Über Triphenylmethane,deren Benzolkerne miteinander verbunden sind

Ohne Zusammenfassung     

Spin-state splittings, highest-occupied-molecular-orbital and lowest-unoccupied-molecular-orbital energies, and chemical hardness

It is known that the exact density functional must give ground-state energies that are piecewise linear as a function of electron number. In this work we prove that this is also true for the lowest-energy excited states of different spin or spatial symmetry. This has three important consequences for chemical applications: the ground state of a molecule must correspond to the state with the maximum highest-occupied-molecular-orbital energy, minimum lowest-unoccupied-molecular-orbital energy, and maximum chemical hardness. The beryllium, carbon, and vanadium atoms, as well as the CH(2) and C(3)H(3) molecules are considered as illustrative examples. Our result also directly and rigorously connects the ionization potential and electron affinity to the stability of spin states.     

Observable T7 lepton flavor symmetry at the Large Hadron Collider

More often than not, models of flavor symmetry rely on the use of nonrenormalizable operators (in the guise of flavons) to accomplish the phenomenologically successful tribimaximal mixing of neutrinos. We show instead how a simple renormalizable two-parameter neutrino mass model of tribimaximal mixing can be constructed with the non-Abelian discrete symmetry T(7) and the gauging of B-L. This is also achieved without the addition of auxiliary symmetries and particles present in almost all other proposals. Most importantly, it is verifiable at the Large Hadron Collider.     

Construction of invariant whiskered tori by a parameterization method. Part I: Maps and flows in finite dimensions

We present theorems which provide the existence of invariant whiskered tori in finite-dimensional exact symplectic maps and flows. The method is based on the study of a functional equation expressing that there is an invariant torus.We show that, given an approximate solution of the invariance equation which satisfies some non-degeneracy conditions, there is a true solution nearby. We call this an a posteriori approach.The proof of the main theorems is based on an iterative method to solve the functional equation.The theorems do not assume that the system is close to integrable nor that it is written in action-angle variables (hence we can deal in a unified way with primary and secondary tori). It also does not assume that the hyperbolic bundles are trivial and much less that the hyperbolic motion can be reduced to constant linear map.The a posteriori formulation allows us to justify approximate solutions produced by many non-rigorous methods (e.g. formal series expansions, numerical methods). The iterative method is not based on transformation theory, but rather on successive corrections. This makes it possible to adapt the method almost verbatim to several infinite-dimensional situations, which we will discuss in a forthcoming paper. We also note that the method leads to fast and efficient algorithms. We plan to develop these improvements in forthcoming papers.     

Beyond the standard model: Working group report

This report summarises the activities of the working group on ‘Physics beyond the Standard Model’. The results of investigations in incorporatingR-parity in grand unification, the possibility of a light charged Higgs boson in extension of MSSM and radiative generation of neutral vector boson self-couplings within the MSSM are described. Also given is an account of activities in neutrino physics, namely a proposal for a study of the atmospheric muon anomaly in deep underground mines, a field theoretic study of neutrino oscillations and a mechanism to generate appropriate masses of three active plus one sterile neutrino species.     

Shear and necking instabilities in nonlinear elasticity

This paper examines the behavior of a class of nonlinearly elastic rods under tension. These rods can suffer longitudinal extension, transverse contraction, shear, and flexure. The deformation is governed by an eighth order, quasilinear system of ordinary differential equations. A convergent perturbation process shows that there is a very rich collection of solutions that bifurcate from the trivial affine configuration. Global results are obtained for hyperelastic rods. These solutions describe instabilities of the shear and necking type and can exhibit hysteresis.

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Résumé On considère le comportement d'une classe de poutres nonlinéairement élastiques en état de tension. Ces poutres peuvent souffrir une extension longitudinale, une contraction transversale, un cisaillement et une fiexion. La déformation est gouvernée par un système quasi-linéaire d'équations différentielles ordinaires du huitième ordre. Un procès convergeant de perturbations montre qu'il y a une collection très riche de solutions qui bifurquent de la configuration banale affine. Dans le cas hypérélastique on obtient des résultats globaux. On montre que ces solutions décrivent des instabilités du type de cisaillement et d'étranglement et peuvent exhiber une hystérésis.

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The research of the first author was supported by National Science Foundation Grant MPS 73-08587 A02. Some of the results reported here were obtained by the second author in his master's thesis.     

Low-frequency dilatational wave propagation through unsaturated porous media containing two immiscible fluids

An analytical theory is presented for the low-frequency behavior of dilatational waves propagating through a homogeneous elastic porous medium containing two immiscible fluids. The theory is based on the Berryman–Thigpen–Chin (BTC) model, in which capillary pressure effects are neglected. We show that the BTC model equations in the frequency domain can be transformed, at sufficiently low frequencies, into a dissipative wave equation (telegraph equation) and a propagating wave equation in the time domain. These partial differential equations describe two independent modes of dilatational wave motion that are analogous to the Biot fast and slow compressional waves in a single-fluid system. The equations can be solved analytically under a variety of initial and boundary conditions. The stipulation of “low frequency” underlying the derivation of our equations in the time domain is shown to require that the excitation frequency of wave motions be much smaller than a critical frequency. This frequency is shown to be the inverse of an intrinsic time scale that depends on an effective kinematic shear viscosity of the interstitial fluids and the intrinsic permeability of the porous medium. Numerical calculations indicate that the critical frequency in both unconsolidated and consolidated materials containing water and a nonaqueous phase liquid ranges typically from kHz to MHz. Thus engineering problems involving the dynamic response of an unsaturated porous medium to low excitation frequencies (e.g., seismic wave stimulation) should be accurately modeled by our equations after suitable initial and boundary conditions are imposed.     

Aβ40 and Aβ42 amyloid fibrils exhibit distinct molecular recycling properties

A critical aspect to understanding the molecular basis of Alzheimer's disease (AD) is the characterization of the kinetics of interconversion between the different species present during amyloid-β protein (Aβ) aggregation. By monitoring hydrogen/deuterium exchange in Aβ fibrils using electrospray ionization mass spectrometry, we demonstrate that the Aβ molecules comprising the fibril continuously dissociate and reassociate, resulting in molecular recycling within the fibril population. Investigations on Aβ40 and Aβ42 amyloid fibrils reveal that molecules making up Aβ40 fibrils recycle to a much greater extent than those of Aβ42. By examining factors that could influence molecular recycling and by running simulations, we show that the rate constant for dissociation of molecules from the fibril (k(off)) is much greater for Aβ40 than that for Aβ42. Importantly, the k(off) values obtained for Aβ40 and Aβ42 reveal that recycling occurs on biologically relevant time scales. These results have implications for understanding the role of Aβ fibrils in neurotoxicity and for designing therapeutic strategies against AD.     

Interactions of halichondrin B and eribulin with tubulin

Compounds that modulate microtubule dynamics include highly effective anticancer drugs, leading to continuing efforts to identify new agents and improve the activity of established ones. Here, we demonstrate that [(3)H]-labeled halichondrin B (HB), a complex, sponge-derived natural product, is bound to and dissociated from tubulin rapidly at one binding site per αβ-heterodimer, with an apparent K(d) of 0.31 μM. We found no HB-induced aggregation of tubulin by high-performance liquid chromatography, even following column equilibration with HB. Binding of [(3)H]HB was competitively inhibited by a newly approved clinical agent, the truncated HB analogue eribulin (apparent K(i), 0.80 μM) and noncompetitively by dolastatin 10 and vincristine (apparent K(i)'s, 0.35 and 5.4 μM, respectively). Our earlier studies demonstrated that HB inhibits nucleotide exchange on β-tubulin, and this, together with the results presented here, indicated the HB site is located on β-tubulin. Using molecular dynamics simulations, we determined complementary conformations of HB and β-tubulin that delineated in atomic detail binding interactions of HB with only β-tubulin, with no involvement of the α-subunit in the binding interaction. Moreover, the HB model served as a template for an eribulin binding model that furthered our understanding of the properties of eribulin as a drug. Overall, these results established a mechanistic basis for the antimitotic activity of the halichondrin class of compounds.