Conformable fractional Sturm‐Liouville equation

In this article, we discuss a conformable fractional Sturm‐Liouville boundary‐value problem. We prove an existence and uniqueness theorem for this equation and formulate a self‐adjoint boundary value problem. We also construct the associated Green function of this problem, and we give the eigenfunction expansions. Finally, we will give some examples.     

The one‐dimensional Schrödinger operator on bounded time scales

In this paper, we consider the one‐dimensional Schrödinger operator on bounded time scales. We construct a space of boundary values of the minimal operator and describe all maximal dissipative, maximal accretive, self‐adjoint, and other extensions of the dissipative Schrödinger operators in terms of boundary conditions. In particular, using Lidskii's theorem, we prove a theorem on completeness of the system of root vectors of the dissipative Schrödinger operators on bounded time scales. Copyright © 2016 John Wiley & Sons, Ltd.     

Fragmentation branching ratios of highly excited hydrocarbon molecules CnH and their cations CnH+ (n<or=4)

We have measured fragmentation branching ratios of neutral C(n)H and C(n)H(+) cations produced in high velocity (4.5 a.u) collisions between incident C(n)H(+) cations and helium atoms. Electron capture gives rise to excited neutral species C(n)H and electronic excitation to excited cations C(n)H(+). Thanks to a dedicated setup, based on coincident detection of all fragments, the dissociations of the neutral and cationic parents were recorded separately and in a complete way. For the fragmentation of C(n)H, the H-loss channel is found to be dominant, as already observed by other authors. By contrast, the H-loss and C-loss channels equally dominate the two-fragment break up of C(n)H(+) species. For these cations, we provide the first fragmentation data (n>2). Results are also discussed in the context of astrochemistry.     

Iron(II) cage complexes of N-heterocyclic amide and bis(trimethylsilyl)amide ligands: synthesis, structure, and magnetic properties

Metallation of hexahydropyrimidopyrimidine (hppH) by [Fe{N(SiMe(3))(2)}(2)] (1) produces the trimetallic iron(II) amide cage complex [{(Me(3)Si)(2)NFe}(2)(hpp)(4)Fe] (2), which contains three iron(II) centers, each of which resides in a distorted tetrahedral environment. An alternative, one-pot route that avoids use of the highly air-sensitive complex 1 is described for the synthesis of the iron(II)-lithium complex [{(Me(3)Si)(2)N}(2)Fe{Li(bta)}](2) (3) (where btaH = benzotriazole), in which both iron(II) centers reside in 3-coordinated pyramidal environments. The structure of 3 is also interpreted in terms of the ring laddering principle developed for alkali metal amides. Magnetic susceptibility measurements reveal that both compounds display very weak antiferromagnetic exchange between the iron(II) centers, and that the iron(II) centers in 2 and 3 possess large negative axial zero-field splittings.     

Chromium chains as polydentate fluoride ligands for lanthanides

Hexametallic chromium(III) chains can act as fluoride donor ligands to lanthanide ions giving {(Cr(6))Ln(x)}(n) complexes; preliminary spectroscopic studies are reported.     

Limits on intrinsic magnetism in graphene

We have studied magnetization of graphene nanocrystals obtained by sonic exfoliation of graphite. No ferromagnetism is detected at any temperature down to 2?K. Neither do we find strong paramagnetism expected due to the massive amount of edge defects. Rather, graphene is strongly diamagnetic, similar to graphite. Our nanocrystals exhibit only a weak paramagnetic contribution noticeable below 50?K. The measurements yield a single species of defects responsible for the paramagnetism, with approximately one magnetic moment per typical graphene crystallite.     

Pentametallic lanthanide-alkoxide square-based pyramids: high energy barrier for thermal relaxation in a holmium single molecule magnet

Pentametallic Ln complexes of formula [Ln(5)O(O(i)Pr)(13)] have been made, where Ln(III) = Sm, Gd, Tb, Ho and Er; slow magnetisation relaxation to 33 K is observed for the Ho complex with an energy barrier of ca. 400 K.     

Helical (isotactic) and syndiotactic silver(I) metallo-supramolecular coordination polymers assembled from a readily prepared bis-pyridylimine ligand containing a 1,5-naphthalene spacer

A ligand in which two pyridylimine binding units are linked by a 1,5-naphthalene spacer is prepared and its silver(I) coordination chemistry investigated. In the solid state, a pair of C-H triplebond N interactions between pyridylimine units link the free ligands into chain structures, with further C-H triplebond N and some -stacking interactions linking these chains into a three-dimensional structure. The spacer constrains the ligand to dinucleate, and with silver(I) the metal coordinates to two pyridylimine units from two separate ligands and this leads to the formation of coordination polymers with a range of different anions. Different twisting motifs within the ligand control the tacticity of these coordination polymers and both isotactic, helical polymers and syndiotactic (achiral) polymers result. The core of the isotactic polymer strands contains two metallo-vectors and results in long-range ordering of the metal centres into a 2 x n grid arrangement. The solution behaviour indicates that exchange between the diastereomeric forms occurs. Since this must involve inversion at the metal centres, atactic species may also form a component of the solution library.     

Octa- and hexametallic iron(III)-potassium phosphonate cages

Two new iron(III)-potassium phosphonate cage complexes with {K(2)Fe(6)} and {K(2)Fe(4)} cores are reported. Magnetic studies reveal antiferromagnetic interactions between the Fe(III) centres occur in these cages.