Diffraction of compatible random substitutions in one dimension

As a guiding example, the diffraction measure of a random local mixture of the two classic Fibonacci substitutions is determined and reanalysed via self-similar measures of Hutchinson type, defined by a finite family of contractions. Our revised approach yields explicit formulas for the pure point and the absolutely continuous parts, as well as a proof for the absence of singular continuous components. This approach is then extended to the family of random noble means substitutions and, as an example with an underlying 2-adic structure, to a locally randomised version of the period doubling chain. As a first step towards a more general approach, we interpret our findings in terms of a disintegration over the Kronecker factor, which is the maximal equicontinuous factor of a covering model set.     

A duality theorem for Tate–Shafarevich groups of curves over algebraically closed fields

In this note, we prove a duality theorem for the Tate–Shafarevich group of a finite discrete Galois module over the function field K of a curve over an algebraically closed field: there is a perfect duality of finite groups Open image in new window for F a finite étale Galois module on K of order invertible in K and with \(F' = {{\mathrm{Hom}}}(F,\mathbf{Q}/\mathbf {Z}(1))\). Furthermore, we prove that \(\mathrm {H}^1(K,G) = 0\) for G a simply connected, quasisplit semisimple group over K not of type \(E_8\).     

Hierarchies from D-brane instantons in globally defined Calabi-Yau orientifolds

We construct the first globally consistent semirealistic type I string vacua on an elliptically fibered manifold where the zero modes of the Euclidean D1-instanton sector allow for the generation of nonperturbative Majorana masses of an intermediate scale. In another class of global models, a D1-brane instanton can generate a Polonyi-type superpotential breaking supersymmetry at an exponentially suppressed scale.     

Testing for a $$\delta $$ -neighborhood of a generalized Pareto copula

Annals of the Institute of Statistical Mathematics - A multivariate distribution function F is in the max-domain of attraction of an extreme value distribution if and only if this is true for the...     

Targeted Photodynamic Therapy of Human Head and Neck Squamous Cell Carcinoma with Anti-epidermal Growth Factor Receptor Antibody Cetuximab and Photosensitizer IR700DX in the Mouse Skin-fold Window Chamber Model

Targeted photodynamic therapy (PDT) in head/neck cancer patients with a conjugate of the anti-epidermal growth factor receptor (EGFR) antibody, Cetuximab and a phthalocyanine photosensitizer IR700DX is under way, but the exact mechanisms of action are still not fully understood. In this study, the EGFR-overexpressing human head/neck OSC-19-luc2-cGFP tumor with transfected GFP gene was used in a skin-fold window chamber model in BALB/c nude mice. The uptake and localization of the conjugate in the tumor and its surrounding normal tissues were studied by an intravital confocal laser scanning microscopy with image analyses. The tumor was also irradiated with 690 nm laser light 24 h after conjugate administration. The vascular and tumor responses were examined by morphological evaluation and immunohistochemistry (IHC). The amount of conjugate in the tumor peaked at 24–48 h after injection. Image analyses of colocalization correlation parameters demonstrated a high fraction of the conjugate IR700DX colocalized in the GFP-expressing tumor cells. PDT-treated tumors showed extensive necrotic/apoptotic destruction with little vascular damage, while IHC showed no HIF-1α expression and decreased EGFR and Ki67 expression with activated caspase-3 overexpression, indicating a direct killing of tumor cells through both necrotic and apoptotic cell death.     

Active Molybdenum‐Based Anode for Dehydrogenative Coupling Reactions

A new and powerful active anode system that can be operated in 1,1,1,3,3,3‐hexafluoro‐2‐propanol (HFIP) has been discovered. In HFIP the molybdenum anode forms a compact, conductive, and electroactive layer of higher‐valent molybdenum species. This system can replace powerful but stoichiometrically required Mo^V reagents for the dehydrogenative coupling of aryls. This electrolytic reaction is more sustainable and allows the conversion of a broad scope of activated arenes.     

Studies toward frondosin A and its analogues. Formal total synthesis of (+/-)-frondosin A

Two reaction sequences commencing with different starting materials were successfully employed for the synthesis of frondosin A analogues, including (+/-)-frondosin A dimethyl ether. Construction of the bicyclo[5.4.0]undecane core in each case was achieved through an expedient microwave-assisted tandem 5-exo cyclization--Claisen rearrangement process.