A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.

     

Analysis of a 2D “liquid”plasma lattice

Adustyplasmacanbedefinedasacomplicatedplasmacontainingsmallsolidmattercalleddustgrainsordustparticles,whichareusuallychargednegatively,duetoelectronshighermobilitythanion,bycollectingelectronsandionsfromthebackgroundplasma.Theuniverseisfilledwithdustyplasmassuchasplanetaryrings,comettails,andnebulae.Also,inindustrialplasmaprocessing,particulatessuspendedinplasmaarethemajorcontaminationinsemiconductormanufacture.Studiesondustyplasmahavebeenextendedtofar-flungtopicssuchaswaves,instabilities,stro…     

Saturated Commutative Spaces of Heisenberg Type

In this paper, we give a partial classification of commutative spaces of Heisenberg type. Several classification results were known previously. In order to avoid complicated technical details, we restrict ourselves to saturated commutative spaces. Our results are presented in Table II.     

Performance evaluation of fiber Bragg grating sensors by digital holographic technique, strain gauge measurement

In view of the growing interest for non-destructive tests of materials, geodynamical monitoring and in general remote sensing, there is a great effort to bring practical optical sensors from research labs to industrial and environmental applications. In this paper, we employ digital holographic technique as an efficient tool for evaluating the strain measurement capability of fiber Bragg gratings (FBG). A cantilever beam has been employed as a test structure under loading test. The strain measurements results obtained by fiber-based sensors have been compared to those obtained by using full-field digital holographic technique and point-wise strain gauge sensors glued on the same cantilever beam. A simple theoretical model is also presented to interpret and compare the experimental results coming from different techniques.     

Fourth-order problems with fully nonlinear boundary conditions

Differential inequality method, bounding function method and topological degree are applied to obtain the existence criterions of at least one solution for the general fourth-order differential equations under nonlinear boundary conditions, and many existing results are complemented.     

Left, right, and inner socles of associative systems

We investigate the basic properties of the different socles that can be considered in not necessarily semiprime associative systems. Among other things, we show that the socle defined as the sum of minimal (or minimal and trivial) inner ideals is always an ideal. When trivial inner ideals are included, this inner socle contains the socles defined in terms of minimal left or right ideals. This revised version was published online in June 2006 with corrections to the Cover Date.     

Dispersion Compensation in Externally Modulated Transmission System Using Chirped Fiber Grating

We present an externally modulated NTSC AM-VSB erbium-doped fiber amplifier (EDFA)-repeated system in the 1550 nm region which uses a chirped fiber grating (CFG) as a dispersion compensation device. In contrast to the conventional externally modulated fiber optical CATV systems, either with or without dispersion compensation fiber (DCF), good performances of carrier-to-noise ratio (CNR) ≥50 dB, composite second order (CSO) ≥74 dB, and composite triple beat (CTB) ≥65 dB were achieved for the full channel band after a 100-km single-mode fiber (SMF) transmission.     

Isospectral theory of Euler equations

Isospectral problem of both 2D and 3D Euler equations of inviscid fluids, is investigated. Connections with the Clay problem are described. Spectral theorem of the Lax pair is studied.