We establish a priori error bounds for monotone stabilized finite element discretizations of stationary second-order mean field games (MFG) on Lipschitz polytopal domains. Under suitable hypotheses, we prove that the approximation is asymptotically n...
We prove a rate of convergence for finite element approximations of stationary, second-order mean field games with nondifferentiable Hamiltonians posed in general bounded polytopal Lipschitz domains with strongly monotone running costs. In particular...
We prove that if a compact smooth polarized complex manifold admits in the corresponding Hodge Kähler class a conformally Kähler, Einstein--Maxwell metric, or more generally, a Kähler metric of constant $(ξ, a, p)$-scalar curvature, then this met...
We study the system of equations of motion for inextensible strings. This system possesses many internal symmetries, and is related to discontinuous systems of conservation laws and the total variation wave equation. We prove existence of generalized...
We prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally c...
crushed by a drunk Peter while attempting a unicycle trick to entertain the party guests as "Pee-Pants the Inebriated Hobo Clown". The injuries prove fatal
Ant Colony Optimisation (ACO) is a well known metaheuristic that has proven successful at solving Travelling Salesman Problems (TSP). However, ACO suffers from two issues; the first is that the technique has significant memory requirements for storin...
We describe the topological types of leaves of generic logarithmic foliations on the complex projective plane. We prove that all leaves, except for a finite many are biholomorphic to $\mathbb{C}$ or homeomorphic to the surface known as Loch Ness mons...
Have you experienced a feeling that is bothering you, yet you are not able to recognise the reason? This feeling is your intuition, a feeling your gut gives you. You experience this, as your senses keep developing through experience from life. Such topics are debatable, and scien…
Eclipse Foundation has provided a trusted home for open source collaboration for over 20 years. Our proven vendor-neutral governance helps projects grow, thrive, and deliver real-world impact, and we …
In this note, we prove that the abstract gradient flow introduced by Baird-Fardoun-Regbaoui \cite{BFR}is well-posed on a closed Riemann surface with conical singularity. Long time existence and convergence of the flow are proved under certain assumpt...
Let $G$ be the classical group, and let Hom$(\mathbb{Z}^m,G)$ denote the space of commuting $m$-tuples in $G$. Baird proved that the cohomology of Hom$(\mathbb{Z}^m,G)$ is identified with a certain ring of invariants of the Weyl group of $G$. In this...
Any smooth tropical plane curve contains a distinguished trivalent graph called its skeleton. In 2020 Morrison and Tewari proved that the so-called big face graphs cannot be the skeleta of tropical curves for genus $12$ and greater. In this paper we...
Entanglement is a digraph complexity measure that origins in fixed-point theory. Its purpose is to count the nested depth of cycles in digraphs. In this paper we prove that the class of undirected graphs of entanglement at most $k$, for arbitrary...
Dynamic models, particularly rate-dependent models, have proven effective in capturing the key phenomenological features of frictional processes, whilst also possessing important mathematical properties that facilitate the design of control and estim...
"The road to hell is paved with good intentions" is a proverb or aphorism. A common meaning of the phrase is that wrongdoings or evil actions are often
In 1989, Dicks and Dunwoody proved the Almost Stability Theorem, which has among its corollaries the Stallings-Swan theorem that groups of cohomological dimension one are free. In this article, we use a nestedness result of Bergman, Bowditch, and Dun...
This paper describes a combinatorial way of obtaining all the eigenvalues of the symmetrized shuffling operators introduced by Victor Reiner, Franco Saliola and Volkmar Welker. It allows us to prove their conjecture that these eigenvalues are integer...
...
We prove the three propositions are equivalent: $(a)$ Every Hausdorff continuum has two or more shore points. $(b)$ Every Hausdorff continuum has two or more non-block points. $(c)$ Every Hausdorff continuum is coastal at each point. Thus it is consi...