The effects of corona treatment on impact and spreading of ink-jet drops on a polymeric film substrate

The effects of varying corona surface treatment on ink drop impact and spreading on a polymer substrate have been investigated. The surface energy of substrates treated with different levels of corona was determined from static contact angle measurement by the Owens and Wendt method. A drop-on-demand print-head was used to eject 38 μm diameter drops of UV-curable graphics ink travelling at 2.7 m/s on to a flat polymer substrate. The kinematic impact phase was imaged with a high speed camera at 500k frames per second, while the spreading phase was imaged at 20k frames per secoiui. The resultant images were analyzed to track the changes in the drop diameter during the different phases of drop spreading. Further experiments were carried out with white-light intetferometry to accurately measure the final diameter of drops which had been printed on different corona treated substrates and UV cured. The results are correlated to characterize the effects of corona treatment on drop impact behavior and final print quality.

On diagonal-Schur complements of block diagonally dominant matrices

It is known that the diagonal-Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices [J.Z. Liu, Y.Q. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365-380], and the same is true for nonsingular H-matrices [J.Z. Liu, J.C. Li, Z.T. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Algebra Appl. 428 (2008) 1009-1030]. In this paper, we research the properties on diagonal-Schur complements of block diagonally dominant matrices and prove that the diagonal-Schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices, and the same holds for generalized block strictly diagonally dominant matrices. (C) 2010 Elsevier Inc. All rights reserved.

Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q(B circle A(-1)) for the Hadamard product of A(-1) and B, and a lower bound on the minimum eigenvalue q(A star B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius rho(A circle B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B. (C) 2009 Elsevier Inc. All rights reserved.

Regenerative polymeric bus architecture for board-level optical interconnects

A scalable multi-channel optical regenerative bus architecture based on the use of polymer waveguides is presented for the first time. The architecture offers high-speed interconnection between electrical cards allowing regenerative bus extension with multiple segments and therefore connection of an arbitrary number of cards onto the bus. In a proof-ofprinciple demonstration, a 4-channel 3-card polymeric bus module is designed and fabricated on standard FR4 substrates. Low insertion losses (≤ -15 dB) and low crosstalk values (< -30 dB) are achieved for the fabricated samples while better than ± 6 μm -1 dB alignment tolerances are obtained. 10 Gb/s data communication with a bit-error-rate (BER) lower than 10-12 is demonstrated for the first time between card interfaces on two different bus modules using a prototype 3R regenerator. © 2012 Optical Society of America.

A polymeric regenerative optical bus for board-level optical interconnections

A scalable polymer waveguide-based regenerative optical bus architecture for use in board-level communications is presented. As a proof-of-principle demonstration, a 4-channel polymer bus formed on a FR4 substrate providing 10 Gb/s/channel data transmission is reported. © 2012 OSA.

4-Channel polymeric optical bus module for board-level optical interconnections

A 4-channel polymeric optical bus module suitable for use in board-level interconnections is presented. Low-loss and low-crosstalk module performance is achieved, while -1 dB alignment tolerances better than ± 8 μm are demonstrated. © 2012 OSA.

Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.

Regression on fixed-rank positive semidefinite matrices: A Riemannian approach

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixedrank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks. © 2011 Gilles Meyer, Silvere Bonnabel and Rodolphe Sepulchre.

Low-rank optimization on the cone of positive semidefinite matrices

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y Y T leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second-order optimization method with guaranteed quadratic convergence. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. In contrast to existing methods, the proposed algorithm converges monotonically to the sought solution. Its numerical efficiency is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. © 2010 Society for Industrial and Applied Mathematics.

Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.