Virtual free ion magnetism and the absence of Jahn-Teller distortion in a linear two-coordinate complex of high-spin iron(II)

M?ssbauer spectroscopy and dc magnetization measurements have been used to characterize the low temperature magnetism of a rigorously linear, two-coordinate complex of high-spin Fe(II), Fe[(C(Si(CH3)3]2 (1). The local C-Fe-C chromophore of 1 exhibits novel slow, single-ion paramagnetic relaxation and fully resolved magnetic hyperfine splitting of its zero field M?ssbauer spectrum over the range approximately 100 to approximately 50K. The hyperfine field at 4.2 K is 152 T! This is the largest magnetic hyperfine field observed for iron to date regardless of spin, oxidation state, or coordination environment. This observation is attributable to the large unquenched orbital angular momentum corresponding to the degenerate ground (dxy, dx2-y2) orbital pair of 1 in local Dinfinityh symmetry. Maintenance of the ground-state degeneracy is required by the Jahn-Teller theorem leading to the unprecedented result that the magnitude of the magnetic moment of 1's 5Deltag ground state is essentially that of the parent free ion (5D4) ground term.     

Fourier transform far-infrared studies on transition metal ion-exchanged zeolites A

FT-FIR spectra of xeolites A containing Mn²⁺, Co²⁺, Ni²⁺, Cu⁺ and Zn²⁺ ions were recorded after heat treatment at 573 K in vacuo. The bands were assigned to the vibrations of the cations with respect to the zeolite framework. From obeying the Butler expression it can be inferred that transition metal ions preferably occupy SI sites in zeolite A. Upon adsorption of rare gas and diatomics the bands of the cation vibration diminish and are unspecifically shifted up- and downscale.     

Determination of chlorophenols in urine of children and suggestion of reference values

During the course of a human biomonitoring project (Biebesheim in Hessen, Germany) we elaborated a simple but sensitive method for the determination of tri- (TCP), tetra- (TeCP) and pentachlorophenol (PCP) in human urine. Urine samples, spiked with internal standards, were treated by acid hydrolysis. After a steam bath distillation the distillates were extracted using solid phase extraction. Derivatization of the chlorophenols was not carried out. GC/ECD system was used for detection. Detection limits of the chlorophenols were found in the range of 0.02 μg/L urine (detection limits of the ECD: 0.52 to 2.76 μg/L). By this method mono- and dichlorophenols cannot be detected. We investigated 24h-urine samples of 339 pupils (age 10 to 12 years). The children live either in the surroundings of a hazardous waste incinerator (SVA) in Biebesheim (n = 193), or controls (i.e. regions without waste incinerator) in the non polluted areas of Odenwald (n = 90) and Rheintal (n = 56). Between these three groups we did not find statistically significant differences in chlorophenol concentrations of the urine samples. The 95-percentiles of the analyzed samples are 0.74 μg/L (2,3,4-TCP), 1.24 μg/L (2,3,5-TCP), 0.70 μg/L (2,3,6–TCP), 1.10 μg/L (2,4,5–TCP), 1.74 μg/L (2,4,6–TCP), 2.84 μg/L (3,4,5–TCP), 4.78 μg/L (2,3,4,5-TeCP), 1.86 μg/L (2,3,4,6-TeCP), 2.90 μg/L (2,3,5,6-TeCP) and 4.39 μg/L (PCP). Received: 24 February 1999 / Revised: 3 May 1999 / Accepted: 6 May 1999     

Direct proof of the tree-level scattering amplitude recursion relation in Yang-mills theory

Recently, by using the known structure of one-loop scattering amplitudes for gluons in Yang-Mills theory, a recursion relation for tree-level scattering amplitudes has been deduced. Here, we give a short and direct proof of this recursion relation based on properties of tree-level amplitudes only.     

Confined multilamellae prefer cylindrical morphology

By evaporating a drop of lipid dispersion we generate the myelin morphology often seen in dissolving surfactant powders. We explain these puzzling nonequilibrium structures using a geometric argument: the bilayer repeat spacing increases and thus the repulsion between bilayers decreases when a multilamellar disk is converted into a myelin without gain or loss of material and with number of bilayers unchanged. Sufficient reduction in bilayer repulsion can compensate for the cost in curvature energy, leading to a net stability of the myelin structure. A numerical estimate predicts the degree of dehydration required to favor myelin structures over flat lamellae.     

Approximate degeneracies of zone boundary phonons in alkali halide crystals

We point out the existence of a pervasive pattern of near degeneracies of phonon frequencies in isobaric alkali halide crystals (NaBr, KCl, RbBr, CsI) which strongly suggests that their dynamical matrices are almost invariant under transformations which exchange positive and negative ions. We extend this hypothesis to a relation between phonon properties of “mirror” alkali halides in which the ions of one crystal are replaced by the oppositely charged isobaric ions of the other, such as RbCl and KBr. Experimental evidence supporting this can also be adduced. Similar near degeneracies universally occurring in NaCl structure alkali halides and alkaline earth oxides are also noted and a possible dynamical basis for understanding these suggested.     

Stochastische Transportprobleme

Zusammenfassung Eine große Zahl betrieblicher Planungsprobleme läßt sich durch Anwendung des klassischen Transportmodells bewältigen, wobei jedoch in vielen Fällen nur eine unbefriedigende Kongruenz zwischen dem Modell und der tatsächlichen Planungssituation erreicht wird, weil die zugrundeliegenden Daten nicht deterministisch sind, sondern zufälligen Schwankungen unterliegen. Deshalb soll im folgenden ein Lösungsansatz entwickelt werden, der es gestattet, stochastische Angebots- und Bedarfsmengen zu berücksichtigen. Es gelingt, diese Problemstellung auf ein deterministisches Transportmodell mit teilweise konvexen, teilweise linearen Kostenverläufen zurückzuführen, für das ein allgemeines Lösungsverfahren angegeben wird.

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Summary In the field of economic planning a lot of problems can be solved by application of theHitchcock-transportation model. As in many cases the input-parameters are not of deterministic, but of stochastic nature this simple model will not fit the actual planning-situation sufficiently. For that reason this paper presents a method for solving transportation problems with stochastic supply and demand. It is possible to transform the original stochastic problem to a special deterministic transportation model with partly convex, partly linear costfunctions for which a general algorithm is presented.

     

The S-matrix of the kinks of the (gyψ)2 model

We consider the particle-kink and kink-kink S-matrix elements of the two-dimensional $\text{(}\text{ψ}\text{ψ)}{}^2$ model, where the Majorana spinor ψ is an O(N) isovector. Our results confirm many qualitative ideas about the model, including the mass spectrum, the decoupling at N = 4, and the isospinor nature of the kinks.     

Perturbative Gauge Theory as a String Theory in Twistor Space

Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of = 4 super Yang-Mills theory and the D-instanton expansion of a certain string theory, namely the topological B model whose target space is the Calabi-Yau supermanifold Dedicated to Freeman Dyson for his 80th birthdayAcknowledgement I am indebted to N. Berkovits for numerous helpful discussions of some of these ideas and pointing out a number of significant references, to F. Cachazo for extensive assistance with computer algebra, to L. Dixon for answering many queries about perturbative Yang-Mills theory, and to M. F. Atiyah and R. Penrose for mathematical consultations. This work was supported in part by NSF Grant PHY-0070928.     

Characteristic angles in the wetting of an angular region: Surface shape

The shape of a liquid surface bounded by an acute or obtuse planar angular sector is considered by using classical analysis methods. For acute angular sectors the two principal curvatures are of the order of the (fixed) mean curvature. But for obtuse sectors, the principal curvatures both diverge as the vertex is approached. The power law divergence becomes stronger with increasing opening angle. Possible implications of this contrasting behavior are suggested. Received 1 February 2001 and Received in final form 14 August 2001