Bundle Pricing Decisions for Fresh Products with Quality Deterioration by Yan Fang, Yiping Jiang, Xingxing Han

“…By adding auxiliary decision variables, this model is converted into a mixed integer linear program. Numerical experiments and sensitive analysis are conducted to provide managerial insights for bundling fresh products with quality deterioration.…”
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Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System by Muhammad Marwan, Gauhar Ali, Ramla Khan

“…Moreover, this iterative scheme is injected into algorithms for a system of integer order dynamical systems to observe Lyapunov exponents and a bifurcation diagram for our proposed fractional-order dynamical model. …”
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Edge δ− Graceful Labeling for Some Cyclic-Related Graphs by Mohamed R. Zeen El Deen

“…In this paper, we introduce a new type of labeling of a graph G with p vertices and q edges called edge δ− graceful labeling, for any positive integer δ, as a bijective mapping f of the edge set EG into the set δ,2δ,3δ,⋯,qδ such that the induced mapping f∗:VG→0,δ,2δ,3δ,⋯,qδ−δ, given by f∗u=∑uv∈EGfuvmodδk, where k=maxp,q, is an injective function. …”
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ν-point energy correletors with FastEEC: Small-x physics from LHC jets by Ankita Budhraja, Hao Chen, Wouter J. Waalewijn

“…In practice, limiting the number of subjets to 16 is sufficient to achieve percent-level precision, which we validate using known integer-ν results and convergence tests for non-integer ν. …”
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Optimal Deployment of Dynamic Wireless Charging Lanes for Electric Vehicles considering the Battery Charging Rate by Jun Du, Mingyang Pei, Bin Jia, Pan Wu

“…First, we propose a mixed-integer model with nonlinear constraints to determine the locations and lengths of the charging lanes. …”
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Mixed Optimal Scheduling Model of Flexible Service System Based on Inverted Triangle by Shipei Hu, Yujun Sun

“…In the study presented in this paper, we built a nonlinear binary integer programming model of a flexible scheduling problem for the Department of Zhejiang Provincial Local Tax Services. …”
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Classification of conformal carroll algebras by Hamid Afshar, Xavier Bekaert, Mojtaba Najafizadeh

“…We further obtain their infinite-dimensional extensions, confcarr ~ z d + 1 $$ {\overset{\sim }{\mathfrak{confcarr}}}_z\left(d+1\right) $$ , and discuss their corresponding finite-dimensional truncated subalgebras when the scaling exponent is integer or half-integer. For all these conformal extensions, we also constrain the 2-point and 3-point correlation functions with electric and/or magnetic features.…”
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Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0) by Aleem Mughal, Noshad Jamil

“…In this labeling, a graph is assigning positive integers to graph vertices, graph edges, or graph faces. …”
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A New Optimization via Simulation Approach for Dynamic Facility Layout Problem with Budget Constraints by Parham Azimi, Hamid Reza Charmchi

“…The heuristic integrates integer programming and discrete event simulation to address DFLPB. …”
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3-Total Edge Product Cordial Labeling for Stellation of Square Grid Graph by Rizwan Ullah, Gul Rahmat, Muhammad Numan, Kraidi Anoh Yannick, Adnan Aslam

“…An edge labeling δ:EG⟶0,1,…,p−1, where p is an integer, 1≤p≤EG, induces a vertex labeling δ∗:VH⟶0,1,…,p−1 defined by δ∗v=δe1δe2⋅δenmodp, where e1,e2,…,en are edges incident to v. …”
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Root Locus Practical Sketching Rules for Fractional-Order Systems by António M. Lopes, J. A. Tenreiro Machado

“…For integer-order systems, there are well-known practical rules for RL sketching. …”
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A Game-Theoretic Approach for the Robust Daily Aircraft Routing Problem by Bin Deng, Hao Guo, Jingfeng Li, Junfeng Huang, Kaiyi Tang, Weidong Li

“…This paper presents a new robust integer mathematical model based on game theory that considers daily aircraft routing. …”
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Multi-duplication fault tolerant scheduling algorithm based on genetic algorithm in heterogeneous systems by Zhong-zheng HE, Chao-guang MEN, Yong-jun CHEN, Xiang LI

“…The fault-tolerant task scheduling mechanisms based on multi-duplication didn’t consider the scheduling makespan,the dependencies between tasks,the failures of the links and the longer scheduling makespan caused by the strict scheduling method in the heterogeneous distributed system.So the reliability calculation method that can involve the processor failures and the link failures was proposed firstly.Then the 0-1 integer linear program was proposed for the general scheduling problem.At last,the RAMD_TGS(reliability-aware multi-duplication task general scheduling) algorithm was proposed to solve the 0-1 integer linear program.The algorithm searched the mapped processor and the start execution time on the mapped processor for the task duplication by the evolution of the genetic algorithm.The experiments show that the RAMD_TGS algorithm can meet the reliability requirements and outperforms the existing scheduling algorithms based on the strict scheduling method in terms of scheduling makespan.The resource usages of the algorithm are also acceptable.…”
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The p-Adic Valuations of Sums of Binomial Coefficients by Yong Zhang, Peisen Yuan

“…Also, for any n∈ℤ+, we have νp∑k=0n−1hn−1k2kk−h/2k≥νpn, where νpn denotes the p-adic order of n. For any integer m≡0modp and positive integer n, we have 1/pn∑k=0pn−1pn−1k2kk/−mk−mm−4/p∑k=0n−1n−1k2kk/−mk∈ℤp, where −˙ is the Legendre symbol and ℤp is the ring of p-adic integers.…”
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On the Characterization and Enumeration of Some Generalized Trapezoidal Numbers by Somphong Jitman, Chakrit Phongthai

“…A trapezoidal number, a sum of at least two consecutive positive integers, is a figurate number that can be represented by points rearranged in the plane as a trapezoid. …”
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Reachability Analysis of Low-Order Discrete State Reaction Networks Obeying Conservation Laws by Gergely Szlobodnyik, Gábor Szederkényi

“…Using this result, the reachability problem is reformulated as an Integer Linear Programming (ILP) feasibility problem. …”
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Period-Doubling Bifurcation of Stochastic Fractional-Order Duffing System via Chebyshev Polynomial Approximation by Youming Lei, Yanyan Wang

“…Fractional-order calculus is more competent than integer-order one when modeling systems with properties of nonlocality and memory effect. …”
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Transparency, nonclassicality, and nonreciprocity in chiral waveguide quantum electrodynamics by Qingtian Miao, G. S. Agarwal

“…In particular, for two qubits detuned antisymmetrically with respect to the central waveguide frequency, we find transparency in forward transmission and in photon numbers for arbitrary values of the input powers provided the phase separation between qubits is an integer multiple of π. Values of g^{(2)}(0) less than unity can be reached even for nonzero value of the intrinsic damping by using phase separation different from integer multiple of π, marking the transition from classical to quantum light. …”
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Analisis Kesalahan dalam Pembuktian Teorema Bilangan Bulat pada Mahasiswa IKIP Budi Utomo Malang by Nok Izatul Yazidah, Yunis Sulistyorini, Era Dewi Kartika

“…This research is motivated by problems related to the proof of the integer theorem. The purpose of this study was to find out what errors were made by students in proving the integer theorem. …”
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Radio and Radial Radio Numbers of Certain Sunflower Extended Graphs by Mohammed K. A. Kaabar, Kins Yenoke

“…Let G=V,E be a connected graph with diameter d and radius ρ. For any integer k, 1≤k≤d, radio k−coloring of G is an assignment φ of color (positive integer) to the vertices of G such that da,b+φa−φb≥1+k, ∀a,b∈VG, where da,b is the distance between a and b in G. …”
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