The N=2 supersymmetric unconstrained matrix GNLS hierarchies

The generalization of the N=2 supersymmetric chiral matrix (k|n,m)--GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N=2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax--pair representation in terms of N=2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N=2 superfields, it reproduces the N=2 chiral matrix (k|n,m)-GNLS hierarchy, while in the scalar case, k=1, it is equivalent to the N=2 supersymmetric multicomponent hierarchy (J. Phys. A29 (1996) 1281, hep-th/9510185). The simplest example --the N=2 unconstrained (1|1,0)--GNLS hierarchy-- and its reduction to the N=2 supersymmetric {\alpha}=1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.Comment: 11 pages, LaTex, misprints correcte

The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators

Using new methods of analysis of integrable systems,based on a general geometric approach to nonlinear PDE,we discuss the Dispersionless Boussinesq Equation, which is equivalent to the Benney-Lax equation,being a system of equations of hydrodynamical type. The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. Highly interesting are the appearences of the Noether and Inverse Noether operators ,leading to multiple infinite hierarchies of these operators as well as recursion operators

United States v. Howard: Refocusing Probable Cause for Probationers and Parolees

This Note argues that the Ninth Circuit rigidly followed circuit precedent to create and apply an incorrect standard to determine whether probable cause existed to believe that Howard resided at an unreported address. The court should have determined the reasonableness of the search by balancing Howard\u27s reduced expectation of privacy as a probationer with legitimate governmental interests. Furthermore, the court\u27s analysis served to protect the property at the unreported address rather than Howard\u27s Fourth Amendment privacy rights. This decision is contrary to the principle articulated in Katz v. United States, which states the Fourth Amendment is intended to protect people, not places

United States v. Howard: Refocusing Probable Cause for Probationers and Parolees

This Note argues that the Ninth Circuit rigidly followed circuit precedent to create and apply an incorrect standard to determine whether probable cause existed to believe that Howard resided at an unreported address. The court should have determined the reasonableness of the search by balancing Howard\u27s reduced expectation of privacy as a probationer with legitimate governmental interests. Furthermore, the court\u27s analysis served to protect the property at the unreported address rather than Howard\u27s Fourth Amendment privacy rights. This decision is contrary to the principle articulated in Katz v. United States, which states the Fourth Amendment is intended to protect people, not places

Step structure of vicinal Ge (001) surfaces

The microscopic details of the step morphology of vicinal Ge(001 ) surfaces are analyzed on an atomic level using scanning tunnelling microscopy. Despite the strong correspondence to vicinal Si (001) surfaces, the step structure of the vicinal Ge(001) surface exhibits some significant differences. Rebonded, as well as nonbonded SB step edges, are observed and, related to the occurrence of both configurations, kinks with a minimum length of a0( ≈ 4 Å) do occur. Kinks in SB rebonded step edges can be regarded as independent excitations whereas for kinks in SB nonbonded step edges this is definitely not the case. Occasionally dimers are found at the SB steps, which are located just in between two dimer rows of the upper terrace. Finally, for the first time a ferromagnetic-like coupling between buckled dimers in the same row is observed close to step edges.\ud \u

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