Data aggregation based on the privacy-preserving element in wireless sensor networks by Wei-ni ZENG, Ya-ping LIN, Shi-ming HE, Jian-ping YU

“…A distributed mechanism was proposed to protect the data privacy during the data aggregation phase.The contributions of this mechanism are:1) Privacy-preserving element taking advantage of the algebraic properties of congruence was defined.In privacy-preserving elements,privacy data could be preserved without the extra data exchange,and the aggregation result could be recovered from the perturbed data in the cluster head.2)A flexible method for generating the privacy-preserving element was given.Thus,nodes could generate their privacy-preserving element without the extra data exchange,and the method was adapted to the dynamic reporting nodes.Extensive analysis showed that:compared with the centralized mechanism,the proposed mechanism has a better resistance to data loss,can avoid the single point problem and also consumes less communication overhead; compared with the other distributed mechanisms,the proposed mechanism is able to preserve privacy more efficiently while consuming less communication overhead.…”
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Mixed methods for viscoelastodynamics and topology optimization by Giacomo Maurelli, Nadia Maini, Paolo Venini

“…Worked numerical examples are presented concerning both the dynamic analysis of viscoelastic structures and their topology optimization.…”
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Point-to-point trajectory planning strategy research for a multi-robot towing system by Ll Tao, ZHAO ZhiGang, ZHU MingTong, ZHAO XiangTang

“…Firstly, the kinematic and dynamic model of the system was established, and inverse kinematics of the system were analyzed and different solutions aiming at different situations were given. …”
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Routes to Multiple Equilibria for Mass-Action Kinetic Systems by Antonio A. Alonso, Irene Otero-Muras, Manuel Pájaro

“…The study is performed on a class of polynomial dynamic systems that, under some mild assumptions, are able to accommodate in their state-space form weakly reversible mass-action kinetic networks. …”
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Nonlinear Normal Modes in a Two-Stage Isolator Using a Modified Finite-Element Galerkin Method by Cheng Li, Hongguang Li

“…A Galerkin projection of the governing equations for the approximate invariant manifolds yields a set of nonlinear algebraic equations in expansion coefficients, which can be solved numerically with a general choice of zero as initial guess for the cases in this work. …”
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Free Vibration Analysis of Rotating Pretwisted Functionally Graded Sandwich Blades by L. T. Liu, Y. X. Hao, W. Zhang, J. Chen

“…The mode shapes are expanded in terms of two-dimensional algebraic polynomials in the Rayleigh–Ritz method, and the static and dynamic natural frequencies of the blade are obtained. …”
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Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross-Section by Zhongmin Wang, Rongrong Li

“…Combining with discretization equations for the differential equation and boundary conditions, an eigen-equation of the system including some dimensionless parameters is formulated in implicit algebraic form, so it is easy to simulate the dynamical behaviors of rotating tapered beams. …”
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Optimal Control for a Family of Systems in Novel State Derivative Space Form with Experiment in a Double Inverted Pendulum System by Yuan-Wei Tseng, Jer-Guang Hsieh

“…It turns out that novel differential Lagrange multipliers must be used to adjoin SDS system constraints (namely, the dynamical equations of the control system) to the integrand of the original cost functional which is a function of state derivatives. …”
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Biodiesel Production by Reactive Flash: A Numerical Simulation by Alejandro Regalado-Méndez, Sigurd Skogestad, Reyna Natividad, Rubí Romero

“…The RF was modeled by an index-2 system of differential algebraic equations, the vapor split (ϕ) was computed by modified Rachford-Rice equation and modified Raoult’s law computed bubble point, and the continuation analysis was tracked on MATCONT. …”
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Transfer functions of a time-varying control system by Volt Avdieiev

“…This makes it possible to transform differential equations into algebraic ones, as a result to use the developed apparatus of linear algebra to solve problems of analysis and synthesis. …”
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Application of the New Mapping Method to Complex Three Coupled Maccari’s System Possessing M-Fractional Derivative by Jan Martinovic, Aziz Ur Rehman, Muhammad Bilal Riaz

“…Following this, a thorough examination of the dynamic nature of the equation is conducted from various perspectives. …”
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A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams by Issam El Hantati, Ahmed Adri, Hatim Fakhreddine, Said Rifai, Rhali Benamar

“…The effect of nonlinearity on the dynamic behaviour of multistepped beams in the free and forced vibration is demonstrated and discussed. …”
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A Cryptographic Scheme for Construction of Substitution Boxes Using Quantic Fractional Transformation by Abid Mahboob, Muhammad Asif, Muhammad Nadeem, Aysha Saleem, Sayed M. Eldin, Imran Siddique

“…In the new era of cryptography, Substitution Boxes (S-Boxes) are very important to raise confusion in cipher text and the security of encryption directly depends on the algebraic strength of S-box. To avoid a hacker attack, researchers are focusing on creating dynamic S-boxes that are much stronger. …”
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ESTABLISHED MODES AND STATIC CHARACTERISTICS OF THREE-PHASE ASYNCHRONOUS MOTOR POWERED WITH SINGLE PHASE NETWORK by V. S. Malyar, V. V. Malyar

“…The resulting nonlinear system of algebraic equations is a discrete analogue of the initial system of differential equations. …”
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Robust Control Design for the Higher Harmonic Vibration Reduction of a Nonlinear Aeroservoelastic Rotor by Byeonguk Im, Kunhyuk Kong, Wonjong Eun, Sangjoon Shin

“…The rotor aeroservoelastic simulation was performed using the multi-body dynamic analysis software DYMORE, equipped with a new improved inflow model employing multiple trailer time-marching free-vortex wakes. …”
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Topology Unveiled: A New Horizon for Economic and Financial Modeling by Yicheng Wei, Junzo Watada, Zijin Wang

“…Sinceits introduction in the 19th century to address geometric problems, topology as a methodology has undergone a series of evolutions, encompassing branches of geometric topology, point-set topology (analytic topology), algebraic topology, and differential topology, gradually permeating into various interdisciplinary applied fields. …”
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Integrability of open boundary driven quantum circuits by Chiara Paletta, Tomaž Prosen

“…By using the Sklyanin's construction of reflection algebra, we obtain the most general solutions of the boundary Yang-Baxter equation for such a setup. …”
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Data on full stationary wave-field measurement of a suspended steel plate punctually loadedMendeley Data by Xuefeng Li, Thomas Brion, Pascal Fossat, Mohamed Ichchou, Olivier Bareille, Abdel-Malek Zine

“…Its value has been illustrated in the research paper “Algebraic K-Space Identification 2D technique for the automatic extraction of complex k-space of 2D structures in presence of uncertainty” [1]. …”
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THE EFFICIENT USE OF HUMAN RESOURCES IN RUSSIA IN CONDITIONS OF CATCHING-UP DEVELOPMENT by G. Ryazanova, P. Tolkachev

“…The relationship of labor productivity with other macroeconomic indicators has been analyzed: the level of wages in current prices and taking into account the Paasche deflator index; dynamics of the gross domestic product; the dynamics of the share of food in the consumer basket; the indicators of changes in clean investments, that is a key factor in economic growth in the national economy. …”
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New version of Universal modeling method for centrifugal compressors calculation development by Yu. B. Galerkin, A. A. Drozdov

“…The math model of Universal modeling method is a sum of algebraic equations for calculation of head losses. …”
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