Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space

Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum and phase transition of the superfluid Fermi gas of atoms with a weak attractive interaction on the canonical noncommutative space. Because the interaction of a BCS-type superfluid Fermi gas originates from a pair of Fermionic quasi-particles with opposite momenta and spins, the Hamiltonian of the Fermi gas on the noncommutative space can be described in terms of the ordinary creation and annihilation operators related to the commutative space, while the noncommutative effect appears only in the coefficients of the interacting Hamiltonian. As a result, we can rigorously solve the energy spectrum of the Fermi gas on the noncommutative space exactly following the way adopted on the commutative space without the use of perturbation theory. In particular, different from the previous results on the noncommutative degenerate electron gas and superconductor where only the first order corrections of the ground state energy level and energy gap were derived, we obtain the nonperturbative energy spectrum for the noncommutative superfluid Fermi gas, and find that each energy level contains a corrected factor of cosine function of noncommutative parameters. In addition, our result shows that the energy gap becomes narrow and the critical temperature of phase transition from a superfluid state to an ordinary fluid state decreases when compared with that in the commutative case

Studying quantum entanglement and quantum discord in the cavity QED models

Based on the two-qubit Jaynes-Cummings model - a common cavity quantum electrodynamics model, and extending to modification of the three-qubit Tavis-Cummings model, we investigate the quantum correlation between light and matter in bipartite quantum systems. By resolving the quantum master equation, we are able to derive the dissipative dynamics in open systems. To gauge the degree of quantum entanglement in the two-qubit system, von Neumann entropy and concurrence are introduced. Quantum discord, which can properly measure the quantum correlation in both closed and open systems, is also introduced. In addition, consideration is given to the impacts of initial entanglement and dissipation strength on quantum discord. Finally we discussed two different cases of nuclei motion: quantum and classical.Comment: 12 pages, 9 figure

Entrepreneurial Finance and Non-diversifiable Risk

We develop a dynamic incomplete-markets model of entrepreneurial firms, and demonstrate the implications of nondiversifiable risks for entrepreneurs' interdependent consumption, portfolio allocation, financing, investment, and business exit decisions. We characterize the optimal capital structure via a generalized tradeoff model where risky debt provides significant diversification benefits. Nondiversifiable risks have several important implications: More risk-averse entrepreneurs default earlier, but choose higher leverage; lack of diversification causes entrepreneurial firms to underinvest relative to public firms, and risky debt partially alleviates this problem; and entrepreneurial risk aversion can overturn the risk-shifting incentives induced by risky debt. We also analytically characterize the idiosyncratic risk premium.Research Grants Council of Hong Kong (project 643507

RFDforFin: Robust Deep Forgery Detection for GAN-generated Fingerprint Images

With the rapid development of the image generation technologies, the malicious abuses of the GAN-generated fingerprint images poses a significant threat to the public safety in certain circumstances. Although the existing universal deep forgery detection approach can be applied to detect the fake fingerprint images, they are easily attacked and have poor robustness. Meanwhile, there is no specifically designed deep forgery detection method for fingerprint images. In this paper, we propose the first deep forgery detection approach for fingerprint images, which combines unique ridge features of fingerprint and generation artifacts of the GAN-generated images, to the best of our knowledge. Specifically, we firstly construct a ridge stream, which exploits the grayscale variations along the ridges to extract unique fingerprint-specific features. Then, we construct a generation artifact stream, in which the FFT-based spectrums of the input fingerprint images are exploited, to extract more robust generation artifact features. At last, the unique ridge features and generation artifact features are fused for binary classification (\textit{i.e.}, real or fake). Comprehensive experiments demonstrate that our proposed approach is effective and robust with low complexities.Comment: 10 pages, 8 figure

Entrepreneurial Finance and Non-diversifiable Risk

Entrepreneurs face significant non-diversifiable business risks. We build a dynamic incomplete markets model of entrepreneurial finance to demonstrate the important implications of nondiversifiable risks for entrepreneurs' interdependent consumption, portfolio allocation, financing, investment, and business exit decisions. The optimal capital structure is determined by a generalized tradeoff model where leverage via risky non-recourse debt provides significant diversification benefits. More risk-averse entrepreneurs default earlier, but also choose higher leverage, even though leverage makes his equity more risky. Non-diversified entrepreneurs demand both systematic and idiosyncratic risk premium. Cash-out option and external equity further improve diversification and raise the entrepreneur's valuation of the firm. Finally, entrepreneurial risk aversion can overturn the risk-shifting incentives induced by risky debt.

Physics-Assisted Reduced-Order Modeling for Identifying Dominant Features of Transonic Buffet

Transonic buffet is a flow instability phenomenon that arises from the interaction between the shock wave and the separated boundary layer. This flow phenomenon is considered to be highly detrimental during flight and poses a significant risk to the structural strength and fatigue life of aircraft. Up to now, there has been a lack of an accurate, efficient, and intuitive metric to predict buffet and impose a feasible constraint on aerodynamic design. In this paper, a Physics-Assisted Variational Autoencoder (PAVAE) is proposed to identify dominant features of transonic buffet, which combines unsupervised reduced-order modeling with additional physical information embedded via a buffet classifier. Specifically, four models with various weights adjusting the contribution of the classifier are trained, so as to investigate the impact of buffet information on the latent space. Statistical results reveal that buffet state can be determined exactly with just one latent space when a proper weight of classifier is chosen. The dominant latent space further reveals a strong relevance with the key flow features located in the boundary layers downstream of shock. Based on this identification, the displacement thickness at 80% chordwise location is proposed as a metric for buffet prediction. This metric achieves an accuracy of 98.5% in buffet state classification, which is more reliable than the existing separation metric used in design. The proposed method integrates the benefits of feature extraction, flow reconstruction, and buffet prediction into a unified framework, demonstrating its potential in low-dimensional representations of high-dimensional flow data and interpreting the "black box" neural network

Fenton Reagent Oxidation and Decolorizing Reaction Kinetics of Reactive Red SBE

AbstractFenton reagent was employed to treat and decolorize the wastewater of Reactive Red SBE by on-line spectrophotometry. The effects of initial FeSO4 concentration, initial H2O2 concentration, pH, reactive red SBE and temperature on the decoloration of reactive red SBE were investigated. The results show that Fenton oxidize process follows pseudo first order kinetics in the first stage and reaction activation energy is 2.608 kJ/mol. The decolorizing reaction rate constants (k) increase with the rise of FeSO4 concentration, H2O2 concentration, temperature, but decrease with the rise of reactive red SBE, and the optimum pH is 3. Initial FeSO4 concentration and initial H2O2 concentration against k are linear correlation