One of the most well-known classical results for site percolation on the square lattice is the equation pc + p ∗ c = 1. In words, this equation means that for all values 6= pc of the parameter p, the following holds: either a.s. there is an infinite open cluster or a.s. there is an infinite closed “star” cluster. This result is closely related to the percolation transition being sharp: below pc...

Hybrid assembly lines include multiple assembly technologies, such as RSW (Resistance Spot Welding) and RLW (Remote Laser Welding). The early-stage design of these automotive assembly lines is a critical, multi-objective task. The design process is typically carried out in industry by continuous iterations between the process design department and the simulation and systems engineering departme...

Long time range atmospheric variability has many sources, and nonlinear mode-interactions could play an important role. Our paper sets to explore such internal mechanisms of the long range variability for the rotating shallow water system (RSW), at its lowest spectral resolution (triad), but for long (decadal) time scales, about 10 Coriolis units. A small Rossby-Froude number ε sets multiple ti...

Spherical t-designs on the unit sphere S ⊂ R, introduced by Delsarte, Goethals, and Seidel (1977), are equal weight numerical integration rules that are exact for all polynomials of degree at most t on S. This talk considers the calculation and properties of of spherical t-designs, in particular for S where most applications reside. Bondarenko, Radchenko, and Viazovska (2013) proved that there ...

The Friction Stir Welding process is now 20 years old and the interest in it and its potential continues to increase dramatically. FSW can be applied to a multitude of products with varying material types and thicknesses. However, a continuous weld is not always required to meet the product performance requirements. Thus, one can consider some form of intermittent weld, such as Friction Stir Sp...

Rugose spiraling whitefly (RSW) is one of the major pests which affects coconut trees. It feeds on tree by sucking up water content as well essential nutrients from leaves. also forms sooty mold in leaves due to process photosynthesis inhibited. Biocontrol pest harmless for trees and crops. The experimental results literature reveal that Pseudomallada astur a potential predator this pest. We in...

We develop techniques to study the phase transition for planar Gaussian percolation models that are not (necessarily) positively correlated. These lack property of positive associations (also known as ‘FKG inequality’), and hence many classical arguments in theory do apply. More precisely, we consider a smooth stationary centred field f and, given level ℓ∈R, connectivity properties excursion se...

Methods: The authors conducted a randomized, controlled trial comparing telemedicine case management to usual care, with blinding of those obtaining outcome data, in 1,665 Medicare recipients with diabetes, aged 55 years or greater, and living in federally designated medically underserved areas of New York State. The primary endpoints were HgbA1c, blood pressure, and low-density lipoprotein (LD...