High-entropy alloys (HEAs) offer tunable compositions and surface structures, presenting significant potential for creating novel active sites to enhance CO2 reduction (CO2RR) catalysis, a key process ...

Python allows free creation of plots, unlike expensive, stagnant graphing calculators. Import NumPy and Matplotlib for basic ...

You scrambled up a Rubik's cube , and now you want to put it back in order. What sequence of moves should you make? Surprise: ...

They even appear in biology, where they're used to help count the possible folding patterns of RNA molecules. And they can be calculated using a simple two-degree polynomial. "The Catalan numbers ...

He withdrew from mathematics and public life in 2006, and even in 2010 ... collaborated on the new finding about how certain polynomials are formed and how they reach out into the number line.

"He even designed the graphs for us so that they could dynamically show the impact of our efforts, whether we were making progress or not, week by week, rather than quarterly as in the past." ...

In this paper, we model the selfish behaviors of cache nodes as selfish caching games on arbitrary directed graphs with heterogeneous content ... we show that a PSNE always exists and can be found in ...

Consider another 10-number set: all the even numbers from 2 to 20 ... Still, mathematicians now refer to it as the polynomial Freiman-Ruzsa conjecture, or PFR. Groups, like many mathematical objects, ...

We show that solving this problem is challenging, since it represents a non-deterministic polynomial-time (NP ... model based on the message passing graph neural network (MPNN) to estimate hidden ...

Even if a computer’s speed could reach the physical limit ... A number of solvable problems can be solved by algorithms that halt in a reasonable amount of time. These “polynomial-time algorithms” are ...