A discrete-adjoint formulation is presented for the three-dimensional Euler equations discretized on a Cartesian mesh with embedded boundaries. The solution algorithm for the adjoint and flow-sensitivity equations leverages the Runge–Kutta time-marching scheme in conjunction with the parallel multigrid method of the flow solver. The matrix-vector products associated with the linearization of th...

We propose gauging matrix models of string theory to eliminate unwanted non-singlet states. To this end we perform a discretised light-cone quantisation of large N gauge theory in 1+1 dimensions, with scalar or fermionic matter fields transforming in the adjoint representation of SU(N). The entire spectrum consists of bosonic and fermionic closed-string excitations, which are free as N → ∞. We ...

We introduce a matrix continued fraction associated with the first-order linear recurrence system Yk = θkYk−1. A Pincherle type convergence theorem is proved. We show that the n-th order linear recurrence relation and previous generalizations of ordinary continued fractions form a special case. We give an application for the numerical computation of a non-dominant solution and discuss special c...

We study the relationship between the eigenvalues of separated self-adjoint boundary conditions and coupled self-adjoint conditions. Given an arbitrary real coupled boundary condition determined by a coupling matrix K we construct a one parameter family of separated conditions and show that all the eigenvalues for K and −K are extrema of the eigencurves of this family. This characterization mak...

Given a self-adjoint operator H 0 , a self-adjoint trace class operator V and a fixed Hilbert-Schmidt operator F with trivial kernel and co-kernel, using limiting absorption principle an explicit set of full Lebesgue measure Λ(H 0 , F) ⊂ R is defined, such that for all points of this set the wave and the scattering matrices can be defined unambiguously. Many well-known properties of the wave an...

We study the large-N limit of adjoint fermion one-matrix models. We find one-cut solutions of the loop equations for the correlators of these models and show that they exhibit third order phase transitions associated with m-th order multi-critical points with string susceptibility exponents γstr = −1/m. We also find critical points which can be interpreted as points of first order phase transit...

This paper introduces and analyzes a new parallel-in-time gradient type method for the solution of convex linear-quadratic discrete-time optimal control (DTOC) problems. Each iteration of the classical gradient method requires the solution of the forward-in-time state equation followed by the solution of the backward-in-time adjoint equation to compute the gradient. To introduce parallelism, th...

The purpose of this paper is an optimal control problem of temperature using the Newton based method and the finite element method. This method is based on the first and second order adjoint technique allowing to obtained a better approximation to the Newton line search direction. The formulation is based on the optimal control theory in which the performance function is expressed by the comput...

In the scattering theory framework, we consider a pair of operators H0, H. For a continuous function φ vanishing at infinity, we set φδ(·) = φ(·/δ) and study the spectrum of the difference φδ(H − λ)− φδ(H0 − λ) for δ → 0. We prove that if λ is in the absolutely continuous spectrum of H0 and H, then the spectrum of this difference converges to a set that can be explicitly described in terms of (...

Motivated by the symmetric version of matrix multiplication we study the plethysm $S^k(\mathfrak{sl}_n)$ of the adjoint representation $\mathfrak{sl}_n$ of the Lie group $SL_n$. In particular, we describe the decomposition of this representation into irreducible components for $k=3$, and find highest weight vectors for all irreducible components. Relations to fast matrix multiplication, in part...