The harmonic product of δ(x1,...,xn)\delta (x_{1},..., x_{n}) and δ(x1)\delta (x_{1}) and two combinatorial identities

In the framework of nonstandard analysis, Bang-He Li and the author defined the product of any two distributions on $R^n$ via their harmonic representations. The product of $\delta (x_{1},..., x_{n})$ and $\delta (x_{1})$ was calculated by Kuribayashi and the author in [LK]. In this paper, the result of [LK] is improved to $$\delta (x_{1},..., x_{n})\circ \delta (x_{1}) =\dfrac{1}{2\pi\rho} \delta (x_{1},..., x_{n}) {mod} {infinitesimals}$$ where $\rho$ is a positive infinitesimal. Moreover two combinatorial identities are obtained as byproducts.Comment: Latex. To appear in Hiroshima Math.

HAR-Net: Joint Learning of Hybrid Attention for Single-stage Object Detection

Object detection has been a challenging task in computer vision. Although significant progress has been made in object detection with deep neural networks, the attention mechanism is far from development. In this paper, we propose the hybrid attention mechanism for single-stage object detection. First, we present the modules of spatial attention, channel attention and aligned attention for single-stage object detection. In particular, stacked dilated convolution layers with symmetrically fixed rates are constructed to learn spatial attention. The channel attention is proposed with the cross-level group normalization and squeeze-and-excitation module. Aligned attention is constructed with organized deformable filters. Second, the three kinds of attention are unified to construct the hybrid attention mechanism. We then embed the hybrid attention into Retina-Net and propose the efficient single-stage HAR-Net for object detection. The attention modules and the proposed HAR-Net are evaluated on the COCO detection dataset. Experiments demonstrate that hybrid attention can significantly improve the detection accuracy and the HAR-Net can achieve the state-of-the-art 45.8\% mAP, outperform existing single-stage object detectors

PP-wave contributions to B→ψππB\to\psi\pi\pi decays in perturbative QCD approach

We present the differential branching fractions for the $B\rightarrow \psi \pi\pi$ decays with the charmonia $\psi=J/\psi,\psi(2S)$ in the invariant mass of the $P$-wave pion pairs in the perturbative QCD approach. The two-pion distribution amplitudes (DAs) corresponding to both longitudinal and transverse polarizations are constructed to capture important final state interactions in the processes. The time-like form factors, normalizing the two-pion DAs, contains contributions from the $\rho$ resonance and radial excitations fitted to the BaBar data. Given the hadronic parameters for the two-pion DAs associated with the longitudinal polarization which were determined in our previous study, and tuning those associated with the transverse polarization, we accommodate well the observed branching ratios and polarization fractions of the $B\rightarrow J/\psi \pi\pi$ decays. Our predictions for the $B\rightarrow \psi(2S) \pi\pi$ modes from the same set of parameters can be tested in future LHCb and BelleII experiments. We also investigate the sources of theoretical uncertainties in our calculation.Comment: 12 pages,3 figure

Conserving and Gapless Hartree-Fock-Bogoliubov theory for 3D dilute Bose gas at finite temperature

The energy spectrum for the three dimensional Bose gas in Bose-Einstein Condensation phase is calculated with Modified Hartree-Fock-Bogoliubov theory, which is both conserving and gapless. From Improved $\Phi -$% derivable theory, the diagrams needed to preserve Ward-Takahashi Identity are resummed in a systematic and nonperturbative way. The results show significant discrepancies with Popov theory at finite temperature. It is valid up to the critical temperature where the dispersion relation of the low energy excitation spectrum changes from linear to quadratic. Because of the repulsive interaction, the critical temperature has a positive shift from that of idea gas, which is in accordance with the result from the previous calculations in the uncondensed phase.Comment: 4pages, 5figure

Three-dimensional lattice Boltzmann models for solid-liquid phase change

A three-dimensional (3 D) multiple-relaxation-time (MRT) and a 3 D single-relaxation-time (SRT) lattice Boltzmann (LB) models are proposed for the solid-liquid phase change. The enthalpy conservation equation can be recovered from the present models. The reasonable relationship of the relaxation times in the MRT model is discussed. Both One-dimensional (1 D) melting and solidification with analytical solutions are respectively calculated by the SRT and MRT models for validation. Compared with the SRT model, the MRT one is more accurate to capture the phase interface. The MRT model is also verified with other published two-dimensional (2 D) numerical results. The validations suggest that the present MRT approach is qualified to simulate the 3 D solid-liquid phase change process. Furthermore, the influences of Rayleigh number and Prandtl number on the 3 D melting are investigated.Comment: 32 pages, 34 figure

Proton cloud and the possibility of direct perceiving of a Hydrogen nucleon

We introduce a concept of proton cloud and calculate the radius of the proton cloud of the Hydrogen atom. Then, we estimate the radius of the proton cloud of a Hydrogen atom on highly excited Rydberg states. Based on the size of proton cloud, the stability of the atom and technical level, we guess that the direct perceiving of the Hydrogen nucleon cloud, or proton cloud, is possible in near future.Comment: 7 pages, 1 figur

Quantum Bit Commitment Protocol Based on Counterfactual Quantum Cryptography

We present a new quantum bit commitment (QBC) protocol based on counterfactual quantum cryptography. We analyze the security of this protocol, find that it can resist the attack presented by QBC's no-go theorem. Our protocol is simple, and probably give a new way of constructing QBC protocol.Comment: 26 pages, 4 figures, 4 table

Practical quantum oblivious transfer and bit commitment protocols

We propose a practical quantum oblivious transfer and a bit commitment protocols which replace the single-photon source with weak coherent pulses and allow error and loss in channel and detectors. These protocols can be realized with available optoelectronic apparatus.Comment: 15 pages, 5 figure

Defuzzify firstly or finally: Dose it matter in fuzzy DEMATEL under uncertain environment?

Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is widely used in many real applications. With the desirable property of efficient handling with the uncertain information in decision making, the fuzzy DEMATEL is heavily studied. Recently, Dytczak and Ginda suggested to defuzzify the fuzzy numbers firstly and then use the classical DEMATEL to obtain the final result. In this short paper, we show that it is not reasonable in some situations. The results of defuzzification at the first step are not coincide with the results of defuzzification at the final step.It seems that the alternative is to defuzzification in the final step in fuzzy DEMATEL

Universality of competitive networks for weighted networks

In this paper, we propose a new model that allows us to investigate this competitive aspect of real networks in quantitative terms. Through theoretical analysis and numerical simulations, we find that the competitive network have the universality for a weighted network. The relation between parameters in the weighted network and the competitiveness in the competitive network is obtained. So we can use the expression of the degree distribution of the competitive model to calculate that and the strength of the weighted network directly. The analytical solution reveals that the degree distribution of the weighted network is correlated with the increment and initial value of edge weights, which is verified by numerical simulations. Moreover, the evolving pattern of a clustering coefficient along with network parameters such as the size of a network, an updating coefficient, an initial weight and the competitiveness are obtained by further simulations. Specially, it is necessary to point out that the initial weight plays equally significant role as updating coefficient in influencing the topological characteristics of the network.Comment: 18 pages, 6 figures. arXiv admin note: text overlap with arXiv:cond-mat/0406238 by other author