On the value distribution theory of elliptic functions

The Nevanlinna characteristic of a nonconstant elliptic function φ (z) satisfiesT(r, φ)=Kr ² (1+o(1)) asr→∞ whereK is a nonzero constant. In this paper, we completely answer the following question: For which polynomialsQ(z, u ₀,...,u _n ) inu ₀,...,u _n , having coefficientsa(z) satisfyingT(r, a)=o(r ²) asr→∞, will the meromorphic functionh _Q (z)=Q(z, ?(z),...,?⁽ⁿ⁾(z)) either be identically zero or satisfyN(r, 1/h _Q )=o(r ²) asr→∞? In fact, we answer this question for rational functionsQ(z, u ₀,...,u _n ) inu ₀,...,u _n , and also obtain analogous results for the Weierstrass functions ζ(z) and σ(z).     

Structure and phase transitions of the lanthanide metals

The structures and phase transitions of the lanthanide metals can be related to f orbital contributions to the bonding. With increasing availability of the f orbitals the structure sequence hexagonal closest packed, double hexagonal closest packed, δ-samarium, cubic closest packed, and body-centered cubic is observed. Increases in temperature and/or pressure result in an increased availability of the f orbitals resulting in predictable phase transitions.     

Composite Bank-Laine functions and a question of Rubel

A Bank-Laine function is an entire function satisfying at every zero of . We determine all Bank-Laine functions of form , with entire. Further, we prove that if is a transcendental entire function of finite order, then there exists a path tending to infinity on which and all its derivatives tend to infinity, thus establishing for finite order a conjecture of Rubel.

     

Phosphonate ligands encourage a platonic relationship between cobalt(II) and alkali metal ions

Two new cobalt(ii) cages are reported where the metal core has a high symmetry related to a Platonic solid; the choice of alkali metal used in the base used for deprotonation appears to influence the resulting structures.     

Response variance prediction in the statistical energy analysis of built-up systems

In the statistical energy analysis (SEA) of high frequency noise and vibration, a complex engineering structure is represented as an assembly of subsystems. The response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem, and these energies are found by employing the principle of power balance. Strictly the computed energy is an average taken over an ensemble of random structures, and for many years there has been interest in extending the SEA prediction to the variance of the energy. A variance prediction method for a general built-up structure is presented here. Closed form expressions for the variance are obtained in terms of the standard SEA parameters and an additional set of parameters alpha(k) that describe the nature of the power input to each subsystem k, and alpha(ks) that describe the nature of the coupling between subsystems k and s. The theory is validated by comparison with Monte Carlo simulations of plate networks and structural-acoustic systems.     

Large Hexadecametallic {MnIII–LnIII} Wheels: Synthesis,Structural, Magnetic,and Theoretical Characterization

The synthesis, gas sorption studies, magnetic properties, and theoretical studies of new molecular wheels of core type {Mn^III₈Ln^III₈} (Ln=Dy, Ho, Er, Y and Yb), using the ligand mdeaH₂, in the presence of ortho‐toluic or benzoic acid are reported. From the seven wheels studied the {Mn₈Dy₈} and {Mn₈Y₈} analogues exhibit SMM behavior as determined from ac susceptibility experiments in a zero static magnetic field. From DFT calculations a S=16 ground state was determined for the {Mn₈Y₈} complex due to weak ferromagnetic Mn^III–Mn^III interactions. Ab initio CASSCF+RASSI‐SO calculations on the {Mn₈Dy₈} wheel estimated the Mn^III–Dy^III exchange interaction as ?0.1 cm^?1. This weak exchange along with unfavorable single‐ion anisotropy of Dy^III/Mn^III ions, however, led to the observation of SMM behavior with fast magnetic relaxation. The orientation of the g‐anisotropy of the Dy^III ions is found to be perpendicular to the plane of the wheel and this suggests the possibility of toroidal magnetic moments in the cluster. The {Mn₈Ln₈} clusters reported here are the largest heterometallic Mn^IIILn^III wheels and the largest {3d–4f} wheels to exhibit SMM behavior reported to date.     

On the diffuse field reciprocity relationship and vibrational energy variance in a random subsystem at high frequencies

A recent paper has shown that under certain conditions the cross-spectral matrix of the forces exerted by a vibrational or acoustic wave field on its surrounding boundaries can be expressed in terms of (i) the energy of the wave field, and (ii) the direct field dynamic stiffness matrix of the boundary. This "diffuse field reciprocity relation" was derived using wave mechanics, and it is not immediately clear how the required wave field properties translate to conditions on the vibrational modes of the system or the applied forcing. This issue is addressed here by deriving an extended version of the reciprocity relation using modal methods, and the conditions required for the extended version to reduce to the existing relation are delineated. It is shown that the existing diffuse field reciprocity relation leads to an anomalous result when used to predict the energy variance of a subsystem, and that this anomaly is resolved by using the present extended version of the relation. A supplementary result arising from the analysis is that for systems with a sufficient degree of randomness the ensemble average of the dynamic stiffness matrix of a random subsystem is equal to the inverse of the ensemble average of the receptance matrix.     

Rigid quantum Monte Carlo simulations of condensed molecular matter: water clusters in the n=2-->8 range

The numerical advantage of quantum Monte Carlo simulations of rigid bodies relative to the flexible simulations is investigated for some simple systems. The results show that if high frequency modes in molecular condensed matter are predominantly in the ground state, the convergence of path integral simulations becomes nonuniform. Rigid body quantum parallel tempering simulations are necessary to accurately capture thermodynamic phenomena in the temperature range where the dynamics are influenced by intermolecular degrees of freedom; the stereographic projection path integral adapted for quantum simulations of asymmetric tops is a significantly more efficient strategy compared with Cartesian coordinate simulations for molecular condensed matter under these conditions. The reweighted random series approach for stereographic path integral Monte Carlo is refined and implemented for the quantum simulation of water clusters treated as an assembly of rigid asymmetric tops.     

Identification of a type III thioesterase reveals the function of an operon crucial for Mtb virulence

Rv0098 is part of an operon, Rv0096-Rv0101, from Mycobacterium tuberculosis (Mtb) that is essential for Mtb's survival in mouse macrophages. This operon also contains an acyl carrier protein and one of the only two nonribosomal peptide synthases in Mtb. Rv0098 is annotated in the genome as a hypothetical protein and was proposed to be an acyl-coenzyme A (CoA) dehydratase. The structure of Rv0098, together with subsequent biochemical analysis, indicated that Rv0098 is a long-chain fatty acyl-CoA thioesterase (FcoT). However, FcoT lacks a general base or a nucleophile that is always found in the catalytic site of type II and type I thioesterases, respectively. The active site of Mtb FcoT reveals the structural basis for its substrate specificity for long-chain acyl-CoA and allows us to propose a catalytic mechanism for the enzyme. The characterization of Mtb FcoT provides a putative function of this operon that is crucial for Mtb pathogenicity.     

The onset of coulomb explosions in polyatomic molecules

With the development of high intensity femtosecond lasers, the ionisation and dissociation dynamics of molecules has become an area of considerable interest. Using the technique of femtosecond laser mass spectrometry (FLMS), the molecules carbon disulphide, pyrimidine, toluene, cyclohexanone and benzaldehyde are studied with pulse widths of 50 fs in the near infrared (IR) wavelength region (790 nm). Results are presented and contrasted for laser beam intensities around 10(15) and 10(16) W cm(-2). For the lower intensities, the mass spectra yield dominant singly charged parent ions. Additionally, the appearance of doubly charged parent ions is evident for carbon disulphide, toluene and benzaldehyde with envelopes of doubly charged satellite species existing in these local regions. Carbon disulphide also reveals a small triply charged component. Such atomic-like features are thought to be a strong fingerprint of FLMS at these intensities. However, upon increasing the laser intensity to approximately 10(16) W cm(-2), parent ion dominance decreases and the appearance of multiply charged atomic species occurs, particularly carbon. This phenomenon has been attributed to Coulomb explosions in which the fast absorption of many photons may produce transient highly ionised parent species which can subsequently blow apart. Copyright 1999 John Wiley & Sons, Ltd.