In this note we define geometric classical r-matrices and quantum Rmatrices, and show how any geometric classical r-matrix can be quantized to a geometric quantum R-matrix. This is one of the simplest nontrivial examples of quantization of solutions of the classical Yang-Baxter equation, which can be explicitly computed. The idea of the above quantization was inspired by the results in [ESS]. W...

This paper analyzes an M/M/2 queueing system with two heterogeneous servers. Both servers goes on vacation when there is no customers waiting for service after this server 1 is always available but the other goes on vacation whenever server 2 is idle. The vacationing server however, returns to serve at a low rate as an arrival finds the other server busy. The system is analyzed in the steady st...

Geometric singularities, such as cusps and self-intersecting surfaces, are major obstacles to the accuracy, convergence, and stability of the numerical solution of the Poisson-Boltzmann (PB) equation. In earlier work, an interface technique based PB solver was developed using the matched interface and boundary (MIB) method, which explicitly enforces the flux jump condition at the solvent-solute...

A common approach to improving the spatial resolution of small animal PET scanners is to reduce the size of scintillation crystals and/or employ high resolution pixellated semiconductor detectors. The large number of detector elements results in the system matrix--an essential part of statistical iterative reconstruction algorithms--becoming impractically large. In this paper, we propose a meth...

In the class of systems with linear precoder and zeroforcing (ZF) DFE for zero-padded MIMO frequency selective channels, existing optimal transceiver designs present two major drawbacks. First, the optimal system requires a large number of bits to encode the full precoding matrix. Second, the full precoding matrix leads to complex computations. These disadvantages become more severe as bandwidt...

Computing the fundamental matrix is the first step of many computer vision applications including camera calibration, image rectification and structure from motion. A new method for the estimation of the fundamental matrix from point correspondences is presented. The minimization of the geometric error is performed based Linfinity norm minimization framework. A single global minimum exists and ...

Valiant’s famous determinant versus permanent problem is the flagship problem in algebraic complexity theory. Mulmuley and Sohoni (Siam J Comput 2001, 2008) introduced geometric complexity theory, an approach to study this and related problems via algebraic geometry and representation theory. Their approach works by multiplying the permanent polynomial with a high power of a linear form (a proc...

A new definition is introduced for the matrix geometric mean of a set of k positive definite n×n matrices together with an iterative method for its computation. The iterative method is locally convergent with cubic convergence and requires O(n3k2) arithmetic operations per step whereas the methods based on the symmetrization technique of Ando, Li and Mathias [Linear Algebra Appl., 385 (2004), p...