Quantum effects on t\rightarrow H^{+}\,b in the MSSM: a window to “virtual” supersymmetry?

We analyze the one-loop effects (strong and electroweak) on the unconventional top quark decay mode within the MSSM. The results are presented in the on-shell renormalization scheme with a physically well motivated definition of . The study of this process at the quantum level is useful to unravel the potential supersymmetric nature of the charged Higgs emerging from that decay. As compared with the standard mode , the corrections to are large, slowly decoupling and persist at a sizeable level even for all sparticle masses well above the LEP 200 discovery range. As a matter of fact, the potential size of the SUSY effects, which amount to corrections of several ten percent, could counterbalance the standard QCD corrections and even make them to appear with the “wrong” sign. Therefore, if the charged Higgs decay of the top quark is kinematically allowed – a possibility which is not excluded by the existing measurements of the branching ratio at the Tevatron – it could be an invaluable laboratory to search for “virtual” supersymmetry. While a first significant test of these effects could possibly be performed at the upgraded Tevatron, a more precise verification would most likely be carried out in future experiments at the LHC. Received: 18 April 1997 / Revised version: 18 June 1997     

Optimal Trajectories for Spacecraft Rendezvous

The efficient execution of a rendezvous maneuver is an essential component of various types of space missions. This work describes the formulation and numerical investigation of the thrust function required to minimize the time or fuel required for the terminal phase of the rendezvous of two spacecraft. The particular rendezvous studied concerns a target spacecraft in a circular orbit and a chaser spacecraft with an initial separation distance and separation velocity in all three dimensions. First, the time-optimal rendezvous is investigated followed by the fuel-optimal rendezvous for three values of the max-thrust acceleration via the sequential gradient-restoration algorithm. Then, the time-optimal rendezvous for given fuel and the fuel-optimal rendezvous for given time are investigated. There are three controls, one determining the thrust magnitude and two determining the thrust direction in space. The time-optimal case results in a two-subarc solution: a max-thrust accelerating subarc followed by a max-thrust braking subarc. The fuel-optimal case results in a four-subarc solution: an initial coasting subarc, followed by a max-thrust braking subarc, followed by another coasting subarc, followed by another max-thrust braking subarc. The time-optimal case with fuel given and the fuel-optimal case with time given result in two, three, or four-subarc solutions depending on the performance index and the constraints. Regardless of the number of subarcs, the optimal thrust distribution requires the thrust magnitude to be at either the maximum value or zero. The coasting periods are finite in duration and their length increases as the time to rendezvous increases and/or as the max allowable thrust increases. Another finding is that, for the fuel-optimal rendezvous with the time unconstrained, the minimum fuel required is nearly constant and independent of the max available thrust. Yet another finding is that, depending on the performance index, constraints, and initial conditions, sometime the initial application of thrust must be delayed, resulting in an optimal rendezvous trajectory which starts with a coasting subarc. This research has been supported by NSF under Grant CMS-0218878.     

Tight Lagrangian homology spheres in compact homogeneous Kähler manifolds

For any irreducible compact homogeneous Kähler manifold, we classify the compact tight Lagrangian submanifolds which have the ?²-homology of a sphere.     

On the Linearization of Semilinear Wave Equations

We consider the class of wave equations u _tt−u _xx=f(u, u _t, u _x). By using the differential invariants, with respect to the equivalence transformation algebra of this class, we characterize subclasses of linearizable equations. Wide classes of general solutions for some nonlinear forms of f(u, u _t, u _x) are found.     

On Saint-Venant's principle in three-dimensional elasticity

Summary Toupin's version of Saint-Venant's principle is extended to bodies of general shape, and an exponential upper bound for the strain energy is obtained. The rate of decay is shnow to depend on the first non-zero proper value of the Steklov problem formulated on suitable parts of the body.

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Sommario Si estende a corpi di forma qualsiasi la formulazione di Toupin del principio di de Saint Venant, ottenendo una maggiorazione di tipo esponenziale per l'energia di deformazione. Si dimostra che la velocità di estinzione dipende dal primo autovalore del problema di Steklov formulato su parti opportune del corpo.

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This research was supported in part by the C.N.R., Gruppo Nazionale per la Fisica Matematica.     

Lanthanide Contraction within a Series of Asymmetric Dinuclear [Ln2] Complexes

A complete isostructural series of dinuclear asymmetric lanthanide complexes has been synthesized by using the ligand 6‐[3‐oxo‐3‐(2‐hydroxyphenyl)propionyl]pyridine‐2‐carboxylic acid (H₃ L ). All complexes have the formula [Ln₂(H L )₂(H₂ L )(NO₃)(py)(H₂O)] (Ln=La ( 1 ), Ce ( 2 ), Pr ( 3 ), Nd ( 4 ), Sm ( 5 ), Eu ( 6 ), Gd ( 7 ), Tb ( 8 ), Dy ( 9 ), Ho ( 10 ), Er ( 11 ), Tm ( 12 ), Yb ( 13 ), Lu ( 14 ), Y ( 15 ); py=pyridine). Complexes of La to Yb and Y have been crystallographically characterized to reveal that the two metal ions are encapsulated within two distinct coordination environments of differing size. Whereas one site maintains the coordination number (nine) through the whole series, the other one increases from nine to ten owing to a change in the coordination mode of an NO₃^? ligand. This series offers a unique opportunity to study in detail the lanthanide contraction within complexes of more than one metal. This analysis shows that various representative parameters proportional to this contraction follow a quadratic decay as a function of the number n of f electrons. Slater’s model for the atomic radii has been used to extract, from these decays, the shielding constant of 4f electrons. The average of O???O distances within the coordination polyhedra shared by both metals and of the Ln???Ln separations follow also a quadratic decay, therefore showing that such dependence holds also for parameters that receive the contribution of two lanthanide ions simultaneously. The magnetic behavior has been studied for all nondiamagnetic complexes. It reveals the effect of the spin–orbit coupling and a weak antiferromagnetic interaction between both metals. Photoluminescent studies of all the complexes in the series reveal a single broad emission band in the visible region, which is related to the coordinated ligand. On the other hand, the Nd, Er, and Yb complexes show features in the near‐IR region due to metal‐based transitions.     

A General Approach To Fabricate Fe3O4 Nanoparticles Decorated with Pd,Au, and Rh: Magnetically Recoverable and Reusable Catalysts for Suzuki C?C Cross‐Coupling Reactions,Hydrogenation, and Sequential Reactions

A facile strategy has been explored for loading noble metals onto the surface of ferrite nanoparticles with the assistance of phosphine‐functionalized linkers. Palladium loading is shown to occur with participation of both the phosphine function and the surface hydroxyl groups. Hybrid nanoparticles containing simultaneously Pd and Au (or Rh) are obtained by successive loading of metals. Similarly, ferrite nanoparticles decorated with Pd, Au, and Rh have also been formed by using the same strategy. The catalytic properties of the new nanoparticles are evidenced in processes such as reduction of 4‐nitrophenol or hydrogenation of styrene. Besides, the sequential process involving a cross‐coupling reaction followed by reduction of 1‐nitrobiphenyl has been successfully achieved by employing Pd/Au decorated nanoferrite particles.