Existence of solutions for impulsive differential models on half lines involving Caputo fractional derivatives

In this article, we establish existence results of at least one solution for two classes of initial value problems of nonlinear impulsive fractional differential models on half lines involving Caputo fractional derivatives. Our analysis rely on the well known fixed point theorem of Schauder and nonlinear alternative of Leray–Schauder type.     

Structure and microstructure of epitaxial Sr n Fe n O3 n −1 films

Thin films of SrFeO_{3??? x} (0?≤?x?≤?0.5) (SFO) grown on a (LaAlO₃)_0.3 (SrAl_0.5Ta_0.5O₃)_0.7 (LSAT) substrate by pulsed laser deposition have been structurally investigated by electron diffraction and high resolution transmission electron microscopy for different post-deposition oxygen treatments. During the deposition and post-growth oxidation, the oxygen-reduced SFO films accept extra oxygen along the tetrahedral layers to minimize the elastic strain energy. The oxidation process stops at a concentration SFO_2.875 and/or SFO_2.75 because a zero misfit with the LSAT substrate is reached. A possible growth mechanism and phase transition mechanism are suggested. The non-oxidized films exhibit twin boundaries having a local perovskite-type structure with a nominal composition close to SFO₃.     

The Effects of Sulphate and Tartrate Ions on the Molecular Organization of Water: Towards Understanding the Hofmeister Series (VI)

Using the 1-propanol (1P) probing methodology we have developed earlier, we characterized the effects of sulphate and tartrate anions on the molecular organization of H₂O. The results indicate that these two large anions belong to a new class of ??hydrophobe-like hydration center??. That is, sulphate and tartrate ions act as ??hydration centers?? with the hydration number 14±3 for both, and leave the bulk H₂O, away from hydration shells, unperturbed in the absence of the probing 1-propanol. As the mole fraction of the probe increases, however, the hydrogen bond probability of bulk H₂O away from hydration shells appears to decrease smoothly, as occurs with ??hydrophobes?? in H₂O. We plot the negative hydration number against the power to reduce the hydrogen bond probability of bulk H₂O for the two large anions. We also plotted the characteristic indices for ??hydrophiles?? and ??hydration centers?? whose characteristics we determined in the same manner earlier. H₂O defines the origin on this map. We found that a typical Hofmeister ranking for each anion matches reasonably well with that of the distance from the origin for each ion, in decreasing order starting from ions plotted in the north-west quadrant (representing the ??hydrophobe-like?? behavior) of the map and then in increasing order from the origin towards the south on the ordinate, the ??hydrophile-like?? behavior. These findings could be useful in understanding the Hofmeister series, pointing to the importance of the contribution made by the effect of each ion on H₂O, in addition to helping understand direct ion-protein interactions.     

Could we use a million cores to solve an integer program?

Given the steady increase in cores per CPU, it is only a matter of time before supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linear optimization problem. We also raise the question of whether best practices in sequential solution of ILPs will be effective in massively parallel environments.     

Synthesis of (+)-boronolide and (+)-deacetylboronolide using Pd-catalyzed carbonylation and lactonization

(+)-Boronolide and (+)-deacetylboronolide were synthesized using Pd-catalyzed CO insertion and lactonization as the key step. As to the ¹³C NMR data of (+)-deacetylboronolide, the assignment at C-6 position should be revised.     

Proton Order–Disorder Phenomena in a Hydrogen‐Bonded Rhodium–η5‐Semiquinone Complex: A Possible Dielectric Response Mechanism

A newly synthesized one‐dimensional (1D) hydrogen‐bonded (H‐bonded) rhodium(II)–η⁵‐semiquinone complex, [Cp*Rh(η⁵‐p‐HSQ‐Me₄)]PF₆ ([ 1 ]PF₆; Cp*=1,2,3,4,5‐pentamethylcyclopentadienyl; HSQ=semiquinone) exhibits a paraelectric–antiferroelectric second‐order phase transition at 237.1 K. Neutron and X‐ray crystal structure analyses reveal that the H‐bonded proton is disordered over two sites in the room‐temperature (RT) phase. The phase transition would arise from this proton disorder together with rotation or libration of the Cp* ring and PF₆^? ion. The relative permittivity ε_b′ along the H‐bonded chains reaches relatively high values (ca., 130) in the RT phase. The temperature dependence of ¹³C CP/MAS NMR spectra demonstrates that the proton is dynamically disordered in the RT phase and that the proton exchange has already occurred in the low‐temperature (LT) phase. Rate constants for the proton exchange are estimated to be 10^?4–10^?6 s in the temperature range of 240–270 K. DFT calculations predict that the protonation/deprotonation of [ 1 ]⁺ leads to interesting hapticity changes of the semiquinone ligand accompanied by reduction/oxidation by the π‐bonded rhodium fragment, producing the stable η⁶‐hydroquinone complex, [Cp*Rh³⁺(η⁶‐p‐H₂Q‐Me₄)]²⁺ ([ 2 ]²⁺), and η⁴‐benzoquinone complex, [Cp*Rh⁺(η⁴‐p‐BQ‐Me₄)] ([ 3 ]), respectively. Possible mechanisms leading to the dielectric response are discussed on the basis of the migration of the protonic solitons comprising of [ 2 ]²⁺ and [ 3 ], which would be generated in the H‐bonded chain.