Preparation of β-Cyclodextrin Modified FusedSilica Capillary and Its Application inCapillary Electrophoresis Enantiom eric Separation

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Noether's theorem on time scales

We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective Euler-Lagrange extremals.     

Triclinic and orthorhombic polymorphs of 2‐iodo‐4‐nitro­aniline: interplay of hydrogen bonds,nitro⃛I interactions and aromatic π–π‐stacking interactions

In the triclinic polymorph of 2‐iodo‐4‐nitro­aniline, C₆H₅IN₂O₂, space group P, the mol­ecules are linked by paired N—­H?O hydrogen bonds into C(8)[R(6)] chains of rings. These chains are linked into sheets by nitro?I interactions, and the sheets are pairwise linked by aromatic π–π‐stacking interactions. In the orthorhombic polymorph, space group Pbca, the mol­ecules are linked by single N—H?O hydrogen bonds into spiral C(8) chains; the chains are linked by nitro?O interactions into sheets, each of which is linked to its two immediate neighbours by aromatic π–π‐stacking inter­actions, so producing a continuous three‐dimensional ­structure.     

From 3D to 2D Transition Metal Nitroprussides by Selective Rupture of Axial Bonds

1-methyl-2-pyrrolidone (1m2p) is a solvent with proven abilities for 2D-solid exfoliation due to its extremely high surface tension. In principle, such a feature could be used also to induce the selective breaking of certain bonds in solids to obtain new materials. Such a hypothesis is demonstrated in this study for transition metal nitroprussides, where 2D solids are obtained from 3D frameworks by selective rupture of axial bonds. This contribution discusses the mechanism involved in such molecular manufacture. The crystal structure for the formed 2D solids was solved and refined from XRD powder patterns recorded using synchrotron radiation. Mössbauer, IR and Raman spectra provided fine details on the electronic structure of the resulting new series of layered materials. The experimental information was complemented with calculations for the molecule configuration in its non-activated and activated forms. In the obtained 2D solids, neighboring layers of about 1 nm of thickness remain separated by activated 1m2p molecules. The interaction between neighboring layers is of a physical nature, without the presence of a chemical bond between them, as corresponds to a 2D material.     

A Theoretical Study of the C–X Bond Cleavage Mediated by Cob(II)Aloxime

The C–X bond cleavage in different methyl halides (CH₃X; X = Cl, Br, I) mediated by 5,6-dimethylbenzimidazole-bis(dimethylglyoximate)cobalt(II) (Co^IICbx) was theoretically investigated in the present work. An S_N2-like mechanism was considered to simulate the chemical process where the cobalt atom acts as the nucleophile and the halogen as the leaving group. The reaction path was computed by means of the intrinsic reaction coordinate method and analyzed in detail through the reaction force formalism, the quantum theory of atoms in molecules (QTAIM), and the calculation of one-electron density derived quantities, such as the source function (SF) and the spin density. A thorough comparison of the results with those obtained in the same reaction occurring in presence of 5,6-dimethylbenzimidazole-bis(dimethylglyoximate)cobalt(I) (Co^ICbx) was conducted to reveal the main differences between the two cases. The reactions mediated by Co^IICbx were observed to be endothermic and possess higher activation energies in contrast to the reactions where the Co^ICbx complex is present. The latter was supported by the reaction force results, which suggest a relationship between the activation energy and the ionization potentials of the different nucleophiles present in the cleavage reaction. Moreover, the SF results indicates that the lower axial ligand (i.e., 5,6-dimethylbenzimidazole) exclusively participates on the first stage of the reaction mediated by the Co^IICbx complex, while for the Co^ICbx case, it appears to have an important role along the whole process. Finally, the QTAIM charge analysis indicates that oxidation of the cobalt atom occurs in both cases; at the same time, it suggests the formation of an uncommon two-center one-electron bond in the Co^IICbx case. The latter was confirmed by means of electron localization calculations, which resulted in a larger electron count at the Co–C interatomic region for the Co^ICbx case upon comparison with its Co^IICbx counterpart.     

Incomplete MaxSAT approaches for combinatorial testing

Journal of Heuristics - We present a Satisfiability (SAT)-based approach for building Mixed Covering Arrays with Constraints of minimum length, referred to as the Covering Array Number problem....     

Race,SES, and mathematics achievement conflicts: how policy and political climate affect academic achievement

Socioeconomic status (SES) has been widely used as a determining factor to explain educational processes and outcomes such as mathematics academic achievement. Research has documented the links between SES and mathematics academic achievement. However, further understanding the complex relationship between contextual factors, such as policy, and its implications for these processes within an ideologically patriarchal society is paramount. After decades of United States school policy and reform—with the most recent focus on Common Core Standards—there continue to be inconsistent notions of what the “real” issues are and how to address those issues. This paper sets out to explore one specific case—House Bill 2281 (HB 2281) and, in effect, the banning of the Mexican–American Studies program in one school district in the US—in understanding the implications of policy in the shaping of the public education system. Implications for mathematics education research are explored.     

The Hahn Quantum Variational Calculus

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann’s direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.