Counting fixed points and rooted closed walks of the singular map x↦xxnx \mapsto x^{x^n} modulo powers of a prime

The "self-power" map $x \mapsto x^x$ modulo $m$ and its generalized form $x \mapsto x^{x^n}$ modulo $m$ are of considerable interest for both theoretical reasons and for potential applications to cryptography. In this paper, we use $p$-adic methods, primarily $p$-adic interpolation, Hensel's lemma, and lifting singular points modulo $p$, to count fixed points and rooted closed walks of equations related to these maps when $m$ is a prime power. In particular, we introduce a new technique for lifting singular solutions of several congruences in several unknowns using the left kernel of the Jacobian matrix.Comment: 18 pages. Version 2 shortens proofs, reduces redundancy, and introduces new technique for counting rooted closed walks. Version 3 updates title to agree with journal publicatio

Task demands dissociate the effects of muscarinic M-1 receptor blockade and protein kinase C inhibition on attentional performance in rats

The cholinergic system is known to be necessary for normal attentional processing. However, the receptors and mechanisms mediating the effects of acetylcholine on attention remain unclear. Previous work in our laboratory suggested that cholinergic muscarinic receptors are critical for maintaining performance in an attention-demanding task in rats. We examined the role of the muscarinic M-1 receptor and protein kinase C (PKC), which is activated by the M-1 receptor, in attention task performance. Rats were trained in an attention-demanding task requiring discrimination of brief (500, 100, 25 ms) visual signals from trials with no signal presentation. The effects of muscarinic M-1 receptor blockade were assessed by administering dicyclomine (0-5.0 mg/kg). The effects of PKC inhibition were assessed by administering chelerythrine chloride (0-2.0 mg/kg). Dicyclomine decreased the accuracy of detecting longer signals in this attention task, including when attentional demands were increased by flashing a houselight throughout the session. Chelerythrine chloride decreased the accuracy of signal detection in the standard version of the task but not when the houselight was flashed throughout the session. The present findings indicate that muscarinic M-1 receptors are critical for maintaining performance when attentional demands are increased, and that PKC activity may contribute to some aspects of attentional performance

Design, construction, and characterization of a prompt gamma activation analysis facility at the Oregon State University TRIGA® reactor

In this work a prompt gamma neutron activation analysis (PGNAA) facility has been designed, built, and characterized at the Oregon State University TRIGA® reactor. PGNAA is a technique used to determine the presence and quantity of trace elements such as boron, hydrogen and carbon which are more difficult to detect with other neutron analysis methods. In PGNAA, isotopes are subjected to a neutron beam, resulting in the formation of an unstable compound nucleus. The compound nucleus immediately decays, producing a series of gamma-rays, whose energies are distinctive to each element. These gamma-rays are then measured using an HPGe detector to determine the elemental composition of the sample. The measured thermal and epithermal neutron fluxes of the PGNAA facility at Oregon State University are 2.81 x 10⁷ ± 5.13 x 10⁵ cm⁻²s⁻¹ and 1.70 x 10⁴ ± 3.11 x 10² cm⁻²s⁻¹ respectively. This gives the facility a cadmium ratio of 106. Measured detection limits for boron, chlorine, and potassium in SRM 1571 orchard leaf standard were, 5.6 x 10⁻⁴mg/g, 8.2 x 10⁻² mg/g and, 1.0 mg/g respectively. Also, the detection limit for hydrogen in high-density polyethylene is, 6.8 x 10⁻²mg/g. Detection limits for additional elements are presented in this work