Lower bounds for polynomials with algebraic coefficients

We give a method, based on algebraic geometry, to show lower bounds for the complexity of polynomials with algebraic coefficients. Typical examples are polynomials with coefficients which are roots of unity, such as

$\text{Σ}\text{j=1}\text{d}\text{e}{}^{\mathrm{<mtext>2\pi i</mtext><mtext>i</mtext>}}\text{X}{}^{\mathrm{i}}$

and

$\text{Σ}\text{j=i}\text{d}\text{e}{}^{\mathrm{<mtext>2\pi i</mtext><mtext>pi</mtext>}}\text{X}{}^{\mathrm{j}}$

where p_j is the jth prime number.We apply the method also to systems of linear equations.     

A New Reference Material and Safe Sampling of Terrorists Peroxide Explosives by a Non‐Volatile Matrix

Highly sensitive peroxide based explosives can be dissolved in ionic liquids for a safe handling. These solutions are easy to use and may be applied as powerful odor sources for analytical testing and training purposes. Moreover, the stabilizing effect of the ionic liquids can be exploited for a safe sampling of large quantities of these explosives. Such samples of triacetone triperoxide are long‐term stable, safe, and valid for forensic evaluations.     

Asymptotic reflection of linear water waves by submerged horizontal porous plates

On the basis of linear water-wave theory, an explicit expression is presented for the reflection coefficient R ^?? when a plane wave is obliquely incident upon a semi-infinite porous plate in water of finite depth. The expression, which correctly models the singularity in velocity at the edge of the plate, does not rely on knowledge of any of the complex-valued eigenvalues or corresponding vertical eigenfunctions in the region occupied by the plate. The solution R ^?? is the asymptotic limit of the reflection coefficient R as a ?? ??, for a plate of finite length a bounded by a rigid vertical wall, and forms the basis of a rapidly convergent expansion for R over a wide range of values of a. The special case of normal incidence is relevant to the design of submerged wave absorbers in a narrow wave tank. Modifications necessary to account for a finite submerged porous plate in a fluid extending to infinity in both horizontal directions are discussed.     

Cell Force-Driven Basement Membrane Disruption Fuels EGF- and Stiffness-Induced Invasive Cell Dissemination from Benign Breast Gland Acini

Local basement membrane (BM) disruption marks the initial step of breast cancer invasion. The activation mechanisms of force-driven BM-weakening remain elusive. We studied the mechanical response of MCF10A-derived human breast cell acini with BMs of tuneable maturation to physical and soluble tumour-like extracellular matrix (ECM) cues. Traction force microscopy (TFM) and elastic resonator interference stress microscopy (ERISM) were used to quantify pro-invasive BM stress and protrusive forces. Substrate stiffening and mechanically impaired BM scaffolds induced the invasive transition of benign acini synergistically. Robust BM scaffolds attenuated this invasive response. Additional oncogenic EGFR activation compromised the BMs’ barrier function, fuelling invasion speed and incidence. Mechanistically, EGFR-PI3-Kinase downstream signalling modulated both MMP- and force-driven BM-weakening processes. We show that breast acini form non-proteolytic and BM-piercing filopodia for continuous matrix mechanosensation, which significantly push and pull on the BM and ECM under pro-invasive conditions. Invasion-triggered acini further shear and compress their BM by contractility-based stresses that were significantly increased (3.7-fold) compared to non-invasive conditions. Overall, the highest amplitudes of protrusive and contractile forces accompanied the highest invasiveness. This work provides a mechanistic concept for tumour ECM-induced mechanically misbalanced breast glands fuelling force-driven BM disruption. Finally, this could facilitate early cell dissemination from pre-invasive lesions to metastasize eventually.     

Limitations of the Tauc Plot Method

The Tauc plot is a method originally developed to derive the optical gap of amorphous semiconductors such as amorphous germanium or silicon. By measuring the absorption coefficient α(hν) and plotting ${(\alpha hv)}^{\frac{1}{2}}$ versus photon energy hν, a value for the optical gap (Tauc gap) is determined. In this way non-direct optical transitions between approximately parabolic bands can be examined. In the last decades, a modification of this method for (poly-) crystalline semiconductors has become popular to study direct and indirect interband transitions. For this purpose, (ahν)ⁿ (n = $\frac{1}{2}$, 2) is plotted against hν to determine a value of the electronic bandgap. Due to the ease of performing UV–vis measurements, this method has nowadays become a standard to analyze various (poly-) crystalline solids, regardless of their different electronic structure. Although this leads partially to widely varying values of the respective bandgap of nominally identical materials, there is still no study that critically questions which peculiarities in the electronic structure prevent a use of the Tauc plot for (poly-) crystalline solids and to which material classes this applies. This study aims to close this gap by discussing the Tauc plot and its limiting factors for exemplary (poly-) crystalline solids with different electronic structures.     

Mechanische Eigenschaften stärkegefüllter Polymerverbunde

Mechanical Properties of Starch-filled Polymercompounds. In continuation of the investigations described in [10] important mechanical properties of native potato, maize and wheat starch granules have been determined. With these results and under precondition of a sufficient interfacial quality the resulting mechanical properties of the composites reinforced with starch granules could become predicted theoretically. These theoretically calculated mechanical parameters have been verified by tensile tests of the different composite materials. For evaluation of the interfacial quality a model for failure of unidirectional reinforced materials has been used, applied to the investigated particle reinforced composites and discussed in detail on the background of a few choosen, biodegradable composites. The results of the investigations certified that the mechanical properties of the matrix materials could become partly improved by their reinforcement with starch granules. At the same time the final costs of the composite materials could be reduced in consequence of the low costs of nativ starch of about 1 DM/kg and the degradation behaviour could also have been accelerated by an increasing amount of starch. The maximum amount of starch has been limited to 40wt-%. Up to this filling ratio the examined materials allowed processing almost without complications.