Squares of primes and powers of 2, II

We prove that the density of integers ≡2 (mod 24), which can be represented as the sum of two squares of primes and k powers of 4, tends to 1 as k→∞ in the sequence k≡0 (mod 3). Consequently, there exists a positive integer k0 such that every large integer ≡4 (mod 24) is the sum of four squares of primes and k0 powers of 4postprin

Large-eddy simulation of turbulent flows and pollutant transport inside and above idealized urban street canyons under different unstable thermal stratification

Large-eddy simulation (LES) is employed to study the behaviours of flows and pollutant transport inside and over idealized urban street canyons under different unstable thermal stratification. Three configurations of idealized street canyon, consisting of building-height-to-street-width (aspect) ratios, 0.5, 1 and 2, are considered. Under unstable stratification, the vertical profiles of streamwise velocity and temperature over the bottom rough surface are more uniform and the turbulent transport of momentum and heat are enhanced. Inside the street canyons, the ventilation performance, which are characterized by the air exchange rate (ACH), pollutant exchange rate (PCH), pollutant retention time and average pollutant concentration, is found improved in unstable stratification.postprin

Numerical modeling of flows and pollutant dispersion within and above urban street canyons under unstable thermal stratification by large-eddy simulation

Recently, with the ever increasing urban areas in developing countries, the problem of air pollution due to vehicular exhaust arouses the concern of different groups of people. Understanding how different factors, such as urban morphology, meteorological conditions and human activities, affect the characteristics of street canyon ventilation, pollutant dispersion above urban areas and pollutant re-entrainment from the shear layer can help us improve air pollution control strategies. Among the factors mentioned above, thermal stratification is a significant one determining the pollutant transport behaviors in certain situation, e.g. when the urban surface is heated by strong solar radiation, which, however, is still not widely explored. The objective of this study is to gain an in-depth understanding of the effects of unstable thermal stratification on the flows and pollutant dispersion within and above urban street canyons through numerical modeling using large-...published_or_final_versio

On exceptional sets for numbers representable by binary sums

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A numerical bound for small prime solutions of some ternary linear equations

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Conditional bounds for small prime solutions of linear equations

Let a 1, a 2, a 3 be non-zero integers with gcd(a 1 a 2, a 3)=1 and let b be an arbitrary integer satisfying gcd (b, a i, a j) =1 for i≠j and b≡a 1+a 2+a 3 (mod 2). In a previous paper [3] which completely settled a problem of A. Baker, the 2nd and 3rd authors proved that if a 1, a 2, a 3 are not all of the same sign, then the equation a 1 p 1+a 2 p 2+a 3 p 3=b has a solution in primes p j satisfying {Mathematical expression} where A>0 is an absolute constant. In this paper, under the Generalized Riemann Hypothesis, the authors obtain a more precise bound for the solutions p j . In particular they obtain A0. An immediate consquence of the main result is that the Linnik's courtant is less than or equal to 2. © 1992 Springer-Verlag.postprin

Upper bounds on n-dimensional Kloosterman sums

Let pm be any prime power and Kn(a,pm) be the Kloosterman sum , where the xi are restricted to values not divisible by p. Let m,n be positive integers with m2 and suppose that pγ||(n+1). We obtain the upper bound |Kn(a,pm)|(n+1,p−1)p1/2min(γ,m−2)pmn/2, for odd p. For p=2 we obtain the same bound, with an extra factor of 2 inserted.postprin

Rectifiability of Optimal Transportation Plans

The purpose of this note is to show that the solution to the Kantorovich optimal transportation problem is supported on a Lipschitz manifold, provided the cost is $C^{2}$ with non-singular mixed second derivative. We use this result to provide a simple proof that solutions to Monge's optimal transportation problem satisfy a change of variables equation almost everywhere

TGFβ1 single-nucleotide polymorphism C-509T alters mucosal cell function in pediatric eosinophilic esophagitis.

Eosinophilic esophagitis (EoE) is a chronic Th2 antigen-driven disorder associated with tissue remodeling. Inflammation and remodeling lead to esophageal rigidity, strictures, and dysphagia. TGFβ1 drives esophageal remodeling including epithelial barrier dysfunction and subepithelial fibrosis. A functional SNP in the TGFβ1 gene that increases its transcription (C-509T) is associated with elevated numbers of esophageal TGFβ1-expressing cells. We utilized esophageal biopsies and fibroblasts from TT-genotype EoE children to understand if TGFβ1 influenced fibroblast and epithelial cell function in vivo. Genotype TT EoE esophageal fibroblasts had higher baseline TGFβ1, collagen1α1, periostin, and MMP2 (p < 0.05) gene expression and distinct contractile properties compared with CC genotype (n = 6 subjects per genotype). In vitro TGFβ1 exposure caused greater induction of target gene expression in genotype CC fibroblasts (p < 0.05). Esophageal biopsies from TT-genotype subjects had significantly less epithelial membrane-bound E-cadherin (p < 0.01) and wider cluster distribution at nanometer resolution. TGFβ1 treatment of stratified primary human esophageal epithelial cells and spheroids disrupted transepithelial resistance (p < 0.001) and E-cadherin localization (p < 0.0001). A TGFβ1-receptor-I inhibitor improved TGFβ1-mediated E-cadherin mislocalization. These data suggest that EoE severity can depend on genotypic differences that increase in vivo exposure to TGFβ1. TGFβ1 inhibition may be a useful therapy in subsets of EoE patients

Scalable Bandwidth and High-Precision Spectral Measurement by Frequency Chirped Comb

A cost-effective scan technique enabling scalable measurement range is presented by injecting a sweep RF signal of 27.5-30 GHz into an electro-optic comb generator. The 10th-order harmonic scans over an extended span (275-300 GHz) where an ultra-narrow (Q >106) resonance is well-resolved with sub-MHz resolution