Remarks on the k-error linear complexity of p(n)-periodic sequences

Recently the first author presented exact formulas for the number of 2ⁿn-periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity and upper and lower bounds for the expected k-error linear complexity, k >2, of a random 2ⁿn-periodic binary sequence. A crucial role for the analysis played the Chan-Games algorithm. We use a more sophisticated generalization of the Chan-Games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the 1-error linear complexity for pⁿn-periodic sequences over Fp, p prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of pⁿn-periodic sequences over Fp

Multi-Plaintiff Litigation in Australia: A Comparative Perspective

Graphene is a single layer of carbon atoms, laid out in a hexagonal lattice. The material has remarkable properties that opened up several new research areas since its discovery in 2004. One promising field is graphene based biosensors, where researchers hope to create new devices that are smaller, cheaper and more reliable than those based on today’s technology. Among several manufacturing methods, graphene grown on silicon carbide is one of the promising ones for biosensing. A chip design has been developed in order to support research into graphene on silicon carbide as a base material for biosensors. Along with the chip, a holder for electrochemical measurements has been designed and an investigation into the requirements of a custom measurement device for the sensor has been undertaken

The Mayflies (Ephemeroptera) of Tennessee, With a Review of the Possibly Threatened Species Occurring Within the State

One hundred and forty-three species of mayflies are reported from the state of Tennessee. Sixteen species (Ameletus cryptostimulus, Choroterpes basalis, Baetis virile, Ephemera blanda, E. simulans, Ephemerella berneri, Heterocloeon curiosum, H. petersi, Labiobaetis ephippiatus, Leptophlebia bradleyi, Macdunnoa brunnea, Paraleptophlebia assimilis, P. debilis, P. mollis, Rhithrogenia pellucida and Siphlonurus mirus) are reported for the first time. Rare and vulnerable species occurring in the state are also discussed. This represents the first comprehensive statewide list of mayflies for Tennessee

Spontaneous stochasticity of velocity in turbulence models

We analyze the phenomenon of spontaneous stochasticity in fluid dynamics formulated as the nonuniqueness of solutions resulting from viscosity at infinitesimal scales acting through intermediate on large scales of the flow. We study the finite-time onset of spontaneous stochasticity in a real version of the GOY shell model of turbulence. This model allows high-accuracy numerical simulations for a wide range of scales (up to ten orders of magnitude) and demonstrates non-chaotic dynamics, but leads to an infinite number of solutions in the vanishing viscosity limit after the blowup time. Thus, the spontaneous stochasticity phenomenon is clearly distinguished from the chaotic behavior in turbulent flows. We provide the numerical and theoretical description of the system dynamics at all stages. This includes the asymptotic analysis before and after the blowup leading to universal (periodic and quasi-periodic) renormalized solutions, followed by nonunique stationary states at large times.Comment: 20 pages, 9 figure

New proofs of determinant evaluations related to plane partitions

We give a new proof of a determinant evaluation due to Andrews, which has been used to enumerate cyclically symmetric and descending plane partitions. We also prove some related results, including a q-analogue of Andrews's determinant.Comment: 25 page