OPTIMAL BIRKHOFF INTERPOLATION AND BIRKHOFF NUMBERS IN SOME FUNCTION SPACES

This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.

An Adaptive Parameter-Free Optimal Number of Market Segments Estimation Algorithm Based on a New Internal Validity Index

An appropriate optimal number of market segments(ONS)estimation is essential for an enterprise to achieve successful market segmentation,but at present,there is a serious lack of attention to this issue in market segmentation.In our study,an independent adaptive ONS estimation method BWCON-NSDK-means++is proposed by integrating a newinternal validity index(IVI)Between-Within-Connectivity(BWCON)and a newstable clustering algorithmNatural-SDK-means++(NSDK-means++)in a novel way.First,to complete the evaluation dimensions of the existing IVIs,we designed a connectivity formula based on the neighbor relationship and proposed the BWCON by integrating the connectivity with other two commonly considered measures of compactness and separation.Then,considering the stability,number of parameters and clustering performance,we proposed the NSDK-means++to participate in the integrationwhere the natural neighbor was used to optimize the initial cluster centers(ICCs)determination strategy in the SDK-means++.At last,to ensure the objectivity of the estimatedONS,we designed a BWCON-based ONS estimation framework that does not require the user to set any parameters in advance and integrated the NSDK-means++into this framework forming a practical ONS estimation tool BWCON-NSDK-means++.The final experimental results showthat the proposed BWCONand NSDK-means++are significantlymore suitable than their respective existing models to participate in the integration for determining theONS,and the proposed BWCON-NSDK-means++is demonstrably superior to the BWCON-KMA,BWCONMBK,BWCON-KM++,BWCON-RKM++,BWCON-SDKM++,BWCON-Single linkage,BWCON-Complete linkage,BWCON-Average linkage and BWCON-Ward linkage in terms of the ONS estimation.Moreover,as an independentmarket segmentation tool,the BWCON-NSDK-means++also outperforms the existing models with respect to the inter-market differentiation and sub-market size.

Designing optimal number of receiving traces based on simulation model

Currently, the selection of receiving traces in geometry design is mostly based on the horizontal layered medium hypothesis, which is unable to meet survey requirements in a complex area. This paper estimates the optimal number of receiving traces in field geometry using a numerical simulation based on a field test conducted in previous research （Zhu et al., 2011）. A mathematical model is established for total energy and average efficiency energy using fixed trace spacing and optimal receiving traces are estimated. Seismic data acquired in a complex work area are used to verify the correctness of the proposed method. Results of model data calculations and actual data processing show that results are in agreement. This indicates that the proposed method is reasonable, correct, sufficiently scientific, and can be regarded as a novel method for use in seismic geometry design in complex geological regions.

Optimal Treatment Strategy for Infectious Diseases with Two Treatment Stages

In this paper, a disease transmission model with two treatment stages is proposed and analyzed. The results indicate that the basic reproduction number is a critical threshold for the prevalence of the disease. If the basic reproduction number is less than one, the disease free equilibrium is globally asymptotically stable. Otherwise, the endemic equilibrium is globally asymptotically stable. Therefore, besides the basic reproduction number, a new marker for characterizing the seriousness of the disease, named as dynamical final infective size, is proposed, which differs from traditional final size because the proposed model includes the natural birth and death. Finally, optimization strategies for limited medical resources are obtained from the perspectives of basic reproduction number and dynamical final infective size, and the real-world disease management scenarios are given based on these finding.

Effect of Sweptback Angle of a Delta Wing on Surface Pressure Distribution at Supersonic Mach Numbers

The purpose of this work is to shed light on the effect of the pivot position on the surface pressure distribution over a 3D wing in different flight conditions.The study is intended to support the design and development of aerospace vehicles where stability analysis,performance optimization,and aircraft design are of primary importance.The following parameters are considered:Mach numbers(M)of 1.3,1.8,2.3,2.8,3.3,and 3.8,angle of incidence(θ)in the range from 5°to 25°,pivot position from h=0.2 to 1.The results of the CFD numerical simulations match available analytical data,thereby providing evidence for the reliability of the used approach.The findings provide valuable insights into the relationship between the surface pressure distribution,the Mach number and the angle of incidence.

Optimized air-ground data fusion method for mine slope modeling

Refined 3D modeling of mine slopes is pivotal for precise prediction of geological hazards.Aiming at the inadequacy of existing single modeling methods in comprehensively representing the overall and localized characteristics of mining slopes,this study introduces a new method that fuses model data from Unmanned aerial vehicles(UAV)tilt photogrammetry and 3D laser scanning through a data alignment algorithm based on control points.First,the mini batch K-Medoids algorithm is utilized to cluster the point cloud data from ground 3D laser scanning.Then,the elbow rule is applied to determine the optimal cluster number(K0),and the feature points are extracted.Next,the nearest neighbor point algorithm is employed to match the feature points obtained from UAV tilt photogrammetry,and the internal point coordinates are adjusted through the distanceweighted average to construct a 3D model.Finally,by integrating an engineering case study,the K0 value is determined to be 8,with a matching accuracy between the two model datasets ranging from 0.0669 to 1.0373 mm.Therefore,compared with the modeling method utilizing K-medoids clustering algorithm,the new modeling method significantly enhances the computational efficiency,the accuracy of selecting the optimal number of feature points in 3D laser scanning,and the precision of the 3D model derived from UAV tilt photogrammetry.This method provides a research foundation for constructing mine slope model.

Optimal Number of Relays in Cooperative Communication in Wireless Sensor Networks

Wireless Sensor Networks (WSN) typically consist of resource constrained micro sensors that organize itself into multihop wireless network. Sensors collect data and send it directly, or through intermediate hops in cooperative communication system, to the collection point. These sensors are powered up by batteries, for which the replacement or recharging is very difficult. With finite energy, we can transmit a finite amount of information. Therefore, minimizing the power consumption for data transmission becomes a most important design consideration for wireless sensor networks. In this paper, we discuss the optimal power consumption in cooperative wireless sensor network that are placed on a grid. We study different cases for the optimal power consumption in such grids by varying the grid distance and number of nodes in the grid. We assume the cases of grids from 2 × 2 up to 5 × 5 in increasing complexity of calculations. The results show that the optimal path that consumes the least power is the path along the diagonal using of the grid when the source and the destination and the furthest two nodes in the grid. This path takes intermediate nodes (relays) along it based on some threshold distances. For example, in 5 × 5 cases;the first threshold between the direct distance and between using one relay in the middle is 31.6 m the second threshold distance is 63.3 m after which using three relays is the best in power consumption between the source and the destination.

Z-numbers的否定及其在多属性决策中的应用

否定命题是数理逻辑中的重要表示方式,也是智能信息处理中刻画信息的关键工具.Znumber是一种新的不确定性语言信息表示方式.回顾了否定的相关研究,并介绍了可能性分布的否定在Z-number理论中的应用.通过最大香农熵和粒子群算法,提出了一种优化模型,用于发现Z-number中隐藏的可能性分布.研究表明,Z-number的否定为语言决策分析和解决复杂问题提供了有效工具.

Application of Evolution Sequential Number Theoretic Optimization in Global Optimization

Synthesis of chemical processes is of non-convex and multi-modal. Deterministic strategies often fail to find global optimum within reasonable time scales. Stochastic methodologies generally approach global solution in probability. In recogniting the state of art status in the discipline, a new approach for global optimization of processes, based on sequential number theoretic optimization (SNTO), is proposed. In this approach, subspaces and feasible points are derived from uniformly scattered points, and iterations over passing the corner of local optimum are enhanced via parallel strategy. The efficiency of the approach proposed is verified by results obtained from various case studies.

On optimal binary signed digit representations of integers

Binary signed digit representation （BSD-R） of an integer is widely used in computer arithmetic, cryptography and digital signal processing. This paper studies what the exact number of optimal BSD-R of an integer is and how to generate them entirely. We also show which kinds of integers have the maximum number of optimal BSD-Rs.

Modelling the Optimal Control of Transmission Dynamics of <i>Mycobacterium ulceran</i>Infection

This paper examines optimal control of transmission dynamics of Mycobacterium ulceran (MU) infection. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations, optimal control and computer simulation. The basic reproduction number of the reduced model system is obtained by using the next generation operator method. It is found that by using Ruth Hurwitz criteria, the disease free equilibrium point is locally asymptotically stable and using centre manifold theory, the model shows the transcritical (forward) bifurcation. Optimal control is applied to the model seeking to minimize the transmission dynamics of MU infection on human and water-bugs. Pontryagin’s maximum principle is used to characterize the optimal levels of the controls. The results of optimality are solved numerically using MATLAB software and the results show that optimal combination of two controls (environmental and health education for prevention) and (water and environmental purification) minimizes the MU infection in the population.

Analysis of Listeriosis Transmission Dynamics with Optimal Control

Listeriosis is an illness caused by the germ Listeria monocytogenes. Generally, humans are infected with listeriosis after eating contaminated food. Listeriosis mostly affects people with weakened immune systems, pregnant women and newborns. In this paper, a model describing the dynamics of Listeriosis is developed and analysed using ordinary differential equations. The model was analysed both quantitatively and qualitatively for its local and global stability, basic reproductive number and parameter contributions to the basic reproductive number to understand the impact of each parameter on the disease spread. The Listeriosis model has been extended to include time dependent control variables such as treatment of both humans and animals, vaccination and education of humans. Pontryagin’s Maximum Principle was introduced to obtain the best optimal control strategies required for curbing Listeriosis infections. Numerical simulation was performed and the results displayed graphically and discussed. Cost effectiveness analysis was conducted using the intervention averted ratio (IAR) concepts and it was revealed that the most effective intervention strategy is the treatment of infected humans and animals.

Stability and Optimal Control of Tuberculosis Spread with an Imperfect Vaccine in the Case of Co-Infection with HIV

This paper focuses on the study and control of a non-linear mathematical epidemic model ( SSvihVELI ) based on a system of ordinary differential equation modeling the spread of tuberculosis infectious with HIV/AIDS coinfection. Existence of both disease free equilibrium and endemic equilibrium is discussed. Reproduction number R0 is determined. Using Lyapunov-Lasalle methods, we analyze the stability of epidemic system around the equilibriums (disease free and endemic equilibrium). The global asymptotic stability of the disease free equilibrium whenever Rvac is proved, where R0 is the reproduction number. We prove also that when R0 is less than one, tuberculosis can be eradicated. Numerical simulations are conducted to approve analytic results. To achieve control of the disease, seeking to reduce the infectious group by the minimum vaccine coverage, a control problem is formulated. The Pontryagin’s maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the Runge Kutta fourth procedure.

A NEW TECHNIQUE FOR COMPAIRING FUZZY NUMBERS USING AN INDEX OF OPTIMISM

Fuzzy numbers are convenient for representing imprecise numerical quantities in a vague environment, and their comparison or ranking is very important for application purposes. Despite many methods suggested in the literature, there is no single measure that is universally applicable to a wide variety of situations. This paper suggested a new method for comparing fuzzy numbers based on the combination of maximizing possibility and minimizing possibility using an index of optimism in [0,1] reflecting the decision makers’ risk taking attitude. The method is simple, but has many comparative advantages.

Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting

In this paper, we study optimal recovery （reconstruction） of functions on the sphere in the average case setting. We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞.

Multimodal Fuzzy Downstream Petroleum Supply Chain:A Novel Pentagonal Fuzzy Optimization

The petroleum industry has a complex,inflexible and challenging supply chain(SC)that impacts both the national economy as well as people’s daily lives with a range of services,including transportation,heating,electricity,lubricants,as well as chemicals and petrochemicals.In the petroleum industry,supply chain management presents several challenges,especially in the logistics sector,that are not found in other industries.In addition,logistical challenges contribute significantly to the cost of oil.Uncertainty regarding customer demand and supply significantly affects SC networks.Hence,SC flexibility can be maintained by addressing uncertainty.On the other hand,in the real world,decision-making challenges are often ambiguous or vague.In some cases,measurements are incorrect owing to measurement errors,instrument faults,etc.,which lead to a pentagonal fuzzy number(PFN)which is the extension of a fuzzy number.Therefore,it is necessary to develop quantitative models to optimize logistics operations and supply chain networks.This study proposed a linear programming model under an uncertain environment.The model minimizes the cost along the refineries,depots,multimode transport and demand nodes.Further developed pentagonal fuzzy optimization,an alternative approach is developed to solve the downstream supply chain using themixed-integer linear programming(MILP)model to obtain a feasible solution to the fuzzy transportation cost problem.In this model,the coefficient of the transportation costs and parameters is assumed to be a pentagonal fuzzy number.Furthermore,defuzzification is performed using an accuracy function.To validate the model and technique and feasibility solution,an illustrative example of the oil and gas SC is considered,providing improved results compared with existing techniques and demonstrating its ability to benefit petroleum companies is the objective of this study.

Ant Colony Optimization Approach Based Genetic Algorithms for Multiobjective Optimal Power Flow Problem under Fuzziness

In this paper, a new optimization system based genetic algorithm is presented. Our approach integrates the merits of both ant colony optimization and genetic algorithm and it has two characteristic features. Firstly, since there is instabilities in the global market, implications of global financial crisis and the rapid fluctuations of prices, a fuzzy representation of the optimal power flow problem has been defined, where the input data involve many parameters whose possible values may be assigned by the expert. Secondly, by enhancing ant colony optimization through genetic algorithm, a strong robustness and more effectively algorithm was created. Also, stable Pareto set of solutions has been detected, where in a practical sense only Pareto optimal solutions that are stable are of interest since there are always uncertainties associated with efficiency data. The results on the standard IEEE systems demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal nondominated solutions of the multiobjective OPF.

2D Minimum Compliance Topology Optimization Based on a Region Partitioning Strategy

This paper presents an extended sequential element rejection and admission(SERA)topology optimizationmethod with a region partitioning strategy.Based on the partitioning of a design domain into solid regions and weak regions,the proposed optimizationmethod sequentially implements finite element analysis(FEA)in these regions.After standard FEA in the solid regions,the boundary displacement of the weak regions is constrained using the numerical solution of the solid regions as Dirichlet boundary conditions.This treatment can alleviate the negative effect of the material interpolation model of the topology optimization method in the weak regions,such as the condition number of the structural global stiffness matrix.For optimization,in which the forward problem requires nonlinear structural analysis,a linear solver can be applied in weak regions to avoid numerical singularities caused by the over-deformedmesh.To enhance the robustness of the proposedmethod,the nonmanifold point and island are identified and handled separately.The performance of the proposed method is verified by three 2D minimum compliance examples.

Global Transmission Dynamics of a Schistosomiasis Model and Its Optimal Control

Drug treatment, snail control, cercariae control, improved sanitation and health education are the effective strategies which are used to control the schistosomiasis. In this paper, we consider a deterministic model for schistosomiasis transmission dynamics in order to explore the role of the several control strategies. The global stability of a schistosomiasis infection model that involves mating structure including male schistosomes, female schistosomes, paired schistosomes and snails is studied by constructing appropriate Lyapunov functions. We derive the basic reproduction number R0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R0. We show that the disease can be eradicated when R0?&le;1;otherwise, the system is persistent. In the case where ?R0?>1, we prove the existence, uniqueness and global asymptotic stability of an endemic steady state. Sensitivity analysis and simulations are carried out in order to determine the relative importance of different control strategies for disease transmission and prevalence. Next, optimal control theory is applied to investigate the control strategies for eliminating schistosomiasis using time dependent controls. The characterization of the optimal control is carried out via the Pontryagins Maximum Principle. The simulation results demonstrate that the insecticide is important in the control of schistosomiasis.

Multi-Objective Optimization of Traffic Signal Timing at Typical Junctions Based on Genetic Algorithms

With the rapid development of urban road traffic and the increasing number of vehicles,how to alleviate traffic congestion is one of the hot issues that need to be urgently addressed in building smart cities.Therefore,in this paper,a nonlinear multi-objective optimization model of urban intersection signal timing based on a Genetic Algorithm was constructed.Specifically,a typical urban intersection was selected as the research object,and drivers’acceleration habits were taken into account.What’s more,the shortest average delay time,the least average number of stops,and the maximum capacity of the intersection were regarded as the optimization objectives.The optimization results show that compared with the Webster method when the vehicle speed is 60 km/h and the acceleration is 2.5 m/s^(2),the signal intersection timing scheme based on the proposed Genetic Algorithm multi-objective optimization reduces the intersection signal cycle time by 14.6%,the average vehicle delay time by 12.9%,the capacity by 16.2%,and the average number of vehicles stop by 0.4%.To verify the simulation results,the authors imported the optimized timing scheme into the constructed Simulation of the Urban Mobility model.The experimental results show that the authors optimized timing scheme is superior to Webster’s in terms of vehicle average loss time reduction,carbon monoxide emission,particulate matter emission,and vehicle fuel consumption.The research in this paper provides a basis for Genetic algorithms in traffic signal control.