Quasi-optical beamformers provide attractive properties for antenna applications at millimetre-wave frequencies. Antennas implemented with these beamformers have demonstrated wide angle switching of ...directive beams, making them suitable as base station antennas for future communication networks. For these applications, it is essential to ensure a high beam crossover gain to provide a robust service to end users within the steering range. Here, we propose a geodesic generalized Luneburg lens antenna operating from 57 to 67 GHz that provides increased crossover gain compared to previously reported geodesic Luneburg lens antennas. The focal curve of the generalized Luneburg lens can be displaced from the beamformer, allowing for a higher angular resolution in the placement of the feed array along the focal curve. The lens is fed with 21 ridge waveguides with an angular separation of 5.1 degrees, thus providing beam steering in a 102-degree range. The peak realized gain varies from 19 to 21 dBi throughout the steering and frequency ranges and the beam crossover gain is roughly 3 dB below the peak gain. The simulations are experimentally validated.
In this paper we consider a 3D three-parameter unfolding close to the normal form of the triple-zero bifurcation exhibited by the Lorenz system. First we study analytically the double-zero degeneracy ...(a double-zero eigenvalue with geometric multiplicity two) and two Hopf bifurcations. We focus on the more complex case in which the double-zero degeneracy organizes several codimension-one singularities, namely transcritical, pitchfork, Hopf and heteroclinic bifurcations. The analysis of the normal form of a Hopf-transcritical bifurcation allows to obtain the expressions for the corresponding bifurcation curves. A degenerate double-zero bifurcation is also considered. The theoretical information obtained is very helpful to start a numerical study of the 3D system. Thus, the presence of degenerate heteroclinic and homoclinic orbits, T-point heteroclinic loops and chaotic attractors is detected. We find numerical evidence that, at least, four curves of codimension-two global bifurcations are related to the triple-zero degeneracy in the system analyzed.
•The 3D system considered is invariant under the change (x, y, z) → (−x, −y, z).•A double-zero degeneracy (a double-zero eigenvalue with geometric multiplicity two) is studied.•Transcritical, pitchfork, Hopf and heteroclinic bifurcations are involved.•Degenerate global connections, T-point heteroclinic loops and chaotic attractors are detected.•Four degenerate global connections related to the triple-zero bifurcation have been found.
Summary
Background
The most commonly used second‐line Helicobacter pylori eradication regimens are bismuth‐containing quadruple therapy and levofloxacin‐containing triple therapy, both offering ...suboptimal results. Combining bismuth and levofloxacin may enhance the efficacy of rescue eradication regimens.
Aims
To evaluate the efficacy and tolerability of a second‐line quadruple regimen containing levofloxacin and bismuth in patients whose previous H. pylori eradication treatment failed.
Methods
This was a prospective multicenter study including patients in whom a standard triple therapy (PPI–clarithromycin–amoxicillin) or a non‐bismuth quadruple therapy (PPI–clarithromycin–amoxicillin–metronidazole, either sequential or concomitant) had failed. Esomeprazole (40 mg b.d.), amoxicillin (1 g b.d.), levofloxacin (500 mg o.d.) and bismuth (240 mg b.d.) was prescribed for 14 days. Eradication was confirmed by 13C‐urea breath test. Compliance was determined through questioning and recovery of empty medication envelopes. Incidence of adverse effects was evaluated by questionnaires.
Results
200 patients were included consecutively (mean age 47 years, 67% women, 13% ulcer). Previous failed therapy included: standard clarithromycin triple therapy (131 patients), sequential (32) and concomitant (37). A total of 96% took all medications correctly. Per‐protocol and intention‐to‐treat eradication rates were 91.1% (95%CI = 87–95%) and 90% (95%CI = 86–94%). Cure rates were similar regardless of previous (failed) treatment or country of origin. Adverse effects were reported in 46% of patients, most commonly nausea (17%) and diarrhoea (16%); 3% were intense but none was serious.
Conclusions
Fourteen‐day bismuth‐ and levofloxacin‐containing quadruple therapy is an effective (≥90% cure rate), simple and safe second‐line strategy in patients whose previous standard triple or non‐bismuth quadruple (sequential or concomitant) therapies have failed.
In this paper, we present different possibilities for the simplest orbital normal form of the Hopf bifurcation. Beyond the classical normal form we present other forms that have the structure of the ...Rayleigh and the van der Pol equations. The results obtained are applied to obtain orbital normal forms for Newtonian systems with one degree of freedom and Liénard systems.
•Different possibilities for simplest orbital normal forms of Hopf bifurcation.•Normal forms with structure of Rayleigh and van der Pol equations.•1DOF Newtonian and Liénard systems preserving Newtonian structure.•Computation of normal form coefficients (invariants of the vector field).•Effect of the terms of the force in the normal form for Newtonian systems.
In this paper, we consider the orbital-reversibility problem for an
n
-dimensional vector field, which consists in determining if there exists a time-reparametrization that transforms the vector ...field into a reversible one. We obtain an orbital normal form that brings out the invariants that prevent the orbital-reversibility. Hence, we obtain a necessary condition for a vector field to be orbital-reversible. Namely, the existence of an orbital normal form which is reversible to the change of sign in some of the state variables. The necessary condition provides an algorithm, based on the vanishing of the orbital normal form terms that avoid the orbital-reversibility, that is applied to some families of planar and three-dimensional systems.
•We introduce a simple two-parameter quadratic three-dimensional system.•It only has six terms, two nonlinearities and one equilibrium.•A homoclinic flip bifurcation of case inward twist Cin is ...present.•Chaotic behavior with Smale horseshoes and strange attractors is warranted.•It is the first example of a 3D vector field exhibiting the case Cin.
In this paper we consider a two-parameter quadratic three-dimensional system with only six terms and two nonlinearities. First we analyze the Hopf bifurcation of its only equilibrium detecting several degeneracies. With this information we numerically obtain various bifurcation diagrams of periodic orbits in which saddle-node and period-doubling bifurcations as well as homoclinic connections appear. A careful study of the homoclinic orbits, in a region of the two-parameter plane where the equilibrium is a real saddle, shows the presence of a homoclinic flip bifurcation of case C. Here this orbit changes from orientable to non-orientable, being the lowest codimension for a homoclinic bifurcation to a real saddle equilibrium that results in chaotic behavior. More specifically, we determine that it corresponds to the case inward twist Cin, in such a way that, as far as we know, it is the first example of a 3D vector field exhibiting this case.
We give a new algorithmic criterium that determines wether an isolated degenerate singular point of a system of differential equations on the plane is monodromic. This criterium involves the ...conservative and dissipative parts associated to the edges and vertices of the Newton diagram of the vector field.
Newton diagram of a planar vector field allows to determine whether a singular point of an analytic system is a monodromic singular point. We solve the monodromy problem for the nilpotent systems and ...we apply our method to a wide family of systems with a degenerate singular point, so-called generalized nilpotent cubic systems.
In this paper we determine the centers of quasi-homogeneous polynomial planar vector fields of degree 0, 1, 2, 3 and 4. In addition, in every case we make a study of the reversibility and the ...analytical integrability of each one of the above centers. We find polynomial centers which are neither orbitally reversible nor analytically integrable, this is a new scenario in respect to the one of non-degenerate and nilpotent centers.
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