Consistency of a linear system of inequalities

We show that a consistency check of a linear system of inequalitiesAxb reduces to check whetherQb0 for a certain matrixQ. It is a direct consequence of the Farkas-Minkowski theorem. Thus, when one has to check consistency for different values ofb, one need not run a numerical algorithm for eachb.On leave at the Electronics Research Laboratory of the University of California at Berkeley in a CNRS/NSF Exchange Program.     

Regular and Chaotic Solutions of Duffing's Equation for Large Forcing

This paper uses an analytical approximation to study the periodicand chaotic solutions of the forced—damped Duffing's equation.The forcing is of fixed frequency and is taken to be a multipleof cos t. The forcing amplitude is large and its reciprocalis used to construct a small parameter , which is used as anexpansion parameter in the approximation. The solutions aredetermined as functions of . The damping is linear and proportionalto the velocity; the constant of proportionality is held fixedin this study.     

Exact results for a generalized classicalO(n) matrix spin model

A generalizedO(n) matrix version of the classical Heisenberg model, introduced by Fuller and Lenard as a classical limit of a quantum model, is solved exactly in one dimension. The free energy is analytic and the pair correlation functions decay exponentially for all finite temperatures. It is shown, however, that even for a finite number of spins the model has a phase transition in then limit. The transition features a specific heat jump, zero long-range order at all temperatures, and zero correlation length at the critical point. The Curie-Weiss version of the model is also solved exactly and shown to have standard mean-field type behavior for all finiten and to differ from the one-dimensional results in then limit.     

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.

     

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.     

Low temperature Mössbauer spectra and magnetic ordering of lithiated ferric molybdate: Li2Fe2(MoO4)3

Powder x-ray diffraction, variable temperature magnetic susceptibility, and zero field Mössbauer spectroscopy measurements were used to characterize the new phase Li₂Fe₂ (MoO₄)₃. This material is obtained topochemically simply by the mixing of solutions of lithium iodide in acetonitrile with solid Fe₂(MoO₄)₃ at ambient temperature. Li₂Fe₂(MoO₄)₃ possesses the high temperature orthorhombic ferric molybdate $$\begin{gathered} Fe_2 (MoO_4 )_3 + 2LiI\xrightarrow{{CH_3 CN}}Li_2 Fe_2 (MoO_4 )_3 + I_2 \hfill \\ (solid)(solution)(solid)(solution) \hfill \\ \end{gathered}$$ structure. Guinier photographs were completely indexed in space group Pnca. Magnetic hyperfine splitting of the zero field Mössbauer spectrum below 12.5 K indicates a three-dimensional magnetically ordered state which susceptibility results show to be weakly ferromagnetic owing to probable canting of antiferromagnetically coupled sublattices.