A DISCRETE TIME TWO-LEVEL MIXED SERVICE PARALLEL POLLING MODEL

We present a discrete time single-server two-level mixed service polling systems with two queue types, one center queue and N normal queues. Two-level means the center queue will be successive served after each normal queue. In the first level, server visits between the center queue and the normal queue. In the second level, normal queues are polled by a cyclic order. Mixed service means the service discipline are exhaustive for center queue, and parallel 1-limited for normal queues. We propose an imbedded Markov chain framework to drive the closed-form expressions for the mean cycle time, mean queue length, and mean waiting time. Numerical examples demonstrate that theoretical and simulation results are identical the new system efficiently differentiates priorities.

Two-level percutaneous endoscopic lumbar discectomy for highly migrated upper lumbar disc herniation: A case report

BACKGROUND The technique of percutaneous endoscopic lumbar discectomy(PELD)as a transforaminal approach has been used to treat highly migrated lower lumbar disc herniations.However,due to the different anatomic characteristics of the upper lumbar spine,conventional transforaminal PELD may fail to remove the highly migrated upper lumbar disc nucleus pulposus.Therefore,the purpose of this study was to describe a novel surgical technique,two-level PELD,for the treatment of highly migrated upper lumbar disc herniations and to report its related clinical outcomes.CASE SUMMARY A 60-year-old male presented with a complaint of pain at his lower back and right lower limb.The patient received 3 mo of conservative treatments but the symptoms were not alleviated.Physical examination revealed a positive femoral nerve stretch test and a negative straight leg raise test for the right leg,and preoperative visual analog scale(VAS)score for the lower back was 6 points and for the right leg was 8 points.Magnetic resonance imaging(MRI)demonstrated L2-L3 disc herniation on the right side and the herniated nucleus pulposus migrated to the upper margin of L2 vertebral body.According to physical examination and imaging findings,surgery was the primary consideration.Therefore,the patient underwent surgical treatment with two-level PELD.The pain symptom was relieved and the VAS score for back and thigh pain was one point postoperatively.The patient was asymptomatic and follow-up MRI scan 1 year after operation revealed no residual nucleus pulposus.CONCLUSION Two-level PELD as a transforaminal approach can be a safe and effective procedure for highly migrated upper lumbar disc herniation.

TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM

In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.

Single photon transport properties in coupled cavity arrays nonlocally coupled to a two-level atom in the presence of dissipation

We discuss the effects of dissipation on the behavior of single photon transport in a system of coupled cavity arrays, with the two nearest cavities nonlocally coupled to a two-level atom. The single photon transmission amplitude is solved exactly by employing the quasi-boson picture. We investigate two different situations of local and nonlocal couplings, respectively. Comparing the dissipative case with the nondissipative one reveals that the dissipation of the system increases the middle dip and lowers the peak of the single photon transmission amplitudes, broadening the line width of the transport spectrum. It should be noted that the influence of the cavity dissipation to the single photon transport spectrum is asymmet- ric. By comparing the nonlocal coupling with the local one, one can find that the enhancement of the middle dip of single photon transmission amplitudes is mostly caused by the atom dissipation and that the reduced peak is mainly caused by the cavity dissipation, no matter whether it is a nonlocal or local coupling case. Whereas in the nonlocal coupling case, when the coupling strength gets stronger, the cavity dissipation has a greater effect on the single photon transport spectrum and the atom dissipation affection becomes weak, so it can be ignored.

Optimal entropy squeezing sudden generation and its control for an effective two-level moving atom entanglement with the two-mode coherent fields

From the viewpoint of quantum information, this paper proposes a concept and a definition of the atomic optimal entropy squeezing sudden generation （AOESSG） for the system of an effective two-level moving atom which entangles with the two-mode coherent fields. It also researches the relationship between the AOESSG and entanglement sudden death of the atom-fields, and discusses the influences of atomic initial state on the AOESSG and obtains the system parameter which controls the AOESSG.

Bio-Inspired Binary Bees Algorithm for a Two-Level Distribution Optimisation Problem

Two uncoupleable distributions, assigning missions to robots and allocating robots to home stations, accompany the use ofmobile service robots in hospitals.In the given problem, two workload-related objectives and five groups of constraints areproposed.A bio-mimicked Binary Bees Algorithm (BBA) is introduced to solve this multiobjective multiconstraint combinatorialoptimisation problem, in which constraint handling technique (Multiobjective Transformation, MOT), multiobjectiveevaluation method (nondominance selection), global search strategy (stochastic search in the variable space), local searchstrategy (Hamming neighbourhood exploitation), and post-processing means (feasibility selection) are the main issues.TheBBA is then demonstrated with a case study, presenting the execution process of the algorithm, and also explaining the change ofelite number in evolutionary process.Its optimisation result provides a group of feasible nondominated two-level distributionschemes.

Weak-Coupling Theory for Semiclassical Periodically Driven Two-Level Systems： Beyond Rotating-Wave Approximation

We present a weak-coupling theory of semiclassical periodically driven two-level systems. The explicit analytical approximating solution is shown to reproduce highly accurately the exact results well beyond the regime of the rotating-wave approximation.

Vacuum induced transparency and slow light phenomena in a two-level atomic ensemble controlled by a cavity

We study the optical properties of a two-level atomic ensemble controlled by a high-finesse cavity. Even though the cavity is initially in the vacuum state in the absence of external driving, the probe response of the atomic ensemble can be dramatically modified. When the collectively enhanced atom–cavity coupling is strong enough and the cavity decay rate is much smaller than the atomic damping rate, an electromagnetically induced transparency-like coherent phenomenon emerges with a dip absorption for the response of the two-level atoms in the cavity without driving, and thus is called vacuum induced transparency. We also show the slow light with very low group velocity in such an atomic ensemble.

Study of Chinese Economic "Growth Drag" Caused by Land Resource in the Perspective of the Modified Two-Level CES Production Function

The purpose of the study is to measure the "growth drag" according to the characteristic of Chinese land resource.Romer model (2001) holds that every country is inevitably affected by the "growth drag" due to the limitation of land resource.So it's of profound strategic significance to measure the "growth drag" according to the character of Chinese land resource.Modified two-level CES production function was employed,and this paper modified the hypothesis of the model.The result indicates that the limitation of Chinese land resource casts shadow over the economic development of China,and the growth rate is 0.4618% lower than that without the limitation of land resource.Through implementing the land resource protection policy along with the technology improvement and the substitute effect of other factors to the land resource,China will keep a steady and balanced economic growth.

THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM

In this paper,we first propose a new stabilized finite element method for the Stokes eigenvalue problem.This new method is based on multiscale enrichment,and is derived from the Stokes eigenvalue problem itself.The convergence of this new stabilized method is proved and the optimal priori error estimates for the eigenfunctions and eigenvalues are also obtained.Moreover,we combine this new stabilized finite element method with the two-level method to give a new two-level stabilized finite element method for the Stokes eigenvalue problem.Furthermore,we have proved a priori error estimates for this new two-level stabilized method.Finally,numerical examples confirm our theoretical analysis and validate the high effectiveness of the new methods.

Two-level stabilized finite element method for Stokes eigenvalue problem

A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O（H2）, which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.

A Novel Two-Level Optimization Strategy for Multi-Debris Active Removal Mission in LEO

Recent studies of the space debris environment in Low Earth Orbit(LEO)have shown that the critical density of space debris has been reached in certain regions.The Active Debris Removal(ADR)mission,to mitigate the space debris density and stabilize the space debris environment,has been considered as a most effective method.In this paper,a novel two-level optimization strategy for multi-debris removal mission in LEO is proposed,which includes the low-level and high-level optimization process.To improve the overall performance of the multi-debris active removal mission and obtain multiple Pareto-optimal solutions,the ADR mission is seen as a Time-Dependant Traveling Salesman Problem(TDTSP)with two objective functions to minimize the total mission duration and the total propellant consumption.The problem includes the sequence optimization to determine the sequence of removal of space debris and the transferring optimization to define the orbital maneuvers.Two optimization models for the two-level optimization strategy are built in solving the multi-debris removal mission,and the optimal Pareto solution is successfully obtained by using the non-dominated sorting genetic algorithm II(NSGA-II).Two test cases are presented,which show that the low level optimization strategy can successfully obtain the optimal sequences and the initial solution of the ADR mission and the high level optimization strategy can efficiently and robustly find the feasible optimal solution for long duration perturbed rendezvous problem.

Optimized two-level placement of test points for multi-objective air monitoring of the Three Gorges Reservoir area

To fit the complicated geographic conditions of the Three Gorges Reservoir area, a two-level multi-objective monitoring system was developed to monitor the atmosphere of the area. Statistical analysis of environmental monitoring data and the macro control principle were employed to configure the upper layer. The lower layer was designed by the application of the thumb rule to a local terrain and specific point sources of pollution therein. The optimized two-level system comprises an upper layer of 16 monitoring stations distributed at places of diverse geographical, ecological, economical and social characteristics, and a lower layer of ]6 sub-machines at each monitoring station of the upper layer. This optimal outcome fits the complicated conditions of the Three Gorges Reservoir area, substantially cuts down the installation cost and the operation cost, and provides accurate monitoring data of atmosphere over the entire area with a high resolution.

TWO-LEVEL METHOD FOR UNSTEADY NAVIER-STOKES EQUATIONS IN STREAM FUNCTION FORM

Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.

Two-level reconstruction of isolated fracture of the lesser tuberosity of the humerus

Fractures of the lesser tuberosity of the humerus are typically met in combination with other injuries of the shoulder. Case reports of isolated lesser tuberosity fractures are particularly rare and, consequently,therapeutic protocols have not yet been completely clarified. Conservative as well as surgical treatment has been recommended, while several operative techniques have been applied. We present a case of a 39-yearold man with an isolated lesser tuberosity fracture who was treated surgically in our institution. Due to fracture comminution, a two-level reconstruction technique with headless screws and buttress plate was applied. As far as we know, this method of fixation of this type of fracture has not been previously described in the literature.The patient tolerated the procedure well and excellent results were obtained at the latest follow-up.

A parallel two-level finite element method for the Navier-Stokes equations

Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.

Effects of an applied low frequency field on the dynamics of a two-level atom interacting with a single-mode field

The effects of an applied low frequency field on the dynamics of a two-level atom interacting with a single-mode field are investigated. It is shown that the time evolution of the atomic population is mainly controlled by the coupling constants and the frequency of the low frequency field, which leads to a low frequency modulation function for the time evolution of the upper state population. The amplitude of the modulation function becomes larger as the coupling constants increase. The frequency of the modulation function is proportional to the frequency of the low frequency field, and decreases with increasing coupling constant.

The breaking point between fast-and slow-light in a degenerate two-level atomic system

This paper investigates the breaking point between fast- and slow-light in a degenerate two-level atomic system, where fast-light can be converted to slow-light arbitrarily on a single transition line by adjusting the strength of the pumping field. An equivalent incoherent pumping rate is introduced in this simplified theoretical model which exploits the dependence of this feature. The experimental observation is presented as evidence of the breaking point where the injected power is about 0.08 mW.

A NEW CLASS OF LINEAR CODES WITH TWO-LEVEL STRUCTURE

The binary extended Golay code has a two-level structure, which can be used in the decoding of the code. However, such structure is not limited to the Golay code, in fact, several binary linear codes can be constructed by a projective method which is related to the structure. In this correspondence, the binary (4n,n + 2k, ≥min(8, n,2d)) linear codes are resulted from quaternary (n,k,d) linear block codes. Based on the structure, the efficient maximum likelihood decoding algorithms can be presented correspondingly for the derived codes.

Design and Implementation of Two-Level Metadata Server in Small-Scale Cluster File System

The reliability and high performance of metadata service is crucial to the store architecture. A novel design of a two-level metadata server file system （TTMFS） is presented, which behaves high reliability and performance. The merits both centralized management and distributed management are considered simultaneously in our design. In this file system, the advanced-metadata server is responsible for manage directory metadata and the whole namespace. The double-metadata server is responsible for maintaining file metadata. And this paper uses the Markov return model to analyze the reliability of the two-level metadata server. The experiment data indicates that the design can provide high throughput.