On sets of irreducible polynomials closed by composition

Let $\mathcal S$ be a set of monic degree $2$ polynomials over a finite field and let $C$ be the compositional semigroup generated by $\mathcal S$. In this paper we establish a necessary and sufficient condition for $C$ to be consisting entirely of irreducible polynomials. The condition we deduce depends on the finite data encoded in a certain graph uniquely determined by the generating set $\mathcal S$. Using this machinery we are able both to show examples of semigroups of irreducible polynomials generated by two degree $2$ polynomials and to give some non-existence results for some of these sets in infinitely many prime fields satisfying certain arithmetic conditions

Cover Crop System to Control Charcoal Rot in Soybeans

This research compares methods of controlling charcoal rot in soybean cultivars from three maturity groups commonly grown in southeast Kansas. The results indicate that a mustard plant that produces high levels of glucosinolates can be used as a cover crop to reduce the charcoal rot disease in soybeans

Cover Crop System to Control Charcoal Rot in Soybeans

This research compares methods of controlling charcoal rot in soybean cultivars from three maturity groups commonly grown in southeast Kansas. The results indicate that a mustard plant that produces high levels of glucosinolates can be used as a cover crop to reduce the charcoal rot disease in soybeans

Self-consistent theory of reversible ligand binding to a spherical cell

In this article, we study the kinetics of reversible ligand binding to receptors on a spherical cell surface using a self-consistent stochastic theory. Binding, dissociation, diffusion and rebinding of ligands are incorporated into the theory in a systematic manner. We derive explicitly the time evolution of the ligand-bound receptor fraction p(t) in various regimes . Contrary to the commonly accepted view, we find that the well-known Berg-Purcell scaling for the association rate is modified as a function of time. Specifically, the effective on-rate changes non-monotonically as a function of time and equals the intrinsic rate at very early as well as late times, while being approximately equal to the Berg-Purcell value at intermediate times. The effective dissociation rate, as it appears in the binding curve or measured in a dissociation experiment, is strongly modified by rebinding events and assumes the Berg-Purcell value except at very late times, where the decay is algebraic and not exponential. In equilibrium, the ligand concentration everywhere in the solution is the same and equals its spatial mean, thus ensuring that there is no depletion in the vicinity of the cell. Implications of our results for binding experiments and numerical simulations of ligand-receptor systems are also discussed.Comment: 23 pages with 4 figure

A solvable model for the diffusion and reaction of neurotransmitters in a synaptic junction

<p>Abstract</p> <p>Background</p> <p>The diffusion and reaction of the transmitter acetylcholine in neuromuscular junctions and the diffusion and binding of Ca²⁺in the dyadic clefts of ventricular myocytes have been extensively modeled by Monte Carlo simulations and by finite-difference and finite-element solutions. However, an analytical solution that can serve as a benchmark for testing these numerical methods has been lacking.</p> <p>Result</p> <p>Here we present an analytical solution to a model for the diffusion and reaction of acetylcholine in a neuromuscular junction and for the diffusion and binding of Ca²⁺in a dyadic cleft. Our model is similar to those previously solved numerically and our results are also qualitatively similar.</p> <p>Conclusion</p> <p>The analytical solution provides a unique benchmark for testing numerical methods and potentially provides a new avenue for modeling biochemical transport.</p

Pediatric phantoms for use in dosimetric calculations

Estimating absorbed doses to children from external and internal radiation sources has become important to the nuclear industry and pediatric nuclear medicine. The Medical Physics and Internal Dosimetry Section at ORNL has recently completed the design of mathematical representations of children of ages newborn, 1 year, and 5 years old. These mathematical representations will be referred to as pediatric phantoms. Using these phantoms, relevant energy deposition data have been developed which establish a meaningful model for use in estimating radiation dose to children. (auth

Hyaluronic acid patellar peri-tentinous injection efficacy in sudden detrained rats

Introduzione L’attività fisica moderata seguita da improvvisa interruzione può influenzare le caratteristiche biologiche del tendine. Lo scopo del lavoro è stato quello di valutare l’attività cellulare, le caratteristiche istologiche, istomorfometriche e microstrutturali del tendine patellare e della sua entesi in condizioni di non allenamento (sedentarietà), allenamento ed improvviso arresto dell’attività fisica. E’ stato ipotizzato che un’iniezione peri-tendinea di acido ialuronico nelle settimane successive all’improvviso arresto dell’attività fisica potesse mantenere l’integrità strutturale e biologica del tendine patellare. Materiali e Metodi 24 ratti Sprague Dawley maschi di 8 settimane sono stati suddivisi in tre gruppi, allenati per 10 settimane, fino a 60-80% VO2max. I ratti sono stati suddivisi in tre gruppi: Non Allenati (6), Allenati (6), Disallenati (12). A 6 dei 12 ratti del gruppo Detrained, è stata praticata un’infiltrazione peri-tendinea a nel tendine patellare destro di 300 μl di acido ialuronico, mentre nei rimanenti 6, è stata praticata l’infiltrazione con soluzione fisiologica. I tendini rotulei espiantati sono stati valutati con coltura cellulare, valutazione biologica molecolare, valutazioni morfologiche microstrutturali, proliferazione, conta ed attività cellulare. Risultati I risultati in vitro hanno evidenziato vitalità e conta cellulare simili fra i Gruppi Trained e Detrained-HA con un incremento significativo del metabolismo cellulare rispetto agli altri Gruppi. La cellularità ha mostrato valori maggiori nei Gruppi Non Allenati e Detrained-NaCl ove si è osservata una biosintesi del collagene III superiore ai Gruppi Trained e Detrained-HA. Contrariamente, la produzione di collagene I e II presentava valori maggiori nei Gruppi Trained e Detrained-HA suggerendo una superiore efficienza tessutale e metabolica di questi ultimi. Conclusioni Questi risultati confermano che l’allenamento ed il suo improvviso arresto hanno effetti sulla struttura tendinea patellare di ratto e che l’iniezione peritendinea di acido ialuronico nel periodo di inattività ha effetti significativi su metabolismo cellulare e sul tendine rispetto al trattamento con soluzione fisiologica.Introduction Different conditions may alter tendon characteristics. Clinical evidence suggests that tendon injuries are more frequent in athletes that change type, intensity and duration of training. Aim of the study was the assessment of training and especially detraining on the patellar tendon (PT) and its enthesis. We also hypotized that peri-tendineous injection with Ialuronic acid in detrained rats could prevent structural tendon integrity. Materials and Methods: 24 male adult Sprague-Dawley rats were divided into 3 groups: 18 rats were trained on a treadmill for 10 weeks. Of these, 6 rats were euthanized immediately after training (trained group), 12 were caged without exercise for 4 weeks before being injected in peri patellar tendon tissue, 1 group with Ialuronic acid (de-trained HA group) and the other with Saline solution and then euthanized (de-trained Saline group). The remaining 6 rats used as controls (untrained rats). Patellar tendons were evaluated with cellular coltures, molecular biological evaluation, microstructural morphologic evaluation, cellular proliferation, cellular number and activity. Results In vitro results showed cells vitality and number similar between Trained and Detrained-HA groups with an increased significance cellular methabolism vs the others groups. Cellularity showed better values in Non Trained and Detrained-NaCl Groups where we saw superior collagen III biosinthesis vs Trained and Detrained-HA Groups. On the other side Collagen I and II showed better values in Trained and Detrained-HA suggesting a better tissue activity of Detrained-HA Group. Conclusion Sudden interruption of physical activity has a negative effect on tendons and peri-tendineous patellar injection with Ialuronic Acid can represent a protective tendon therapy after a sudden detraining period

The Intrinsic Origin of Spin Echoes in Dipolar Solids Generated by Strong Pi Pulses

In spectroscopy, it is conventional to treat pulses much stronger than the linewidth as delta-functions. In NMR, this assumption leads to the prediction that pi pulses do not refocus the dipolar coupling. However, NMR spin echo measurements in dipolar solids defy these conventional expectations when more than one pi pulse is used. Observed effects include a long tail in the CPMG echo train for short delays between pi pulses, an even-odd asymmetry in the echo amplitudes for long delays, an unusual fingerprint pattern for intermediate delays, and a strong sensitivity to pi-pulse phase. Experiments that set limits on possible extrinsic causes for the phenomena are reported. We find that the action of the system's internal Hamiltonian during any real pulse is sufficient to cause the effects. Exact numerical calculations, combined with average Hamiltonian theory, identify novel terms that are sensitive to parameters such as pulse phase, dipolar coupling, and system size. Visualization of the entire density matrix shows a unique flow of quantum coherence from non-observable to observable channels when applying repeated pi pulses.Comment: 24 pages, 27 figures. Revised from helpful referee comments. Added new Table IV, new paragraphs on pages 3 and 1

Calibration of the Milagro Cosmic Ray Telescope

The Milagro detector is an air shower array which uses the water Cherenkov technique and is capable of continuously monitoring the sky at energies near 1 TeV. The detector consists of 20000 metric tons of pure water instrumented with 723 photo-multiplier tubes (PMTs). The PMTs are arranged in a two-layer structure on a lattice of 3 m spacing covering 5000 $m^2$ area. The direction of the shower is determined from the relative timing of the PMT signals, necessitating a common time reference and amplitude slewing corrections to improve the time resolution. The calibration system to provide these consists of a pulsed laser driving 30 diffusing light sources deployed in the pond to allow cross-calibration of the PMTs. The system is capable of calibrating times and the pulse-heights from the PMTs using the time-over-threshold technique. The absolute energy scale is provided using single muons passing through the detector. The description of the calibration system of the Milagro detector and its prototype Milagrito will be presented.Comment: 4 pages, submitted to the XXVI International Cosmic Ray Conferenc