Note on Generalized Quantum Gates and Quantum Operations

Recently, Gudder proved that the set of all generalized quantum gates coincides the set of all contractions in a finite-dimensional Hilbert space (S. Gudder, Int. J. Theor. Phys. 47:268–279, 2008). In this note, we proved that the set of all generalized quantum gates is a proper subset of the set of all contractions on an infinite dimensional separable Hilbert space ℋ. Meanwhile, we proved that the quantum operation deduced by an isometry is an extreme point of the set of all quantum operations on ℋ. This subject is supported by NSF of China (10571113).     

Adiabatic approximation in PT-symmetric quantum mechanics

In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics, which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.     

Scaling properties of image textures: A detrending fluctuation analysis approach

The aim of this paper is to explore the application of detrended fluctuation analysis (DFA) to study roughness features of images. Unidimensional sequences at different image orientations are extracted and their average scaling exponent is estimated. In this form, the existence of anisotropies can be detected when considerable variations in the scaling exponent at different image orientation are observed. Different images from grass to solar granulation are analyzed and the underlying physics of such results is briefly commented.     

Learning-based compressed sensing for infrared image super resolution

This paper presents an infrared image super-resolution method based on compressed sensing (CS). First, the reconstruction model under the CS framework is established and a Toeplitz matrix is selected as the sensing matrix. Compared with traditional learning-based methods, the proposed method uses a set of sub-dictionaries instead of two coupled dictionaries to recover high resolution (HR) images. And Toeplitz sensing matrix allows the proposed method time-efficient. Second, all training samples are divided into several feature spaces by using the proposed adaptive k-means classification method, which is more accurate than the standard k-means method. On the basis of this approach, a complex nonlinear mapping from the HR space to low resolution (LR) space can be converted into several compact linear mappings. Finally, the relationships between HR and LR image patches can be obtained by multi-sub-dictionaries and HR infrared images are reconstructed by the input LR images and multi-sub-dictionaries. The experimental results show that the proposed method is quantitatively and qualitatively more effective than other state-of-the-art methods.     

Total Routhian Surface Calculations on Hf Isotopes

The two-dimensional total routhian surface calculations have been carried out to stud）, the triaxial superdeformed structure of a neutron-rich nucleus ^173 Hf firstly. In particular the effects of the rotational frequency ω and pairing-energy gap parameter A are discussed in detail in the course of shaping its triaxial superdeformation; additionally the neutron-shell correction energy is analyzed with emphasis in the confirmed triaxial superdeformed nucleus ^173Hf. Finally, more systematical results have been investigated for some confirmed superdeformed nuclei experimentally and a few predicted triaxial superdeformed nuclei theoretically with quadropole deformation ε2 ≈0.4 and triaxial deformation γ≈20° or 30° in the Z = 72 region.     

On the use of averaging stopping power of recoiled nuclei for determining maximum neutron energy of 241Am–Be by superheated drop detectors

The average stopping power of the recoiled nuclei generated by neutron elastic interactions with the Freon-12 drops in a superheated drop detector has been used to determine the maximum neutron energy of the ²⁴¹Am–Be source. In an elastic interaction of neutrons with the Freon-12 liquid, the nuclei of ¹²C, ¹⁹F and ³⁵Cl with different values of stopping power are scattered. The stopping power of these scattered nuclei corresponding to the energy transferred to them through the head-on collision was extracted from the SRIM code. The stopping power values were weighted by considering the neutron–nucleus elastic scattering cross section and the number of each nucleus in the Freon-12 molecule and the average stopping power was calculated from known neutron energy.The maximum energy of the ²⁴¹Am–Be neutron source was estimated as 10.9 ± 3.0 MeV. The consistency between the determined energy and the other reported values confirms the validity of using the average stopping power in the superheated drop detectors. The average stopping power was also used to determine the threshold neutron energy as a function of external applied pressure at different temperatures. Knowing the threshold neutron energy as function of applied pressure, can be used in pressure scanning method for neutron spectrometry by superheated drop detectors.     

MHD squeezed flow of water functionalized metallic nanoparticles over a sensor surface

Present study is devoted to analyze the magnetohydrodynamics (MHD) squeezed flow of nanofluid over a sensor surface. Modeling of the problem is based on the geometry and the interaction of three different kinds of metallic nanoparticles namely: copper (Cu), alumina (Al₂O₃) and titanium dioxide (TiO₂) with the homogeneous mixture of base fluid (water). The self-similar numerical solutions are presented for the reduced form of the system of coupled ordinary differential equations. The effects of nanoparticles volume friction, permeable velocity and squeezing parameter for the flow and heat transfer within the boundary layer are presented through graphs. Comparison among the solvent are constructed for both skin friction and Nusselt number. Flow behavior of the working nanofluid according to the present geometry has analyzed through Stream lines. Conclusion is drawn on the basis of entire investigation and it is found that in squeezing flow phenomena Cu–water gives the better heat transfer performance as compare with the rest of mixtures.     

Strong lensing of a regular black hole with an electrodynamics source

In this paper we have investigated the gravitational lensing phenomenon in the strong field regime for a regular, charged, static black holes with non-linear electrodynamics source. We have obtained the angle of deflection and compared it to a Schwarzschild black hole and Reissner Nordström black hole with similar properties. We have also done a graphical study of the relativistic image positions and magnifications. We hope that this method may be useful in the detection of non-luminous bodies like this current black hole.     

Modified scaling function projective synchronization of chaotic systems

This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle's invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.     

A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy

In this Letter, a generalized Tu formula is firstly presented to construct Hamiltonian structures of fractional soliton equations. The obtained results can be reduced to the classical Hamiltonian hierarchy of AKNS in ordinary calculus.