Here Dfij = ∂fi/∂zj is the Jacobian matrix of f , J is the Poisson matrix, and I is the n × n identity matrix. Equivalently, Stokes’ theorem can be used to show that the loop action, A[γ] = ∮ γ pdq, is preserved by f for any contractible loop γ on X. If f preserves the loop action for all loops, even those that are not contractible, then it is exact symplectic. When n = 1, the symplectic condit...

We examine the equivalence between the Konishi anomaly equations and the matrix model loop equations in N = 1 gauge theories, the mass deformation of N = 4 supersymmetric Yang-Mills. We perform the superfunctional integral of two adjoint chiral superfields to obtain an effective N = 1 theory of the third adjoint chiral superfield. By choosing an appropriate holomorphic variation, the Konishi an...

In this paper, electromagnetic scattering problems are analyzed using an electric field integral equation (EFIE) formulation that is based on loop-star basis functions so as to avoid low-frequency instability problems. Moreover, to improve the convergence rate of iterative methods, a block matrix preconditioner (BMP) is applied to the EFIE formulation based on loop star-basis functions. Because...

We derive the loop equations for the d-dimensional n-Hermitian matrix model. These are a consequence of the Schwinger-Dyson equations of the model. Moreover we show that in leading order of large N the loop equations form a closed set. In particular we derive the loop equations for the n = 2 matrix model recently proposed to describe the coupling of Two-dimensional quantum gravity to conformal ...

An n× n partial Latin square P is called α-dense if each row and column has at most αn non-empty cells and each symbol occurs at most αn times in P . An n× n array A where each cell contains a subset of {1, . . . , n} is a (βn, βn, βn)-array if each symbol occurs at most βn times in each row and column and each cell contains a set of size at most βn. Combining the notions of completing partial ...

A bstract An improved PV-reduction (Passarino-Veltman) method for one-loop integrals with auxiliary vector R has been proposed in [1, 2]. It also shown that the new is a self-completed [3]. Analytic reduction coefficients can be easily produced by recursion relations this method, where Gram determinant appears denominators. The singularity caused well-known fact and it important to address thes...