We show the existence of D = 4 nonabelian solutions approaching asymptotically a dilatonic Melvin spacetime background. An exact solution generalizing the Chamseddine-Volkov soliton for a nonzero external U(1) magnetic field is also reported.

Interest in the heavy fermion metals has motivated us to examine the quantum phases and their Fermi surfaces within the Kondo lattice model. We demonstrate that the model is soluble asymptotically exactly in any dimension d>1, when the Kondo coupling is small compared with the RKKY interaction and in the presence of antiferromagnetic ordering. We show that the Kondo coupling is exactly marginal...

Using geometric engineering in the context of type II strings, we obtain exact solutions for the moduli space of the Coulomb branch of all N = 2 gauge theories in four dimensions involving products of SU gauge groups with arbitrary number of bi-fundamental matter for chosen pairs, as well as an arbitrary number of fundamental matter for each factor. Asymptotic freedom restricts the possibilitie...

The conformal-gauge two-dimensional quantum gravity is formulated in the framework of the BRS quantization and solved completely in the Heisenberg picture: All n-point Wightman functions are explicitly obtained. The eld-equation anomaly is shown to exist as in other gauges, but there is no other subtlety. At the critical dimension D = 26 of the bosonic string, the eld-equation anomaly is shown ...

A five-dimensional solution to Einstein’s equations coupled to a scalar field has been proposed as a partial solution to the cosmological constant problem: the effect of arbitrary vacuum energy (tension) of a 3-brane is cancelled; however, the scalar field becomes singular at some finite proper distance in the extra dimension. We show that in the original model with a vanishing bulk potential f...

This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation ct+∇·(uf(c))−∇·(D∇c)+λc = 0. The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L-norm, independent of the diffusion parameter D. The resulting a posteriori error estimate is used to de...