On birational Torelli theorems

Archiv der Mathematik - Let G be a simple simply-connected connected linear algebraic group over $${\mathbb {C}}$$ . We prove a 2-birational Torelli theorem for the moduli space of semistable...     

Red-emitting β-diketonate Eu(III) Complexes With Substituted 1,10-phenanthroline Derivatives: Optoelectronic and Spectroscopic Analysis

Journal of Fluorescence - A series of europium diketonate complexes with 1-phenyl-1,3-butanedione (PBD) and 1,10-phenanthroline derivatives were synthesized and explored spectroscopically....     

A Novel Method for Permeability Estimation from Micro-tomographic Images

Transport in Porous Media - A methodology has been developed to create a pore network model (PNM) from the geometrical/topological information extracted from the micro-tomographic images of a...     

Synthesis and formulation of self-immolative PEG-aryl azide block copolymers and click-to-release reactivity with trans-cyclooctene

Self-immolative aryl azides can react with trans-cyclooctenes (TCO), triphenylphosphines or hydrogen sulfide (H₂S) to activate prodrugs, imaging probes and drug delivery systems. To date, the synthesis of polymers containing these aryl azide self-immolative linkers and their reactivity with a strained alkene (i.e., in a bioorthogonal reaction) has not been explored. Also, due to the instability of aryl azides towards light and high temperatures, the polymerization methods compatible with aryl azides are limited. Through systematic investigation of the reversible addition-fragmentation chain transfer (RAFT) and atom transfer radical polymerization (ATRP) methods, a self-immolative PEG-aryl azide block copolymer (PEG₄₅-b-ABOC₂₈ 2 ) and a non-responsive 4-fluoroaryl block copolymer (PEG₄₅-b-FBOC₂₄ 3 ) was prepared. ATRP provided the desired polymers in a highly controlled manner, whereas the RAFT conditions led to higher levels of aryl azide polymer degradation. The ATRP derived polymers 2 and 3 were formulated into nanoparticles of approximately 200 nm diameter, and particle triggering was demonstrated by the [3+2]-cycloaddition reaction of TCO with PEG₄₅-b-ABOC₂₈ 2 in solution (pure polymer) and as a formulated nanoparticle. Preliminary in vitro cell viability studies suggested that the stimuli-responsive aryl azide polymers/nanoparticles are not cytotoxic up to 200 μg/ml concentrations.     

Scrambled Geometric Net Integration Over General Product Spaces

Quasi-Monte Carlo (QMC) sampling has been developed for integration over \([0,1]^s\) where it has superior accuracy to Monte Carlo (MC) for integrands of bounded variation. Scrambled net quadrature allows replication-based error estimation for QMC with at least the same accuracy and for smooth enough integrands even better accuracy than plain QMC. Integration over triangles, spheres, disks and Cartesian products of such spaces is more difficult for QMC because the induced integrand on a unit cube may fail to have the desired regularity. In this paper, we present a construction of point sets for numerical integration over Cartesian products of s spaces of dimension d, with triangles (\(d=2\)) being of special interest. The point sets are transformations of randomized (t, m, s)-nets using recursive geometric partitions. The resulting integral estimates are unbiased, and their variance is o(1 / n) for any integrand in \(L^2\) of the product space. Under smoothness assumptions on the integrand, our randomized QMC algorithm has variance \(O(n^{-1 - 2/d} (\log n)^{s-1})\), for integration over s-fold Cartesian products of d-dimensional domains, compared to \(O(n^{-1})\) for ordinary MC.     

Designing the Molybdopterin Core through Regioselective Coupling of Building Blocks

Molybdopterin is an essential cofactor for all forms of life. The cofactor is composed of a pterin moiety appended to a dithiolene‐functionalized pyran ring, and through the dithiolene moiety it binds metal ions. Different synthetic strategies for dithiolene‐functionalized pyran precursors that have been designed and synthesized are discussed. These precursors also harbor 1,2‐diketone or osone functionality that has been condensed with 1,2‐diaminobenzene or other heterocycles resulting in several quinoxaline or pterin derivatives. Use of additives improves the regioselectivity of the complexes. The molecules have been characterized by ¹H and ¹³C NMR and IR spectroscopies, as well as by mass spectrometry. In addition, several compounds have been crystallographically characterized. The geometries of the synthesized molecules are more planar than the geometry of the cofactor found in proteins.