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.     

α- and γ-Regiocontrol and Enantiospecificity in the Copper-Catalyzed Substitution Reaction of Propargylic Phosphates with Grignard Reagents

The regioselectivity (r.s.) and enantiospecificity (e.s.) of the substitution reactions of secondary propargylic alcohol derivatives using reagents derived from ArMgBr and Cu salts were studied. First, the picolinate, 3-methylpicolinate, and diethylphosphonate derivatives of Ph(CH₂)₂CH(OH)C≡CTMS were reacted with PhMgBr/CuCN in ratios of 2.5:2.7–2.5:0.25. The use of 2.5:0.25 ratio in THF/DME (6:1) at 0 °C for 1 h afforded the α-substitution product from the phosphate with ≥98 % r.s. and 99 % e.s. CuBr⋅Me₂S gave similar selectivity. The reaction system was then applied to phosphates derived from R¹CH(OH)C≡CR² and ArMgBr to obtain synthetically sufficient r.s. and e.s. values with R²=TMS, Ph, whereas iPr was borderline in terms of size as an R¹ substituent. The presence of a substituent at the o-position of Ar marginally affected the selectivity. We also found that the use of PhMgBr/Cu(acac)₂ in a 2:1 ratio in THF produced the γ-substitution products (allenes) with high r.s. and e.s.     

High Pressure Synthesis of Cycloadduct of Fullerene C60 with 2H-Pyran-2-one∗∗

Under high pressure conditions, fullerene C₆₀ smoothly reacts with 2H-pyran-2-one to give a [4+2] cycloadduct, which can be reduced to an alcohol derivative.

     

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.