2D homogeneous turbulence is relevant to geophysical turbulence on large horizontal scales because of the thinness of Earth’s atmosphere and ocean (i.e., H/L 1) and Earth’s rotation (i.e., Ro 1) and stable stratification (i.e., Fr 1), both of which tend to suppress vertical flow and make the 2D horizontal velocity component dominant. A detailed explanation for this involves the theory for geost...

We give a simple proof of Chebotarëv’s theorem: Let p be a prime and ω a primitive pth root of unity. Then all minors of the matrix ( ω ij )p−1 i,j=0 are non-zero. Let p be a prime and ω a primitive pth root of unity. We write Fp for the field with p elements. In 1926, Chebotarëv proved the following theorem (see [3]): Theorem. For any sets I, J ⊆ Fp with equal cardinality, the matrix (ω )i∈I,j...

The Chandra Deep Field-North survey, which has at its center the Hubble Deep Field-North, has reached an exposure of 1 Ms and is now available to the public for analysis. This great astronomical resource will soon be released to the community in the form of a catalog paper with accurate X-ray fluxes in four bands and astrometry good to ≈ 0.6 ′′ –1.2 ′′ over the entire ACIS-I field. The scientif...

We present an integrated study of multi-stage hydraulic fracture stimulation of two parallel horizontal wells in the Bakken formation in the Williston Basin, North Dakota. There are two distinct parts of this study: development of a geomechanical model for the study area, and analysis of the microseismic and hydraulic fracturing data. Despite the limited amount of well log data available, we es...

Jianqing Fan Department of Statistics University of North Carolina Chapel Hill, N.C. 27514 Kernel density estimates are frequently used, based on a second order kernel. Thus, the bias inherent to the estimates has an order of O(h~). In this note, a method of corr~cting the bias in the kernel density estimates is provided, which reduces the bias to a smaller order. Effectively, this method produ...

where Q is an indefinite quadratic form on Z, f(m,n) is a doubly periodic function on Z such that the sums of f(m,n)q over all vertical and all horizontal lines in Z vanish. Some of these series appeared as coefficients in univalued triple Massey products on elliptic curves computed via homological mirror symmetry in [3]. In particular, in this context the condition of vanishing of sums over ve...

where Q is an indefinite quadratic form on Z, f(m,n) is a doubly periodic function on Z such that the sums of f(m,n)q over all vertical and all horizontal lines in Z vanish. Some of these series appeared as coefficients in univalued triple Massey products on elliptic curves computed via homological mirror symmetry in [3]. In particular, in this context the condition of vanishing of sums over ve...

Ultra High Energy (UHE) neutrino Astronomy and relic Neutrino masses may play a key role in solving the Ultra High Energy Cosmic Ray (UHECR) puzzle within the Z-Showering model. Tau air-shower originated by UHE neutrino in matter may probe and amplify this expected UHE neutrino Astronomy. The discover of upcoming and horizontal τ air-showers (UPTAUs, HORTAUs), born by UHE, ντ interacting inside...

Ultra High Energy (UHE) neutrino Astronomy and relic Neutrino masses may play a key role in solving the Ultra High Energy Cosmic Ray (UHECR) puzzle within the Z-Showering model. Tau air-shower originated by UHE neutrino in matter may probe and amplify this expected UHE neutrino Astronomy. The discover of upcoming and horizontal τ air-showers (UPTAUs, HORTAUs), born by UHE, ντ interacting inside...

the normalized full gradient (nfg) method defined by berezkin (1967, 1973 and 1998) is used for downward continuation maps. analytical downward continuation is a method to estimate the field closer to the source and consequently results in a better resolution of underground rock distribution. however, the usefulness of this process is limited by the fact that the operation is extremely sensitiv...