Topological Classification and Structural Stability of Strongly Continuous Groups

The present paper is devoted to the study of some qualitative properties of C ₀-groups via topological equivalence, also called conjugacy. The special case of the evolution groups is analysed. We show that hyperbolicity implies structural stability. Our constructions improve existing similar results for groups with bounded generators, and apply to linear differential equations with unbounded coefficient operator.     

Asymptotic behaviour for a nonlocal diffusion equation on a lattice

In this paper we study the asymptotic behaviour as t → ∞ of solutions to a nonlocal diffusion problem on a lattice, namely, with t ≥ 0 and . We assume that J is nonnegative and verifies . We find that solutions decay to zero as t → ∞ and prove an optimal decay rate using, as our main tool, the discrete Fourier transform.      

Conformally Einstein products and nearly Kähler manifolds

In the first part of this note we study compact Riemannian manifolds (M, g) whose Riemannian product with is conformally Einstein. We then consider 6-dimensional almost Hermitian manifolds of type W ₁ + W ₄ in the Gray–Hervella classification admitting a parallel vector field and show that (under some mild assumption) they are obtained as Riemannian cylinders over compact Sasaki–Einstein 5-dimensional manifolds.      

Platinum species in the pores of NaX, NaY and NaA zeolites studied using EPR, XAS and FTIR spectroscopies

The results of X-band EPR, X-ray absorption and Fourier transform infrared spectroscopy on Pt(NH(3))(4)(2+) exchanged NaX, NaY and NaA zeolites reveal after oxygen calcination at 573 K that diamagnetic Pt(2+) is not the only product. Calcination provides Pt(3+) cations, but depending on the heating rate, the decomposition of amino groups during calcination also produces hydrogen that reduces Pt(3+) to Pt(2+) and Pt(+). NaX (Si/Al = 1.23) has a more negative framework charge than NaY (Si/Al = 2.31), so Pt(3+) can be stabilized only in NaX, whereas lower oxidation states of Pt such as Pt(+) can be stabilized in both, NaX and NaY, and neither of the paramagnetic Pt cations are stabilized in NaUSY (Si/Al = 3). The autoreduction process allows controlling the number of Pt(3+) and Pt(+) in the NaX zeolite by changing the calcination heating rate: a heating rate of 1.25 K min(-1) gives only Pt(+), but 0.5 K min(-1) gives a Pt(3+)/Pt(+) ratio close to 1. The structure of the support is also important for the synthesis of Pt species. While isolated paramagnetic Pt ions were stabilized in faujasite zeolites (NaX and NaY), a paramagnetic Pt dimer was obtained in a Linde type A zeolite (LTA, Si/Al = 1) by applying the same preparation methods. The fraction of paramagnetic Pt species which were characterized by X-band EPR spectroscopy amounts to 2-18% of the total Pt in the zeolites, the remaining Pt must be diamagnetic.     

Heterospin systems constructed from [Cu2Ln]3+ and [Ni(mnt)2]1-,2- Tectons: First 3p-3d-4f complexes (mnt = maleonitriledithiolato)

New heterospin complexes have been obtained by combining the binuclear complexes [{Cu(H(2)O)L(1)}Ln(O(2)NO)(3)] or [{CuL(2)}Ln(O(2)NO)(3)] (L(1) = N,N'-propylene-di(3-methoxysalicylideneiminato); L(2) = N,N'-ethylene-di(3-methoxysalicylideneiminato); Ln = Gd(3+), Sm(3+), Tb(3+)), with the mononuclear [CuL(1)(2)] and the nickel dithiolene complexes [Ni(mnt)(2)](q)- (q = 1, 2; mnt = maleonitriledithiolate), as follows: (1)infinity[{CuL(1)}(2)Ln(O(2)NO){Ni(mnt)(2)}].Solv.CH(3)CN (Ln = Gd(3+), Solv = CH(3)OH (1), Ln = Sm(3+), Solv = CH(3)CN (2)) and [{(CH(3)OH)CuL(2)}(2)Sm(O(2)NO)][Ni(mnt)(2)] (3) with [Ni(mnt)2]2-, [{(CH(3)CN)CuL(1)}(2)Ln(H(2)O)][Ni(mnt)(2)]3.2CH(3)CN (Ln = Gd(3+) (4), Sm(3+) (5), Tb(3+) (6)), and [{(CH(3)OH)CuL(2)}{CuL(2)}Gd(O(2)NO){Ni(mnt)(2)}][Ni(mnt)(2)].CH(2)Cl(2) (7) with [Ni(mnt))(2]*-. Trinuclear, almost linear, [CuLnCu] motifs are found in all the compounds. In the isostructural 1 and 2, two trans cyano groups from a [Ni(mnt)2]2- unit bridge two trimetallic nodes through axial coordination to the Cu centers, thus leading to the establishment of infinite chains. 3 is an ionic compound, containing discrete [{(CH(3)OH)CuL(2)}(2)Sm(O(2)NO)](2+) cations and [Ni(mnt)(2)](2-) anions. Within the series 4-6, layers of discrete [CuLnCu](3+) motifs alternate with stacks of interacting [Ni(mnt)(2)](*-) radical anions, for which two overlap modes, providing two different types of stacks, can be disclosed. The strength of the intermolecular interactions between the open-shell species is estimated through extended Hückel calculations. In compound 7, [Ni(mnt)(2)](*-) radical anions coordinate group one of the Cu centers of a trinuclear [Cu(2)Gd] motif through a CN, while discrete [Ni(mnt)(2)](*-) units are also present, overlapping in between, but also with the coordinated ones. Furthermore, the [Cu(2)Gd] moieties dimerize each other upon linkage by two nitrato groups, both acting as chelate toward the gadolinium ion from one unit and monodentate toward a Cu ion from the other unit. The magnetic properties of the gadolinium-containing complexes have been determined. Ferromagnetic exchange interactions within the trinuclear [Cu(2)Gd] motifs occur. In the compounds 4 and 7, the [Ni(mnt)(2)](*-) radical anions contribution to the magnetization is clearly observed in the high-temperature regime, and most of it vanishes upon temperature decrease, very likely because of the rather strong antiferromagnetic exchange interactions between the open-shell species. The extent of the exchange interaction in the compound 7, which was found to be antiferromagnetic, between the coordinated Cu center and the corresponding [Ni(mnt)(2)](*-) radical anion, bearing mostly a 3p spin type, was estimated through CASSCF/CASPT2 calculations. Compound 6 exhibits a slow relaxation of the magnetization.     

Single-molecule electrophoresis of beta-hairpin peptides by electrical recordings and Langevin dynamics simulations

We used single-channel electrical recordings and Langevin molecular dynamics simulations to explore the electrophoretic translocation of various beta-hairpin peptides across the staphylococcal alpha-hemolysin (alphaHL) protein pore at single-molecule resolution. The beta-hairpin peptides, which varied in their folding properties, corresponded to the C terminal residues of the B1 domain of protein G. The translocation time was strongly dependent on the electric force and was correlated with the folding features of the beta-hairpin peptides. Highly unfolded peptides entered the pore in an extended conformation, resulting in fast single-file translocation events. In contrast, the translocation of the folded beta-hairpin peptides occurred more slowly. In this case, the beta-hairpin peptides traversed the alphaHL pore in a misfolded or fully folded conformation. This study demonstrates that the interaction between a polypeptide and a beta-barrel protein pore is dependent on the folding features of the polypeptide.     

Effect of the metal environment on the ferromagnetic interaction in the Co-NC-W pairs of octacyanotungstate(V)-Cobalt(II) three-dimensional networks

State of the art CASSCF and CASPT2 calculations have been performed to elucidate the nature of ferromagnetism of CoII-NC-WV pairs in the three-dimensional compound [[WV(CN)2]2[(micro-CN)4CoII(H2O)2]3.4H2O]n, which has been recently synthesized and investigated by a number of experimental techniques (Herrera, J. M.; Bleuzen, A.; Dromzée, Y.; Julve, M.; Lloret, F.; Verdaguer, M. Inorg. Chem. 2003, 42, 7052-7059). In this network, the Co ions are in the high-spin (S = 3/2) state, while the single unpaired electron on the W centers occupies the lowest orbital of the dz2 type of the 5d shell. In agreement with the suggestion made by Herrera et al., we find that the ferromagnetism is due to a certain occupation scheme of the orbitals from the parent octahedral t2g shell on CoII sites, in which the orbital accommodating the unpaired electron is orthogonal to the dz2 orbitals of the surrounding W ions. We investigate the stabilization of such an orbital configuration on the Co sites and find that it cannot be achieved in the ground state of isolated mononuclear fragments [CoII(NC)4(OH2)2]2- for any conformations of the coordinated water molecules and Co-N-C bond angles. On the other hand, it is stabilized by the interaction of the complex with neighboring W ions, which are simulated here by effective potentials. The calculated exchange coupling constants for the CoII-NC-WV binuclear fragments are in reasonable agreement with the measured Curie-Weiss constant for this compound. As additional evidence for the inferred electronic configuration on the Co sites, the ligand-field transitions, the temperature-dependent magnetic susceptibility, and the field-dependent low-temperature magnetization, simulated ab initio for the mononuclear Co fragments, are in agreement with the available data for another compound [WIV[(micro-CN)4-CoII(H2O)2]2.4H2O]n containing diamagnetic W and high-spin Co ions in an isostructural environment.     

A Nonlinear Sandwich Shell Theory Accounting for Transverse Core Compressibility

The present study is concerned with an advanced theory of sandwich shells with transversely compressible core. The model is based on the standard Kirchhoff‐Love hypothesis for the face sheets and a third‐order displacement expansion for the core. Consistent equations of motion and boundary conditions are derived by means of Hamilton's variational principle. The model is applied to a postbuckling analysis of cylindrical shells under axial compression.     

Morse–Novikov cohomology of locally conformally Kähler manifolds

A locally conformally Kähler (LCK) manifold is a complex manifold admitting a Kähler covering, with the monodromy acting on this covering by holomorphic homotheties. We define three cohomology invariants, the Lee class, the Morse–Novikov class, and the Bott–Chern class, of an LCK-structure. These invariants play together the same role as the Kähler class in Kähler geometry. If these classes coincide for two LCK-structures, the difference between these structures can be expressed by a smooth potential, similar to the Kähler case. We show that the Morse–Novikov class and the Bott–Chern class of a Vaisman manifold vanish. Moreover, for any LCK-structure on a manifold, admitting a Vaisman structure, we prove that its Morse–Novikov class vanishes. We show that a compact LCK-manifold M$M$ with vanishing Bott–Chern class admits a holomorphic embedding into a Hopf manifold, if _dimCM?3${dim}_{\mathbb{C}}M?3$, a result which parallels the Kodaira embedding theorem.