First, we build a computational procedure to reconstruct the convex body from a pre-given surface area measure. Nontrivially, we prove the convergence of this procedure. Then, the sufficient and necessary conditions of a Sobolev binary function to be a…
We use tools from free probability to study the spectra of Hermitian operators on infinite graphs. Special attention is devoted to universal covering trees of finite graphs. For operators on these graphs, we derive a new variational formula for the spe…
In the past years, the enumeration of plane lattice walks confined to a convex cone—normalized into the first quadrant—has received a lot of attention, stimulated the development of several original approaches, and led to a rich collection of results….
In this paper, we study the images of multilinear graded polynomials on the graded algebra of upper triangular matrices . For positive integers , we classify these images on endowed with a particular elementary -grading. As a consequence, we obtain th…
In Kiukas, Lahti, and Ylinen (2006, Journal of Mathematical Physics 47, 072104), the authors asked the following general question. When is a positive operator measure projection valued? A version of this question formulated in terms of operator moments…
In this paper, we considered the global strong solution to the 3D incompressible micropolar equations with fractional partial dissipation. Whether or not the classical solution to the 3D Navier–Stokes equations can develop finite-time singularity remai…
Hardin and Taylor proved that any function on the reals—even a nowhere continuous one—can be correctly predicted, based solely on its past behavior, at almost every point in time. They showed that one could even arrange for the predictors to be robust …
In this paper, we compute the Fourier expansion of the Shintani lift of nearly holomorphic modular forms. As an application, we deduce modularity properties of generating series of cycle integrals of nearly holomorphic modular forms.