Character Formulae for Ortho-symplectic Lie Superalgebras osp(n∣2)\mathfrak{osp}(n|2)

The character formula of any finite dimensional irreducible module $L_\lambda$ for Lie superalgebra $\mathfrak{osp}(n|2)$ is computed. As a by-product, the decomposition of tensor module $L_\lambda\otimes \mathbb{C}^{n|2}$, where $\mathbb{C}^{n|2}$ is the natural representation, is obtained.Comment: 26 page

Generalized Verma Modules and Character Formulae for osp(3∣2m)\mathfrak{osp}(3|2m)

The character formula of any finite dimensional irreducible module for Lie superalgebra $\mathfrak{osp}(3|2m)$ is obtained in terms of characters of generalized Verma modules.Comment: 20 page

Hom-Lie superalgebra structures on finite-dimensional simple Lie superalgebras

Hom-Lie superalgebras, which can be considered as a deformation of Lie superalgebras, are $\mathbb{Z}_2$-graded generalization of Hom-Lie algebras. In this paper, we prove that there is only the trivial Hom-Lie superalgebra structure over a finite-dimensional simple Lie superalgebra.Comment: 12 page

A new structure of two-dimensional allotropes of group V elements

The elemental two-dimensional (2D) materials such as graphene, silicene, germanene, and black phosphorus have attracted considerable attention due to their fascinating physical properties. Structurally they possess the honeycomb or distorted honeycomb lattices, which are composed of six-atom rings. Here we find a new structure of 2D allotropes of group V elements composed of eight-atom rings, which we name as the octagonal tiling (OT) structure. First-principles calculations indicate that these allotropes are dynamically stable and are also thermally stable at temperatures up to 600 K. These allotropes are semiconductors with band gaps ranging from 0.3 to 2.0 eV, thus they are potentially useful in near- and mid-infrared optoelectronic devices. OT-Bi is also a 2D topological insulator (TI) with a band gap of 0.33 eV, which is the largest among the reported elemental 2D TIs, and this gap can be increased further by applying compressive strains

The qq-Schur algebras and qq-Schur dualities of finite type

We formulate a $q$-Schur algebra associated to an arbitrary $W$-invariant finite set $X_{\texttt f}$ of integral weights for a complex simple Lie algebra with Weyl group $W$. We establish a $q$-Schur duality between the $q$-Schur algebra and Hecke algebra associated to $W$. We then realize geometrically the $q$-Schur algebra and duality, and construct a canonical basis for the $q$-Schur algebra with positivity. With suitable choices of $X_{\texttt f}$ in classical types, we recover the $q$-Schur algebras in the literature. Our $q$-Schur algebras are closely related to the category $\mathcal O$, where the type $G_2$ is studied in detail.Comment: v3, 33 pages, mild corrections, J. Inst. Math. Jussieu (to appear

A Simplification Method of Polymorphic Boolean Functions

Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be described by a polymorphic Boolean function. For the first time, this brief presents a simplification method of the polymorphic Boolean function

Combination of e+/e- ratio from AMS-02 and gamma ray line from Fermi-LAT with implication for Dark Matter

The precise AMS-02 data provide definite information for the e+/e- ratio in 100 - 350 GeV region. Assuming that the recent gamma ray line observed by Fermi-LAT experiment is product of dark matter in space and taken as input. We make a global fit for the AMS-02 e+/e- spectrum with both dark matter and pulsar contribution. For this spectrum over 130 GeV, pulsar is the dominant contribution. We also investigate the constrains on hadron production from dark matter annihilation.Comment: 11 pages, 7 figure

Generate Identity-Preserving Faces by Generative Adversarial Networks

Generating identity-preserving faces aims to generate various face images keeping the same identity given a target face image. Although considerable generative models have been developed in recent years, it is still challenging to simultaneously acquire high quality of facial images and preserve the identity. Here we propose a compelling method using generative adversarial networks (GAN). Concretely, we leverage the generator of trained GAN to generate plausible faces and FaceNet as an identity-similarity discriminator to ensure the identity. Experimental results show that our method is qualified to generate both plausible and identity-preserving faces with high quality. In addition, our method provides a universal framework which can be realized in various ways by combining different face generators and identity-similarity discriminator.Comment: 9 page

The simplified weighted sum function and its average sensitivity

In this paper we simplify the definition of the weighted sum Boolean function which used to be inconvenient to compute and use. We show that the new function has essentially the same properties as the previous one. In particular, the bound on the average sensitivity of the weighted sum Boolean function remains unchanged after the simplification.Comment: 9 page

Monogamy of α\alphath Power Entanglement Measurement in Qubit Systems

In this paper, we study the $\alpha$th power monogamy properties related to the entanglement measure in bipartite states. The monogamy relations related to the $\alpha$th power of negativity and the Convex- Roof Extended Negativity are obtained for N-qubit states. We also give a tighter bound of hierarchical monogamy inequality for the entanglement of formation. We find that the GHZ state and W state can be used to distinguish the $\alpha$th power the concurrence for $0<\alpha<2$. Furthermore, we compare concurrence with negativity in terms of monogamy property and investigate the difference between them.Comment: 6 pages, 2 figure