We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemerédi’s theorem, which asserts that any subset of the integers of positive density contains progressions of arbitrary length. The second, which is the main new ingredient of this paper, is a certain transference principle. This allows us to deduce from Szemerédi’s theo...

We develop a star-network of connections between a central city and peripheral villages and analyze the epidemic dynamics of a vector-borne disease as influenced by daily commuters. We obtain an analytical solution for the global basic reproductive number R0 and investigate its dependence on key parameters for disease control. We find that in a star-network topology the central hub is not alway...

The effect of low concentrations of Fe203, AI203 and Bi203 on the sintering behaviour of (ZrO2)o.83 (YO1.s)o.17, made by alkoxide synthesis, has been investigated. The best results are achieved with Bi203 as a sinter agent and a relative density of 95% is obtained at 1200 K. The effects of these impurities on the electrical conductivity of the bulk and the grain boundaries has been investigated...

We present an experimental investigation of the segmental relaxation behavior of polystyrene (PS) chains that are confined in a micellar core tethered by a poly(acrylic acid) (PAA) block corona on the dry film surface, along with various core density and molecular weight of PS block from below to well above the entanglement molecular weight. The results show that the onset temperature of PS cha...

A density-of-states Monte Carlo method is proposed for simulations of solid-liquid phase equilibria. A modified Wang-Landau density-of-states sampling approach is used to perform a random walk in regions of potential energy and volume relevant to solid-liquid equilibrium. The method provides a direct estimate of the relative density of states [Omega(U,V)] and thus the relative free energy withi...

The U.S. population has been migrating to places with high perceived quality of life. With homothetic preferences, such migration can follow from the increased demand for amenities that accompanies broad-based technological progress. Under the baseline calibration of a general equilibrium model, a place with amenities for which individuals would initially pay five percent of their income grows ...

Well described tools for comparing two populations via their cumulative distribution functions F and F0 are the so-called relative distribution R (t) = F { F−1 0 (t) } and the corresponding relative density (or grade density) r (t). The authors propose a kerneltype estimator for the relative density r (t) in the situation where independent samples of right-censored observations are available fr...

A spore assay was developed to measure the relative density of spores of the nematophagous fungus Hirsutella rhossiliensis in soil. Orchard soil containing H. rhossiliensis-parasitized Criconemella xenoplax was placed in vials and incubated for 0-120 days before the addition of probe nematodes, Heterorhabditis heliothidis juveniles. After 18 hours, H. heliothidis were extracted from the soil an...

Recent developments in additive manufacturing techniques have motivated an increasing number of researchers to study regular porous biomaterials that are based on repeating unit cells. The physical and mechanical properties of such porous biomaterials have therefore received increasing attention during recent years. One of the areas that have revived is analytical study of the mechanical behavi...

The invasive Asian citrus psyllid (Diaphorina citri Kuwayama) is the vector of the bacterial pathogen (‘Candidatus Liberibacter asiaticus’) that is the putative causal agent of citrus greening disease (Huanglongbing disease) in citrus in many areas of the world. The capacity to predict the potential geographic distribution, phenology and relative abundance of the pest and disease is pivotal to ...