Ricardo Bermudez-Otero and Tobias Galla discuss the mathematics describing the evolution of human languages. The sounds and structures of the world's approximately 7,000 languages never stop changing. Just compare the English in Romeo and Juliet or the Spanish in Don Quixote to the modern...

Math may sometimes seem as if it's comprised of countless meaningless unconnected exercises, but in reality, it's much more. It's figuring out how to do something, and, even better, why something works the way it does. The math you're doing now can open doors for you so that you can answer deep...

We've seen that the availability of hospital beds is important during a pandemic, and it's important during normal times as well. Whether it's for emergency medical help or for a scheduled procedure (for example, chemotherapy), access to hospital space, staff, and equipment can be a matter of life...

In many places, fire seasons keep getting longer with larger and ever more destructive wildfires. Teams of mathematicians, computer scientists, meteorologists, and firefighters are working to reduce the number of large fires before they happen and to contain those that do occur. Mark Finney talks...

Math is often described as the science of patterns, which makes it a natural subject to help in the study of the underlying causes of patterns found in nature, for example, bands of vegetation that often occur on gently sloped terrains in certain near-desert ecosystems worldwide. We are starting to...

Math's connection with cooking extends beyond the mathematical constant that sounds like a dessert. For example, using differential equations to model fluid flow and heat transfer, research teams have found how spaghetti curls as it's cooked, how to rotate a pan to make the perfect crepe (thin...

Zhihong Chen, Dongsheng Li. Source: Advances in Differential Equations, Volume 26, Number 1/2, 83--106.Abstract: In this paper, we consider a system related to Maxwell's equations, which has different structure with general elliptic systems. The existence of the weak solution is obtained in...

Yanan Li, Zhijian Yang. Source: Advances in Differential Equations, Volume 26, Number 1/2, 45--82.Abstract: The paper investigates the existence of strong global and exponential attractors and their continuity for a class of semilinear wave equations with fractional damping in $\Omega\subset...

Xiaoming Wang, Hao Wu. Source: Advances in Differential Equations, Volume 26, Number 1/2, 1--44.Abstract: We study the Navier-Stokes-Darcy-Boussinesq system that models the thermal convection of a fluid overlying a saturated porous medium in a general decomposed domain. In both two and three...

Luis Pedro Montejano, Luis Núñez-Betancourt. Source: Journal of Commutative Algebra, Volume 12, Number 4, 539--557.Abstract: The [math] -vector [math] of a graph [math] is defined in terms of its clique vector [math] by the equation [math] where [math] is the largest cardinality of a clique in...