An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth.

We present an algorithm for the approximation of bivariate functions by “low-rank splines”, that is, sums of outer products of univariate splines. Our approach is motivated by the Adaptive Cross Approximation (ACA) algorithm for low-rank matrix approximation as well as the use of low-rank function approximation in the recent extension of the chebfun package to two dimensions. We show that our p...

Let G be a finite group having an order preserving and rank preserving action on a finite ranked poset P. Let P/G denote the quotient poset. A well known result in algebraic Sperner theory asserts that an order raising G-linear map on V (P) (the complex vector space with P as basis) satisfying the full rank property induces an order raising linear map on V (P/G), also satisfying the full rank p...

The goal of an estimator is to approximate the unknown distribution of the language from its partial evidence. In this thesis, a rank consistent estimator is defined as an estimator that preserves the ranking frequencies of all the full parse trees in the treebank proved to be rank consistent with respect to the training treebank. The rank consistency property adopts Laplace’s Principle of Insu...

We provide the degrees of freedom (DoF) characterization for the 3-user MT×MR multiple-input multiple-output (MIMO) interference channel (IC) with rank-deficient channel matrices, where each transmitter is equipped with MT antennas and each receiver with MR antennas, and the interfering channel matrices from each transmitter to the other two receivers are of ranks D1 and D2, respectively. One i...

Array processing is an area of study devoted to processing the signals received from an antenna array and extracting information of interest. It has played an important role in widespread applications like radar, sonar, and wireless communications. Numerous adaptive array processing algorithms have been reported in the literature in the last several decades. These algorithms, in a general view,...

In this paper we study the structure of standard Einstein solvmanifolds of arbitrary rank. Also the validity of a variational method for finding standard Einstein solvmanifolds is proved.

Let Γ be a finitely generated, torsion-free, two step nilpotent group. Let C(Γ) be the universal C∗-algebra of Γ. We show that acsr(C∗(Γ)) = acsr(C((Γ̂)1), where for a unital C∗-algebra A, acsr(A) is the absolute connected stable rank of A, and where (Γ̂)1 is the space of one-dimensional representations of Γ. For the case of stable rank, we have close results. In the process, we give a stable ran...