A New Inertia Theorem for Stein Equations,Inertia of Invertible Hermitian Block Toeplitz Matrices and Matrix Orthogonal Polynomials

In this paper we present an inertia result for Stein equations with an indefinite right hand side. This result is applied to establish connnections between the inertia of invertible hermitian block Toeplitz matrices and associated orthogonal polynomials.     

Waves and fracture in an inhomogeneous lattice structure

We analyze a crack propagating in an inhomogeneous rectangular lattice in the state of anti-plane shear. The filtering properties of such a lattice are linked to the energy dissipation due to waves initiated by the crack. The influence of the inhomogeneities within the lattice on the lattice trapping is investigated.     

Using light to bioactivate surfaces: A new way of creating oriented, active immunobiosensors

Ultraviolet light can be used to immobilize biomolecules onto thiol reactive surfaces in order to, e.g., make biosensors. The mechanism involves light-induced formation of free, reactive thiol groups in disulphide containing molecules. This technology allows for the creation of arrays of biomolecules with a high degree of reproducibility, circumventing the need for often expensive nano/micro-dispensing technologies. The ultimate size of the immobilized spots is defined by the focal area of the UV beam. Light-induced immobilization has the added benefit that the immobilized molecules will be spatially oriented and covalently bound to the surface. In this paper, we demonstrate the utility of a sensor array created with the new sensor technology when integrated into a microfluidic system. Protein arrays made using light-induced immobilization showed successful antigen/antibody binding in a flow cell allowing the visualisation of real time binding and enzyme activity. This new technology is ideal for the creation of protein/DNA microarrays, can replace present micro-dispensing arraying technologies and is ideal as a molecular imprinting technology.     

Predicting the event and time horizon of bankruptcy using financial ratios and the maturity schedule of long-term debt

We study the problem of simultaneous and coherent assessment the probability of a firm’s bankruptcy at various time horizons in future. In contrast with usual (one-period) formulations of the problem, such multi-period formulation better matches the nature of bankruptcy process (bankruptcy occurs in time) and allows an easier and more natural incorporation of bankruptcy (default) prognoses in valuation of risky debt and equity, optimization of corporate capital structure etc. The study uses a new mathematical apparatus—multi-alternative decision rules of statistical decision theory. We investigate a new type of predictive variables that can be extracted from the maturity schedule of a firm’s long-term debt. The study develops Bayesian-type forecasting rules that use both maturity schedule factors and traditional financial ratios. These rules noticeably enhance bankruptcy prediction (compared with the familiar one-period Z-score rules of Altman) for bankruptcy within the first 1, 2 or 3 years. Predictive factors derived from schedule information enhance bankruptcy prediction at distant time horizons.     

A novel chelatofore functionalized spiropyran of the 2‐oxaindane series

A novel chelatofore functionalized spiropyran of the 2‐oxaindane series, namely 8‐formyl‐7‐hydroxy‐3′,3′‐dimethylspiro[2H‐chromene‐2,1′(3′H)‐2‐benzofuran], C₁₉H₁₆O₄, is reported. In the crystalline state, dimers are formed as a result of the π–π stacking of aromatic groups of the 2H‐chromene part of the molecule and C—H...O interactions. The C_spiro—O bond length in the pyran ring is 1.4558 (10) Å, which is longer than or equal to the bond length in thermo‐ and photochromic 2‐oxaindane spiropyrans synthesized previously, except for the 7,8‐benzo/6‐NO₂ derivative, in which this bond length is 1.465 (2) Å.     

Cosmological Acceleration from Virtual Gravitons

Intrinsic properties of the space itself and quantum fluctuations of its geometry are sufficient to provide a mechanism for the acceleration of cosmological expansion (dark energy effect). Applying Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy approach to self-consistent equations of one-loop quantum gravity, we found exact solutions that yield acceleration. The permanent creation and annihilation of virtual gravitons is not in exact balance because of the expansion of the Universe. The excess energy comes from the spontaneous process of graviton creation and is trapped by the background. It provides the macroscopic quantum effect of cosmic acceleration.     

Cotunnite-Structured Titanium Dioxide and the Hardest known Oxide

Combined theoretical and experimental investigations led to the discovery of a new polymorph of titanium dioxide with titanium nine-coordinated to oxygen in the cotunnite (PbCl 2 ) structure. Hardness measurements on the cotunnite-structured TiO 2 synthesized at pressures above 60 GPa and temperatures above 1000 K reveal that this material is the hardest oxide yet discovered. Furthermore, it is one of the least compressible (with a measured bulk modulus of 431 GPa) and hardest (with a microhardness of 38 GPa) polycrystalline materials studied thus far.