Analytic Expression for Exact Ground State Energy Based on an Operator Method for a Class of Anharmonic Potentials

A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic expressions for the exact ground state energy have also been derived specifically for a large class of the one-dimensional oscillator with cubic-quartic anharmonic terms. Our analytical results can be used to check the accuracy of existing numerical methods, for instance the method of state-dependent diagonalization. Our results also agree with the asymptotic behavior in the divergent pertubative expansion of quartic harmonic oscillator.Comment: LaTeX with six figure (gif) files; Submitted to Phys. Rev.

A unified approach for exactly solvable potentials in quantum mechanics using shift operators

We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new class of solvable potentials.Comment: RevTex, 8 page

VLBI observation of giant radio galaxy J1313+696 at 2.3/8.4 GHz

We report the result of VLBI observation of the giant radio galaxy J1313+696 (4C +69.15) at 2.3/8.4 GHz, only the core component of the giant radio galaxy was detected in the VLBI observation at the dual frequencies. The result shows a steep spectrum core with $\alpha=-0.82$ ($S \propto \nu^{\alpha}$) between 2.3 GHz and 8.4 GHz. The steep spectrum core may be a sign of renewed activity. Considering also the upper limit flux density of 2.0 mJy at 0.6 GHz from Konar et al. 2004 the core has a GHz-peaked spectrum, implying that the core is compact and absorbed. Further high resolution VLBI observations are needed to identify if the steep spectrum core is consisting of a core and steep spectrum jet.Comment: 3 pages, 3 figure

Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima

The Fano resonance for Anderson impurity systems

We present a general theory for the Fano resonance in Anderson impurity systems. It is shown that the broadening of the impurity level leads to an additional and important contribution to the Fano resonance around the Fermi surface, especially in the mixed valence regime. This contribution results from the interference between the Kondo resonance and the broadened impurity level. Being applied to the scanning tunnelling microscopic experiments, we find that our theory gives a consistent and quantitative account for the Fano resonance lineshapes for both Co and Ti impurities on Au or Ag surfaces. The Ti systems are found to be in the mixed valence regime.Comment: 4 pages, 5 figures, published versio

Polysaccharides from Portulaca oleracea L Improve Exercise Endurance and Decrease Oxidative Stress in Forced Swimming Mice

Purpose: To explore the effects of polysaccharides from Portulaca oleracea L. (POP) on exercise endurance and oxidative stress in forced-swimming mice.Methods: Forty-eight mice were divided into four groups of twelve animals each. All treatments were administered orally and daily for 28 days. Group A received isotonic saline solution (50 ml/kg bodyweight) as control group; B, C and D groups received 100, 200 and 400 mg/kg body wt. of POP as treatment groups, respectively. After the final treatment with POP, the mice were subjected to swimming to exhaustion and the exhaustive swimming time, blood lactic acid (BLA), blood glucose, malondialdehyde (MDA), superoxide dismutase (SOD), glutathione peroxidase (GPx) and catalase (CAT) were measured.Results: The exhaustive swimming time of the POP-treated groups (967.3 ± 79.2, 1234.8 ± 97.6 and 1314.3 ± 107.3 s) was significantly longer than that of the control group (513.6 ± 41.2 s) (p < 0.05). After the exhaustive swimming exercise, BLA levels of the POP-treated groups (8.63 ± 0.91, 8.04 ± 0.86 and 7.51 ± 0.78 mmol/L) were significantly lower than that of the control group (11.39 ± 1.17 mmol/L) (p < 0.05). MDA levels of the POP-treated groups (2.69 ± 0.21, 2.41 ± 0.17 and 2.37 ± 0.23 U/mg.pro) were significantly lower than that of the control group (3.21 ± 0.29 U/mg.pro) (p < 0.05). On the other hand, blood glucose levels of the POP-treated groups (5.47 ± 0.48, 5.74 ± 0.57 and 6.04 ± 0.51 mmol/L) were significantly higher than that of the control group (4.89 ± 0.32 mmol/L) (p < 0.05). SOD levels of the POP-treated groups (124.36 ± 14.87, 136.39±13.48 and 145.87 ± 17.39 U/mg.pro) were significantly higher than that of the control group (108.41 ± 11.63 U/mg.pro) (p < 0.05). GPx levels of the POPtreated groups (68.24 ± 4.68, 71.33 ± 5.29 and 72.64 ± 5.99 U/mg.pro) were significantly higher than that of the control group (53.17 ± 5.24 U/mg.pro) (p < 0.05). CAT levels of the POP-treated groups (23.57 ± 1.71, 24.28 ± 2.14 and 26.72 ± 2.21 U/mg.pro) were significantly higher than that of the control group (19.48 ± 2.03 U/mg.pro) (p < 0.05).Conclusion: This study provides compelling evidence that POP can improve exercise endurance and decrease oxidative stress in forced swimming mice.Keywords: Polysaccharides, Portulaca oleracea L., Oxidative stress, Swimming, Exercise endurance

General Approach to Functional Forms for the Exponential Quadratic Operators in Coordinate-Momentum Space

In a recent paper [Nieto M M 1996 Quantum and Semiclassical Optics, 8 1061; quant-ph/9605032], the one dimensional squeezed and harmonic oscillator time-displacement operators were reordered in coordinate-momentum space. In this paper, we give a general approach for reordering multi-dimensional exponential quadratic operator(EQO) in coordinate-momentum space. An explicit computational formula is provided and applied to the single mode and double-mode EQO through the squeezed operator and the time displacement operator of the harmonic oscillator.Comment: To appear in J. Phys. A: Mathematics and Genera