Compact embeddings of some weighted fractional Sobolev spaces on \Rn

In this paper, we study a family of general fractional Sobolev spaces \MsqpOm when \Om=\Rn or \Om is a bounded domain, having a compact, Lipschitz boundary \Bdy, in \Rn for $n\geq2$. Among other results, some compact embedding results of \MVsqpRn\hookrightarrow\LqRn and \MVsqpRn\hookrightarrow\LlRn for suitable potential functions $V(x)$ are described

Algebraic differential independence regarding the Riemann ζ\boldsymbol{\zeta}-function and the Euler Γ\boldsymbol{\Gamma}-function

In this paper, we prove that $\boldsymbol{\zeta}$ cannot be a solution to any nontrivial algebraic differential equation whose coefficients are polynomials in $\boldsymbol{\Gamma},\boldsymbol{\Gamma}^{(n)}$ and $\boldsymbol{\Gamma}^{(\ell n)}$ over the ring of polynomials in $\mathbf{C}$, where $\ell,n\geq1$ are positive integers

An Upper Bound for Hessian Matrices of Positive Solutions of Heat Equations

We prove global and local upper bounds for the Hessian of log positive solutions of the heat equation on a Riemannian manifold. The metric is either fixed or evolves under the Ricci flow. These upper bounds supplement the well-known global lower bound

On Fermat Diophantine functional equations and little Picard theorem

We discuss equivalence conditions on the non-existence of non-trivial meromorphic solution to the Fermat Diophantine equations $f^m(z)+g^n(z)=1$ with integers $m,n\geq2$, from which other approaches to prove little Picard theorem are provided

Super-pixel cloud detection using Hierarchical Fusion CNN

Cloud detection plays a very important role in the process of remote sensing images. This paper designs a super-pixel level cloud detection method based on convolutional neural network (CNN) and deep forest. Firstly, remote sensing images are segmented into super-pixels through the combination of SLIC and SEEDS. Structured forests is carried out to compute edge probability of each pixel, based on which super-pixels are segmented more precisely. Segmented super-pixels compose a super-pixel level remote sensing database. Though cloud detection is essentially a binary classification problem, our database is labeled into four categories: thick cloud, cirrus cloud, building and other culture, to improve the generalization ability of our proposed models. Secondly, super-pixel level database is used to train our cloud detection models based on CNN and deep forest. Considering super-pixel level remote sensing images contain less semantic information compared with general object classification database, we propose a Hierarchical Fusion CNN (HFCNN). It takes full advantage of low-level features like color and texture information and is more applicable to cloud detection task. In test phase, every super-pixel in remote sensing images is classified by our proposed models and then combined to recover final binary mask by our proposed distance metric, which is used to determine ambiguous super-pixels. Experimental results show that, compared with conventional methods, HFCNN can achieve better precision and recall

ACC for log canonical threshold polytopes

We show that the log canonical threshold polytopes of varieties with log canonical singularities satisfy the ascending chain condition.Comment: 33 pages, to appear in American Journal of Mathematic

On the value distribution of the Riemann zeta-function and the Euler gamma-function

We prove some uniqueness results for the Riemann zeta-function and the Euler gamma-function by virtue of shared values using the value distribution theory

High Throughput and Low Cost LDPC Reconciliation for Quantum Key Distribution

Reconciliation is a crucial procedure in post-processing of Quantum Key Distribution (QKD), which is used for correcting the error bits in sifted key strings. Although most studies about reconciliation of QKD focus on how to improve the efficiency, throughput optimizations have become the highlight in high-speed QKD systems. Many researchers adpot high cost GPU implementations to improve the throughput. In this paper, an alternative high throughput and efficiency solution implemented in low cost CPU is proposed. The main contribution of the research is the design of a quantized LDPC decoder including improved RCBP-based check node processing and saturation-oriented variable node processing. Experiment results show that the throughput up to 60Mbps is achieved using the bi-directional approach with reconciliation efficiency approaching to 1.1, which is the optimal combination of throughput and efficiency in Discrete-Variable QKD (DV-QKD). Meanwhile, the performance remains stable when Quantum Bit Error Rate (QBER) varies from 1% to 8%

Bus Manufacturing Workshop Scheduling Method with Routing Buffer

Aiming at solving the problem that the moving route is complicated and the scheduling is difficult in the routing buffer of the bus in the manufacturing workshop, a routing buffer mathematical programming model for bus manufacturing workshop is proposed. We design a moving approach for minimizing the total setup cost for moving in routing buffer. The framework and the solution ofthe optimization problem of such a bus manufacturing workshop scheduling with routing buffer arepresented. The evaluation results show that, comparing with the irregularly guided moving method, the proposed method can better guide the bus movement in routing buffer by reducing the total setup time of all buses processed at the next stage, and obtaining a better scheduling optimization solution with minimize maximum total completion time.Comment: The paper has been accepted by IJSPM, and this is the authors' version of the pape

Modeling and Simulation of Practical Quantum Secure Communication Network

As the Quantum Key Distribution (QKD) technology supporting the pointto-point application matures, the need to build the Quantum Secure Communication Network (QSCN) to guarantee the security of a large scale of nodes becomes urgent. Considering the project time and expense control, it is the first choice to build the QSCN based on an existing classical network. Suitable modeling and simulation are very important to construct a QSCN successfully and efficiently. In this paper, a practical QSCN model, which can reflect the network state well, is proposed. The model considers the volatile traffic demand of the classical network and the real key generation capability of the QKD devices, which can enhance the accuracy of simulation to a great extent. In addition, two unique QSCN performance indicators, ITS (information-theoretic secure) communication capability and ITS communication efficiency, are proposed in the model, which are necessary supplements for the evaluation of a QSCN except for those traditional performance indicators of classical networks. Finally, the accuracy of the proposed QSCN model and the necessity of the proposed performance indicators are verified by plentiful simulations results.Comment: 20 pages, 6 figure