Frobenius theorem and invariants for Hamiltonian systems

We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence of a two-dimensional foliation to which the motion is constrained. In particular, we derive a new infinite class of potentials for which the motion is assurately restricted to a two-dimensional foliation. In some cases, Frobenius theorem allows the explicit construction of an associated invariant. It is proven the inverse result that, if an invariant is known, then it always can be furnished by Frobenius theorem

Downregulation of Tumor Necrosis Factor Expression in the Human Mono-Mac-6 Cell Line

Mono-Mac-6 cells, but not U937 cells, can be Induced to rapidly express tumor necrosis factor (TNF) mRNA and protein when triggered with Ilpopolysaccharlde (LPS) at 1 pg/mI. Preincubatlon of the cells for 3 d with low amounts of LPS (10 ng/mI) results In nearly complete suppression of TNF secretion. This downreguiatlon appears to occur at the pretranslational level since specIfIc mRNA is virtually undetectable under these conditions. By contrast, the same prelncubatlon with 10 ng/mI LPS results in enhanced phagocytosls (28.6-67.2% for Staphylococcus aureus), demonstrating that not all monocyte functions are suppressed. While these results show that only stringent exclusion of LPS from culture media allows for Induction of TNF In the Mono-Mac-6 cell line, the pronounced effect of LPS preincubatlon may also provide a suitable model with which to study the mechanisms of LPS-lnduced desensitizatIon

In situ hybridization in Vitis vinifera L.

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Entanglement, fidelity and topological entropy in a quantum phase transition to topological order

We present a numerical study of a quantum phase transition from a spin-polarized to a topologically ordered phase in a system of spin-1/2 particles on a torus. We demonstrate that this non-symmetry-breaking topological quantum phase transition (TOQPT) is of second order. The transition is analyzed via the ground state energy and fidelity, block entanglement, Wilson loops, and the recently proposed topological entropy. Only the topological entropy distinguishes the TOQPT from a standard QPT, and remarkably, does so already for small system sizes. Thus the topological entropy serves as a proper order parameter. We demonstrate that our conclusions are robust under the addition of random perturbations, not only in the topological phase, but also in the spin polarized phase and even at the critical point.Comment: replaced with published versio

Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries

Symmetries of the near horizon of a Black Hole by Group Theoretic methods

We use group theoretic methods to obtain the extended Lie point symmetries of the quantum dynamics of a scalar particle probing the near horizon structure of a black hole. Symmetries of the classical equations of motion for a charged particle in the field of an inverse square potential and a monopole, in the presence of certain model magnetic fields and potentials are also studied. Our analysis gives the generators and Lie algebras generating the inherent symmetries.Comment: To appear in Int. J. Mod. Phys.

Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions

Exactly solving a spinless fermionic system in two and three dimensions, we investigate the scaling behavior of the block entropy in critical and non-critical phases. The scaling of the block entropy crucially depends on the nature of the excitation spectrum of the system and on the topology of the Fermi surface. Noticeably, in the critical phases the scaling violates the area law and acquires a logarithmic correction \emph{only} when a well defined Fermi surface exists in the system. When the area law is violated, we accurately verify a conjecture for the prefactor of the logarithmic correction, proposed by D. Gioev and I. Klich [quant-ph/0504151].Comment: 4 pages, 4 figure

Radiation Tests for Orbiting Astronomical Observatory Scientific Report No. 1

Radiation test for orbiting astronomical observatory antenna