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We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of Kátai's orthogonality cri ...
The J-domain proteins (JDP) form the largest protein family among cellular chaperones. In cooperation with the Hsp70 chaperone system, these co-chaperones orchestrate a plethora of distinct functions, including those that help maintain cellular proteostasi ...
The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...
The melanization reaction is a rapid and important immune mechanism in arthropods. It results in the production of melanin at the site of injury and around invading microbes. The enzymes responsible for melanogenesis are phenoloxidases (PO), which catalyze ...
We prove an asymptotic formula for the shifted convolution of the divisor functions d(k)(n) and d(n) with k >= 4, which is uniform in the shift parameter and which has a power saving error term, improving results obtained previously by Fouvry and Tenenbaum ...
Macrophages are a heterogeneous group of cells that are capable of carrying out distinct functions in different tissues, as well as in different locations within a given tissue. Some of these tissue macrophages lie on, or close to, the outer (abluminal) su ...
We compute three-term semiclassical asymptotic expansions of counting functions and Riesz-means of the eigenvalues of the Laplacian on spheres and hemispheres, for both Dirichlet and Neumann boundary conditions. Specifically for Riesz-means we prove upper ...
Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...
Given a level set E of an arbitrary multiplicative function f, we establish, by building on the fundamental work of Frantzikinakis and Host [14, 15], a structure theorem that gives a decomposition of 1E into an almost periodic and a pseudo-random part ...
Precipitation isotope data were used to determine the origin of groundwater in the Badain Jaran Desert (BJD) in the study of Wu et al. (2017). Both precipitation and its isotope composition vary seasonally, so arithmetic averages of precipitation isotope v ...
