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Building upon previous works by Young, Chernov-Zhang and Bruin-Melbourne-Terhesiu, we present a general scheme to improve bounds on the statistical properties (in particular, decay of correlations, and rates in the almost sure invariant…
In this paper, we demonstrate the existence of positive solutions for certain weakly coupled elliptic systems of sublinear growth under homogeneous Dirichlet boundary conditions. Our findings generalize existing results related to sublinear…
We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example.…
We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…
We show that the symmetry algebra of the $SL(2,R)_{k}/U(1)$ coset model is a non-linear deformation of $W_{\infty}$, characterized by $k$. This is a universal $W$-algebra which linearizes in the large $k$ limit and truncates to $W_{N}$ for…
The Su-Schrieffer-Heeger model is extended to the three and higher dimensional systems. Nearly or absolutely flat midgap surface and hypersurface bands are predicted based on the topological analysis, which do not require fine tuning of…
A well-known theorem of Lax and Wendroff states that if the sequence of approximate solutions to a system of hyperbolic conservation laws generated by a conservative consistent numerical scheme converges boundedly a.e. as the mesh parameter…
Lowest bound S-state energy of Coulomb three-body systems ($N^{Z+}\mu^-e^-$) having a positively charged nucleus of charge number Z ($N^{Z+}$), a negatively charged muon ($\mu^-$) and an electron ($e^-$), is investigated in the framework of…
We propose a novel construction of finite hypergraphs and relational structures that is based on reduced products with Cayley graphs of groupoids. To this end we construct groupoids whose Cayley graphs have large girth not just in the usual…
We study the mixed topological / holomorphic Chern-Simons theory of Costello, Witten and Yamazaki on an orbifold $(\Sigma\times{\mathbb C})/{\mathbb Z}_2$, obtaining a description of lattice integrable systems in the presence of a boundary.…
A new approximation formalism is applied to study the bound states of the Hellmann potential, which represents the superposition of the attractive Coulomb potential $-a/r$ and the Yukawa potential $b\exp (-\delta r)/r$ of arbitrary strength…
For any (possibly singular) hyperelliptic curve, we give the definition of a hyperelliptic refined spectral curve and the hyperelliptic refined topological recursion, generalising the formulation for a special class of genus-zero curves by…
The structure of Hamiltonian reductions of the Wess-Zumino-Novikov-Witten (WZNW) theory by first class Kac-Moody constraints is analyzed in detail. Lie algebraic conditions are given for ensuring the presence of exact integrability,…
We show that a Kleinian surface group, or hyperbolic 3-manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection of coefficients that depend…
We develop a new nonlinear method to model structure formation in general relativity from a generalization of the relativistic Lagrangian perturbation schemes, controlled by Szekeres (and LTB) exact solutions. The overall approach can be…
Finite quantum field theories may be constructed from the most general renormalizable quantum field theory by forbidding, order by order in the perturbative loop expansion, all ultraviolet-divergent renormalizations of the physical…
We shall describe a new construction of equilibrium states for a class of partially hyperbolic systems. This generalises our construction for Gibbs measures in the uniformly hyperbolic setting. This more general setting introduces new…
In this work, we leverage the Hamiltonian kind structure for accurate uncertainty propagation through a nonlinear dynamical system. The developed approach utilizes the fact that the stationary probability density function is purely a…
We investigate the low density limit of the Homogeneous Electron system, often called the {\it Strictly Correlated} regime. We begin with a systematic presentation of the expansion around infinite $r_S$, based on the first quantized…
We study fine P\'olya-Szeg\H{o} rearrangement inequalities into weighted intervals for Sobolev functions and functions of bounded variation defined on metric measure spaces supporting an isoperimetric inequality. We then specialize this…