Pseudo-differential and Fourier series operators on the torus T = (R/2πZ) are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence between toroidal and Euclidean symbols of pseudo-differential operators is established. Periodization of operators and hyperbolic partial differenti...

Gaussian network is known to be an alternative to toroidal network since it has the same number of nodes with less diameter, which makes it perform better than toroidal network. Spanning trees are said to be independent if all trees are rooted at the same node r and for any other node u, the nodes of the paths from r to u in all trees are distinct except the nodes r and u. In this paper, we inv...

2 Derivative Estimates for Rectangular Lattice Topology 4 2.1 Rectangle Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Cylindrical Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Toroidal Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Spherical T...

1 Introduction Let G be simple finite dimensional Lie algebra over complex

In the early Universe matter was crushed to high densities, in a manner similar to that encountered in gravitational collapse to black holes. String theory suggests that the large entropy of black holes can be understood in terms of fractional branes and antibranes. We assume a similar physics for the matter in the early Universe, taking a toroidal compactification and letting branes wrap aroun...

We calculate the semi-inclusive decay rate of an average string state with toroidal compactification in the the superstring theory. We also apply this calculation to a brane-inflation model in a warped geometry and find that the decay rate is greatly suppressed if the final strings are both massive and enhanced for massless radiation.

We study the underlying gauge symmetry algebra of the N = 2 string, which is broken down to a subalgebra in any spacetime background. For given toroidal backgrounds, the unbroken gauge symmetries (corresponding to holomorphic and antiholomorphic worldsheet currents) generate area-preserving diffeomorphism algebras of null 2-tori. A minimal Lie algebraic closure containing all the gauge symmetri...

Muhammad Ajmal 1, Waqas Nazeer 2, Mobeen Munir 2, Shin Min Kang 3,4 and Young Chel Kwun 5,* 1 Department of Mathematics, Government Muhammdan Anglo Orintal College, Lahore 54000, Pakistan; [email protected] 2 Division of Science and Technology, University of Education, Lahore 54000, Pakistan; [email protected] (W.N.); [email protected] (M.M.) 3 Department of Mathematics and Research In...

The authors of [13] have proposed a conjectural construction of mirror symmetry for Calabi-Yau threefolds. They argue from the physics that in a neighbourhood of the large complex structure limit (see [8] for the definition of large complex structure limits), any Calabi-Yau threefold X with a mirror Y should admit a family of supersymmetric toroidal 3-cycles. In mathematical terminology, this s...