In this letter, a definition of the higher dimensional Lax pair for a lower dimensional system which may be a chaotic system is given. A special concrete (2+1)-dimensional Lax pair for a general (1+1)-dimensional three order autonomous partial differential equation is studied. The result shows that any (1+1)-dimensional three order semi-linear autonomous system (no matter it is integrable or no...

This study examines the acoustic characteristics of English high tense and lax vowels (/i, I, u, ʊ/) and the perceptual difference of those vowels between English speakers and Korean speakers of English. In Experiment I, the first three formant values and duration of the four vowels in /hVd/ carrier were measured. The result shows that the high tense vowels have larger F2–F1 values and longer d...

Acoustic data elicited from 34 native speakers of Korean living in the United States provide evidence for diachronic change in the voice onset time (VOT) of phrase-initial aspirated and lax stop phonemes. While older speakers produce aspirated and lax stops with clearly differentiated average VOT values, many younger speakers appear to have neutralized this difference, producing VOTs for aspira...

To guarantee the correction of numerical simulation programs implementing the fi-nite element method, it is necessary to formalize the mathematical notions and results that allowto establish the soundness of the method. The Lax-Milgram theorem is one of those theoreticalcornerstones: under some completeness and coercivity assumptions, it states existence and unique-ness of the s...

— We discuss a local reduction theorem for 0-parameter solutions of a higher order Painlevé equation and its underlying Lax pair near a simple turning point of the first kind when the size of the Lax pair is greater than 2. As a typical example of such higher order Painlevé equations the Noumi-Yamada systems are mainly considered. Résumé (Sur une réduction locale au voisinage d’un point tournan...

We study the extension of integrable equations which possess the Lax representations to noncommutative spaces. We construct various noncommutative Lax equations by the Lax-pair generating technique and the Sato theory. The Sato theory has revealed essential aspects of the integrability of commutative soliton equations and the noncommutative extension is worth studying. We succeed in deriving va...

Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and its supersymmetric version. They allow to infer several relations involving the Lax matrices for this model in a fast way. It is shown that the super Lax ope...

The Toda flows are examples of integrable Hamiltonian systems which are of great interest from the point of view of pure mathematics as well as in applications. They originated as a description of a 1-dimensional lattice of particles with exponential interaction [29]. Flaschka [14] found a Lax pair for the equations and Moser [25] analyzed the dynamics and scattering behavior of the system. Adl...

Clearly produced vowels exhibit longer duration and more extreme spectral properties than plain, conversational vowels. These features also characterize tense relative to lax vowels. This study explored the interaction of clear-speech and tensity effects by comparing clear and plain productions of three English tense-lax vowel pairs (/i-ɪ/, /ɑ-ʌ/, /u-ʊ/ in /kVd/ words). Both temporal and spectr...

We consider scalar conservation laws with convex flux and random initial data. The Hopf–Lax formula induces a deterministic evolution of the law of the initial data. In a recent article, we derived a kinetic theory and Lax equations to describe the evolution of the law under the assumption that the initial datum is a spectrally negative Markov process. Here we show that: (i) the Lax equations a...