Surface effect on the wrinkling of an elastic sheet under tension

Wrinkling of stretched elastic sheets is widely observed, and the scaling relations between the amplitude and wavelength of the wrinkles have been proposed by Cerda and Mahadevan. However, the surface effects should be taken into account when the sheet is even thinner. The surface energy was considered in this work, and the discrepancies with the classical theory has been discussed. A dimensionless parameter has been proposed to represent the size-dependence. A method of characterizing mechanical properties of thin film using wrinkles considering surface effects has also been proposed.Comment: 6 pages, no figur

Quantum Action Principle with Generalized Uncertainty Principle

One of the common features in all promising candidates of quantum gravity is the existence of a minimal length scale, which naturally emerges with a generalized uncertainty principle, or equivalently a modified commutation relation. Schwinger's quantum action principle was modified to incorporate this modification, and was applied to the calculation of the kernel of a free particle, partly recovering the result previously studied using path integral.Comment: 8 pages, no figur

Canonical bases for the quantum linear supergroups

We give a combinatorial construction for the canonical bases of the $\pm$-parts of the quantum enveloping superalgebra \bfU(\mathfrak{gl}_{m|n}) and discuss their relationship with the Kazhdan-Lusztig bases for the quantum Schur superalgebras \bsS(m|n,r) introduced in \cite{DR}. We will also extend this relationship to the induced bases for simple polynomial representations of \bfU(\mathfrak{gl}_{m|n}).Comment: 30 page

A realisation of the quantum linear superalgebra

We reconstruct the quantum enveloping superalgebra ${\bf U}(\mathfrak{gl}_{m|n})$ over $\mathbb Q(v)$ via (finite dimensional) quantum Schur superalgebras. In particular, we obtain a new basis containing the standard generators of ${\bf U}(\mathfrak{gl}_{m|n})$ and explicit multiplication formulas between the generators and an arbitrary basis element.Comment: 43 page

A note on colored HOMFLY polynomials for hyperbolic knots from WZW models

Using the correspondence between Chern-Simons theories and Wess-Zumino-Witten models we present the necessary tools to calculate colored HOMFLY polynomials for hyperbolic knots. For two-bridge hyperbolic knots we derive the colored HOMFLY invariants in terms of crossing matrices of the underlying Wess-Zumino-Witten model. Our analysis extends previous works by incorporating non-trivial multiplicities for the primaries appearing in the crossing matrices, so as to describe colorings of HOMFLY invariants beyond the totally symmetric or anti-symmetric representations of SU(N). The crossing matrices directly relate to 6j-symbols of the quantum group U_q(su(N)). We present powerful methods to calculate such quantum 6j-symbols for general N. This allows us to determine previously unknown colored HOMFLY polynomials for two-bridge hyperbolic knots. We give explicitly the HOMFLY polynomials colored by the representation {2,1} for two-bridge hyperbolic knots with up to eight crossings. Yet, the scope of application of our techniques goes beyond knot theory; e.g., our findings can be used to study correlators in Wess-Zumino-Witten conformal field theories or -- in the limit to classical groups -- to determine color factors for Yang Mills amplitudes.Comment: 72 pages, 15 figures; v2: explicit HOMFLY polynomials for more knots included, refs. added and typos corrected; v3: Appendix with sample calculation adde

Possible Realization and Protection of Valley-Polarized Quantum Hall Effect in Mn/WS2

By using the first-principles calculations and model analyses, we found that the combination of defected tungsten disulfide monolayer and sparse manganese adsorption may give a KK` valley spin splitting up to 210 meV. This system also has a tunable magnetic anisotropy energy, a clean band gap, and an appropriate band alignment, with the Fermi level sitting right above the top of valence bands at the K-valleys. Therefore, it can be used for the realization of the valley-polarized anomalous Hall effect and for the exploration of other valley related physics without using optical methods. A protective environment can be formed by covering it with a hexagonal BN layer, without much disturbance to the benign properties of Mn/WS2.Comment: 16 pages, 4 figure

Chinese Typeface Transformation with Hierarchical Adversarial Network

In this paper, we explore automated typeface generation through image style transfer which has shown great promise in natural image generation. Existing style transfer methods for natural images generally assume that the source and target images share similar high-frequency features. However, this assumption is no longer true in typeface transformation. Inspired by the recent advancement in Generative Adversarial Networks (GANs), we propose a Hierarchical Adversarial Network (HAN) for typeface transformation. The proposed HAN consists of two sub-networks: a transfer network and a hierarchical adversarial discriminator. The transfer network maps characters from one typeface to another. A unique characteristic of typefaces is that the same radicals may have quite different appearances in different characters even under the same typeface. Hence, a stage-decoder is employed by the transfer network to leverage multiple feature layers, aiming to capture both the global and local features. The hierarchical adversarial discriminator implicitly measures data discrepancy between the generated domain and the target domain. To leverage the complementary discriminating capability of different feature layers, a hierarchical structure is proposed for the discriminator. We have experimentally demonstrated that HAN is an effective framework for typeface transfer and characters restoration.Comment: 8 pages(exclude reference), 6 figure

Cross-Modality Hashing with Partial Correspondence

Learning a hashing function for cross-media search is very desirable due to its low storage cost and fast query speed. However, the data crawled from Internet cannot always guarantee good correspondence among different modalities which affects the learning for hashing function. In this paper, we focus on cross-modal hashing with partially corresponded data. The data without full correspondence are made in use to enhance the hashing performance. The experiments on Wiki and NUS-WIDE datasets demonstrates that the proposed method outperforms some state-of-the-art hashing approaches with fewer correspondence information

Coexistence curves and molecule number densities of AdS black holes in the reduced parameter space

In this paper, we investigate the coexistence curves and molecule number densities of $f(R)$ AdS black holes and Gauss-Bonnet AdS black holes. Specifically, we work with the reduced parameter space and derive the analytic expressions of the universal coexistence curves that are independent of theory parameters. Moreover, we obtain the explicit expressions of the physical quantity describing the difference of the number densities of black hole molecules between the small and large black hole. It is found that both the coexistence curve and the difference of the molecule number densities of $f(R)$ AdS black holes coincide with those of RN-AdS black holes. It may be attributed to the same equation of state they share in the reduced parameter space. The difference of the molecule number densities between the small and large Gauss-Bonnet AdS black hole exhibits different behavior. This may be attributed to the fact that the charge of RN-AdS black hole is non-trivial. Our research will not only deepen the understanding of both the physics along the coexistence curve and the underlying microscopic freedom of AdS black holes, but also highlight the importance of the law of corresponding states

Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surface

This paper is devoted to the study of reducing subspaces for multiplication operator $M_\phi$ on the Dirichlet space with symbol of finite Blaschke product. The reducing subspaces of $M_\phi$ on the Dirichlet space and Bergman space are related. Our strategy is to use local inverses and Riemann surface to study the reducing subspaces of $M_\phi$ on the Bergman space, and we discover a new way to study the Riemann surface for $\phi^{-1}\circ\phi$. By this means, we determine the reducing subspaces of $M_\phi$ on the Dirichlet space when the order of $\phi$ is $5$; $6$; $7$ and answer some questions of Douglas-Putinar-Wang \cite{DPW12}