Abstract: The problem of packing equal circles in a rectangular container refers to the task of placing a given number of non-overlapping equal circles into a fixed rectangular container while ...

Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. Non-Commercial (NC): Only non-commercial uses of the work are permitted. No ...

The original version of this story appeared in Quanta Magazine. If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle ...

The digital revolution was supposed to free us. Information at our fingertips, music without scarcity, art unbound from the shackles of plastic discs and corporate gatekeepers. And in a way it did. A ...

We see that if you add $101_2 + 101_2$ using algorithm 3.14, you get $1000_2$ instead of $1010_2$, and the problem is because the first line in the loop should ...

1 Warwick Mathematics Institute, The University of Warwick, Coventry, United Kingdom 2 School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang, China To ...

“Water activity” or “the activity of water” (typically abbreviated as “aw”) is a critical parameter in food science that influences microbial growth and chemical reactions (including enzymatic ...

Copyright 2026 The Associated Press. All Rights Reserved. Copyright 2026 The Associated Press. All Rights Reserved. Speaking to the Conference of Mayors Friday ...

1 Tianjin University of Technology and Education, Tianjin, China. 2 Lvliang Vocational and Technical College, Lvliang, China. In modern society, dense crowd detection technology is particularly ...