American mathematicians solve Ramanujan's “deathbed” puzzle

Minneapolis, Jul 23: The former Minneapolis police officer charged with murder in the death of George Floyd was charged Wednesday with multiple felony counts of tax evasion.

Derek Chauvin and his wife, Kellie May Chauvin, were each charged in Washington County with six counts of filing false or fraudulent tax returns for the tax years 2014 through 2019 and three counts of failing to file tax returns for 2016, 2017 and 2018.

Floyd, a Black man who was handcuffed, died May 25 after Chauvin, who is white, pressed his knee against Floyd's neck for nearly eight minutes as Floyd pleaded for air.

Chauvin is charged with second-degree murder, third-degree murder and manslaughter. He and three other officers who were at the scene were fired.

Chauvin is in custody on the charges in the Floyd case. Kellie Chauvin, who filed for divorce after Floyd's death, is not in custody.

Online court records didn't list attorneys for either in the tax evasion case, and calls to Kellie Chauvin did not go through.

Washington County Attorney Pete Orput said the investigation into the Chauvins was started in June by the Minnesota Department of Revenue and Oakdale Police Department.

Authorities allege in the criminal complaints that the Chauvins failed to file income tax returns and pay state income taxes, and that they underreported and underpaid taxes on income they earned from various jobs each year.

The complaints allege that they also failed to pay proper sales tax on a $100,000 BMW purchased in Minnesota in 2018.

Prosecutors say the Chauvins bought the car in Minnetonka but registered it in Florida, where they paid lower sales taxes.

London, May 20: The current physical distancing guidelines of 6 feet may be insufficient to prevent COVID-19 transmission, according to a study which says a mild cough in low wind speeds can propel saliva droplets by as much as 18 feet.

Researchers, including those from the University of Nicosia in Cyprus, said a good baseline for studying the airborne transmission of viruses, like the one behind the COVID-19 pandemic, is a deeper understanding of how particles travel through the air when people cough.

In the study, published in the journal Physics of Fluids, they said even with a slight breeze of about four kilometres per hour (kph), saliva travels 18 feet in 5 seconds.

"The droplet cloud will affect both adults and children of different heights," said study co-author Dimitris Drikakis from the University of Nicosia.

According to the scientists, shorter adults and children could be at higher risk if they are located within the trajectory of the saliva droplets.

They said saliva is a complex fluid, which travels suspended in a bulk of surrounding air released by a cough, adding that many factors affect how saliva droplets travel in the air.

These factors, the study noted, include the size and number of droplets, how they interact with one another and the surrounding air as they disperse and evaporate, how heat and mass are transferred, and the humidity and temperature of the surrounding air.

In the study, the scientists created a computer simulation to examine the state of every saliva droplet moving through the air in front of a coughing person.

The model considered the effects of humidity, dispersion force, interactions of molecules of saliva and air, and how the droplets change from liquid to vapour and evaporate, along with a grid representing the space in front of a coughing person.

Each grid, the scientists said, holds information about variables like pressure, fluid velocity, temperature, droplet mass, and droplet position.

The study analysed the fates of nearly 1,008 simulated saliva droplets, and solved as many as 3.7 million equations.

"The purpose of the mathematical modelling and simulation is to take into account all the real coupling or interaction mechanisms that may take place between the main bulk fluid flow and the saliva droplets, and between the saliva droplets themselves," explained Talib Dbouk, another co-author of the study.

However, the researchers added that further studies are needed to determine the effect of ground surface temperature on the behaviour of saliva in air.

They also believe that indoor environments, especially ones with air conditioning, may significantly affect the particle movement through air.

This work is important since it concerns safety distance guidelines, and advances the understanding of the transmission of airborne diseases, Drikakis said.

Washington, May 1: The United States on Thursday recorded 29,625 new coronavirus cases, and 2,035 deaths in the last 24 hours, according to Johns Hopkins University.

The total number of coronavirus cases has reached 1,069,534 and the death toll stands at 63,001, CNN reported.

The novel coronavirus has infected more than 3.2 million people and killed at least 233,000 globally, according to Johns Hopkins University.