Fraunhofer diffraction at the two-dimensional quadratically distorted (QD) Grating

A two-dimensional (2D) mathematical model of quadratically distorted (QD) grating is established with the principles of Fraunhofer diffraction and Fourier optics. Discrete sampling and bisection algorithm are applied for finding numerical solution of the diffraction pattern of QD grating. This 2D mathematical model allows the precise design of QD grating and improves the optical performance of simultaneous multiplane imaging system.Comment: 4 pages, 6 figure

Inequalities of Hermite-Hadamard type for extended ss-convex functions and applications to means

In the paper, the authors introduce a new concept "extended $s$-convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and apply these inequalities to derive some inequalities of special means.Comment: 17 page

Gradient Estimate on the Neumann Semigroup and Applications

We prove the following sharp upper bound for the gradient of the Neumann semigroup $P_t$ on a $d$-dimensional compact domain \OO with boundary either $C^2$-smooth or convex: \|\nn P_t\|_{1\to \infty}\le \ff{c}{t^{(d+1)/2}},\ \ t>0, where $c>0$ is a constant depending on the domain and $\|\cdot\|_{1\to\infty}$ is the operator norm from L^1(\OO) to L^\infty(\OO). This estimate implies a Gaussian type point-wise upper bound for the gradient of the Neumann heat kernel, which is applied to the study of the Hardy spaces, Riesz transforms, and regularity of solutions to the inhomogeneous Neumann problem on compact convex domains

Half-arc-transitive graphs of prime-cube order of small valencies

A graph is called {\em half-arc-transitive} if its full automorphism group acts transitively on vertices and edges, but not on arcs. It is well known that for any prime $p$ there is no tetravalent half-arc-transitive graph of order $p$ or $p^2$. Xu~[Half-transitive graphs of prime-cube order, J. Algebraic Combin. 1 (1992) 275-282] classified half-arc-transitive graphs of order $p^3$ and valency $4$. In this paper we classify half-arc-transitive graphs of order $p^3$ and valency $6$ or $8$. In particular, the first known infinite family of half-arc-transitive Cayley graphs on non-metacyclic $p$-groups is constructed.Comment: 13 page

Learning to Rank Binary Codes

Binary codes have been widely used in vision problems as a compact feature representation to achieve both space and time advantages. Various methods have been proposed to learn data-dependent hash functions which map a feature vector to a binary code. However, considerable data information is inevitably lost during the binarization step which also causes ambiguity in measuring sample similarity using Hamming distance. Besides, the learned hash functions cannot be changed after training, which makes them incapable of adapting to new data outside the training data set. To address both issues, in this paper we propose a flexible bitwise weight learning framework based on the binary codes obtained by state-of-the-art hashing methods, and incorporate the learned weights into the weighted Hamming distance computation. We then formulate the proposed framework as a ranking problem and leverage the Ranking SVM model to offline tackle the weight learning. The framework is further extended to an online mode which updates the weights at each time new data comes, thereby making it scalable to large and dynamic data sets. Extensive experimental results demonstrate significant performance gains of using binary codes with bitwise weighting in image retrieval tasks. It is appealing that the online weight learning leads to comparable accuracy with its offline counterpart, which thus makes our approach practical for realistic applications

Improved Analytical Delay Models for RC-Coupled Interconnects

As the process technologies scale into deep submicron region, crosstalk delay is becoming increasingly severe, especially for global on-chip buses. To cope with this problem, accurate delay models of coupled interconnects are needed. In particular, delay models based on analytical approaches are desirable, because they not only are largely transparent to technology, but also explicitly establish the connections between delays of coupled interconnects and transition patterns, thereby enabling crosstalk alleviating techniques such as crosstalk avoidance codes (CACs). Unfortunately, existing analytical delay models, such as the widely cited model in [1], have limited accuracy and do not account for loading capacitance. In this paper, we propose analytical delay models for coupled interconnects that address these disadvantages. By accounting for more wires and eschewing the Elmore delay, our delay models achieve better accuracy than the model in [1].Comment: 10 pages, 2 figure

On the minimal affinizations over the quantum affine algebras of type CnC_n

In this paper, we study the minimal affinizations over the quantum affine algebras of type $C_n$ by using the theory of cluster algebras. We show that the $q$-characters of a large family of minimal affinizations of type $C_n$ satisfy some systems of equations. These equations correspond to mutation equations of some cluster algebras. Furthermore, we show that the minimal affinizations in these equations correspond to cluster variables in these cluster algebras.Comment: arXiv admin note: substantial text overlap with arXiv:1501.00146, arXiv:1502.0242

A new example of limit variety of aperiodic monoids

A limit variety is a variety that is minimal with respect to being non-finitely based. The two limit varieties of Marcel Jackson are the only known examples of limit varieties of aperiodic monoids. Our previous work had shown that there exists a limit subvariety of aperiodic monoids that is different from Marcel Jackson's limit varieties. In this paper, we introduce a new limit variety of aperiodic monoids.Comment: 16 pages, 1 figur

Rapid heating and cooling in two-dimensional Yukawa systems

Simulations are reported to investigate solid superheating and liquid supercooling of two-dimensional (2D) systems with a Yukawa interparticle potential. Motivated by experiments where a dusty plasma is heated and then cooled suddenly, we track particle motion using a simulation with Langevin dynamics. Hysteresis is observed when the temperature is varied rapidly in a heating and cooling cycle. As in the experiment, transient solid superheating, but not liquid supercooling, is observed. Solid superheating, which is characterized by solid structure above the melting point, is found to be promoted by a higher rate of temperature increase.Comment: 7 pages, 5 figure

Effect of interaction strength on the evolution of cooperation

Cooperative behaviors are ubiquitous in nature,which is a puzzle to evolutionary biology,because the defector always gains more benefit than the cooperator,thus,the cooperator should decrease and vanish over time.This typical "prisoners' dilemma" phenomenon has been widely researched in recent years.The interaction strength between cooperators and defectors is introduced in this paper(in human society,it can be understood as the tolerance of cooperators).We find that only when the maximum interaction strength is between two critical values,the cooperator and defector can coexist,otherwise, 1) if it is greater than the upper value,the cooperator will vanish, 2) if it is less than the lower value,a bistable state will appear