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OBJECTIVES—: This pilot study evaluated whether contrast-enhanced subharmonic imaging (SHI) could be used to characterize adnexal masses before surgical intervention. METHODS—: Ten women (with 12 lesions) scheduled for surgery of an ovarian mass underwent an SHI examination of their adnexal region using a modified LOGIQ E9 scanner (GE Healthcare, Waukesha, WI) with an endocavitary transducer, in which digital clips were acquired by pulse destruction-replenishment SHI across the lesions. Time-intensity curves were created offline to quantitatively evaluate SHI parameters (fractional tumor perfusion, peak contrast intensity, time to peak contrast enhancement, and area under the time-intensity curve), which were compared to pathologic characterizations of the lesions. RESULTS—: Of the 12 masses, 8 were benign, and 4 were malignant. A qualitative analysis of the SHI images by an experienced radiologist resulted in diagnostic accuracy of 70%, compared to 56% without contrast, whereas an inexperienced radiologist improved from 50% to 58% accuracy, demonstrating the benefit of SHI. A quantitative analysis of SHI parameters produced diagnostic accuracy as high as 81%. Peak contrast intensity was significantly greater in malignant than benign masses (mean ± SD, 0.109 ± 0.088 versus 0.046 ± 0.030 arbitrary units; P = .046). Malignant masses also showed significantly greater perfusion than benign masses (24.79% ± 25.34% versus 7.62% ± 6.50%; P = .045). When the radiologist reads were combined with the most predictive quantitative SHI parameter (percent perfusion), diagnostic accuracy improved to 84% for the experienced radiologist and 96% for the novice radiologist. CONCLUSIONS—: Results indicate that SHI for presurgical characterization of adnexal masses may improve the determination of malignancy and diagnostic accuracy, albeit based on a small sample size.

OBJECTIVES—: To investigate 3-dimensional subharmonic aided pressure estimation (SHAPE) for measuring intraplaque pressure and the pressure gradient across the plaque cap as novel biomarkers for potentially predicting plaque vulnerability. METHODS—: Twenty-seven rabbits received a high-cholesterol diet for 2 weeks before a balloon catheter injury to denude the endothelium of the aorta, followed by 8 to 10 weeks of the high-cholesterol diet to create arteriosclerotic plaques. SHAPE imagings of the resulting plaques were performed 12, 16, and 20 weeks after injury using a LOGIQ 9 scanner with a 4D10L probe (GE Healthcare, Milwaukee, WI) before and during an infusion of Definity (Lantheus Medical Imaging, North Billerica, MA) and Sonazoid (GE Healthcare, Oslo, Norway). The ratios of the maximum subharmonic magnitudes at baseline and during the infusion were correlated with the intraplaque pressure and pressure gradient across the plaque cap obtained from direct measurements. RESULTS—: Ten rabbits died prematurely after the balloon injury procedure or due to toxicity from the high-cholesterol diet, whereas 2 rabbits were excluded for other conditions. Five rabbits were scanned in the 12-, 16-, and 20-week groups, respectively. Even after 20 weeks, the plaques that developed were very small (mean ± SD, 0.9 ± 0.4 × 0.14 ± 0.05 cm). Definity performed better than Sonazoid in this application but still only achieved a moderate correlation with pressure across the plaque cap (Definity, r = −0.40; Sonazoid, r = 0.22) and intraplaque pressure (Definity, r = −0.19; Sonazoid, r = −0.11). CONCLUSIONS—: Initial findings from plaque pressure estimation using 3-dimensional SHAPE technique showed only moderate correlations with reference standards, but that may be have been due to weaknesses in the animal model studied.

How variations in Earth’s orbit pace the glacial-interglacial cycles of the Quaternary are probably one of the greatest mysteries of modern climate science. Supposing coevolution of climate, ...

In this paper, we investigate the existence and multiplicity of harmonic and subharmonic solutions for second-order quasilinear equation (ϕp(x′))′+g(x)=e(t), where ϕp:R→R,ϕp(u)=|u|p−2u,p>1, g satisfies the superlinear condition at infinity. We prove that the given equation possesses harmonic and subharmonic solutions by using the phase-plane analysis methods and a generalized version of the Poincare-Birkhoff twist theorem.

Objectives To use subharmonic imaging (SHI) to depict the vascularity of pancreatic masses compared to contrast-enhanced endoscopic ultrasound (EUS) and pathologic results. Methods Sixteen patients scheduled for biopsy of a pancreatic mass were enrolled in an Institutional Review Board–approved study. Pulse-inversion SHI (transmitting/receiving at 2.5/1.25 MHz) was performed on a LOGIQ 9 system (GE Healthcare, Milwaukee, WI) with a 4C transducer, whereas contrast harmonic EUS (transmitting/receiving at 4.7/9.4 MHz) was performed with a radial endoscope (GF-UTC180; Olympus Corporation, Tokyo, Japan) connected to a ProSound SSD α-10 scanner (Hitachi Aloka, Tokyo, Japan). Two injections of the contrast agent Definity (Lantheus Medical Imaging, North Billerica, MA) were administrated (0.3–0.4 and 0.6–0.8 mL for EUS and SHI, respectively). Contrast-to-tissue ratios (CTRs) in the mass and an adjacent vessel were calculated. Four physicians independently scored the images (benign to malignant) for diagnostic accuracy and inter-reader agreement. Results One patient dropped out before imaging, leaving 11 adenocarcinomas, 1 gastrointestinal stromal tumor with pancreatic infiltration, and 3 benign masses. Marked subharmonic signals were obtained in all patients, with intratumoral blood flow clearly visualized with SHI. Significantly greater CTRs were obtained in the masses with SHI than with EUS (mean ± SD, 1.71 ± 1.63 versus 0.63 ± 0.89; P = .016). There were no differences in the CTR in the surrounding vessels or when grouped by pathologic results (P > .60). The accuracies for contrast EUS and SHI were low (

Although non-linear phenomena are common in human and non-human animal vocalisations, their functional relevance remains poorly understood. One theory posits that non-linear phenomena generate unpredictability in vocalisations, which increases the auditory impact of vocal signals, and makes animals less likely to habituate to call repetition. Female koalas (Phascolarctos cinereus) produce vocal signals when they reject male copulation attempts that contain relatively high levels of non-linear phenomena, and thus may function as attention grabbing vocal signals during the breeding season. To test this hypothesis, we used playback experiments: firstly, to determine whether female rejection calls induce heightened behavioural responses in free-ranging male koalas during the breeding season, and secondly, to examine how the relative amount of non-linear phenomena in rejection calls influences male behavioural response. The results show that male koalas look for longer towards speakers broadcasting playback sequences of male bellows followed by a series of female rejection calls than those broadcasting only male bellows. In addition, female rejection call sequences with more subharmonics, higher harmonics-to-noise ratios, and less biphonation produced the greatest male looking responses. Our findings support the hypothesis that female koala rejection calls function to grab male attention during the breeding season, and indicate that subharmonics are the main acoustic feature that increases the auditory impact of these vocal signals.

We study Phragmen–Lindelof type estimates for subharmonic and holomorphic functions in one variable and discuss the relation between the two cases. Our main result gives for the type of results which we consider necessary and almost sufficient conditions under which these principles hold.

Structures with shunt stubs in a subharmonic ratio that realize bandpass performance have limited application due to the inherent problem of fixed transmission zero positions in the stopband. By application of the principle of splitting, the subharmonic stubs into cascades of transmission line sections, structures can be realized that have transmission zeros at arbitrary positions. A bandpass filter employing stepped impedance stubs is developed, and it is shown that moderate bandwidth can be achieved. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:3012–3015, 2014

We consider a relativistic particle under the action of a time-periodic central force field in the plane. When it is attractive at a given level there are many subharmonic and quasiperiodic motions.

SUMMARY The progressive miniaturization of electronic components today makes feasible to exploit the nanoscale level. At this scale, phenomena peculiar of the quantum world arise, which can be exploited to realize innovative and potential breakthrough devices. In this paper, the dynamic behavior of one such device, the Casimir nonlinear oscillator is analyzed. Using the Melnikov's method, we prove that under the effect of a weak damping and a weak periodic forcing, complex behaviors in the form of Smale's horseshoes arise, and the mechanism leading to their birth is revealed. Copyright © 2012 John Wiley & Sons, Ltd.

This article demonstrates a high-frequency 0.35-μm SiGe HBT subharmonic downconverter with reactive in-phase and quadrature-phase (I/Q) generators.Two reactive I/Q generators are integrated in our work to provide differential quadrature RF and LO signal. The I/Q subharmonic downconverter with single-ended LO, RF, and IF (I/Q) ports has a conversion gain of 1 dB, IP1dB of −10 dBm, IIP3 of 0 dBm, and IIP2 of 21 dBm at 16.4 GHz. The magnitude and phase errors between the I and Q channels are 1.34% and 0.6°, respectively. The dc power consumption of this I/Q mixer without output buffers is approximately 5 mW. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 1516–1520, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25281

In this paper we consider the von Karman plate equations. We show that a suitable function, defined on the solution to these equations is subharmonic. Then we derive bounds on the integral of the second gradient of the solution.

Ferroresonance is characterised by the existence of multiple periodic and non periodic steady states. Depending upon the initial condition the response of a ferroresonant circuit may settle to any one of the following: fundamental, subharmonic, quasi-periodic or chaotic. This paper is concerned with the isolated subharmonic ferroresonant solutions. The initial conditions are obtained by a class of temporal methods and it is referred to here as ‘temporal bifurcation diagram’ approach. Starting with initial conditions provided by temporal bifurcation diagram, a continuation procedure predicts multiple subharmonic solutions. Analysis of isolated subharmonic solutions reveals that in general they form a closed loop. Further, odd symmetric subharmonic solutions give rise to pitchfork bifurcations. The paper also reports the effect of core loss nonlinearity and transformer saturation on the isolated subharmonic solutions. Copyright © 2010 John Wiley & Sons, Ltd.

Male concave-eared torrent frogs (Odorrana tormota) have an unusually large call repertoire and have been shown to communicate ultrasonically. We investigated the individual specificity of male advertisement calls in order to explore the acoustic bases of individual recognition, which was demonstrated in an accompanying study. Vocalizations of 15 marked males were recorded in the field. A quantitative analysis of the signals revealed eight basic call-types. Two of them (the single- and multi-note long-calls) were investigated in more detail. Long-calls were characterized by pronounced and varying frequency modulation patterns, and abundant occurrence of nonlinear phenomena (NLP), i.e., frequency jumps, subharmonics, biphonations and deterministic chaos. The occurrence of NLP was predictable from the contour of the fundamental frequency in the harmonic segment preceding the onset of the NLP, and this prediction showed individual-specific patterns. Fifteen acoustic variables of the long calls were measured, all of which were significantly different among individuals, except biphonic segment duration. Discriminant function analysis (DFA) showed that 54.6% of the calls could be correctly assigned to individual frogs. The correct classification was above chance level, suggesting that individual specificity of calls underlie the ability of males to behaviorally discriminate the vocal signals of their neighbors from those of strangers, a remarkable feat for a frog species with a diverse vocal repertoire. The DFA classification results were lower than those for other anurans, however. We hypothesize that there is a tradeoff between an increase in the fundamental frequency of vocalizations to avoid masking by low-frequency ambient background noise, and a decrease in individual-specific vocal tract information extractable from the signal.

Most general-purpose analyzers for harmonic analysis on distribution lines are designed to sample the data of one or two power supply periods. In other words, these analyzers process waveforms and display the results based on the assumption that the analyzed waveforms contain no noninteger components, such as subharmonics and interharmonics. When waveforms containing noninteger components are analyzed with these general-purpose analyzers, the results often indicate components that are not actually present. This paper proposes a technique of waveform judgment and explains its method of application. The technique allows noninteger components to be recognized in analyzed waveforms from the properties of Lissajous figures, and clarifies the types of components and the time windows necessary for appropriate analysis. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 166(2): 32– 38, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20536

OBJECTIVE The purpose of this study was to quantify perfusion in vivo using contrast-enhanced subharmonic imaging (SHI). METHODS A modified LOGIQ 9 scanner (GE Healthcare, Milwaukee, WI) operating in gray scale SHI mode was used to measure SHI time-intensity curves in vivo. Four dogs received intravenous contrast bolus injections (dose, 0.1 mL/kg), and renal SHI was performed. After 3 contrast agent injections, a microvascular staining technique based on stable (nonradioactive) isotope-labeled microspheres (BioPhysics Assay Laboratory Inc, Worcester, MA) was used to quantify the degree of perfusion in 8 sections of each kidney. Low perfusion states were induced by ligating surgically exposed segmental renal arteries followed by contrast agent injections and microvascular staining. Digital clips were transferred to a personal computer, and SHI time-intensity curves were acquired in each section using Image-Pro Plus software (Media Cybernetics, Silver Spring, MD). Subharmonic fractional blood volumes were calculated, and the perfusion was estimated from the initial slope of the fractional blood volume uptake averaged over 3 injections. Subharmonic perfusion data were compared with the gold standard (ie, the microspheres) using linear regression analysis. RESULTS In vivo gray scale SHI clearly showed flow and, thus, perfusion in the kidneys with almost complete suppression of tissue signals. In total, 270 SHI time-intensity curves were acquired, which reduced to 94 perfusion estimates after averaging. Subharmonic perfusion estimates correlated significantly with microsphere results (r = 0.57; P < .0001). The best SHI perfusion estimates occurred for high perfusion states in the anterior of the kidneys (r = 0.73; P = .0001). The corresponding root mean square error was 2.4%. CONCLUSIONS Subharmonic perfusion estimates have been obtained in vivo. The perfusion estimates were in reasonable to good agreement with a microvascular staining technique.

The pant hoot calls produced by common chimpanzees (Pan troglodytes) are multi-call vocalizations that have figured prominently in investigations of acoustic communication in this species. Although pant hoots are predominantly harmonically structured, they can exhibit an acoustic complexity that has recently been linked to nonlinearity in the vocal-fold dynamics underlying typical mammalian sound production. We examined the occurrence of these sorts of nonlinear phenomena in pant hoot vocalizations, contrasting quieter and lower-pitched “introduction” components with loud and high-pitched “climax” calls in the same bouts. Spectrographic evidence revealed four kinds of nonlinear phenomena, including discrete frequency jumps, subharmonics, biphonation, and deterministic chaos. While these events were virtually never observed during the introduction, they occurred in more than half of the climax calls. Biphonation was by far the most common phenomenon, followed by subharmonics, chaos, and frequency jumps. Individual callers varied in the degree to which their climax calls exhibited nonlinear phenomena, but were consistent in showing more biphonation than other forms. These outcomes show that nonlinear phenomena are routinely present in chimpanzee pant hoots, and help lay the foundation for investigating the function of such events. Am. J. Primatol. 64:277–291, 2004. © 2004 Wiley-Liss, Inc.

In this paper, we examine what type of bifurcation develops when an extremely small periodic force drives a van der Pol oscillator that generates the duck solution. We create the bifurcation diagrams and explain the structures of bifurcation in the fundamental harmonic entrainment region, 1/2 subharmonic entrainment region, and 1/3 subharmonic entrainment region. In each region, we observed the cascade generation of the period-doubling bifurcation in the extremely small periodic force range, and the occurrence of chaos. We also discovered the very interesting phenomenon of the existence of two duck solutions when driven by an extremely small periodic force. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(4): 51–59, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20093

A subharmonic injection-locked balanced oscillator is presented in this paper. Subharmonic injection locking is preferred to fundamental injection locking, because the central injection point is a virtual short-circuit at the fundamental frequency for a balanced oscillator. An analytical model is described to predict the locking range whereby power series are used to model the device's nonlinearity. An injection-locked balanced oscillator is designed at 5.8 GHz and very good agreement is achieved between the predicted and measured locking ranges. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 41: 306–309, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20124

Consider a real valued Morse function f on a C 2 closed connected n -dimensional manifold M . It is proved that a suitable Riemannian metric exists on M , such that f is harmonic outside the set of critical points of f of index 0 and n . The proof is based on a result of Calabi [1], providing a criterion for a closed one-form on a closed connected manifold to be harmonic with respect to some Riemannian metric.

By critical point theory, a new approach is provided to study the existence of periodic and subharmonic solutions of the second order difference equation is a positive integer. This is probably the first time critical point theory has been applied to deal with the existence of periodic solutions of difference systems.This project is supported by TRATOYT of China and by the State Education Commission Trans-Century Training Program Foundation for the Talents.

The design of a 215 GHz subharmonic waveguide mixer utilizing an antiparallel pair of quasivertical Schottky diodes is presented. The impedance matching is provided by series and parallel waveguide tuners. A single sideband noise temperature of 3500 K and conversion loss of 9.2 dB have been measured (antenna loss included). © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 27: 93–97, 2000.

We study the relation between the growth of a subharmonic function in the half spaceR n+1 + and the size of its asymptotic set. In

Preliminary results on KUV 02464+3239, a pulsating DA white dwarf are presented. Located near the red edge of the DAV instability strip, KUV 02464+3239 shows large amplitude and long period pulsation modes. Up to now only one mode was known from a 50-minute-long light curve. Our more extended observations allowed the identification of three additional frequencies. The presence of previously known harmonics were confirmed and weak subharmonics are also noticeable at some parts of the light curve. This suggests the dominance of nonlinear pulsation effects from time to time., Comment: 3 pages, 3 eps figures; has been accepted for publication in Astronomische Nachrichten (Vol. 8, 2007), proceedings of the British-Hungarian-French N+N+N Workshop for Young Researchers

Asymmetrische Oszillatoren treten in Mechanik, Physik und Technik auf, Beispiele sind asymmetrische Schwingungen von Schalen, gekrummten Staben, Pendelsystemen, Josephson-Kontakten, SQUIDs und hangenden Kabeln. –- Es wird gezeigt, das subharmonische asymmetrische Schwingungen und das Einsetzen von Chaos auf dieselbe Weise wie symmetrische Schwingungen untersucht werden konen, allerdings entstehen stets Komponenten mit geraden Harmonischen und konstante Komponenten von Anfang an, so das die Analyse viel komplizierter ist. Beispiele unterstreichen den grosen Einflus der Asymmetrie. Asymmetric oscillators often occur in mechanics, physics, and technology. Examples are asymmetric vibrations of shells, curved bars, pendulum systems, Josephson junctions, SQUIDs, and hanging cables. –- It is shown that subharmonic asymmetric vibrations and the onset of chaos can be investigated in the same way as symmetric vibrations, but now even harmonic and constant components always arise from the very beginning, so that the analysis is much more complicated. Examples indicate the great influence of the asymmetry.

Reported here are the results of direct optical subharmonically injection-locked oscillators at 5.455 and 15.011 GHz. Multiplication of subharmonics was achieved mainly by overmodulation of a laser diode. Significant locking ranges were attained, and subharmonic factors of up to 1/15 were used. © 1993 John Wiley & sons, Inc.

For forced nonlinear oscillators, different subharmonic vibrations are investigated analytically by higher approximations, checked by computer algebra, and numerically by a damped Newton procedure combined with a continuation algorithm (BIFPACK package by R. Seydel). Especially for a damping value which leads to a frequency region with chaotic behaviour, second subharmonic vibrations appear with amplitudes of the same size as for the harmonic vibrations, whereas third subharmonic vibrations appear only for lower frequencies. This gives an explaination for the existence of second and later on of third subharmonic periodic windows in the period doubling route to chaos. Fur zwangserregte nichtlineare Oszillatoren werden verschiedene subharmonische Schwingungen untersucht, auf analytischem Wege durch hohere Approximationen, die computeralgebraisch gepruft wurden, und auf numerischem Wege durch eine gedampfte Newtonprozedur verbunden mit einem Fortsetzungsalgorithmus (Programmpaket BIFPACK von R. Seydel). Insbesondere ergeben sich fur einen Dampfungswert, der zu einem Frequenzbereich mit chaotischem Verhalten fuhrt, zweite subharmonische Schwingungen mit Amplituden gleicher Grose wie fur die harmonischen Schwingungen, wahrend dritte subharmonische Schwingungen erst bei niedrigeren Frequenzen auftreten. Dies gibt eine Erklarung fur die Existenz zweiter und spater dritter subharmonischer Fenster bei der Periodenverdoppelungsroute zum Chaos.

In recursive digital filters, quantization of signals can result in instabilities such as limit cycles and subharmonics. the aim of this paper is to analyse these instabilities in periodically excited recursive digital filters and to present methods to suppress the unwanted phenomena. A new type of digital filter structure is introduced which is free from subharmonics for discrete-time periodic input signals with a given period N. Using the theory of cyclotomic polynomials, this structure is extended to suppress subharmonics for input signals which are periodic with a divisor of N. A general principle is described to convert a stable, autonomous state space digital filter into one which is free from subharmonics under any periodic excitation with a given period N.

Consider the semilinear wave equation u tt −u xx= g(u,t), u(x,t)=u(x,t+2kπ), t∈R,x∈[0,π], u(0,t)=u(π,t)=0, t∈R, where g∈C 0 (R 2 ,R) and g is 2π-periodic in t. The aim of this paper is to search for distinct 2πk-periodic solutions («subharmonics») which have small amplitude and are such that 2πk is the minimal period

On etudie des solutions periodiques du systeme hamiltonien −Jx˙=H'(t,x) ou J est la matrice symplectique standard et H∈C 2 (R×R 2n ,R) est T-periodique en la premiere variable pour tout (t,x). H'(t,x) note le gradient partiel par rapport a la seconde variable

A phase increment method is introduced to construct the response curves for the damped Duffing oscillator in primary, superharmonic, and subharmonic resonances. Non-linear parameters can be arbitrarily large. The algorithm is numerically stable. All resonance response curves are constructed in a unified manner. Closed loop curves are obtained in subharmonic resonances as opposed to open ended ones predicted by the perturbation method. Higher order resonances are constructed without difficulties. Loops are also observed in superharmonic resonances when non-linearity is not small.