Minimization of maximum absolute deviation in integers

A resource allocation problem of the integer minimization of maximum absolute deviation of monotone functions is under investigation. The optimal solution is shown to belong to one of the four possible classes. The optimality conditions of two kinds (“local” and “global” ones) are derived along with an algorithm, which utilizes the solutions of simple min-max and max-min integer allocation problems.The Apportionment problem is considered as an application.     

Single-exposure super-resolved interferometric microscopy by red-green-blue multiplexing

We present single-exposure super-resolved interferometric microscopy (SESRIM) as a novel approach capable of providing one-dimensional (1-D) super-resolution (SR) imaging in holographic microscopy using a single illumination shot. The single-exposure SR working principle is achieved by combining angular and wavelength multiplexing incoming from a set of tilted beams with different wavelengths where each wavelength is tuned with the red-green-blue (RGB) channels of a color CCD. Thus, the information included in each color channel is retrieved by holographic recording using a single-color CCD capture and by analyzing the RGB channels. Finally, 1-D SR imaging is obtained after the digital postprocessing stage yielding the generation of a synthetic aperture. Experimental results are reported validating the proposed SESRIM approach while an extension of the proposed approach to the two-dimensional case is considered.     

Iodinated aluminum(III) corroles with long-lived triplet excited states

The first reported iodination of a corrole leads to selective functionalization of the four C-H bonds on one pole of the macrocycle. An aluminum(III) complex of the tetraiodinated corrole, which exhibits red fluorescence, possesses a long-lived triplet excited state.     

Variables that influence cellular uptake and cytotoxic/cytoprotective effects of macrocyclic iron complexes

Determination of the cellular uptake of macrocyclic iron(III) complexes by a facile method, accompanied by cell viability tests under both basal and induced oxidative stress, demonstrates that protection against intracellular oxidative stress requires reasonably high internalization and favorable anti/prooxidant profiles. Of the four tested complexes, only amphipolar iron(III) corrole met these criteria.     

Adiabatic processes in frequency conversion

Adiabatic evolution, an important dynamical process in a variety of classical and quantum systems providing a robust way of steering a system into a desired state 1 - 5 , was introduced only recently to frequency conversion 6 - 9 . Adiabatic frequency conversion allowed the achievement of efficient scalable broadband frequency conversion 8 , 9 and was applied successfully to the conversion of ultrashort pulses, demonstrating near‐100% efficiency for ultrabroadband spectrum 10 - 16 . The underlying analogy between undepleted pump nonlinear processes and coherently excited quantum systems was extended in the past few years to multi‐level quantum systems, demonstrating new concepts in frequency conversion, such as complete frequency conversion through an absorption band 17 - 20 . Additionally, the undepleted pump restriction was removed, enabling the exploration of adiabatic processes in the fully nonlinear dynamics regime of nonlinear optics 21 - 26 . In this article, the basic concept of adiabatic frequency conversion is introduced, and recent advances in ultrashort physics, multi‐process systems, and the fully nonlinear dynamics regime are reviewed.     

Structure and chemistry of N-substituted corroles and their rhodium(I) and zinc(II) metal-ion complexes

In the present work we report on the detailed structural features of the chiral N21- and N22-substituted benzyl and picolyl derivatives of tris(pentafluorophenyl)corrole [H3(tpfc)]. The main difference between the isomers is that substitution on N22 creates a much more crowded environment, reflected in higher deformation of the corrole ring from planarity and of the meso-aryls from perpendicular orientation. The effects of metal-ion chelation on corrole geometry are demonstrated by structural investigations of the zinc(II) and rhodium(I) complexes of the N21- and N22-alkylated corroles. The major finding is the intramolecular coordination of the pyridine moiety of the picolyl substituent in the case of [ZnII(N21-picolyl-tpfc)]. This pyridine is readily attracted to the zinc ion as an axial ligand, thus replacing the external pyridine molecule of the precursor [ZnII(N21-benzyl-tpfc)(py)]. The change is associated with a considerable flattening of the corrole ring in order to allow a more convenient coordination of the zinc ion to all four pyrrole nitrogen atoms (at Zn-N(pyr-role) distances of 1.956-1.987 A for the nonsubstituted sites, and 2.224-2.247 A for the substituted sites). These structural investigations also aid a good understanding of the spectroscopic characteristics of the derivatives.     

Bond-Shift Rearrangement in Solid Li3P7(Monoglyme)3: A P MAS NMR Study

The ³¹P MAS NMR spectrum of solid Li₃P₇(monoglyme)₃ has been reinvestigated over a wide temperature range (−70 to +77°C) and under conditions of better resolution (Larmor frequency of 162 MHz and spinning rate of 30 kHz) than previously measured (121 MHz and 13 kHz). At low temperatures three spinning sideband (ssb) manifolds are observed: a singlet (centered at −45 ppm relative to 85% H₃PO₄) due to the apical atom (A) of the P₇-cage trianion; a 1 : 1 : 1 triplet (at −110, −117, and −124.5 ppm) due to the negatively charged equatorial (E) atoms, and a one to two doublet (at −161 and −168.5 ppm) due to the basal (B) atoms. These results are consistent with the P₇ cage having nearly, but not perfect, C_3v symmetry. The compound appears to be well ordered in the solid state with very little structural dispersity. On heating, the NMR lines broaden and eventually coalesce into a single ssb manifold. This behavior is ascribed to bond-shift rearrangement similar to the Cope rearrangement in bullvalene. A MAS 2D exchange experiment and a quantitative analysis of the 1D NMR lineshapes indicate that, unlike in solution where the rearrangement involves a single bond shift at a time, in the solid the process involves a succession of two bond shifts: The first leads to an intermediate species in which the rearranged P₇ cage is inverted, while in the subsequent step a second bond shift takes place that also restores the original orientation of the cage in the lattice. The overall effect of the double bond shift is equivalent to cyclic permutation of the phosphorus atoms within the five member rings of the P₇-cage. The quantitative analysis of the dynamic lineshapes shows that this cyclic permutation proceeds at a different rate in one ring (k_d¹) than in the other two (k_d^2,3). The kinetic parameters for these processes are E_a¹=18.7 kJ/mol, E_a^2,3=58.0 kJ/mol, k_d¹(17°C)=k_d^2,3(17°C)=10⁴ s⁻¹. No indications for independent threefold molecular jumps of the P₇ cage were found.