Harmonic analysis on discrete Abelian groups

Let be an Abelian group and let denote the linear space of all complex-valued functions defined on equipped with the product topology. We prove that the following are equivalent.

(i) Every nonzero translation invariant closed subspace of contains an exponential; that is, a nonzero multiplicative function.

(ii) The torsion free rank of is less than the continuum.

     

Surviving rate of graphs and Firefighter Problem

The Firefighter Problem on a graph can be viewed as a simplified model of the spread of contagion, fire, rumor, computer virus, etc. The fire breaks out at one or more vertices in a graph at the first round, and the fire-fighter chooses some vertices to protect. The fire spreads to all non-protected neighbors at the beginning of each time-step. The process stops when the fire can no longer spread. The Firefighter Problem has attracted considerable attention since it was introduced in 1995. In this paper we provide a survey on recent research progress of this field, including algorithms and complexity, Fire-fighter Problem for special graphs (finite and infinite) and digraphs, surviving rate and burning number of graphs. We also collect some open problems and possible research subjects.     

Task offloading for vehicular edge computing with imperfect CSI: A deep reinforcement approach

This article examines a multi-user mobile edge computing (MEC) system for the Internet of Vehicle (IoV), where one edge point (EP) nearby the vehicles can help assist in processing the compute-intensive tasks. For the MEC networks, the majority of existing works concentrate on the minimization of system cost of task offloading under the perfect channel estimation, which however fails to consider the practical limitation of imperfect channel estimation (CSI) because of vehicles’ high-mobility. Therefore, the goal of our study is to reduce the delay as well as energy consumption (EC) of computation and communication with imperfect CSI, which are the two significant performance metrics of MEC network. With this aim, we first express the system cost as a form of the linear combination of the delay and EC, and then formulate the optimization problem for the system cost. Moreover, a novel deep approach is proposed, which is integrated by deep reinforcement learning (DRL) with the Lagrange multiplier to jointly minimize the system cost. In particular, the DRL algorithm is employed to obtain the capable offloading strategy, while the Lagrange multiplier is used to obtain the bandwidth allocation. The simulated results are finally presented to show that the devised approach outperforms the traditional ones.     

The ride comfort vs. handling compromise for off-road vehicles

When designing vehicle suspension systems, it is well-known that spring and damper characteristics required for good handling on a vehicle are not the same as those required for good ride comfort. Any choice of spring and damper characteristic is therefore necessarily a compromise between ride comfort and handling. The compromise is more pronounced on off-road vehicles, as they require good ride comfort over rough off-road terrain, as well as acceptable on-road handling. In this paper, the ride comfort vs. handling compromise for off-road vehicles is investigated by means of three case studies. All three case studies indicate that the spring and damper charcteristics required for ride comfort and handling lie on opposite extremes of the design space. Design criteria for a semi-active suspension system, that could significantly reduce, or even eliminate the ride comfort vs. handling compromise, are proposed. The system should be capable of switching safely and predictably between a stiff spring and high damping mode (for handling) as well as a soft spring and low damping mode (for ride comfort). A possible solution to the compromise, in the form of a four state, semi-active hydropneumatic spring-damper system, is proposed.     

Development and validation of off-road tire-gravelly soil interaction using advanced computational techniques

This paper presents a novel modelling technique to compute the interaction between an 8x4 off-road truck and gravelly soil (sand with gravel soil). The off-road truck tire size 315/80R22.5 is modelled using the Finite Element Analysis (FEA) technique and validated using manufacturer-provided data in static and dynamic responses. The gravelly soil is modelled using Smoothed-Particle Hydrodynamics (SPH) technique and calibrated against physical measurements using pressure-sinkage and direct shear-strength tests. The tire-gravelly soil interaction is captured using the node symmetric node to segment with edge treatment algorithm deployed for interaction between FEA and SPH elements. The model setup consists of four tires presenting the four axles of the truck, the first tire is a free-rolling steering tire, the second and third tires are driven tires and the fourth tire is a free-rolling push tire. The truck tires-gravelly soil interaction is computed and validated against physical measurements performed in Göteborg, Sweden. The effect of gravelly soil compaction and truck loading on the tire performance is discussed and investigated.     

基于整车控制参数同步采集的车辆异响识别分析

针对整车控制参数引发的车辆异响问题,介绍了一种基于整车控制参数与NVH数据同步采集的分析方法,通过采用数据协议和格式的双转换,实现了整车/发动机控制参数和整车NVH测试数据的同步采集,并通过控制参数和NVH信号的时域相关性分析,快速准确地定位异响原因。通过底盘冲击异响、涡轮气流异响、整车换挡抖动异响三个案例,介绍了整车控制参数同步采集在工程中的实际应用,快速准确的识别异响原因,并完成优化验证,为异响排查和控制提供了新的方法和思路。 关键词：整车异响;车辆控制参数;数据同步采集;相关性分析     

The relationship between preservice elementary teachers’ solutions to a pattern generalization problem and difficulties they anticipate in teaching it

To explore the relationship between elementary preservice teachers’ (PTs’) solutions to a pattern generalization problem and the difficulties they expected to encounter when teaching the same problem to students, we administered a task-based questionnaire to 154 participants at a large Southwestern university in the US. Employing inductive content analysis, we identified possible links between PTs' solutions and their anticipated difficulties. PTs who solved the problem using figurative reasoning tended to anticipate difficulties related to pedagogical moves to support students’ mathematical understanding. In contrast, PTs who solved the problem using algebraic formulations were likely to anticipate difficulties related to teaching algebraic knowledge and supporting procedural fluency. Also, only PTs who solved the problem using figurative reasoning anticipated difficulties associated with eliciting and evaluating student thinking, whereas PTs who used formulas to solve the problem expected difficulties related to their own self-efficacy and confidence. We discuss three implications for mathematics teacher education.     

Designing a forwarder operation considering tolerable soil disturbance and minimum total cost

A model is developed to minimize the sum of road construction plus forwarding costs with the constraint that rut depth caused by the forwarder cannot exceed a maximum depth during the anticipated season of operation. Road spacing, forwarder trail spacing, forwarder size, forwarder load capacity, and tire inflation pressures are used as decision variables in developing the transportation plan. The total cost was minimized using the optimum road spacing approach. The model identifies whether the cumulative rut depth caused by the forwarder exceeds the maximum allowable rut depth at the point of or prior to the spacing that minimizes the cost, and if so, the rut depth limits the road spacing. If the road spacing at the point of minimum cost is less than the road spacing at the maximum allowable rut depth, road spacing is not constrained by rut depth. This model will help logging managers to evaluate the trade-offs between specified decision variables and then to design an optimum forwarder operation with tolerable soil disturbance and minimum total cost. The solution procedure of the model is described and a computer program is used to apply this model using a numerical example.     

Gossip algorithms for heterogeneous multi-vehicle routing problems

In this paper we address a class of heterogeneous multi-vehicle task assignment and routing problems. We propose two distributed algorithms based on gossip communication: the first algorithm is based on a local exact optimization and the second is based on a local approximate greedy heuristic. We consider the case where a set of heterogeneous tasks arbitrarily distributed in a plane has to be serviced by a set of mobile robots, each with a given movement speed and task execution speed. Our goal is to minimize the maximum execution time of robots.     

Point classification of second order ODEs and its application to Painlevé equations

The first part of this work is a review of the point classification of second order ODEs done by Ruslan Sharipov. His works were published in 1997-1998 in the Electronic Archive at LANL. The second part is an application of this classification to Painlevé equations. In particular, it allows us to solve the equivalence problem for Painlevé equations in an algorithmic form.