During April 20-22,2022,colleagues and friends gathered at the Institute of Pure&Applied Mathematics(IPAM),at the University of California at Los Angeles to celebrate Professor Stanley Osher's 8Oth birthday in...During April 20-22,2022,colleagues and friends gathered at the Institute of Pure&Applied Mathematics(IPAM),at the University of California at Los Angeles to celebrate Professor Stanley Osher's 8Oth birthday in a conference focusing on recent developments in"Optimization,Shape analysis,High-dimensional differential equations in science and Engineering,and machine learning Research(OSHER)"This conference hosted in-person talks by mathematicians,scientists,and industrial professionals worldwide.Those who could not attend extended their warm regards and expressed their appreciation for Professor Osher.展开更多
They are going to get a gift for their son's birthday!What to buy?Cross off the items rhyming with animals.The one item left on the list will be their birthday gift for him!
When Grandma shouted to Grandpa to eat,Grandpa always liked to hide,and Grandma would look for him,find him,and laugh happily when she saw him.On Grandma's 80th birthday,Grandpa disappeared again.This time,the who...When Grandma shouted to Grandpa to eat,Grandpa always liked to hide,and Grandma would look for him,find him,and laugh happily when she saw him.On Grandma's 80th birthday,Grandpa disappeared again.This time,the whole family looked for Grandpa together.Who would find Grandpa?展开更多
Jordyn Perez,nearing her 8th birthday,was presented with a novel idea by her mother:donating her birthday gifts to a childrens hospi-tal.Initially uncertain,Jordyn contemplated the suggestion,realizing the greater nee...Jordyn Perez,nearing her 8th birthday,was presented with a novel idea by her mother:donating her birthday gifts to a childrens hospi-tal.Initially uncertain,Jordyn contemplated the suggestion,realizing the greater need of hospital-ized children.“I was like,‘Okay,that's cool,’”she said.“I already had everything I needed,and these kids who were going through difficult times at the hospital needed it more than I did.”展开更多
A birthday is an important day in many cultures.In America,family and friends have a party for the birthday boy or girl.They celebrate with balloons,party hats,games,gifts and more.There is always a birthday cake with...A birthday is an important day in many cultures.In America,family and friends have a party for the birthday boy or girl.They celebrate with balloons,party hats,games,gifts and more.There is always a birthday cake with candles.There is one candlefor eachyear of the birthday child's age.展开更多
Activity 1.Think about the following questions and write down your answers before reading the text.1.What kind of presents do you think the neighbors might prepare for the 88⁃year⁃old lady?
Yesterday was my twelfth birthday.There was a party.My parents were busy all day.They bought some snacks.Then they cooked some fish,chicken,beef and vegetables.My cousin brought some fruit and drinks to my party.There...Yesterday was my twelfth birthday.There was a party.My parents were busy all day.They bought some snacks.Then they cooked some fish,chicken,beef and vegetables.My cousin brought some fruit and drinks to my party.There was a nice cake on the table.Everything was ready.At eleven o'clock,I looked out of the window and saw my friends.展开更多
Dulwich Pudong Celebrates Founder's Day 2023,Dulwich Founder's Day 2023 is an annual tradition that celebrates the founding of Dulwich College Lonpon in 1619.On May 27,thousands of staff,students,and parents c...Dulwich Pudong Celebrates Founder's Day 2023,Dulwich Founder's Day 2023 is an annual tradition that celebrates the founding of Dulwich College Lonpon in 1619.On May 27,thousands of staff,students,and parents came together on campus for activities,food,fun and of course amazing performances by Dulwich students.This one was extra special as it marks the official kickoff of the countdown to Dulwich Pudong's 20-year anniversary birthday party in September.展开更多
When I was young,I was always looking forward to my birthday’s coming.I dreamed of the cake,the presents,and the best wishes from others.However,when I woke up,what I first saw was always a bowl of noodles,which we c...When I was young,I was always looking forward to my birthday’s coming.I dreamed of the cake,the presents,and the best wishes from others.However,when I woke up,what I first saw was always a bowl of noodles,which we called “changshou mian” in Chinese.展开更多
This coming September will mark the 90th birthday of Academician Wanzhen LU,one of the best scientists in the field of analytical chemistry and petroleum chemistry both in China and around the world.Academician LU was...This coming September will mark the 90th birthday of Academician Wanzhen LU,one of the best scientists in the field of analytical chemistry and petroleum chemistry both in China and around the world.Academician LU was born in Tianjin,Peoples’Republic of China on September 29,1924.Her father is a famous展开更多
They were a couple in their late thirties,and they lookedunmistakably married.They sat on the banquette opposite usin a little narrow restaurant,having dinner.The man had
Probabilistic techniques are widely used in the analysis of algorithms to estimate the computational complexity of algorithms or a computational problem.Traditionally,such analyses are performed using paper-and-pencil...Probabilistic techniques are widely used in the analysis of algorithms to estimate the computational complexity of algorithms or a computational problem.Traditionally,such analyses are performed using paper-and-pencil proofs and the results are sometimes validated using simulation techniques.These techniques are informal and thus may result in an inaccurate analysis.In this paper,we propose a formal technique for analyzing the expected time complexity of algorithms using higher-order-logic theorem proving.The approach calls for mathematically modeling the algorithm along with its inputs,using indicator random variables,in higher-order logic.This model is then used to formally reason about the expected time complexity of the underlying algorithm in a theorem prover.The paper includes the higher-order-logic formalization of indicator random variables,which are fundamental to the proposed infrastructure.In order to illustrate the practical effiectiveness and utilization of the proposed infrastructure,the paper also includes the analysis of algorithms for three well-known problems,i.e.,the hat-check problem,the birthday paradox and the hiring problem.展开更多
文摘During April 20-22,2022,colleagues and friends gathered at the Institute of Pure&Applied Mathematics(IPAM),at the University of California at Los Angeles to celebrate Professor Stanley Osher's 8Oth birthday in a conference focusing on recent developments in"Optimization,Shape analysis,High-dimensional differential equations in science and Engineering,and machine learning Research(OSHER)"This conference hosted in-person talks by mathematicians,scientists,and industrial professionals worldwide.Those who could not attend extended their warm regards and expressed their appreciation for Professor Osher.
文摘They are going to get a gift for their son's birthday!What to buy?Cross off the items rhyming with animals.The one item left on the list will be their birthday gift for him!
文摘When Grandma shouted to Grandpa to eat,Grandpa always liked to hide,and Grandma would look for him,find him,and laugh happily when she saw him.On Grandma's 80th birthday,Grandpa disappeared again.This time,the whole family looked for Grandpa together.Who would find Grandpa?
文摘Jordyn Perez,nearing her 8th birthday,was presented with a novel idea by her mother:donating her birthday gifts to a childrens hospi-tal.Initially uncertain,Jordyn contemplated the suggestion,realizing the greater need of hospital-ized children.“I was like,‘Okay,that's cool,’”she said.“I already had everything I needed,and these kids who were going through difficult times at the hospital needed it more than I did.”
文摘A birthday is an important day in many cultures.In America,family and friends have a party for the birthday boy or girl.They celebrate with balloons,party hats,games,gifts and more.There is always a birthday cake with candles.There is one candlefor eachyear of the birthday child's age.
文摘Activity 1.Think about the following questions and write down your answers before reading the text.1.What kind of presents do you think the neighbors might prepare for the 88⁃year⁃old lady?
文摘Yesterday was my twelfth birthday.There was a party.My parents were busy all day.They bought some snacks.Then they cooked some fish,chicken,beef and vegetables.My cousin brought some fruit and drinks to my party.There was a nice cake on the table.Everything was ready.At eleven o'clock,I looked out of the window and saw my friends.
文摘Dulwich Pudong Celebrates Founder's Day 2023,Dulwich Founder's Day 2023 is an annual tradition that celebrates the founding of Dulwich College Lonpon in 1619.On May 27,thousands of staff,students,and parents came together on campus for activities,food,fun and of course amazing performances by Dulwich students.This one was extra special as it marks the official kickoff of the countdown to Dulwich Pudong's 20-year anniversary birthday party in September.
文摘When I was young,I was always looking forward to my birthday’s coming.I dreamed of the cake,the presents,and the best wishes from others.However,when I woke up,what I first saw was always a bowl of noodles,which we called “changshou mian” in Chinese.
文摘This coming September will mark the 90th birthday of Academician Wanzhen LU,one of the best scientists in the field of analytical chemistry and petroleum chemistry both in China and around the world.Academician LU was born in Tianjin,Peoples’Republic of China on September 29,1924.Her father is a famous
文摘They were a couple in their late thirties,and they lookedunmistakably married.They sat on the banquette opposite usin a little narrow restaurant,having dinner.The man had
文摘Probabilistic techniques are widely used in the analysis of algorithms to estimate the computational complexity of algorithms or a computational problem.Traditionally,such analyses are performed using paper-and-pencil proofs and the results are sometimes validated using simulation techniques.These techniques are informal and thus may result in an inaccurate analysis.In this paper,we propose a formal technique for analyzing the expected time complexity of algorithms using higher-order-logic theorem proving.The approach calls for mathematically modeling the algorithm along with its inputs,using indicator random variables,in higher-order logic.This model is then used to formally reason about the expected time complexity of the underlying algorithm in a theorem prover.The paper includes the higher-order-logic formalization of indicator random variables,which are fundamental to the proposed infrastructure.In order to illustrate the practical effiectiveness and utilization of the proposed infrastructure,the paper also includes the analysis of algorithms for three well-known problems,i.e.,the hat-check problem,the birthday paradox and the hiring problem.
