一类周期模型的周期解及次调和分歧的存在性

本文建立一类病菌与免疫系统竞争的周期模型,利用重合度理论及Lyapunov稳定性理论分别证明模型周期解的存在性及稳定性,并讨论次调和分歧的存在性.     

The existence of subharmonic solutions with prescribed minimal period for forced pendulum equations with impulses

In this paper, we study the existence of subharmonic solutions with prescribed minimal period for forced pendulum equations with impulses via variational methods and critical point theory. We give new sufficient conditions for the existence of subharmonic solutions with prescribed minimal period of forced pendulum equations. Our results improve some known results in the literature.     

Simultaneous grayscale and subharmonic ultrasound imaging on a modified commercial scanner

Objective

To demonstrate the feasibility of simultaneous dual fundamental grayscale and subharmonic imaging on a modified commercial scanner.

Motivation

The ability to generate signals at half the insonation frequency is exclusive to ultrasound contrast agents (UCA). Thus, subharmonic imaging (SHI; transmitting at f₀ and receiving at f₀/2) provides improved visualization of UCA within the vasculature via suppression of the surrounding tissue echoes. While this capability has proven useful in a variety of clinical applications, the SHI suppression of surrounding tissue landmarks (which are needed for sonographic navigation) also limits it use as a primary imaging modality. In this paper we present results using a commercial ultrasound scanner modified to allow imaging in both grayscale (f₀ = 4.0 MHz) and SHI (f₀ = 2.5 MHz, f₀/2 = 1.25 MHz) modes in real time.

Methods

A Logiq 9 ultrasound scanner (GE Healthcare, Milwaukee, WI) with a 4C curvilinear probe was modified to provide this capability. Four commercially available UCA (Definity, Lantheus Medical Imaging, North Billerica, MA; Optison, GE Healthcare, Princeton, NJ; SonoVue, Bracco Imaging, Milan, Italy; and Sonazoid, GE Healthcare, Oslo, Norway) were all investigated in vitro over an acoustic output range of 3.34 MPa. In vivo the subharmonic response of Sonazoid was investigated in the portal veins of four canines (open abdominal cavity) and four patients with suspected portal hypertension.

Results

In vitro, the four UCA showed an average maximum subharmonic amplitude of 44.1 ± 5.4 dB above the noise floor with a maximum subharmonic amplitude of 48.6 ± 1.6 dB provided by Sonazoid. The average in vivo maximum signal above the noise floor from Sonazoid was 20.8 ± 2.3 dB in canines and 33.9 ± 5.2 dB in humans. Subharmonic amplitude as a function of acoustic output in both groups matched the S-curve behavior of the agent observed in vitro. The dual grayscale imaging provided easier sonographic navigation, while the degree of tissue suppression in SHI mode varied greatly on a case by case basis.

Conclusions

These results demonstrate the feasibility of dual grayscale and SHI on a modified commercial scanner. The ability to simultaneously visualize both imaging modes in real time should improve the applicability of SHI as a future primary clinical imaging modality.     

Subharmonic and grazing bifurcations for a simple bilinear oscillator

In this paper, subharmonic and grazing bifurcations for a simple bilinear oscillator, namely the limit discontinuous case of the smooth and discontinuous (SD) oscillator are studied. This system is an important model that can be used to investigate the transition from smooth to discontinuous dynamics. A combination of analytical and numerical methods is used to investigate the existence, stability and bifurcations of symmetric and asymmetric subharmonic orbits. Grazing bifurcations for a particular periodic orbit are also discussed and numerical results suggest that the bifurcations are discontinuous. We show via concrete numerical experiments that the dynamics of the system for the case of large dissipation is quite different from that for the case of small dissipation.     

Subharmonic solutions for nonautonomous sublinear second order Hamiltonian systems

Some existence theorems are obtained for subharmonic solutions of nonautonomous second order Hamiltonian systems by the minimax methods in critical point theory.     

Periodic and subharmonic solutions of second-order Hamiltonian systems

Some solvability conditions of periodic solutions and subharmonic solutions are obtained for a class of new superquadratic non-autonomous second-order Hamiltonian systems by the minimax methods in critical point theory.     

Generalization of weierstrass canonical integrals

In this paper we prove that a subharmonic function in ℝ ^m of finite λ-type can be represented (within some subharmonic function) as the sum of a generalized Weierstrass canonical integral and a function of finite λ-type which tends to zero uniformly on compacts of ℝ ^m . The known Brelot-Hadamard representation of subharmonic functions in ℝ ^m of finite order can be obtained as a corollary from this result. Moreover, some properties of R-remainders of λ-admissible mass distributions are investigated.     

Shear-layer acoustic radiation in an excited subsonic jet: experimental study

The subharmonic acoustic radiation of a tone excited subsonic jet shear-layer has been investigated experimentally. Two jet velocities $U_j=20\text{m}?{\text{s}}^{\mathrm{?1}}$ and $U_j=40\text{m}?{\text{s}}^{\mathrm{?1}}$ were studied. For $U_j=20\text{m}?{\text{s}}^{\mathrm{?1}}$, the natural boundary-layer at the nozzle exit is laminar. When the perturbation is applied, the fluctuations of the first and the second subharmonics of the excitation frequency are detected in the shear-layer. In addition, the first subharmonic near pressure field along the spreading jet is constituted of two strong maxima of sinusoidal shape. The far-field directivity pattern displays two lobes separated by an extinction angle ${\theta }^{?}$ at around 85° from the jet axis. These observations follow the results of Bridges about the vortex pairing noise. On the other hand, for $U_j=40\text{m}?{\text{s}}^{\mathrm{?1}}$, the initial boundary-layer is transitional and only the first subharmonic is observed in the presence of the excitation. The near pressure field is of Gaussian shape in the jet periphery and the acoustic far-field is superdirective as observed by Laufer and Yen. The state of the initial shear-layer seems to be the key feature to distinguish these two different radiation patterns. To cite this article: V. Fleury et al., C. R. Mecanique 333 (2005).     

Hypercontractivity for log-subharmonic functions

We prove strong hypercontractivity (SHC) inequalities for logarithmically subharmonic functions on Rn and different classes of measures: Gaussian measures on Rn, symmetric Bernoulli and symmetric uniform probability measures on R, as well as their convolutions. Surprisingly, a slightly weaker strong hypercontractivity property holds for any symmetric measure on R. A log-Sobolev inequality (LSI) is deduced from the (SHC) for compactly supported measures on Rn, still for log-subharmonic functions. An analogous (LSI) is proved for Gaussian measures on Rn and for other measures for which we know the (SHC) holds. Our log-Sobolev inequality holds in the log-subharmonic category with a constant smaller than the one for Gaussian measure in the classical context.