Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum by Jia-Bao Liu, S. Morteza Mirafzal, Ali Zafari

“…If all the eigenvalues of the adjacency matrix of the graph Γ are integers, then we say that Γ is an integral graph. …”
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Dynamic heterogeneous scheduling method based on Stackelberg game model in container cloud by Wei ZENG, Hongchao HU, Lingshu LI, Shumin HUO

“…Container technology promotes the rapid development of cloud computing with its flexible and efficient features, but it also introduces security threats such as co-resident attacks, escape attacks, and common mode attacks.In response to these security threats, a dynamic heterogeneous scheduling method based on Stackelberg game in the container cloud was proposed.First, a heterogeneous mirrored resource pool is constructed to suppress the spread of attacks based on common-mode vulnerabilities on the cloud.Then, the offensive and defense interaction process is modeled as a Stackelberg game model.Finally, the offensive and defensive model is analyzed, and the system scheduling problem is modeled as a mixed integer non-linear programming problem to solve the system's optimal scheduling strategy.Experiments show that the proposed method can improve the defense effect of the cloud platform and reduce the system defense overhead.…”
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Robust Fractional-Order PID Controller Tuning Based on Bode’s Optimal Loop Shaping by Lu Liu, Shuo Zhang

“…The proposed fractional-order PID controller does not have any restriction on the controlled plant, so it can be widely applied on both integer-order and fractional-order systems.…”
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5G millimeter wave cell search algorithm with beam sweeping by Min SHEN, Jing LIANG, Jiazhi HOU

“…Due to the high carrier frequency of the 5G millimeter wave,a large initial access frequency may cause inaccurate time-frequency synchronization at the transmitting and receiving ends and incorrect detection of the physical layer cell identifier.A cell search scheme for 5G millimeter waves to send synchronization signals in a beam sweeping mode at high frequencies was analyzed and simulated.Specifically,a multi-directional synchronization signal block sent by a DFT codebook at the base station side was proposed.The terminal used an omnidirectional antenna to receive multi-beam signals and used a series of synchronization algorithms to complete time,frequency synchronization,and physical layer cell identification.Simulation results show that the proposed main synchronization signal detection algorithm with cross-correlation of pre-stored integer frequency offset and received signal has good cell search performance on 5G millimeter-wave channels.…”
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Research on maximizing energy efficiency for relay-aided D2D communication by Xue WANG, Tao JIN, Zhihong QIAN, Liangshuai HU, Xin WANG

“…In order to optimize the energy efficiency for relay-aided D2D communication underlaying cellular network,an algorithm was proposed while guaranteeing the quality of service of D2D users and cellular users.Firstly,the problem was formulated as a mixed integer nonlinear fractional programming problem,with the goal of maximizing the energy efficiency of all D2D users.Then,the maximizing energy efficiency problem was divided into three sub-problems,such as power allocation,relay selection and subcarrier assignment.Finally,the power allocation problem,the relay selection problem and the subcarrier assignment problem were addressed by Dinkelbach method and Lagrange multiplier method,Q-learning and Hungarian algorithm,respectively.The simulation results show that the proposed algorithm can improve the total energy efficiency of D2D users compared with existing algorithms.…”
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Integrated Project Scheduling and Staff Assignment with Controllable Processing Times by Victor Fernandez-Viagas, Jose M. Framinan

“…This type of problems usually appears in service companies, where both tasks scheduling and staff assignment are closely related. An integer programming model for the problem is proposed, together with some extensions to cope with different situations. …”
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Finite-infinite range inequalities in the complex plane by H. N. Mhaskar

“…For any p, 0<P≤∞, there exist positive constants c1, c2 depending only on E, ω, σ and p such that for every integer n≥1 and every polynomial P of degree at most n, ∫E\K|ωnP|pdσ≤c1exp(−c2n)∫K|ωnP|pdσ. …”
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Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R2 by Josef Diblík, Hana Halfarová, Jan Šafařík

“…Two-dimensional linear discrete systems x(k+1)=Ax(k)+∑l=1nBlxl(k-ml),  k≥0, are analyzed, where m1,m2,…,mn are constant integer delays, 0<m1<m2<⋯<mn, A, B1,…,Bn are constant 2×2 matrices, A=(aij), Bl=(bijl),  i,j=1,2,  l=1,2,…,n, and x:{-mn,-mn+1,…}→R2. …”
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First-Train Timetable Synchronization in Metro Networks under Origin-Destination Demand Conditions by Hetian Chai, Xiaopeng Tian, Huimin Niu

“…Subjected to train operation and connection constraints, a biobjective nonlinear integer programming model is formulated to minimize the total travel time of OD-dependent passenger demands and the deviation between the known and expected schedules. …”
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Study on Vibration Characteristic of Trilobe Raceway Cylindrical Roller Bearing with Elastic Support by Sun Xue, Deng Sier, Zhang Yuanjun, Chen Guoding

“…By using the predict-correct integer algorithm with variable step,the dynamics equation is solved,and the influence of structural parameters of elastic support and working conditions on the vibration characteristics of the bearing is investigated. …”
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An efficient method to generate elliptic curves by ZHOU Chang-ying1, Kwok-Yan-Lam1, ZHOU Zheng-ou2

“…This condition can be relaxed to include primes of the form 2ip+1 （i is a small integer） without compromising security. Hence, the number of elliptic curves suitable for use by public key cryptosystems is increased greatly. …”
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Optimization on Production-Inventory Problem with Multistage and Varying Demand by Duan Gang, Chen Li, Li Yin-Zhen, Song Jie-Yan, Akhtar Tanweer

“…This paper addresses production-inventory problem for the manufacturer by explicitly taking into account multistage and varying demand. A nonlinear hybrid integer constrained optimization is modeled to minimize the total cost including setup cost and holding cost in the planning horizon. …”
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Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation by Jan Freundlich

“…The studies show that the selection of appropriate damping coefficients and fractional derivative order of damping model enables us to fit more accurately dynamic characteristic of the beam in comparison with using integer order derivative damping model.…”
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Containerships Sailing Speed and Fleet Deployment Optimization under a Time-Based Differentiated Freight Rate Strategy by Hualong Yang, Yuwei Xing

“…Then, the optimization problem is formulated as a mixed-integer nonlinear programming. Its goal is to maximize the total profits of a container liner shipping. …”
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Balanced optimal almost binary sequence pairs of period N≡1（mod4） by Xiuping PENG, Hongxiao LI, Shide WANG, Hongbin LIN

“…Based on the combinatorial design theory， the constructions of balanced optimal almost binary sequence pairs of period N≡1（mod 4）were researched.The maximal cross-correlation values θ_c were obtained by different combinations of （almost） binary sequence pairs.Furthermore， three new bounds on the autocorrelation values under the precondition of the value of θ_c=1，2，3 were presented individually.Meanwhile，four types of balanced（almost）optimal almost binary sequence pairs were generated， which satisfied the cross-correlation values and autocorrelation theory bounds.Through the constructions， the range of the cross-correlation values is expanded and the cross-correlation value of the optimal binary sequence pairs is further reduced.More than odd， the value of sequence length parameter f can be any integer， which enriches the existence space of the optimal binary sequence pair.…”
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Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions by Zhi-Xian Yu, Rong Yuan, Cheng-Hsiung Hsu, Ming-Shu Peng

“…This work investigates traveling waves for a class of delayed cellular neural networks with nonmonotonic output functions on the one-dimensional integer lattice Z. The dynamics of each given cell depends on itself and its nearest m left or l right neighborhood cells with distributed delay due to, for example, finite switching speed and finite velocity of signal transmission. …”
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Capacitated Multiple Allocation Hub Covering Flow Problem by Orhan Feyzioğlu, Nazmi Sener

“…The problem is developed as a mixed-integer linearoptimization problem. According to the results obtained from computational experiments, weshow that taking into account both flow related costs and capacities of network componentsconcurrently is very important to have a cost effective design.…”
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Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis by Hang Zheng, Yonghui Xia, Yuzhen Bai, Guo Lei

“…Finally, by comparison between the integer-order Wu–Zhang system and the fractional-order Wu–Zhang system, we see that the phase portrait, nonzero equilibrium points, and the corresponding exact travelling wave solutions all depend on the derivative order α. …”
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Self-adaptive encryption algorithm for image based on affine and composed chaos by Chang-ci WEN, Qin WANG, Fu-min HUANG, Zhi-shu YUAN, Chun-sheng TAO

“…On the basis of three-dimensional affine transformation in limited integer domain and composed chaos,a novel digital image encryption algorithm was proposed.Firstly,it scrambled pixels’ position and confused pixels’ value according to corresponding coordination.Secondly,it took a series of nonlinear diffusion,substitution and re-diffusion.In the process of substitution,it introduced pixels’ value to perturb multiple chaos systems that were coupled together for self-adaptive encryption.The algorithm proceeded the above two steps for 3 times to defend chosen plaintext attack,and had huge key space to defend violent attack.The scrambling function in it was compatible with images at any ratio of length to width without any preprocessing; the constructed whole chaos system which had a simple form was designed modularly,and could be realized parallel conveniently.…”
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Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model by Jian Song

“…We will consider the following nonlinear impulsive delay differential equation N′(t)=r(t)N(t)((K(t)−N(t−mw))/(K(t)+λ(t)N(t−mw))), a.e. t>0, t≠tk, N(tk+)=(1+bk)N(tk), K=1,2,…, where m is a positive integer, r(t), K(t), λ(t) are positive periodic functions of periodic ω. …”
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