Left versus right canonical Wiener-Hopf factorization and realization

For an arbitrary rational matrix function, not necessarily analytic at infinity, the existence of a right canonical Wiener-Hopf factorization is characterized in terms of a left canonical Wiener-Hopf factorization. Formulas for the factors in a right factorization are given in terms of the formulas for the factors in a given left factorization. All formulas are based on a special representation of a rational matrix function involving a quintet of matrices.     

An Experimental Investigation into the Acoustic Characteristics of Fluid-filled Porous Structures—A Simplified Model of the Human Skull Cancellous Structure

In nature, shape and structure evolve from the struggle for better performance. Often, biological structures combine multiple beneficial properties, making research into mimicking them very complex. Presented here is a summary of observations from a series of experiments performed on a material that closely resembles the human skull bone’s cancellous structure under acoustic loads. Transmission loss through flat and curved open-cell polyurethane foam samples is observed using air and water as the two interstitial fluids. Reduction in strength and stiffness caused by porosity can be recovered partially by filling the interstitial pores with a fluid. The test findings demonstrate the influence of the interstitial fluid on the mechanical characteristics of a porous structure in a quantitative manner. It is also demonstrated that the transmission loss does not depend only on the mass per unit area of the structure as predicted by acoustic mass law. Current tests also demonstrate that the transmission loss is more sensitive to the interstitial fluid than the shape and support conditions of the structures. Test observations thus support the concepts of “moisture-sensitivity of biological design” and the “law of hierarchy in natural design”.     

Holographic thin-beam reconstruction technique for the study of 3-D refractive-index field

A thin-beam holographic reconstruction technique to study the 3-D refractive index field of a phase object is described. The advantages and drawbacks of this method are discussed.     

Solid-state laser intensity stabilization at the 10(-8) level

A high-power, low-noise photodetector, in conjunction with a current shunt actuator, is used in an ac-coupled servo to stabilize the intensity of a 10-W cw Nd:YAG laser. A relative intensity noise of 1 x 10(-8) Hz(-1/2) at 10 Hz is achieved.     

The evaluation of character Euler double sums

Euler considered sums of the form

Relative Artin motives and the reductive Borel–Serre compactification of a locally symmetric variety

We introduce the notion of Artin motives and cohomological motives over a scheme X. Given a cohomological motive M over X, we consider the universal Artin motive mapping to M and denote it w⁰_X(M)\omega^{0}_{X}(M). We use this to define a motive \mathbbE_X\mathbb{E}_{X} over X which is an invariant of the singularities of X. The first half of the paper is devoted to the study of the functors w⁰_X\omega^{0}_{X} and the computation of the motives \mathbbE_X\mathbb{E}_{X}.     

Detection of activated, TIMP-free MMPs

MMP inhibitor-tethered resins provide a method for detection of activated MMPs in tissues. These measurements will help to elucidate in situ mechanisms of MMP activation, further our understanding of the tumor microenvironment, and facilitate development of MMP-inhibitor therapy.