The number of convex pentagons and hexagons in an nn-triangular net

In this paper, we obtain the counting formulaes of convex pentagons and convex hexagons, respectively, in an $n$-triangular net by solving the corresponding recursive formulaes.Comment: 6 page

The solutions of four qq-functional equations

In this note we obtain the solutions of four $q$-functional equations and express the solutions in $q$-operator forms. These equations give sufficient conditions for $q$-operator methods.Comment: 5 page

Geometric RTT realization of Uv(gln)+U_v(gl_n)^+

In this paper, we give a BLM realization of the positive part of the quantum group of $U_v(gl_n)$ with respect to RTT relations.Comment: 14 pages, No figure

Unifying Treatment of Discord via Relative Entropy

A new form of zero-discord state via Petz's monotonicity condition on relative entropy with equality has been derived systematically. A generalization of symmetric zero-discord states is presented and the related physical implications are discussed.Comment: 12 pages, LaTeX. Some parts are deleted. Any comments are welcome

An alternate circular summation formula of theta functions and its applications

We prove a general alternate circular summation formula of theta functions, which implies a great deal of theta-function identities. In particular, we recover several identities in Ramanujan's Notebook from this identity. We also obtain two formulaes for $(q;q)_\infty^{2n}$.Comment: 11 pages,0 figure

A semi-finite proof of Jacobi's triple product identity

Jacobi's triple product identity is proved from one of Euler's $q$-exponential functions in an elementary way.Comment: 2 pages, 0 figur

Lower bound on concurrence for arbitrary-dimensional tripartite quantum systems

In this paper, we study the concurrence of arbitrary dimensional tripartite quantum systems. An explicit operational lower bound of concurrence is obtained in terms of the concurrence of sub-states. A given example show that our lower bound may improve the well known existing lower bounds of concurrence. The significance of our result is to get a lower bound when we study the concurrence of arbitrary dimensional multipartite quantum systems.Comment: 1 figures, Quantum Information Processing 201

On small set of one-way LOCC indistinguishability of maximally entangled states

In this paper, we study the one-way local operations and classical communication (LOCC) problem. In $\mathbb{C}^d\otimes\mathbb{C}^d$ with $d\geq4$, we construct a set of $3\lceil\sqrt{d}\rceil-1$ one-way LOCC indistinguishable maximally entangled states which are generalized Bell states. Moreover, we show that there are four maximally entangled states which cannot be perfectly distinguished by one-way LOCC measurements for any dimension $d\geq 4$.Comment: 10 pages.Very recently, we became aware of related work \cite{Zhang2} in which the same $\lceil\frac{d}{2}\rceil+2$ states in $\mathbb{C}^d\otimes\mathbb{C}^d$ is proved to be one-way LOCC indistinguishable. arXiv admin note: text overlap with arXiv:1310.4220 by other autho

Secondary cosmic-ray nucleus spectra disfavor particle transport in the Galaxy without reacceleration

The precise observations of Galactic cosmic ray fluxes of the secondary family, such as Li, Be, B, are expected to have significant implications on our understanding of the cosmic ray origin and propagation. Here we employ the recent very precise measurements of those species by the Alpha Magnetic Spectrometer on the International Space Station, together with their parent species (C and O), as well as the data collected by the Voyager-1 spacecraft outside the heliosphere and the Advanced Composition Explorer, to investigate the propagation of cosmic rays in the Milky Way. We consider the diffusion of cosmic rays plus reacceleration or convection effect during the propagation, and find that the reacceleration model can fit the data significantly better than the convection model. We further find that for the reacceleration model, the spectral hardenings of both the primary and secondary particles can be well described by the injection hardening without including additional propagation hardening. This is due to that the reacceleration effect results in a steeper secondary-to-primary ratio at low energies, and can thus naturally reproduce the fact that the secondary spectra harden more than the primary spectra found by AMS-02.Comment: 12 pages, 3 figures, 1 table; accepted by JCA

Semantic Image Synthesis with Spatially-Adaptive Normalization

We propose spatially-adaptive normalization, a simple but effective layer for synthesizing photorealistic images given an input semantic layout. Previous methods directly feed the semantic layout as input to the deep network, which is then processed through stacks of convolution, normalization, and nonlinearity layers. We show that this is suboptimal as the normalization layers tend to ``wash away'' semantic information. To address the issue, we propose using the input layout for modulating the activations in normalization layers through a spatially-adaptive, learned transformation. Experiments on several challenging datasets demonstrate the advantage of the proposed method over existing approaches, regarding both visual fidelity and alignment with input layouts. Finally, our model allows user control over both semantic and style. Code is available at https://github.com/NVlabs/SPADE .Comment: Accepted as a CVPR 2019 oral pape