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We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional non-compact manifold. To facilitate the reading of the paper, we first present the arguments in the setting of Cartan–Hadamard manifolds and then subsequently discuss the general case. For this purpose, we employ the heat kernel techniques as well as some comparison theorems of Riemannian geometry, thus generalizing the arguments in the flat case following the approach presented in Albeverio et al. (2004). 相似文献
2.
Teoman
zer 《Chaos, solitons, and fractals》2008,38(3):722-730
Symmetry group properties and similarity solutions of the variant nonlinear long-wave equations in the form of system of nonlinear partial differential equations are analyzed. Lie symmetry group analysis of the variant nonlinear long-wave equations presents that the system has only two-parameter point symmetry group that corresponds to only traveling wave solutions. The symmetry groups yield the general reduced similarity form of the system, which is in the system of nonlinear ordinary differential equations. By using the improved tanh method the similarity solutions are obtained from the reduced system of equations. In addition, some graphical representations of the solitary and periodic solutions are presented. 相似文献
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We report efficient cw laser operation of laser diode pumped Pr(3+)-doped LiYF4 crystals in the visible spectral region. Using two InGaN laser diodes emitting at λ(P)=443.9?nm with maximum output power of 1?W each and a 2.9-mm-long crystal with a doping concentration of 0.5%, output powers of 938?mW, 418?mW, 384?mW, and 773?mW were achieved for the laser wavelengths 639.5?nm, 607.2?nm, 545.9?nm, and 522.6?nm, respectively. The maximum absorbed pump powers were approximately 1.5?W, resulting in slope efficiencies of 63.6%, 32.0%, 52.1%, and 61.5%, as well as electro-optical efficiencies of 9.4%, 4.2%, 3.8%, and 7.7%, respectively. Within these experiments, laser diode-pumped laser action at 545.9?nm was demonstrated for what is believed to be the first time. 相似文献
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Teoman Karadag Zehra Yildiz Teymuraz Abbasov 《Journal of Dispersion Science and Technology》2013,34(6):826-830
In this article, magnetizing properties of the packed beds that are constructed from the mixture of the ferromagnetic spheres of various sizes, pieces of wires and chips are investigated both experimentally and theoretically in order to determine the effect of the volumetric packing factor on the magnetizing properties of the bed. The average magnetizing curve has been determined by maintaining the external homogeneous magnetic field (H) higher than 150 kA/m. 相似文献
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Symmetry groups, symmetry reductions, optimal system, conservation laws and invariant solutions of the shallow water wave equation with nonlocal term are studied. First, Lie symmetries based on the invariance criterion for nonlocal equations and the solution approach for nonlocal determining equations are found and then the reduced equations and optimal system are obtained. Finally, new conservation laws are generated and some similarity solutions for symmetry reduction forms are discussed. 相似文献
7.
Teoman Gün Yury Kuzminykh Friedjof Tellkamp Klaus Petermann Günter Huber 《Applied Physics A: Materials Science & Processing》2008,93(2):387-391
In this contribution, we report on the 2-dimensional (2D) layer-by-layer growth of Yb(10%):Y3Al5O12 (YAG) and Yb3Al5O12 (YbAG) PLD-films on {100}-oriented YAG. The epitaxial growth was observed in situ by Reflection High Energy Electron Diffraction
(RHEED) as intensity oscillations of the specularly reflected electron beam. The properties of the films were investigated
ex situ by means of X-ray diffraction (XRD), atomic force microscopy (AFM), and optical spectroscopy. The optical emission
spectra of the films are similar to those of the corresponding crystalline bulk materials. 相似文献
8.
In this study we have obtained the dependence of the electronic distribution on the gate shape and the applied gate voltage in a quantum Hall effect based Aharonov–Bohm interferometer using a method presented in our previous studies. We have discussed the relation between the distribution of incompressible strips and observation of Aharonov–Bohm oscillations. We have obtained the distributions of the incompressible strips for various gate voltages and have shown that a gate potential sweep and a magnetic field sweep would be equivalent. Our calculations also predict that for wider gate separations it is possible observe a silent region while sweeping the magnetic field or the gate voltage. 相似文献
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In the present work, a Klein–Gordon particle with singular interactions supported on embedded curves on Riemannian manifolds is discussed from a more direct and physical perspective, via the heat kernel approach. It is shown that the renormalized problem is well-defined, and the ground state energy is unique and finite. The renormalization group invariance of the model is discussed, and it is observed that the model is asymptotically free. 相似文献