We use generalized power series to construct algebraically a nonstandard model of the theory of the real eld with exponentiation. This model enables us to show the undeenability of the zeta function and certain non-elementary and improper integrals. We also use this model to answer a question of Hardy by showing that the compositional inverse to the function (log x)(log log x) is not asymptotic...

The group theory of the spontaneous breaking of SU(N) is explored. Two specific cases are analyzed in detail: (i) SU(N) is broken to SO(N) via a scalar field vacuum expectation value for a second-rank symmetric tensor multiplet, and (ii) SU(2N) or SU(2N +1) is broken to Sp(2N) via a scalar field vacuum expectation value for a secondrank antisymmetric tensor multiplet. The case of the spontaneou...

1,0 h representing (1+1) geometry, and ~ 1/50,000 in magnitude to 3,0 h of (3+1) geometry. The non vanishing of the 1,0 h term representing (1+1) geometry contravenes predictions of no relic gravitational waves and makes predictions if the prior universe was a single event a la Steinhardt or a multiverse in the form suggested by Tegmark. I.e. change in the application of 0 φ ≅ && of inflation. ...

This paper aims to provide the first investigation of the productivity effect of outsourcing by using the Korean industry data at the three-digit ISIC level. We find that there are positive productivity gains from material outsourcing. The impact of material outsourcing increases when we account for the share of imports from China. This is due to the growth of Chinese exports to Korea over the ...

Using the differential geometry of curves and surfaces, the L-equivalent soliton equations of the some (2+1)-dimensional integrable spin systems are found. These equations include the modified Novikov-Veselov, Kadomtsev-Petviashvili, Nizhnik-Novikov-Veselov and other equations. Some aspects of the connection between geometry and multidimensional soliton equations are discussed.

Alexander Larin 1,2, Phillip C. Womble 1 and Vladimir Dobrokhotov 3,* 1 VAON LLC, KY, USA, 2200 Lapsley Lane, Bowling Green, KY 42103, USA; [email protected] (A.L.); [email protected] (P.C.W.) 2 Department of Physics and Astronomy, University of Louisville, Louisville, KY 40292, USA 3 Applied Physics Institute, Western Kentucky University, Bowling Green, KY 42101, USA * Correspon...

Correlation functions of the global E 8 symmetry currents in the Heterotic 5-brane theory. We consider the 5-brane placed at one end of the world in the Heterotic E 8 × E 8 theory. The low energy theory is a 6 dimensional (1, 0) superconformal theory with E 8 as a global symmetry. We calculate the two-point correlator of the E 8 current in 6 dimensions and in 4 dimensions after compactification...