On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form

2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50The principle eigenvalue and the maximum principle for second-order elliptic equations is studied. New necessary and sufficient conditions for symmetric and nonsymmetric operators are obtained. Applications for the estimation of the first eigenvalue are given

A multifaceted approach to understanding unexpected sound change: the bilabial trills of Vanuatu’s Malekula Island

This paper demonstrates that unexpected sound changes are best explained by an approach that accounts for different motivations: phonetic, structural and social. Here, we focus on a multifaceted investigation of the crosslinguistically uncommon bilabial trills to show the complex interaction between different drivers of sound change. In this paper, we highlight and examine the prenasalized voiced bilabial trill mʙ and plain voiceless bilabial trill P [ʙ̥] found in a number of Oceanic languages spoken on Malekula Island in Vanuatu. We offer a comparative-historical analysis, and we identify the various forces that have led to the emergence and persistence of mʙ and P in Malekula languages: the historical articulatory environments, the particular make-up of the consonant inventories of these languages, complementary sound changes and phonological processes, contact with non-Austronesian languages, and in-group identity attachment. Furthermore, we offer a hypothesis for the relative timing of these factors on the historical pathway of Malekula’s bilabial trills

What are task-sets: a single, integrated representation or a collection of multiple control representations?

Performing two randomly alternating tasks typically results in higher reaction times (RTs) following a task switch, relative to a task repetition. These task switch costs (TSC) reflect processes of switching between control settings for different tasks. The present study investigated whether task sets operate as a single, integrated representation or as an agglomeration of relatively independent components. In a cued task switch paradigm, target detection (present/absent) and discrimination (blue/green/right-/left-tilted) tasks alternated randomly across trials. The target was either a color or an orientation singleton among homogeneous distractors. Across two trials, the task and target-defining dimension repeated or changed randomly. For task switch trials, agglomerated task sets predict a difference between dimension changes and repetitions: joint task and dimension switches require full task set reconfiguration, while dimension repetitions permit re-using some control settings from the previous trial. By contrast, integrated task sets always require full switches, predicting dimension repetition effects (DREs) to be absent across task switches. RT analyses showed significant DREs across task switches as well as repetitions supporting the notion of agglomerated task sets. Additionally, two event-related potentials (ERP) were analyzed: the Posterior-Contralateral-Negativity (PCN) indexing spatial selection dynamics, and the Sustained-Posterior-Contralateral-Negativity (SPCN) indexing post-selective perceptual/semantic analysis. Significant DREs across task switches were observed for both the PCN and SPCN components. Together, DREs across task switches for RTs and two functionally distinct ERP components suggest that re-using control settings across different tasks is possible. The results thus support the “agglomerated-task-set” hypothesis, and are inconsistent with “integrated task sets.

A multifaceted approach to understanding unexpected sound change. The bilabial trills of Vanuatu’s Malekula Island

This paper demonstrates that unexpected sound changes are best explained by an approach that accounts for different motivations: phonetic, structural and social. Here, we focus on a multifaceted investigation of the crosslinguistically uncommon bilabial trills to show the complex interaction between different drivers of sound change. In this paper, we highlight and examine the prenasalized voiced bilabial trill mʙ and plain voiceless bilabial trill P [ʙ̥] found in a number of Oceanic languages spoken on Malekula Island in Vanuatu. We offer a comparative-historical analysis, and we identify the various forces that have led to the emergence and persistence of mʙ and P in Malekula languages: the historical articulatory environments, the particular make-up of the consonant inventories of these languages, complementary sound changes and phonological processes, contact with non-Austronesian languages, and in-group identity attachment. Furthermore, we offer a hypothesis for the relative timing of these factors on the historical pathway of Malekula’s bilabial trills

Stimulated Raman adiabatic passage analogs in classical physics

Stimulated Raman adiabatic passage (STIRAP) is a well established technique for producing coherent population transfer in a three-state quantum system. We here exploit the resemblance between the Schrodinger equation for such a quantum system and the Newton equation of motion for a classical system undergoing torque to discuss several classical analogs of STIRAP, notably the motion of a moving charged particle subject to the Lorentz force of a quasistatic magnetic field, the orientation of a magnetic moment in a slowly varying magnetic field, the Coriolis effect and the inertial frame dragging effect. Like STIRAP, those phenomena occur for counterintuitively ordered field pulses and are robustly insensitive to small changes in the interaction properties