Noether's Theorem and time-dependent quantum invariants

The time dependent-integrals of motion, linear in position and momentum operators, of a quantum system are extracted from Noether's theorem prescription by means of special time-dependent variations of coordinates. For the stationary case of the generalized two-dimensional harmonic oscillator, the time-independent integrals of motion are shown to correspond to special Bragg-type symmetry properties. A detailed study for the non-stationary case of this quantum system is presented. The linear integrals of motion are constructed explicitly for the case of varying mass and coupling strength. They are obtained also from Noether's theorem. The general treatment for a multi-dimensional quadratic system is indicated, and it is shown that the time-dependent variations that give rise to the linear invariants, as conserved quantities, satisfy the corresponding classical homogeneous equations of motion for the coordinates.Comment: Plain TeX, 23 pages, preprint of Instituto de Ciencias Nucleares, UNAM Departamento de F\ii sica and Matem\'aticas Aplicadas, No. 01 (1994

Search for double beta decay of Zinc and Tungsten with the help of low-background ZnWO4 crystal scintillators

Double beta processes in 64-Zn, 70-Zn, 180-W, and 186-W have been searched for with the help of large volume (0.1-0.7 kg) low background ZnWO4 crystal scintillators at the Gran Sasso National Laboratories of the INFN. Total time of measurements exceeds 10 thousands hours. New improved half-life limits on double electron capture and electron capture with positron emission in 64-Zn have been set, in particular (all the limits are at 90% C.L.): T1/2(0nu2EC)> 1.1e20 yr, T1/2(2nuECbeta+)>7.0e20 yr, and T1/2(0nuECbeta+)>4.3e20 yr. The different modes of double beta processes in 70-Zn, 180-W, and 186-W have been restricted at the level of 1e17-1e20 yr.Comment: 20 p., submitted to Phys. Rev.

The pseudo-spin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line

Based on the Relativistic continuum Hartree-Bogoliubov (RCHB) theory, the pseudo-spin approximation in exotic nuclei is investigated in Zr and Sn isotopes from the proton drip line to the neutron drip line. The quality of the pseudo-spin approximation is shown to be connected with the competition between the centrifugal barrier (CB) and the pseudo-spin orbital potential (PSOP). The PSOP depends on the derivative of the difference between the scalar and vector potentials $dV/dr$. If $dV/dr = 0$, the pseudo-spin symmetry is exact. The pseudo-spin symmetry is found to be a good approximation for normal nuclei and to become much better for exotic nuclei with highly diffuse potential, which have $dV/dr \sim 0$. The energy splitting of the pseudo-spin partners is smaller for orbitals near the Fermi surface (even in the continuum) than the deeply bound orbitals. The lower components of the Dirac wave functions for the pseudo-spin partners are very similar and almost equal in magnitude.Comment: 22 pages, 9figure

An expression module of WIPF1-coexpressed genes identifies patients with favorable prognosis in three tumor types

Wiskott–Aldrich syndrome (WAS) predisposes patients to leukemia and lymphoma. WAS is caused by mutations in the protein WASP which impair its interaction with the WIPF1 protein. Here, we aim to identify a module of WIPF1-coexpressed genes and to assess its use as a prognostic signature for colorectal cancer, glioma, and breast cancer patients. Two public colorectal cancer microarray data sets were used for discovery and validation of the WIPF1 co-expression module. Based on expression of the WIPF1 signature, we classified more than 400 additional tumors with microarray data from our own experiments or from publicly available data sets according to their WIPF1 signature expression. This allowed us to separate patient populations for colorectal cancers, breast cancers, and gliomas for which clinical characteristics like survival times and times to relapse were analyzed. Groups of colorectal cancer, breast cancer, and glioma patients with low expression of the WIPF1 co-expression module generally had a favorable prognosis. In addition, the majority of WIPF1 signature genes are individually correlated with disease outcome in different studies. Literature gene network analysis revealed that among WIPF1 co-expressed genes known direct transcriptional targets of c-myc, ESR1 and p53 are enriched. The mean expression profile of WIPF1 signature genes is correlated with the profile of a proliferation signature. The WIPF1 signature is the first microarray-based prognostic expression signature primarily developed for colorectal cancer that is instrumental in other tumor types: low expression of the WIPF1 module is associated with better prognosis

Robust Output Regulation of Strongly Passive Linear Systems with Multivalued Maximally Monotone Controls

The use of multivalued controls derived from a special maximally monotone operator are studied in this paper. Starting with a strongly passive linear system (with possible parametric uncertainty and external disturbances) a multivalued control law is derived, ensuring regulation of the output to a desired value. The methodology used falls in a passivity-based control context, where we study how the multivalued control affects the dissipation equation of the closed-loop system, from which we derive its robustness properties. Finally, some numerical examples together with implementation issues are presented to support the main result

Multivalued Robust Tracking Control of Lagrange Systems: Continuous and Discrete-Time Algorithms

The robust trajectory tracking of fully actuated Lagrange systems is studied. Exogenous perturbations as well as parameter uncertainties are taken into account. A family of set-valued passivity-based controllers is proposed, including first-order sliding-mode schemes. The existence of solutions and the stability of the closed-loop system are established in continuous time. An implicit discretization approach is proposed and the well posedness and the stability of the closed-loop system are studied. Numerical simulations illustrate the effectiveness of the proposed discrete-time controller