On representations of quantum groups Uq(fm(K,H))U_{q}(f_{m}(K,H))

We construct families of irreducible representations for a class of quantum groups $U_{q}(f_{m}(K,H)$. First, we realize these quantum groups as Hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for $U_{q}(f_{m}(K,H))$. Second, we study the relationship between $U_{q}(f_{m}(K,H))$ and $U_{q}(f_{m}(K))$. As a result, any finite dimensional weight representation of $U_{q}(f_{m}(K,H))$ is proved to be completely reducible. Finally, we study the Whittaker model for the center of $U_{q}(f_{m}(K,H))$, and a classification of all irreducible Whittaker representations of $U_{q}(f_{m}(K,H))$ is obtained.Comment: Some minor modifications to the first versio

Acoustic Prism for Continuous Beam Steering Based on Piezoelectric Metamaterial

This paper investigates an acoustic prism for continuous acoustic beam steering by a simple frequency sweep. This idea takes advantages of acoustic wave velocity shifting in metamaterials in the vicinity of local resonance. We apply this concept into the piezoelectric metamaterial consisting of host medium and piezoelectric LC shunt. Theoretical modeling and FEM simulations are carried out. It is shown that the phase velocity of acoustic wave changes dramatically in the vicinity of local resonance. The directions of acoustic wave can be adjusted continuously between 2 to 16 degrees by a simple sweep of the excitation frequency. Such an electro-mechanical coupling system has a feature of adjusting local resonance without altering the mechanical part of the system.Comment: 11 pages, 11 figure

Stability of the sum of two solitary waves for (gDNLS) in the energy space

In this paper, we continue the study in \cite{MiaoTX:DNLS:Stab}. We use the perturbation argument, modulational analysis and the energy argument in \cite{MartelMT:Stab:gKdV, MartelMT:Stab:NLS} to show the stability of the sum of two solitary waves with weak interactions for the generalized derivative Schr\"{o}dinger equation (gDNLS) in the energy space. Here (gDNLS) hasn't the Galilean transformation invariance, the pseudo-conformal invariance and the gauge transformation invariance, and the case $\sigma>1$ we considered corresponds to the $L^2$-supercritical case.Comment: 41page

Detecting the Major Charge-Carrier Scattering Mechanism in Graphene Antidot Lattices

Charge carrier scattering is critical to the electrical properties of two-dimensional materials such as graphene, transition metal dichalcogenide monolayers, black phosphorene, and tellurene. Beyond pristine two-dimensional materials, further tailored properties can be achieved by nanoporous patterns such as nano- or atomic-scale pores (antidots) across the material. As one example, structure-dependent electrical/optical properties for graphene antidot lattices (GALs) have been studied in recent years. However, detailed charge carrier scattering mechanism is still not fully understood, which hinders the future improvement and potential applications of such metamaterials. In this paper, the energy sensitivity of charge-carrier scattering and thus the dominant scattering mechanisms are revealed for GALs by analyzing the maximum Seebeck coefficient with a tuned gate voltage and thus shifted Fermi levels. It shows that the scattering from pore-edge-trapped charges is dominant, especially at elevated temperatures. For thermoelectric interests, the gate-voltage-dependent power factor of different GAL samples are measured as high as 509 at 400 K for a GAL with the square pattern. Such a high power factor is improved by more than one order of magnitude from the values for the state-of-the-art bulk thermoelectric materials. With their high thermal conductivities and power factors, these GALs can be well suitable for "active coolers" within electronic devices, where heat generated at the hot spot can be removed with both passive heat conduction and active Peltier cooling

The Cosmological Constant as a Function of Extrinsic Curvature and Spatial Curvature

In this paper we suppose that the cosmological constant will change when the universe expends. For a general consideration, the cosmological constant is assumed to be a function of scale factor and Hubble constant. According to the ADM formulation, to the FRW metric, the extrinsic curvature $I$ equals $-6H^{2}$ and spatial curvature $R$ equals $6k/a^{2}$. Therefore we suppose cosmological constant is a function of extrinsic curvature and spatial curvature. We investigate the cosmological evolution of FRW universe in these models. At last we investigate two particular models which could fit the observation data about dark energy well. Actually a changeless cosmological constant is not essential. If when the universe expands, the cosmological constant changes slowly and gradually flows to a constant, the observation data about dark energy could also be fitted well by this kind of theory.Comment: 8 pages, 4 figure

Fermion correction to the mass of the scalar glueball in QCD sum rule

Contributions of fermions to the mass of the scalar glueball $0^{++}$ are calculated at two-loop level in the framework of QCD sum rules. It obviously changes the coefficients in the operator product expansion (OPE) and shifts the mass of glueball.Comment: 5 pages, 2 figure

Parallel in time algorithm with spectral-subdomain enhancement for Volterra integral equations

This paper proposes a parallel in time (called also time parareal) method to solve Volterra integral equations of the second kind. The parallel in time approach follows the same spirit as the domain decomposition that consists of breaking the domain of computation into subdomains and solving iteratively the sub-problems in a parallel way. To obtain high order of accuracy, a spectral collocation accuracy enhancement in subdomains will be employed. Our main contributions in this work are two folds: (i) a time parareal method is designed for the integral equations, which to our knowledge is the first of its kind. The new method is an iterative process combining a coarse prediction in the whole domain with fine corrections in subdomains by using spectral approximation, leading to an algorithm of very high accuracy; (ii) a rigorous convergence analysis of the overall method is provided. The numerical experiment confirms that the overall computational cost is considerably reduced while the desired spectral rate of convergence can be obtained

On the Performance of Sparse Recovery via L_p-minimization (0<=p <=1)

It is known that a high-dimensional sparse vector x* in R^n can be recovered from low-dimensional measurements y= A^{m*n} x* (m<n) . In this paper, we investigate the recovering ability of l_p-minimization (0<=p<=1) as p varies, where l_p-minimization returns a vector with the least l_p ``norm'' among all the vectors x satisfying Ax=y. Besides analyzing the performance of strong recovery where l_p-minimization needs to recover all the sparse vectors up to certain sparsity, we also for the first time analyze the performance of ``weak'' recovery of l_p-minimization (0<=p<1) where the aim is to recover all the sparse vectors on one support with fixed sign pattern. When m/n goes to 1, we provide sharp thresholds of the sparsity ratio that differentiates the success and failure via l_p-minimization. For strong recovery, the threshold strictly decreases from 0.5 to 0.239 as p increases from 0 to 1. Surprisingly, for weak recovery, the threshold is 2/3 for all p in [0,1), while the threshold is 1 for l_1-minimization. We also explicitly demonstrate that l_p-minimization (p<1) can return a denser solution than l_1-minimization. For any m/n<1, we provide bounds of sparsity ratio for strong recovery and weak recovery respectively below which l_p-minimization succeeds with overwhelming probability. Our bound of strong recovery improves on the existing bounds when m/n is large. Regarding the recovery threshold, l_p-minimization has a higher threshold with smaller p for strong recovery; the threshold is the same for all p for sectional recovery; and l_1-minimization can outperform l_p-minimization for weak recovery. These are in contrast to traditional wisdom that l_p-minimization has better sparse recovery ability than l_1-minimization since it is closer to l_0-minimization. We provide an intuitive explanation to our findings and use numerical examples to illustrate the theoretical predictions

An Improved Error Term for Turaˊ\acute{\rm a}n Number of Expanded Non-degenerate 2-graphs

For a 2-graph $F$, let $H_F^{(r)}$ be the $r$-graph obtained from $F$ by enlarging each edge with a new set of $r-2$ vertices. We show that if $\chi(F)=\ell>r \geq 2$, then ${\rm ex}(n,H_F^{(r)})= t_r (n,\ell-1)+ \Theta( {\rm biex}(n,F)n^{r-2}),$ where $t_r (n,\ell-1)$ is the number of edges of an $n$-vertex complete balanced $\ell-1$ partite $r$-graph and ${\rm biex}(n,F)$ is the extremal number of the decomposition family of $F$. Since ${\rm biex}(n,F)=O(n^{2-\gamma})$ for some $\gamma>0$, this improves on the bound ${\rm ex}(n,H_F^{(r)})= t_r (n,\ell-1)+ o(n^r)$ by Mubayi (2016). Furthermore, our result implies that ${\rm ex}(n,H_F^{(r)})= t_r (n,\ell-1)$ when $F$ is edge-critical, which is an extension of the result of Pikhurko (2013)

Spin alignment of vector mesons in unpolarized hadron-hadron collisions at high energies

We argue that spin alignment of the vector mesons observed in unpolarized hadron-hadron collisions is closely related to the single spin left-right asymmetry observed in transversely polarized hadron-hadron collisions. We present the numerical results obtained from the type of spin-correlation imposed by the existence of the single-spin left-right asymmetries. We compare the results with the available data and make predictions for future experiments.Comment: submitted to Phys. Rev .