Existence of a renormalized solution to the quasilinear Riccati-type equation in Lorentz spaces

In this paper, we prove the existence of a renormalized solution for the quasilinear Riccati-type equation with low integrability-measure data in Lorentz spaces. The result is established in both regular and singular cases. Our proof is based on the gradient estimates for a solution to a class of quasilinear elliptic equations.     

Dynamic Picone's identity and its applications

We prove some Picone-type identities and inequalities for a class of first-order nonlinear dynamic systems and derive various weighted inequalities of Wirtinger type and Hardy type on time scales. As applications we study oscillatory and related properties of these systems including Reid's roundabout theorem on disconjugacy, Sturm's separation and comparison theorems, as well as a variational method in the oscillation theory.     

Morley’s trisector Theorem for isosceles tetrahedron

We extend Morley’s trisector theorem in the plane to an isosceles tetrahedron in three-dimensional space. We will show that the Morley tetrahedron of an isosceles tetrahedron is also isosceles tetrahedron. Furthermore, by the formula for distance in barycentric coordinate, we introduce and prove a general theorem on an isosceles tetrahedron.

     

A stochastic model of the influence of buffer gas collisions on Mollow spectra

In this paper, using the idea introduced in (K. Wódkiewicz, Noise in strong laser-atom interaction, Proceedings of the VI International School of Coherent Optics, Ustron, Poland, September (1985) 19–26) and developed in (Cao Long Van, Stochastic Models of Isolated Collisions: Applications to Optical Phenomena, paper presented in LAMP Conference’89, Trieste, Italy (1989) II) we consider the influence of collisional fluctuations on the Mollow spectra of resonance fluorescence (RF). The fluctuations are taken into account by a simple shift of the constant detuning, involved in a set of optical Bloch equations by collision frequency noise which is modelled by a two-step random telegraph signal (RTS). We consider in detail the Mollow spectra for RF in the case of an arbitrary detuning of the laser frequency, where the emitter is a member of a statistical ensemble in thermodynamic equilibrium with the buffer gas at temperature T which is treated as a colored environment, and velocity v is distributed with the Maxwell-Boltzmann density.     

Pulse propagation in an autoionization medium with double Fano profile

We discuss the propagation of a short laser pulse in an auto- ionizing (AI) medium with degenerate double Fano model. By solving numerically the coupled equations for atoms and fields we show that by the proper choice of Fano parameters involved in the problem (contrary to the case considered in (E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A60 (1999)) we have now two Fano asymmetry parameters) one can eliminate almost completely the absorption in the pulse propagation. It means that we have the transparency in the medium. From the connection between population trapping in short pulsed laser field and transparency in the propagation of the laser pulse which has been fixed by Paspalakis et al., Phys. Rev. A60 (1999) we conclude that this proper choice leads to the presence of the population trapping (or the existence of the “dark” states) in the atomic system. Moreover, instead of one value of the laser detuning for which the dark states exist in the case of one AI level, we find numerically two such values in the case of two AI levels.     

Atomic spectroscopy with surface wave plasmas

The use of microwave induced plasmas, particularly of surface wave plasmas, as detectors in atomic emission spectrometry for elemental analysis is reviewed. Surface wave plasmas have been produced at low HF power and used as gas chromatographic detectors. The analytical performances for the detection of non-metals with a Fourier transform spectrometer and a two-channel filter unit are reported. The excitation behavior of non-metals in helium-based mixed gas-plasmas has also be studied. In particular, the effect of power and of nitrogen concentration on the bromine emission has been systematically investigated. A nine-fold improvement of the detection limits for bromine can be obtained in a high power (900 W) helium-nitrogen (0.1–0.2%) plasma.     

Rat pups and random robots generate similar self‐organized and intentional behavior

Biorobotic research continually demonstrates that behavior and cognition can be the emergent products of (1) embodied agents that are (2) dynamically embedded within an environment and (3) equipped with simple sensorimotor rules. Thigmotaxis is an orientation response to contact manifested in infant rats by wall following, corner burrowing, and group aggregation. Orientation responses have been long thought to be mediated only by sensory or central processes. Here we show that a random control architecture in a morphologically similar robot embedded in a scaled environment can reproduce thigmotaxic behaviors seen in infant rats. We conclude that (1) and (2) may play a larger role than previously thought in the generation of complex behaviors. © 2006 Wiley Periodicals, Inc. Complexity 12: 53–66, 2006     

A stable second‐order mass‐weighted upwind scheme for unstructured meshes

In this paper, an original second‐order upwind scheme for convection terms is described and implemented in the context of a Control‐Volume Finite‐Element Method (CVFEM). The proposed scheme is a second‐order extension of the first‐order MAss‐Weighted upwind (MAW) scheme proposed by Saabas and Baliga (Numer. Heat Transfer 1994; 26B :381–407). The proposed second‐order scheme inherits the well‐known stability characteristics of the MAW scheme, but exhibits less artificial viscosity and ensures much higher accuracy. Consequently, and in contrast with nearly all second‐order upwind schemes available in the literature, the proposed second‐order MAW scheme does not need limiters. Some test cases including two pure convection problems, the driven cavity and steady and unsteady flows over a circular cylinder, have been undertaken successfully to validate the new scheme. The verification tests show that the proposed scheme exhibits a low level of artificial viscosity in the pure convection problems; exhibits second‐order accuracy for the driven cavity; gives accurate reattachment lengths for low‐Reynolds steady flow over a circular cylinder; and gives constant‐amplitude vortex shedding for the case of high‐Reynolds unsteady flow over a circular cylinder. Copyright © 2005 John Wiley & Sons, Ltd.     

Pseudodifferential operators with real analytic symbols and approximation methods for pseudodifferential equations

This paper introduces some methods (including an approximation method) for investigating pseudodifferential equations and related problems (Cauchy problems, boundary value problems,…) based on the technique of pseudodifferential operators with real analytic symbols.