Inequalities of Hermite-Hadamard type for extended ss-convex functions and applications to means

In the paper, the authors introduce a new concept "extended $s$-convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and apply these inequalities to derive some inequalities of special means.Comment: 17 page

Boundary-Aware Network for Fast and High-Accuracy Portrait Segmentation

Compared with other semantic segmentation tasks, portrait segmentation requires both higher precision and faster inference speed. However, this problem has not been well studied in previous works. In this paper, we propose a lightweight network architecture, called Boundary-Aware Network (BANet) which selectively extracts detail information in boundary area to make high-quality segmentation output with real-time( >25FPS) speed. In addition, we design a new loss function called refine loss which supervises the network with image level gradient information. Our model is able to produce finer segmentation results which has richer details than annotations

Antiferromagnetism of Repulsively Interacting Fermions in a harmonic trap

We propose a Real-Space Gutzwiller variational approach and apply it to a system of repulsively interacting ultracold fermions with spin 1/2 trapped in an optical lattice with a harmonic confinement. Using the Real-Space Gutzwiller variational approach, we find that in system with balanced spin-mixtures on a square lattice, antiferromagnetism either appears in a checkerboard pattern or forms a ring and antiferromagnetic order is stable in the regions where the particle density is close to one, which is consistent with the recent results obtained by the Real-Space Dynamical Mean-field Theory approach. We also investigate the imbalanced case and find that antiferromagnetic order is suppressed there

U(2) algebraic model applied to stretching vibrational spectra of tetrahedral molecules

The highly excited stretching vibrational energy levels and the intensities of infrared transitions in tetrahedral molecules are studied in a U(2) algebraic model. Its applications to silane and silicon tetrafluoride are presented with smaller standard deviations than those of other models.Comment: Revtex, 6 pages, no figure, to appear in Int. J. Theor. Phy

Trigonometric protocols for shortcuts to adiabatic transport of cold atoms in anharmonic traps

Shortcuts to adiabaticity have been proposed to speed up the "slow" adiabatic transport of an atom or a wave packet of atoms. However, the freedom of the inverse engineering approach with appropriate boundary conditions provides thousands of trap trajectories for different purposes, for example, time and energy minimizations. In this paper, we propose trigonometric protocols for fast and robust atomic transport, taking into account cubic or quartic anharmonicities. The numerical results have illustrated that such trigonometric protocols, particular cosine ansatz, is more robust and the corresponding final energy excitation is smaller, as compared to sine trajectories implemented in previous experiments.Comment: 5 pages, 5 figure

Fast and optimal transport of atoms with non-harmonic traps

We investigate the fast transport of an atom or a packet of atoms by different kinds of non-harmonic traps including power-law traps. The study is based on the reverse engineering method. Exact results are obtained and applied to design robust transport protocols. The optimization of the transport trajectory is performed with classical trajectories, and remains valid for the transport of a wave packet.Comment: 7 pages, 4 figure

Double-periodic quasi-periodic graphene superlattice: non-Bragg band gap and electronic transport

Electronic band gap and transport in quasi-periodic graphene superlattice of double-periodic sequence have been investigated. It is found that such quasi-periodic structure can possess a zero-averaged wave number (zero-$\bar{k}$) gap which associated with an unusual Dirac point. Different from Bragg gap, the zero-$\bar{k}$ gap is less sensitive to the incidence angle, and robust against the lattice constants. The locations of Dirac point and multi-Dirac-points in the graphene superlattices of various sequences are also compared. The control of electron transport over the zero-$\bar{k}$ band gap in graphene superlattice may facilitate the development of many graphene-based electronics.Comment: 8 pages, 11 figure

Hermite-Hadamard type integral inequalities for functions whose first derivatives are of convexity

In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose first derivatives are of convexity and apply these inequalities to construct inequalities of special means.Comment: 18 page

Irreducible bases in icosahedral group space

The irreducible bases in the icosahedral group space are calculated explicitly by reducing the regular representation. The symmetry adapted bases of the system with {\bf I} or {\bf I}$_{h}$ symmetry can be calculated easily and generally by applying those irreducible bases to wavefunctions of the system, if they are not vanishing. As examples, the submatrices of the H\"{u}ckel Hamiltonians for Carbon-60 and Carbon-240 are re-calculated by the irreducible bases.Comment: Revtex 16 page

Correlations of spin states for icosahedral double group

The irreducible bases of the group space of the icosahedral double groups {\bf I'} and {\bf I$_{h}'$} are calculated explicitly. Applying those bases on the spin states $|j,\mu>$, we present a simple formula to combine the spin states into the symmetrical adapted bases, belonging to a given row of a given irreducible representations of {\bf I'} and {\bf I$_{h}'$}.Comment: latex file 11 pages, send the figure to person who wants to need, submitted to Chemical Phys. Lette