Constructing a Space from the System of Geodesic Equations

Given a space it is easy to obtain the system of geodesic equations on it. In this paper the inverse problem of reconstructing the space from the geodesic equations is addressed. A procedure is developed for obtaining the metric tensor from the Christoffel symbols. The procedure is extended for determining if a second order quadratically semi-linear system can be expressed as a system of geodesic equations, provided it has terms only quadratic in the first derivative apart from the second derivative term. A computer code has been developed for dealing with larger systems of geodesic equations

How Does Your Reading Stack Up? Effective Teaching Practices Make for Successful Reading Experiences in the Classroom

This article provides teachers concrete strategies for applying knowledge of how people learn and effective teaching practices to decisions about classroom implementation of science content area readings. This article promotes Iowa Teaching Standards 1, 3, 4, 5, and 6

Bcl-2 antagonizes apoptotic cell death induced by two new ceramide analogues

AbstractCeramides which arise in part from the breakdown of sphingomyelin comprise a class of antiproliferative lipids and have been implicated in the regulation of programmed cell death better known as apoptosis. In the present study, two new synthetic ceramide analogues, N-thioacetylsphingosine and FS-5, were used in Molt4 cells to induce cell death. Besides their cytotoxic effects at concentrations ≥14 μM the data obtained clearly show that both analogues induced apoptosis at concentrations below this critical concentration as assessed by trypan blue exclusion and cleavage of the death substrate poly-(ADP-ribose) polymerase (PARP). Additional experiments in bcl-2-transfected Molt4 cells revealed that the apoptotic but not the lytic effects of the analogues were antagonized by the apoptosis inhibitor Bcl-2. Furthermore, neither N-thio-acetylsphingosine nor FS-5 induced PARP cleavage in bcl-2-transfected Molt4 cells indicating that the induction of apoptotic cell death by cell permeable ceramides is not due to unspecific disturbance of the cell membrane

Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced unitary representations corresponding to prequantization; and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polarization. These representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations.Comment: 29 pages, part 1 of two papers, published versio

On the Complexity of Case-Based Planning

We analyze the computational complexity of problems related to case-based planning: planning when a plan for a similar instance is known, and planning from a library of plans. We prove that planning from a single case has the same complexity than generative planning (i.e., planning "from scratch"); using an extended definition of cases, complexity is reduced if the domain stored in the case is similar to the one to search plans for. Planning from a library of cases is shown to have the same complexity. In both cases, the complexity of planning remains, in the worst case, PSPACE-complete

Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order

Two-dimensional spin-orbital magnets with strong exchange frustration have recently been predicted to facilitate the realization of a quantum critical point in the Gross-Neveu-SO(3) universality class. In contrast to previously known Gross-Neveu-type universality classes, this quantum critical point separates a Dirac semimetal and a long-range-ordered phase, in which the fermion spectrum is only partially gapped out. Here, we characterize the quantum critical behavior of the Gross-Neveu-SO(3) universality class by employing three complementary field-theoretical techniques beyond their leading orders. We compute the correlation-length exponent nu, the order-parameter anomalous dimension eta(phi), and the fermion anomalous dimension eta(psi) using a three-loop epsilon expansion around the upper critical space-time dimension of four, a second-order large-N expansion (with the fermion anomalous dimension obtained even at the third order), as well as a functional renormalization group approach in the improved local potential approximation. For the physically relevant case of N = 3 flavors of two-component Dirac fermions in 2 + 1 space-time dimensions, we obtain the estimates 1/nu = 1.03(15), eta(phi) = 0.42(7), and eta(psi) = 0.180(10) from averaging over the results of the different techniques, with the displayed uncertainty representing the degree of consistency among the three methods