The Thinking Process of Students Using Trial and Error Strategies in Generalizing Linear Patterns by Yayan Eryk Setiawan

“… Patterns generalization learning at the junior high school is more emphasis on the generalization of linear patterns. One problem in generalizing linear patterns is that students do not know the process of using trial and error strategies to generalize linear patterns. …”
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Multiple-Input Multiple-Output (MIMO) Linear Systems Extreme Inputs/Outputs by David O. Smallwood

“…A linear structure is excited at multiple points with a stationary normal random process. …”
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Solution of applied one-dimensional linear boundary-value problems with automatic precision by A. V. Korovaytsev, E. A. Korovaytseva, V. A. Lomovskoy

“…Possible basic types of applied one-dimensional linear boundary problems in problems of chemical kinetics, structures strength, aerohydroelasticity, and wave processes in continuous media are analyzed. …”
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An efficient quantum algorithm for ab initio approximations of non-linear response functions by Tyler Kharazi, Torin F. Stetina, Liwen Ko, Guang Hao Low, K. Birgitta Whaley

“…Abstract We develop and analyze a fault-tolerant quantum algorithm for non-linear response properties of molecular and condensed phase systems. …”
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Recent Advances in Arc-linear Motors for Direct-drive Applications: A Review by Zhenbao Pan, Jiwen Zhao, Shuhua Fang, Jinhao Cai, Qiangren Xu

“…The arc-linear motor (ALM) is a new type of special motor derived from the linear motor, which has the merits of high torque, compact structure and fast dynamic response. …”
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Development of a Numerical Model for an Expanding Tube with Linear Explosive Using AUTODYN by Mijin Choi, Jung-Ryul Lee, Cheol-Won Kong

“…Pyrotechnic devices have been employed in satellite launch vehicle missions, generally for the separation of structural subsystems such as stage and satellite separation. …”
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Linear Stability Analysis on Flow-Induced Vibration of an Elastically Mounted Rotating Cylinder by Jianfeng Lu, Zhiyu Zhang, Xing Zhang

“…In this paper, we present a linear stability analysis on flow-induced vibration of an elastically mounted cylinder subjected to forced rotation. …”
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Cons-training tensor networks: Embedding and optimization over discrete linear constraints by Javier Lopez-Piqueres, Jing Chen

“…In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures. …”
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Linear random boundary value problems containing weakly correlated forcing functions by Ning-Mao Xia

“…This paper concerns linear random boundary value problems that contain random variables In the boundary conditions and weakly correlated processes in the differential equations. …”
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Physically non-cloneable arbiter-type function with non-linear path pairs by A. A. Ivaniuk, A. Y. Shamyna

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The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks by Jia-Bao Liu, Jing Chen, Jing Zhao, Shaohui Wang

“…Let Hn be the linear heptagonal networks with 2n heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. …”
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Efficient knowledge graph to text powered by LLGM: linear latent graph model by Xiaokang Zhao, Yao Zheng, Yubo Shan, Jingyuan Li, Kun Zhang, Yuanzhuo Wang

“…LLGM’s core innovations are three-fold: (1) a Multi-head Statistical Attention (MSA) mechanism that achieves linear O(N) complexity by replacing pairwise token interactions with efficient statistical approximations, drastically reducing the primary computational bottleneck; (2) a Graph Latent Self-Attention (GLSA) module that efficiently encodes explicit graph structures using dimension-reduced intermediate representations, preserving relational fidelity with fewer parameters; and (3) a Graph Periodicity Projector (GPP) that optimizes feed-forward networks by decomposing representations into periodic and non-periodic components, adeptly capturing both regular and unique graph patterns. …”
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Applications of AG-Groupoids in Decision-Making via Linear Diophantine Fuzzy Sets by Faisal Yousafzai, Muhammad Danish Zia, Mohammed M. Khalaf, Esmail Hassan Abdullatif Al-Sabri, Rashad Ismail

“…In this paper, we investigated the notion of a linear Diophantine fuzzy set (LDFS) by using the concept of a score function to build the LDF-score left (right) ideals and LDF-score (0,2)-ideals in an AG-groupoid. …”
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The linear electromagnetic gyrokinetic global simulation by using the numerical Lie-transform code by Guodong Zhang, Jinxiang You, Zihao Wang, Tiannan Wu, Yuefeng Qiu, Lu Wang, Shaojie Wang

“…The simulation results including the real frequency, linear growth rate, and mode structures of the ion temperature gradient mode and the trapped electron mode as well as the kinetic ballooning mode from NLT are consistent with those from previous Eulerian and particle in cell codes. …”
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Results of the clinical evaluation of the low-dose protocols of the digital linear tomography of the chest by I. G. Kamyshanskaya, V. M. Cheremisin, A. V. Vodovatov, A. N. Boriskina

“…The second stage of the study was performed as a prospective cohort survey aimed at the evaluation of the structure of X-ray examinations, patient doses and clinical image quality of the digital linear tomograms in antitubercular early treatment center. …”
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Reflections of linearly polarized electromagnetic waves from a multilayer periodic mirror by D. Kh. Nurligareev, I. A. Nedospasov, K. Yu. Kharitonova

“…The purpose of the article is to carry out a theoretical and experimental study of the angular reflection spectrum of linearly polarized electromagnetic waves from a multilayer periodic mirror on a transparent substrate to exact analytical expressions for reflection and transmission coefficients generalizing the cases of incidence of plane transverse electric (TE) and transverse magnetic (TM) modes on limited periodically structured media with a stepped refractive index profile.Methods. …”
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Twisting light without spin: chirality-sensitive forces from linear polarization by Giuseppina Simone

“…While chirality-dependent forces have traditional required circularly polarized light, here, it is demonstrated their emergence under linearly polarized illumination through photonic structure-induced helicity. …”
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Linear active disturbance rejection control for ball mill coal-pulverizing systems by DONG Jun-yi, SUN Li, LI Dong-hai

“…This paper analyzes the dynamic characteristics of the BMCP system and proposes a control strategy based on a decentralized linear active disturbance rejection controller (LADRC). …”
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The Radiative Transfer in Accretion Discs with Linear Plank Function: Role of Scattering Effect by Fahimeh Habibi, Maryam Samadi

“…The emergent intensity as well as other radiative quantities are analytically obtained related to the vertical structure of disc while a linear Planck function is applied. …”
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Modal Regression Estimation by Local Linear Approach in High-Dimensional Data Case by Fatimah A. Almulhim, Mohammed B. Alamari, Ali Laksaci, Zoulikha Kaid

“…The result is stated under standard conditions, characterizing both the functional structure of the data and the local linear approximation properties of the model. …”
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