How many servers are best in a dual-priority system?

We ask the question, “for minimizing mean response time (sojourn time), which is preferable: one fast server of speed 1, or k slow servers each of speed 1/k?” Our setting is the system with two priority classes of customers, high priority and low priority, where PH is a phase-type distribution. We find that multiple slow servers are often preferable, and we demonstrate exactly how many servers are preferable as a function of the load and service time distribution. In addition, we find that the optimal number of servers with respect to the high priority jobs may be very different from that preferred by low priority jobs, and we characterize these preferences. We also study the optimal number of servers with respect to overall mean response time, averaged over high and low priority jobs. Lastly, we ascertain the effect of the service demand variability of high priority jobs on low priority jobs.     

Continuity and random dynamics of the non-autonomous stochastic FitzHugh–Nagumo system on RN

In this article, we use the so-called difference estimate method to investigate the continuity and random dynamics of the non-autonomous stochastic FitzHugh–Nagumo system with a general nonlinearity. Firstly, under weak assumptions on the noise coefficient, we prove the existence of a pullback attractor in $L^2\left({\mathbb{R}}^N\right)\times L^2\left({\mathbb{R}}^N\right)$ by using the tail estimate method and a certain compact embedding on bounded domains. Secondly, although the difference of the first component of solutions possesses at most $p$-times integrability where $p$ is the growth exponent of the nonlinearity, we overcome the absence of higher-order integrability and establish the continuity of solutions in $(L^p\left({\mathbb{R}}^N\right)\cap H^1\left({\mathbb{R}}^N\right))\times L^2\left({\mathbb{R}}^N\right)$ with respect to the initial values belonging to $L^2\left({\mathbb{R}}^N\right)\times L^2\left({\mathbb{R}}^N\right)$. As an application of the result on the continuity, the existence of a pullback attractor in $(L^p\left({\mathbb{R}}^N\right)\cap H^1\left({\mathbb{R}}^N\right))\times L^2\left({\mathbb{R}}^N\right)$ is proved for arbitrary $N\ge 1$ and $p>2$.     

A sensitivity study of the Navier–Stokes-α model

We present a sensitivity study of the Navier Stokes-$\alpha$ model with respect to perturbations of the differential filter length $\alpha$. The parameter-sensitivity is evaluated using the sensitivity equations method. Once formulated, the sensitivity equations are discretized and computed alongside the NS$\alpha$ model using the same finite elements in space, and Crank–Nicolson in time. We provide a complete stability analysis of the scheme, along with the results of several benchmark problems in both 2D and 3D. We further demonstrate a practical technique to utilize sensitivity calculations to determine the reliability of the NS$\alpha$ model in problem-specific settings. Lastly, we investigate the sensitivity and reliability of important functionals of the velocity and pressure solutions.     

Rational and semi-rational solutions of the y-nonlocal Davey–Stewartson I equation

The nonlocal Davey–Stewartson (DS) I equation with a parity-time-symmetric potential with respect to the $y$-direction, which is called the $y$-nonlocal DS I equation, is a two-dimensional analogue of the nonlocal nonlinear Schrödinger (NLS) equation. The multi-breather solutions for the $y$-nonlocal DS I equation are derived by using the Hirota bilinear method. Lump-type solutions and hybrid solutions consisting of lumps sitting on periodic line waves are generated by long wave limits of the obtained soliton solutions. Also, various types of analytical solutions for the nonlocal NLS equation with negative nonlinearity, including both the Akhmediev breathers and the Peregrine rogue waves sitting on periodic line waves, can be generated with appropriate constraints on the parameters of the obtained exact solutions of the $y$-nonlocal DS I equation. Particularly, we show that a family of hybrid solitons describing the Peregrine rogue wave that coexists with the Akhmediev breather, both of them sitting on a spatially-periodic background can be thus obtained.     

21世纪什么最重要?数据!简

对于大多数企业而言,大数据最显而易见的价值,在于客户洞察和用户定位,企业们将前所未有的了解自己的用户,并制定出清晰的、收益可预期的商业策略;当然,大数据的价值并不仅仅限于此,凭借大数据策略,企业们能够更好的优化供应链,更好的制定产品策略、价格策略,更好的评估运营风险,乃至评估客户风险等。先行意味着更大的机遇,同时也面临着更多的挑战。     

影讯简

杰瑞·尤斯曼与玛姬·泰勒夫妇的作品里，任何一个单位元素，云朵、湖水、树木、蜜蜂、斑马……都是我们再熟悉不过的，这些都是构成真实世界的真实元素。但是两位摄影师打乱了物体原本的规律，在视觉上运用真实的元素把我们带入了另外一个内心的“真实”世界。