Characterization of trace spaces on regular trees via dyadic norms

In this paper, we study the traces of Orlicz-Sobolev spaces on a regular rooted tree. After giving a dyadic decomposition of the boundary of the regular tree, we present a characterization on the trace spaces of those first order Orlicz-Sobolev spaces whose Young function is of the form $t^p\log^\lambda(e+t)$, based on integral averages on dyadic elements of the dyadic decomposition.Comment: 23 page

Meson properties in magnetized quark matter

We study neutral and charged meson properties in magnetic field. Taking bosolization method in a two-flavor Nambu--Jona-Lasinio model, we derive effective meson Lagrangian density with minimal coupling to the magnetic field, by employing derivative expansion for both the meson fields and Schwinger phases. We extract from the effective Lagrangian density the meson curvature, pole and screening masses. As the only Goldstone mode, the neutral pion controls the thermodynamics of the system and propagates the lang range quark interaction. The magnetic field breaks down the space symmetry, and the quark interaction region changes from a sphere in vacuum to a ellipsoid in magnetic field.Comment: 10 pages, 3 figure

Meson Spectral Functions at Finite Temperature and Isospin Density with Functional Renormalization Group

The pion superfluid and the corresponding Goldstone and soft modes are investigated in two-flavor quark-meson model with functional renormalization group. By solving the flow equations for the effective potential and the meson two-point functions at finite temperature and isospin density, the critical temperature for the superfluid increases sizeably in comparison with solving the flow equation for the potential only. The spectral function for the soft mode shows clearly a transition from meson gas to quark gas with increasing temperature and a crossover from BEC to BCS pairing of quarks with increasing isospin density.Comment: 14 pages, 7 figure

Conductance fluctuation and shot noise in disordered graphene systems, a perturbation expansion approach

We report the investigation of conductance fluctuation and shot noise in disordered graphene systems with two kinds of disorder, Anderson type impurities and random dopants. To avoid the brute-force calculation which is time consuming and impractical at low doping concentration, we develop an expansion method based on the coherent potential approximation (CPA) to calculate the average of four Green's functions and the results are obtained by truncating the expansion up to 6th order in terms of "single-site-T-matrix". Since our expansion is with respect to "single-site-T-matrix" instead of disorder strength $W$, good result can be obtained at 6th order for finite $W$. We benchmark our results against brute-force method on disordered graphene systems as well as the two dimensional square lattice model systems for both Anderson disorder and the random doping. The results show that in the regime where the disorder strength $W$ is small or the doping concentration is low, our results agree well with the results obtained from the brute-force method. Specifically, for the graphene system with Anderson impurities, our results for conductance fluctuation show good agreement for $W$ up to $0.4t$, where $t$ is the hopping energy. While for average shot noise, the results are good for $W$ up to $0.2t$. When the graphene system is doped with low concentration 1%, the conductance fluctuation and shot noise agrees with brute-force results for large $W$ which is comparable to the hopping energy $t$. At large doping concentration 10%, good agreement can be reached for conductance fluctuation and shot noise for $W$ up to $0.4t$. We have also tested our formalism on square lattice with similar results. Our formalism can be easily combined with linear muffin-tin orbital first-principles transport calculations for light doping nano-scaled systems, making prediction on variability of nano-devices.Comment: 8 pages, 8 figure

Pressure induced band structure evolution of halide perovskites: a first-principles atomic and electronic structure study

Density functional theory (DFT) based calculations have been conducted to draw a broad picture of pressure induced band structure evolution in various phases of organic and inorganic halide perovskite materials. Under a wide range of pressure applied, distinct band structure behaviors including magnitude change of band gap, direct-indirect/indirect-direct band gap transitions and CBM/VBM shifts, have been observed between organic and inorganic perovskites among different phases. Through atomic and electronic structure calculations, band gap narrowing/widening has been rationalized through crystal orbitals coupling transformations; direct-indirect mutual transitions were explained based on structural symmetry evolution; different VBM/CBM shifts behaviors between organic and inorganic perovskites were analyzed focusing on orientation and polarity of molecules/atoms outside the octahedrals. These results provide a comprehensive guidance for further experimental investigations on pressure engineering of perovskite materials.Comment: Additional Contact: Yang Huang [email protected]

DG Poisson algebra and its universal enveloping algebra

In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.Comment: Accepted by Science China Mathematic

Traces of weighted function spaces: dyadic norms and Whitney extensions

The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well adapted to extending functions using the Whitney extension operator.Comment: 40 page

Universal enveloping algebras of differential graded Poisson algebras

In this paper, we introduce the notion of differential graded Poisson algebra and study its universal enveloping algebra. From any differential graded Poisson algebra $A$, we construct two isomorphic differential graded algebras: $A^e$ and $A^E$. It is proved that the category of differential graded Poisson modules over $A$ is isomorphic to the category of differential graded modules over $A^e$, and $A^e$ is the unique universal enveloping algebra of $A$ up to isomorphisms. As applications of the universal property of $A^e$, we prove that $(A^e)^{op}\cong (A^{op})^e$ and $(A\otimes_{\Bbbk}B)^e\cong A^e\otimes_{\Bbbk}B^e$ as differential graded algebras. As consequences, we obtain that ``$e$'' is a monoidal functor and establish links among the universal enveloping algebras of differential graded Poisson algebras, differential graded Lie algebras and associative algebras.Comment: 37 pages, the abstract is rewritten, another construction of the universal enveloping algebra is given and several typos are fixe

Universal enveloping algebras of Poisson Ore extensions

We prove that the universal enveloping algebra of a Poisson-Ore extension is a length two iterated Ore extension of the original universal enveloping algebra. As consequences, we observe certain ring-theoretic invariants of the universal enveloping algebras that are preserved under iterated Poisson-Ore extensions. We apply our results to iterated quadratic Poisson algebras arising from semiclassical limits of quantized coordinate rings and a family of graded Poisson algebras of Poisson structures of rank at most two.Comment: 13 page

Visual Tracking via Shallow and Deep Collaborative Model

In this paper, we propose a robust tracking method based on the collaboration of a generative model and a discriminative classifier, where features are learned by shallow and deep architectures, respectively. For the generative model, we introduce a block-based incremental learning scheme, in which a local binary mask is constructed to deal with occlusion. The similarity degrees between the local patches and their corresponding subspace are integrated to formulate a more accurate global appearance model. In the discriminative model, we exploit the advances of deep learning architectures to learn generic features which are robust to both background clutters and foreground appearance variations. To this end, we first construct a discriminative training set from auxiliary video sequences. A deep classification neural network is then trained offline on this training set. Through online fine-tuning, both the hierarchical feature extractor and the classifier can be adapted to the appearance change of the target for effective online tracking. The collaboration of these two models achieves a good balance in handling occlusion and target appearance change, which are two contradictory challenging factors in visual tracking. Both quantitative and qualitative evaluations against several state-of-the-art algorithms on challenging image sequences demonstrate the accuracy and the robustness of the proposed tracker.Comment: Undergraduate Thesis, appearing in Pattern Recognitio