Research on the Utilization of Metro Regenerative Braking Energy Based on an Improved Differential Evolution Algorithm by Di Liu, Song-Qing Zhu, Yun-Rui Bi, Kun Liu, You-Xiong Xu

“…In this paper, we establish two integer programming models of train operation that maximize the overlap time between train traction and braking in peak hours and nonpeak hours. …”
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Z 2 flux binding to higher-spin impurities in the Kitaev spin liquid by Masahiro O. Takahashi, Wen-Han Kao, Satoshi Fujimoto, Natalia B. Perkins

“…Our findings reveal that impurity magnetization exhibits an integer/half-integer spin dependence, which aligns with analytical predictions, and a flux-sector transition from bound-flux to zero-flux occurs at low coupling strengths, independent of the impurity spin. …”
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An improved sunflower optimization algorithm for cluster selection with secured data transmission using cryptographic techniques in WSNS-IoT by Yuvaraja M., Sureshkumar S., Joseph James S., Ishwarya Niranjana M.

“…In this article, we investigate a fully integer interval multi-objective transportation problem (FIIMOTP) and a fully fuzzy integer multi-objective transportation problem (FFIMOTP). …”
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Optimal Operation Scheme with Short-Turn, Express, and Local Services in an Urban Rail Transit Line by Tao Feng, Siyu Tao, Zhengyang Li

“…The problem is first decomposed into two subproblems: the service route design problem and the passenger assignment problem. Then, a mixed-integer nonlinear program (MINLP) model is formulated, and linearization techniques are utilized to transform the MINLP model into a mixed-integer linear programming (MILP) model that can be easily solved by commercial optimization solvers. …”
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Achieving Fair Spectrum Allocation and Reduced Spectrum Handoff in Wireless Sensor Networks: Modeling via Biobjective Optimization by Sang-Seon Byun, Kimmo Kansanen, Ilangko Balasingham, Joon-Min Gil

“…We cast this problem into a multiobjective mixed integer nonconvex nonlinear programming that is definitely difficult to solve at least globally without any aid of conversion or approximation. …”
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External Fractional-Order Gradient Vector Perona-Malik Diffusion for Sinogram Restoration of Low-Dosed X-Ray Computed Tomography by Shaoxiang Hu

“…Therefore, we adopt a novel fractional-order diffusion scheme, named external fractional-order gradient vector Perona-Malik diffusion (EFOGV-PMD), by only replacing integer-order derivatives of “external” gradient vector to their fractional-order counterparts while keeping integer-order derivatives of gradient vector for diffusion coefficients since the ability of edge indicator for 1-order derivative is demonstrated both in theory and applications. …”
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A Comparative Study of Natural Convection Flow of Fractional Maxwell Fluid with Uniform Heat Flux and Radiation by Ruihua Tang, Sadique Rehman, Aamir Farooq, Muhammad Kamran, Muhammad Imran Qureshi, Asfand Fahad, Jia-Bao Liu

“…The well-known Maxwell fluid equation with an integer-order derivative has been extended to a non-integer-order derivative, i.e., fractional derivative. …”
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A Group Rotate-Vector Algorithm for Mixed-Variable Optimization Problems by Zhongming Li, Lutao Yan, Haiyuan Li, Lianxin Wang

“…To address the simultaneous search and optimization of multiple variable types in nonlinear mixed integer programming problems, a grouping and comprehensive processing method is employed. …”
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Optimal Control Problem Investigation for Linear Time-Invariant Systems of Fractional Order with Lumped Parameters Described by Equations with Riemann-Liouville Derivative by V. A. Kubyshkin, S. S. Postnov

“…The problem setting with nonlocal initial conditions is considered which differs from other known settings for integer-order systems and fractional-order systems described in terms of equations with Caputo derivative. …”
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Maximum-likelihood Regression with Systematic Errors for Astronomy and the Physical Sciences. I. Methodology and Goodness-of-fit Statistic of Poisson Data by Massimiliano Bonamente, Yang Chen, Dale Zimmerman

“…This paper presents a new statistical method that enables the use of systematic errors in the maximum-likelihood regression of integer-count Poisson data to a parametric model. …”
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Research on Coal-Rock Fracture Image Edge Detection Based on Tikhonov Regularization and Fractional Order Differential Operator by Chunsheng Liu, Chunping Ren

“…The results show that, compared with integer order differential, the error rate and omission rate of fractional order differential algorithm are smaller, the quality factor is larger, and the execution time and memory footprint are smaller. …”
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A Short Turning Strategy for Train Scheduling Optimization in an Urban Rail Transit Line: The Case of Beijing Subway Line 4 by Miao Zhang, Yihui Wang, Shuai Su, Tao Tang, Bin Ning

“…The MINLP model is then transformed into a mixed integer linear programming (MILP) model according to several transformation properties. …”
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The Multiresolving Sets of Graphs with Prescribed Multisimilar Equivalence Classes by Varanoot Khemmani, Supachoke Isariyapalakul

“…For a multiset {a1,a2,…,ak} and an integer c, we define {a1,a2,…,ak}+c,c,…,c=a1+c,a2+c,…,ak+c. …”
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Maximizing the lifetime of wireless sensor networks in trains for monitoring long-distance goods transportation by Huiting Xu, Xi Jin, Fanxin Kong, Qingxu Deng

“…We first formulate the problem with a realistic discrete power model as a mixed integer linear programming problem. Then, a two-step efficient deployment heuristic is proposed to satisfy these constraints step by step. …”
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Baseband Transceiver Design of a High Definition Radio FM System Using Joint Theoretical Analysis and FPGA Implementation by Chien-Sheng Chen, Chyuan-Der Lu, Ho-Nien Shou, Le-Wei Lin

“…Content includes data format allocation, constellation mapping, orthogonal frequency division multiplexing (OFDM) modulation of the transmitter, timing synchronization, OFDM demodulation, integer and fraction carrier frequency (integer carrier frequency offset (ICFO) and fractional CFO (FCFO)) estimation, and channel estimation of the receiver. …”
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Locating Routing Problem (LRP) of distribution of priority support items to ground forces in war conditions by Milad Abolghasemian, Hamid Bigdeli, Nader Shamami

“…Additionally, a mixed-integer linear programming model is proposed for routing prioritized support items. …”
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Proof of Some Conjectures of Melham Using Ramanujan’s  1ψ1 Formula by Bipul Kumar Sarmah

“…Melham on representation of an integer n as sums of polygonal numbers.…”
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On the equation x2+2a⋅3b=yn by Florian Luca

“…We find all positive integer solutions (x,y,a,b,n) of x2+2a⋅3b=yn with n≥3 and coprime x and y.…”
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Diverse Dynamic Behaviors and Firing Activities of the Modified Fractional-Order Hindmarsh–Rose Neuronal Model Induced by Fractional-Order by Xin Yang, GuangJun Zhang, XueRen Li, Dong Wang

“…Second, when injecting a direct current stimulus, compared with the integer-order model, the system has more varying dynamic behaviors and firing pattern transitions. …”
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Multi-Item Multiperiodic Inventory Control Problem with Variable Demand and Discounts: A Particle Swarm Optimization Algorithm by Seyed Mohsen Mousavi, S. T. A. Niaki, Ardeshir Bahreininejad, Siti Nurmaya Musa

“…The orders are placed in batch sizes and the decision variables are assumed integer. Moreover, all unit discounts for a number of products and incremental quantity discount for some other items are considered. …”
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