Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...

This thesis develops a body of versatile algorithmic techniques. We demonstrate the power and generality of these techniques by applying them to a wide variety of problems. These problems are drawn from such diverse areas of study as computational geometry, VLSI theory, operations research, and molecular biology. The algorithmic techniques described in this thesis are centered around a family o...

the index of matrix a in cn.n is equivalent to the dimension of largest jor-dan block corresponding to the zero eigenvalue of a. in this paper, indicialequations and normal equations for solving inconsistent singular linear systemof equations are investigated.

This paper investigates a restricted version of the Quadratic Assignment Problem (QAP), where one of the coefficient matrices is an Anti-Monge matrix with non-decreasing rows and columns and the other coefficient matrix is a symmetric Toeplitz matrix. This restricted version is called the Anti-Monge–Toeplitz QAP. There are three well-known combinatorial problems that can be modeled via the Anti...

We introduce a convergent finite difference method for solving the optimal transportation problem on sphere. The applies to both traditional squared geodesic cost (arising in mesh generation) and logarithmic reflector antenna design problem). At each point sphere, we replace surface PDE with Generated Jacobian equation posed local tangent plane using normal coordinates. discretization is inspir...

In this paper, we obtain boundary Harnack estimates and comparison theorem for nonnegative solutions to the linearized Monge-Ampère equations under natural assumptions on the domain, Monge-Ampère measures and boundary data. Our results are boundary versions of Caffarelli and Gutiérrez’s interior Harnack inequality for the linearized Monge-Ampère equations. As an application, we obtain sharp upp...

One major change of the future revision of the International System of Units is a new definition of the ampere based on the elementary charge e. Replacing the former definition based on Ampère’s force law will allow one to fully benefit from quantum physics to realize the ampere. However, a quantum realization of the ampere from e, accurate to within 10−8 in relative value and fulfilling tracea...