Goldbach’s conjecture in arithmetic progressions: number and size of exceptional prime moduli
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DOI: 10.1007/s00013-016-0993-0
Abstract: Set $${T=N^{\frac{1}{3}-\epsilon}}$$T=N13-ϵ. It is proved that for all but $${\ll TL^{-H},\,H > 0}$$≪TL-H,H>0, exceptional prime numbers $${k\leq T}$$k≤T and almost all integers b1, b2 co-prime to k, almost all integers $${n\sim N}$$n∼N satisfying $${n\equiv b_{1}+b_{2}(mod\,k)}$$n≡b1+b2(modk)… read more here.
Keywords: progressions number; number size; conjecture arithmetic; exceptional prime ... See more keywords
Characterization of particle number size distribution and new particle formation in an urban environment in Lanzhou, China
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DOI: 10.1016/j.jaerosci.2016.10.010
Abstract: Abstract A scanning mobility particle sizer was utilized for the real-time measurement of particles in the size range of 14.6 nm to 661.2 nm from August 14 to November 18, 2014, to characterize the evolution of particle… read more here.
Keywords: mode; particle number; number; particle ... See more keywords
The Relationship of Cloud Number and Size With Their Large‐Scale Environment in Deep Tropical Convection
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DOI: 10.1029/2019gl083964
Abstract: Accurately representing the properties and impact of tropical convection in climate models requires an understanding of the relationships between the state of a convective cloud ensemble and the environment it is embedded in. We investigate… read more here.
Keywords: relationship; tropical convection; number size; environment ... See more keywords