Ju l 2 00 6 Density of non - residues in short intervals

Density of non-residues in Burgess-type intervals and applications

We show that for any fixed ε > 0, there are numbers δ > 0 and p0 > 2 with the following property: for every prime p > p0 and every integer N such that p1/(4 √ e )+ε 6 N 6 p, the sequence 1, 2, . . . , N contains at least δN quadratic non-residues modulo p. We use this result to obtain strong upper bounds on the sizes of the least quadratic non-residues in Beatty and Piatetski–Shapiro sequences....

ar X iv : h ep - t h / 01 04 08 6 v 3 2 8 Ju l 2 00 3 Non Standard Extended Noncommutativity of Coordinates

We present in this short note an idea about a possible extension of the standard noncommutative algebra of coordinates to the formal differential operators framework. In this sense, we develop an analysis and derive an extended noncommutative structure given by [xa, xb]⋆ = i(θ + χ)ab where θab is the standard noncommutativity parameter and χab(x) ≡ χ μ ab(x)∂μ = 1 2(xaθ μ b − xbθ μ a)∂μ is an a...

ar X iv : 0 90 6 . 40 82 v 2 [ m at h . L O ] 2 2 Ju l 2 00 9 Semantic interpolation ∗

We treat interpolation for various logics. In the full non-monotonic case, we connect the existence of interpolants to laws about abstract size, and to generalized Hamming relations. We also mention revision a la Parikh.

Ju l 2 00 4 SHORT INTRODUCTION TO NONSTANDARD ANALYSIS ( to be completed )

qc / 0 50 70 69 v 1 1 6 Ju l 2 00 5 Energy - Momentum Distribution in Weyl Metrics

In this paper, we evaluate energy and momentum density distributions for the Weyl metric by using the well-known prescriptions of Einstein, Landau-Lifshitz, Papaterou and Möller. The metric under consideration is the static axisymmetric vacuum solution to the Einstein field equations and one of the field equations represents the Laplace equation. Curzon metric is the special case of this spacet...