Subharmonic solutions for a class of non-quadratic second order Hamiltonian systems

In this paper, some existence theorems are obtained for infinitely subharmonic solutions of second order Hamiltonian systems under non-quadratic conditions. The approach is the minimax principle. Our results greatly extend and improve some known results.     

Drastic acceleration of fibrillation of insulin by transient cavitation bubble

Amyloid-fibril formation of proteins can be accelerated by ultrasonic irradiation to the peptide solutions. Although this phenomenon contributes to understanding pathogenic behavior of amyloidosis, its physical mechanism has not been clarified, because several factors (cavitation, temperature increase, stirring effect, and so on) related to ultrasonic irradiation can participate in the fibrillation reaction. Here, we independently study contributions of the possible factors, using insulin, which is extremely stable and then suitable for the mechanism clarification. We find that the optimized ultrasonic irradiation can drastically accelerate the fibrillation reaction; the time for completing the reaction is shortened compared with the high-speed (1200 rpm) stirring agitation by a factor of 430. The fibrillation reaction proceeds only when the subharmonic-mode intensity exceeds a threshold, indicating generation of the transient cavitation bubbles. Our results reveal that not the temperature increase but the transient cavitation bubbles work as the dominant accelerator of the fibrillation reaction.     

Axiomatic Potential Theory,Asymptotic Values and Elliptic Differential Operators

In [14] Fernández, Heinonen and Llorente extend the Hornblower's results, about boundary behaviour of subharmonic functions in the unit disc of the complex plane, to subharmonic functions in the unit ball or the upper half space in higher dimensions. In this paper we establish that those results are also valid in the much more general setting of linear axiomatic potential theory. The interest of our general formulation relies on the applications to differential operators. We apply our result to Laplace–Beltrami operator and some uniformly elliptic second order operators in divergence form.     

ON COMPLETE OPEN MANIFOLDS WITH NON-NEGATIVE CURVATURE ALONG RAY DIRECTIONS

1IntroductionSupposeMisan-dimensionalmemanllianmanifold.Itiscalledopenifit'sconnectedandnoncompact.Therearemanybeautifulresultsaboutcompleteopenmanifoldswithnon-negativecurvature,seeforexample[1]-[7].Furtherstudyshowsthatthepropertiesofraysonopenmanifoldsareimportant.Manyresultsarealsotrueunderweakercurvatureconditions.InthesequelwewillalwaysassumethatMisacompleteopenmanifold.SupposepEM,uETPM.Wecalluaraydirectionifthereisarayissuingfrompsuchthatvistangenttothisray(Wedefinearaytobeageodes…     

Subharmonic and bursting oscillations of a ferromagnetic mass fixed on a spring and subjected to an AC electromagnet

This paper considers the dynamics of an electromechanical system consisting of a ferromagnetic mass fixed on a spring and subjected to an AC electromagnet. Subharmonic and bursting oscillations are found and their shape analyzed when one varies the viscous damping coefficient, the number of turns of the coil, the frequency and amplitude of the AC voltage. Pulse packages patterns and sharp burstings are observed in the motion of the mechanical part.     

Subharmonic branching at a reversible 1:1 resonance

We investigate the bifurcation of q-periodic points from a fixed point of a 2-parameter family of n-dimensional reversible diffeomorphisms (n ≥ 4). The focus is on the codimension 2 non-semisimple 1:1 resonance case, that is, when the linearization at the fixed point has a pair of double eigenvalues on the unit circle, exp ( ± 2iπp/q) (with gcd(p, q) = 1), with geometric multiplicity 1. Through a modified version of Lyapunov Schmidt reduction, the reduced bifurcation equations are obtained. These are then analysed using reversible normal form theory and (reversible) singularity theory. We obtain the existence of two branches of symmetric q-periodic orbits bifurcating from the fixed point. We also describe the corresponding bifurcation scenario for a family of reversible systems in the case of a two-fold resonance, cfr. [12 Knobloch, J. and Vanderbauwhede, A., Hopf bifurcation at k-fold resonances in reversible systems, Preprint Technische Universiteit at Ilmenau, No. M 16/95. [Google Scholar] 5 Buzzi, C.A. and Lamb, J.S.W., Reversible equivariant Hopf bifurcation. Archive for Rational Mechanics and Analysis. In press. [Google Scholar]].     

Subharmonic aided pressure estimation for monitoring interstitial fluid pressure in tumours – In vitro and in vivo proof of concept

The feasibility of using subharmonic aided pressure estimation (SHAPE) to noninvasively estimate interstitial fluid pressure (IFP) was studied. In vitro, radiofrequency signals, from 0.2 ml/l of Definity (Lantheus Medical Imaging, N Billerica, MA) were acquired within a water-tank with a Sonix RP ultrasound scanner (Analogic Ultrasound, Richmond, BC, Canada; f_T/R = 6.7/3.35 MHz and f_T/R = 10/5 MHz) and the subharmonic amplitudes of the signals were compared over 0–50 mmHg. In vivo, five swine with naturally occurring melanomas were studied. Subharmonic signals were acquired from tumours and surrounding tissue during infusion of Definity and compared to needle-based pressure measurements. Both in vitro and in vivo, an inverse linear relationship between hydrostatic pressure and subharmonic amplitude was observed with r² = 0.63–0.95; p < 0.05, maximum amplitude drop 11.36 dB at 10 MHz and −8 dB, and r² as high as 0.97; p < 0.02 (10 MHz and −4/−8 dB most promising), respectively, indicating that SHAPE may be useful in monitoring IFP.     

Elliptic averaging methods using the sum of Jacobian elliptic delta and zeta functions as the generating solution

The present paper describes an improved version of the elliptic averaging method that provides a highly accurate periodic solution of a non-linear system based on the single-degree-of-freedom Duffing oscillator with a snap-through spring. In the proposed method, the sum of the Jacobian elliptic delta and zeta functions is used as the generating solution of the averaging method. The proposed method can be used to obtain the non-odd-order solution, which includes both even- and odd-order harmonic components. The stability analysis for the approximate solution obtained by the present method is also discussed. The stability of the solution is determined from the characteristic multiplier based on Floquet’s theorem. The proposed method is applied to a fundamental oscillator in a non-linear system. The numerical results demonstrate that the proposed method is very effective for analyzing the periodic solution of half-swing mode for systems based on Duffing oscillators with a snap-through spring.     

Reverse triangle inequalities for potentials

We study the reverse triangle inequalities for suprema of logarithmic potentials on compact sets of the plane. This research is motivated by the inequalities for products of supremum norms of polynomials. We find sharp additive constants in the inequalities for potentials, and give applications of our results to the generalized polynomials.We also obtain sharp inequalities for products of norms of the weighted polynomials , and for sums of potentials with external fields. An important part of our work in the weighted case is a Riesz decomposition for the weighted farthest-point distance function.     

周期流形的不变环面和次调和分支

本文通过精华Ｆｌｏｑｕｅｔ方法在周期流形的周期轨道邻域建立起适当的局部坐标，然后应用平均法和积分流形及Ｆｅｎｉｃｈｅｌ不变流形理论来证明不变环面和次调和轨道的存在性和法向双曲性．大多数传统的假设被放弃，而大多数已知的结果被推广．文中还给出了一个例子作为应用