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In this section and in section 2 and 3 we will generalize the summation rule obtained by L.C. Hsu [7], involving Stirling numbers of the second kind. Given four real numbers a, b, α and β with α 6= 0 and β 6= 0, L.C. Hsu and H.Q. Yu [11], L.C. Hsu and P.J. Shiue [9] defined the symmetric Stirling-type pairs (〈a, b, α, β〉pairs, for short) {s, s} = {s(n, k), s(n, k)} = {s(n, k, a, b;α, β), s(n, k...
We first give a brief introduction to the field of property testing. Section 3 gives upper bounds for the canonical property of “monotonicity testing,” and Section 4 shows how to derive property testing lower bounds from communication complexity lower bounds. We won’t need to develop any new communication complexity; our existing toolbox (specifically, Disjointness) is already rich enough to de...
We show a lower estimate of the Milnor number of an isolated hypersurface singularity, via its Newton number. We also obtain analogous estimate of the Milnor number of an isolated singularity of a similar complete intersection variety. Introduction We study the Newton number of a polyhedron in order to calculate the Milnor number of an isolated singularity defined by an analytic mapping. Sectio...
In a comment to Dahlberg, Edmark and Lundqvist (2012), Nekby and Pettersson-Lidbom (2012) argue (i) that the refugee placement program should be measured with contracted rather than actually placed refugees, and claim that the correlation between the two measures is insignificant and close to zero; (ii) that instead of using the rotating individual panel, we should have used the full cross-sect...
This paper explores the possibility of estimating smallscale vector wind fields from SAR data by applying certain dynamical constraints to the wind field. The method is illustrated for the case of a diverging surface flow field that is intended to represent a precipitationinduced downdraft. A simulated radar cross section map generated from this flow field is used to reconstruct the wind field ...
The hierarchy problem can be addressed by extending the four-dimensional space-time to include an extra compact spatial dimension with non-trivial “warped” metric, as first suggested by Randall and Sundrum. If the Randall-Sundrum framework is realized in string theory, the effective value of the string scale in the vicinity of the infrared boundary should be in the TeV domain. The most attracti...
The distorted wave Born approximation ~DWBA! method has been successfully used in modeling the acoustic backscattering by weakly scattering zooplankton @Stanton et al., J. Acoust. Soc. Am. 94, 3463–3472 ~1993!, Wiebe et al., IEEE J. Ocean. Eng. 22~3!, 445–464 ~1997!#. However, the previously developed DWBA model ignores the imaginary part of the scattering amplitude and thus results in a zero-e...
We develop a systematic treatment for the quasi-zero modes, which play an important role in nonabelian gauge theories. It can be used to derive the analytic forms for the constrained instantons in the Yang-Mills-Higgs theory. This will automatically sum up contributions to all orders in ρ, the instanton size. We also give the analytic expressions for the instanton-antiinstanton pair, with an ar...
Azimuthal asymmetries in exclusive electroproduction of a real photon from a longitudinally polarized deuterium target are measured with respect to target polarization alone and with respect to target polarization combined with beam helicity and/or beam charge. The asymmetries appear in the distribution of the real photons in the azimuthal angle φ around the virtual photon direction, relative t...
We present new results for the jet-veto efficiency and zero-jet cross section in Higgs production through gluon fusion. We incorporate the N3LO corrections to the total cross section, the NNLO corrections to the 1-jet rate, NNLL resummation for the jet pt and LL resummation for the jet radius dependence. Our results include known finite-mass corrections and are obtained using the jet-veto effic...
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