Non-vanishing Fourier coefficients of modular forms

In this paper, we generalize D. H. Lehmer's result to give a sufficient condition for level one cusp forms $f$ with integral Fourier coefficients such that the smallest $n$ for which the coefficients $a_n(f)=0$ must be a prime. Then we describe a method to compute a bound $B$ of $n$ such that $a_n(f)\ne0$ for all $n<B$. As examples, we achieve the explicit bounds $B_k$ for the unique cusp form $\Delta_{k}$ of level one and weight k with $k=16, 18, 20, 22, 26$ such that $a_n(\Delta_k)\ne0$ for all $n<B_k$.Comment: We add the case of $k=18$ in this revision. For the weight 16 case, we have one more polynomial which could be used to improve the bound in this cas

Liouville type theorems, a priori estimates and existence of solutions for non-critical higher order Lane-Emden-Hardy equations

In this paper, we are concerned with the non-critical higher order Lane-Emden-Hardy equations \begin{equation*} (-\Delta)^{m}u(x)=\frac{u^{p}(x)}{|x|^{a}} \,\,\,\,\,\,\,\,\,\,\,\, \text{in} \,\,\, \mathbb{R}^{n} \end{equation*} with $n\geq3$, $1\leq m<\frac{n}{2}$, $0\leq a<2m$, $1<p<\frac{n+2m-2a}{n-2m}$ if $0\leq a<2$, and $1<p<\infty$ if $2\leq a<2m$. We prove Liouville theorems for nonnegative classical solutions to the above Lane-Emden-Hardy equations (Theorem \ref{Thm0}), that is, the unique nonnegative solution is $u\equiv0$. As an application, we derive a priori estimates and existence of positive solutions to non-critical higher order Lane-Emden equations in bounded domains (Theorem \ref{Thm1} and \ref{Thm2}). The results for critical order Hardy-H\'{e}non equations have been established by Chen, Dai and Qin \cite{CDQ} recently.Comment: arXiv admin note: substantial text overlap with arXiv:1808.06609; text overlap with arXiv:1808.0158

Bandwidth-Aware Scheduling with SDN in Hadoop: A New Trend for Big Data

Software Defined Networking (SDN) is a revolutionary network architecture that separates out network control functions from the underlying equipment and is an increasingly trend to help enterprises build more manageable data centers where big data processing emerges as an important part of applications. To concurrently process large-scale data, MapReduce with an open source implementation named Hadoop is proposed. In practical Hadoop systems one kind of issue that vitally impacts the overall performance is know as the NP-complete minimum make span problem. One main solution is to assign tasks on data local nodes to avoid link occupation since network bandwidth is a scarce resource. Many methodologies for enhancing data locality are proposed such as the HDS and state-of-the-art scheduler BAR. However, all of them either ignore allocating tasks in a global view or disregard available bandwidth as the basis for scheduling. In this paper we propose a heuristic bandwidth-aware task scheduler BASS to combine Hadoop with SDN. It is not only able to guarantee data locality in a global view but also can efficiently assign tasks in an optimized way. Both examples and experiments demonstrate that BASS has the best performance in terms of job completion time. To our knowledge, BASS is the first to exploit talent of SDN for big data processing and we believe it points out a new trend for large-scale data processing

The Revenue and Cost of the Airline Company

The airline industry is characterized by a number of business models with the most prominent being the Full Service Network Carriers (FSNC) and Low Cost Carriers (LCC) models. The main difference between full service network carriers and low cost carriers is how the airline companies operation their revenue and cost.The advanced developments in telecommunications, air pollutions and the competition of high rail are three new challenges for the airline industry globally while an increasing passengers and the government policies are two big issues for Asia/Pacific regional airline companies. The fuel price and human-related costs are two big issues affecting the company’s cost. Code-sharing and advertising are two possibly ways in increasing company’s revenue, cutting down the fuel cost, advertising costs, controlling the human cost and cooperating with airports are four possibly ways in reducing company’s cost

Observation of quasiperiodic dynamics in a one-dimensional quantum walk of single photons in space

We realize quasi-periodic dynamics of a quantum walker over 2.5 quasi-periods by realizing the walker as a single photon passing through a quantum-walk optical-interferometer network. We introduce fully controllable polarization-independent phase shifters in each optical path to realize arbitrary site-dependent phase shifts, and we employ large clear-aperture beam displacers, while maintaining high-visibility interference, to enable reaching 10 quantum-walk steps. By varying the half-wave-plate setting, we control the quantum-coin bias thereby observing a transition from quasi-periodic dynamics to ballistic diffusion.Comment: 5 pages, 4 figure

Single Bitmap Block Truncation Coding of Color Images Using Hill Climbing Algorithm

Recently, the use of digital images in various fields is increasing rapidly. To increase the number of images stored and get faster transmission of them, it is necessary to reduce the size of these images. Single bitmap block truncation coding (SBBTC) schemes are compression techniques, which are used to generate a common bitmap to quantize the R, G and B planes in color image. As one of the traditional SBBTC schemes, weighted plane (W-plane) method is famous for its simplicity and low time consumption. However, the W-plane method also has poor performance in visual quality. This paper proposes an improved SBBTC scheme based on W-plane method using parallel computing and hill climbing algorithm. Compared with various schemes, the simulation results of the proposed scheme are better than that of the reference schemes in visual quality and time consumption

Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection

We propose a long-distance continuous-variable quantum key distribution (CVQKD) with four-state protocol using non-Gaussian state-discrimination detection. A photon subtraction operation, which is deployed at the transmitter, is used for splitting the signal required for generating the non-Gaussian operation to lengthen the maximum transmission distance of CVQKD. Whereby an improved state-discrimination detector, which can be deemed as an optimized quantum measurement that allows the discrimination of nonorthogonal coherent states beating the standard quantum limit, is applied at the receiver to codetermine the measurement result with conventional coherent detector. By tactfully exploiting multiplexing technique, the resulting signals can be simultaneously transmitted through an untrusted quantum channel, and subsequently sent to the state-discrimination detector and coherent detector respectively. Security analysis shows that the proposed scheme can lengthen the maximum transmission distance up to hundreds of kilometers. Furthermore, by taking finite-size effect and composable security into account we obtain the tightest bound of the secure distance, which is more practical than that obtained in the asymptotic limit.Comment: 13 pages, 9 figure

A Survey on Network Tomography with Network Coding

The overhead of internal network monitoring motivates techniques of network tomography. Network coding (NC) presents a new opportunity for network tomography as NC introduces topology-dependent correlation that can be further exploited in topology estimation. Compared with traditional methods, network tomography with NC has many advantages such as the improvement of tomography accuracy and the reduction of complexity in choosing monitoring paths. In this paper we first introduce the problem of tomography with NC and then propose the taxonomy criteria to classify various methods. We also present existing solutions and future trend. We expect that our comprehensive review on network tomography with NC can serve as a good reference for researchers and practitioners working in the area

Linear optical demonstration of quantum speed-up with a single qudit

Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding quantum physics, the origin of the power of quantum algorithm is still an open question. Non-classical correlation is regarded as the most possible answer for the open question. However we experimentally realize a quantum speed-up algorithm on four-level system with linear optical elements and prove that even a single qudit is enough for designing an oracle-based algorithm which can solve a model problem twice faster than any classical algorithm. The algorithm can be generalized to higher dimensional qudits with the same two-to-one speed-up ratio.Comment: 5 pages, 3 figure

DCE: A Novel Delay Correlation Measurement for Tomography with Passive Realization

Tomography is important for network design and routing optimization. Prior approaches require either precise time synchronization or complex cooperation. Furthermore, active tomography consumes explicit probeing resulting in limited scalability. To address the first issue we propose a novel Delay Correlation Estimation methodology named DCE with no need of synchronization and special cooperation. For the second issue we develop a passive realization mechanism merely using regular data flow without explicit bandwidth consumption. Extensive simulations in OMNeT++ are made to evaluate its accuracy where we show that DCE measured delay correlation is highly identical with the true value. Also from test result we find that mechanism of passive realization is able to achieve both regular data transmission and purpose of tomography with excellent robustness versus different background traffic and package size.Comment: 5 page