use of emergency contraceptives in private health facilities such as LCS and pharmacies was summed up by one of the facility mangers as follows:"*"Most of the clients like the emergency contraceptives. I know someone who takes it virtually every day. She claims she can enjoy sex with her boyfriend and still prevent pregnancy." (pharmacy assistant)*"
One of the facility managers at the public health facilities also had this to say about the emergency contraceptives:"*"The clients abuse them when we give it to them. In order not for them to abuse it we do not sell the emergency contraceptives." (public health nurse)*"
The Jadelle implants and the copper IUDs were the long-acting reversible contraceptives (LARC) identified in both private and public health facilities. There were no LARC methods available in pharmacies and LCS. The implant was not available in the public hospital compared with 33 % of the private hospitals. Forty three percent (43 %) of both private and public clinics/maternity homes had implants. The copper IUD was available in twenty eight (28 %) of the private clinics/maternity homes as compared with 43 % public clinics/maternity homes. There was no statistically significant relationship between the availability of implants and copper IUDs and type of health facility (public/private). One of the main reasons for the low availability of LARC methods in both public and private health facilities particularly the hospitals and clinics/maternity was summarized by a facility manager as follows;"*"No one in this unit has been trained to do insertion of the IUDs or implants. My immediate boss will soon undergo the training but till then we do not sell the implants or IUDs." (public health nurse)*"
Facility managers' perspectives on factors affecting the availability of contraceptives in public and private health as perceived by facility managers {#Sec13}
------------------------------------------------------------------------------------------------------------------------------------------------------
This study sought to determine why these facilities sold the particular type of contraceptives they had in stock. The major factors or themes that emerged from these discussions were 'policies', 'training', 'competition', 'preference' 'demand', 'profit' and 'infrastructure'. Some of the facility managers talked extensively about these factors.**Demand-** "*The demand of the people determines what we have. We sell what people ask for. Some of these contraceptives do not sell fast and if you stock them they might expire."(pharmacy assistant)***Preference-***"The females themselves do not like the female condoms. They say it is difficult and unpleasant to use them and they prefer them as bangles. I only have a sample just for display."(public health nurse)***Policy-***"The pharmacy council does not allow us to sell certain drugs so we cannot sell injections" (chemical shop owner)***Infrastructure-***"We do not have a place specifically for family planning. The maternity ward also doubles as the family planning unit. Plans are underway to put in place a family planning unit" (medical assistant)*
Discussion {#Sec14}
==========
In the Ga East municipality of Ghana where this survey was carried out, eleven categories of modern contraceptive methods were identified ranging from combined oral contraceptives to spermicides.
For the private health facilities such as pharmacies and LCS, the combined oral contraceptives, the emergency contraceptives and the male condoms were the most available contraceptives compared with other modern contraceptives such as injectables and LARCs. The most available modern contraceptive in the public health facilities was the injectables and it was the only method available in all the public hospitals and clinics (100 %) in the municipality. Contrary to expectations, one private pharmacy also had available the injectables. None of the LCS had injectables available.
Hong *et al.* \[[@CR19]\] lists the most available modern methods of contraceptives in Ghana as the pills, the injectables and the male condoms.
Findings from our study however indicates that the injectables might be available only to women who patronize public health facilities but not to those who patronize private health facilities like LCS and pharmacies. From the discussions with the facility managers, it was clear that the injectables were not available because of policies which do not allow the sale of these modern contraceptives in pharmacies and LCS.
In Ghana, LCS are on the increase and evidence shows that more women are patronizing these services \[[@CR20]\]. Lebetkin *et al.* \[[@CR20]\] recently in their study have shown that it is possible to equip these facilities to effectively administer these injectables. It would be great if policies surrounding the sale of these injectables are therefore re-looked at to enable the sale of these injectables at LCS and pharmacies. Safer and easier to handle injectables such as 'sayana press' which has also been shown to work in some selected countries can also be introduced to these facilities to increase the availability of injectables to women who patronize LCS and pharmacies \[[@CR21]\].
The availability of long acting reversible contraceptives (LARC) methods such as the implants and the copper IUDs in this study was low with only 7 out of the 51 health facilities (14 %) having them in stock. None of chemical shops and pharmacies sampled had these LARC methods. The levenogestrel IUD was also not available in any of the health facilities surveyed. The facility managers in the LCS and pharmacies attributed this to policies on the sale of these LARC whilst those in the public hospitals and clinics attributed this to the lack of trained personnel on the insertion of these methods.
This observation highlights a growing challenge observed by Aryeetey *et al.* \[[@CR6]\] in which it was made apparent that awareness of LARC methods in the Ga East municipality was low. It also adds to the growing perception that this is one of the key barriers that need to be addressed in order to increase the utilization of contraceptives in Ghana and in particular public health facilities, is the health service barrier \[[@CR6], [@CR15]\]. It also underlines the problem of inadequately trained staff in insertion of these methods since these methods can only be inserted in facilities with trained providers \[[@CR15]\]. Findings from this study also suggest the utility of motivating an increase the number of private hospitals and clinics/ maternity homes as well as public hospitals and clinics/maternity health centres which offer family planning in the municipality if there is to be an increase in availability of LARC methods since these methods require surgical procedures that can be carried out only in these types of facilities. The introduction of the CHPs concept in this area and the probable setting up of CHPs compounds in the municipality is a step in the right direction.
Finally, this present study also demonstrated the different brands of contraceptives under each category of contraceptive identified. *Secure* was discovered as the most available brand of contraceptive pills particularly in private health facilities. This is in accordance with the Ghana Demographic and Health Survey \[[@CR9]\] which reports that *Secure* is the most popular brand of contraceptive pills in Ghana. Other contraceptive pills identified during this study include, *Microgynon*, *Blue, Yasmin, Primolut-n, Overette, Microlut* and *Micronor*. The Ghana Demographic and Health Survey \[[@CR9]\] confirms the availability of these brands in Ghana in addition to other brands such as *Lo-femenal, My pearl, N/M, OC, Duofem, Oral, Skill* and *Hot* which were not identified in the health facilities sampled for this study. A limitation of our study which was the small number of public health facilities available and hence a small sample of facilities were used could account for this. Nevertheless, the absence of other brands of contraceptive pills in this study as compared to the Ghana Demographic and Health Survey \[[@CR9]\] could be an indication of the decline in the options available to users of this method particularly in this municipality and this could cause a subsequent decline in its use.
Conclusions {#Sec15}
===========
This comparative study on the availability of modern contraceptives in both private and public health facilities has brought to light the low availability of some contraceptives particularly the female condom and LARC methods such as implants and IUDs in these facilities.
This study has also revealed the high availability of methods such as emergency contraceptives and spermicides in private institutions as compared with public ones. Methods such as the injectables are more available in public health facilities compared with private ones.
Recommendations {#Sec16}
===============
We recommend that policies regarding the sale of injectables in LCS and pharmacies be re-looked at to increase availability and possible use of these methods. Increasing the number of trained personnel in LARC methods in both private and public hospitals as well as clinic/maternity homes may positively affect their availability in the currently authorized outlets.
Martha A. Abdulai, Sam Newton, Seth Owusu-Agyei and Sam Adjei contributed equally to this work.
**Competing interests**
The authors declare that they have no competing interests.
**Authors' contributions**
KKA, SA and AKL conceived the idea. CTN, KKA and AKL were involved in analyzing the data. All the authors (KKA, AKL, CTN, MAA, SN, SOA and SA) were involved in drafting the final manuscript. All authors have proof read the final manuscript.
The authors acknowledge the administrative support provided by the Ghana Health Service, Kintampo Health Research Centre, Centre for Health and Social Services and the School of Public Health of theUniversity of Ghana, Legon, Accra. We are also grateful to the Ga East Municipal Health Directorate and all study participants.
|
Downtown Martinsburg Historic District
Downtown Martinsburg Historic District is a national historic district located at Martinsburg, Berkeley County, West Virginia. It encompasses 281 contributing buildings. It includes government and industrial buildings, several schools, firehouses, and churches, the two main commercial and professional areas along Queen and King Streets, a major hospital, and surrounding residential areas. The buildings reflect a number of popular 19th-century architectural styles including Gothic Revival, Italianate, and Queen Anne.
It was listed on the National Register of Historic Places in 1980.
References
Category:Historic districts in Martinsburg, West Virginia
Category:Queen Anne architecture in West Virginia
Category:Gothic Revival architecture in West Virginia
Category:Italianate architecture in West Virginia
Category:Historic districts on the National Register of Historic Places in West Virginia |
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CDL-A Company Solo and Team OTR Drivers - New Pay IncreaseDescription: CDL-A Company Solo and Team OTR Drivers - New Pay Increase If you're looking for a company with a competitive pay package, monthly bonus, paid holidays and much more, consider Guaranteed Company: Guaranteed Transport ServiceLocation: SpartanburgPosted on: 03/22/2019 |
//
// Generated by class-dump 3.5 (64 bit) (Debug version compiled Jul 6 2018 12:02:43).
//
// class-dump is Copyright (C) 1997-1998, 2000-2001, 2004-2015 by Steve Nygard.
//
#import <AppKit/NSControl.h>
@class NSShadow;
@interface BCColorPickerBaseView : NSControl
{
BOOL _hideSelection;
id _bc_target;
SEL _bc_action;
NSShadow *_markerShadow;
}
+ (void)drawFrameInRect:(struct CGRect)arg1 forView:(id)arg2 block:(CDUnknownBlockType)arg3;
+ (void)drawFrameInRect:(struct CGRect)arg1 outlineWidth:(double)arg2 cornerRadius:(double)arg3 block:(CDUnknownBlockType)arg4;
- (void).cxx_destruct;
@property(retain, nonatomic) NSShadow *markerShadow; // @synthesize markerShadow=_markerShadow;
@property SEL bc_action; // @synthesize bc_action=_bc_action;
@property(nonatomic) __weak id bc_target; // @synthesize bc_target=_bc_target;
@property(nonatomic) BOOL hideSelection; // @synthesize hideSelection=_hideSelection;
- (BOOL)acceptsFirstMouse:(id)arg1;
- (void)drawMarkerInRect:(struct CGRect)arg1;
- (void)drawCheckerboardPatternInRect:(struct CGRect)arg1;
- (void)drawBackgroundInRect:(struct CGRect)arg1 dirtyRect:(struct CGRect)arg2;
- (struct CGRect)contentBounds;
- (void)drawRect:(struct CGRect)arg1;
- (id)initInBounds:(struct CGRect)arg1;
- (void)setAction:(SEL)arg1;
- (void)setTarget:(id)arg1;
- (SEL)action;
- (id)target;
@end
|
package com.guoxiaoxing.phoenix.picture.edit.widget.blur
import com.guoxiaoxing.phoenix.R
/**
* ## Mosaic mode supported in current version
*
* Created by lxw
*/
enum class BlurMode {
Grid {
override fun getModeBgResource() = R.drawable.phoenix_selector_edit_image_traditional_mosaic
},
Blur {
override fun getModeBgResource() = R.drawable.phoenix_selector_edit_image_brush_mosaic
};
abstract fun getModeBgResource(): Int
} |
Q:
Creating an array from JSON data in GAS
I am trying to make an array like value1,value2,value3 that I can iterate through later.
I have the following so far:
var url = 'URL_STRING';
var headers = {
headers: {
Username: 'USERNAME',
"Authorization": "Bearer " + 'KEY'
},
contentType: "application/x-www-form-urlencoded",
};
var response = UrlFetchApp.fetch(url, headers);
var json = response.getContentText();
var obj = JSON.parse(json);
var audits = obj.audits;
Logger.log(audits)
The log shows:
[{
id = value1
}, {
id = value2
}, {
id = value3
}]
I thought I would be able to do something like var arr[] = obj.audits.id but this does not work.
A:
Use map:
const audits =[{
id : "value1"
}, {
id : "value2"
}, {
id : "value3"
}];
const arr = audits.map(({id:v})=>v);
console.log(arr);
|
Studies of the biogenic amine transporters. II. A brief study on the use of [3H]DA-uptake-inhibition to transporter-binding-inhibition ratios for the in vitro evaluation of putative cocaine antagonists.
The cocaine receptor on the dopamine transporter is a logical target binding site for the design and synthesis of novel agents for evaluation as possible cocaine antagonists. Although there is no widely accepted and validated assay for detecting a cocaine antagonist, one commonly accepted strategy is to compare the IC50 value of a test agent for inhibition of [3H]dopamine uptake and its IC50 value for inhibition of the binding of a transporter ligand such as [125I]RTI-55. The goal of such a comparison is to guide the synthesis of agents which have high "uptake-to-binding ratios", i.e. agents which are much more potent in the binding assay than they are in the uptake assay. In the present study we tested the hypothesis that ratios different from unity can result from the fact that the two assays are conducted under markedly different conditions. The results showed that conducting the uptake and binding assays under identical conditions reduced the GBR12935 uptake-to-binding ratio of 6.20 (under standard assay conditions) to 0.36. These data indicate that uptake-to-binding ratios must be interpreted with caution, and emphasizes the need for simpler and less expensive methods than cocaine self-administration paradigms to screen compounds as modulators of cocaine reinforcement. |
OTTAWA -- A new analysis says governments can wrestle recreational-pot proceeds away from criminals -- just so long as they're not counting on an early windfall from legalized weed.
The study, to be released Tuesday by the C.D. Howe Institute think tank, estimates legalized cannabis would generate about $675 million in 2018 in combined federal and provincial revenue through existing sales taxes.
However, if authorities want to raise even more cash in the early days of legalization through additional taxes, they risk undermining their stated priority of squeezing out organized crime, the report says.
The study comes as the Trudeau government prepares to introduce legislation Thursday to begin the process of legalizing pot.
"The government does actually have to choose at the outset between minimizing the black market and a large amount of revenue generation -- it can't do both," study author Rosalie Wyonch said in an interview.
"However, if they do manage to nearly, fully legitimize the market, that's when they can start to implement higher tax rates without necessarily re-entrenching the illicit market."
Using a $9-per-gram example, Wyonch estimates 90 per cent of Canada's weed market would be legitimate if existing sales taxes were the only taxes applied.
But if governments seek to lift their total tax revenues on pot sales to around $1 billion, she said, illicit sales would likely grow to about half of Canada's marijuana market.
Policy-makers could hit that threshold by tacking on as little as one loonie per gram, she added.
Wyonch, a C.D. Howe policy analyst, said while the legal-pot revenues will be modest at first, there's potential for more money to be made once the market matures and large companies streamline their operations.
To produce her numbers, she said she used price estimates of illegal pot, by province, that were included in a report published last November by the parliamentary budget office.
That report found sales tax revenue on cannabis in 2018 could be as low as $356 million and as high as $959 million, with a likely take of about $618 million. The calculations were also based on legalized pot selling for $9 per gram -- in line with current street prices.
It also suggested that pricing legal pot too high would allow the black market to continue to flourish. If prices stay too low, it said, governments could be seen to be encouraging its use.
Other studies have predicted far bigger marijuana-fuelled windfalls for Ottawa.
CIBC World Markets has estimated federal and provincial taxes could be as much as $5 billion a year from legal pot, while Deloitte has projected as much as $22.6 billion in economic activity from recreational marijuana, including $5 billion to $8.7 billion per year in retail market sales.
The Trudeau government has said that any eventual pot proceeds would be earmarked for addiction treatment, mental health support and education programs.
The feds have also said their goals include keeping pot away from young people and the proceeds of its sale out of the hands of organized crime.
Last month, Finance Minister Bill Morneau said the government had yet to fully explore how much revenue it expects legal pot to generate. |
41
Evaluate -2 + -17 + (4 + -23 + 20 - -28).
10
-135 + -1 - (6 + (-13 - (29 - 30 - -1)))
-129
-3 + 9 + 2 + 0 + 180 + -190 + -5
-7
What is 17 + (30 - 39) + -10 + (1 - 16)?
-17
Calculate 1544 - 1539 - (-25 - 0).
30
Evaluate (6 - 1) + (-4 - 4) + (106 - 113).
-10
-3 + 11 + (-3389 - -3373 - (0 + -19))
11
Calculate 3 - (6 + -4) - (23 + -13) - (-2 - 90).
83
Evaluate (40 + -249 - -113) + 117.
21
What is the value of 48 - 91 - (-17 - 11)?
-15
Evaluate 2 + -2 - -2 - (-31 - (77 - 76)).
34
What is -6 + -15 + (5 - (13 + -16))?
-13
7 - -2 - ((11 - 2) + -101 + 101)
0
Calculate -24 + 48 + -22 + (4 + -8 - 5).
-7
Calculate 16 + -2 - (58 - (48 - -2)) - -48.
54
Calculate -27 + (-1 + 30 - (-1021 - -1019)).
4
Calculate -40 + (38 - -3 - 22).
-21
Calculate 50 + 4 + -31 + (-5 - -29).
47
What is the value of 52 + 33 - 66 - 7?
12
Evaluate -7 - (6 - (-17 + -16) - 11).
-35
What is 98 - (29 + -79 + 115)?
33
What is 36 + -28 + -9 - (-8 + (16 - 8))?
-1
(104 - (519 + -491)) + (1 + -1 + -1 - -5)
80
Evaluate 7255 + -7315 + (1 - -19).
-40
Calculate 128 + -187 + (-4 - -10) + -13 + -7.
-73
What is 0 - 33 - (-35 - -9)?
-7
Calculate (7 - 2) + 7 + (106 - 77).
41
Evaluate (-4 + 0 - -2) + -28 + (-1218 - -1211).
-37
27 + (-44 - -54) + (21 - 0)
58
(-47 - -44) + (4 - (0 + 26))
-25
Evaluate (-17 - -13 - -9 - (39 - (2 + -5))) + 7.
-30
What is -52 + -37 + (46 - -35) - (47 - 0)?
-55
Calculate (-7 - (14 - -7)) + (-35 - -20).
-43
What is -60 + 49 - ((14 - (18 - 9)) + 70)?
-86
114 + -133 + (-5 - (-4 - -9))
-29
Evaluate (-4 - (2 - 1)) + 3 + (14 - 4) - 10.
-2
What is the value of -1 + 9 + -56 + 41 - (16 + -33 + 50)?
-40
Calculate 17 + 6 + -8 - 14 - (53 + -7).
-45
Evaluate (50 + -135 - 10) + 16.
-79
Evaluate -87 + 149 + -81 + (-7 - -18).
-8
(-72 - -2) + (-300 - -294 - (2 - (11 + 0)))
-67
Calculate -1 - (6 + -14 + -18 + 69).
-44
5 + 28 - (27 - 47 - -8)
45
9 - (-5 + (20 - 11) + (1 - -4) - 4)
4
What is the value of (11 + (-12 - -17) - -9) + -35 + -42?
-52
Evaluate -44 - (4 - 10 - 10) - 15.
-43
What is the value of (10 - 43) + (1 - 16)?
-48
What is 0 + -1 + 1 + (1189 - 1197) + 34?
26
What is (-41 - 1) + 63 - (16 - -2)?
3
Evaluate 1776 - 1966 - (1 - 135).
-56
Evaluate -8 - (100 + -49 + -42).
-17
Evaluate 10 + -18 - ((52 - 11 - -11) + 4).
-64
(5 - 49 - 39) + 29
-54
Calculate -7 + 2 + (9 - 4) - (-5 - (-111 + 1)).
-105
Calculate -20 - (-50 + -8 + -36 + 15).
59
What is (-16 + 1 + -2 - (-16 - -11)) + (-632 - -693)?
49
49 + -10 + -13 + (0 - -5) - (307 - 315)
39
What is the value of -57 + (86 - 86) + 107?
50
13 - ((25 - (-28 - -42) - (25 + 1)) + 4)
24
What is 88 + -2 - (-17067 - -17052)?
101
What is 50 - -4 - ((394 - 405) + (1 - -19))?
45
Calculate -2 + 68 + (-34 + 30 - ((2 - 1) + -5)).
66
What is the value of 28 + (-2 - (4 - (16 + -6))) + -40 + 42?
34
(87 - -5) + 41 + (-103 - -42)
72
-77 + 0 + 0 + -41
-118
Calculate (-47 - 3) + (-24 - (-8 + -30)).
-36
Calculate 0 + 8 + -7 + -37 + 88 + -110.
-58
Calculate 59 + (-54 - (1 - 12)).
16
What is the value of -57 + (-132 - (80 + -311))?
42
Evaluate 14 + -1 - (7 - -166 - 130).
-30
Evaluate -36 + (-77 - -144 - 70).
-39
(963 + -948 - (-4 + 8 - -16)) + (-75 - 0)
-80
-30 - (0 + -15 + -8) - ((-2 - -20) + 2)
-27
What is (14 - 0 - (-1 + 2)) + (-26 - -9)?
-4
What is the value of -13 + (36 + -13 - 4) + -3 - -1?
4
Evaluate -28 + (-45 - -36) - 9.
-46
What is -103 + 67 + (-117 - -79)?
-74
-1 + 16 + (-8 - -17)
24
Evaluate -34 - 0 - (-40 - (-190 + 114)).
-70
Evaluate 82 + 0 - (-9 - ((1 - -5) + -76 + 70)).
91
What is -8 - -17 - (-3 + 5 - 3 - (-17 + 10))?
3
What is the value of 26 + 30 + -84 + 106?
78
What is the value of (-8 - -11) + 60 + 0 + -24 + 12?
51
What is the value of (-1 - -3 - (-6 + -2)) + 195 + -202 + -97?
-94
Calculate 2 + 61 - (1198 - 1183).
48
Evaluate -13 + -30 - (468 - 493).
-18
What is -46 + 82 - (18 - -23)?
-5
11 - (5 - ((1 - -8) + (35 - (-15 - -13))))
52
What is 0 + (-2 - 2) + 0 - (52 + -31) - -10?
-15
What is 6 - -24 - (64 - 51)?
17
What is the value of -17 + (-38 - -29) + (-54 - 28)?
-108
What is 23 + -6 + 6 + -4 + -65?
-46
What is the value of 94 - (8 + -44 - -87)?
43
(1 - (-5 - (-4 - 0))) + (-69 - -75)
8
79 + (-18 - (-12 + -4) - 12) + 3
68
What is (-14 - 98 - -73) + 20?
-19
Evaluate 325 - 295 - (-6 - 47).
83
Evaluate 45 + -2 + 31 + -49.
25
What is (-1 - -4 - 19) + (313 - 310) - (2 + 23)?
-38
Calculate 11 - (-66 - (-19 - (-7 + -4)) - 1).
70
(-1 - (0 - -8)) + (-1186 - -1163)
-32
(1 - 2 - (-736 - -761)) + -44
-70
What is -17 + 0 + (-91 - -141 - 54)?
-21
What is the value of 1 - 72 - (84 + (-80 - -32) + -25)?
-82
-1 - 15 - (36 - (134 - 39 - -29))
72
What is the value of -74 + 11 + (10 - (9 + 18)) + 9 + -5?
-76
Calculate (-20 + 25 - 19) + 64 + 0 + 11 + -4.
57
Evaluate -11 + 28 + -34 + 27 + 14.
24
What is (-4 - 4) + 0 - (111 - 101) - (52 - 42)?
-28
What is the value of 1084 + -1133 - (1 + -37)?
-13
Calculate 33 + (19 - (-32 + 56)) + 70.
98
Calculate (-36 - -2) + (-82 + -5 - -73).
-48
(-25 - 0 - (-112 + 93) - (0 + -39)) + -11
22
What is the value of 3 + -57 + 5 + -73?
-122
What is the value of (-3 - 8) + (85 - 89) - -11?
-4
Evaluate 12 - (-3 + 10 + -6) - (-1 + 15 - -3).
-6
Evaluate (7 - (3 + 39)) + 22 + (-3 - 75 - 1).
-92
What is 4 + (2 - (13 - 7 - (-11 - -6)) - 27)?
-32
Calculate 128 + (1 - 65) + -35.
29
Calculate (2 + -1 - 1) + (-22 - (-15 + 14 + 4)).
-25
Calculate -1 - (4 - (22 - 2)) - (-148 + -47 + 108).
102
What is the value of 11 + (-72 - -42) - ((-1 - 0) + 5 - 10)?
-13
What is (5 - (17 + -38)) + (-22 - -26)?
30
Evaluate -3 + 4 + 5 + (0 - 16 - (-32 - 11)).
33
What is -17 - (-14 - ((-21 - 14) + -3) - 19)?
-22
What is 49 - (-67 - -36 - -66)?
14
Calculate 7 + -90 + 91 + 53 + 1.
62
What is the value of -7 - (37 + (-3 - 2) + 20)?
-59
Evaluate (-28 + 4 - -7 - -121) + (-2 - 5) + -2.
95
75 + -49 + -53 + 29
2
What is 122 - 170 - (-5 - 11)?
-32
What is -8 + 0 + (-16 + -117 + 112 - (0 - 30))?
1
Calculate -56 + (-2 + -1 + 264 + -255 - -17).
-33
What is 30 + -4 + (3 + -4 - (-10 + 12))?
23
What is the value of (2 - 22) + -14 + -18 + 84?
32
Calculate 13 + -10 + (-22 - 9) + 13.
-15
What is the value of 24 - ((23 - 44) + 2 + 13)?
30
Evaluate -20 + -4 + 17 - (5 + 16) - 18.
-46
What is the value of -105 + (47 - -64) + -1 + -1?
4
What is the value of -30 - -1 - ((39 - 103) + 52)?
-17
63 + 66 + -70 + -12
47
What is (1 - (2 - -3)) + (12 - 17) + 11?
2
Calculate -16 + -1032 + 1085 + (-2 - 0).
35
Evaluate 20 + -26 + 14 + -6 - (-73 + -1 + -4).
80
Evaluate 35 - 1 - (-946 - -1000).
-20
What is the value of 19 - (8 + (-50 - -22) - 4)?
43
What is the value of 14 + (46 - (47 + 47) - 31)?
-65
What is (-8 + 1 - (-10 - (26 + -26))) + (49 - 2)?
50
Evaluate -69 - -3 - (-7 + 20 + -23 + 2).
-58
What is the value of (-4 - -9) + -6 + (-4 - 1) + 13 + 1?
8
What is the value of -2 + -3 + 27 + -23 - (-1320 + 1420)?
-101
Calculate -91 + 5 + (-8 - -5) + (-33 - -17) + 26.
-79
Calculate -58 + -18 - -46 - 39.
-69
(0 - 3 - -1 - -4) + (-127 - -122) + -72
-75
What is the value of (7 - -20) + (-4 - (-10 - (2 + -13)))?
22
Evaluate (10 - (52 - 25)) + (44 - -1).
28
Calculate -937 + 965 - (5 + -12 + 24).
11
Calculate 149 + -93 - (25 - -7).
24
(-111 + -24 - -131) + 1 + 15
12
What is (-88 - (24 - 66 - -35)) + 1?
-80
Evaluate 14 - (-21 - (-9 + 30 + -97)).
-41
-24 + (-139 - -47 - -44)
-72
What is the value of 4 + -38 + (142 + -56 - 75)?
-23
(-1 - (-2 + (-15 - -17))) + (-12 - -2)
-11
Calculate 38 + (40 - 1 - 14 - 31).
32
What is (-22 - 19 - -52) + 13?
24
Evaluate 83 + (43 + (13 - 43) - 38).
58
What is the value of -7 + 60 + (5 - (10 + 5 + -4))?
47
-75 - (-139 + 70) - (9 - (4 - 2))
-13
Calculate 0 + 16 - (-8 - -36) - -127.
115
-4 + (9 - 1 - (3 + 22 + -18 - -8))
-11
What is the value of (0 - -28) + -81 + 106?
53
Evaluate 50 - 22 - (3 + 29).
-4
Calculate 46 + -58 + 26 - 0 - -134.
148
What is 10 + 13 - (-1 + 20 + -4)?
8
Calculate (17 - -16) + -1362 + 1436.
107
-16 + (60 - 43) + -16
-15
97 - -15 - (-522 - -580)
54
Calculate 4 + -8 + (15 - 14) + (44 - (0 - 2)).
43
Evaluate 22 - -17 - (3 - -32) - -42.
46
What is (-20 - 1) + -7 + 13 + (14 - (29 + -3))?
-27
(-2 - 0 - 1) + (-18 - 5)
-26
What is the value of -90 + (22 + 3 + -13 - -2) + 5 + -7?
-78
Evaluate 45 + -12 + (12 + 1 - (0 - -1)).
45
What is the value of 22 - 4 - (-2 - (19 - -3))?
42
(14 - 1) + 0 + -1047 + 1098 + -5 + 49
108
Calculate -9 - ((6 - -4 - 1) + (16 - 22) + 10) |
Yixin to focus on online payment
China Telecom Corp Ltd said on Wednesday that its new messaging product Yixin marks a major step in the company's attempt to diversify into Internet business.
The country's biggest fixed-line and third-largest mobile operator by user numbers hopes that growth in the new field can help compensate for an expected slowdown in its infrastructure-based broadband, fixed-line and mobile businesses.
"We need a new growth engine as the growth of our traditional businesses will slow down," Wang Xiaochu, the company's chairman and chief executive officer, said at a news briefing in Hong Kong. He made the comments after reporting 15.9 percent profit growth in the first half to 10.2 billion yuan ($1.66 billion).
But Wang added that China Telecom's Internet business wouldn't be on par with industry giants such as Tencent Holdings Ltd and NetEase Inc.
Instead, in order to leverage its extensive infrastructure, the State-owned enterprise will focus on online payment.
He added that the country's biggest broadband provider would maintain a cautious attitude toward acquisitions, and would look instead at cooperation based on the model of Yixin, which was jointly launched on Monday with NetEase, one of the country's leading Internet companies.
The new service looks like an upgraded version of WeChat, which was developed by Tencent and is currently the nation's most popular mobile messaging service, with around 500 million users worldwide.
Besides offering text, image and voice messaging like WeChat, Yixin also offers music and e-mail linkage services. It also allows users to send SMS and voicemails to mobile phones with no Internet connection. A joint venture has been formed to run the service.
China Telecom has a controlling 73 percent stake in the venture, which has registered capital of 200 million yuan. NetEase holds the remaining stake.
More than 1 million people downloaded the Yixin service within 24 hours of its launch. Wang said that games, which are the most profitable component of China's Internet industry, would be launched in the service. NetEase is one of the nation's top operators of online games.
Yixin is supposed to be a major competitor of WeChat, which was recently monetized through the addition of games.
On Wednesday, China Telecom rose 1 percent to HK$4.06 (52 US cents) in Hong Kong trading. The stock has dropped 5.4 percent this year, compared with a 3.8 percent decline in the benchmark Hang Seng Index.
Its operating revenue grew 14 percent year-on-year in the first half, to 157.5 billion yuan. Revenue was 139.2 billion if sales of mobile terminals were excluded, up 10 percent year-on-year. The company added 13.88 million mobile subscribers in the January-June period, bringing its total number of subscribers up to 175 million.
The company added 18.28 million 3G users in the first half, bringing the proportion of its 3G users to 50 percent. That surpassed both its both its larger rivals, China Mobile Ltd and China Unicom (Hong Kong) Ltd. |
111 F.2d 260 (1940)
UNITED STATES
v.
WEISMAN.
No. 278.
Circuit Court of Appeals, Second Circuit.
April 22, 1940
*261 Before L. HAND, CHASE, and CLARK, Circuit Judges.
George Wolf, of New York City, for appellant.
John T. Cahill, U. S. Atty., of New York City (Walter R. Mansfield and Jerome Doyle, Asst. U. S. Attys., both of New York City, of Counsel) for appellee.
L. HAND, Circuit Judge.
The defendant appeals from a sentence of six months following a conviction by the district judge for refusing to answer two questions, put to him by a grand jury on January 26, 1940. The questions were: first, whether he had ever received any cables at Murray's Restaurant, Sixth Avenue, New York; second, whether he knew anyone who visited, lived in, or stayed at, Shanghai in the years 1934 to 1939. The defendant had already been before the grand jury a number of times in December, 1939, and January, 1940, and had answered a few questions, but in the main had claimed his privilege against crimination. On January 22, he had denied that he had received any cables at Murray's Restaurant in 1934, but had immediately asked to retract the answer, and had thereupon asserted his privilege. Similarly on the 24th he had at first denied that he knew anyone who had visited Shanghai in 1934, but had immediately asked to retract; as to 1939 he also denied knowing anyone, but that denial he let stand. These answers the prosecution urges as an abanddonment of the privilege; but we agree with the defendant that they were slips, and not really intended as an abandonment. The defendant's attorney, who was of course not with him before the grand jury, had instructed him to claim his privilege, and nothing had happened to change that purpose which he had claimed again and again. We shall, therefore, dispose of the appeal on the assumption that the privilege, whatever it was, remained.
The two questions were on their face innocent, and it lay upon the defendant to show that answers to them might criminate him. United States v. Burr (In re Willie), Fed.Cas. No. 14,692e; State v. Thaden, 43 Minn. 253, 255, *262 45 N.W. 447; Regina v. Boyes, 1 B. & S. 311, 321; United States v. Zwillman, 2 Cir. 108 F.2d 802. Whether he had the burden of proof upon that issue we need not decide, for we think in any case he proved his excuse. Obviously a witness may not be compelled to do more than show that the answer is likely to be dangerous to him, else he will be forced to disclose those very facts which the privilege protects. Logically, indeed, he is boxed in a paradox, for he must prove the criminatory character of what it is his privilege to suppress just because it is criminatory. The only practicable solution is to be content with the door's being set a little ajar, and while at times this no doubt partially destroys the privilege, and at times it permits the suppression of competent evidence, nothing better is available. All this has been long understood, but it is not so clear to what facts the privilege extends. Does it protect more than those which "tend" to prove a crime? Does it also cover those which can only be clues to the discovery of other facts which in turn so "tend"? The doctrine of Counselman v. Hitchcock, 142 U.S. 547, 12 S.Ct. 195, 35 L.Ed. 1110, goes as far as the second; though we need not say how far it has been affected by later decisions. Mason v. United States, 244 U.S. 362, 37 S.Ct. 621, 61 L.Ed. 1198. All crimes are composed of definite elements, and nobody supposes that the privilege is confined to answers which directly admit one of these; it covers also such as logically, though mediately, lead to any of them; such as are rungs of the rational ladder by which they may be reached. A witness would, for example, be privileged from answering whether he left his home with a burglar's jimmy in his pocket, though that is no part of the crime of burglary. This, as we shall try to show, is as far as we need go here.
The defendant offered in evidence an indictment found in the year 1937 by the grand jury of the Southern District of New York against thirty persons (not including himself), charging a conspiracy to import narcotic drugs from Shanghai, payment to be made either by messenger, or by cable, direct to China; cables also being sent from New York to advise the shippers that the drugs had arrived, upon which "arrangements would * * * be made, likewise in code, by cable for the transmission of the next shipment". This indictment the judge ruled out, but it was clearly competent, and we shall dispose of the appeal as though he had admitted it. The defendant's examination was part of an investigation afoot about the importation of narcotics, in the course of which the prosecution had secured possession of three cables from Shanghai, to which the question almost certainly referred. These were addressed to one, "L. C. Spiegel, 1247 Sixth Avenue" (Murray's Restaurant) and were in code; they were all dated in March, 1937, and were apparently among those mentioned in the indictment. An article had appeared in a New York newspaper, declaring that the federal district attorney would soon indict, as a dealer in narcotics, "the owner of a big advertising agency", who had been the "one-time partner of a big gangster", and who had been "in hiding for a month". The defendant was in fact the head of an advertising agency, and it had been the accomplice of a "gangster". He had in fact gone to Florida under circumstances which suggest that he was trying to hide; and the prosecution had questioned his family about his business between 1934 and 1939, and had secured the books of his business.
With this background it is easy to see that the danger from an answer to the first question was real. If the defendant had in fact received the three cables at Murray's Restaurant, there was reason to suppose either that, in spite of his denial, he was the Spiegel to whom they were addressed, or that he was acting on Spiegel's behalf. The indictment was in turn evidence that some such cables had been used in executing the conspiracy, and there was an antecedent probability that the prosecution's cables were among these. Further, the defendant was plainly justified in supposing that he was the object of pursuit by the district attorney; and, while the irresponsible gossip of a newspaper is a weak reed, there is always the possibility that it may for once be right. It directly pointed to the defendant, and it would certainly have disturbed any but the most hardy.
The case for the privilege against answering the second question was not so strong; yet strong enough in our judgment. The defendant might *263 of course have known people living in Shanghai, or visiting there, without being implicated in the conspiracy of which Shanghai was the focus. But we are to take the question in its setting, including the other question and the information of which we may reasonably infer the prosecution had possession. United States v. Zwillman, supra, 108 F.2d 802. The persons in Shanghai with whom the owner of a New York Advertising business would be likely to be acquainted, were not many, and among them would be the senders, or sender, of any cables received at Murray's Restaurant. Those were in code, and, as we have already said, were presumptively among the cables by which the conspiracy had been carried out. Again we are to remember that the defendant had been the object of much more than casual interest by the prosecution. These things made it perilous for him to answer; if he had acknowledged such acquaintances, it would probably have directly connected him with the principals in the conspiracy.
Mason v. United States, supra, 244 U. S. 362, 37 S.Ct. 621, 61 L.Ed. 1198, certainly does make against our conclusion, at least as to the second question. The Alaska statute there in question made it a crime to take part in a game of cards played for money; and the questions were merely whether the defendants had seen a game of cards being played, from which of course it did not follow that it was being played for money, or that they had taken a hand in it, if it had been. Yet it is also true that an affirmative answer would have been an admission of one of the three elements of which their guilt would be composed: (1) a game of cards; (2) a money stake; (3) the witness a hand in the game. Nevertheless, we think that the decision did not necessarily go further than to hold that not even answers which directly "tend" to prove the crime are inevitably protected; that there must be some reason to fear that the disclosure will put the witness in pressing danger. Indeed, perhaps in the end we should say no more than that the chase must not get too hot; or the scent, too fresh. In any event we are satisfied that if the privilege is to be of any value, a situation like that at bar must fall within it.
Judgment reversed; defendant discharged.
|
Q:
Ruby Array#include method not working as intended
Why is the include method not working well? The original question is from the Euler project, Problem 23. I couldn't figure out how to debug it.
My code:
def proper_divisors(n)
(1...n).select {|x| n % x == 0 }.inject(0){|x,y| x + y}
end
def abundant?(n)
(1...n).select {|x| n % x == 0 }.inject(0){|x,y| x + y} > n
end
def non_abundant_sums
s = 0
arr = (12..40).select { |n| n if abundant?(n) }
p arr
(1..40).each do |x|
p x unless arr.include?(proper_divisors(x) - x)
s = s + x unless arr.include?(proper_divisors(x) - x)
end
s
end
p non_abundant_sums
Using p x unless arr.include?(proper_divisors(x) - x) in the above code prints 1 through 40:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40
What I want it to print is 1 through 39:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39
A:
A solution based on the original methods from the example.
In file problem_23.rb:
def proper_divisors(n)
(1...n).select {|x| n % x == 0 }.inject(0) {|x,y| x + y}
end
def abundant?(n)
proper_divisors(n) > n
end
def non_abundant_sum(low_n, high_n, debug=false)
puts "get all the abundant numbers within range #{low_n} to #{high_n}" if debug
arr = (low_n..high_n).select {|n| n if abundant?(n)}
puts arr.sort.inspect if debug
# http://ruby-doc.org/core-2.1.2/Array.html#method-i-repeated_combination
puts "all combinations of two abundant numbers" if debug
arr = arr.repeated_combination(2).to_a
puts arr.inspect if debug
puts "all unique sums of two abundant number combinations" if debug
arr = arr.map {|x| x[0] + x[1]}.uniq
puts arr.sort.inspect if debug
puts "only select numbers within range" if debug
arr = arr.select {|x| low_n <= x && x <= high_n}
puts arr.inspect if debug
puts "all positive integers within range" if debug
arr2 = (low_n..high_n).map {|i| i}
puts arr2.inspect if debug
puts "all positive integers less all the sums of two abundant numbers" if debug
arr = arr2 - arr
puts arr.inspect if debug
puts "sum of all the positive integers which cannot be written as the sum of two abundant numbers within range #{low_n} to #{high_n}" if debug
arr.inject(0) {|sum,n| sum + n}
end
puts non_abundant_sum(12, 40, true)
Running the code:
$ ruby problem_23.rb
get all the abundant numbers within range 12 to 40
[12, 18, 20, 24, 30, 36, 40]
all combinations of two abundant numbers
[[12, 12], [12, 18], [12, 20], [12, 24], [12, 30], [12, 36], [12, 40], [18, 18], [18, 20], [18, 24], [18, 30], [18, 36], [18, 40], [20, 20], [20, 24], [20, 30], [20, 36], [20, 40], [24, 24], [24, 30], [24, 36], [24, 40], [30, 30], [30, 36], [30, 40], [36, 36], [36, 40], [40, 40]]
all unique sums of two abundant number combinations
[24, 30, 32, 36, 38, 40, 42, 44, 48, 50, 52, 54, 56, 58, 60, 64, 66, 70, 72, 76, 80]
only select numbers within range
[24, 30, 32, 36, 38, 40]
all positive integers within range
[12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]
all positive integers less all the sums of two abundant numbers
[12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39]
sum of all the positive integers which cannot be written as the sum of two abundant numbers within range 12 to 40
554
|
; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
; RUN: opt < %s -instcombine -S | FileCheck %s
target datalayout = "e-p:32:32:32-i1:8:8-i8:8:8-i16:16:16-i32:32:32-i64:32:64-f32:32:32-f64:32:64-v64:64:64-v128:128:128-a0:0:64-f80:128:128"
define i32 @test1(i32 %A) {
; CHECK-LABEL: @test1(
; CHECK-NEXT: ret i32 %A
;
%B = or i32 %A, 0
ret i32 %B
}
define i32 @test2(i32 %A) {
; CHECK-LABEL: @test2(
; CHECK-NEXT: ret i32 -1
;
%B = or i32 %A, -1
ret i32 %B
}
define i8 @test2a(i8 %A) {
; CHECK-LABEL: @test2a(
; CHECK-NEXT: ret i8 -1
;
%B = or i8 %A, -1
ret i8 %B
}
define i1 @test3(i1 %A) {
; CHECK-LABEL: @test3(
; CHECK-NEXT: ret i1 %A
;
%B = or i1 %A, false
ret i1 %B
}
define i1 @test4(i1 %A) {
; CHECK-LABEL: @test4(
; CHECK-NEXT: ret i1 true
;
%B = or i1 %A, true
ret i1 %B
}
define i1 @test5(i1 %A) {
; CHECK-LABEL: @test5(
; CHECK-NEXT: ret i1 %A
;
%B = or i1 %A, %A
ret i1 %B
}
define i32 @test6(i32 %A) {
; CHECK-LABEL: @test6(
; CHECK-NEXT: ret i32 %A
;
%B = or i32 %A, %A
ret i32 %B
}
; A | ~A == -1
define i32 @test7(i32 %A) {
; CHECK-LABEL: @test7(
; CHECK-NEXT: ret i32 -1
;
%NotA = xor i32 -1, %A
%B = or i32 %A, %NotA
ret i32 %B
}
define i8 @test8(i8 %A) {
; CHECK-LABEL: @test8(
; CHECK-NEXT: ret i8 -1
;
%B = or i8 %A, -2
%C = or i8 %B, 1
ret i8 %C
}
; Test that (A|c1)|(B|c2) == (A|B)|(c1|c2)
define i8 @test9(i8 %A, i8 %B) {
; CHECK-LABEL: @test9(
; CHECK-NEXT: ret i8 -1
;
%C = or i8 %A, 1
%D = or i8 %B, -2
%E = or i8 %C, %D
ret i8 %E
}
define i8 @test10(i8 %A) {
; CHECK-LABEL: @test10(
; CHECK-NEXT: ret i8 -2
;
%B = or i8 %A, 1
%C = and i8 %B, -2
; (X & C1) | C2 --> (X | C2) & (C1|C2)
%D = or i8 %C, -2
ret i8 %D
}
define i8 @test11(i8 %A) {
; CHECK-LABEL: @test11(
; CHECK-NEXT: ret i8 -1
;
%B = or i8 %A, -2
%C = xor i8 %B, 13
; (X ^ C1) | C2 --> (X | C2) ^ (C1&~C2)
%D = or i8 %C, 1
%E = xor i8 %D, 12
ret i8 %E
}
define i32 @test12(i32 %A) {
; Should be eliminated
; CHECK-LABEL: @test12(
; CHECK-NEXT: [[C:%.*]] = and i32 %A, 8
; CHECK-NEXT: ret i32 [[C]]
;
%B = or i32 %A, 4
%C = and i32 %B, 8
ret i32 %C
}
define i32 @test13(i32 %A) {
; CHECK-LABEL: @test13(
; CHECK-NEXT: ret i32 8
;
%B = or i32 %A, 12
; Always equal to 8
%C = and i32 %B, 8
ret i32 %C
}
define i1 @test14(i32 %A, i32 %B) {
; CHECK-LABEL: @test14(
; CHECK-NEXT: [[TMP1:%.*]] = icmp ne i32 %A, %B
; CHECK-NEXT: ret i1 [[TMP1]]
;
%C1 = icmp ult i32 %A, %B
%C2 = icmp ugt i32 %A, %B
; (A < B) | (A > B) === A != B
%D = or i1 %C1, %C2
ret i1 %D
}
define i1 @test15(i32 %A, i32 %B) {
; CHECK-LABEL: @test15(
; CHECK-NEXT: [[TMP1:%.*]] = icmp ule i32 %A, %B
; CHECK-NEXT: ret i1 [[TMP1]]
;
%C1 = icmp ult i32 %A, %B
%C2 = icmp eq i32 %A, %B
; (A < B) | (A == B) === A <= B
%D = or i1 %C1, %C2
ret i1 %D
}
define i32 @test16(i32 %A) {
; CHECK-LABEL: @test16(
; CHECK-NEXT: ret i32 %A
;
%B = and i32 %A, 1
; -2 = ~1
%C = and i32 %A, -2
; %D = and int %B, -1 == %B
%D = or i32 %B, %C
ret i32 %D
}
define i32 @test17(i32 %A) {
; CHECK-LABEL: @test17(
; CHECK-NEXT: [[D:%.*]] = and i32 %A, 5
; CHECK-NEXT: ret i32 [[D]]
;
%B = and i32 %A, 1
%C = and i32 %A, 4
; %D = and int %B, 5
%D = or i32 %B, %C
ret i32 %D
}
define i1 @test18(i32 %A) {
; CHECK-LABEL: @test18(
; CHECK-NEXT: [[A_OFF:%.*]] = add i32 %A, -50
; CHECK-NEXT: [[TMP1:%.*]] = icmp ugt i32 [[A_OFF]], 49
; CHECK-NEXT: ret i1 [[TMP1]]
;
%B = icmp sge i32 %A, 100
%C = icmp slt i32 %A, 50
;; (A-50) >u 50
%D = or i1 %B, %C
ret i1 %D
}
define i1 @test19(i32 %A) {
; CHECK-LABEL: @test19(
; CHECK-NEXT: [[TMP1:%.*]] = or i32 %A, 1
; CHECK-NEXT: [[TMP2:%.*]] = icmp eq i32 [[TMP1]], 51
; CHECK-NEXT: ret i1 [[TMP2]]
;
%B = icmp eq i32 %A, 50
%C = icmp eq i32 %A, 51
;; (A&-2) == 50
%D = or i1 %B, %C
ret i1 %D
}
define i32 @test20(i32 %x) {
; CHECK-LABEL: @test20(
; CHECK-NEXT: ret i32 %x
;
%y = and i32 %x, 123
%z = or i32 %y, %x
ret i32 %z
}
define i32 @test21(i32 %tmp.1) {
; CHECK-LABEL: @test21(
; CHECK-NEXT: [[TMP_1_MASK1:%.*]] = add i32 %tmp.1, 2
; CHECK-NEXT: ret i32 [[TMP_1_MASK1]]
;
%tmp.1.mask1 = add i32 %tmp.1, 2
%tmp.3 = and i32 %tmp.1.mask1, -2
%tmp.5 = and i32 %tmp.1, 1
;; add tmp.1, 2
%tmp.6 = or i32 %tmp.5, %tmp.3
ret i32 %tmp.6
}
define i32 @test22(i32 %B) {
; CHECK-LABEL: @test22(
; CHECK-NEXT: ret i32 %B
;
%ELIM41 = and i32 %B, 1
%ELIM7 = and i32 %B, -2
%ELIM5 = or i32 %ELIM41, %ELIM7
ret i32 %ELIM5
}
define i16 @test23(i16 %A) {
; CHECK-LABEL: @test23(
; CHECK-NEXT: [[B:%.*]] = lshr i16 %A, 1
; CHECK-NEXT: [[D:%.*]] = xor i16 [[B]], -24575
; CHECK-NEXT: ret i16 [[D]]
;
%B = lshr i16 %A, 1
;; fold or into xor
%C = or i16 %B, -32768
%D = xor i16 %C, 8193
ret i16 %D
}
; PR1738
define i1 @test24(double %X, double %Y) {
; CHECK-LABEL: @test24(
; CHECK-NEXT: [[TMP1:%.*]] = fcmp uno double %Y, %X
; CHECK-NEXT: ret i1 [[TMP1]]
;
%tmp9 = fcmp uno double %X, 0.000000e+00
%tmp13 = fcmp uno double %Y, 0.000000e+00
%bothcond = or i1 %tmp13, %tmp9
ret i1 %bothcond
}
; PR3266 & PR5276
define i1 @test25(i32 %A, i32 %B) {
; CHECK-LABEL: @test25(
; CHECK-NEXT: [[NOTLHS:%.*]] = icmp ne i32 %A, 0
; CHECK-NEXT: [[NOTRHS:%.*]] = icmp ne i32 %B, 57
; CHECK-NEXT: [[F:%.*]] = and i1 [[NOTRHS]], [[NOTLHS]]
; CHECK-NEXT: ret i1 [[F]]
;
%C = icmp eq i32 %A, 0
%D = icmp eq i32 %B, 57
%E = or i1 %C, %D
%F = xor i1 %E, -1
ret i1 %F
}
; PR5634
define i1 @test26(i32 %A, i32 %B) {
; CHECK-LABEL: @test26(
; CHECK-NEXT: [[TMP1:%.*]] = or i32 %A, %B
; CHECK-NEXT: [[TMP2:%.*]] = icmp eq i32 [[TMP1]], 0
; CHECK-NEXT: ret i1 [[TMP2]]
;
%C1 = icmp eq i32 %A, 0
%C2 = icmp eq i32 %B, 0
; (A == 0) & (A == 0) --> (A|B) == 0
%D = and i1 %C1, %C2
ret i1 %D
}
define i1 @test27(i32* %A, i32* %B) {
; CHECK-LABEL: @test27(
; CHECK-NEXT: [[TMP1:%.*]] = icmp eq i32* %A, null
; CHECK-NEXT: [[TMP2:%.*]] = icmp eq i32* %B, null
; CHECK-NEXT: [[E:%.*]] = and i1 [[TMP1]], [[TMP2]]
; CHECK-NEXT: ret i1 [[E]]
;
%C1 = ptrtoint i32* %A to i32
%C2 = ptrtoint i32* %B to i32
%D = or i32 %C1, %C2
%E = icmp eq i32 %D, 0
ret i1 %E
}
; PR5634
define i1 @test28(i32 %A, i32 %B) {
; CHECK-LABEL: @test28(
; CHECK-NEXT: [[TMP1:%.*]] = or i32 %A, %B
; CHECK-NEXT: [[TMP2:%.*]] = icmp ne i32 [[TMP1]], 0
; CHECK-NEXT: ret i1 [[TMP2]]
;
%C1 = icmp ne i32 %A, 0
%C2 = icmp ne i32 %B, 0
; (A != 0) | (A != 0) --> (A|B) != 0
%D = or i1 %C1, %C2
ret i1 %D
}
define i1 @test29(i32* %A, i32* %B) {
; CHECK-LABEL: @test29(
; CHECK-NEXT: [[TMP1:%.*]] = icmp ne i32* %A, null
; CHECK-NEXT: [[TMP2:%.*]] = icmp ne i32* %B, null
; CHECK-NEXT: [[E:%.*]] = or i1 [[TMP1]], [[TMP2]]
; CHECK-NEXT: ret i1 [[E]]
;
%C1 = ptrtoint i32* %A to i32
%C2 = ptrtoint i32* %B to i32
%D = or i32 %C1, %C2
%E = icmp ne i32 %D, 0
ret i1 %E
}
; PR4216
define i32 @test30(i32 %A) {
; CHECK-LABEL: @test30(
; CHECK-NEXT: [[D:%.*]] = and i32 %A, -58312
; CHECK-NEXT: [[E:%.*]] = or i32 [[D]], 32962
; CHECK-NEXT: ret i32 [[E]]
;
%B = or i32 %A, 32962
%C = and i32 %A, -65536
%D = and i32 %B, 40186
%E = or i32 %D, %C
ret i32 %E
}
; PR4216
define i64 @test31(i64 %A) {
; CHECK-LABEL: @test31(
; CHECK-NEXT: [[E:%.*]] = and i64 %A, 4294908984
; CHECK-NEXT: [[F:%.*]] = or i64 [[E]], 32962
; CHECK-NEXT: ret i64 [[F]]
;
%B = or i64 %A, 194
%D = and i64 %B, 250
%C = or i64 %A, 32768
%E = and i64 %C, 4294941696
%F = or i64 %D, %E
ret i64 %F
}
; codegen is mature enough to handle vector selects.
define <4 x i32> @test32(<4 x i1> %and.i1352, <4 x i32> %vecinit6.i176, <4 x i32> %vecinit6.i191) {
; CHECK-LABEL: @test32(
; CHECK-NEXT: [[OR_I:%.*]] = select <4 x i1> %and.i1352, <4 x i32> %vecinit6.i176, <4 x i32> %vecinit6.i191
; CHECK-NEXT: ret <4 x i32> [[OR_I]]
;
%and.i135 = sext <4 x i1> %and.i1352 to <4 x i32>
%and.i129 = and <4 x i32> %vecinit6.i176, %and.i135
%neg.i = xor <4 x i32> %and.i135, <i32 -1, i32 -1, i32 -1, i32 -1>
%and.i = and <4 x i32> %vecinit6.i191, %neg.i
%or.i = or <4 x i32> %and.i, %and.i129
ret <4 x i32> %or.i
}
define i1 @test33(i1 %X, i1 %Y) {
; CHECK-LABEL: @test33(
; CHECK-NEXT: [[B:%.*]] = or i1 %X, %Y
; CHECK-NEXT: ret i1 [[B]]
;
%a = or i1 %X, %Y
%b = or i1 %a, %X
ret i1 %b
}
define i32 @test34(i32 %X, i32 %Y) {
; CHECK-LABEL: @test34(
; CHECK-NEXT: [[B:%.*]] = or i32 %X, %Y
; CHECK-NEXT: ret i32 [[B]]
;
%a = or i32 %X, %Y
%b = or i32 %Y, %a
ret i32 %b
}
define i32 @test35(i32 %a, i32 %b) {
; CHECK-LABEL: @test35(
; CHECK-NEXT: [[TMP1:%.*]] = or i32 %a, %b
; CHECK-NEXT: [[TMP2:%.*]] = or i32 [[TMP1]], 1135
; CHECK-NEXT: ret i32 [[TMP2]]
;
%1 = or i32 %a, 1135
%2 = or i32 %1, %b
ret i32 %2
}
define i1 @test36(i32 %x) {
; CHECK-LABEL: @test36(
; CHECK-NEXT: [[X_OFF:%.*]] = add i32 %x, -23
; CHECK-NEXT: [[TMP1:%.*]] = icmp ult i32 [[X_OFF]], 3
; CHECK-NEXT: ret i1 [[TMP1]]
;
%cmp1 = icmp eq i32 %x, 23
%cmp2 = icmp eq i32 %x, 24
%ret1 = or i1 %cmp1, %cmp2
%cmp3 = icmp eq i32 %x, 25
%ret2 = or i1 %ret1, %cmp3
ret i1 %ret2
}
define i32 @orsext_to_sel(i32 %x, i1 %y) {
; CHECK-LABEL: @orsext_to_sel(
; CHECK-NEXT: [[OR:%.*]] = select i1 %y, i32 -1, i32 %x
; CHECK-NEXT: ret i32 [[OR]]
;
%sext = sext i1 %y to i32
%or = or i32 %sext, %x
ret i32 %or
}
define i32 @orsext_to_sel_swap(i32 %x, i1 %y) {
; CHECK-LABEL: @orsext_to_sel_swap(
; CHECK-NEXT: [[OR:%.*]] = select i1 %y, i32 -1, i32 %x
; CHECK-NEXT: ret i32 [[OR]]
;
%sext = sext i1 %y to i32
%or = or i32 %x, %sext
ret i32 %or
}
define i32 @orsext_to_sel_multi_use(i32 %x, i1 %y) {
; CHECK-LABEL: @orsext_to_sel_multi_use(
; CHECK-NEXT: [[SEXT:%.*]] = sext i1 %y to i32
; CHECK-NEXT: [[OR:%.*]] = or i32 [[SEXT]], %x
; CHECK-NEXT: [[ADD:%.*]] = add i32 [[SEXT]], [[OR]]
; CHECK-NEXT: ret i32 [[ADD]]
;
%sext = sext i1 %y to i32
%or = or i32 %sext, %x
%add = add i32 %sext, %or
ret i32 %add
}
define <2 x i32> @orsext_to_sel_vec(<2 x i32> %x, <2 x i1> %y) {
; CHECK-LABEL: @orsext_to_sel_vec(
; CHECK-NEXT: [[OR:%.*]] = select <2 x i1> %y, <2 x i32> <i32 -1, i32 -1>, <2 x i32> %x
; CHECK-NEXT: ret <2 x i32> [[OR]]
;
%sext = sext <2 x i1> %y to <2 x i32>
%or = or <2 x i32> %sext, %x
ret <2 x i32> %or
}
define <2 x i132> @orsext_to_sel_vec_swap(<2 x i132> %x, <2 x i1> %y) {
; CHECK-LABEL: @orsext_to_sel_vec_swap(
; CHECK-NEXT: [[OR:%.*]] = select <2 x i1> %y, <2 x i132> <i132 -1, i132 -1>, <2 x i132> %x
; CHECK-NEXT: ret <2 x i132> [[OR]]
;
%sext = sext <2 x i1> %y to <2 x i132>
%or = or <2 x i132> %x, %sext
ret <2 x i132> %or
}
define i32 @test39(i32 %a, i32 %b) {
; CHECK-LABEL: @test39(
; CHECK-NEXT: [[OR:%.*]] = or i32 %a, %b
; CHECK-NEXT: ret i32 [[OR]]
;
%xor = xor i32 %a, -1
%and = and i32 %xor, %b
%or = or i32 %and, %a
ret i32 %or
}
define i32 @test40(i32 %a, i32 %b) {
; CHECK-LABEL: @test40(
; CHECK-NEXT: [[TMP1:%.*]] = xor i32 %a, -1
; CHECK-NEXT: [[OR:%.*]] = or i32 [[TMP1]], %b
; CHECK-NEXT: ret i32 [[OR]]
;
%and = and i32 %a, %b
%xor = xor i32 %a, -1
%or = or i32 %and, %xor
ret i32 %or
}
define i32 @test41(i32 %a, i32 %b) {
; CHECK-LABEL: @test41(
; CHECK-NEXT: [[TMP1:%.*]] = xor i32 %a, -1
; CHECK-NEXT: [[OR:%.*]] = xor i32 [[TMP1]], %b
; CHECK-NEXT: ret i32 [[OR]]
;
%and = and i32 %a, %b
%nega = xor i32 %a, -1
%xor = xor i32 %nega, %b
%or = or i32 %and, %xor
ret i32 %or
}
define i32 @test42(i32 %a, i32 %b) {
; CHECK-LABEL: @test42(
; CHECK-NEXT: [[TMP1:%.*]] = xor i32 %a, -1
; CHECK-NEXT: [[OR:%.*]] = xor i32 [[TMP1]], %b
; CHECK-NEXT: ret i32 [[OR]]
;
%nega = xor i32 %a, -1
%xor = xor i32 %nega, %b
%and = and i32 %a, %b
%or = or i32 %xor, %and
ret i32 %or
}
define i32 @test43(i32 %a, i32 %b) {
; CHECK-LABEL: @test43(
; CHECK-NEXT: [[OR:%.*]] = xor i32 %a, %b
; CHECK-NEXT: ret i32 [[OR]]
;
%neg = xor i32 %b, -1
%and = and i32 %a, %neg
%xor = xor i32 %a, %b
%or = or i32 %and, %xor
ret i32 %or
}
define i32 @test44(i32 %a, i32 %b) {
; CHECK-LABEL: @test44(
; CHECK-NEXT: [[OR:%.*]] = xor i32 %a, %b
; CHECK-NEXT: ret i32 [[OR]]
;
%xor = xor i32 %a, %b
%neg = xor i32 %b, -1
%and = and i32 %a, %neg
%or = or i32 %xor, %and
ret i32 %or
}
define i32 @test45(i32 %x, i32 %y, i32 %z) {
; CHECK-LABEL: @test45(
; CHECK-NEXT: [[TMP1:%.*]] = and i32 %x, %z
; CHECK-NEXT: [[OR1:%.*]] = or i32 [[TMP1]], %y
; CHECK-NEXT: ret i32 [[OR1]]
;
%or = or i32 %y, %z
%and = and i32 %x, %or
%or1 = or i32 %and, %y
ret i32 %or1
}
define i1 @test46(i8 signext %c) {
; CHECK-LABEL: @test46(
; CHECK-NEXT: [[TMP1:%.*]] = and i8 %c, -33
; CHECK-NEXT: [[TMP2:%.*]] = add i8 [[TMP1]], -65
; CHECK-NEXT: [[TMP3:%.*]] = icmp ult i8 [[TMP2]], 26
; CHECK-NEXT: ret i1 [[TMP3]]
;
%c.off = add i8 %c, -97
%cmp1 = icmp ult i8 %c.off, 26
%c.off17 = add i8 %c, -65
%cmp2 = icmp ult i8 %c.off17, 26
%or = or i1 %cmp1, %cmp2
ret i1 %or
}
define i1 @test47(i8 signext %c) {
; CHECK-LABEL: @test47(
; CHECK-NEXT: [[TMP1:%.*]] = and i8 %c, -33
; CHECK-NEXT: [[TMP2:%.*]] = add i8 [[TMP1]], -65
; CHECK-NEXT: [[TMP3:%.*]] = icmp ult i8 [[TMP2]], 27
; CHECK-NEXT: ret i1 [[TMP3]]
;
%c.off = add i8 %c, -65
%cmp1 = icmp ule i8 %c.off, 26
%c.off17 = add i8 %c, -97
%cmp2 = icmp ule i8 %c.off17, 26
%or = or i1 %cmp1, %cmp2
ret i1 %or
}
define i1 @test48(i64 %x, i1 %b) {
; CHECK-LABEL: @test48(
; CHECK-NEXT: ret i1 true
;
%1 = icmp ult i64 %x, 2305843009213693952
%2 = icmp ugt i64 %x, 2305843009213693951
%.b = or i1 %2, %b
%3 = or i1 %1, %.b
ret i1 %3
}
|
Tag: Support
It seems that the controversy revolving around Kapil Sharma has now increased to an extent that Twitter is campaigning for boycotting his ongoing show on Sony Channel. Navjot Singh Sidhu was recently trolled and bashed online for his comments wherein he had claimed that the ones responsible for the Pulwama attacks should indeed be condemned but one cannot blame an entire country Pakistan for the same. While he was trolled on Twitter and netizens even asked Sony to fire Sidhu from The Kapil Sharma Show, recently Kapil spoke about the controversy. Speaking of how Sidhu was at the receiving end and how ‘#BoycottKapilSharmShow’ became a trending hashtag for netizens, Kapil Sharma had commented that the youth should be focusing on the real and genuine problem and that firing Navjot Singh Sidh
Shooting and post-production activities will completely stop in Mumbai tomorrow afternoon for a couple of hours as film technicians will offer their respect to the CRPF jawans killed in the Pulwama terror attack on February 14. All film shoots and post-production activities will come to a halt between 2 pm and 4 pm on February 17, as the Federation of Western India Cine Employees (FWICE) office bearers along with the members of its affiliated associations will come to the gate of Film City Studios in Goregaon, Mumbai, to pay their respect to the slain jawans. FWICE General Secretary Ashok Dubey confirms, “Our association has decided that no shooting of any movies all over India will happen on Sunday between 2 pm to 4 pm. The entire film industry will remain shut. We will offer shraddhanj
JALANDHAR: Deputy Commissioner Jalandhar Varinder Kumar Sharma has sought support from the Educational Institutions to make Ghar-Ghar Rozgar scheme a huge success by upgrading the skills of unemployed youth.
A group of cross-party MPs, members of House of Lords, business and community leaders besides local council leaders convened to discuss progress of 'Western Rail Link to Heathrow' project during an all party parliamentary group (APPG)
NEW DELHI: Congress President Rahul Gandhi and several other opposition leaders on Sunday extended their full support to West Bengal Chief Minister Mamata Banerjee in her sit-in against the Centre over CBI move in the state, saying the happenings in Bengal were part of the unrelenting attack on India's institutions by Prime Minister Narendra Modi and the BJP.
The Cooperation Minister, Punjab, S. Sukhjinder Singh Randhawa today released the State Focus Paper for the year 2019-20 prepared by NABARD in the State Credit Seminar held in Chandigarh. The seminar was attended by Vishwajeet Khanna, Additional Chief Secretary cum Finance Commissioner Development ,
Thakurnagar (West Bengal): Prime Minister Narendra Modi on Saturday urged West Bengal's ruling Trinamool Congress to support the Citizenship Amendment Bill in Parliament to give the refugees living in India the right to citizenship.
Vikram Bhatt comes out in support of Rajkumar Hirani, says we should wait for justice to prevail on the #MeToo situation
Vikram Bhatt recently released his latest column regarding one of the most talked about trends, #MeToo. The director came out in support of Rajkumar Hirani who was accused of sexual harassment by one of the crew members of Sanju. The female crew member claimed that the director had molested her for...
After the sexual misconduct claim, Boney Kapoor comes out in support of Rajkumar Hirani
#MeToo movement took India by storm in 2018 where major names were accused of sexual harassment, abuse, and misconduct. The top names from Bollywood included Alok Nath, Nana Patekar, Sajid Khan and Vikas Bahl among others who have been reprimanded for their past. In the latest development, filmmaker Rajkumar Hirani was accused of sex... |
Q:
html email template issue
Hi i have two objects case and task,in between these am created lookup relationship now in the email template I was referring the both task fields and case fields,when I am firing a workflow the merge fields are not fetching the values......
Example
Hi {!Case.Name},{!Case.family name}
Hello {!Task.firstname}{!Task.LastName}
can u please give any suggestion that I am using the correct Syntax.
A:
If workflow is on Case, then it is impossible using Text or HTML emails to show children record merge fields (i.e. Tasks) because the target object in scope for the email template is the target object of the workflow
To show Tasks - and since there can be more than one Task for a Case, you'll need to think about your business logic as to which task or tasks to show. Once having done that, you will need to:
Make the email template a VF email template
Create a custom component to show the related task (or tasks). The custom component uses a custom controller to fetch the related task(s) given a Case.Id that is passed to the component.
VF template
... markup for Hi! ...
<c:taskList caseId={!Case.Id}/> <!-- show tasks here in email body -->
... more markup, if any -- e.g. a footer
VF component
<apex:component access="global" controller="TasksController">
<apex:attribute name="caseId" type="ID" required="true" assignTo={!csId}/>
<apex:repeat value="{!tasks}" var="t"> <!-- can also use dataTable or straight <table> -->
.. markup for a Task row ..
</apex:repeat>
</apex:component>
Component controller
public class TasksController {
public ID csId {get; set;} // gets value before getTasks() is called
public Task[] getTasks() {
return csId != null
? [select id, ... from Task where whatId = :csId ...]
: new List<Task>(); // avoids preview exception
}
}
|
---
abstract: |
In this work we deal with the following nonlinear Schrödinger equation $$\left\{
\begin{array}{l}-\epsilon^2\Delta u + V(x)u = f(u) \ \ \mbox{in
$\mathbb{R}^N$}\\
u \in H^1(\mathbb{R}^N),
\end{array}
\right.$$ where $N \geq 3$, $f$ is a subcritical power-type nonlinearity and $V$ is a positive potential satisfying a local condition. We prove the existence and concentration of nodal solutions which concentrate around a $k-$ dimensional sphere of $\mathbb{R}^N$, where $1 \leq k \leq N-1$, as $\epsilon \to 0$. The radius of such sphere is related with the local minimum of a function which takes into account the potential $V$. Variational methods are used together with the penalization technique in order to overcome the lack of compactness.
author:
- |
Giovany M. Figueiredo[^1]\
Faculdade de Matemática\
Universidade Federal do Pará\
66075-110, Belém - Pa, Brazil.\
e-mail:\
\
and\
Marcos T. O. Pimenta[^2] [^3]\
Departamento de Matemática e Computação\
Faculdade de Ciências e Tecnologia\
Universidade Estadual Paulista - Unesp\
19060-900, Presidente Prudente - SP, Brazil.\
e-mail:\
title: Nodal solutions of a NLS equation concentrating on lower dimensional spheres
---
[ 35J60, 35J10, 35J20.]{}
[ variational methods, nodal solutions, concentration on manifolds.]{}
Introduction
============
In the last decades, motivated by the great interest that this problem catch in quantum mechanics, so many researchers have dedicated their efforts on the study of the Nonlinear Schrödinger equation $$i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m}\Delta \psi + W(x)\psi - |\psi|^{p-1}\psi \quad (t,x) \in \mathbb{R}\times \mathbb{R}^N.$$ Of particular interest are the so called [*standing wave solutions*]{} which consists in solutions with a particle-like behavior. It is obtained by the [*Ansatz*]{} $\psi(t,x) = e^{-iEt/\hbar}u(x)$ which associate the NLS equation to its stationary version $$-\epsilon^2\Delta u + V(x)u = |u|^{p-1}u \quad \mbox{in $\mathbb{R}^N$}
\label{IP1}$$ where $\epsilon^2=\hbar^2/2m$ and $V(x) = W(x) - E$. As far as (\[IP1\]) is concerned, the behavior of the solutions when $\epsilon \to 0$ has a great physical interest since it describes the transition from quantum to the classical mechanics, being called [*semiclassical states*]{}. On this specific subject, many authors have worked on [*spike-layered solutions*]{} which are nontrivial ground-state points of the associated energy functional and tend to concentrate around one or more critical points of the potential $V$. We could cite some quite influent works on this subject, as the pioneering work of Floer and Weinstein [@Floer], which have inspired the works of Rabinowitz [@Rabinowitz], Wang [@Wang], Del Pino and Felmer [@DelPino], which have influenced so many other works by their own in the last three decades.
In the last ten years, solutions which concentrate on higher dimensional sets has been received more and more attention. The first work which seems to show this kind of result is [@Montenegro] in which the authors study a NLS equation on a bounded domain with Neumann boundary condition and prove the existence of a sequence of solutions which concentrate on some component of the boundary. One of the first works dealing with solutions concentrating around a sphere is [@Ambrosetti1] in which Ambrosetti, Malchiodi and Ni give necessary and sufficient conditions under which (\[IP1\]) exhibit solutions concentrating around a sphere. The radius of such a sphere is given by a minimum point of a function $\mathcal{M}$, which takes into account the value of the radial potential $V(|x|)$. The role played by $\mathcal{M}$ is in order to balance the potential energy (coming from $V$) and the volume energy which arise from the other terms of the energy functional (see the introduction of [@Ambrosetti1] for more details). In fact, sphere concentrating solutions show a rather different behavior when compared with spike-layered ones. To be more specific, in [@Ambrosetti1], the authors prove the existence of sphere concentrating solutions to (\[IP1\]) even for critical or supercritical exponent $p$. This is in a strike contrast with the fact that, as showed in [@Cingolani], no spike-layered solution exists to (\[IP1\]) for $p = 2^*-1$. Other significant difference is that the energy of the sphere concentrating solutions tend to zero, in contrast with those of spike-layered solutions, whose energy converge to the mountain-pass level of the energy functional. In these and so many other works ([@Ambrosetti2; @Ruiz; @Daprile; @Ianni] for example), Lyapunov-Schmidt reduction methods have been used in order to construct the sphere-concentrating solutions for Schrödinger equations, Schrödinger-Poisson systems other related problems.
More recently, in [@Bonheure1] Bonheure [*et al*]{} proved the existence of solutions concentrating around a $k-$dimensional sphere of $\mathbb{R}^N$, for all $k \in \{1,...,N-1\}$ to the following equation $$-\epsilon^2\Delta u + V(x)u = K(x)f(u) \quad \mbox{in
$\mathbb{R}^N$,}
\label{IP2}$$ where the potentials $V$ and $K$ satisfy rather generic conditions, allowing $V$ even to vanish on the infinity. To do so they use a modification of the penalization technique, originally presented in [@DelPino], in such a way that compactness is recovered to the modified energy functional. Because of the generality of conditions under with $V$ and $K$ are subjected, in order to prove that the solutions of the modified problem are solutions of the original one, they made a thorough analysis with some barrier functions which bounds the solutions from above. In [@Bonheure2] the authors employ a similar argument in order to show the existence of solutions concentrating on circumferences of $\mathbb{R}^3$, to a Schrödinger-Poisson system.
In the [*spike-layered*]{} solutions setting, the existence of sign-changing (or nodal) solutions was investigated by some authors. In [@Soares1] and [@Soares2], Alves and Soares study problem (\[IP2\]), with $K$ to be a constant, and prove the existence of nodal solutions which concentrate at minima of the potential $V$. In the first work they consider $f$ as a subcritical power-type nonlinearity and in the second, as presenting a critical exponential growth at infinity. In both they employ the penalization technique together with a careful analysis of the profile of the solutions. In [@Sato], Y. Sato have proposed a different kind of penalization in order to show the existence of multi-peak nodal solutions to a Schrödinger equation with a vanishing potential.
A question that naturally arises is whether there exist a sequence of nodal solutions to the NLS equation which concentrate around a $k-$dimensional sphere. In this work we give a positive answer to this question. More specifically, we study the existence and concentration of nodal solutions to the following nonlinear Schrödinger equation
$$\left\{
\begin{array}{l}-\epsilon^2\Delta u + V(x)u = f(u) \ \ \mbox{in
$\mathbb{R}^N$}\\
u \in H^1(\mathbb{R}^N),
\end{array}
\right. \label{P}$$
where $N \geq 3$, exhibiting a cylindrical symmetry which implies in this sort of concentration. The nonlinearity $f$ is assumed to be a $C^1(\mathbb{R})$ odd function satisfying
- There exists $\nu > 1$ such that $f(|s|) = o(|s|^\nu)$ as $s \to 0$;
- There exist $c_ 1, c_2 > 0$ such that $ |f'(s)| \leq c_1 + c_2|s|^{p-1}$ where $1 < p < \frac{N-k+2}{(N-k-2)}$ and $k$ is like in Section \[section1.1\];
- There exists $\theta > 2 $ such that $$0 < \theta F(s) \leq f(s)s, \quad \mbox{for $s \neq 0$},$$ where $F(s) = \int_0^s f(t)dt$;
- $s \mapsto f(s)/s$ is increasing in $s > 0$ and decreasing for $s < 0$.
The potential $V$ will be assumed to satisfy a symmetry condition which we explain in the next section.
Statement of the main result {#section1.1}
----------------------------
Let $1 \leq k \leq N-1$ be an integer which determine the dimension of the sphere in which the solutions obtained are going to concentrate. Consider $\mathcal{H}$ a $(N-k-1)-$dimensional linear subspace of $\mathbb{R}^N$ and note that $\mathcal{H}^\perp$ is a $(k+1)-$dimensional subspace. All along the paper we use the notation for $x\in \mathbb{R}^N$ as $x = (x',x'')$ in which $x'\in \mathcal{H}$, $x''\in \mathcal{H}^\perp$ are such that $x = x' + x''$.
From now on, if $h:\mathbb{R}^N \to \mathbb{R}$ is a function, by saying that $h(x',x'') = h(x',|x''|)$ (which rigorously does not make sense), we mean that $h(x',y) = h(x',z)$ for all $y,z \in \mathcal{H}^\perp$ such that $|y| = |z|$.
The condition in $V$ which is considered is the following:
- There exists $V_0 > 0$ such that $V_0 \leq V(x)$ and, for all $x \in \mathbb{R}^N$, $V(x) = V(x',x'') = V(x',|x''|)$.
Unlike spike layered solutions, whose concentration occurs around minimum points of $V$, the solutions we are going to study concentrate around minimum points of an auxiliary potential. To see how we define it, let us consider the limit problem $$-\Delta u + a u= f(u) \quad \mbox{in $\mathbb{R}^{N-k}$}.
\label{PL}$$ It is well known (see [@Rabinowitz] for instance) that there exists a ground state solution $w\in H^1(\mathbb{R}^{N-k})$ of $(\ref{PL})$ which minimizes the energy functional $$I_{a}(u) = \frac{1}{2}\int_{\mathbb{R}^{N-k}}\left(|\nabla u|^2 + au^2 \right)dx - \int_{\mathbb{R}^{N-k}}F(u)dx,$$ in the corresponding Nehari manifold given by $$\mathcal{N}_{a} = \{u \in H^1(\mathbb{R}^{N-k})\backslash\{0\}; I_{a}'(u)u = 0\}.$$
We define the [*ground-energy function*]{} $\mathcal{E}: \mathbb{R}^+ \to \mathbb{R}^+$, by $$\mathcal{E}(a) = \inf_{\mathcal{N}_{a}}I_{a}.$$ Finally, we define the [*auxiliary potential*]{} $\mathcal{M}:\mathbb{R}^N \to (0,+\infty]$ by $$\mathcal{M}(x) = |x''|^k \mathcal{E}(V(x))$$ where $x = (x',x'')$, $x'\in \mathcal{H}$ and $x''\in \mathcal{H}^\perp$.
On the auxiliary potential $\mathcal{M}$ we impose the following condition
- There exists an open bounded set $\Omega \subset \mathbb{R}^N$ such that, if $(x',x'') \in \Omega$ then $(x',y'') \in \Omega$ for all $y''\in \mathcal{H}^\perp$, $|x''|=|y''|$. Moreover
$$0 < \mathcal{M}_0 : = \inf_{x \in \Omega} \mathcal{M}(x) < \inf_{x\in \partial \Omega} \mathcal{M}(x).$$
Now we can finally state our main result.
Let $f$ satisfying $(f_1) - (f_4)$ and $V$ such that $(V_1)$ and $(\mathcal{M}_1)$ hold. Then for each sequence $\epsilon_n \to 0$, there exists a subsequence still denoted by $(\epsilon_n)$ such that (\[P\]) (with $\epsilon = \epsilon_n$) has a nodal bound state $u_n$ such that, $u(x',x'') = u(x',|x''|)$ and, if $\epsilon_nP^1_n$ and $\epsilon_nP^2_n$ are respectively a minimum and a maximum point of $u_n$, then $\epsilon_nP^i_n \in \Omega$, $i = 1,2$ for $n$ sufficiently large, $$\epsilon_nP_n^i \to x_0, \quad \mbox{as $n \to \infty$}
\label{Pconcentration}$$ where $\mathcal{M}(x_0) = \mathcal{M}_0$ and $$|u_n(x)| \leq C\left(e^{-\frac{\beta}{\epsilon_n} d_k(x,\epsilon_n P_n^1)} + e^{-\frac{\beta}{\epsilon_n} d_k(x,\epsilon_nP_n^2)}\right) \quad x\in \mathbb{R}^N,$$ where $C, \beta > 0$ and $d_k$ is the distance defined in (\[distancedk\]). \[theorem1.1\]
The arguments in proving the existence of solutions were strongly influenced by the works of Alves and Souto [@AlvesSouto], in which they prove the existence of nodal solutions to a Schrödinger-Poisson system. In the concentration, we follow closely the arguments in [@Soares1] and [@Bonheure1; @Bonheure2].
After our work has been finished we found the very recent paper [@Fei] in which the author uses a similar argumentation in order to prove the existence of a sequence of nodal multi-peak solutions which concentrate around the minimum points of a modified potential, associated to a vanishing potential. The existence arguments in both works rely on a minimization of the penalized energy functional on the nodal Nehari set and the concentration arguments follow the same general lines. Nevertheless, it is worth pointing out that in our work, since we get sphere concentrating solutions, several technicals difficulties arise. Moreover, in our work proving that the solution of the modified problem is in fact a solution of the original one involves different comparison functions, since our penalization is slightly different.
In Section 2 we present the penalization scheme and the variational framework. In Section 3 we prove the existence of the nodal solutions of the modified problem. In Section 4 we exhibit the concentration arguments in order to prove that the solutions of the modified problem concentrates around a k-dimensional sphere and in the last section we complete the prove of the Theorem \[theorem1.1\] by showing that the solutions of the modified problem satisfy the original one.
The penalized nonlinearity and the variational framework
========================================================
The penalization we are going to apply is a variation of the classical method of Del Pino and Felmer in [@DelPino], developed by Y. Sato in [@Sato] in order to allow its use in finding nodal solutions. Fixing $2 < \tau < \theta$, let $r_\epsilon > 0$ such that $$\frac{f(r_\epsilon)}{r_\epsilon} = \epsilon^\tau \quad \mbox{and} \quad \frac{f(-r_\epsilon)}{-r_\epsilon} = \epsilon^\tau.$$
Since $r_\epsilon \to 0$ as $\epsilon \to 0$, $(f_1)$ implies that $$\epsilon^\tau = \frac{f(|r_\epsilon|)}{|r_\epsilon|} \leq |r_\epsilon|^{\nu-1}.$$ Thus $\epsilon^\frac{\tau}{\nu-1} \leq |r_\epsilon|$ and we can choose an odd function $\tilde{f}_\epsilon \in C^1(\mathbb{R})$ satisfying $$\tilde{f}_{\epsilon}(s) = \left\{
\begin{array}{rl}
f(s) & \mbox{if \,$|s| \leq \frac{1}{2}\epsilon^\frac{\tau}{\nu-1}$,}\\
\epsilon^\tau s & \mbox{if \,$|s| \geq \epsilon^\frac{\tau}{\nu-1}$,}
\end{array}\right.$$ $$|\tilde{f}_{\epsilon}(s)| \leq \epsilon^\tau|s| \quad \mbox{for all $s \in \mathbb{R}$,}
\label{penalization1}$$ $$0 \leq \tilde{f}_{\epsilon}'(s) \leq 2\epsilon^\tau \quad \mbox{for all $s \in \mathbb{R}$}
\label{penalization2}$$ and $$\mbox{ $s \mapsto \tilde{f}_\epsilon(s)/s$ is increasing for $s > 0$ and decreasing for $s < 0$.}
\label{penalization3}$$
Let us define $g_\epsilon(x,s): = \chi_\Omega(x)f(s) + (1 - \chi_\Omega(x))\tilde{f}_{\epsilon}(s)$, where $\chi_\Omega$ is the characteristic function of $\Omega$. Note that by $(f_1) - (f_4)$, $g$ is a Charathéodory function, such that $g_\epsilon(x',x'',s) = g_\epsilon(x',|x''|,s)$ satisfying
- $g_\epsilon(x,s) = o(|s|^\nu)$, as $s \to 0$, uniformly in compact sets of $\mathbb{R}^N$.
- There exist $c_ 1, c_2 > 0$ such that $ |g_\epsilon(x,s)| \leq c_1|s| + c_2|s|^p$ where $1 < p < \frac{N+2}{N-2}$;
- There exists $\theta > 2$ such that:
- $0 < \theta G_\epsilon(x,s) \leq g_\epsilon(x,s)s$, for $x \in \Omega$ and $s \neq 0$,
- $0 < 2 G_\epsilon(x,s) \leq g_\epsilon(x,s)s,$ for $x\in \mathbb{R}^N\backslash\Omega$ and $s \neq 0$,
where $G_\epsilon(x,s) = \int_0^s g_\epsilon(x,t)dt$.
- $s \mapsto \frac{g_\epsilon(x,s)}{s}$ is a nondecreasing function for $s > 0$ and nonincreasing for $s < 0$, for all $x\in \mathbb{R}^N$.
In a first moment, the concern will be with the penalized problem $$-\epsilon^2\Delta u + V(x)u = g_\epsilon(x,u) \ \ \mbox{in
$\mathbb{R}^N$}. \label{P1}$$ Taking $v_\epsilon(x) = u_\epsilon(\epsilon x)$, we relate each solution $u_\epsilon$ of (\[P1\]) with a solution $v_\epsilon$ of $$-\Delta v + V(\epsilon x)v = g_\epsilon(\epsilon x,u) \ \ \mbox{in
$\mathbb{R}^N$}. \label{P2}$$
In order to obtain solutions of $(\ref{P2})$ with a partial symmetry, let us consider the following subspace of $H^1(\mathbb{R}^N)$, $$\tilde{H} := \left\{v \in H^1(\mathbb{R}^N); \int (|\nabla v|^2 + V(\epsilon x)v^2) < +\infty \, \, \mbox{and} \, \, v(x',x'') = v(x',|x''|)\right\}$$ which is a Hilbert space when endowed with the inner product $$\langle u,v \rangle_\epsilon = \left( \int (\nabla u \nabla v + V(\epsilon x)uv) \right),$$ which gives rise to the following norm $$\|v\|_\epsilon= \left( \int (|\nabla v|^2 + V(\epsilon x)v^2 \right)^\frac{1}{2}.$$
Since the approach is variational, let us consider the energy functional $I_\epsilon: \tilde{H} \to \mathbb{R}$, whose Euler-Lagrange equation is (\[P2\]), given by $$I_\epsilon(v) = \frac{1}{2}\int( |\nabla v|^2 + V(\epsilon x)v^2) - \int G_\epsilon(\epsilon x,v).$$ By standard arguments, one can prove that $I_\epsilon \in C^2(\tilde{H}, \mathbb{R})$.
In this section and through the rest of the paper, we omit the $dx$ in all the integrals and, when the domain over which the integral is calculated is $\mathbb{R}^N$ we write $\int$ rather than $\int_{\mathbb{R}^N}$.
Existence results
=================
Let us consider the Nehari manifold associated to (\[P2\]), which is well defined by $(g_4)$ and given by $$\mathcal{N}_\epsilon = \{v \in \tilde{H} \backslash \{0\}; I_\epsilon'(v)v = 0\}.$$
Since we are looking for nodal solutions, let us consider the so called nodal Nehari set $$\mathcal{N}_\epsilon^\pm = \{v \in \tilde{H}; v^\pm \neq 0 \ \ \mbox{and} \ \ I_\epsilon'(v)v^\pm = 0\}.$$ Although $\mathcal{N}_\epsilon^\pm$ is not a manifold since $u \mapsto u^+$ in $H^1(\mathbb{R}^N)$ lacks differentiability, it is a set which contain all nodal solutions of (\[P2\]).
Next result try to infer informations of $I_\epsilon$ with respect to $\mathcal{N}_\epsilon^\pm$ in the same way that one is used to do with $\mathcal{N}_\epsilon$.
Let $v \in \tilde{H}$ such that $v^\pm \neq 0$. Then there exist $t,s > 0$ such that $t v^+ + s v^- \in \mathcal{N}_\epsilon^\pm$. \[lemma1\]
First of all let us prove that, for all $v \in \tilde{H}\backslash\{0\}$, there exists $t > 0$ such that $tv \in \mathcal{N}_\epsilon$. Indeed, if $\Gamma = (supp v \cap \Omega_\epsilon) \cup \{x \in \mathbb{R}^N; \, |v(x)|\leq \frac{1}{2}\epsilon^\frac{\tau}{\nu - 1}\}$, note that $|\Gamma| > 0$ (since $v \in H^1(\mathbb{R}^N)$) and then $$\begin{aligned}
I_\epsilon(tv)& = & \frac{t^2}{2}\|v\|^2_\epsilon - \int_\Gamma F(tv) - \int_{\mathbb{R}^n\backslash\Gamma} G(\epsilon x,v)\\
& \leq & \frac{t^2}{2}\|v\|^2_\epsilon - t^\theta \int_\Gamma |v|^\theta - \frac{t^\tau}{2}\int_{\mathbb{R}^n\backslash\Gamma} |v|\\
& \to & -\infty,\end{aligned}$$ as $t \to \infty$. Then, if $v \in \tilde{H}$ is such that $v^\pm \neq 0$, there exist $t,s > 0$ such that $$I'_\epsilon(tv^+)tv^+ = 0 \quad \mbox{and} \quad I'_\epsilon(sv^-)sv^- = 0.$$ Then, it is clear that $$I'_\epsilon(tv^+ + sv^-)(tv^+ + sv^-) = I'_\epsilon(tv^+)tv^+ + I'_\epsilon(sv^-)sv^- = 0.$$
For a fixed $v \in \tilde{H}$, let us consider $\psi_v:[0, +\infty)\times [0,+\infty) \to \mathbb{R}$ given by $$\psi_v(t,s) = I_\epsilon(t v^+ + s v^-),$$ and note that by the smoothness of $g$, $\psi_v \in C^2(\mathbb{R}^2, \mathbb{R})$.
Let $v \in \mathcal{N}_\epsilon^\pm$, then $(t,s) = (1,1)$ is a strict global maximum point of $\psi_v$. \[lemma2\]
First of all let us note that if $v \in \mathcal{N}_\epsilon^\pm$, by $(g_3)$ $$\lim_{|(t,s)| \to \infty}\psi_v(t,s) = -\infty.$$ Then there exists $R>0$ such that $$\psi_v(t,s) < 0, \quad \mbox{if $|(t,s)| \geq R.$}
\label{eq1}$$ Since $$\nabla\psi_v(t,s) = \left(I_\epsilon'(tv^+)v^+, I_\epsilon'(sv^-)v^-\right),$$ standard calculations about the behavior of $t \mapsto I_\epsilon(tv^+)$ and $s \mapsto I_\epsilon(sv^-)$ and the fact that $v \in \mathcal{N}_\epsilon^\pm$, implies that $\psi_v$ has just one critical point given by $(t,s) = (1,1)$.
As we prove in Lemma \[lemma4\] (which is totally independent of this one), $\psi_v(1,1) = I_\epsilon(v) \geq \rho > 0$. By (\[eq1\]) in order to get the result its enough to prove that $(1,1)$ is a local maximum point of $\psi_v$. Note that $$D^2\psi_v(t,s)=
\left(
\begin{array}{cc}
I_\epsilon''(tv^+)(v^+,v^+) & 0\\
\\
0 & I_\epsilon''(sv^-)(v^-,v^-)
\end{array} \right)$$ and then $$\begin{aligned}
\det(D^2\psi_v(1,1)) & = & I_\epsilon''(v^+)(v^+,v^+) . I_\epsilon''(v^-)(v^-,v^-)\\
& = & \left(\int \left(g_\epsilon(\epsilon x,v^+)v^+ - g_\epsilon'(\epsilon x,v^+){v^+}^2\right)\right)\\
& & . \left(\int \left(g_\epsilon(\epsilon x,v^-)v^- - g_\epsilon'(\epsilon x,v^-){v^-}^2\right)\right).\end{aligned}$$ By definition of $g_\epsilon$ and $(g_4)$, the last integral is greater or equal to $$\begin{array}{c}
\displaystyle \left(\int_{(supp(v^+)\cap\Omega_\epsilon) \cup \{|v^+| \leq \frac{1}{2}\epsilon^\frac{\tau}{\nu-1}\})} \left(f(v^+)v^+ - f'(v^+){v^+}^2\right)\right) \\
. \displaystyle
\left(\int_{supp(v^-)\cap(\Omega_\epsilon \cup \{|v^-| < \frac{1}{2}\epsilon^\frac{\tau}{\nu-1}\})} \left(f(v^-)v^- - f'(x,v^-){v^-}^2\right)\right)\\
> 0.
\end{array}$$ In the last inequality we have used that by $(f_4)$, $$f(s)s - f'(s)s^2 < 0, \quad \mbox{for all $s\neq 0$}$$ and as $v^\pm \in \tilde{H}$, $|supp(v^+)\cap(\Omega_\epsilon \cup \{|v^+| < a\})| > 0$ and $|supp(v^-)\cap(\Omega_\epsilon \cup \{|v^-| < a\}| > 0$, where $\Omega_\epsilon: = \epsilon^{-1}\Omega$.
Since $D^2\psi_v(1,1)$ is a positive definite form, we have just to verify that $\frac{\partial^2 \psi_v}{\partial t^2} = I_\epsilon''(tv^+){v^+}^2 < 0$. But this follows since $1$ is a maximum point of $t \mapsto I_\epsilon(tv^+)$.
Still as a consequence of the arguments employed in the construction of the Nehari manifold as in [@Rabinowitz], it follows the following result.
Let $v \in \tilde{H}$ such that $v^\pm \neq 0$ and $$I_\epsilon'(v)v^\pm \leq 0,$$ then there exists $t,s \in (0,1]$ such that $$tv^+ + sv^- \in \mathcal{N}_\epsilon^\pm.$$ \[lemma3\]
In fact, let $t \in \mathbb{R}$ such that $I_\epsilon'(tv^+)tv^+ = 0$. Suppose by contradiction that $t > 1$, then $$\begin{aligned}
\|v^+\|^2 & = & \int \frac{g_\epsilon(\epsilon x,tv^+)v^+}{t} = \int_{v^+ > 0} \frac{g_\epsilon(\epsilon x,tv^+){v^+}^2}{tv^+}\\
& = & \int_{supp(v^+)\cap(\Omega_\epsilon\cup\{|tv^+| < \frac{1}{2}\epsilon^\frac{\tau}{\nu-1}\}}\frac{f(tv^+){tv^+}^2}{v^+} + \\
& & \int_{supp(v^+)\cap(\Omega_\epsilon\cup\{|tv^+| \geq \frac{1}{2}\epsilon^\frac{\tau}{\nu-1}\}\}}\frac{g_\epsilon(\epsilon x,tv^+){v^+}^2}{tv^+} \\
& > & \int_{supp(v^+)\cap(\Omega_\epsilon\cup\{|tv^+| < \frac{1}{2}\epsilon^\frac{\tau}{\nu-1}\}}f(v^+)v^+\\
& & + \int_{supp(v^+)\cap(\Omega_\epsilon\cup\{|v^+| \geq \frac{1}{2}\epsilon^\frac{\tau}{\nu-1}\}\}}\frac{g_\epsilon(\epsilon x,v^+){v^+}^2}{v^+} \\
& = & \int g_\epsilon(\epsilon x,v^+)v^+,\end{aligned}$$ which implies that $I_\epsilon'(v)v^+ > 0$, contradicting the hypothesis. The same argument applies to $v^-$ and $s$.
Let us define $$d_\epsilon := \inf_{\mathcal{N}_\epsilon^\pm} I_\epsilon,$$ and note that if there exists a solution of (\[P2\]) in the energy level $d_\epsilon$, then it is the solution with least energy among all nodal ones.
Now we are going to state and prove the main result of this section.
For sufficiently small $\epsilon > 0$, there exists a nodal solution of (\[P2\]), $v_\epsilon \in \tilde{H}$ such that $I_\epsilon(v_\epsilon) = d_\epsilon$. \[theorem2\]
Before proceed with the proof of Theorem \[theorem2\] let us state some technical result about $\mathcal{N}_\epsilon^\pm$.
It holds that
$i)$
: There exists $\rho > 0$ such that $\|v\|_\epsilon \geq \rho$ for all $v \in \mathcal{N}_\epsilon$.
$ii)$
: There exists a constant $C > 0$ such that, for all $v \in \mathcal{N}_\epsilon$, $\displaystyle I_\epsilon(v) \geq C\|v\|_\epsilon^2$.
\[lemma4\]
The proof of $i)$ follows by standard arguments. Let us prove just $ii)$, which in fact also follows by very known arguments. Note that, if $v \in \mathcal{N}_\epsilon$, by $(g_3)$ $$\begin{aligned}
I_\epsilon(v) = I_\epsilon(v) -\frac{1}{\theta}{I'}_\epsilon(v)v & = & \left( \frac{1}{2} - \frac{1}{\theta}\right) \parallel v\parallel_\epsilon^2 +\frac{1}{\theta} \int_{{\mathbb{R}}^N} \left( g(x,v)v - \theta G(x,v)\right)dx\\
& \geq & \left( \frac{1}{2} - \frac{1}{\theta}\right) \parallel v\parallel_\epsilon^2 +\frac{1}{\theta} \int_{\Omega_\epsilon^c} \left( g(\epsilon x,v_n)v - \theta G(\epsilon x,v)\right)dx\\
& \geq & \left( \frac{1}{2} - \frac{1}{\theta}\right) \parallel v\parallel_\epsilon^2 +\frac{(2-\theta)}{\theta}\int_{\Omega_\epsilon^c} G(x,u_n)dx\\
& \geq & \left( \frac{1}{2} - \frac{1}{\theta}\right) \parallel v\parallel_\epsilon^2 + \frac{(2-\theta)}{2\theta}\int_{ \Omega_\epsilon^c} \epsilon^\tau v^2 dx\\
& = & \left(\frac{\theta - 2}{2\theta}\right)\int_{\mathbb{R}^N} \left(|\nabla v|^2 +(V(\epsilon x)-\epsilon^\tau) v^2\right)dx\\
& = & \left(\frac{\theta - 2}{2\theta}\right)\int_{\mathbb{R}^N} \left(|\nabla v|^2 +(V_0-\epsilon^\tau) v^2\right)dx\\
& \geq &C \parallel v\parallel_\epsilon^2, \end{aligned}$$ where $C > 0$ for $\epsilon > 0$ sufficiently small.
The proof will be carried out into two steps. In the first one we prove that $d_\epsilon$ is attained by a function $u_\epsilon \in \tilde{H}$.
Let $(w_n)$ be a minimizing sequence for $I_\epsilon$ in $\mathcal{N}_\epsilon^\pm$, i.e., a sequence $(w_n) \subset \mathcal{N}_\epsilon^\pm$ such that $$\lim_{n \to \infty} I_\epsilon(w_n) = d_\epsilon.
\label{eq2}$$
Note that by (\[eq2\]) and Lemma \[lemma4\], $(w_n)$ is a bounded sequence in $\tilde{H}$. Then there exists $w_\epsilon$ such that $w_n \rightharpoonup w_\epsilon$ in $\tilde{H}$ up to a subsequence. In the same way as in Lemma 2.3 in [@Castro], it is possible to show that $v \mapsto v^\pm$ is a continuous function of $\tilde{H}$ into itself, from which follows that $w_n^\pm \rightharpoonup w_\epsilon^\pm$ in $\tilde{H}$. As a consequence, up to a subsequence $$w_n^\pm \to w_\epsilon^\pm, \quad \mbox{a.e. in $\mathbb{R}^N$}.
\label{eq5}$$ and $$w_n^\pm \to w_\epsilon^\pm, \quad \mbox{in $L^r(\Omega_\epsilon)$, for $1 \leq r < \frac{2(N-k)}{N-k-2}$}
\label{eq5.1}$$ where $w_\epsilon^\pm \neq 0$ by the same arguments in Lemma 2.8 in [@Sato].
Since $w_\epsilon^\pm \neq 0$, let $t_\epsilon, s_\epsilon > 0$ be such that $t_\epsilon w_\epsilon^+ + s_\epsilon w_\epsilon^- \in \mathcal{N}_\epsilon^\pm$. By weak lower-semicontinously of $\|\cdot\|$ and by Sobolev embeddings it follows that $$\|t_\epsilon w_\epsilon^+ + s_\epsilon w_\epsilon^-\|_\epsilon \leq \liminf_{n \to \infty} \|t_\epsilon w_n^+ + s_\epsilon w_n^-\|_\epsilon
\label{eq5.2}$$ and $$\int_{\Omega_\epsilon} F(t_\epsilon w_\epsilon^+ + s_\epsilon w_\epsilon^-) = \liminf_{n \to \infty} \int_{\Omega_\epsilon} F(t_\epsilon w_n^+ + s_\epsilon w_n^-).
\label{eq5.3}$$
Now the real essence of the modification of penalization really comes up. Note that for $\epsilon > 0$ sufficiently small $$I_ {\epsilon, \mathbb{R}^N\backslash \Omega_\epsilon}(v):= \frac{1}{2}\int_{\mathbb{R}^N\backslash \Omega_\epsilon}\left(|\nabla v|^2 + V(\epsilon x)v^2\right) - \int_{\mathbb{R}^N\backslash \Omega_\epsilon}\tilde{F}_{\epsilon}(v)$$ is a strictly convex functional in $\tilde{H}({\mathbb{R}^n\backslash \Omega_\epsilon}) = \left\{ v \in H^1(\mathbb{R}^N\backslash\Omega_\epsilon), \int_{\mathbb{R}^N\backslash\Omega_\epsilon}\left(|\nabla v|^2 + V(\epsilon x)v^2\right) < \infty \right\}$. In fact, for $v,h \in \tilde{H}({\mathbb{R}^n\backslash \Omega_\epsilon})$, $h \neq 0$, by (\[penalization2\]) and Sobolev embeddings $$\begin{aligned}
I_ {\epsilon, \mathbb{R}^N\backslash \Omega_\epsilon}''(v)(h,h) & = & \|h\|_{\epsilon,\mathbb{R}^n\backslash \Omega_\epsilon}^2 - \int_{\mathbb{R}^n\backslash \Omega_\epsilon}\tilde{f}_{\epsilon}'(v)h^2\\
& \geq & \|h\|_{\epsilon,\mathbb{R}^n\backslash \Omega_\epsilon}^2\left(1 - \epsilon^\tau\right) > 0,\end{aligned}$$ for $\epsilon > 0$ sufficiently small. Then, by convex analysis it follows that $I_ {\epsilon, \mathbb{R}^N\backslash \Omega_\epsilon}$ is weakly lower semicontinuous. Then (\[eq5.2\]), (\[eq5.3\]) and this fact imply that $$\begin{aligned}
I_\epsilon(t_\epsilon w_\epsilon^+ + s_\epsilon w_\epsilon^-) & \leq & \liminf_{n \to \infty} I_\epsilon(t_\epsilon w_\epsilon^+ + s_\epsilon w_\epsilon^-)\\
& \leq & \liminf_{n \to \infty} (I_\epsilon(t_\epsilon w_\epsilon^+) + I_\epsilon(s_\epsilon w_\epsilon^-))\\
& \leq & \liminf_{n \to \infty} (I_\epsilon(w_\epsilon^+) + I_\epsilon(w_\epsilon^-))\\
& = & b_\epsilon.\end{aligned}$$
Hence $I_\epsilon(t_\epsilon w_\epsilon^+ + s_\epsilon w_\epsilon^-) = b_\epsilon$.
The second step is proving that $v_\epsilon \in \tilde{H}$ which minimizes $I_\epsilon$ on $\mathcal{N}_\epsilon^\pm$ is a critical point of $I_\epsilon$ in $\tilde{H}$. This can be done by employing the same arguments of Section 3 in [@Bartsch]. For the sake of completeness we include all the details of this proof.
Supposing by contradiction that $I_\epsilon'(v_\epsilon) \neq 0$, there exists $\delta, \lambda > 0$ such that $$\| I_\epsilon'(v)\|_* \geq \lambda, \quad \mbox{for all $v \in B_\delta(v_\epsilon) \subset \tilde{H}$.}
\label{eq9}$$
Let us consider the function $(t,s) \mapsto tv_\epsilon^+ + sv_\epsilon^-$ defined on $D = \left( \frac{1}{2}, \frac{3}{2} \right)$ and note that by Lemma \[lemma2\] $$\delta_\epsilon:= \max_{(t,s) \in \partial D} I_\epsilon( tv_\epsilon^+ + sv_\epsilon^-) < I_\epsilon(v_\epsilon) = d_\epsilon.
\label{eq10}$$ Taking $\rho = \min\left\{\frac{d_\epsilon - \delta_\epsilon}{2}, \frac{\lambda\delta}{24}\right\}$ and $S = B_{\delta/3}(v_\epsilon)$, Lemma 2.3 in [@Willem] yields a deformation $\eta$ such that
$i)$
: $\eta(1,v) = v$ for all $v \not\in I_\epsilon^{-1}([d_\epsilon-2\rho,d_\epsilon+2\rho])$,
$ii)$
: $\eta(1,I_\epsilon^{d_\epsilon+\rho}\cap S) \subset I_\epsilon^{d_\epsilon-\rho}$,
$iii)$
: $I_\epsilon(\eta(1,v)) \leq I_\epsilon(v)$, for all $u \in \tilde{H}$.
$$\max_{(t,s)\in \overline{D}}I_\epsilon(\eta(1,tv_\epsilon^+ + sv_\epsilon^-)) < d_\epsilon.$$
In fact, if $(t,s)\neq (1,1)$, then by Lemma \[lemma2\], $$I_\epsilon(\eta(1,tv_\epsilon^+ + sv_\epsilon^-)) \leq I_\epsilon(tv_\epsilon^+ + sv_\epsilon^-) < d_\epsilon.$$ On the other hand, by $ii)$, $$I_\epsilon(\eta(1,v_\epsilon)) < d_\epsilon - \rho,$$ which proves the claim.
Now, let us prove that there exists $(t,s) \in D$ such that $\eta(1,tv_\epsilon^+ + sv_\epsilon^-) \cap \mathcal{N}_\epsilon^\pm \neq \emptyset$, which together with the Claim, contradicts the definition of $d_\epsilon$.
Define $h(t,s) = \eta(1,tv_\epsilon^+ + sv_\epsilon^-)$ and $\Psi_0, \Psi_1: \mathbb{R}^2 \to \mathbb{R}^2$ by $$\Psi_0(t,s) = (I_\epsilon'(t v_\epsilon^+)v_\epsilon^+, I_\epsilon'(s v_\epsilon^-)v_\epsilon^-),$$ and $$\Psi_1(t,s) = \left(\frac{1}{t}I_\epsilon'(h(t,s)^+)h(t,s)^+, \frac{1}{s}I_\epsilon'(h(t,s)^-)h(t,s)^-)\right).$$ By results of Brower Degree Theory, $\deg(\Psi_0,D,(0,0)) = 1$. On the other hand, note that by (\[eq10\]), $(t,s)\mapsto tv_\epsilon^+ + sv_\epsilon^-$ coincides with $h$ on $\partial D$. Hence $\Psi_0 = \Psi_1$ on $\partial D$ and then $\deg(\Psi_1,D,(0,0)) = \deg(\Psi_0,D,(0,0)) = 1$. Therefore there exists $(t,s) \in D$ such that $\Psi_1(t,s) = (0,0)$ and consequently $$\eta(1,tv_ \epsilon^+ + sv_\epsilon^-) = h(t,s) \in \mathcal{N}_\epsilon^\pm.$$
Finally, this contradiction proves the theorem.
Concentration results
=====================
Let us introduce a sequence $\epsilon_n \to 0$ as $n \to \infty$ and, for each $n \in \mathbb{N}$, let us denote by $v_n$ the solution $v_{\epsilon_n}$ given by Theorem \[theorem2\] and consider $d_n:= d_{\epsilon_n}$, $\|\cdot\|_n:=\|\cdot\|_{\epsilon_n}$ and $I_n: = I_{\epsilon_n}$.
The following result provides an upper estimate for the sequence of minimax values $d_n$. Its proof is inspired in the arguments of Alves and Soares in [@Soares1].
$$\limsup_{n \to \infty}\epsilon_n^k d_n \leq 2\omega_k\inf_{\Omega\cap \mathcal{H}^\perp} \mathcal{M}$$ and $$\epsilon_n^k\|v_n\|_n^2 \leq C.$$ \[lemma5.1\]
Let $z_0=(x_0,y_0) \in \Omega$ be such that $\mathcal{M}(z_0) = \inf_{x \in \Omega} \mathcal{M}(x)$. Since $\Omega$ is an open set, there exists $R > 0$ such that $B_{2R}(z_0) \subset \Omega$. Let us choose points $z_1,z_2 \in \partial B_R(z_0)$ such that, if $z_i=(Q_i',Q_i'')$, then $|Q_1'' - Q_2''| = 2R$. Note that $B_R(z_i) \subset \Omega$ for $i = 1,2$. In the rest of this proof, $i \in \{1,2\}$. Let us choose smooth cut-off functions $\psi_i:\mathbb{R}^{N-k} \to \mathbb{R}$ such that $\psi_i = 1$ in $B_{\mathbb{R}^{N-k}}((Q_i',|Q_i''|),R/4)$ and $\psi_i = 0$ in $\mathbb{R}^{N-k} \backslash B_{\mathbb{R}^{N-k}}((Q_i',|Q_i''|),R/2)$.
Let $w_i \in H^1(\mathbb{R}^{N-k})$, be a ground-state solution of $$-\Delta u + V(z_i) u= f(u) \quad \mbox{in $\mathbb{R}^{N-k}$}$$ and $w_{n,z_i}:\mathbb{R}^N \to \mathbb{R}$ be given by $$w_{n,z_i}(x',x'') = \psi_i(\epsilon_n x',\epsilon_n |x''|)w_i \left(x' - \frac{Q_i'}{\epsilon_n},|x''| - \frac{|Q_i''|}{\epsilon_n}\right).$$ We associate for each $w_{n,z_i}(x)$ its $k-$dimensional counterpart $\tilde{w}_{n,z_i}(x',r) = w_{n,z_i}(x',x'')$ where $|x''| = r \in \mathbb{R}$. It is well known the existence of $t_{i_n} > 0$ such that $t_{i_n}w_{n,z_i} \in \mathcal{N}_{\epsilon_n}$. By the construction we have made so far, it is straightforward to see that $$\overline{w}_n := t_{1_n}w_{n,z_1} - t_{2_n}w_{n,z_2} \in \mathcal{N}_{\epsilon_n}^\pm.$$
Using the fact that $I_n$ is even, we have $$d_n \leq I_n(\overline{w}_n) = I_n(t_{1_n}w_{n,z_1} ) + I_n(t_{2_n}w_{n,z_2}).
\label{eq11}$$
By a change of variable, let us note that for $i \in \{1,2\}$, $I_n(t_nw_{n,z_i})$ is equal to $$\begin{array}{l}
\displaystyle\frac{t_{i_n}^2}{2}\int_{\mathbb{R}^N}\left(|\nabla w_{n,z_i}|^2 + V(\epsilon_n x)w_{n,z_i}^2\right)dx - \int_{\mathbb{R}^N}G_n(\epsilon_n x, t_{i_n}w_{n,z_i})dx \\ \\
= \displaystyle\omega_k\left[ \frac{t_{i_n}^2}{2}\int_{\mathbb{R}^{N-k-1}}\int_0^{+\infty}r^k\left(|\nabla\tilde{w}_{n,z_i}(x',r)|^2 + V(\epsilon_n x', \epsilon_n r)\tilde{w}_{n,z_i}(x',r)^2\right)drdx'\right.\\ \\
\displaystyle\left. - \int_{\mathbb{R}^{N-k-1}}\int_0^{+\infty}r^kG_n(\epsilon_n x, \epsilon_n r,t_{i_n}\tilde{w}_{n,z_i}(x',r))drdx'\right] \\ \\
= \displaystyle\omega_k\left[ \frac{t_{i_n}^2}{2}\int_{\mathbb{R}^{N-k-1}} \int_{\frac{-|Q_i''|}{\epsilon_n}}^{+\infty}\left(\sigma + \frac{|Q_i''|}{\epsilon_n}\right)^k\left(|\nabla(\psi_i(\epsilon_n x' + Q_i',\epsilon_n\sigma+|Q_i''|)w_i(x',\sigma)) |^2\right. \right.\\ \\
\displaystyle\left. \left. + V(\epsilon_n x' + \epsilon_nQ_i',\epsilon_n\sigma + |Q_i''|)(\psi_i(\epsilon_n x' + \epsilon_n Q_i',\epsilon_n\sigma+|Q_i''|)w_i(x',\sigma)^2\right)d\sigma dx'\right.\\ \\
\displaystyle\left. - \hspace{-0.2cm} \int_{\frac{-|Q_i''|}{\epsilon_n}}^{+\infty}\hspace{-0.2cm}\left(\sigma \hspace{-0.1cm} + \hspace{-0.1cm} \frac{|Q_i''|}{\epsilon_n}\right)^k \hspace{-0.3cm}G_n(\epsilon_n x' \hspace{-0.2cm}+ \hspace{-0.1cm} \epsilon_n Q_i',\epsilon_n\sigma \hspace{-0.1cm} + \hspace{-0.1cm} |Q_i''|, t_{i_n}\psi_i(\epsilon_n x' \hspace{-0.1cm}+ \hspace{-0.1cm} \epsilon_n Q_i', \epsilon_n\sigma \hspace{-0.1cm}+ \hspace{-0.1cm}|Q_i''|)w_i(x',\sigma))d\sigma dx' \hspace{-0.1cm}\right] \\ \\
= \displaystyle\epsilon_n^{-k}\omega_k|Q_i|^k I_{V(z_i)}(t_{i_n}w_i) + o(1) \leq \epsilon_n^{-k}\omega_k |Q_i|^k \mathcal{E}(V(z_i)) = \epsilon_n^{-k}\omega_k\mathcal{M}(z_i) + o(1).
\displaystyle\end{array}$$
By the last inequality and (\[eq11\]) we have $$\epsilon_n^k d_n \leq \omega_k\left(\mathcal{M}(z_1) + \mathcal{M}(z_2)\right) + o(1)
\label{eq12}$$ and making $R \to 0$, continuity of $V$ and $\mathcal{M}$ implies in the result.
Now, in order to see that $$\epsilon_n^k\|v_n\|_n^2 \leq C,$$ just observe that $v_n \in \mathcal{N}_{\epsilon_n}$ and use $ii)$ of Lemma \[lemma4\].
The next lemma implies that solutions found in Theorem \[theorem2\] do not vanish when $n \to \infty$.
Let $P_n^1$, $P_n^2$ be local maximum and minimum points of $v_n$, respectively. Then $P_n^i \in \Omega_{\epsilon_n}:=\epsilon_n^{-1}\Omega$, $$v_n(P_n^1) \geq a \quad \mbox{and} \quad v_n(P_n^2) \leq -a,$$ where $a > 0$ is such that $ f(a)/a= V_0/2$. \[lemma5.2\]
First of all let us prove that $P_n^i \in \Omega_{\epsilon_n}$. Suppose by contradiction that $P_n^1 \not \in \Omega_{\epsilon_n}$. Since $P_n^1$ is a local maximum point, it follows that $\Delta v_n(P_n^1) \leq 0$. By definition of $g_n$ we have $$V_0 v_n(P_n^1) \leq-\Delta v_n(P_n^1) + V(\epsilon_n P_n^1)v_n(P_n^1) = \tilde{f}_{\epsilon_n}(v_n(P_n^1)) \leq \epsilon_n^\tau v_n(P_n^1),$$ which is impossible for $\epsilon > 0$ sufficiently small. A similar argument applies to $P_n^2$.
Since $P_n^1 \in \Omega_{\epsilon_n}$ and $v_n(P_n^1) > 0$, from the definition of $g_n$ we have $$0 \geq \Delta v_n(P_n^1) = \left(V(\epsilon_n P_n^1) - \frac{f(v_n(P_n^1))}{v_n(P_n^1)}\right)v_n(P_n^1).$$ Supposing by contradiction that $v_n(P_n^1) < a$. By the choice of $a > 0$ and $(f_5)$ it follows that $$V_0 \leq V(\epsilon_n P_n^1) \leq \frac{f(v_n(P_n^1))}{v_n(P_n^1)} \leq \frac{f(a)}{a} = \frac{V_0}{2},
\label{eq13}$$ which is a contradiction. Analogously we prove that $v_n(P_n^2) \leq -a$.
By the last result, there exist $P^1, P^2 \in \Omega$ such that, along a subsequence $$\lim_{n \to \infty} \epsilon_n P_n^i = P^i, \quad i \in \{1,2\}.
\label{Pi}$$
The same argument of [@Soares1] with short modifications can be used to prove the following result.
Using the same notation that in the last result, it follows that $$\lim_{n \to \infty}|P_n^1 - P_n^2| = +\infty.
\label{eq14}$$ \[lemma5.3\]
Let $y_n = (y_n',y_n'') \subset \mathbb{R}^N$ be a sequence such that $\epsilon_ny_n \to (\bar{y}',\bar{y}'') \in \overline{\Omega}$ as $n \to \infty$. Denoting $\tilde{v}_n(x',r):= v_n(x', x'')$ where $|x''| = r$, let us define $\tilde{w}_n: \mathbb{R}^{N-k-1}\times [-|y_n|,+\infty) \to \mathbb{R}$ by $$\tilde{w}_n(x',r):= \tilde{v}_n(x',r + |y_n''|).$$ Then there exists $\tilde{w} \in H^1(\mathbb{R}^{N-k})$ such that $\tilde{w}_n \to \tilde{w}$ in $C^2_{loc}(\mathbb{R}^{N-k})$ and $\tilde{w}$ satisfies the limit problem $$-\Delta \tilde{w} + V(\bar{y}',|\bar{y}''|)\tilde{w} = \tilde{g}_n(x',r, \tilde{w}) \quad \mbox{in $\mathbb{R}^{N-k}$,}
\label{Plim}$$ where $\tilde{g}_n(x',r,s) := \chi(x',r)f(s) + (1-\chi(x',r))\tilde{f}_{\epsilon_n}(s)$ and $\chi(x',r)=\lim_{n\to\infty}\chi_\Omega(\epsilon_n x' + \epsilon_ny_n',\epsilon_n r + \epsilon_n|y_n''|)$. \[lemma5.4\]
The proof is analogous to [@Bonheure1]\[Lemma 4.3\] but we sketch it here for the sake of completeness.
Note that $\tilde{w}_n$ satisfies the following problem $$-\Delta\tilde{w}_n- \frac{k}{(r + |y_n''|)}\frac{\tilde{w}_n}{\partial r} + V\hspace{-0.1cm}(\epsilon_n x' + \epsilon_n y_n',\epsilon_n r+ \epsilon_n|y_n''|)\tilde{w}_n \hspace{-0.1cm} = \hspace{-0.1cm} g_n(\epsilon_n x' + \epsilon_n y_n',\hspace{-0.1cm} \epsilon_n r+ \epsilon_n|y_n''|, \hspace{-0.1cm}\tilde{w}_n),
\label{PRtrans}$$ in $\mathbb{R}^{N-k-1}\times [-|y_n|,+\infty)$.
By Lemma \[lemma5.1\] it follows that $$\int_{\mathbb{R}^{N-k-1}} \int_{-|y_n''|}^{+\infty}\left(|\nabla \tilde{w}_n|^2 + V(\epsilon_n x' + \epsilon_n y_n',\epsilon_n r + \epsilon_n|y_n''|)\tilde{w}_n^2\right)dr dx'\leq C,
\label{estimatelemma5.4}$$ uniformly in $n$ and then, for some $\tilde{w}\in H^1(\mathbb{R}^{N-k})$, $$\tilde{w_n} \rightharpoonup \tilde{w} \quad \mbox{in $H^1(\mathbb{R}^{N-k})$.}
\label{convergencelemma5.4}$$
By choosing a sequence $R_n \to \infty$ such that $\epsilon_n R_n \to 0$ and considering a smooth cut-off function in $\mathbb{R}^{N-k}$, $\eta_R$ such that $0 \leq \eta_R \leq 1$, $\eta_R(z) = 1$ if $|z| \leq \frac{R}{2}$ and $\eta_R(z) = 0$ if $|z| > R$, and $\|\nabla \eta_R\|_\infty \leq \frac{C}{R}$, it can be proved using (\[estimatelemma5.4\]) that $\overline{w}_n(z) := \eta_{R_n}(z)\tilde{w}_n(z)$ is bounded in $H^1(\mathbb{R}^{N-k})$, uniformly in $n$.
Since $\overline{w}_n$ satisfies (\[PRtrans\]) in $B(0,R_n)$, it follows by classical elliptic estimates that $$\|\overline{w}_n\|_{W^{2,q}(B(0,R))} \leq C
\label{bootstrap}$$ for sufficiently large $n\in \mathbb{N}$, where $R > 0$ is fixed.
By (\[convergencelemma5.4\]) and (\[bootstrap\]) it follows that $\tilde{w}_n \to \tilde{w}$ in $C^2_{loc}(\mathbb{R}^{N-k})$ and that $\tilde{w}$ satisfies (\[Plim\]).
Since the concentration set is expected to be a sphere in $\mathbb{R}^N$, it is natural to introduce the distance between two $k-$dimensional spheres in $\mathbb{R}^N$, which gives rise to neighborhoods in which we want to estimate the mass of solutions. For $x=(x',x''),y=(y',y'') \in \mathbb{R}^N$, let $$d_k(x,y) = \sqrt{(x'-y')^2 + (|x''| - |y''|)^2},
\label{distancedk}$$ which corresponds to the distance between $k-$dimensional spheres centered at the origin, parallel to $\mathcal{H}^\perp$ and of radius $|x''|$ and $|y''|$, respectively. According to this distance, the balls are given by $$B_k(x,r) = \{y \in \mathbb{R}^N; \, d_k(x,y) < r\}.$$
From now on, for $\Lambda \subset \mathbb{R}^N$ we denote $$I_{n,\Lambda}(v) = \frac{1}{2}\int_\Lambda \left(|\nabla v|^2 + V(\epsilon_n x)v^2\right)dx - \int_\Lambda G_n(\epsilon_n x,v)dx.$$
The following is the main step in proving the concentration result.
Suppose all the assumptions of Theorem \[theorem1.1\] to hold. Then,
- $\displaystyle \lim_{n \to \infty} \epsilon_n^kd_n = 2\omega_k\inf_\Omega \mathcal{M}$.\
- $\displaystyle \lim_{n \to \infty} \mathcal{M}(\epsilon_n P_n^i) = \inf_\Omega \mathcal{M}$, $i \in \{1,2\}$.\
\[prop5.6\]
Let us get started with $i)$. By Lemma \[lemma5.1\] it follows that $$\limsup_{n \to \infty} \epsilon_n^k d_n \leq 2\omega_k\inf_\Omega \mathcal{M}.
\label{eq15}$$
In order to prove that $$\liminf_{n \to \infty} \epsilon_n^k d_n \geq 2\omega_k\inf_\Omega \mathcal{M},
\label{eq15.1}$$ we use some ideas of [@DelPino]\[Lemma 2.2\].
By Lemmas \[lemma5.2\] and \[lemma5.4\] it follows that $\tilde{w}^i_n(x',r):= \tilde{v}_n(x',r + P_n^i) \to \tilde{w}_i$ in $C^2_{loc}(\mathbb{R}^{N-k})$, where $\tilde{w}_i \neq 0$ and satisfies (\[Plim\]) with $(\bar{y}',\bar{y}'') = P^i$.
For each $R > 0$ and up to a subsequence in $n$, Lemma \[lemma5.4\] with calculations similar to which have resulted in (\[eq12\]) implies that $$\begin{aligned}
\epsilon_n^k I_{n,B_k(P^i,R)}(v_n) & = & \omega_k|{P^i}''|^k \left(\frac{1}{2}\int_{B_R(0)} \left(|\nabla \tilde{w}_i|^2 + V(P^i)\tilde{w}_i^2\right)dz \right. - \\
& & \left. \int_{B_R(0)} \tilde{G}(r,\tilde{w}_i)dz\right) + o_n(1)\\
& \geq & \omega_k|{P^i}''|^k \left(\frac{1}{2}\int_{B_R(0)} \left({|{\nabla \tilde{w}_i}|}^2 + V(P^i)\tilde{w}_i^2\right)dz - \right. \\
& & \left. \int_{B_R(0)} F(\tilde{w}_i)dz \right) + o_n(1).\end{aligned}$$ Since $\tilde{w}_i \in H^1(\mathbb{R}^{N-k})$, it follows that for a given $\eta > 0$, there exists $R > 0$ such that $$\liminf_{n \to \infty}\epsilon_n^k I_{n,B_k(y_n,R)}(v_n) \geq \omega_k\mathcal{M}(P^i) - \eta.$$
Taking into account Lemma \[lemma5.3\], it follows that for $n$ large enough $B_k(P_n^1,R)$ and $B_k(P_n^2,R)$ are disjoint and then $$\epsilon_n^kI_{n}(v_n) = \epsilon_n^k I_{n,B_k(P_n^1,R)}(v_n) + \epsilon_n^k I_{n,B_k(P_n^2,R)}(v_n) + I_{n,\mathbb{R}^N\backslash B_{n,R}}(v_n),$$ where $B_{n,R}:=B_k(P_n^1,R) \cup B_k(P_n^2,R)$.
Now, calculations similar to (2.21) in [@Pimenta] implies that $\liminf_{n \to \infty}I_{n,\mathbb{R}^N\backslash B_{n,R}}(v_n) \geq -\eta$ for $R > 0$ sufficiently large and then
$$\begin{aligned}
\liminf_{n\to\infty} \epsilon_n^kI_n(v_n) & \geq & \omega_k \left(\mathcal{M}(P^1) + \mathcal{M}(P^2)\right) -3\eta\\
& \geq & 2\omega_k\inf_\Omega \mathcal{M} - 3\eta.\end{aligned}$$
Since the last inequality holds for all $\eta > 0$, (\[eq15.1\]) is proved.
To prove $ii)$ let us suppose by contradiction that $$\mathcal{M}(P^i) > \inf_\Omega \mathcal{M}, \quad i \in \{1,2\}.$$ where $P^i$ is given by (\[Pi\]). Just by arguing as in the first item, one can see that $$\liminf_{n\to\infty} \epsilon_n^kI_n(v_n) \geq \omega_k \left(\mathcal{M}(P^1) + \mathcal{M}(P^2)\right) > 2\omega_k\inf_\Omega \mathcal{M},$$ which contradicts the statement of Lemma \[lemma5.1\]. This contradiction proves the proposition.
Proof of Theorem \[theorem1.1\]
===============================
Let $v_n$ be as in the beginning of Section 4 and $u_n(x):=v_n(\epsilon_n^{-1}x)$.
$$\lim_{n \to \infty}\|v_n\|_{L^\infty(\Omega_n\backslash\left(B_k(P_n^1,R) \cup B_k(P_n^2,R))\right)} = 0.$$ \[prop5.1\]
The prove follows by contradiction. Let us suppose that there exist $\eta > 0$ and sequences $R_n \to \infty$ and $(y_n) \subset \Omega_n\backslash\left(B_k(P_n^1,R_n) \cup B_k(P_n^1,R_n)\right)$ such that $$|v_n(y_n)| \geq \eta.$$ Since $\epsilon_n y_n \in \Omega$, it follows that $\epsilon_n y_n \to \bar{y} \in \Omega$ up to a subsequence.
Then following the arguments in Proposition \[prop5.6\] it is possible to show that $$\epsilon_n^k d_n = I_n(v_n) \geq 3\omega_k \inf_{\Omega}\mathcal{M},$$ which contradicts Lemma \[lemma5.1\].
By standard elliptic regularity theory it is possible to show that $v_n \in C^2(\mathbb{R}^N)$. Then, by continuity, Proposition \[prop5.1\] implies that $$\|v_n\|_{L^\infty{\partial(\left(B_k(P_n^1,R_n) \cup B_k(P_n^1,R_n)\right))}} = o_n(1)
\label{boundarydecay}$$
In order to prove the exponential decay with respect to $\epsilon_n$ of the functions $u_\epsilon$, let us take as a comparison function $$W(x) = C(e^{-\beta d_k(x,P_n^1)} + e^{-\beta d_k(x,P_n^2)}),$$ defined in $\mathbb{R}^N \backslash \left(B_k(P_n^1,R) \cup B_k(P_n^1,R)\right)$, where $C > 0$ is to be choosen. For sufficiently small $\beta > 0$ (independent of $\epsilon_n$), it follows that $$\left(-\Delta + V(\epsilon_nx) - \frac{g_n(\epsilon_x,v_n)}{v_n}\right)(W \, \pm\, v_n) \geq 0 \quad \mbox{in $\mathbb{R}^N \backslash \left(B_k(P_n^1,R) \cup B_k(P_n^1,R)\right)$.}$$ Then, by (\[boundarydecay\]), for $x \in \partial \left(B_k(P_n^1,R) \cup B_k(P_n^1,R)\right)$ $$W(x) \pm v_n(x) = C2e^{-\beta R} \pm v_n \geq 0$$ for a sufficiently large constant $C > 0$ which does not depend on $n$. Hence Maximum Principle applies and $$|v_n| \leq W(x), \quad \mbox{on $\mathbb{R}^N \backslash \left(B_k(P_n^1,R) \cup B_k(P_n^1,R)\right)$.}$$
Then there exists a sufficiently large constant $C > 0$ such that $$|v_n(x)| \leq C\left(e^{-\beta d_k(x,P_n^1)} + e^{-\beta d_k(x,P_n^2)}\right),$$ for $x \in \mathbb{R}^N \backslash \left(B_k(P_n^1,R) \cup B_k(P_n^1,R)\right)$, which implies that $$\displaystyle |u_n(x)| \leq C\left(e^{-\frac{\beta}{\epsilon_n} d_k(x,\epsilon_n P_n^1)} + e^{-\frac{\beta}{\epsilon_n} d_k(x,\epsilon_nP_n^2)}\right)
\label{decayestimate}$$ for $x \in \mathbb{R}^N \backslash \left(B_k(\epsilon_n P_n^1,\epsilon_nR) \cup B_k(\epsilon_n P_n^1,\epsilon_n R)\right)$. In particular it holds that $$\|u_n\|_{L^\infty(\mathbb{R}^N\backslash\Omega)} \leq C e^\frac{-\beta}{\epsilon_n}$$ which implies that $u_n$ satisfies the original problem. The proof of (\[Pconcentration\]) follows by (\[Pi\]) and item [*ii)*]{} of Proposition \[prop5.6\]. Therefore the proof of Theorem \[theorem1.1\] follows.
**Acknowledgment.**
We would like to express our gratitude to Prof. Antonio Suárez for some discussions on this subject.
**Competing interests.** The authors declare that they have no competing interests.
**Author’s contribution.**All the author wrote, review and approve the final manuscript.
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[^1]: Supported by PROCAD/CASADINHO 552101/2011-7, CNPq/PQ 301242/2011-9 and CNPq/CSF 200237/2012-8
[^2]: Corresponding author
[^3]: Supported by FAPESP 2014/16136-1 and CNPq 442520/2014-0
|
IN THE COURT OF CRIMINAL APPEALS OF TENNESSEE
AT JACKSON FILED
MAY SESSION, 1998 August 14, 1998
Cecil Crowson, Jr.
Appellate C ourt Clerk
STATE OF TE NNE SSE E, ) C.C.A. NO. 02C01-9708-CR-00309
)
Appellee, )
) SHELBY COUNTY
V. )
)
) HON. W. FRED AXLEY, JUDGE
BRIAN J. HUN TER , )
)
Appe llant. ) (INTERLOCUTORY APPEAL)
FOR THE APPELLANT: FOR THE APPELLEE:
W. MARK WARD JOHN KNOX WALKUP
201 Poplar Avenue, Suite 2-01 Attorney General & Reporter
Memphis, TN 38103
PETER M. COUGHLAN
GARLAND ERGUDEN Assistant Attorney General
242 Poplar Avenue 2nd Floor, Cordell Hull Building
Memphis, TN 38103 425 Fifth Avenu e North
Nashville, TN 37243
JOH N W. P IERO TTI
District Attorn ey Ge neral
JOHNNY R. McFARLAND
Assistant District Attorney General
Criminal Justice Center, Suite 301
201 Poplar Avenue
Memphis, TN 38103
OPINION FILED ________________________
AFFIRMED
THOMAS T. WOODALL, JUDGE
OPINION
The Appellant, Brian J. Hunter, appeals by permission pursuant to Rule 9 of
the Tenn essee Rules o f Appella te Proce dure. A ppellant w as indicted for second
degree murde r and wa s tried by a ju ry in the Sh elby Co unty Criminal Court. At the
end of the State’s proof, the Appellant moved for a judgment of acquittal which was
overruled by the trial court. Following the conclusion of the evidenc e, the trial cou rt,
over the objection of Appellant, charged the jury on the lesser grade offense of
voluntary manslaughter. The State did not request the trial court to charge the
lesser grade o ffense of voluntary mans laughte r. The jury w as ultima tely unab le to
reach a verdict. Wh en polled , the jury state d that they found A ppellant n ot guilty of
second degree murder, but were unable to reach a verdict as to whether he was
guilty of voluntary man slaughter. The trial court declared a mistrial on the voluntary
mans laughte r charge .
The State was prepared to retry Appellant on the voluntary manslaughter
charge, however, Appellant filed a Motion to Dismiss the indictment. Appellant
argued the following three issue s in his Motion to D ismiss: (1) the trial court erred
in charg ing voluntary manslaughter; (2) the trial court erred in charging a lesser
grade offense since Appellant waived the right to charge lesser grade offenses; and
(3) a re-trial on the lesser grade offense of voluntary m anslau ghter wo uld cons titute
doub le jeopardy. After taking Appellant’s motion under advisement, the trial court,
in a written o rder with find ings of fac t and con clusions of law, den ied the m otion.
Appellant subsequently filed a Motion to Reconsider Dismissal Based on
Dou ble Jeopa rdy and/o r Motion fo r Interlocuto ry Appeal. After taking that motion
-2-
under advisem ent, the trial court denied Appellant’s Motion to Reconsider Dismissal
but grante d App ellants ’s Motio n for Inte rlocuto ry App eal. Th is Cou rt subs eque ntly
granted Appellant’s app lication for an interlocutory appeal by order entered
Septem ber 16, 1 997.
In Appe llant’s Design ation as to Appella te Record, Appellant states that “the
only issue to be raised on ap peal is whether double jeopardy prevents the retrial of
the [Appellant] for the lesse r [grade] offense o f voluntary man slaughter.” How ever,
Appellant goes on to s ay that “[i]ncident to this inquiry, [Appellant] will challenge the
sufficiency of the evidence presented at the first trial to support voluntary
manslaughter and whether the trial judge was obligated to and erred in instructing
the jury as to voluntary m anslaughte r.”
An appeal is approp riate und er Rule 9 of the Te nness ee Ru les of Ap pellate
Procedu re if the appellant will suffer “irreparable injury,” if there will otherwise be
“needless, expensive and p rotrac ted litiga tion,” an d if there is a “need to develop a
uniform body of law.” Although p ermission to a ppeal was g ranted by this Co urt
pursuant to Rule 9, we are of the opinio n that it was improvid ently gran ted in part.
After reviewing the issues presented by Appellant, we will not address the issue
pertaining to the trial court charging the lesser grade offense of voluntary
manslau ghter. Issues relating solely to prior proceedings such as evidentiary
rulings, jury charges, and arguments by counsel, are generally not appropriate for
appellate review unde r Rule 9. Since there is no conviction for voluntary
manslaughter in the instant case, Appellant cannot appeal this type issue by way of
interlocutory appe al. In other words, the trial court’s ch arge on volun tary
-3-
manslaughter is not presently an issue in the pending case before us, and we
therefore decline to addres s it.
As to the sufficiency of the evidence of the voluntary manslaughter charge, we
find that the evidence was not insufficient as a matter of law to suppo rt a conviction
for volunta ry ma nslau ghter. W e will brie fly sum mariz e the fa cts in th is case for the
purposes of our review. The Appellant and the victim, Bill Herrington , were
neighbors in an East Memphis apartment complex. On September 14, 1994, Ford
Beach was living with the Appellant, and Beach arrived at the apartment between
5:00 and 5:30 p.m. Herringto n, Appellant, and another friend, S teve Fortini, were
already there drinking and talking. Late that afternoon, there was a scuffle between
Herrington and the Appellant in the kitchen. Herrington and the Appellant then
visited Herrington’s apartment and again be came involved in a heated argum ent,
during which H errington ’s wife told A ppellant to go hom e after their pushing and
shoving cause d wine to b e spilled.
That same evening, after Herrington had eaten dinner and taken a nap, he
returned to the Appellant’s apartment after Beach had gone to sleep on the couch.
Upon entering the apartment, Herrington told Beach that he wanted to “straighten
things out” with the Appellant. Appellant and Herrington went back into the
Appe llant’s bedroom so that Beach could sleep. Beach heard nothing further from
the bedroom until he was awakened by the “click, clock” noise of an automatic pistol
being “racke d.” Be ach h eard th ree sh ots in rapid succession as he ran out of the
apartm ent.
-4-
Appellant described Herrington that evening as “hostile and irate,” angry that
Appellant had poss ibly told a secret entruste d to him by H errington and angry
regarding Appellant’s lack of c once rn ove r his m edica l cond ition. Du ring the ir
discussion in the bedroom, Appellant excused himself to use the bathroom. When
he returned, he saw Herrington holding a Beretta which Appellant kept und erneath
his bed. While the gun was aimed away from the Appellant, Herrington was
describing his “perfect plan” to kill the Appellant. Herrington stuck the gun against
Appe llant’s ear and threatened his life. After A ppella nt beg ged fo r his life, Herrington
dropped the gun into Appellant’s lap and leaned back against the bed. When
Appellant tried to put the gun away on top of the desk, Herrington said, “Someone
is going to die to night,” a nd a s truggle ensued. Three shots were fired in succession
during this struggle, then the Appellant ran to call 911 and stayed there until the
police arrive d.
Voluntary manslaughter is the unlawful and intentional or knowing killing of a
victim as a result of a state of passion produced by adequate provocation. Tenn.
Code Ann. § 3 9-13-21 1. It is clear from the evidence presented that a rational trier
of fact could have found Appellant guilty of voluntary manslaughter. As a side note,
it can then be said that the trial court did not err by charg ing voluntary ma nslaughter.
W e will now address the merits of whether double jeopardy prohibits retrial for
voluntary manslaughter when the jury acquitted the Appellant of second degree
murder. Over objection by Appellant’s trial counsel, the trial court charged the jury
on voluntary man slaug hter in addition to secon d degree m urder. W hile the trial court
stated upon th e record he believe d the Ap pellant to be guilty of murder in the second
degree or nothing else, he held that State v. Sum mera ll, 926 S.W.2d 272, 278-79
-5-
(Tenn. Crim. App. 1995), required the trial court to instruct the jury on the charge of
voluntary manslaughter based upon the evidence. Appellant argues that by virtue
of the jury’s verdict of not guilty as to second degree murder, the jury rejected at
least one of the essential elements nece ssary to su pport a find ing of guilt as to
voluntary man slaughter.
Second degree murder is the unlawful and knowing killing of the victim. Tenn.
Code Ann. § 39-13-210. As mentioned previously, voluntary manslaughter is the
unlawful and intentional or knowing killing of a victim as a result of a state of passion
produced by adequate provocation. Tenn. Code Ann. § 39-13-211. Appellant
argues that the case of Wh itwell v. State, 520 S .W .2d 33 8 (Te nn. 19 75) is
controlling. In W hitwell, the defendants were indicted and tried for the grand larceny
of cattle and receiving and concealing stolen property. Defendants were acquitted
by the jury o f grand larc eny and the jury exp ressly de termine d that the d efenda nts
did not know that they were stealing the cattle. The jury was unable to reach a
verdict on the charges of receiving and concealing stolen property or the lesser
charges of petit larcen y. A mistrial was declared by the trial court. Th e defen dants
appealed on the basis that the jury’s verdict nullified the criminal intent element
essential for their conviction and, therefore, double jeopardy principles would be
violated if they we re retrie d. The Ten ness ee Su prem e Cou rt held th at “the ju ry’s
finding a lack of intent to steal clearly exonerates defendants of an essential element
of petit larceny,” and remanded the case to the trial court to dismiss all charges. Id.
at 344.
Appe llant’s case differs from tha t of W hitwell in that th e only d ifferenc e in the
eleme nts of the offenses of grand and petit larceny at that time was the m onetary
-6-
amount of prope rty taken b y the defe ndants . There is not a se parate eleme nt as
there is in the case sub judice. As the State co rrectly points out in its brief, the jury
could have found that both elements of second degree m urder were m et and still
acqu it of second degree murder, so long as the jury found the Appellant acted in a
state of passion produced by adequate provocation. This additional element of
passion produced by adequate provocation reduces second degree murder to
voluntary manslau ghter, even thou gh all elemen ts of second d egree m urder have
been met. Also, Appellant justified his actions as self-defense at trial. Self-defense
implies Appellant had at least a “knowing” menta l state in orde r to com mit a killing
of another human being. The verdict of acquittal as to second degre e mu rder in th is
case does n ot man date a finding that the jury determined the element of a “knowing”
killing to be a bsent.
A more recent case distinguishes W hitwell and holds that “the double jeopardy
clauses of the state and federal constitutions do not preclude retrial of a defendant
after a mist rial was decla red at a n earlier trial because the jury could not reach a
verdict on de fenda nt’s gu ilt of lesse r offens es inclu ded in the crime for which he was
indicted.” State v. Seagroves, 691 S.W.2d 537, 541 (Te nn. 1985). T he court
pointed out in Seagroves that the defendant in W hitwell was either guilty of the
greater offense of no offense at all. Such is not the true in the case sub judice.
Accordingly, we find no violation of App ellant’s cons titutiona l rights a gains t doub le
jeopard y.
We affirm the ju dgme nt of the trial co urt.
____________________________________
-7-
THOMAS T. W OODALL, Judge
CONCUR:
___________________________________
JOHN H. PEAY, Judge
___________________________________
DAVID G. HAYES, Judge
-8-
|
WASHINGTON – US President Donald Trump reacted combatively on Friday to widespread criticism of his plan to impose tariffs on imports of steel and aluminum to protect domestic producers.
“When a country (USA) is losing many billions of dollars on trade with virtually every country it does business with, trade wars are good, and easy to win,” he said on Twitter.
“Example, when we are down $100 billion with a certain country and they get cute, don’t trade anymore-we win big. It’s easy!” he added.
The president’s announcement Thursday that he will order tariffs of 25 percent and 10 percent, respectively, on imported steel and aluminum, spurred a 420-point drop on the New York Stock Exchange and expressions of alarm.
Some of the sharpest criticism of the planned tariffs came from Trump’s fellow Republicans, most of them ardent free-traders.
“Kooky 18th century protectionism will jack up prices on American families – and will prompt retaliation from other countries,” Sen. Ben Sasse said in a statement.
“Make no mistake: If the President goes through with this, it will kill American jobs – that’s what every trade war ultimately does,” the Nebraska Republican said.
The top Republican in Congress, House Speaker Paul Ryan, said that US workers and firms could suffer from “unintended consequences” if the tariffs were imposed, while European Commission chairman Jean-Claude Juncker was one of several international leaders threatening retaliation for the levies.
Roberto Azevedo, the director-general of the World Trade Organization (WTO), broke with his usual practice by commenting publicly on Trump’s announcement.
“The WTO is clearly concerned at the announcement of US plans for tariffs on steel and aluminum. The potential for escalation is real, as we have seen from the initial responses of others. A trade war is in no one’s interests,” Azevedo said.
Asked Friday about the negative reception to Trump’s tariff idea, White House spokeswoman Sarah Sanders said that the president was not concerned and that he remained “pretty committed to moving this forward.
Paradoxically, Trump’s proposal got a much warmer response from some Democrats, such as Ohio Sen. Sherrod Brown, who described the tariffs as “long overdue” action to aid steelworkers in his state.
Trump also won plaudits from the country’s largest labor federation.
“For years, we have called attention to the predatory practices of some steel exporting countries,” AFL-CIO President Richard Trumka said. “This is a great first step toward addressing trade cheating.”
The president’s decision was not unanimously popular within his own administration.
Gary D. Cohn, the director of the National Economic Council, “threatened to resign if the White House followed through with stiff and sweeping tariffs, according to people who have spoken with him in recent days,” The New York Times reported.
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Serverless currently vulnerable to Arbitrary File Write - yamafaktory
https://github.com/serverless/serverless/issues/7402
======
yamafaktory
How big companies are dealing with such a case? At my company, we have a
mandatory audit step in the CI. Of course, one can still bypass it by dropping
the step in order to deploy but I'm curious to know how others deal with that.
|
import React, { Component } from 'react';
import PropTypes from 'prop-types';
import {
changeRequestParams,
addRequestHeader,
changeRequestHeader,
removeRequestHeader,
updateFileObject,
focusHeaderTextbox,
unfocusTypingHeader,
} from './Actions';
import GraphiQLWrapper from './GraphiQLWrapper';
const styles = require('./ApiExplorer.scss');
class ApiRequest extends Component {
constructor(props) {
super(props);
this.state = {};
this.state.accessKeyVisible = false;
this.state.bodyAllowedMethods = ['POST'];
this.state.tabIndex = 0;
}
onRequestParamsChanged = newValue => {
this.props.dispatch(changeRequestParams(newValue));
};
onHeaderValueChanged(e) {
const index = parseInt(e.target.getAttribute('data-header-id'), 10);
const key = e.target.getAttribute('data-element-name');
const newValue = e.target.value;
this.props.dispatch(changeRequestHeader(index, key, newValue, false));
}
onDeleteHeaderClicked(e) {
const index = parseInt(e.target.getAttribute('data-header-id'), 10);
this.props.dispatch(removeRequestHeader(index));
}
onNewHeaderKeyChanged(e) {
this.handleTypingTimeouts();
this.props.dispatch(addRequestHeader(e.target.value, ''));
}
onNewHeaderValueChanged(e) {
this.handleTypingTimeouts();
this.props.dispatch(addRequestHeader('', e.target.value));
}
onKeyUpAtNewHeaderField(e) {
if (e.keyCode === 13) {
this.props.dispatch(
addRequestHeader(this.state.newHeader.key, this.state.newHeader.value)
);
}
}
getUrlBar() {
return (
<div
id="stickyHeader"
className={
styles.apiPostRequestWrapper +
' ' +
styles.wd100 +
' ' +
styles.stickyHeader
}
>
<div className={'col-xs-12 ' + styles.padd_remove}>
<div
className={
'input-group ' +
styles.inputGroupWrapper +
' ' +
styles.cursorNotAllowed
}
>
<div
className={
'input-group-btn ' +
styles.inputGroupBtn +
' ' +
styles.cursorNotAllowed
}
>
<button type="button" className={'btn btn-default'}>
POST
</button>
</div>
<input
value={this.props.url}
type="text"
className={
styles.inputGroupInput +
' form-control ' +
styles.cursorNotAllowed
}
/>
</div>
</div>
<div className={styles.stickySeparator} />
</div>
);
}
getHeaderTitleView() {
return (
<div className={styles.responseWrapper}>
<div className={'col-xs-12 ' + styles.padd_remove}>
<div className={styles.responseHeader}>Request Headers</div>
</div>
</div>
);
}
getHeaderRows() {
const rows = this.props.headers.map((header, i) => {
return (
<tr key={i}>
{header.isNewHeader ? null : (
<td>
<input
type="checkbox"
name="sponsored"
className={styles.common_checkbox + ' common_checkbox'}
id={i + 1}
checked={header.isActive}
data-header-id={i}
onChange={this.onHeaderValueChanged.bind(this)}
data-element-name="isActive"
/>
<label
htmlFor={i + 1}
className={
styles.common_checkbox_label + ' common_checkbox_label'
}
/>
</td>
)}
<td
colSpan={header.isNewHeader ? '2' : '1'}
className={
header.isNewHeader
? styles.border_right +
' ' +
styles.tableTdLeft +
' ' +
styles.borderTop +
' ' +
styles.tableEnterKey
: styles.border_right
}
>
<input
className={'form-control ' + styles.responseTableInput}
value={header.key}
disabled={header.isDisabled === true ? true : false}
data-header-id={i}
placeholder="Enter Key"
data-element-name="key"
onChange={this.onHeaderValueChanged.bind(this)}
onFocus={this.handleFocus}
onBlur={this.handleBlur}
type="text"
data-test={`header-key-${i}`}
/>
</td>
<td
colSpan={header.isNewHeader ? '2' : '1'}
className={
header.isNewHeader
? styles.borderTop +
' ' +
styles.tableEnterKey +
' ' +
styles.tableLastTd
: ''
}
>
<input
className={'form-control ' + styles.responseTableInput}
value={header.value}
disabled={header.isDisabled === true ? true : false}
data-header-id={i}
placeholder="Enter Value"
data-element-name="value"
onChange={this.onHeaderValueChanged.bind(this)}
onFocus={this.handleFocus}
onBlur={this.handleBlur}
data-test={`header-value-${i}`}
type={
header.key === 'X-Hasura-Access-Key' &&
!this.state.accessKeyVisible
? 'password'
: 'text'
}
/>
</td>
{header.isNewHeader ? null : (
<td>
{header.key === 'X-Hasura-Access-Key' ? (
<i
className={styles.showAccessKey + ' fa fa-eye'}
data-header-id={i}
aria-hidden="true"
onClick={this.onShowAccessKeyClicked.bind(this)}
/>
) : null}
<i
className={styles.closeHeader + ' fa fa-times'}
data-header-id={i}
aria-hidden="true"
onClick={this.onDeleteHeaderClicked.bind(this)}
/>
</td>
)}
</tr>
);
});
return rows;
}
getHeaderTableView() {
return (
<div className={styles.responseTable}>
<table className={'table ' + styles.tableBorder}>
<thead>
<tr>
<th className={styles.wd4 + ' ' + styles.headerHeading} />
<th
className={
styles.wd48 +
' ' +
styles.border_right +
' ' +
styles.headerHeading
}
>
Key
</th>
<th className={styles.wd48 + ' ' + styles.headerHeading}>
Value
</th>
<th className={styles.wd4 + ' ' + styles.headerHeading} />
</tr>
</thead>
<tbody>{this.getHeaderRows()}</tbody>
</table>
</div>
);
}
getHeaderBody() {
return (
<div className={styles.responseHeader + ' ' + styles.marginBottom}>
Request Body
</div>
);
}
getValidBody() {
switch (this.props.bodyType) {
case 'graphql':
return (
<GraphiQLWrapper
data={this.props}
dispatch={this.props.dispatch}
headerFocus={this.props.headerFocus}
/>
);
default:
return '';
}
}
handleFocus = () => {
this.props.dispatch(focusHeaderTextbox());
};
handleBlur = () => {
this.props.dispatch(unfocusTypingHeader());
};
handleFileChange(e) {
if (e.target.files.length > 0) {
this.props.dispatch(updateFileObject(e.target.files[0]));
}
}
render() {
return (
<div className={styles.apiRequestWrapper}>
{this.getUrlBar()}
<hr />
{this.getHeaderTitleView()}
{this.getHeaderTableView()}
{this.getValidBody()}
</div>
);
}
}
ApiRequest.propTypes = {
method: PropTypes.string.isRequired,
url: PropTypes.string.isRequired,
headers: PropTypes.array,
params: PropTypes.string,
dispatch: PropTypes.func.isRequired,
explorerData: PropTypes.object.isRequired,
credentials: PropTypes.object.isRequired,
bodyType: PropTypes.string.isRequired,
route: PropTypes.object.isRequired,
numberOfTables: PropTypes.number.isRequired,
headerFocus: PropTypes.bool.isRequired,
};
export default ApiRequest;
|
Q:
linq inner join sub query and conditional select
I have the following sql select statement that I am trying to convert to Linq:
SELECT a.lastname,a.firstname,a.program,a.[start],a.[end],
CASE WHEN a.[end] IS NULL AND a.[start] < c.lastStart THEN 1 ELSE 0 END as error,
CASE WHEN a.[end] IS NULL AND a.[start] = c.lastStart THEN 1 ELSE 0 END as loggedOn
FROM usagelog a
INNER JOIN (SELECT b.username,max(b.[start]) AS lastStart FROM usagelog b GROUP BY b.username) c
ON a.username = c.username
ORDER BY a.lastname, a.firstname,a.program,a.[start]
The results should look like the following:
SQL Results
I've got the following so far:
var query = (from u in UsageLogs
orderby u.lastname,u.firstname,u.program.u.start
select new
{
lastname = u.lastname,
firstname = u.firstname,
program = u.program,
start = u.start,
end = u.end
})
I'm stuck on how to write the inner join with the additional select statement and the 'CASE' statements.
Any help would be appreciated.
A:
you can use Lambda expressions group by and for conditional select use inline condition like below:
var query = (from u in UsageLogs
join c in (UsageLogs.GroupBy(r => r.username).Select(r => new {username = r.Key, lastStart = r.Max(p => p.start)))
on u.username equals c.username
orderby u.lastname,u.firstname,u.program.u.start
select new
{
lastname = u.lastname,
firstname = u.firstname,
program = u.program,
start = u.start,
end = u.end,
error = (u.end == NULL && u.start < c.lastStart) ? 1 : 0,
loggedOn = (u.end == NULL && u.start == c.lastStart) ? 1 : 0,
});
|
Lovely anniversary dinner at Chez Panisse (downstairs)
It has been a few years since we last ate downstairs at Chez Panisse, but we had a really wonderful evening last night celebrating our anniversary.
Dinner started with an aperitif of Lillet with a lemon twist, something I had never had before. Quite lovely and a pleasant accompaniement to some roasted almonds.
We then had little sausages made of fish and shellfish that we one of the best things I've ever eaten -- just tasting so fresh and sweet in a light sauce. Don't know what was in the sauce -- light but complex and most likely a shellfish base with some paprika (which we were told was in it) and only a little butter. We had a lovely champagne with this -- don't remember the producer, which I had not had before, but it's their house champagne.
This was followed by a rich concentrated clear squab broth with porcini and fresh pasta, seasoned with a bit of fresh parsely. With this we had a very fine Oregon pinot noir.
The maincourse was an herbed and grilled rack and loin of lamb, which was served with fried artichokes and a very silky parsnip puree.
We also had a cheese course with three lovely hard cheeses. Unfortunately I don't recall precisely what they were -- all were new to me. The standout was a very nice blue from the Auvergne, which reminded me of a blue Wensleydale. Yum. With this we drank a bandol.
Dessert was crepes suzette with a refreshing tangerine sherbet. A fabulous finish to a lovely relaxed evening. Just wish we could afford to do it more often! |
Can Cardano/ADA make you a millionaire? We look a 6 potential scenarios, from the extremely likely to the outrageous, but still possible!
Sign up for an account at Binance and support the channel every time you trade! No extra cost for you. Sign up using this link: https://www.binance.com/?ref=35520478
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rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
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ETH donations:
0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
Image credit:
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If you were to invest $1.000 in Ripple XRP today, how much money could you expect to make? Let's look at 8 possible scenarios!
Sign up for an account at Binance and support the channel every time you trade! No extra cost for you. Sign up using this link: https://www.binance.com/?ref=35520478
Find me on social media:
https://twitter.com/TheGermanInvest
fb.me/thegermaninvestor
Wanna support the channel with donations?
XRP donations:
rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
BTC donations:
1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
ETH donations:
0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
Articles used:
Esoteric Trading Solutions valuation: https://www.youtube.com/watch?v=nSwSJQf1FOg
Can Ripple XRP Make You A Millionaire?
https://www.youtube.com/watch?v=_D6NMXdj5Jk
Image credit:
bitcoinexchangeguide.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://www.coindesk.com/euro-exim-bank-taps-ripples-xrapid-for-cross-border-settlements
Image credit:
coin4world.com
Ryan Zagone, Director of Regulatory Relations at Ripple, took part in a panel at the CATO Institute the other day and let some information on Ripple's future slip. Let's talk about it.
Sign up for an account at Binance and support the channel every time you trade! No extra cost for you. Sign up using this link: https://www.binance.com/?ref=35520478
Find me on social media:
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fb.me/thegermaninvestor
Wanna support the channel with donations?
XRP donations:
rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
BTC donations:
1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
ETH donations:
0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
Watch the full stream:
https://www.youtube.com/watch?v=kAi0DupEnyY
Image credit:
ethereumworldnews.com
Become my patron and get awesome perks! https://www.patreon.com/thegermaninvestor
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___________________________________
Other ways to support the channel:
Buy me a coffee! Takes a minute and works with your paypal account.
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Crypto donations more your thing?
XRP:
rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
BTC:
1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
ETH:
0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
ADA:
DdzFFzCqrht6pwTRcZpq2og9XpXV8abhAjVPxx5L7bDL4EtG9QegNSgntYUKmMDfe45vSW4Du3fXVdaAMHNVC8BV64gaTBDaVKgv2bPC
Or, you could sign up for an account at Binance and support the channel every time you trade! No extra cost for you. Sign up using this link: https://www.binance.com/?ref=35520478
___________________________________
Got any questions? Mail me at [email protected] and I may read out and respond to your question in an upcoming video! Your mail might be shown in the video, including the sender address and sender name.
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
Articles used in this video:
https://www.ethnews.com/pay-to-publish-a-look-inside-a-coin-journal-editors-inbox
https://breakermag.com/we-asked-crypto-news-outlets-if-theyd-take-money-to-cover-a-project-more-than-half-said-yes/
Image credit:
spinsucks.com
Thank you for watching! There’s a lot of good stuff in the description below, so make sure to click “read more” to see the full text!
___________________________________
Do you enjoy my content and want to support the channel? You’re awesome, thanks! Here’s a few ways to do that:
You could buy me a coffee! Takes a minute and works with your paypal account.
https://ko-fi.com/thegermaninvestor
Crypto donations more your thing?
XRP:
rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
BTC:
1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
ETH:
0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
Or, you could sign up for an account at Binance and support the channel every time you trade! No extra cost for you. Sign up using this link: https://www.binance.com/?ref=35520478
___________________________________
Got any questions? Mail me at [email protected] and I may read out and respond to your question in an upcoming video! Your mail might be shown in the video, including the sender address and sender name.
___________________________________
Find me on social media:
https://twitter.com/TheGermanInvest
https://fb.me/thegermaninvestor
___________________________________
Will Investing $1000 In Ripple XRP Make You Rich?
https://www.youtube.com/watch?v=deLyCkBqf8Y
Image credit:
ripplenews.tech
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
Sign up for a Binance account and trade hundreds of cryptocurrencies: https://www.binance.com/?ref=35520478
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Support the channel:
Tip-jar: https://ko-fi.com/thegermaninvestor
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://twitter.com/internetarchive/status/1078825088500273153
https://archive.org/donate/cryptocurrency/
https://www.ccn.com/bitcoin-on-track-to-replace-gold-as-dominant-store-of-value-crypto-vc/
https://medium.com/bakkt-blog/first-capital-raise-739db1bab6d3
https://ethereumworldnews.com/bakkt-launch-postponed-and-an-update-to-be-provided-in-early-2019/
https://www.ccn.com/no-to-bitcoin-cash-opennode-rejects-roger-vers-1-25m-fund-offer/
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___________________________________
Other ways to support the channel:
Buy me a coffee! Takes a minute and works with your paypal account.
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Crypto donations more your thing?
XRP:
rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
BTC:
1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
ETH:
0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
ADA:
DdzFFzCqrht6pwTRcZpq2og9XpXV8abhAjVPxx5L7bDL4EtG9QegNSgntYUKmMDfe45vSW4Du3fXVdaAMHNVC8BV64gaTBDaVKgv2bPC
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___________________________________
Got any questions? Mail me at [email protected] and I may read out and respond to your question in an upcoming video! Your mail might be shown in the video, including the sender address and sender name.
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
Articles used in this video:
https://coingape.com/coinfield-exchange-xrp-as-base-currency-is-now-live-in-61-countries/
https://twitter.com/coinfieldEX
Image credit:
altnews.nu
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Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Image credit:
news.yale.edu
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://www.ccn.com/ethereum-surges-13-overnight-crypto-market-punching-for-a-strong-recovery
https://ethereumworldnews.com/daily-volume-reaches-new-2019-high-in-monday-crypto-rally/
https://ethereumworldnews.com/spend-ripple-xrp-in-more-than-40-million-locations-across-180-countries/
https://cointelegraph.com/news/japan-e-commerce-giant-rakutens-new-payment-app-appears-to-support-crypto
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bitcoinist.com
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Got any questions? Mail me at [email protected] and I may read out and respond to your question in an upcoming video! Your mail might be shown in the video, including the sender address and sender name.
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
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ethereumworldnews.com
Today, we talk Bearableguy123's prediction of XRP hitting $589...possibly, maybe - and the implications of the prediction.
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Articles used:
https://ambcrypto.com/will-xrp-go-to-589-after-the-launch-of-xrapid-bearableguy123s-theory-tested/
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___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://www.coindesk.com/swift-chief-announces-integration-with-r3-at-paris-fintech-forum
Image credit:
ethereumworldnews.com
Can EOS make you a millionaire? I take you through 7 scenarios, from the very likely to the utterly outrageous, in this video!
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Image credit:
eostalk.io
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://ambcrypto.com/xrp-worth-over-750-million-moved-between-multiple-accounts-follows-the-path-taken-by-coinbase/
https://www.ccn.com/bitcoin-cash-single-mining-pool-controls-half-of-hashrate/
https://www.ccn.com/bitcoin-is-societys-best-hope-for-a-private-form-of-electronic-money-says-arthur-hayes/
https://ethereumworldnews.com/binance-confirms-support-for-the-january-ethereum-eth-constantinople-hard-fork/
Image credit:
hackernoon.com
There's been a lot of discussion around the future potential of the crypto market, with opinions split on whether 1000x growth is still serious. Let's talk about it!
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ETH donations:
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Articles used:
https://cointelegraph.com/news/can-crypto-record-a-1-000x-return-and-reach-200-trillion-market-cap
Image credit:
coingape.com
A lot of people think Ripple XRP is seriously undervalued and should hit $10, $334, or even $1000 soon. How valid are those judgments?
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Articles used:
https://ethereumworldnews.com/how-xrp-is-seriously-undervalued-right-now-and-some-sec-loopholes/
https://smartereum.com/19533/yoshitaka-kitao-ripple-prediction-2018-heres-why-the-predicted-10-usd-ripple-xrp-value-is-still-achievable-this-year-xrp-news-today-sat-aug-25/
https://smartereum.com/18212/ripple-news-today-ripple-will-soon-become-the-number-one-cryptocurrency-choice-for-various-banks-brad-garlinghouse-xrp-news-today-news-sat-aug-25/
https://dailyhodl.com/2018/08/23/institutional-investors-are-buying-xrp-at-a-record-rate-ripple-ceo/
Image credit:
dailyhodl.com
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Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://ethereumworldnews.com/xrp-base-pair-binance-2018/
Image credit:
ripplecoinnews.com
Ripple has incredibly technology, is getting adopted at a rapid pace, and is incredibly undervalued. When will that change? And will Ripple then dominate the crypto markets?
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Articles used:
https://www.exodus.io/releases/
https://globenewswire.com/news-release/2018/07/30/1543887/0/en/DCEX-to-Launch-First-Digital-Currency-Exchange-to-Use-XRP-as-Exclusive-Base-Currency-Powered-by-AlphaPoint-Blockchain-Technology.html
https://www.cryptoninjas.net/2018/08/16/ripples-xrapid-onboards-3-new-xrp-exchange-partners-including-bittrex/
https://www.youtube.com/watch?v=nSwSJQf1FOg
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://www.crypto-economy.net/en/cardano-ada-moves-a-step-closer-to-the-shelley-release/
https://bitcoinist.com/russia-ditch-usd-bitcoin-prof/
https://nulltx.com/neo-developers-announce-upcoming-consensus-algorithm-improvements/
https://www.coindesk.com/shapeshift-cuts-staff-by-a-third-in-latest-industry-layoffs
Image credit:
mashable.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://cointelegraph.com/news/jpmorgan-chase-launches-jpm-coin-using-crypto-to-speed-settlements
https://www.coindesk.com/latest-xrp-ledger-release-boosts-censorship-resistance-and-more
Image credit:
coincodex.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
Sign up for a Binance account and trade hundreds of cryptocurrencies: https://www.binance.com/?ref=35520478
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://dailyhodl.com/2019/01/02/confirmed-12-companies-adopting-ripples-xrp-based-payment-solution-xrapid/
https://www.ethnews.com/thailand-to-introduce-blockchain-based-voting
https://bitcoinist.com/weiss-2019-predict-bitcoin-new-ath/
https://cointelegraph.com/news/major-consulting-firm-mckinsey-finds-little-evidence-of-practical-blockchain-use-cases
Image credit:
nulltx.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://ethereumworldnews.com/crypto-boomed-four-times-bitcoin-rally-inevitable-analyst/
https://www.coindesk.com/ripple-scores-minor-victory-in-us-securities-class-action
https://cointelegraph.com/news/samsung-announces-galaxy-s10-crypto-partners-bitcoin-and-ethereum-support
https://cointelegraph.com/news/nasdaq-begins-listing-brave-new-coins-bitcoin-and-ethereum-price-indices
Image credit:
coindesk.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://ambcrypto.com/fidelity-announces-bitcoin-btc-custody-service-live-with-a-select-group-of-eligible-clients/
https://www.coindesk.com/tom-jessop-fidelity-talk
https://cointelegraph.com/news/okex-lists-tron-on-customer-to-customer-trading-platform
Image credit:
bitcoinist.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
Sign up for a Binance account and trade hundreds of cryptocurrencies: https://www.binance.com/?ref=35520478
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://cointelegraph.com/news/ethereum-reclaims-top-altcoin-position-rises-500-000-clear-of-xrps-market-cap
https://www.coindesk.com/bitcoin-price-suffers-worst-monthly-losing-streak-in-7-years
https://cointelegraph.com/news/japan-e-commerce-giant-dmm-shutters-crypto-mining-business-due-to-declining-profitability
https://ambcrypto.com/fortnite-scales-up-monero-xmrs-adoption-added-as-a-means-of-payment-for-its-online-merch-store/
https://www.ccn.com/tron-cryptocurrencys-development-team-grows-from-2-to-over-40/
Image credit:
thetimes.co.uk
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
Sign up for a Binance account and trade hundreds of cryptocurrencies: https://www.binance.com/?ref=35520478
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://ethereumworldnews.com/huobi-group-to-launch-a-one-of-a-kind-exchange-dedicated-to-eos/
https://cointelegraph.com/news/ex-cia-official-claims-blockchain-is-biggest-threat-to-future-of-us-national-security
https://www.ccn.com/cryptocurrency-exchange-kraken-adds-bitcoin-cash-and-ripple-margin-trading/
https://www.ccn.com/singapore-crypto-exchange-switcheo-announce-sdusd-stablecoin-support/
Image credit:
cryptonewsasia.io
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://www.ethnews.com/red-eyes-black-dragon-raiden-networks-alpha-live-on-ethereum
https://cointelegraph.com/news/ethereum-co-founder-calls-the-cryptobottom-of-2018
https://ethereumworldnews.com/eos-unbeaten-remains-1st-on-chinas-latest-ccid-rank/
https://bitcoinexchangeguide.com/kucoin-removes-10-coins-from-exchange-and-ceases-trading-citing-special-treatment-rule/
Image credit:
nulltx.com
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Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://www.ccn.com/bitcoin-too-scammy-volatile-for-mainstream-adoption-analyst-mark-dow/
https://ambcrypto.com/ripple-partner-national-bank-of-kuwait-ties-up-with-swifts-global-payments-innovation/
https://www.coindesk.com/the-first-cryptocurrency-to-use-mimblewimble-privacy-tech-is-now-live
https://www.coindesk.com/bittorrent-is-launching-its-own-cryptocurrency-on-the-tron-network
Image credit:
ripplecoinnews.com
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://ambcrypto.com/bitcoin-btc-to-surpass-all-time-high-rally-price-of-20000-by-2021-claims-canada-based-financial-institution/
https://cointelegraph.com/news/kaspersky-ceo-cryptocurrencies-are-great-but-the-world-is-not-ready-yet
Image credit:
cnbc.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://ambcrypto.com/ripple-xrp-could-trigger-the-bull-run-of-2019-and-overtake-bitcoin-btc/
https://www.cnbc.com/2018/10/01/ripple-xrp-cryptocurrency-product-xrapid-goes-live-for-first-time.html
https://ripple.com/insights/ripplenet-expands-to-40-countries-improving-remittances-and-sme-payments/
https://www.ccn.com/uae-firm-taps-ripple-blockchain-ripplenet-to-launch-cross-border-payments/
Image credit:
dailyhodl.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://nulltx.com/indian-police-bash-crypto/
https://cointelegraph.com/news/huobi-and-okex-to-support-upcoming-ethereum-constantinople-hard-fork
https://ethereumworldnews.com/bitcoin-sv-starts-2019-with-a-new-logo-which-imitates-bitcoins-appearance/
https://www.coindesk.com/ethereum-studio-consensys-teams-up-with-chip-manufacturer-amd
Image credit:
ccn.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://ambcrypto.com/cardano-adas-charles-hoskinson-new-revamps-remove-unnecessary-rules-simplifies-system-and-gets-rid-of-redundancies/
https://ambcrypto.com/tron-trxs-nitron-summit-fills-the-community-with-hopes-of-putting-eos-behind/
https://www.ccn.com/turkish-crypto-exchange-sistemkoins-disturbing-security-flaw-reveals-major-withdrawal-complaints/
https://www.ccn.com/unreasonable-number-of-subpoenas-shows-why-crypto-exchanges-are-fleeing-the-us/
https://www.coindesk.com/japans-sbi-invests-15-million-in-crypto-card-wallet-maker-tangem
Image credit:
coingape.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://www.coindesk.com/countdown-restarts-tomorrow-for-sec-decision-on-cboe-vaneck-bitcoin-etf
https://cointelegraph.com/news/coinbase-adds-bitcoin-cash-support-to-wallet-app
https://ambcrypto.com/xrp-sbi-ceo-yoshitaka-kitao-says-xrps-market-cap-will-easily-overtake-that-of-bitcoins-in-2019/
https://www.coindesk.com/elon-musk-calls-bitcoin-brilliant-better-than-paper-money-for-value-transfer
https://cointelegraph.com/news/new-samsung-galaxy-s10-includes-cryptocurrency-key-storage
Image credit:
ripplecoinnews.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
Sign up for a Binance account and trade hundreds of cryptocurrencies: https://www.binance.com/?ref=35520478
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://www.ethnews.com/spains-central-bank-warns-against-crypto-usage-citing-lack-of-regulation
https://cointelegraph.com/news/ripple-mastercard-and-barclays-invest-in-ripple-based-remittance-firm-sendfriend
https://ambcrypto.com/bitcoin-btc-does-not-need-any-more-contentious-forks-this-year-cobra/
https://www.coindesk.com/binances-decentralized-exchange-is-about-to-launch-for-public-testing
Image credit:
thenextweb.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://cointelegraph.com/news/crypto-market-rally-continues-with-bitcoin-above-4-900-tech-stocks-bounce-back
https://cointelegraph.com/news/bloomberg-bitcoins-recent-renaissance-could-be-linked-to-algorithmic-trading
https://www.coindesk.com/these-3-factors-were-likely-behind-bitcoins-price-surge-to-5k
Image credit:
smartereum.com
The markets are looking good, IOTA gets a massive partnership and we have a price prediction for Bitcoin at $25.000 before the end of the year. Should we expect that bull market any moment now?
Sign up for an account at Binance and support the channel every time you trade! No extra cost for you. Sign up using this link: https://www.binance.com/?ref=35520478
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rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
BTC donations:
1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
ETH donations:
0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
Articles used:
https://www.newsbtc.com/2018/08/27/bitcoin-price-watch-btc-usd-forming-breakout-pattern-above-6600/
https://www.newsbtc.com/2018/08/27/ripple-price-analysis-xrp-usd-broke-key-resistance-could-test-0-3400/
https://cointelegraph.com/news/crypto-markets-see-few-gains-as-most-of-top-coins-are-slumping
https://ambcrypto.com/iota-miota-will-be-the-new-protocol-standard-says-japanese-tech-giant-fujitsu/
https://www.ccn.com/indias-central-bank-quietly-forms-new-cryptocurrency-blockchain-research-unit/
https://www.ccn.com/interview-coinbase-uk-ceo-explains-why-a-lack-of-regulation-is-the-biggest-problem-facing-cryptocurrency/
Image credit:
bleepingcomputer.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://ambcrypto.com/xrp-powered-corda-settler-ties-up-with-hyperledgers-indy-project-r3-explains-the-details/
https://www.ccn.com/circles-otc-crypto-trading-desk-saw-24-billion-in-volume-in-2018/
https://cointelegraph.com/news/proof-of-keys-event-aims-to-challenge-perceived-centralization-of-cryptocurrencies
https://cointelegraph.com/news/us-retail-giant-overstock-to-use-bitcoin-to-pay-its-taxes-in-ohio
https://www.coindesk.com/coinbase-vaishali-mehta-compliance-trusttoken-trueusd-stablecoin
Image credit:
coindesk.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://cointelegraph.com/news/visa-to-purchase-ripple-cross-border-payments-partner-earthport
https://cointelegraph.com/news/2019-will-see-entry-of-more-institutional-players-in-crypto-says-asia-fintech-pwc-leader
https://cointelegraph.com/news/unconfirmed-chinese-media-reports-jihan-wu-jenke-group-to-soon-resign-as-bitmain-ceos
https://www.ccn.com/extremely-bearish-crypto-vc-says-bitmain-layoffs-could-spell-doom-for-bitcoin-cash-and-litecoin/
https://ambcrypto.com/tron-trx-records-more-than-80-dapps-on-the-network-justin-sun-stays-true-to-the-promise-made-to-the-community/
Image credit:
crushthestreet.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
Sign up for a Binance account and trade hundreds of cryptocurrencies: https://www.binance.com/?ref=35520478
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://www.coindesk.com/nasdaq-to-add-bitcoin-and-ethereum-indices-to-global-data-service
https://ambcrypto.com/ripples-xrapid-is-the-future-says-alastair-constance/
https://ethereumworldnews.com/bithumb-announces-plans-to-launch-a-crypto-exchange-in-the-uae/
https://cointelegraph.com/news/altcoin-beam-announces-plans-to-incorporate-mimblewimble-lightning-network
https://www.coindesk.com/status-launches-a-tap-to-pay-crypto-hardware-wallet
Image credit:
bizjournals.com
Get a Ledger Nano S to securely store all your coins: https://www.ledger.com?r=01ec22a02ddd
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XRP: rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
Bitcoin: 1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
Ethereum: 0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
___________________________________
Special thanks to my lovely patreon supporters:
Roy Dopson, Steve, Nathan from the UK
___________________________________
This video is an informational entertainment product about cryptocurrencies such as Bitcoin, Ethereum, and XRP, and does not constitute financial advice. I am a cryptocurrency commentator who gives his personal opinions about news, market movements, investments, and cryptocurrencies, not a professional financial advisor. All news are sourced from the list of articles given below and I am not liable for mistakes and misinformation contained within them.
Articles used in this video:
https://ethereumworldnews.com/litecoin-ltc-beam-to-explore-mimblewimble-for-confidential-transactions/
https://www.ccn.com/watch-ethereum-creator-crypto-eos-tron-piles-trash
https://www.coindesk.com/ripple-teams-with-10-new-universities-for-blockchain-research-initiative
https://cointelegraph.com/news/wyoming-passes-bill-to-recognize-cryptocurrencies-as-money
https://www.coindesk.com/swiss-stock-exchange-six-plans-blockchain-platform-in-h2
Image credit:
coincentral.com
Can Ripple XRP make you a millionaire? I take you through 8 scenarios, from the very likely to the utterly outrageous, in this video!
Sign up for an account at Binance and support the channel every time you trade! No extra cost for you. Sign up using this link: https://www.binance.com/?ref=35520478
XRP donations:
rMiUTEDwxYuRKVikjHfLtP6Bf7rj73qddQ
BTC donations:
1KxmWPoTsVQZAxkYsWqcGqFzknMGtAYxMZ
ETH donations:
0xa6C657C3aa3D602E8B2f54Bc8358D026e209795A
Find me on social media:
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Articles used:
https://www.youtube.com/watch?v=nSwSJQf1FOg
Image credit:
bitdays.jp |
The Missouri Tigers are set to start spring ball in less than one week. Over the next few days, PowerMizzou.com will take an in-depth look at the roster as we start our spring ball previews. Today, we continue on defense with a look at the linebackers.
The Challengers: No new player on campus for spring ball can match the hype of Josh Tatum, who comes to Mizzou from the City College of San Francisco. He should be in the mix early. In addition, Will Ebner and Tyler Crane will be in the discussion for playing time early and often. Freshman Andrew Wilson is on campus and has an opportunity to make a claim for playing time much like Lambert did in the spring two years ago.
Spring Prediction: Look for Tatum to push his way into the starting trio by the end of spring ball. Ebner showed great things on special teams a season ago and could well take the same route Weatherspoon did to see plenty of time as a sophomore. Crane is an interesting case. He played as a true freshman, then redshirted in his second season. He could push for time at linebacker as well.
Things Could Change If... The interesting thing here is how many linebackers actually play. The Tigers see so many spread offenses that only two backers are on the field at many times. Lambert, Spoon and Tatum figure to be the top three. How many reserves see action? It is likely just one or two. There will be a premium on playing time here and anyone that wants a spot must have a good spring.
PowerMizzou.com will preview every position prior to the first spring practice. Coming later today: The cornerbacks.
PowerMizzou.com's spring football coverage is sponsored by Pension & Benefits Live. Jesse Cox (stljesstx) and Tim Killday (Killer) would appreciate the opportunity to be a resource to you for company benefits and/or individual health and life insurance needs.
No one covers the Tigers like PowerMizzou.com. To follow the Tigers year-round, sign up today to start your Free Seven-Day Trial. |
United States Court of Appeals
Fifth Circuit
IN THE UNITED STATES COURT OF APPEALS F I L E D
FOR THE FIFTH CIRCUIT
January 11, 2007
Charles R. Fulbruge III
No. 06-60494 Clerk
Summary Calendar
DANNY HOUK
Plaintiff - Appellant
v.
PEOPLOUNGERS INC
Defendant - Appellee
Appeal from the United States District Court
for the Northern District of Mississippi, Aberdeen
USDC No. 1:04-CV-333
Before KING, HIGGINBOTHAM, and GARZA, Circuit Judges.
PER CURIAM:*
Plaintiff-appellant Danny Houk appeals the district court’s
grant of summary judgment to defendant-appellee Peoploungers,
Inc. (“Peoploungers”), arguing that genuine issues of material
fact remain with regard to Houk’s claim of age discrimination
under the Age Discrimination in Employment Act of 1967 (“ADEA”),
29 U.S.C. §§ 621 et seq.1 Houk was fired by Peoploungers for
*
Pursuant to 5TH CIR. R. 47.5, the court has determined that
this opinion should not be published and is not precedent except
under the limited circumstances set forth in 5TH CIR. R. 47.5.4.
1
Houk initially appealed the district court’s grant of
summary judgment to Peoploungers on his state law claim for
1
leaving work early one day without permission, but contends that
he did have permission from a supervisor and that this factual
dispute--along with his replacement by a worker nine years
younger than him--forestalls summary judgment.
We review a grant of summary judgment de novo, viewing all
evidence in the light most favorable to the nonmoving party and
drawing all reasonable inferences in that party’s favor. See
Crawford v. Formosa Plastics Corp., 234 F.3d 899, 902 (5th Cir.
2000). “Summary judgment is proper when the evidence reflects no
genuine issues of material fact and the non-movant is entitled to
judgment as a matter of law.” Id. (citing FED. R. CIV. P. 56(c)).
“A genuine issue of material fact exists ‘if the evidence is such
that a reasonable jury could return a verdict for the non-moving
party.’” Id. (quoting Anderson v. Liberty Lobby, Inc., 477 U.S.
242, 248 (1986)).
Under the burden-shifting framework for discrimination
claims established by McDonnell Douglas Corp. v. Green, 411 U.S.
792, 802-04 (1973), Houk has the initial burden of establishing a
prima facie case of discrimination by showing that “(1) he was
discharged; (2) he was qualified for the position; (3) he was
within the protected class at the time of discharge; and (4) he
was either i) replaced by someone outside the protected class,
ii) replaced by someone younger, or iii) otherwise discharged
defamation, but Houk conceded this claim in his reply brief.
2
because of his age.” Bodenheimer v. PPG Indus., Inc., 5 F.3d
955, 957 (5th Cir. 1993). If Houk meets these requirements, “a
presumption of discrimination arises which the defendant must
then rebut by articulating a legitimate, nondiscriminatory reason
for the discharge.” Id. If Peoploungers satisfies this burden,
“the presumption of age discrimination established by [Houk’s]
prima facie case dissolves,” id., and Houk must show either that
(1) Peoploungers’s reason is not true, but is instead a pretext
for age discrimination, or (2) Peoploungers’s reason, while true,
is only one reason for its actions, and Houk’s age was a
motivating factor for his discharge. Rachid v. Jack in the Box,
Inc., 376 F.3d 305, 312 (5th Cir. 2004).
Assuming arguendo that Houk established a prima facie case
of age discrimination, the district court properly recognized
that no genuine issue of material fact exists as to whether
Peoploungers’s given reason for the discharge was either
pretextual or accompanied by an age-based reason. Although the
parties dispute whether and under what terms Houk’s direct
supervisor gave Houk permission to leave early, the only evidence
presented as to the managers who made the decision to fire Houk
indicates that they believed that Houk did not have permission to
leave. Cf. Mayberry v. Vought Aircraft Co., 55 F.3d 1086, 1091
(5th Cir. 1995) (“The question is not whether an employer made an
erroneous decision; it is whether the decision was made with
3
discriminatory motive.”). And even if we were to infer, as Houk
urges, that Houk’s direct supervisor must have told the decision
makers that Houk had permission to leave, the evidence does not
show that Peoploungers’s given reason is a pretext for age
discrimination or that age was in any way a factor in Houk’s
termination.
Houk points out that he was replaced with a worker who was
nine years younger than him. Houk’s successor, however, was not
hired or promoted into the job, but was merely another worker
already in Houk’s department who was assigned to take over Houk’s
workload after the firing. Further, Houk was fired at age 48,
only a year and a half after he was hired at age 46 by one of the
same managers ultimately involved in the decision to fire him,
making his claim of age discrimination even more tenuous. Cf.
Brown v. CSC Logic, Inc., 82 F.3d 651, 658 (5th Cir. 1996)
(holding that the hiring and firing of an employee by the same
actor within a period of a few years “gives rise to an inference
that age discrimination was not the motive behind [the]
termination”).
Finally, despite the importance that Houk places on the less
severe, 30-day probation given to the two younger workers that
left with Houk on the day in question, there is simply no
evidence indicating that the different treatment was based on
age. One of the younger workers, Houk’s son, left with Houk
because Houk was his ride, and the other worker was Houk’s work
4
partner, whose work would have been less efficient without Houk.
More significantly, neither of those workers had a history of
walking off the job without permission, whereas Houk admits that
he quit without notice and walked off the job without permission
in an earlier stint with Peoploungers in 2001, providing a
legitimate justification for punishing Houk more harshly this
time around.
Because Houk points to no evidence that Peoploungers’s
reason for firing him is a pretext for age discrimination or that
age was a motivating factor in his discharge, the district court
properly granted summary judgment to Peoploungers.
AFFIRMED. Costs shall be borne by plaintiff-appellant.
5
|
Q:
EAV database design for model with multiple attributes (other models)
I have a model that possesses a lot of attributes with multiple values that are either representations of lists or other models. My research led me to consider an Entity-Attribute-Value design to represent such but I have seen more discouragement from more knowledgeable people than recommendations.
One that sticks to me is this comment:
In a nutshell, EAV is useful when your list of attributes is frequently growing, or when it's so large that most rows would be filled with mostly NULLs if you made every attribute a column. It becomes an anti-pattern when used outside of that context.
by Karl Bielefeldt.
Basically my model is student_report. It has the following attributes based on the actual form:
id
creator
revision history
department
references
funding (optional, variable/not fixed)
comments
objectives (paragraph)
scope (paragraph)
creator, revision history, department, references, funding and comments are other models that this form will rely on.
My initial plan is to create student_report with only the following:
id
id of creator
objectives
other paragraph-style content
while the others: revision history, department, references, funding and comments will posses the foreign key student_report_id.
For the variable/not fixed models such as references and funding, I plan to use a mediator table to connect student_form to the "list" of those to normalize the DB:
student_report
| id | name |
|----|-----------------|
| 1 | Abraham Smith |
| 2 | Betty Gladstone |
| 3 | Chen Hong |
references
| id | name |
|----|--------------|
| 1 | Reference 1 |
| 2 | Reference 2 |
| 10 | Reference 10 |
report_references
| user_id | reference_id |
|---------|--------------|
| 1 | 2 |
| 1 | 3 |
| 2 | 10 |
Is my proposed solution enough? This will be a small-scale project and I doubt this will require hundreds of use a day.
A:
EAV helps you capture data when the data model is not well understood. It allows you to skip over data analysis and to come up with a single design that is so adaptable that it will handle a body of data no matter what the actual structure of the data is.
But there's a downside. Since you haven't analyzed the data at storage time, you have to analyze the data when you go to retrieve it and turn it into something useful, such as a report or an extract. Otherwise your results are meaningless. This downside can, in some circumstances be much larger than the upside you experienced earlier.
In your case, you seem to have a good understanding of the attributes you want to store, and the semantics of those attributes. It also looks unlikely that the attribute list is going to have to expand based on surprises.
So I advise you to avoid EAV, and instead concentrate on how to compose relations out of attributes. Relations are simply collections of attributes, grouped together in some way that is meangful and useful. You can read books about this topic, if you care to.
In SQL, tables represent relations. Tables have rows, that represent tuples. Tables have columns, that represent attributes. The intersection of a row and a table provides a location where a value can be stored. In !NF, each location stores a "simple" value.
Your design looks pretty good to me. I think it will serve you better than an EAV model would. I don't know whether it's completely normalized, and I'm not sure it has to be.
|
I. Field of the Invention
This invention relates generally to small watercraft and more particularly to an improved anchoring arrangement for such watercraft.
II. Discussion of the Prior Art
It is well established that in anchoring a small boat that the rope length between the boat and anchor should be five feet for each foot of depth and that the anchor rope be secured as low as possible on the boat, such as on the bow eye. However, to clip an anchor rope to the bow eye when the boat is afloat in choppy waters exposes the operator to a risk of falling overboard. |
Structural organization of the mouse metabotropic glutamate receptor subtype 3 gene and its regulation by growth factors in cultured cortical astrocytes.
Metabotropic glutamate receptors (mGluRs) belong to the class of G protein-coupled receptors and consist of eight different subtypes. We have characterized the structural organization of the mouse mGluR3 gene by genomic cloning in combination with rapid amplification of 5'- and 3'-cDNA ends and examined regulatory expression of mGluR3 mRNA in cultured cortical astrocytes. The mGluR3 gene consists of six exons and spans over 95 kb. Exon 1 and its preceding putative promoter are located distantly from the following protein-coding region. In the mGluR family, mGluR3 and mGluR5 are both expressed in neuronal and glial cells and are upregulated during the early postnatal period. They are, however, coupled to two distinct signaling cascades and have been shown to exert opposite influences on some functions of cultured astrocytes. In cultured astrocytes, mGluR3 and mGluR5 mRNA levels were significantly increased by exposure to epidermal growth factor (EGF), basic fibroblast growth factor (bFGF), or transforming growth factor-alpha; and EGF was more efficacious than bFGF in producing this increase. Hence, mGluR3 and mGluR5 mRNAs are concertedly upregulated in cultured astrocytes by specific growth factors. This finding suggests that the two mGluR subtypes may play an important role in maintaining the proper balance of astrocyte functions via two distinct signal transduction mechanisms. |
1. Field
Embodiments of the present invention relate to a method for manufacturing a device and to a lithographic apparatus.
2. Background
A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging with a radiation beam with a radiation beam mode onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
U.S. Appl. Publ. No. 2007/081138 A1, incorporated herein by reference in its entirety, describes a device manufacturing method using a lithographic apparatus in which, during an alignment calibration process in the lithographic apparatus using a sensor to detect a property of a projected image at substrate level, a diffuser is inserted into the radiation beam to increase the range of angles of radiation incident on the substrate. Thereby it can be ensured that sufficient radiation enters the sensor even when there is a mismatch between the radiation beam mode used and the acceptance NA of the sensor.
It may be a disadvantage of the known apparatus and the known method that the diffuser is to be physically moved from a first position outside the path of the radiation beam to a second position inside the radiation beam. This movement requires some time to complete and may negatively effect the through-put time of the apparatus.
It may be a further disadvantage of the known apparatus and the known method that they may not function well with any possible illumination mode, i.e. the radiation beam mode used for illumination of the substrate. For example, for an illumination mode with a very steep illumination profile in one or more very narrow angular ranges, such as a steep quadrupole profile filling only a small portion of the pupil, the mismatch between the illumination mode and the sensor acceptance range may be too large to allow to be compensated for by the diffuser. In particular, as the form of the diffuser will depend on the degree and nature of the mismatch between the illumination mode and the sensor acceptance range, it may be needed to use a diffuser of a form that is not available.
It may be a further disadvantage of the known apparatus and the known method that the mechanical movement of the diffuser over quite a significant distance may result in disturbances to the illumination beam, e.g. to mechanical vibrations.
It may be a further disadvantage of the known apparatus and the known method that the resulting diffuse beam may not be compatible with a measurement and/or alignment system of the lithographic apparatus. For example, a diffuse beam may conflict with performing an interferometric measurement on the beam quality or using an interferometric alignment method.
It may be a further disadvantage of the known apparatus and the known method that the effect of the diffuser is limited to increasing the range of angles at which radiation of the illumination beam is incident on a marker on the patterning device. |
# Copyright (C) 2017-2020 Pier Carlo Chiodi
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import unittest
import yaml
from .cfg_base import TestConfigParserBase
from pierky.arouteserver.config.clients import ConfigParserClients
from pierky.arouteserver.config.general import ConfigParserGeneral
class TestConfigParserClients(TestConfigParserBase):
FILE_PATH = "config.d/clients.yml"
CONFIG_PARSER_CLASS = ConfigParserClients
SHORT_DESCR = "Clients config parser"
def test_valid_cfg(self):
"""{}: valid configuration"""
self._contains_err()
def test_unknown_statement(self):
"""{}: unknown statement"""
self.cfg[0]["test"] = "test"
self._contains_err("Unknown statement at 'clients' level: 'test'.")
def test_as(self):
"""{}: AS number"""
for v in (-1, 0, "test"):
self.cfg[0]["asn"] = v
self._contains_err("Error parsing 'asn' at 'clients' level - Invalid ASN: {}.".format(v))
def test_ip(self):
"""{}: IP address"""
for v in ("192.0.2.1/24", "2001:db8::1/64"):
self.cfg[0]["ip"] = v
self._contains_err("Error parsing 'ip' at 'clients' level - Invalid IP address: {}.".format(v))
for v in ("192.0.2.1", "10.0.1.1", "1.2.3.4", "fe80::1", "2001:DB8::1"):
self.cfg[0]["ip"] = v
self._contains_err()
def test_duplicate_ip(self):
"""{}: duplicate IP addresses"""
self.cfg[0]["ip"] = "192.0.2.1"
self.cfg[1]["ip"] = self.cfg[0]["ip"]
self._contains_err("Duplicate IP address found: 192.0.2.1.")
def test_next_hop_policy_no_authorized_addresses_with_list(self):
"""{}: next_hop.policy != authorized_addresses, list given"""
self.cfg[0]["cfg"]["filtering"]["next_hop"]["policy"] = "strict"
self.cfg[0]["cfg"]["filtering"]["next_hop"]["authorized_addresses_list"] = ["192.168.0.1"]
self._contains_err("AS3333 192.0.2.11 is not 'authorized_addresses' but the 'authorized_addresses_list' option is set")
def test_next_hop_policy_authorized_addresses_empty(self):
"""{}: next_hop.policy authorized_addresses, empty list"""
self.cfg[0]["cfg"]["filtering"]["next_hop"]["policy"] = "authorized_addresses"
self._contains_err("set to 'authorized_addresses' but the list of authorized IP addresses ('authorized_addresses_list') is empty")
def test_next_hop_policy_authorized_addresses_invalid(self):
"""{}: next_hop.policy authorized_addresses, invalid list"""
self.cfg[0]["cfg"]["filtering"]["next_hop"]["policy"] = "authorized_addresses"
self.cfg[0]["cfg"]["filtering"]["next_hop"]["authorized_addresses_list"] = "test"
self._contains_err("Error parsing 'authorized_addresses_list' at 'clients.cfg.filtering.next_hop' level - Invalid format: must be a list.")
def test_next_hop_policy_authorized_addresses_invalid_address(self):
"""{}: next_hop.policy authorized_addresses, invalid IP addr"""
self.cfg[0]["cfg"]["filtering"]["next_hop"]["policy"] = "authorized_addresses"
self.cfg[0]["cfg"]["filtering"]["next_hop"]["authorized_addresses_list"] = ["test"]
self._contains_err("Error parsing 'authorized_addresses_list' at 'clients.cfg.filtering.next_hop' level - Invalid IP address: test.")
def test_next_hop_policy_both(self):
"""{}: next_hop.policy and next_hop_policy"""
self.cfg[0]["cfg"]["filtering"]["next_hop_policy"] = "strict"
self.cfg[0]["cfg"]["filtering"]["next_hop"]["policy"] = "authorized_addresses"
self.cfg[0]["cfg"]["filtering"]["next_hop"]["authorized_addresses_list"] = ["test"]
self._contains_err("Can't use the new 'next_hop' and the old 'next_hop_policy' statements simultaneously")
def test_next_hop_policy_authorized_addresses_ok(self):
"""{}: next_hop.policy authorized_addresses, ok"""
self.cfg[0]["cfg"]["filtering"]["next_hop"]["policy"] = "authorized_addresses"
self.cfg[0]["cfg"]["filtering"]["next_hop"]["authorized_addresses_list"] = ["192.168.0.1"]
self._contains_err()
def test_multiple_ip_addresses(self):
"""{}: clients with multiple IP addresses"""
clients_config = [
"clients:",
" - asn: 111",
" ip:",
" - '192.0.2.11'",
" - '2001:db8:1:1::11'",
" - asn: 222",
" ip:",
" - '192.0.2.21'",
" - '2001:db8:1:1::21'",
]
general = ConfigParserGeneral()
general._load_from_yaml("\n".join([
"cfg:",
" rs_as: 999",
" router_id: 192.0.2.2",
]))
general.parse()
self.cfg = ConfigParserClients(general_cfg=general)
self.cfg._load_from_yaml("\n".join(clients_config))
self._contains_err()
# Duplicate address.
clients_config = [
"clients:",
" - asn: 111",
" ip:",
" - '192.0.2.11'",
" - '2001:db8:1:1::11'",
" - asn: 222",
" ip:",
" - '192.0.2.11'",
" - '2001:db8:1:1::21'",
]
self.cfg = ConfigParserClients(general_cfg=general)
self.cfg._load_from_yaml("\n".join(clients_config))
self._contains_err("Duplicate IP address found: 192.0.2.11")
def test_inherit_from_general_cfg(self):
"""{}: inherit from general cfg"""
general = ConfigParserGeneral()
general._load_from_yaml("\n".join([
"cfg:",
" rs_as: 999",
" router_id: 192.0.2.2"
]))
general.parse()
self.cfg = ConfigParserClients(general_cfg=general)
self.cfg._load_from_yaml("\n".join([
"clients:",
" - asn: 111",
" ip: 192.0.2.11",
" - asn: 222",
" ip: 192.0.2.21",
" cfg:",
" passive: False",
" prepend_rs_as: True",
" add_path: True",
" filtering:",
" irrdb:",
" enforce_origin_in_as_set: False",
" enforce_prefix_in_as_set: False",
" white_list_pref:",
" - prefix: 192.0.2.0",
" length: 24",
" white_list_asn:",
" - 11",
" - 12",
" white_list_route:",
" - prefix: 192.0.2.0",
" length: 24",
" le: 32",
" asn: 65534",
" rpki_bgp_origin_validation:",
" enabled: True",
" reject_invalid: False",
" reject_invalid_as_in_as_path: False",
" max_as_path_len: 64",
" ipv4_pref_len:",
" min: 1",
" max: 2",
" ipv6_pref_len:",
" min: 3",
" max: 4",
" # test pre v0.6.0 format for next_hop",
" next_hop_policy: same-as",
" max_prefix:",
" # test pre v0.13.0 format for peering_db",
" peering_db: False",
" limit_ipv4: 10",
" limit_ipv6: 20",
" reject_policy:",
" policy: tag",
" graceful_shutdown:",
" enabled: True",
" - asn: 333",
" ip: 192.0.2.31",
" cfg:",
" filtering:",
" next_hop:",
" policy: 'authorized_addresses'",
" authorized_addresses_list:",
" - '192.0.2.31'",
" - '192.0.2.32'",
" - '2001:db8:0:0::31'",
" irrdb:",
" # testing optional ASN",
" white_list_route:",
" - prefix: 192.0.2.0",
" length: 24",
" le: 32"
]))
self.cfg.parse()
self._contains_err()
client = self.cfg[0]
self.assertEqual(client["cfg"]["passive"], True)
self.assertEqual(client["cfg"]["add_path"], False)
self.assertEqual(client["cfg"]["prepend_rs_as"], False)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["enforce_origin_in_as_set"], True)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["enforce_prefix_in_as_set"], True)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_pref"], None)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_asn"], None)
self.assertEqual(client["cfg"]["filtering"]["rpki_bgp_origin_validation"]["enabled"], False)
self.assertEqual(client["cfg"]["filtering"]["rpki_bgp_origin_validation"]["reject_invalid"], True)
self.assertEqual(client["cfg"]["filtering"]["reject_invalid_as_in_as_path"], True)
self.assertEqual(client["cfg"]["filtering"]["max_as_path_len"], 32)
self.assertEqual(client["cfg"]["filtering"]["ipv4_pref_len"]["min"], 8)
self.assertEqual(client["cfg"]["filtering"]["ipv4_pref_len"]["max"], 24)
self.assertEqual(client["cfg"]["filtering"]["ipv6_pref_len"]["min"], 12)
self.assertEqual(client["cfg"]["filtering"]["ipv6_pref_len"]["max"], 48)
self.assertEqual(client["cfg"]["filtering"]["next_hop"]["policy"], "strict")
self.assertEqual(client["cfg"]["filtering"]["max_prefix"]["limit_ipv4"], None)
self.assertEqual(client["cfg"]["filtering"]["max_prefix"]["limit_ipv6"], None)
self.assertEqual(client["cfg"]["filtering"]["max_prefix"]["peering_db"]["enabled"], True)
self.assertEqual(client["cfg"]["filtering"]["reject_policy"]["policy"], "reject")
client = self.cfg[1]
self.assertEqual(client["cfg"]["passive"], False)
self.assertEqual(client["cfg"]["add_path"], True)
self.assertEqual(client["cfg"]["prepend_rs_as"], True)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["enforce_origin_in_as_set"], False)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["enforce_prefix_in_as_set"], False)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_pref"][0]["prefix"], "192.0.2.0")
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_pref"][0]["length"], 24)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_asn"], [11, 12])
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_route"][0]["prefix"], "192.0.2.0")
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_route"][0]["length"], 24)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_route"][0]["le"], 32)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_route"][0]["asn"], 65534)
self.assertEqual(client["cfg"]["filtering"]["rpki_bgp_origin_validation"]["enabled"], True)
self.assertEqual(client["cfg"]["filtering"]["rpki_bgp_origin_validation"]["reject_invalid"], False)
self.assertEqual(client["cfg"]["filtering"]["reject_invalid_as_in_as_path"], False)
self.assertEqual(client["cfg"]["filtering"]["max_as_path_len"], 64)
self.assertEqual(client["cfg"]["filtering"]["ipv4_pref_len"]["min"], 1)
self.assertEqual(client["cfg"]["filtering"]["ipv4_pref_len"]["max"], 2)
self.assertEqual(client["cfg"]["filtering"]["ipv6_pref_len"]["min"], 3)
self.assertEqual(client["cfg"]["filtering"]["ipv6_pref_len"]["max"], 4)
self.assertEqual(client["cfg"]["filtering"]["next_hop"]["policy"], "same-as")
self.assertEqual(client["cfg"]["filtering"]["max_prefix"]["limit_ipv4"], 10)
self.assertEqual(client["cfg"]["filtering"]["max_prefix"]["limit_ipv6"], 20)
self.assertEqual(client["cfg"]["filtering"]["max_prefix"]["peering_db"]["enabled"], False)
self.assertEqual(client["cfg"]["filtering"]["reject_policy"]["policy"], "tag")
self.assertEqual(client["cfg"]["graceful_shutdown"]["enabled"], True)
client = self.cfg[2]
self.assertEqual(client["cfg"]["filtering"]["next_hop"]["policy"], "authorized_addresses")
self.assertEqual(client["cfg"]["filtering"]["next_hop"]["authorized_addresses_list"], [
"192.0.2.31", "192.0.2.32", "2001:db8:0:0::31"
])
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_route"][0]["prefix"], "192.0.2.0")
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_route"][0]["length"], 24)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_route"][0]["le"], 32)
self.assertEqual(client["cfg"]["filtering"]["irrdb"]["white_list_route"][0]["asn"], None)
def test_blackhole_filtering_propagation(self):
"""{}: inherit from general cfg - blackhole filtering"""
clients_config = [
"clients:",
" - asn: 111",
" ip: 192.0.2.11",
" cfg:",
" blackhole_filtering:",
" - asn: 222",
" ip: 192.0.2.21",
" cfg:",
" blackhole_filtering:",
" announce_to_client: True",
" - asn: 333",
" ip: 192.0.2.31",
" cfg:",
" blackhole_filtering:",
" announce_to_client: False",
]
general = ConfigParserGeneral()
general._load_from_yaml("\n".join([
"cfg:",
" rs_as: 999",
" router_id: 192.0.2.2",
]))
general.parse()
self.cfg = ConfigParserClients(general_cfg=general)
self.cfg._load_from_yaml("\n".join(clients_config))
self.cfg.parse()
self._contains_err()
self.assertIs(general["blackhole_filtering"]["announce_to_client"], True)
client = self.cfg[0]
self.assertIs(client["cfg"]["blackhole_filtering"]["announce_to_client"], True)
client = self.cfg[1]
self.assertIs(client["cfg"]["blackhole_filtering"]["announce_to_client"], True)
client = self.cfg[2]
self.assertIs(client["cfg"]["blackhole_filtering"]["announce_to_client"], False)
# ------------------------
general = ConfigParserGeneral()
general._load_from_yaml("\n".join([
"cfg:",
" rs_as: 999",
" router_id: 192.0.2.2",
" blackhole_filtering:",
" announce_to_client: False"
]))
general.parse()
self.cfg = ConfigParserClients(general_cfg=general)
self.cfg._load_from_yaml("\n".join(clients_config))
self.cfg.parse()
self._contains_err()
self.assertTrue(general["blackhole_filtering"]["announce_to_client"] is False)
client = self.cfg[0]
self.assertIs(client["cfg"]["blackhole_filtering"]["announce_to_client"], False)
client = self.cfg[1]
self.assertIs(client["cfg"]["blackhole_filtering"]["announce_to_client"], True)
client = self.cfg[2]
self.assertIs(client["cfg"]["blackhole_filtering"]["announce_to_client"], False)
def test_custom_bgp_communities_ok(self):
"""{}: custom BGP communities"""
clients_config = [
"clients:",
" - asn: 111",
" ip: 192.0.2.11",
" - asn: 222",
" ip: 192.0.2.21",
" cfg:",
" attach_custom_communities:"
]
yaml_lines = clients_config + [
" - test1",
" - test2",
]
general = ConfigParserGeneral()
general._load_from_yaml("\n".join([
"cfg:",
" rs_as: 999",
" router_id: 192.0.2.2",
" custom_communities:",
" test1:",
" std: '1:1'"
]))
general.parse()
self.cfg = ConfigParserClients(general_cfg=general)
self.cfg._load_from_yaml("\n".join(yaml_lines))
self._contains_err("The custom BGP community test2 referenced on client AS222 192.0.2.21 is not declared on the general configuration.")
yaml_lines = clients_config + [
" - test1",
]
self.cfg = ConfigParserClients(general_cfg=general)
self.cfg._load_from_yaml("\n".join(yaml_lines))
self._contains_err()
def test_global_only_option(self):
"""{}: global only option"""
clients_config = [
"clients:",
" - asn: 222",
" ip: 192.0.2.21",
" cfg:",
" filtering:",
" irrdb:",
" allow_longer_prefixes: True"
]
general = ConfigParserGeneral()
general._load_from_yaml("\n".join([
"cfg:",
" rs_as: 999",
" router_id: 192.0.2.2",
]))
general.parse()
self.cfg = ConfigParserClients(general_cfg=general)
self.cfg._load_from_yaml("\n".join(clients_config))
self._contains_err("Unknown statement at 'clients.cfg.filtering.irrdb' level: 'allow_longer_prefixes'")
|
Q:
dsPIC33EP512MU810 ADC channel to pin mapping
I am using dsPIC33EP512MU810 and want to use ADC1 to read the analogue value from PORTB.R0.
Using MicroC Pro for dsPIC compiler, I am using their ADC library. The function ADC_GET_Sample(unsigned int channel) requires respective channel to read from.
I have gone through the datasheet multiple times, but can't figure out the channel to pin mapping for this MCU.
Can someone please help me out?
A:
Take a look on page 9 of:
http://ww1.microchip.com/downloads/en/DeviceDoc/70616g.pdf
Pins marked as ANx (like AN0, AN2 ... AN31) are your ADC channels.
For example AN0 (ADC channel 0) is on RB0 (pin 25 of MCU), AN29 (channel 29) is on RE5 (pin 3 of MCU), and so on...
|
User Reviews
DaVinci Restaurant
Posted by Steve on 2015-02-25
Not recommended
Used to be my favorite local restaurant , now I can no longer go back after the last few visits the food quality has gone from soso to disappointing. The original owner had a pretty good staff all gone . The food tastes nothing like the original.
DaVinci Restaurant
Posted by PdG on 2014-07-10
Nice atmosphere
My veal scaloppini ranked second to a TV dinner, soggy with bad taste ..... the spaghetti of side dish was âswollenâ probably from soaking in water and tasted like it and the sauce was eligible for medicare.
DaVinci Restaurant
Posted by Ben Horawitz on 2013-11-11
Pizza to die for!!!!
We used to order pizza regularly from Davinci's in ft. lauderdale. After leaving the publix on jog and boynton we decided to try the Davinci in Boynton, ordered "The Davinci" most amazing pizza I've ever seen/tasted. Who ever is making this pizza is "the
DaVinci Restaurant
Posted by Ida Campagnola on 2012-04-10
Gathering
We recently had a group of 50 friends and family attend a luncheon at Da Vinci's after a Memorial Mass. I can't praise the restaruant enough. The food and service was excellent and everyone was so pleased. We thank the owners, chef and wait staff for ma
DaVinci Restaurant
Posted by kac on 2011-11-18
Love it!
I love this place. I get take out a lot for myself, but always go there when I have company in town. Everyone I have brought there has enjoyed the food. The staff is always really nice.
DaVinci Restaurant
Posted by Martin on 2011-05-09
Our favorite spot!
My wife and I go to Da Vinci's at least twice a week. We usually have dinner at the bar. We both love the atmosphere there and the food is always delicious! The owners are there most days and they really do make their customers feel welcome.
DaVinci Restaurant
Posted by Nina on 2011-04-08
Enjoyable
Food was good, plenty of it. Definitely would return next time I am in town.
DaVinci Restaurant
Posted by Cindy Blunk on 2011-04-07
Veal picatta to die for
My husband & I recently visited family in West Palm Beach area & frequented Da Vinci's Restaurant 3 separate occasions while there. The service, staff and food are outstanding!! What a great value for your money and a romantic decor'. We highly recomme |
Each day thousands of visitors are fed by the ashram. The preparation of food inevitably produces waste peelings. ‘Premix’ is the combination of wet food waste and wood chip. One of many buckets of the day’s ‘premix’ is emptied on to the compost heap, over a layer of elephant dung. Slurry (cow’s urine and manure) and dry leaves are added to the compost heap. Thus, heaps of organic waste are formed each day to form healthy fertile soil. African worms are also being farmed to aid the composting process.
In this way, the ashram recycles at least one ton of compost a day. The circle is complete when students from GreenFriends learn to grow plants on campus using the compost. The ashram is growing vegetables, and uses the compost as fertilizers.
By choosing to compost waste, we are actually completing the natural cycle and following nature’s path. Our own food and organic waste is transformed into healthy fertile soil. Composting completes the natural cycle, reversing the modern trend. As we restore balance and harmony to Nature, the same qualities blossom in us, and we smile gratefully, seeing the bounty of Nature offered lovingly to us. |
Ferroelectric metal-organic framework with a high dielectric constant.
Hydrothermal reaction of (l)-N-(4'-cyanobenzy)-(S)-proline with CdCl2 as a Lewis acid catalyst and NaN3 gives colorless block compound 1, in which 1 displays a complicated 3D framework. Ferroelectric and dielectric property measurements reveal that 1 exhibits physical properties comparable to that of a typical ferroelectric compound with a dipole relaxation process and a dielectric constant of ca. 38.6 that makes it, by definition, a high dielectric material. |
Time magazine columnist Joe Klein called CNN “an embarrassment to our profession,” surprising a New York City audience on Sunday by declaring Fox News “the only option” for straight news at 6 p.m.
Hardly a rabid right-winger, Klein nevertheless felt compelled to lament the decline of liberal media bastions like CNN and MSNBC during a conversation with Jeff Greenfield at the 92nd Street Y.
He singled out for particular criticism CNN’s endlessly breathless coverage of missing Malaysia Flight 370 (RELATED: The five most ridiculous aspects of CNN’s missing Malaysian flight coverage).
“I come home, and I turn on CNN at 6 o’clock at night — because that’s something I kind of do in preparation for the 6:30 network news, to see what Wolf [Blitzer] is being really hyperbolic about — and he’s talking about the plane!” Klein lamented.
“It is such an embarrassment to our profession that CNN has gone in the toilet the way it has,” he continued. “You know, I miss being able to turn on a straight newscast. And it turns out, the only place you can go to get one, at 6 o’clock at night, is Fox.”
That set off some grumbles from the Manhattan audience, prompting Klein and Greenfield to defend reporter Bret Baier’s performance on Fox’s 6 p.m. “Special Report.”
“The other option is to go to MSBNC and see the Reverend Al Sharpton, who I still consider to be a major criminal,” Klein quipped, prompting audience applause. “I mean, the guy can have a job on network TV, on an NBC cable network, and he still hasn’t apologized for Tawana Brawley? Gimme a break.”
Sharpton — now host of MSNBC’s “PoliticsNation” at 6 PM — maintained a very different public persona in 1988, when he promoted black teenager Tawana Brawley’s false and defamatory narrative that she’d been raped by three white males, including a police officer.
WATCH:
[h/t Mediaite]
Follow Brendan on Twitter
Content created by The Daily Caller News Foundation is available without charge to any eligible news publisher that can provide a large audience. For licensing opportunities of our original content, please contact licensing@ dailycallernewsfoundation.org.
Content created by The Daily Caller News Foundation is available without charge to any eligible news publisher that can provide a large audience. For licensing opportunities of our original content, please contact licensing@dailycallernewsfoundation.org. |
Bert Twiddletoe, A truly heroic hero
A short, tubby shape stood in the doorway to”The inn of the severed arm”. He had a small dignified nose, and his body was covered in rusty metal armour. He walked up to the innkeeper, a fat man with thin, greasy hair, a pig nose and a dirty, beer stained apron. The armor clad man took a deep bow before saying:
”Excuse me sir, I’m Bert Twiddletoe, a great hero and dragonslayer! Would it be too much of me to ask if yewould give me accomodations for the cold winter night? I will of course award ye efforts.”
The innkeeper scratched his almost bald head with short, fat fingers.
”Whass’ datt yu’ be sayin’?” he muttered, almost incoherently.
Bert twitched his nose, annoyed by the innkeepers complete lack of manners. He thought for a while, then he said:
”What I said was: Would you let me stay in your beautiful abode?”
The Innkeeper scratched his head yet again.
”Sorry, don’t speak franceian,” he said, mighty proud that he had figured out what language the weird man was speaking.
”WHAT I SAID WAS: GIVE ME A FRIGGIN’ ROOM IN YER FRIGGIN’ INN BECAUSE I’M FREEZIN’ MY FRIGGIN’ ARSE OFF!” Bert shouted in pure outrage, his face as red as a tomato in harvest season.
The innkeeper smiled, rage was a language he spoke fluidlently: ”No need for shoutin’, you could’ve just be sayin so in the beginnin place,” he said and reached for a key. Bert’s face slowly turned back into a normal colour as he put three gold coins on the counter, took the keys and went up too his room.
Bert looked at the small dirty room he’d been given and sighed. He went over to the small, filthy bed and looked in wonder at the yellow stains on the blankets. Had they been red he might have understood, red being the colour most often left after glorious, heroic battles. But yellow?
Bert scratched his head and went over to the bed, removed his rusty armor and thought of all his glorious battles, all his wonderful treasure (which had, according to Bert, been stolen while he was out saving a princess), he then went over to look at the bathroom. There was none.
”Well, I’ll be a goose in mating season! Some thieving scoundrel has stolen my bathing accomadations! I’ll have to report this to the innkeeper as soon as humanly possible!” he mumbled to himself, strapped on his armour and ran downstairs to complain.
Bert stood outside in the cold, dark night, banging on the inn’s door. ”LET ME IN! I DIDN’T MEAN TO WAKE YOU, GOOD SIR! PLEASE! I’VE PAID ALREADY!” he shouted, after a while he stopped banging on the door.
”That oafish lout… Throwing me out just for waking him… If I wasn’t bound by the knight’s moral codex I’d… I’d… I’d… do something really mean!” Bert mumbled and walked away from the inn.
He looked around him, the white snow covered the rooftops of the village of Rax. Bert shivered in the cold, his armour not doing much to warm his frozen body, he didn’t know much about Rax, but he knew he didn’t like it here. He therefore decided to use his exceptionally magnificent skills in the outdoors to find shelter and make a fire.
”Ok… so how did this work… Rock on… rock?… Yeah… Uhmm… Ok… Sparks on… What have I forgotten… Oh… hmm… I know! WOOD!” Bert mumbled to himself, all his attempts at making fire up until now had been a complete failure, but he had at least found shelter in a large cave.
”Wood… Wood… Where do you get wood?” Bert asked himself over and over again, then it struck him: TREES!
He ran outside and choose a large oak, he then drew his sword and started chopping at it. A few hours later, he had successfully cut down a tree, not the large oak, but a smaller, and in Bert’s opinion, much more convinient bush. He dragged the bush back to the cave, dumped it on the floor, took his two rocks, and smashed them together.
After a great deal of smashing, Bert proudly looked at the result of his labor, a burning bush, he ignored the fact that it was already morning. He sat down to enjoy his glorious fire when suddenly, he heard sounds from outside.
”An’ I said to tha chump, if ya don’t gimme yer money, I’ll chop off yer toe!”, a dark voice said, the voice was followed by rough chorus of laughter from two other voices.
Bert shot up, what horrible people could this be? Talking about chopping off toes in mid-morning, then laughing about it? Brigands, or thieves mayhaps?
Orcs or ogres? There was no use in sitting here thinking about it, the voices were coming closer.
Finding a good dark place in the depths of the cavern, which he, now that he came to think about it, hadn’t investigated yet. He ran into the dark cavern, found himself a good rock, and hid.
The voices were almost inside the cavern now, then something struck him: THE BUSH! He’d forgotten the damnable bush! Well, it was too late now, all he could do now was to sit back and see what happened next.
Bert held his breath in anticipation, and then they came in, three large brutish looking men. (But for the rest of his days, Bert would refer to them as Ogres). Two of them were holding a large brown bag, the third carrying a large bow, something inside the bag moved and there came muffled sounds.
”By all that’s holy! That’s the sound of someone in need! Those.. Those… vile ogres have kidnapped some maiden!” Bert mumbled to himself and instinctivly grabbed the hilt of his rusty sword.
The three men put the bag down and looked around.
”Hey, James, Homer, cum ’ere! There’s ’een someone here lately, look, it’s a burnt bush!”, one of the large men said to the others.
The larger of the three, which Bert now thought of as ”Homer the Evil”, although he would later find out that he was the one named James, went over to the bush and looked at it. This, Bert thought, was the perfect time for action, as James bent over to examine the bush, Bert jumped out from behind the bush with his sword in hand, he took a defensive stance and shouted: ”WOE IS THY EVIL KIDNAPPERS! I, BERT YE HEROIC, WILL SAVE YE ENTRAPPED ONE AND SLAY YE! FLEE QUICKLY AND I WILL SPARE YE PITIFUL LIVES!”
The three men quickly pulled together.
”What ’id he say?” one of them said
”I dunno, but he’s got a sword, I says we run and don’t look back,”
The largest one shook his head.
”Maybes we can be talkin to him, lemme try…
He-llo we hun-ters,” he pointed at himself and then continued: ”We.. Come… in… Peace..,” he said and pointed at his bow and put it down on the ground.
”Then thy must at least be evil hunters ?” Bert said and scratched his head.
The spokesperson of the hunters held up his hands.
”No, we, just, normal, hunters…” he said
”Ah! I see, you serve me lies, evil ones, WELL I SEE RIGHT THROUGH THY SCHEMES! EN GUARDE!” Bert shouted and attacked.
The three hunters ran outside in a wild frenzy.
Bert stood back and enjoyed his work, once again, Bert the good had once again slapped the ugly face of evil into a bloody pulp, now all he had to do was free the prisoner.
He went over to the bag, opened it, and looked into a flock of white birds. As the birds flew out the cave Bert stood for himself thinking…
He finally found a conclusion to this most disturbing bag of birds, what he had freed had been nothing less than a full blooded witch! And as Bert opened the bag, the witch had fled in the form of birds!
Of course, that was the only thing that could possibly have happened, the other bit, about the men really being hunters was too silly to even consider.
Bert smiled and laid down on the cold stone floor. He thought about all the heroic things he would do tomorrow, closed his eyes, and went to sleep. |
Students Denied Lunch Because Of Lack Of Funds
This is an archived article and the information in the article may be outdated. Please look at the time stamp on the story to see when it was last updated.
Students Denied Lunch Because Of Lack Of Funds
(CNN) — Sorry, kid. No money, no lunch.
Students at an Attleboro, Massachusetts, middle school went hungry this week if they had a negative balance on their pre-paid lunch cards.
Five cents of debt was enough for cafeteria employees at the Coehlo Middle School in instruct kids at least one day this week to dump out the food they would have normally eaten, CNN affiliate WJAR, Rhode Island, reported.
About 25 children left the lunchroom with empty stomachs, said Whitson’s Culinary Group in a statement. The company runs the school’s cafeteria. |
Saving 1 Million Euros in the Utilities Industry with Kaizen and Data Quality
Featuring Mark Humphries
One of the toughest challenges for any company is demonstrating the financial impact of poor data quality and as a result they go hunting for errors first, with the hope of linking to business value later.
In this interview, past contributor Mark Humphries of Essent in Belgium, shares practical advice of how to develop a complete data quality strategy that starts with customer needs and ultimately ends in major data quality improvement.
Dylan Jones: It’s been awhile since we featured on the site Mark, what data quality work have you been involved with lately?
Mark Humphries: About a year ago now in my role as Billing Manager I was worried about the number of customers that called every month about their bills and the number of corrections that we were making as a result.
We had just started an ambitious growth plan, and we were already seeing success. One of my worries was that the growth would generate more calls and more corrections and part of the deal with the growth plan is that we had to do it without increasing headcount.
It was clear to me that we had to do what we could so that less customers felt the need to call us and challenge the bills.
When we looked into this one of the highlights was what we called bill shocks. For example a customer pays €100 a month as part of his budget plan, but then by the annual meter reading he suddenly receives his annual bill for €200. The annual bill, based on measured consumption should be a small correction and sometimes a credit note if the customer has consumed less than we estimated.
So we started a Kaizen for this specific problem.
Dylan Jones: How are payments calculated?
Mark Humphries: We calculate the monthly payments based on expected consumption for the year. If the actual consumption is line with this, then the annual bill will be a small adjustment.
First things first, how could we accurately measure our performance and get an idea for the potential improvements?
This isn’t obvious, because for one customer who is paying €500 a month then an annual bill of €100 is maybe a small adjustment but for another who is paying €60 a month then €100 is a major problem.
Eventually we settled on a ratio – the net annual bill divided by the monthly advance amount.
In this way everything is normalised.
Dylan Jones: So, what did you find?
Mark Humphries: Well the nice thing that we saw was that over the previous 12 months this index had steadily reduced from 5 to under 1 and was continuing towards zero where it should be.
This was a welcome confirmation that a big data cleaning exercise from a year previously really had worked. Then the focus had been on estimated consumption and meter reading dates.
The bad news though, was that there was far too much variability. Although the averages were good, the variation was too high, so yes we still had a problem, but the question was did it correlate to the calls that we were receiving?
So we explored the next step in the Kaizen methodology which is to analyse the facts.
We looked at the correlation behind the observed deviation and an number of undesirable events such as calls, corrected bills, customers who leave and customers that we eventually drop due to bad payment. This was a big surprise for me, because we established a very clear link to the calls, not just for the large bills but also for the large repayments.
Dylan Jones: Ah I see, interesting, were there any tools or techniques used to help discover that link between variation of billed amount and the number of calls?
Mark Humphries: A lot of the work was done in Excel, but we also used Mintitab for the regression analysis. Minitab is very performant running just on a laptop and is good for generating a range of graphics that enabled us to visualise complex relationships.
Dylan Jones: What about customer churn, did you find a link to people closing their account?
Mark Humphries: Good question. So what we found actually was that there was no link with customers leaving. Customers with an unexpectedly high bill called us and complained, but didn’t leave.
What did happen though with a small number of customers is that they didn’t pay that bill, and we ended up dropping them. This turned out to be very important because these were the customers on a tight budget.
Dylan Jones: I see, can you give an example so our readers can see how you worked through the process.
Mark Humphries: Absolutely. It’s a great example actually of how data quality management really demands that you understand your business and in particular the needs and behaviours of your different customer segments.
So let’s say we were billing a customer €50 a month based on expected annual consumption worth €600 a year. That was OK and they could budget for it. Then suddenly we present them with a bill for €120. At that point they just don’t have the money and can’t pay, we end up dropping them and losing the €120.
If in the beginning of the year we had calculated €60 a month instead of €50 a month, they could have budgeted. It was all there in the data and we could build a business case around call reduction and non-payment reduction. The only question now was where was it going wrong.
The next step took some time. We focused on what we knew at the beginning of the billing cycle and what could possibly have an impact on the calculation of the monthly bills and how reality might turn out differently.
Dylan Jones: How did you make the calculations?
Mark Humphries: We created a large dataset based on two years of billing history and then used Minitab to perform a regression analysis of the various inputs. This took several iterations before we arrived at credible conclusions, but the final conclusions were beautifully simple.
Dylan Jones: What was driving the variation?
Mark Humphries: The biggest drivers behind the variations were found to be:
The quality of the meter reading at the start of the billing cycle
The source of estimate consumption that we used to calculate the monthly bills and
The sales channel
Let me explain these one at a time.
Each meter reading that we receive is tagged with a quality indicator – read by the meter reading company, supplied by the customer or estimated.
What we saw is that when the customer or the meter reading company read the meter the billing goes fine, but when the reading is estimated, then the probability of a high annual bill is increased. And it’s the meter reading at the start of the cycle that counts.
With each meter reading we also receive expected consumption for the coming year from the meter reading company. However, when a customer moves house we ignored this and asked the customer what he expected to consume at his new address. It turns out that the meter reading companies estimates, which are based on the previous occupant’s consumption, are far better than the customer’s. This is quite a remarkable conclusion because it means that energy consumption depends more on the house or flat than on who’s living in it.
Lastly there was also a link with the sales channels, but that’s commercially sensitive information, so I can’t explain it any further.
We are currently in the process of implementing the improvements, but in the end the root cause comes down to data quality, specifically in this case the quality of the meter readings and the quality of the projected consumption.
The first solution is to react to estimated meter readings. We are contacting the customer and encouraging him to go and check his meter against the estimates. Since we are now tackling this at the beginning of the billing cycle, there
For the second, we now know that the meter reading company knows best, and by default we will use their estimates. The projected savings are around €1M per year from these simple changes.
Dylan Jones: That’s a significant amount of savings for one process, very impressive, particularly when you consider it over a 3 year return period, certainly enough to fund a data quality team! What other lessons can you share for members who want to learn from your experience and try this themselves?
Mark Humphries: Sure, well some of the most important lessons to draw from this story are:
Firstly although the root causes are to be found in data quality, this started as a process issue “why are customers complaining about their bills?”. In particular, by focusing on the customer and the bottom line you’re homing in on some very targeted areas that you know will get peoples attention.
Secondly we took the time to accurately measure the size of the problem and to make a valid estimate of the potential savings before we even looked for the root causes. Data quality is not just about profiling data and finding defects, you’ve really got to create a solid business case to help prioritise the most critical initiatives.
Thirdly the root cause analysis was very data intensive. All my data management and data quality experience was very relevant at this stage, but this meant that we could justify our conclusions, they really were fact based. I enjoyed the moment when I was asked in board room how big a sample we had taken and I could reply that the sample was all annual bills from the last two years.
The final lesson I would cite is that I had looked at the problem of estimated meter readings previously in isolation, and then I had dismissed it as priority.
In that exercise I concluded that only 1 estimated reading in 20 caused a problem and that with less than 10% estimates overall the impact was negligible. This time I came at the problem from a different angle. I started with an undesirable output and worked back to the root cause.
Dylan Jones: Can you quickly list the tools and techniques that you adopted in this data quality improvement initiative so that others who are getting started can get a shortlist of areas they know will help them?
Mark Humphries: To get at the data we just used old fashioned SQL and our own knowledge of the data model.
A lot of the initial investigative work was done with Excel. Then to really pull the correlations out of the data we used Minitab.
For the methodology we applied Kaizen.
None of this is high end stuff and I think that’s important. In this whole exercise we did a lot of iterations. I have highlighted the important stages, but there were a lot of blind alleys that didn’t lead anywhere.
Having direct access to the data, being able to refine the dataset and perform new analyses was important.
The structure of the Kaizen approach, although simple, was also important, especially the emphasis on forgetting about the solution until you really understand the problem.
Dylan Jones: What I like most about this case study Mark is that you really started with the customer.
By working back from their pain and needs you were able to model the process and map the data to it correctly to support your analysis.
A lot of people do the reverse by profiling data, finding defects then hunting for business pain. As a result they often struggle to discover the real business impact.
I think you’ve raised some really valuable lessons, well done to you and your team, thanks for sharing.
Contributions by Mark Humphries:
In this presentation, Mark Humphries provides an explanation of how he has been able to successfully combine data quality and process improvement techniques to create a more comprehensive transformation process for organisations.
In this interview, past contributor Mark Humphries of Essent in Belgium, shares practical advice of how to develop a complete data quality strategy that starts with customer needs and ultimately ends in major data quality improvement. |
Q:
Javascript: Get body of an ID
I am trying to get body content of iframe using either Javascript or jQuery. I have tried to solve the problem several ways, but none of them worked for me.
The solutions I tried looked like these:
document.getElementById('iframe').document.innerHTML;
$("#content").contents().find("body").html();
A:
document.getElementById("iframe").contentWindow.document.body.innerHTML
|
Month: April 2018
Iranian President Hassan Rouhani voiced support for the country’s military forces to develop advance weapons, including missiles, to enhance the Islamic Republic’s deterrence capabilities. “I am support the Artesh [Iran’s regular army] and Sepah [Islamic Revolution Guards Corps] to make |
Cell Cycle Synchronization of Schizosaccharomyces pombe by Centrifugal Elutriation of Small Cells.
Division of Schizosaccharomyces pombe by medial fission produces identically sized daughter cells that grow by tip extension until their own division is prompted by reaching the same critical size for division as the parental cell. The fidelity of this size control in the absence of perturbation means that cells of the same size are at the same point in the cell cycle. Size selection of small cells from an asynchronous culture by centrifugal elutriation permits generation of synchronous cultures large enough for biochemical analysis. The changes observed in the synchronized cell cycle progression of such cultures are representative of those that accompany cell cycle progression of individual cells. Here, we describe how size selection with the Beckman Coulter JE-5.0 rotor can be used to generate synchronized cultures. Because of the continuous passage of medium through the rotor throughout the procedure, elutriation is considered to have less impact on the integrity of the cell cycle than other approaches. Two protocols are presented here: The first generates a 2-L culture ideal for detailed biochemical analysis, whereas the second allows rapid generation and simultaneous analysis of three smaller (200-mL) cultures. |
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