A Hybrid Simulated Annealing Heuristic for Multistage Heterogeneous Fleet Scheduling with Fleet Sizing Decisions by Bing Li, Xinyu Yang, Hua Xuan

“…The problem is formulated as mixed integer programming model. The matrix formulation denoting vehicle allocation scheme is explored according to the characteristic of this problem. …”
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Design of task dividing and offloading algorithm in mobile edge computing by Jing LU, Hanlin LI, Lin GAO

“…Mobile edge computing (MEC) emerges as a new paradigm that pushes the computing infrastructure from the remote cloud data center to the edge equipments.It provides a new solution to meet the delay sensitive and computing intensive requirements of Internet of things (IoT).In this work, the problem of tasks offloading and scheduling in the multi-user and multi-server MEC system was considered.Specifically, each user had a task-dependent application and the tasks could be either executed locally or remotely according to the dependence.Thus, the network performance was improved by unloading and scheduling the sub tasks.Quality of experience (QoE) and fairness between users were used to characterize the network performance, and the optimization problem was modeled as a joint dependent task offloading and scheduling (J-DTOS) problem.The J-DTOS problem was a non-linear mixed integer programming, which was NP-hard in general.The original problem was reformulated by introducing intermediate variables and proposing a near-optimal solution.Simulation results show that the proposed offloading and scheduling design can significantly improve the performance of the system.…”
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The number of nonunimodular roots of a reciprocal polynomial by Stankov, Dragan

“…We introduce a sequence $P_{d}$ of monic reciprocal polynomials with integer coefficients having the central coefficients fixed as well as the peripheral coefficients. …”
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The product of r−k and ∇δ on ℝm by C. K. Li

“…In 1990, Li and Fisher introduced a computable delta sequence in an m-dimensional space to obtain a noncommutative neutrix product of r−k and Δδ (Δ denotes the Laplacian) for any positive integer k between 1 and m−1 inclusive. Cheng and Li (1991) utilized a net δϵ(x) (similar to the δn(x)) and the normalization procedure of μ(x)x+λ to deduce a commutative neutrix product of r−k and δ for any positive real number k. …”
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Optimizing Aircraft Operations in Case of Increasing Demand for Limited Airport Capacity by Soner Demirel, Ertan Çınar

“…The mathematical model was formed by employing mixed integer linear programming. The parameters, decision variables, and constraints were defined to cover the problem. …”
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A Bertrand Duopoly Game with Long-Memory Effects by Baogui Xin, Fangrui Cao, Wei Peng, Abdelalim A. Elsadany

“…Reconsidering the Bertrand duopoly game based on the concept of long short-term memory, we construct a fractional-order Bertrand duopoly game by extending the integer-order game to its corresponding fractional-order form. …”
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Diverse Exact Soliton Solutions of the Time Fractional Clannish Random Walker’s Parabolic Equation via Dual Novel Techniques by Imran Siddique, Khush Bukht Mehdi, M. Ali Akbar, Hamiden Abd El-Wahed Khalifa, Asim Zafar

“…These methods can also be used to extract the novel exact traveling wave solutions for solving any types of integer and fractional differential equations arising in mathematical physics.…”
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Node Selection Algorithms with Data Accuracy Guarantee in Service-Oriented Wireless Sensor Networks by Hongju Cheng, Ronglie Guo, Yuzhong Chen

“…Firstly, we have formulated this problem into an integer nonlinear programming problem to illustrate its NP-hard property. …”
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Oscillator with a Sum of Noninteger-Order Nonlinearities by L. Cveticanin, T. Pogány

“…Mathematical model of the system is a second-order differential equation with a nonlinearity of polynomial type, whose terms are of integer and/or noninteger order. For the case when only one nonlinear term exists, the exact analytical solution of the differential equation is determined as a cosine-Ateb function. …”
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Developing a Low-Cost Safety Improvement Program for Intersections in an Urban Roadway Network: A Case Study by Promothes Saha

“…Countermeasures were proposed and analyzed to address those crash types identified in the crash characterization. Linear integer optimization technique was employed to identify the best set of countermeasures within a limited budget. …”
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Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras by Madjid Eshaghi Gordji, Badrkhan Alizadeh, Young Whan Lee, Gwang Hui Kim

“…Let n>1 be an integer, let A be an algebra, and X be an A-module. …”
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Stochastic Portfolio Selection Problem with Reliability Criteria by Xiangsong Meng, Lixing Yang

“…The equivalent linear (mixed integer) programming models are also deduced for different evaluation strategies. …”
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Study on extended reality enhancement technology in 5G-Advanced by XIAO Yang

“…In addition, the power consumption can be reduced by introducing the non-integer discontinuous reception mechanism and the playout buffer. …”
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Mobility aware edge service migration strategy by Dapeng WU, Ji LYU, Zhidu LI, Ruyan WANG

“…To address the problem of load imbalance among edge servers and quality of service degradation caused by dynamic changes of user locations in mobile edge computing networks,a mobility aware edge service migration algorithm was proposed.Firstly,the optimization problem was formulated as a mix integer nonlinear programming problem,with the goal of minimizing the perceived delay of user service request.Then,the delay optimization problem was decoupled into the edge service migration and edge node selection sub-problems based on the Lyapunov optimization approach.Thereafter,the fast edge decision algorithm was proposed to optimize the resource allocation and edge service migration under a given radio access strategy.Finally,the asynchronous optimal response algorithm was proposed to iterate out the optimal radio access strategy.Simulation results validate the proposed algorithm can reduce the perceived delay under the service migration cost constraint while comparing with other existing algorithms.…”
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Inelastic Interaction and Blowup New Solutions of Nonlinear and Dispersive Long Gravity Waves by Haiyong Qin, Mostafa M. A. Khater, Raghda A. M. Attia

“…A new fractional operator is used to convert the fractional form of the BK system to a nonlinear ordinary differential system with an integer order. Many novel traveling wave solutions are constructed that do not exist earlier. …”
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Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example by Sheng Zhang, Yuanyuan Wei, Bo Xu

“…More specifically, a linear spectral problem associated with the KdV equation of integer order is first equipped with local time-fractional derivative. …”
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Optimizing Intermodal Transport and Hub Location Problem for ECOWAS in the Context of Improving Intra-African Trade by Shi Jihui, Kesewa Opoku Agyemang, Cheng Zhaolin

“…The ten highest-ranking nodes identified from the mixed-integer linear program adopted as candidate hubs, thus selecting Ibeshe ferry terminal in Lagos and Tema Harbour in Accra for waterway; Thies, Ibadan, Conakry, Monrovia and Thies for railway; and Thies and Ibadan for road. …”
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A class of gap series with small growth in the unit disc by L. R. Sons, Zhuan Ye

“…Let β>0 and let α be an integer which is at least 2. If f is an analytic function in the unit disc D which has power series representation f(z)=∑k=0∞ak zkα, limsupk→∞ (log+|ak|/logk)=α(1+β), then the first author has proved that f is unbounded in every sector {z∈D:Φ−ϵ<argz<Φ+ϵ, for ϵ>0}. …”
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Robust Position Control of PMSM Using Fractional-Order Sliding Mode Controller by Jiacai Huang, Hongsheng Li, YangQuan Chen, Qinghong Xu

“…In the existing SMC method, the sliding surface is usually designed based on the integer-order integration or differentiation of the state variables, while in this proposed robust FOSMC algorithm, the sliding surface is designed based on the fractional-order calculus of the state variables. …”
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On convergence properties of GPD expansion through Mellin/conformal moments and orthogonal polynomials by Hao-Cheng Zhang, Xiangdong Ji

“…., we propose a method to handle the ordering of the multiple summations and convert them into multiple Mellin-Barnes integrals via analytical continuations of integer summation indices.…”
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