Acyclic orientations on the Sierpinski gasket

We study the number of acyclic orientations on the generalized two-dimensional Sierpinski gasket $SG_{2,b}(n)$ at stage $n$ with $b$ equal to two and three, and determine the asymptotic behaviors. We also derive upper bounds for the asymptotic growth constants for $SG_{2,b}$ and $d$-dimensional Sierpinski gasket $SG_d$.Comment: 20 pages, 8 figures and 6 table

Analytical and scale model research aimed at improved hangglider design

Research consisted of a theoretical analysis which attempts to predict aerodynamic characteristics using lifting surface theory and finite-element structural analysis as well as an experimental investigation using 1/5 scale elastically similar models in the NASA Ames 2m x 3m (7' x 10') wind tunnel. Experimental data were compared with theoretical results in the development of a computer program which may be used in the design and evaluation of ultralight gliders

Computer aided design and analysis of gear tooth geometry

A simulation method for gear hobbing and shaping of straight and spiral bevel gears is presented. The method is based upon an enveloping theory for gear tooth profile generation. The procedure is applicable in the computer aided design of standard and nonstandard tooth forms. An inverse procedure for finding a conjugate gear tooth profile is presented for arbitrary cutter geometry. The kinematic relations for the tooth surfaces of straight and spiral bevel gears are proposed. The tooth surface equations for these gears are formulated in a manner suitable for their automated numerical development and solution

On the threshold-width of graphs

The GG-width of a class of graphs GG is defined as follows. A graph G has GG-width k if there are k independent sets N1,...,Nk in G such that G can be embedded into a graph H in GG such that for every edge e in H which is not an edge in G, there exists an i such that both endpoints of e are in Ni. For the class TH of threshold graphs we show that TH-width is NP-complete and we present fixed-parameter algorithms. We also show that for each k, graphs of TH-width at most k are characterized by a finite collection of forbidden induced subgraphs

Mechanistic target of rapamycin (mTOR) signaling genes in decapod crustaceans: cloning and tissue expression of mTOR, Akt, Rheb, and S6 kinase in the green crab, Carcinus maenas, and blackback land crab, Gecarcinus lateralis

Mechanistic target of rapamycin (mTOR) controls global translation of mRNA into protein by phosphorylating p70 S6 kinase (S6K) and eIF4E-binding protein-1. Akt and Rheb, a GTP-binding protein, regulate mTOR protein kinase activity. Molting in crustaceans is regulated by ecdysteroids synthesized by a pair of molting glands, or Y-organs (YOs), located in the cephalothorax. During premolt, the YOs hypertrophy and increase production of ecdysteroids. Rapamycin (1 μM) inhibited ecdysteroid secretion in Carcinus maenas and Gecarcinus lateralis YOs in vitro, indicating that ecdysteroidogenesis requires mTOR-dependent protein synthesis. The effects of molting on the expression of four key mTOR signaling genes (mTOR, Akt, Rheb, and S6K) in the YO was investigated. Partial cDNAs encoding green crab (C. maenas) mTOR (4031 bp), Akt (855 bp), and S6K (918 bp) were obtained from expressed sequence tags. Identity/similarity of the deduced amino acid sequence of the C. maenas cDNAs to human orthologs were 72%/81% for Cm-mTOR, 58%/73% for Cm-Akt, and 77%/88% for Cm-S6K. mTOR, Akt, S6K, and elongation factor 2 (EF2) in C. maenas and blackback land crab (G. lateralis) were expressed in all tissues examined. The two species differed in the effects of molting on gene expression in the YO. In G. lateralis, Gl-mTOR, Gl-Akt, and Gl-EF2 mRNA levels were increased during premolt. By contrast, molting had no effect on the expression of Cm-mTOR, Cm-Akt, Cm-S6K, Cm-Rheb, and Cm-EF2. These data suggest that YO activation during premolt involves up regulation of mTOR signaling genes in G. lateralis, but is not required in C. maenas

Roles of mechanistic target of rapamycin and transforming growth factor-B signaling in the molting gland (Y-organ) of the blackback land crab, Gecarcinus lateralis

Molting in decapod crustaceans is controlled by molt-inhibiting hormone (MIH), an eyestalk neuropeptide that suppresses production of ecdysteroids by a pair of molting glands (Y-organs or YOs). Eyestalk ablation (ESA) activates the YOs, which hypertrophy and increase ecdysteroid secretion. At mid premolt, which occurs 7–14 days post-ESA, the YO transitions to the committed state; hemolymph ecdysteroid titers increase further and the animal reaches ecdysis ~ 3 weeks post-ESA. Two conserved signaling pathways, mechanistic target of rapamycin (mTOR) and transforming growth factor-β (TGF-β), are expressed in the Gecarcinus lateralis YO. Rapamycin, an mTOR antagonist, inhibits YO ecdysteroidogenesis in vitro. In this study, rapamycin lowered hemolymph ecdysteroid titer in ESA G. lateralis in vivo; levels were significantly lower than in control animals at all intervals (1–14 days post-ESA). Injection of SB431542, an activin TGF-β receptor antagonist, lowered hemolymph ecdysteroid titers 7 and 14 days post-ESA, but had no effect on ecdysteroid titers at 1 and 3 days post-ESA. mRNA levels of mTOR signaling genes Gl-mTOR, Gl-Akt, and Gl-S6k were increased by 3 days post-ESA; the increases in Gl-mTOR and Gl-Akt mRNA levels were blocked by SB431542. Gl-elongation factor 2 and Gl-Rheb mRNA levels were not affected by ESA, but SB431542 lowered mRNA levels at Days 3 and 7 post-ESA. The mRNA level of an activin TGF-β peptide, Gl-myostatin-like factor (Mstn), increased 5.5-fold from 0 to 3 days post-ESA, followed by a 50-fold decrease from 3 to 7 days post-ESA. These data suggest that (1) YO activation involves an up regulation of the mTOR signaling pathway; (2) mTOR is required for YO commitment; and (3) a Mstn-like factor mediates the transition of the YO from the activated to the committed state

Coherent spin mixing dynamics in a spin-1 atomic condensate

We study the coherent off-equilibrium spin mixing inside an atomic condensate. Using mean field theory and adopting the single spatial mode approximation (SMA), the condensate spin dynamics is found to be well described by that of a nonrigid pendulum, and displays a variety of periodic oscillations in an external magnetic field. Our results illuminate several recent experimental observations and provide critical insights into the observation of coherent interaction-driven oscillations in a spin-1 condensate.Comment: 6 pages, 5 eps figures, update the discussion of the experimental result