Limiting Lagrangians: A primal approach

In this paper, we consider a convex program with either a finite or an infinite number of constraints and its formal Lagrangian dual. We show that either the primal program satisfies a general condition which implies there is no duality gap or that there is a nonzero vectord with the following properties: First, wheneverd is added to the objective function, where is a positive number not greater than one, the resulting program satisfies the general sufficient condition cited above for no duality gap. Second, the optimal value of this perturbed program is attained and tends to the optimal value of the original program as tends to zero. Third, the optimal solutions of the perturbed programs form a minimizing sequence of the original program. As a consequence of the above, we derive the limiting Lagrangian theory of Borwein, Duffin, and Jeroslow.The authors are indebted to an unknown referee who suggested the very short and elegant proofs of Lemma 2.3 and Theorem 2.3.This work was completed while the first author was a member of the College of Management, Georgia Institute of Technology, Atlanta, Georgia.     

Orlicz spaces for a family of measures

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A uniform asymptotic expansion for the Jacobian elliptic functions n(u,k)

The usual two term approximation for the Jacobian elliptic functions n (u, k) when the modulusk is close to unity (see for example [3], [4], [5]) is shown to be nonuniform when |u|K, whereK is the quarter period. The nonuniformity is shown to be weak, with the remainder term becoming of the same order as the last retained term in the approximation. A formal application of the method of matched asymptotic expansions is then used to obtain a uniformly valid two term expansion fors n(u, k). Uniform expansions forc n(u, k) andd n(u, k) can also be developed in a similar manner.

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Zusammenfassung Wir zeigen, daß die übliche zweigliedrige Entwicklung der Jacobischen elliptischen Funktions n(u, k) fürk1 (siehe zum Beispiel [3], [4], [5]) nicht uniform ist, falls |u|K, woK die Viertelperiode ist. Es wird gezeigt, daß diese Nichtuniformität schwach ist wo der Restterm dieselbe Ordnung annimmt wie der letzte Term in der Entwicklung. Eine formale Anwendung der Methode der Matched Asymptotic Expansions wird dann benutzt um eine uniform gültige zweigliedrige Entwicklung fürs n(u, k) zu erhalten. Uniforme Entwicklungen fürc n(u, k) undd n(u, k) erhält man in analoger Weise.

     

A two-stage nonlinear cochlear model possesses automatic gain control

A model of the cochlea is explored using as stimuli two simultaneously presented sinusoids of equal amplitude. The model consists of two stages: a linear bandpass filter, followed by a reservoir-type representation of the hair-cell/nerve-fiber complex. Fast Fourier transforms of the model's output were computed. While the amplitudes of the individual response components were strongly nonlinear functions of intensity, the ratio of the magnitudes of the response components at the frequencies of the two stimulating sinusoids was found to be nearly equal, over a wide intensity range, to the ratio of the amplitudes which those stimulating sinusoids possessed at the output of the filter. Thus the reservoir stage exerts "automatic gain control".     

Confusion effects with sinusoidal and narrow-band noise forward maskers

In some forward-masking conditions, signal thresholds may be elevated by the listener's inability to distinguish the signal from the preceding masker. In this study, such "confusion" effects are investigated for both sinusoidal and narrow-band noise forward maskers combined with sinusoidal signals of varying duration. Results for the sinusoidal maskers show effects of off-frequency listening for brief signals and possibly small effects of confusion for longer signals. Results for the narrow-band noise maskers show a marked influence of confusion over a wide range of signal durations. This range is in good agreement with that predicted from previous work with "pulsing" maskers [D. Neff, J. Acoust. Soc. Am. 78, 1966-1976 (1985)]. These results suggest that studies using narrow-band noise forward maskers or studies of psychophysical suppression should include direct tests for confusion effects in key conditions.     

The constant-volume-velocity nature of hearing aids: conclusions based on computer simulations

In the literature there are several references which imply that various parts of a hearing aid are sources of constant volume velocity. Reported herein are the findings of an investigation of the validity of such statements. A computer scheme, referenced elsewhere, for modeling in situ hearing aids was utilized to test the constant-volume-velocity hypothesis. In particular, capabilities of the receiver, ear hook, and earmold tip to deliver constant volume velocity were investigated via a computer. To facilitate such an investigation, a universal receiver/earmold model was created. This model was broken down into "source" and "load"at three locations: the receive output, output of the ear hook, and medial tip of the earmold. At each location comparisons were made between computed values of source and load impedance. The constant-volume-velocity hypothesis was assumed to be valid for those cases where source impedance was much, much greater than load impedance. Plots of such impedances show that, for the cases investigated, this rarely occurred, except over certain frequency bands. With the exception of in-the-ear hearing aids, these results appear to contradict inferences made in the literature about the constant-volume-velocity nature of hearing aids.     

Joint production of ϕ mesons andπ ±,π 0,p,\bar p,K s 0 andK ± in hadronic interactions

The joint production of ? mesons andπ ^±,π ⁰,p, \(\bar p\) ,K _s ⁰ andK ^± is investigated using a sample of 600,000 inclusive ? meson events obtained in hadron Be interactions with incidentπ ^±,p, \(\bar p\) andK ^± beams. Evidence is presented for the joint production of ? mesons and strange particles produced with non-strange incident beams. With incidentK ^± beam the number of additional strange particles is suppressed. The results are found to be in agreement with the qualitative predictions of a parton fusion model. The comparison with the Lund model for lowp _T processes is fair.     

High-p T αα andαp interactions

Properties of secondaries associated with a high-p _T charged trigger particle (3<p _T <5 GeV/c) were studied for αp and αα interactions at c.m. energies \(\sqrt s = 88\) GeV and 125 GeV, respectively. Thep _T distributions of secondaries in the away-jet and trigger-jet regions were compared with those for high-p _{T pp} interactions. No statistically significant differences were seen, except at lowp _T . Momentum and angular distributions of spectator and leading protons were studied as a function of charge and rapidity of the trigger hadron. The observed correlations between trigger charge and number of spectator protons provide evidence of valence quark contributions to the trigger jet.     

Inclusive ϕ production inK − p interactions at 110 GeV/c and search for structure in φ π−

Results on inclusive ? production inK ^? p interactions at 110 GeV/c are presented. The production cross section is found to be larger than in πp andpp interactions at similar energies, suggesting OZI allowed \(s\bar s\) fusion to be the dominant mechanism in ? production. Thex distributions of ? and \(\bar K^{*0} \) are found to be similar to each other over the entirex range suggesting an overall strangeness suppression factor of 0.20±0.04 in the sea to be the dominant source of the difference in the cross section for ? and \(\bar K^{*0} \) . There is no evidence of a narrowφπ ^? state around 2.1 GeV/c² as suggested byK ⁺ experiments, but there is some excess of events in the region 1.94?1.98 GeV/c² consistent with theF-meson mass as observed ine ⁺ e ^? experiments.     

Local properties of equilibrium states and the particle spectrum in quantum field theory

It is shown that in a quantum field theory describing free, scalar particles with masses m _i , i there exist locally normal equilibrium states with finite energy density for all temperature >0 if and only if . This result lends support to the conjecture that the nuclearity criterion proposed by Buchholz and Wichmann is sensitive to the thermodynamical properties of field-theoretic models.