Maths whizz Lily Miyazaki feels like her number has finally come up after qualifying for the US Open.

The Tokyo-born Brit had a wild card for Wimbledon last year, but has now reached the main draw of a grand slam under her own steam for the first time.

Miyazaki, who earned a masters degree in mathematical science in the United States four years ago, beat Slovakia’s Viktoria Hruncakova in the final round of qualifying at Flushing Meadows.

The 27-year-old now has to solve the puzzle of how to get past Russian Margarita Betova on Monday for a first grand slam match win.

“Playing Wimbledon last year was amazing,” said Miyazaki. “But I think that, as a wild card, I don’t know how to explain it, but I don’t know if you truly believe like you belong.

“And I played Caroline Garcia, obviously she’s a pretty good player and I was really nervous going into that match. So hopefully this time I feel like I belong here. So that experience definitely helped me.”

Miyazaki joins Katie Boulter and Jodie Burrage as the British contingent in the women’s draw.

She also shares a coach, Craig Veal, with British number two Burrage, who was in the stands supporting her compatriot.

“For her to qualify, it was killing me,” said Burrage, 24. “When she was one-set all, I had to go to practice and throughout it I was shouting at my physio asking what the score was.

“I was hardly focusing on my practice because I wanted to be there watching her, but it’s so good she has qualified, with me and ‘Boults’ being in the main draw.

“It’s nice when you are friends and you can enjoy success with them and hopefully next week we can do some damage in the main draw. We’ve all got the games to be able to.”

Burrage faces Russian Anna Blinkova on Tuesday, while British number one Boulter meets France’s Diane Parry.

Great Britain’s Keely Hodgkinson was forced to settle for another World Championships silver.

The 21-year-old was beaten to 800m gold by Kenya’s Mary Moraa in Budapest just 13 months after she also finished second in Eugene.

Hodgkinson clocked one minute 56.34 seconds with defending champion Athing Mu in third and GB’s Jemma Reekie fifth.

Hodgkinson had been beaten into silver by Mu at last year’s World Championships before Moraa took gold at the Commonwealth Games ahead of her.

Before the final, the Olympic silver medallist admitted she owed them both but was unable to beat Moraa despite overhauling Mu in the final 50m on Sunday night.

Kenya’s Mary Moraa won a thrilling 800m final on Sunday’s final day of the 2023 World Athletics Championships in Budapest, Hungary

Against a stacked field, Moraa ran a tactically brilliant race staying on the shoulder of the USA’s Athing Mu, the 2022 world champion, before powering past her down the home stretch to take victory in 1:56.02.

Great Britain’s Keely Hodgkinson, who stayed off the pace for most of the race, stormed through to overtake Mu late and take silver in 1:56.34.

Mu, who has raced sparingly this season, finishing third in 1:56.61.

Jamaica’s Adelle Tracey, who clocked a lifetime best 1:58.99 in her semi-final, produced another lifetime best of 1:58.41 for seventh place.

Andy Farrell says Ireland are “devastated” to have lost veteran prop Cian Healy to injury ahead of the Rugby World Cup in France.

Healy has been left out of his country’s 33-man squad and is facing up to 10 weeks on the sidelines due to a calf issue sustained in Saturday evening’s 17-13 warm-up win over Samoa.

The 35-year-old – Ireland’s third most-capped player with 125 appearances – was helped off the pitch by medical staff in Bayonne and was later pictured on crutches.

Munster loosehead Jeremy Loughman will fill the void, with head coach Farrell holding faint hope of Healy possibly being fit to feature in the latter stages of the tournament.

“He’s just had a scan as we got off the plane and he’ll be out for a spell of time that won’t be right, unfortunately, for Cian and for us, certainly for the start of the competition,” said Farrell, speaking in Dublin.

“We’ll see how his rehab goes during it, you’d never know towards the back end if he could be a replacement or not.

“It’s devastating, isn’t it? That’s sport, that’s life, that’s rugby. Cian’s big enough and old enough and experienced enough to be through these type of things before.

“I remember in 2013 on the Lions (tour) he got injured early and had to fly home. He’s experienced something like this and understands that these things happen. He’s devastated as we are for him.

“The prognosis is something between five, six to 10 weeks. How that rehab carries on is something that we’ll keep a track of as we go.”

Healy’s absence was the headline news from Farrell’s selection, but was hardly a shock given he was still hobbling when boarding the plane to return to Dublin from Biarritz earlier on Sunday.

Captain Johnny Sexton says his Leinster team-mate will be missed.

“I only just found out literally five minutes ago,” said Sexton. “He has been through ups and downs in his career, he’s a very, very decorated player, a great player. We’re going to miss him.

“I’m gutted for him to miss this tournament. It has meant a lot to him in how he has prepared for it and how he has trained.”

Ulster pair Jacob Stockdale and Tom Stewart, Connacht back-rower Cian Prendergast, Leinster fly-half Ciaran Frawley and uncapped Munster hooker Diarmuid Barron also failed to make the cut.

But Dan Sheehan, Ronan Kelleher, Jack Conan, Dave Kilcoyne and Keith Earls have been picked, despite recent injury issues, with Farrell opting for a 18-15 split of forwards and backs.

Ireland begin their campaign on September 9 against Romania in Bordeaux and also face Tonga, world champions South Africa and Scotland in Pool B.

“It’s obviously difficult because you’re shattering somebody’s dream, but I would hope that through all campaigns you don’t let bad news become a shock,” Farrell said of cutting down his squad.

“We think we have an extremely gifted squad and I also feel the balance is right.

“We’re the lucky ones that get to chase the dream for the wider group and the nation itself.

“If we can’t get excited for that and the first game against Romania, we’re in the wrong job. I think we’re in a great place, ready to take this challenge head on.”

Lewis Hamilton said he “paid the price” for Mercedes’ strategy blunder at the start of Sunday’s Dutch Grand Prix.

Following a first-lap downpour in Zandvoort, Mercedes were too slow to put both Hamilton and team-mate George Russell on the intermediate tyres.

The poorly-timed stops left Hamilton and Russell – who was third on the grid – 13th and 17th when the order shuffled out.

“We should have pitted, but we didn’t, and we paid the price for that,” said Hamilton who eventually crossed the line sixth as Max Verstappen claimed his ninth win in succession.

“Today I had the pace, and I was on pace with Max, but we were just out of position.

“I was pretty happy with my drive to back into the points. I got sixth. But it could have been higher, for sure.”

Sergio Perez started seventh but assumed the lead of the race after he was called in by his quick-thinking Red Bull team on the first lap.

With the rain still falling, Verstappen, quite rightly, stopped the next time round but Russell stayed out on the slick rubber despite the worsening conditions.

Hamilton, who started 13th, was also sent round for another lap despite the seven-time world champion’s obvious concerns.

“We should have come in, man,” said Hamilton over the radio. “It is very wet.”

“Copy, Lewis,” said his race engineer Peter Bonnington. “We’re going to stay out. We’re going to have to brave this.”

But at the end of the third lap, Hamilton was in for wet tyres. He rejoined the track in last place.

Russell was still sliding around on slicks before he was changed on to the wet rubber at the end of lap four.

“I was forecast a podium,” said Russell on the radio. “F***, how did we mess this up?”

Russell was classified 17th after he collided with Norris in the closing stages and sustained a left-rear puncture.

“The race was over before it really got started,” said the 25-year-old Englishman. “The information we got about the weather was totally wrong.

“We thought the rain would last a couple of minutes but it clearly lasted for longer. It was a real shame. A podium was missed.

“As a team we need to review because we are getting the information coming into us and it was misjudging the weather. It is not anything to do with racing or engineering. It was just a weather misinterpretation and that ruined our afternoon.

“So we need to look into that, to see why the others decided to pit and what information they had that we didn’t, and make sure we don’t make the same mistake again.”

Mercedes team principal Toto Wolff said: “That was a difficult day for us. In the opening 15 laps, we got pretty much everything wrong that we could have done – and that cost us any chance of fighting for the podium. We will review thoroughly.”

Forgotten man Darwin Nunez came off the bench to fire 10-man Liverpool to a sensational 2-1 win at Newcastle as they staged a late, late show.

Trailing to former Everton striker Anthony Gordon’s opener and at a numerical disadvantage following Virgil van Dijk’s dismissal, the Reds refused to accept defeat and got their reward when the £85million Uruguay international levelled with nine minutes remaining and then snatched victory three minutes into stoppage time.

The Magpies were left to reflect on missed chances – Alisson produced a stunning first-half save to deny Miguel Almiron, who later hit a post – but Jurgen Klopp’s men scrapped impressively to ensure their unbeaten run against the Tyneside club extended to 14 games.

Klopp celebrated wildly in front of the home dugout and on the pitch after the final whistle as the home fans among a crowd of 52,214 trudged away barely able to believe what they had witnessed.

St Mirren manager Stephen Robinson praised his “outstanding” side as he focused on the positives after a late blow against Aberdeen cost them top spot in the cinch Premiership.

Saints fought back to lead 2-1 thanks to Greg Kiltie’s penalty and a strike from substitute Alex Greive and were moments away from a seventh straight win.

But a VAR review led to a penalty for handball against Alex Gogic and Bojan Miovski levelled 10 minutes into stoppage-time.

St Mirren had recovered from a late blow in the first half when Jonny Hayes’ free-kick nestled in the far corner in Aberdeen’s first attack of note in the 42nd minute.

And Robinson wants his players to quickly brush off the last-gasp setback.

Robinson said: “I thought we dominated the game from start to finish. We created all of the chances and luck didn’t go our way with certain things.

“All I can ask for is that level of quality and I got that. Some of the football we played and the quality of the chances we created were a credit to that group of players. I would rather talk about them than about decisions or things that went against us.

“That’s all I can ask of those boys who are very, very talented and I’m very proud of them.

“They feel that they should have another two points but ultimately we don’t.

“If we play like that, as we have done for the last seven games, we’ll be fine. We controlled the game and passed the ball really well and opened up an Aberdeen side which has spent a lot of money.

“They are a very good side, make no mistake about that. They are doing very well and doing very well in Europe but we made them look average because of our performance. They are a good side but our quality was outstanding.

“All I can say to the boys is to keep going as we are heading in the right direction.”

There was further drama after Miovski hit the net as the striker’s penalty was subjected to a VAR check for a “double touch”.

Robinson, whose side had two goals disallowed for offside, said: “You’re always going to have that throughout games and these things happen sometimes. It didn’t go our way. It would be wrong for me to make a comment as it wouldn’t be an educated comment as I’ve not seen it from any great angle.”

Aberdeen were a shadow of the side that drew 2-2 with Swedish champions BK Hacken in Gothenburg on Thursday.

Manager Barry Robson said: “First and foremost credit to St Mirren. I thought they were excellent.

“We looked a yard off it all over the pitch. But, when you can’t win it then you don’t lose it. I thought we hung in there and fought right until the end.

“It was hard to go from the high of Hacken to playing the form team in Scotland. They had won their first six games this season and we have been on the road for a long time.

“I think the fans helped us in the end. We needed to get something out of the game and thanks to them we did.  We probably got a few VAR decisions as well.”

Meanwhile, Robson claimed he was “hugely” confident that Miovski would still be at the club next week amid reports Southampton are preparing a bid for the North Macedonia striker.

Christian Horner has hailed “untouchable” Max Verstappen as the best driver in the world after the Red Bull star overcame a chaotic rain-hit Dutch Grand Prix to equal Sebastian Vettel’s record of nine wins in a row.

Despite two separate downpours wreaking havoc at the beginning and conclusion of Sunday’s 72-lap race in Zandvoort, Verstappen delivered in front of 105,000 expectant fans to take the chequered flag ahead of Aston Martin’s Fernando Alonso, with Pierre Gasly completing the podium.

Verstappen’s Red Bull team-mate Sergio Perez, slapped with a five-second penalty for speeding in the pit-lane, finished fourth while Lewis Hamilton – who bemoaned his Mercedes team’s poor strategy in the inclement conditions – came home in sixth place.

Verstappen, who has won 11 of the 13 rounds so far, will head to next weekend’s Italian Grand Prix in Monza 138 points clear in the drivers’ championship.

There remains an outside chance he could complete his hat-trick of titles at the Japanese Grand Prix on September 24 with half-a-dozen rounds still to run.

“Max is in a period of his career where he is just simply untouchable,” said Red Bull team principal Horner, who oversaw Vettel’s streak of nine straight wins a decade ago.

“I don’t think there is any driver on the grid that would be able to achieve what he is doing in that car.

“To win nine races in a row is insane, and it is something that none of us would have envisaged, and I never thought we would repeat it after we managed it with Sebastian. What we are witnessing is a driver that is generational.

“Max has been in incredible form for the past three years, and the most impressive thing for me is all the pressure that he is under here.

“With the expectation of 100,000 Dutch fans, a lot would have cracked under that pressure, but he kept his composure and delivered, as he has done so many times.”

Come wind, rain or shine, 25-year-old Verstappen is the man for all occasions. On pole, he found himself down in 13th place after seven drivers – including team-mate Perez – took advantage of a sudden first-lap downpour to move on to wet tyres.

But by lap 13, Verstappen – who at one stage was lapping his home track four seconds faster than Perez and two seconds quicker than anybody else – was back in the lead.

His record-equalling feat was placed in doubt when the rain returned with vengeance with a dozen laps to go, and Zhou Guanyu crashed out, and the race was stopped.

A 43-minute delay and six-lap dash to the chequered flag followed, but Verstappen denied Alonso any hope of taking his first win in a decade with an assured drive. He finished 3.7 sec clear of the Spaniard.

As Verstappen ensured Red Bull’s unbeaten run remained, Hamilton’s afternoon was scuppered by Mercedes’ dithering following the first-lap downpour.

Hamilton was not called in for wet tyres until the end of lap three with team-mate George Russell following in on the next lap. When the dust settled, Hamilton and Russell, who started third, were 16th and 18th respectively.

From there it was a damage-limitation exercise for both men, with Hamilton driving well to take sixth place.

Russell might have finished seventh but for a late duel with countryman Lando Norris leaving him with race-ending harm to his Mercedes. Norris crossed the line in seventh place.

Tony Docherty admitted he was delighted his players finally reaped the rewards all their hard work deserved as they picked up their first cinch Premiership win of the season.

Luke McCowan scored the only goal of the game for the Dark Blues in the second half against Hearts with a sublime lobbed finish at Kilmac Stadium.

The 25-year-old scored a similar goal in pre-season but this time it really counted, securing all three points.

Docherty said: “It doesn’t surprise me with Luke.

“He did it pre-season against Fleetwood Town from further out.

“Luke McCowan typifies the type of player I have in that changing room.

“I am really pleased for him but more pleased for the squad in terms of they got their rewards today for all the hard work they put in.

“I am absolutely delighted and it was no more than the players deserve as we put in a lot of hard work in the last couple of weeks on the training ground.

“We had a game plan and I thought the players carried that out to the letter. I thought we were worthy of our win.”

There was confusion before kick-off with McCowan originally named in the starting line-up with Josh Mulligan on the bench.

New team sheets were then released with the duo swapping positions but just before kick-off, McCowan was back in the team with Mulligan as a substitute.

However, Docherty played down the mix-up.

He added: “There was something happened before the game.

“You can put that down to human error. It was human error, that’s all I am saying.”

Hearts technical director Steven Naismith did not pull his punches in his assessment of his side’s performance.

“We weren’t good enough today. It’s as simple as that,” he said.

“I don’t think we deserved much out of the game. We are fortunate at half-time to be 0-0, we never really caused them many problems and they caused us more problems.

“That’s a reflection of the first half. We needed to make three changes which did make an impact.

“For 15 to 20 minutes we caused them loads of problems, but I felt we went away from what was getting us good situations. We went away from that and started making the wrong pass.

“Ultimately it’s a poor day, we don’t get anything from the game.

“As the game wore on I thought Dundee saw the game out well. They made passes at the right time, frustrated us.

“We were powder puff towards the end and that’s never going to get you anything.”

Dominica's Thea LaFond made her mark on history during the fiercely contested women's triple jump at the World Athletics Championships in Budapest, Hungary. Despite finishing fifth, LaFond's performance was nothing short of remarkable, as she broke her own national record not once, but twice during the competition, with jumps of 14.71m and 14.90m. These marks would have secured her a medal in most world championships, highlighting the level of competition she faced.

 The women's triple jump event was a showcase of unparalleled athleticism and grit, with Yulimar Rojas of Venezuela securing her fourth world title with a leap of 15.08m on her final jump. The competition was defined by its intensity, with Rojas narrowly making the final round of jumps after initially being tied for eighth. Ukraine's Maryna Bekh-Romanchuk clinched the silver medal with a season's best of 15.00m, while Cuba's Leyanis Perez-Hernandez secured the bronze with a jump of 14.96m.

 Jamaica's Shanieka Ricketts, a two-time world championship silver medalist, claimed fourth place with a season's best of 14.93m, while Cuba's Liadagmis Povea's best effort of 14.87m placed her in sixth position in the closely contested contest.

 Reflecting on her remarkable journey, LaFond expressed the historic significance of the event.

 "So the competition was really, honestly like history making, to be honest. I mean, you're talking about probably the hardest women's triple term final in the history of the World Championships and it was it was a battle and I'm happy to be part of it and as happy as able to fight, but it was definitely a battle," she said.

 LaFond acknowledged the work she had put in to refine her technique leading up to the event.

 "Earlier this year we did talk about working on different parts of the phases and to the question of did it all come together at the right time, honestly, no. I mean that 1490 was not a perfect jump. It was far from it, which only tells me that there's more left in the tank and I'm excited to see what comes next," she told Sportsmax.TV.

 While her performance would have secured a medal in most years, LaFond faced the challenge of competing in a highly competitive field. "To be honest, 14.90m would have won a medal any year and it's like it's definitely frustrating, you know, but it is quite an honor to be competing in the sport at the height of the sport, truly. But yeah, it's a tough reality."

LaFond candidly expressed her feelings about the thrilling finale of the competition, where Rojas clinched victory with her final jump.

 "It was definitely, I don't even know if the word is deflating. It was just kind of annoying," she confessed. "She was definitely the most vulnerable she's ever looked in the competition, definitely in any major championships, but definitely not deflating. Annoying definitely, but there's nothing deflating over here."

 Amidst the intense competition and emotions, LaFond highlighted the remarkable progression of the sport.

 "Six women over 14.80m. That just means that our sport is getting insane and we're definitely pushing the limits to what people even thought the sport could be," she said.

"And to see so many women, so, so many minority women at that, I'm at the top of the sport. It's really a great feeling. And I really hope that you know, other, you know, little brown girls around the world are finding inspiration through what we do."

 

 

 

Steve Borthwick insists England will urgently address the defensive crisis that threatens to torpedo their Word Cup.

Fiji plundered three tries in a seismic 30-22 victory at Twickenham as England’s preparation for the tournament in France continue to unravel amid a run of five defeats in six games.

Most concerning of all is a defence overseen by Kevin Sinfield that has now been breached 30 times in Borthwick’s nine Tests in charge, each outing seeing an average of 26 points leaked.

Fiji were typically ruthless in attack but also met willing victims and with the World Cup opener against Argentina arriving in less than two weeks, England must resurrect a fundamental of their game.

Borthwick has stated that he is happy with his management team as scrutiny of Sinfield’s work grows, but the head coach is demanding an immediate improvement in the team’s work without the ball.

“I’m very clear that I was disappointed with the defence. We conceded too many tries and we missed too many tackles,” Borthwick said.

“Our focus is on ensuring we are much better than that against Argentina in two weeks’ time.

“The dropping off tackles has not been the case with what we’ve seen recently, but there were a lot against Fiji – more than 20 missed tackles. I think the total was 27.

“Now Fiji have exceptional power and speed, and that hurt us. But what we have to do is look at those tackles and what we could have done better.

“We didn’t want that result. We were clearly disappointed by the game and disappointed by aspects of that performance.

“Whilst there are areas of our performance which saw signs of growth, you can’t slip off that many tackles in a Test match.”

Captain Johnny Sexton admits he instantly regretted the heated exchange with referee Jaco Peyper which caused him to miss Ireland’s Rugby World Cup warm-up matches through suspension.

Fly-half Sexton was hit with a three-match ban for misconduct for his behaviour following Leinster’s Heineken Champions Cup final defeat to La Rochelle on May 20 in Dublin.

The 38-year-old, who did not play in that match due to injury and is set to retire after the upcoming tournament in France, says the incident was a “mistake in the heat of the moment”.

He was on Sunday afternoon confirmed in Andy Farrell’s squad for the World Cup and is likely to make his return in his country’s Pool B opener on September 9 against Romania in Bordeaux.

Asked if he had any regrets about the on-field altercation with South African official Peyper at the Aviva Stadium, he said: “Of course, yeah. I’ve held my hands up since day one.

“I made a mistake in the heat of the moment.

“I was obviously very emotional on the day not being part of what I had mapped out from the start of the year as playing my last game for Leinster in the Aviva, winning a European cup.

“It’s what I dreamt of and then obviously to miss that, there’s a lot of emotion that goes with it and in that split second I went on to console my team-mates, I made a remark and I regretted it instantly.

“You make mistakes, you say sorry and hold your hands up and that’s what I’ve done.”

Sexton was forced off by a groin injury while helping Ireland clinch the Six Nations Grand Slam against England in March and has not played competitively since.

He watched from the stands this month as his country defeated Italy, England and Samoa.

Without the suspension, the 29-10 success over Steve Borthwick’s side on August 19 would have been Sexton’s final Dublin appearance.

“It’s been incredibly frustrating to have to sit and watch, it’s obviously my own fault,” he continued.

“But that’s been life, I’ve just had to do what I could for the team and try and learn by watching the guys and contribute where I could.

“It was particularly tough last weekend in the Aviva. You live and learn and it’s time to move on now.”

Sexton, who has 113 Ireland caps, was appointed skipper following the 2019 World Cup in Japan.

The 2018 world player of the year feels “very privileged” to have the chance to lead his country into the forthcoming competition.

“(It means) a huge amount,” he said. “If someone told me four years ago I’d be back here captain, I would have taken it 100 per cent.

“There’s been a lot put into this team by the management over the last four years and to get their vote of confidence four years ago to do it with this as the end goal, it’s been huge.

“I’m very proud for myself, my family and just for the group that we have. It’s a very privileged position to be in with such a good group.”

Assistant boss Juanma Lillo admitted he did not enjoy standing in for Pep Guardiola after Manchester City’s hard-fought 2-1 win at Sheffield United.

Guardiola watched his side extend their 100 per cent start to go top of the Premier League from Barcelona, where he is recovering from back surgery.

City turned in a dominant display at a sold-out Bramall Lane, but went close to letting two points slip when Blades substitute Jayden Bogle fired an 85th-minute equaliser.

Bogle cancelled out Erling Haaland’s second-half header – the Norway striker had missed a penalty before the break – only for Rodri to rescue City by smashing home an 88th-minute winner.

When asked if he enjoyed taking charge in Guardiola’s absence, Lillo said: “Not at all. I much prefer being with Pep. Especially when it’s a question of health, I don’t enjoy this at all. We miss his presence now more than ever.

“I haven’t spoken to him after the match. During the match I spoke to him at some moments, but generally he was speaking to the other members of the technical staff. But he’s been totally present today.”

City dominated possession throughout and were rarely troubled by the Blades, who produced a resolute and disciplined defensive display.

Haaland steered his 37th-minute penalty on to a post after Blades skipper John Egan had handled, but made amends by heading his side in front in the 63rd minute.

“Generally I thought we played really well today,” said Lillo, who confirmed Phil Foden had started on the bench due to an upset stomach. “It was a lot closer to what we wanted.

“From the second half I thought we really found our rhythm and we were able to win the ball back a lot quicker.

“We were able to find the new spaces created from winning the ball back quicker and we could have scored more before the first goal went in.”

Blades boss Paul Heckingbottom feels his side, back in the top flight after a two-year absence, are also improving despite losing their first three matches.

Heckingbottom said: “I’m pleased with the performance. You need a perfect performance to beat them because that wasn’t a below-par City.

“We got punished for two things we should do better. The sickener for me is the nature of how Rodri has lashed it in.

“It just comes after Phil (Foden) has mis-controlled the ball and just drops into his path.

“It’s a kick in the teeth after all the good play they had had and they way we had dealt with it. We’ve lost a point, but we’ll focus on the performance I think.

“Game on game we’ve got better and we certainly believe we’re going to have enough.”

Novak Djokovic has had his fair share of rivalries over his career but says the latest, with Carlos Alcaraz, is bringing the very best out of him.

Djokovic begins his quest for a 24th grand slam title at the US Open on Monday having already eclipsed the totals of his illustrious peers, Roger Federer and Rafael Nadal.

But the man likely to be standing in his way is Alcaraz, the defending champion who beat Djokovic in the Wimbledon final last month.

Djokovic got a measure of revenge when he outlasted the 20-year-old Spaniard in a near four-hour final in Cincinnati a week ago.

The duo may be at the opposite end of their careers but they have already built a rivalry which looks set to endure for as long as Djokovic, 36, continues to pick up a racket.

“He’s always pushing me to the limit,” said the Serbian. “I think I do to him pretty much the same thing. That’s why we produced a memorable final.

“It was one of the best, most exciting, and most difficult finals I was ever part of in best-of-three, no doubt, throughout my career.

“That’s why I fell on the ground after I won the match because it felt like winning a grand slam, to be honest. The amount of exchanges and rallies. It was physically so demanding and gruelling that I felt very exhausted for the next few days.

“Those are kind of the moments in matches that I still push myself on a daily basis, day in and day out, practice, sacrifice, commitment. At 36, I still have the drive.”

If Djokovic wins his first-round match, against Frenchman Alexandre Muller, he will overtake Alcaraz to become world number one again.

Alcaraz, the top seed, starts his campaign on Tuesday against Dominik Koepfer of Germany.

Iga Swiatek opens proceedings on Monday against Rebecca Peterson of Sweden as she bids to defend the title she won last year.

“On one hand you always want to kind of take experience from last year, find all these positive things that happened, take strength from that,” said the world number one from Poland.

“On the other hand you have to remember that it’s a totally different story. A lot can happen during like these 12 months.

“So I try to take everything step by step, not really go forward with my thoughts, think that I need to do something more because last year I won.”

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