Role of the orbitally degenerate Mn(III) ions in the single-molecule magnet behavior of the cyanide cluster ([MnII(tmphen)2]3[Mn(III)(CN)6]2) (tmphen = 3,4,7,8-tetramethyl-1,10-phenanthroline)

We report a new theoretical model that accounts for the unusual magnetic properties of the cyanide cluster ([MnII(tmphen)2]3[MnIII(CN)6]2) (tmphen = 3,4,7,8-tetramethyl-1,10-phenanthroline). The model takes into account (1) the spin-orbit interaction, (2) the trigonal component of the crystal field acting on the ground-state cubic (3)T(1) terms of the apical Mn(III) ions, and (3) the isotropic contribution to the exchange interaction between Mn(III) and Mn(II) ions. The ground state of the cluster was shown to be the state with the total angular momentum projection |M(J)| = 15/2; the energies of the low-lying levels obtained from this treatment increase with decreasing |M(J)| values, a situation that leads to a barrier for the reversal of magnetization (U(eff) approximately 30 cm(-1)). The new model explains the recently discovered single-molecule magnet behavior of the ([MnII(tmphen)2]3[MnIII(CN)6]2)in contrast to the traditional approach that takes into account only the ground-state spin (S) and a negative zero-field splitting parameter (D(S) < 0).     

Angular pattern of minijet transverse energy flow in hadron and nuclear collisions

The azimuthal asymmetry of a minijet system produced at the early stage of nucleon–nucleon and nuclear collisions in a central rapidity window is studied. We show that in pp collisions the minijet transverse energy production in a central rapidity window is essentially unbalanced in the azimuth due to asymmetric contributions in which only one minijet hits the acceptance window. We further study the angular pattern of the transverse energy flow generated by the semihard degrees of freedom at the early stage of high energy nuclear collisions and its dependence on the number of semihard collisions in the models both including and neglecting soft contributions to the inelastic cross section at RHIC and LHC energies as well as on the choice of the infrared cutoff. Received: 19 January 1999 / Revised version: 18 February 2000 / Published online: 26 July 2000     

Extended triple-bridged Ni(II)- and Co(II)-hydroxamate trinuclear complexes: synthesis, crystal structures, and magnetic properties

Crystal structures of new trinuclear complexes [Ni 3(mu-OAc F) 4(mu-AA) 2(tmen) 2], [Ni 3(mu-OAc F) 4(mu-BA) 2(tmen) 2], and [Co 3(mu-OAc F) 4(mu-BA) 2(tmen) 2] have been determined (OAc F = CF 3COO (-), AA = acetohydroxamate anion, BA = benzohydroxamate anion, tmen = N, N, N', N'-tetramethylethylenediamine). In each structure, the metal ions have distorted octahedral coordination and are triply bridged by one hydroxamate and two trifluoroacetate bridges. Magnetic properties of these compounds and of relative [Co 3(mu-OAc F) 4(mu-AA) 2(tmen) 2] were studied by susceptibility and magnetization measurements. It was shown that for nickel trimers the intramolecular magnetic coupling is weak ferromagnetic in the case of the complex with the AA group, and there is nearly no coupling in the case with BA group. Rather large zero field splitting was obtained for the distorted octahedral environments of the terminal nickel ions. The cobalt trimers were additionally studied by magnetic circular dichroism (MCD) measurements. The exchange interaction of the cobalt complexes is antiferromagnetic.     

Stable maps of Polish spaces

We define the notions of stable and transquotient maps and study the relation between these classes of maps. The class of stable maps contains all closed and open maps and their compositions. The transquotient maps preserve the property of being a Polish space, and every stable map between separable metric spaces is transquotient.

In particular, a composition of closed and open maps (the intermediary spaces may not be metric) preserves the property of being a Polish space. This generalizes the results of Sierpinski and Vainstein for open and closed maps.

     

The Las-Vegas Processor Identity Problem (How and When to Be Unique)

We study the classical problem of assigning unique identifiers to identical concurrent processes. In this paper, we consider the asynchronous shared memory model, and the correctness requirement is that upon termination of the algorithm, the processes must have unique IDs always. Our results include tight characterization of the problem in several respects. We call a protocol solving this task Las Vegas if it has finite expected termination time. Our main positive result is the first Las-Vegas protocol that solves the problem. The protocol terminates in O(log n) expected asychronous rounds, using O(n) shared memory space, where n is the number of participating processes. The new protocol improves on all previous solutions simultaneously in running time (exponentially), probability of termination (to 1), and space requirement. The protocol works under the assumption that the asynchronous schedule is oblivious, i.e., independent of the actual unfolding execution. On the negative side, we show that there is no finite-state Las-Vegas protocol for the problem if the schedule may depend on the history of the shared memory (an adaptive schedule). We also show that any Las-Vegas protocol must know n in advance (which implies that crash faults cannot be tolerated) and that the running time is Ω(log n). For the case of an arbitrary (nonoblivious) adversarial schedule, we present a Las-Vegas protocol that uses O(n) unbounded registers. For the read-modify-write model, we present a constant-space deterministic algorithm.     

Minijet transverse-energy production in the next-to-leading order in hadron and nuclear collisions

The transverse-energy flow generated by minijets in hadron and nuclear collisions into a given rapidity window in the central region is calculated in the next-to-leading-order (NLO) in QCD at RHIC and LHC energies. The NLO transverse-energy production in pp collision cross sections is larger than that in the leading-order (LO) ones by the factors of and at RHIC and LHC energies, respectively. These results were then used to calculate the transverse-energy spectrum in nuclear collisions in a Glauber geometrical model. We show that accounting for NLO corrections in the elementary pp collisions leads to a substantial broadening of the distribution for the nuclear ones, while its form remains practically unchanged. Received: 11 May 1999 / Published online: 22 October 1999     

Deuteron Quadrupolar Chemical Exchange Saturation Transfer (Q-CEST) Solid-State NMR for Static Powder Samples: Approach and Applications to Amyloid-β Fibrils

We provide an experimental and computational framework for ²H quadrupolar chemical exchange saturation transfer NMR experiments (Q-CEST) under static solid-state conditions for the quantification of dynamics on μs-ms timescales. Simulations using simple 2-site exchange models provide insights into the relation between spin dynamics and motions. Biological applications focus on two sites of amyloid-β fibrils in the 3-fold symmetric polymorph. The first site, the methyl group of A2 of the disordered N-terminal domain, undergoes diffusive motions and conformational exchange due to transient interactions. Earlier ²H rotating frame relaxation and quadrupolar CPMG measurements are combined with the Q-CEST approach to characterize the multiple conformational states of the domain. The second site, the methyl group of M35, spans the water-accessible cavity inside the fibrils’ core and undergoes extensive rotameric exchange. Q-CEST permits us to refine the rotameric exchange model for this site and allows the more precise determination of populations and rotameric exchange rate constants than line shape analysis.     

Deuteron Solid-State NMR Relaxation Measurements Reveal Two Distinct Conformational Exchange Processes in the Disordered N-Terminal Domain of Amyloid-β Fibrils

We employed deuterium solid-state NMR techniques under static conditions to discern the details of the μs–ms timescale motions in the flexible N-terminal subdomain of Aβ_1–40 amyloid fibrils, which spans residues 1–16. In particular, we utilized a rotating frame (R_1ρ) and the newly developed time domain quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) relaxation measurements at the selectively deuterated side chains of A2, H6, and G9. The two experiments are complementary in terms of probing somewhat different timescales of motions, governed by the tensor parameters and the sampling window of the magnetization decay curves. The results indicated two mobile “free” states of the N-terminal domain undergoing global diffusive motions, with isotropic diffusion coefficients of 0.7−1 ⋅ 10⁸ and 0.3−3 ⋅ 10⁶ad² s⁻¹. The free states are also involved in the conformational exchange with a single bound state, in which the diffusive motions are quenched, likely due to transient interactions with the structured hydrophobic core. The conformational exchange rate constants are 2−3 ⋅ 10⁵ s⁻¹ and 2−3 ⋅ 10⁴ s⁻¹ for the fast and slow diffusion free states, respectively.     

Enhancing the blocking temperature in single-molecule magnets by incorporating 3d-5d exchange interactions

We report the first single-molecule magnet (SMM) to incorporate the [Os(CN)(6)](3-) moiety. The compound (1) has a trimeric, cyanide-bridged Mn(III)-Os(III)-Mn(III) skeleton in which Mn(III) designates a [Mn(5-Brsalen)(MeOH)](+) unit (5-Brsalen=N,N'-ethylenebis(5-bromosalicylideneiminato)). X-ray crystallographic experiments reveal that 1 is isostructural with the Mn(III)-Fe(III)-Mn(III) analogue (2). Both compounds exhibit a frequency-dependent out-of-phase χ'(T) alternating current (ac) susceptibility signal that is suggestive of SMM behaviour. From the Arrhenius expression, the effective barrier for 1 is found to be Δ(eff)/k(B)=19 K (τ(0)=5.0×10(-7) s; k(B)=Boltzmann constant), whereas only the onset (1.5 kHz, 1.8 K) of χ'(T) is observed for 2, thus indicating a higher blocking temperature for 1. The strong spin-orbit coupling present in Os(III) isolates the E'(1g(1/2))(O(h)*) Kramers doublet that exhibits orbital contributions to the single-ion anisotropy. Magnetic susceptibility and inelastic neutron-scattering measurements reveal that substitution of [Fe(CN)(6)](3-) by the [Os(CN)(6)](3-) anion results in larger ferromagnetic, anisotropic exchange interactions going from quasi-Ising exchange interactions in 2 to pure Ising exchange for 1 with J(parallel)(MnOs)=-30.6 cm(-1). The combination of diffuse magnetic orbitals and the Ising-type exchange interaction effectively contributes to a higher blocking temperature. This result is in accordance with theoretical predictions and paves the way for the design of a new generation of SMMs with enhanced SMM properties.