On the approximation of the limit cycles function

We consider planar vector fields depending on a real parameter. It is assumed that this vector field has a family of limit cycles which can be described by means of the limit cycles function $l$. We prove a relationship between the multiplicity of a limit cycle of this family and the order of a zero of the limit cycles function. Moreover, we present a procedure to approximate $l(x)$, which is based on the Newton scheme applied to the Poincar'e function and represents a continuation method. Finally, we demonstrate the effectiveness of the proposed procedure by means of a Li'enard system. The obtained result supports a conjecture by Lins, de Melo and Pugh

Dulac-Cherkas functions for generalized Liénard systems

Dulac-Cherkas functions can be used to derive an upper bound for the number of limit cycles of planar autonomous differential systems including criteria for the non-existence of limit cycles, at the same time they provide information about their stability and hyperbolicity. In this paper, we present a method to construct  a special class of Dulac-Cherkas functions for  generalized Liénard systems of the type $\frac{dx}{dt} = y, \quad  \frac{dy}{dt} = \sum_{j=0}^l h_j(x) y^j$ with $l \ge 1$. In case $1 \le l \le 3$,  linear differential equations play a key role in this process, for $l \ge 4$, we have to solve a system of linear differential and algebraic equations, where the number of equations is larger than the number of unknowns. Finally,  we show that Dulac-Cherkas functions can be used to construct generalized Liénard systems with any $l$ possessing limit cycles

Existence and stability of solutions with periodically moving weak internal layers

We consider the periodic parabolic differential equation $ep^2 Big( fracpartial^2 upartial x^2 -fracpartial upartial t Big)=f(u,x,t,ep)$ under the assumption that $ve$ is a small positive parameter and that the degenerate equation $f(u,x,t,0) =0$ has two intersecting solutions. We derive conditions such that there exists an asymptotically stable solution $u_p(x,t,ep)$ which is $T$-periodic in $t$, satisfies no-flux boundary conditions and tends to the stable composed root of the degenerate equation as $eprightarrow 0$

Second order analysis of geometric functionals of Boolean models

This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second version mainly resolves minor LaTeX problems.

Repetitive high energy pulsed power technology development for industrial applications

The technology base for Repetitive High Energy Pulsed Power (RHEPP) was originally developed to support defense program applications. As RHEPP technology matures, its potential for use in commercial applications can be explored based on inherent strengths of high average power, high dose rate, cost efficient scaling with power, and potential for long life performance. The 300 kW, 2 MeV RHEPP II accelerator is now in operation as a designated DOE User Facility, exploring applications where high dose-rate (> 10{sup 8} Gy/s) may be advantageous, or very high average power is needed to meet throughput requirements. Material surface and bulk property modification, food safety, and large-scale timber disinfestation are applications presently under development. Work is also in progress to generate the reliability database required for the design of 2nd generation systems

Defective Erythrocyte Pyruvate Kinase with Impaired Kinetics and Reduced Optimal Activity

A unique mutant form of erythrocyte pyruvate kinase has been found associated with chronic haemolytic anaemia in a child who is apparently doubly heterozygous for the mutant isoenzyme and for pyruvate kinase deficiency of the classical quantitative type. Clinical and laboratory findings conformed closely to those typically observed in homozygous pyruvate kinase deficiency anaemia. Assayed in fresh haemolysates, the isoenzyme exhibited reduced optimal activity ( c 45% of normal) and an increased Michaelis constant for phosphoenolpyruvate (four to five times greater than normal). The kinetic anomaly was only partially corrected by activation with fructose-1,6-disphosphate. Despite some common characteristics, this isoenzyme appears distinct from others reported in the literature and lends support to the polymorphous nature of heritable baemolytic anaemias secondary to defective pyruvate kinase.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73844/1/j.1365-2141.1972.tb05713.x.pd

Influence of L-carnitine on litter characteristics from gilts harvested at day 40, 55, and 70 of gestation

Swine research, 2005 is known as Swine day, 2005A total of 59 gilts were used to determine the effects of supplemental L-carnitine on reproductive performance. Experimental treatments were arranged in a 2 × 3 factorial with main effects of L-carnitine (0 or 50 ppm) and day of gestation (40, 55, or 70). All gilts received a constant feed allowance of 3.86 lb/day and a top-dress containing either 0 or 88 mg of L-carnitine, starting on the first day of breeding and continuing until the day of harvest. Total litter size, total litter weight, and crown-to-rump length of fetuses were not different (P>0.10) between treatments at any gestation length. By d 70 of gestation, average fetus weight was heavier (P = 0.06) for fetuses from gilts fed L-carnitine, compared with fetuses from gilts fed the control diet. In addition, at d 70, fetal insulin-like growth factor- II (IGF-II) concentrations were lower (P = 0.09) for fetuses from gilts fed L-carnitine than for fetuses from gilts fed the control diet. Feeding L-carnitine may have decreased fetal IGF-II, therefore increasing cell proliferation and delaying cell differentiation. These results show that providing supplemental Lcarnitine to gestating gilts has beneficial effects on average fetal weight, possibly observed because of its ability to reduce fetal IGF-II concentrations

Innovations in air sampling to detect plant pathogens

Many innovations in the development and use of air sampling devices have occurred in plant pathology since the first description of the Hirst spore trap. These include improvements in capture efficiency at relatively high air-volume collection rates, methods to enhance the ease of sample processing with downstream diagnostic methods and even full automation of sampling, diagnosis and wireless reporting of results. Other innovations have been to mount air samplers on mobile platforms such as UAVs and ground vehicles to allow sampling at different altitudes and locations in a short space of time to identify potential sources and population structure. Geographical Information Systems and the application to a network of samplers can allow a greater prediction of airborne inoculum and dispersal dynamics. This field of technology is now developing quickly as novel diagnostic methods allow increasingly rapid and accurate quantifications of airborne species and genetic traits. Sampling and interpretation of results, particularly action-thresholds, is improved by understanding components of air dispersal and dilution processes and can add greater precision in the application of crop protection products as part of integrated pest and disease management decisions. The applications of air samplers are likely to increase, with much greater adoption by growers or industry support workers to aid in crop protection decisions. The same devices are likely to improve information available for detection of allergens causing hay fever and asthma or provide valuable metadata for regional plant disease dynamics

Digital Quantum Simulation with Rydberg Atoms

We discuss in detail the implementation of an open-system quantum simulator with Rydberg states of neutral atoms held in an optical lattice. Our scheme allows one to realize both coherent as well as dissipative dynamics of complex spin models involving many-body interactions and constraints. The central building block of the simulation scheme is constituted by a mesoscopic Rydberg gate that permits the entanglement of several atoms in an efficient, robust and quick protocol. In addition, optical pumping on ancillary atoms provides the dissipative ingredient for engineering the coupling between the system and a tailored environment. As an illustration, we discuss how the simulator enables the simulation of coherent evolution of quantum spin models such as the two-dimensional Heisenberg model and Kitaev's toric code, which involves four-body spin interactions. We moreover show that in principle also the simulation of lattice fermions can be achieved. As an example for controlled dissipative dynamics, we discuss ground state cooling of frustration-free spin Hamiltonians.Comment: submitted to special issue "Quantum Information with Neutral Particles" of "Quantum Information Processing