Auxin transport, which is mediated by specialized influx and efflux carriers, plays a major role in many aspects of plant growth and development. AUXIN1 (AUX1) has been demonstrated to encode a high-affinity auxin influx carrier. In Arabidopsis thaliana, AUX1 belongs to a small multigene family comprising four highly conserved genes (i.e., AUX1 and LIKE AUX1 [LAX] genes LAX1, LAX2, and LAX3). W...

This paper presents results from an ongoing investigation into stop consonants in Waima’a, focusing on the issue of tense v. lax ejectives. Sources tend to describe ejectives in a given language as either tense or lax; however ejectives in Waima'a, do not fit squarely into either category [4]. Here we compare ejectives in word-initial and word-medial contexts, to specifically address the role o...

We exhibit the elliptic Calogero-Moser system as a Hitchin system of G-principal Higgs pairs. The group G, though naturally associated to any root system, is not semi-simple. We then interpret the Lax pairs with spectral parameter of [dP1] and [BSC1] in terms of equivariant embeddings of the Hitchin system of G into that of GL(N).

The tensorial form of the Lax pair equations are given in a compact and geometrically transparent form in the presence of Cartan’s torsion tensor. Three dimensional spacetimes admitting Lax tensors are analyzed in detail. Solutions to Lax tensor equations include interesting examples as separable coordinates and the Toda lattice.

We introduce 3N × 3N Lax pair with spectral parameter for Calogero-Inozemtsev model. The one degree of freedom case appears to have 2 × 2 Lax representation. We derive it from the elliptic Gaudin model via some reduction procedure and prove algebraic integrability. This Lax pair provides elliptic linear problem for the Painlevé VI equation in elliptic form.

We introduce partial (co)actions of a Hopf algebra on an algebra A. To this end, we introduce first the notion of lax coring, generalizing Wisbauer's notion of weak coring. We also have the dual notion of lax ring. We then introduce partial and lax entwining structures. Several duality results are given, and we develop Galois theory for partial entwining structures.

Soliton equations are infinite-dimensional integrable systems described by nonlinear evolution equations. As one of the soliton equations, long wave equation takes on profound significance of theory and reality. By using the method of nonlinearization, the relation between long wave equation and second-order eigenvalue problem is generated. Based on the nonlinearized Lax pairs, Euler-Lagrange f...

We analize the structure of the general solution of the Riemann problem for a striclty hyperbolic system of conservation laws whose characteristic elds are neither genuinely non-linear nor linearly degenerate in the sense of Lax.

We find the Lax pair for a system of reduced Maxwell–Bloch equations that describes the propagation of twocomponent extremely short electromagnetic pulses through the medium containing two-level quantum particles with arbitrary dipole moments.

We consider two Lax systems for the homogeneous Painlevé II equation: one of size 2×2 studied by Flaschka and Newell in the early 1980s, and one of size 4×4 introduced by Delvaux, Kuijlaars, and Zhang and Duits and Geudens in the early 2010s. We prove that solutions to the 4×4 system can be derived from those to the 2 × 2 system via an integral transform, and consequently relate the Stokes mult...