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In a statement issued through its state-run media, the National Defense Commission, the North's highest governing agency, headed by its young leader Kim Jong-un, said that "a variety of satellites and long-range rockets which will be launched by the D.P.R.K. one after another and a nuclear test of higher level which will be carried out by it in the upcoming all-out action" will be aimed at deterring the hostile policy of "the U.S., the sworn enemy of the Korean people."

The statement, which used the acronym for the North's official name, Democratic People's Republic of Korea, did not clarify when it would conduct such a test, which would be the first since Mr. Kim came to power in December 2011. But citing preparations at the Punggye test site in northeastern North Korea, South Korean officials and news media said that Pyongyang can conduct a new underground nuclear test there on short notice.

North Korea had previously hinted at the possibility of conducting a nuclear test, as its Foreign Ministry did on Wednesday when it issued a scathing statement rejecting a unanimous resolution that the Security Council adopted on Tuesday. The resolution tightened sanctions and condemned North Korea's Dec. 12 rocket launching as a violation of earlier resolutions banning the country from conducting any tests involving ballistic missile technology.

The North's statement on Thursday indicated that Mr. Kim, despite recent hints of economic reform and openness in North Korea, was likely to follow the pattern his father, Kim Jong il had established when he ran the country: a cycle of a rocket launching, U.N. condemnation and nuclear test.

Mr. Kim's posture threw a direct challenge to President Obama as he starts his second term, and to Park Geun-hye, who will be sworn in as president of South Korea next month.

After years of tensions with North Korea, both Mr. Obama and Ms. Park recently said they were keeping the door open for dialogue with North Korea on the premise that such engagement would lead to the eventual dismantling of its nuclear weapons program.

On Thursday, the North's National Defense Commission said the Security Council's move convinced it to "launch an all-out action" to foil Washington's hostile policy and "safeguard the sovereignty of the country and the nation." It said that North Korea's drive to rebuild its moribund economy and its rocket program, until now billed as a peaceful space project, will now "all orientate toward the purpose of winning in the all-out action for foiling the U.S."

"Settling accounts with the U.S. needs to be done with force, not with words as it regards jungle law as the rule of its survival," it said.

The North's comments came as Washington reaffirmed its policy of punishing North Korea for moving toward the development of long-range missiles tipped with a nuclear warhead, spearheading international backing for the Security Council resolution.

North Korea's Foreign Ministry said Wednesday that it would take "physical counteraction" to bolster its "nuclear deterrence both qualitatively and quantitatively."

In recent months, international experts have detected what appear to be new tunneling activities and efforts to fix flood damage in the Punggye-ri nuclear test site in northeastern North Korea. The North conducted an underground nuclear test in Punggye-ri in 2006 and in 2009.

North Korea said its Unha-3 rocket December put a scientific satellite into orbit. But Washington said the launching was a cover for testing technology for intercontinental ballistic missiles. After analyzing the debris of the rocket North Korea fired in December to put a satellite into orbit, South Korean officials said North Korea indigenously built crucial components of a missile that can fly more than 6,200 miles.

A new nuclear test by the North could help bolster its efforts to build a nuclear device small enough to mount on long-range missiles.

In recent years, North Korea has made it increasingly clear that it is determined to keep its nuclear weapons at whatever costs, undermining a once-popular belief that the Pyongyang government's brinkmanship was a mere bargaining ploy designed to get as many concessions as possible in exchange for nuclear weapons.

Choi Jin-wook, an analyst at the Korea Institute for National Unification in Seoul, said, "This is a strong message from North Korea, basically saying that no matter how much economic aid it receives, no matter how flexible other countries become, it will be negotiating only on the premise that it will be accepted and treated as a nuclear power."

He continued, "The North is sending a wake-up alarm to Washington and Seoul."

For years, Rodriguez was Henin's mentor and tactician in chief, a diminutive, Argentine-born coach who systematically helped the sensitive Henin overcome her fears and limitations to become the world's No. 1 player and a multiple Grand Slam champion.       

But Rodriguez is back at the heart of the women's game, and he was in the stands again on a steamy Thursday afternoon observing every nuance as his new pupil, Li Na, played one of the best big matches of her career to defeat Maria Sharapova, 6-2, 6-2 to reach the Australian Open final.       

That the sixth-seeded Li could beat the second-seeded Sharapova was no big surprise. One of China's biggest sports stars, Li is one of the game's true quality players and was a finalist here in 2011, but that she could beat Sharapova so easily was definitely a surprise.       

Sharapova had lost just nine games in five matches heading into the semifinal. Mischievous number crunchers were calculating her earnings per minute of court time: well over $1,000.       

But Li, who shares the same agent  (Max Eisenbud), will end up with the bigger paycheck after feasting on Sharapova's second serve and winning a clear majority of their physical baseline rallies.       

Asked if her lack of a major test in the earlier rounds might have played a role in her minor-key performance on Thursday, Sharapova demurred.  "I can't think of it that way; I certainly can't use that as an excuse," she said. "When I go into any match, I'm trying to win with the best scoreline I can. That's my goal.

"Today I felt like I had my fair share of opportunities," she said. "It's not like they weren't there. I just couldn't take them today."       

Sharapova's average second-serve speed was a very respectable 93 miles per hour, but she won just 6 of 24 points with it as Li broke her serve seven times in all. She was also particularly effective in stretching the 6-foot-2 Sharapova wide to her forehand with sliced serves and well-struck crosscourt forehands of her own. Sharapova's forehand, when she is on balance, is a major weapon, but less effective on the run.       

"She was aggressive," Sharapova said. "She was taking the first ball and doing something with it, and when I was trying to, I was making too many unforced errors."       

Sharapova still holds an 8-5 record over Li and won all three of their matches in 2012 when Li struggled to produce an encore to her remarkable 2011 season, when she reached the final at the Australian Open and then became the first Chinese player to win a Grand Slam singles title at the French Open.       

But she appears to be re-gathering momentum in 2013, six months after she and her husband, Jiang Shan, made the mutual decision to demote Jiang from coach back to husband and hire Rodriguez.       

He has been pushing Li particularly hard in physical training, and Li, who likes a joke, turned toward Rodriguez and the rest of her team during her postmatch interview and gave a new directive.       

"You don't need to push me anymore," she said. "I will push me."

Rodriguez knows Sharapova's game very well and also knows what it takes to beat her. Henin, who retired in 2011 because of an elbow problem, was 7-3 during her career against the much taller Sharapova.

And though Li and Henin are different players — Henin's signature shot was a one-handed backhand — they share a certain innate vulnerability. Li has struggled with her on-court composure over the years and lost memorably but painfully at last year's Australian Open in the fourth round to Kim Clijsters after holding four match points and a 6-2 lead in the second-set tiebreaker.

But Li held on Thursday, closing out the match on her second match point, and she has yet to drop a set in this tournament despite a difficult draw that included Julia Goerges in the fourth round, the fourth-seeded Agnieszka Radwanska in the quarterfinals and now Sharapova, who was in the hunt for the No. 1 ranking.

Her return to the final should spark greater interest in China than in Melbourne, where the women's semifinals on Thursday were not sold out and where there are still tickets available for Saturday's women's final (the later men's rounds have long been sold out).       

Her success here was also the latest coup for veteran players. Serena Williams won two Grand Slam singles titles and the Olympic gold medal last year at age 30. Li is 30 herself, something that the retired player turned Australian television presenter Rennae Stubbs likes to tease her about.       

But as Sharapova rediscovered, Li has a dangerous return of serve, and when Stubbs made mention of Li's age in the post-match interview, Li smiled.       

"You know," Li said, "The truth is I'm younger than you."

MELBOURNE, Australia (AP) — China's Li Na has overpowered second-seeded Maria Sharapova 6-2, 6-2 to advance to the Australian Open final and a chance for her second Grand Slam title.

Li, who won the 2011 French Open and was the losing finalist here to Kim Clijsters the same year, broke Sharapova's serve in the fifth and seventh games of the second set on Thursday.

Sharapova had dropped only nine games in five matches en route to the semifinals, a tournament record.

The sixth-seeded Li, who has been working since August with Justine Henin's former coach, Carlos Rodriquez, will play either defending champion Victoria Azarenka or 19-year-old American Sloane Stephens in Saturday night's final.

 As the region suffers through a brutal cold snap this week, with temperatures so punishing that uncovered slivers of flesh feel like paper cuts and the slightest wind can send a chill through the teeth like a Popsicle, the best solution seems not to leave home. But for many people whose boilers were flooded by seawater during Hurricane Sandy and still languish, awaiting repair, home is as frigid as the outdoors.

 "I've been through a lot," said Mr. Choi, 27, who resuscitated the turtles, but not before discovering that his pipes had burst, leaving miniature ice rinks in the middle of his floor. "It just feels like another problem after another problem."

 Residents who have made do with cold homes under extra blankets and triple socks since the storm hit in October face new challenges as the thermometer continues to dip. Temperatures this week have been about 10 to 15 degrees lower than midwinter averages, according to the National Weather Service, and are expected to slide into the teens over the next few nights, and could even fall into the single digits in parts of the region.

As of Tuesday, New York City's Rapid Repairs construction teams had restored heat, hot water or power to 12,247 residences in 7,112 buildings, according to Peter Spencer, the spokesman for the Mayor's Office of Housing Recovery. But work is continuing in an additional 1,893 buildings, a substantial portion of which, Mr. Spencer estimated, remain without heat.

Devon Lawrence's home in Far Rockaway, Queens, was washed through with ocean water that damaged his boiler and heating system beyond repair. At night, he tucks his 75-year-old mother, who has dementia and suffers from diabetes, under two blankets — she never takes off the four pairs of pants, three jackets and hat she wears indoors to hold off the seeping cold. Though the boiler was replaced by contractors from the Rapid Repairs program, the repairs have not been completed, he said. For now, Mr. Lawrence, 48, is heating his home with a kerosene heater and has spent $450 on kerosene in the past few weeks, dipping into money he was given by the Federal Emergency Management Agency that should be going toward repairing his house, he said.

"I'm worried about everything," Mr. Lawrence said. "When you wake up in the morning, you will breathe fog. If we are not properly covered we could suffer from hypothermia."

 Joseph McKellar, the executive director of Queens Congregations United for Action, a coalition of 40 faith-based organizations, called for the city to spend more money helping people get heat in their homes, saying the low temperatures had put people's lives at risk. Last week a homeless day laborer was found dead inside an abandoned storm-damaged home on Staten Island, according to the coalition. Other scenes of hardship were playing out throughout the region. At a public school in the Belle Harbor section of the Rockaways, students were evacuated on Wednesday to a school across the street after a boiler malfunctioned and temperatures in the school dropped.

In Sea Bright, N.J., Mayor Dina Long said that though only a quarter of the residents had returned to the borough, those with heating issues had been taken care of. But at Borough Hall itself, the boiler that had replaced the one the hurricane destroyed was not working. Business was conducted on Wednesday in jackets and sweaters, according to Kathy Morris, a staff member.

There are no more space heaters to give away at the Martin Luther King Center in Long Beach, on Long Island, said James Hodge, the site coordinator. He added that the center ran out on Tuesday. Mr. Hodge, 36, does not have heat at his home, which he shares with two of his brothers. "We've thought about everyone else and then at night we're cold," he said 

Some people have taken matters into their own hands. Doreen Greenwood, a real estate agent and the chief of the volunteer Gerritsen Beach Fire Department, has gone out each night with an ambulance full of space heaters, knocking on doors, and offering them to anyone who is icy.

And in the Arverne section of the Rockaways, Hazel Beckett, 73, a retired nurse, said she was toasty, even though her heating system was still a work in progress. She has been roasting red bricks on the stove. "That's been throwing beautiful heat," she said.

He was a decade older, a suave lawyer who courted her with flowers, rides in his powder-blue Cadillac and trips to glittering Manhattan nightclubs. He was married, though not to her.

Before long, tiring of his unfulfilled promises to divorce his wife, she ended their affair. He hired three men, who threw lye in her face, blinding her, and went to prison for more than a decade.

Afterward, she married him.

Linda Riss Pugach, whose blinding by her lover, Burton N. Pugach, in 1959 became a news media sensation, and whose marriage to Mr. Pugach in 1974 became an equally sensational sequel, died at Forest Hills Hospital in Queens on Tuesday at 75.

The cause was heart failure, said Mr. Pugach, her husband of more than 38 years and her only immediate survivor.

In 1974, The New York Times called the attack on Miss Riss "one of the most celebrated crimes of passion in New York history." In the years since, the strange romance of Mr. and Mrs. Pugach (pronounced POOH-gash) has seldom been far from public view.

A book about the couple, "A Very Different Love Story," by Berry Stainback, was published in 1976. More recently, the Pugaches were the subject of a widely seen documentary, "Crazy Love."

Part cautionary tale, part psychological study, part riveting disaster narrative, the film, directed by Dan Klores, was released in 2007 to favorable, if somewhat astonished, notices.

In the decades after their marriage, the Pugaches seemed hungry for limelight. Although reporters who visited their home in the Rego Park section of Queens wrote often of their unremitting bickering, the couple just as often appeared in the newspapers or on television to declare their mutual devotion.

They received renewed attention in 1997, when Mr. Pugach, known as Burt, went on trial in Queens on charges that he had sexually abused a woman and threatened to kill her.

At the trial, at which Mr. Pugach represented himself, Mrs. Pugach testified on his behalf, telling him in open court, "You're a wonderful, caring husband." The alleged victim in the case was Mr. Pugach's mistress of five years.

Mr. Pugach, who was convicted of only a single count — harassment in the second degree — of the 11 with which he was charged in that case, was sentenced to 15 days in jail.

"We loved each other more than any other couple could have," Mr. Pugach, intermittently weeping, said of his wife in a discursive telephone interview on Wednesday. He added, "Ours was a storybook romance."

But to judge from the news accounts then and now, the story in question was "Beauty and the Beast." Or, more precisely, it was that story's unseen second act — the one in which the title union has degenerated into long, grinding yet strangely indissoluble banality.

Linda Eleanor Riss was born in the Bronx on Feb. 23, 1937. Her parents divorced when she was very young, and she was reared by her mother, her grandmother and an aunt.

She graduated from James Monroe High School in the Bronx; when she met Mr. Pugach, who specialized in negligence law, she was working as a secretary at an air-conditioner dealership on Tremont Avenue there.

After breaking off her affair with Mr. Pugach, Miss Riss became engaged to another man.

The attack, in June 1959, scarred her face and left her almost completely blind; over time, she lost what sight remained. To the end of Mrs. Pugach's life, her face was framed by large dark glasses.

After the attack, Mr. Pugach appeared determined to continue their relationship. He telephoned her to suggest that they reconcile and later wrote her a torrent of letters from prison.

"At one point," The Times reported in 1959, "he was said to have promised, 'I'll get you a Seeing Eye dog for Christmas.' "

The obesity rate for African-Americans in New York City is higher than the city average, and city health department officials say minority neighborhoods would be among the key beneficiaries of a rule that would limit the sale of super-size, calorie-laden beverages.

But the N.A.A.C.P. has close ties to big soft-drink companies, particularly Coca-Cola, whose longtime Atlanta law firm, King & Spalding, wrote the amicus brief filed by the civil rights group in support of a lawsuit aimed at blocking Mr. Bloomberg's soda rules, which are set to take effect in March.

Coca-Cola has also donated tens of thousands of dollars to a health education program, Project HELP, developed by the National Association for the Advancement of Colored People. The amicus brief describes that program, but not the financial contributions of the beverage company. The brief was filed jointly with another organization, the Hispanic Federation, whose former president, Lillian Rodríguez López, recently took a job at Coca-Cola.

The N.A.A.C.P.'s New York office referred questions to the American Beverage Association, the soft-drink industry's lobbying group and the primary plaintiff in the suit against the city's new soda rules. The association referred questions to Coca-Cola, which did not immediately respond.

At the hearing on Wednesday in State Supreme Court in Manhattan, lawyers for the beverage industry argued that the Board of Health had overreached its authority by unilaterally ratifying the new rules. The city rejected that argument, saying the restrictions were well within the board's purview to regulate public health matters.

The hearing ended with no immediate ruling; Justice Milton A. Tingling Jr., who presided, adjourned without comment. The beverage industry said it was requesting a stay of the soda restrictions while the case was being resolved.

While the industry has successfully fended off higher soda taxes and restrictions across the country, it has been increasingly under siege from public health officials concerned about the adverse effects of sugary drinks.

New York unveiled its soda plan in May, and other states and cities have since pursued similar measures. On Wednesday, Gov. Deval L. Patrick of Massachusetts proposed that soda no longer be exempt from the state's sales tax; lawmakers in Hawaii and Nebraska have also recently proposed higher taxes on sales of sugary drinks.

In its amicus brief, the N.A.A.C.P. acknowledged that obesity was a significant problem among blacks and Hispanics. But the group urged the city to create a more holistic program to attack the problem, including an increase in financing for physical education programs in public schools.

Mr. Bloomberg's plan, the brief argued, would disproportionately hurt minority-owned small businesses, which faced competition from larger convenience stores like 7-Eleven that would be exempt from the soda restrictions because of a quirk in New York's regulatory structure.

"At its worst, the ban arbitrarily discriminates against citizens and small-business owners in African-American and Hispanic communities," the brief said.

The plan has also been ardently opposed by several members of the City Council's Black, Latino and Asian Caucus.

The city's health commissioner, Dr. Thomas A. Farley, said Wednesday that he was "disappointed" the N.A.A.C.P. had opposed the plan. "African-Americans are suffering disproportionately in this crisis, and I don't think the N.A.A.C.P. should be siding with the big soda companies," he said. "They are attacking public health officials who are trying to respond to that crisis."

According to the health department, about 70 percent of black New Yorkers and 66 percent of Hispanic New Yorkers are obese or overweight, compared with 52 percent of white non-Hispanic residents, based on a 2011 survey.