Crystal structure and nontrivial magnetic properties of CuII binuclear complex based on 4-methyl-2,6-bis{[2-(4,6-dimethyl-pyrimidin-2-yl)hydrazono]methyl}phenol

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Electron–phonon effect on the ground-state binding energy of hydrogenic impurity in quantum-well wire in presence of an electric field

The hydrogenic impurity binding energy in rectangular quantum well wire including both barriers of finite height and an applied electric field are studied. The polaron effects on the ground-state binding energy in electric field are investigated by means of Landau-Pekar variation technique. The results for the binding energy as well as polaronic correction are obtained as a function of the size of the wire, the applied electric field and the position of the impurity. Our calculations are compared with previous results in quantum wires of comparable dimensions.     

Label-free detection of charged macromolecules by using a field-effect-based sensor platform: Experiments and possible mechanisms of signal generation

The possibilities and limitations of a direct electrical detection of charged macromolecules using a field-effect-based sensor platform is evaluated, mainly focusing on capacitive EIS (electrolyte-insulator-semiconductor) devices. The experimentally obtained results on the detection of DNA immobilisation and hybridisation as well as the monitoring of layer-by-layer adsorbed charged polyelectrolyte (PE) multilayers have been discussed by using two basic possible mechanisms of signal generation, namely the intrinsic charge of the macromolecules and the charge redistribution within the intermolecular spaces or in the multilayer. The effects of the layer-by-layer adsorption conditions (unbuffered and pH buffer solution), and the number and polarity of charged layers on the sensor response have been systematically investigated by means of capacitance–voltage (C–V), constant–capacitance (ConCap) and impedance spectroscopy (IS) methods. PACS 82.47.Rs; 82.80.Fk; 85.30.Tv; 87.15.Kg; 87.14.Gg     

The polaron effect on the binding energy of a shallow donor impurity in quantum-well wires in an electric field

Using a variational technique, the effect of electron-longitudinal optical (LO) phonon interaction on the ground and the first few excited states of a hydrogenic impurity in a semiconductor quantum wire of rectangular cross section under an external electric field is studied theoretically for the impurity atom doped at various positions. The results for the binding energy as well as polaronic correction are obtained as a function of the size of the wire, the applied uniform electric field and the position of the impurity. It is found that the presence of optical phonons changes significantly the values of the impurity binding energies of the system. Taking into account the electron–LO phonon interaction the 1s→2p_y and 1s→2p_z transition energies are calculated as a function of applied electric field for different impurity positions.     

Nonuniqueness in a Free Boundary Problem from Combustion

We study a parabolic free boundary problem with a fixed gradient condition which serves as a simplified model for the propagation of premixed equidiffusional flames. We give a rigorous justification of an example due to J.L. Vázquez that the initial data in the form of two circular humps leads to the nonuniqueness of limit solutions if the supports of the humps touch at the time of their maximal expansion. A. Petrosyan was supported in part by NSF grant DMS-0701015. N.K. Yip was supported in part by NSF grant DMS-0406033.     

A minimum problem with free boundary for a degenerate quasilinear operator

In this paper we prove regularity (near flat points) of the free boundary 0\}\cap\Omega$" align="middle" border="0"> in the Alt-Caffarelli type minimum problem for the p-Laplace operator: 0\}}\right)dx\rightarrow \min\qquad (1 Received: 3 June 2003, Accepted: 9 June 2004, Published online: 8 February 2005Mathematics Subject Classification (2000): 35R35, 35J60The first author is partially supported by NSF Grant DMS-0202801 and NSF CAREER Grant DMS-0239771     

Regularity of a free boundary in parabolic potential theory

We study the regularity of the free boundary in a Stefan-type problem

with no sign assumptions on and the time derivative .