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1

Hu, Shu-Ping. "Generalized Degrees of Freedom." Journal of Cost Analysis and Parametrics 9, no. 2 (2016): 93–111. http://dx.doi.org/10.1080/1941658x.2016.1191388.

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2

Sebastian, Joyson, and Suhas Diggavi. "Generalized Degrees of Freedom of Noncoherent Diamond Networks." IEEE Transactions on Information Theory 66, no. 8 (2020): 5228–60. http://dx.doi.org/10.1109/tit.2020.2983169.

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3

Barhoumi, Abdessatar, Bilel Kacem Ben Ammou, and Hafedh Rguigui. "Infinite degrees of freedom Weyl representation: Characterization and application." Infinite Dimensional Analysis, Quantum Probability and Related Topics 21, no. 01 (2018): 1850002. http://dx.doi.org/10.1142/s0219025718500029.

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By means of infinite-dimensional nuclear spaces, we generalize important results on the representation of the Weyl commutation relations. For this purpose, we construct a new nuclear Lie group generalizing the groups introduced by Parthasarathy [An Introduction to Quantum Stochastic Calculus (Birkhäuser, 1992)] and Gelfand–Vilenkin [Generalized Functions (Academic Press, 1964)] (see Ref. 15). Then we give an explicit construction of Weyl representations generated from a non-Fock representation. Moreover, we characterize all these Weyl representations in quantum white noise setting.
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4

Tu, I.-Ping, Su-Yun Huang, and Dai-Ni Hsieh. "The generalized degrees of freedom of multilinear principal component analysis." Journal of Multivariate Analysis 173 (September 2019): 26–37. http://dx.doi.org/10.1016/j.jmva.2019.01.010.

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5

Zeng, Peng, Qinqin Hu, and Xiaoyu Li. "Geometry and Degrees of Freedom of Linearly Constrained Generalized Lasso." Scandinavian Journal of Statistics 44, no. 4 (2017): 989–1008. http://dx.doi.org/10.1111/sjos.12288.

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6

Nagarajan, S., and D. A. Turcic. "Lagrangian Formulation of the Equations of Motion for Elastic Mechanisms With Mutual Dependence Between Rigid Body and Elastic Motions: Part II—System Equations." Journal of Dynamic Systems, Measurement, and Control 112, no. 2 (1990): 215–24. http://dx.doi.org/10.1115/1.2896128.

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The first step in the derivation of the equations of motion for general elastic mechanism systems was described in Part I of this work. The equations were derived at the elemental level using Lagrange’s equation and the generalized coordinates were both the rigid body degrees of freedom, and the elastic degrees of freedom of element ‘e’. Each rigid body degree of freedom gave rise to a scalar equation of motion, and the elastic degrees of freedom of element e gave rise to a vector equation of motion. Since both the rigid body degrees of freedom and elastic degrees of freedom are considered as generalized coordinates, the equations derived take into account the mutual dependence between the rigid body and elastic motions. This is important for mechanisms that are built using lightweight and flexible members and which operate at high speeds. A schematic diagram of how the equations of motion are obtained in this work is shown in Fig. 1 in Part I. The transformation step in the figure refers to the rotational transformation of the nodal elastic displacements (which were measured in the element coordinate system), so that they are measured in terms of the reference coordinate system. This transformation is necessary in order to ensure compatibility of the displacement, velocity and acceleration of the degrees of freedom that are common to two or more links during the assembly of the equations of motion. This final set of equations after assembly are obtained in closed form, and, given external torques and forces, can be solved for the rigid body and elastic response simultaneously taking into account the mutual dependence between the two responses.
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7

Shi, Junpeng, Guoping Hu, Xiaofei Zhang, and Hao Zhou. "Generalized Nested Array: Optimization for Degrees of Freedom and Mutual Coupling." IEEE Communications Letters 22, no. 6 (2018): 1208–11. http://dx.doi.org/10.1109/lcomm.2018.2821672.

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8

Sebastian, Joyson, and Suhas N. Diggavi. "Generalized Degrees Freedom of Noncoherent MIMO Channels With Asymmetric Link Strengths." IEEE Transactions on Information Theory 66, no. 7 (2020): 4431–48. http://dx.doi.org/10.1109/tit.2020.2978183.

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9

Abouraddy, Ayman F., Timothy M. Yarnall, and Bahaa E. A. Saleh. "Generalized optical interferometry for modal analysis in arbitrary degrees of freedom." Optics Letters 37, no. 14 (2012): 2889. http://dx.doi.org/10.1364/ol.37.002889.

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10

Gogilidze, S. A., V. V. Sanadze, and F. G. Tkebuchava. "Elimination of gauge degrees of freedom in the generalized Hamiltonian formalism." Theoretical and Mathematical Physics 79, no. 1 (1989): 391–96. http://dx.doi.org/10.1007/bf01015779.

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11

Hu, Qinqin, Peng Zeng, and Lu Lin. "The dual and degrees of freedom of linearly constrained generalized lasso." Computational Statistics & Data Analysis 86 (June 2015): 13–26. http://dx.doi.org/10.1016/j.csda.2014.12.010.

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12

Poshteh, Mohammad Bagher Jahani, Behrouz Mirza, and Fatemeh Oboudiat. "Generalized Ehrenfest's equations and phase transition in black holes." International Journal of Modern Physics D 24, no. 03 (2015): 1550029. http://dx.doi.org/10.1142/s0218271815500297.

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In this paper, we generalize Ehrenfest's equations to systems having two work terms, i.e. systems with three degrees of freedom. For black holes with two work terms we obtain nine equations instead of two to be satisfied at the critical point of a second-order phase transition. We finally generalize this method to a system with an arbitrary number of degrees of freedom and found there is [Formula: see text] equations to be satisfied at the point of a second-order phase transition where N is number of work terms in the first law of thermodynamics.
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13

de Rham, Claudia, Matteo Fasiello, and Andrew J. Tolley. "Stable FLRW solutions in generalized massive gravity." International Journal of Modern Physics D 23, no. 13 (2014): 1443006. http://dx.doi.org/10.1142/s0218271814430068.

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We present exact Friedmann Lemaítre Robertson Walkers (FLRW) solutions in generalized massive gravity where the mass parameters are naturally promoted to Lorentz-invariant functions of the Stückelberg fields. This new dependence relaxes the constraint that would otherwise prevent massive gravity from possessing exact FLRW solutions. It does so without the need to introduce additional degrees of freedom. We find self-accelerating cosmological solutions and show that, with a mild restriction on the region of phase space, these cosmological solutions exhibit full stability, i.e. absence of ghosts and gradient instabilities for all the tensor, vector and scalar modes, for all cosmic time. We perform the full decoupling limit analysis, including vector degrees of freedom, which can be used to confirm the existence of an active Vainshtein mechanism about these solutions.
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14

Nagarajan, S., and David A. Turcic. "Lagrangian Formulation of the Equations of Motion for Elastic Mechanisms With Mutual Dependence Between Rigid Body and Elastic Motions: Part I—Element Level Equations." Journal of Dynamic Systems, Measurement, and Control 112, no. 2 (1990): 203–14. http://dx.doi.org/10.1115/1.2896127.

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Equations of motion are derived using Lagrange’s equation for elastic mechanism systems. The elastic links are modeled using the finite element method. Both rigid body degrees of freedom and the elastic degrees of freedom are considered as generalized coordinates in the derivation. Previous work in the area of analysis of general elastic mechanisms usually involve the assumption that the rigid body motion or the nominal motion of the system is unaffected by the elastic motion. The nonlinear differential equations of motion derived in this work do not make this assumption and thus allow for the rigid body motion and the elastic motion to influence each other. Also the equations obtained are in closed form for the entire mechanism system, in terms of a minimum number of variables, which are the rigid body and the elastic degrees of freedom. These equations represent a more realistic model of light-weight high-speed mechanisms, having closed and open loop multi degree of freedom chains, and geometrically complex elastic links.
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15

Djerassi, S. "Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom." Journal of Applied Mechanics 65, no. 3 (1998): 719–26. http://dx.doi.org/10.1115/1.2789116.

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This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.
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16

ZENG, Daxing. "Type Synthesis of Three Degrees of Freedom Rotational Generalized Decoupling Parallel Mechanism." Journal of Mechanical Engineering 53, no. 3 (2017): 17. http://dx.doi.org/10.3901/jme.2017.03.017.

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17

Sakata, A. "Evaluation of generalized degrees of freedom for sparse estimation by replica method." Journal of Statistical Mechanics: Theory and Experiment 2016, no. 12 (2016): 123302. http://dx.doi.org/10.1088/1742-5468/2016/12/123302.

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18

Jafar, Syed A., and Sriram Vishwanath. "Generalized Degrees of Freedom of the Symmetric Gaussian $K$ User Interference Channel." IEEE Transactions on Information Theory 56, no. 7 (2010): 3297–303. http://dx.doi.org/10.1109/tit.2010.2048494.

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19

Chaaban, Anas, and Aydin Sezgin. "On the Generalized Degrees of Freedom of the Gaussian Interference Relay Channel." IEEE Transactions on Information Theory 58, no. 7 (2012): 4432–61. http://dx.doi.org/10.1109/tit.2012.2191712.

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20

Huang, Chiachi, Viveck R. Cadambe, and Syed Ali Jafar. "Interference Alignment and the Generalized Degrees of Freedom of the $X$ Channel." IEEE Transactions on Information Theory 58, no. 8 (2012): 5130–50. http://dx.doi.org/10.1109/tit.2012.2201343.

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21

Fan, Huo, Hong Zheng, Chunguang Li, and Siming He. "A decomposition technique of generalized degrees of freedom for mixedmode crack problems." International Journal for Numerical Methods in Engineering 112, no. 7 (2017): 803–31. http://dx.doi.org/10.1002/nme.5533.

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22

Yehia, H. M. "Generalized natural mechanical systems of two degrees of freedom with quadratic integrals." Journal of Physics A: Mathematical and General 25, no. 1 (1992): 197–221. http://dx.doi.org/10.1088/0305-4470/25/1/024.

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23

You, Chong, Samuel Müller, and John T. Ormerod. "On generalized degrees of freedom with application in linear mixed models selection." Statistics and Computing 26, no. 1-2 (2014): 199–210. http://dx.doi.org/10.1007/s11222-014-9488-7.

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24

Shaikh, Abdul Hayee, Xiaoyu Dang, and Daqing Huang. "New Generalized Multi-Structured MIMO Radar Configuration With Increased Degrees of Freedom." IEEE Communications Letters 25, no. 4 (2021): 1293–97. http://dx.doi.org/10.1109/lcomm.2021.3049855.

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25

ISIDRO, JOSÉ M. "GENERALIZED COMPLEX GEOMETRY AND THE PLANCK CONE." International Journal of Modern Physics A 21, no. 06 (2006): 1189–97. http://dx.doi.org/10.1142/s0217751x06025201.

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Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalized complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of degrees of freedom are respectively described by a symplectic structure and a complex structure on classical phase space. In this paper we analyze the role played by generalized complex geometry in the classical and quantum mechanics of a finite number of degrees of freedom. We identify generalized complex geometry as an appropriate geometrical setup for dualities. The latter are interpreted as transformations connecting points in the interior of the Planck cone with points in the exterior, and vice versa. The Planck cone bears some resemblance with the relativistic light-cone. However the latter cannot be traversed by physical particles, while dualities do connect the region outside the Planck cone with the region inside, and vice versa.
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26

Fenton, R. G., B. Benhabib, and A. A. Goldenberg. "Optimal Point-to-Point Motion Control of Robots With Redundant Degrees of Freedom." Journal of Engineering for Industry 108, no. 2 (1986): 120–26. http://dx.doi.org/10.1115/1.3187046.

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Control of a kinematically redundant robot arm requires an optimization procedure to determine the motion of the end effector. The criterion for optimization can be minimum motion time, minimum joint displacement increments or a combined merit function specified according to the requirements of the user. Three different methods may be used to perform the computations and obtain the joint coordinate increments for the point-to-point motion control of the robot. The methods are the “direct,” the “pseudoinverse” and the “generalized inverse” methods. These methods are described in detail in this paper, and results obtained with the three methods are compared on the basis of performing simulated tasks. It is concluded that the generalized inverse method is the most suitable, general method for point-to-point control of robots with more than six degrees-of-freedom.
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27

KANDA, Yasuyuki, Hiroshi OKADA, Shigeo IRAHA, Jun TOMIYAMA, and Genki YAGAWA. "FRACTURE MECHANICS PARAMETER COMPUTATION USING GENERALIZED FINITE ELEMENT WITH DRILLING DEGREES OF FREEDOM." Doboku Gakkai Ronbunshuu A 63, no. 3 (2007): 464–74. http://dx.doi.org/10.2208/jsceja.63.464.

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28

Gao, Xiaoli, and Yixin Fang. "A note on the generalized degrees of freedom under the L1 loss function." Journal of Statistical Planning and Inference 141, no. 2 (2011): 677–86. http://dx.doi.org/10.1016/j.jspi.2010.07.006.

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29

Lincoff, James, Sukanya Sasmal, and Teresa Head-Gordon. "Comparing generalized ensemble methods for sampling of systems with many degrees of freedom." Journal of Chemical Physics 145, no. 17 (2016): 174107. http://dx.doi.org/10.1063/1.4965439.

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30

Li, Q. S., L. F. Yang, and G. Q. Li. "The quadratic finite element/strip with generalized degrees of freedom and their application." Finite Elements in Analysis and Design 37, no. 4 (2001): 325–39. http://dx.doi.org/10.1016/s0168-874x(00)00046-9.

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31

Shi, Junpeng, Guoping Hu, Xiaofei Zhang, Fenggang Sun, Wang Zheng, and Yu Xiao. "Generalized Co-Prime MIMO Radar for DOA Estimation With Enhanced Degrees of Freedom." IEEE Sensors Journal 18, no. 3 (2018): 1203–12. http://dx.doi.org/10.1109/jsen.2017.2782746.

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32

Xu, Hua, Lu Feng Yang, and Zhen Ping She. "Mode-III Stress Intensity Factor by Williams Element with Generalized Degrees of Freedom." Advanced Materials Research 487 (March 2012): 242–46. http://dx.doi.org/10.4028/www.scientific.net/amr.487.242.

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Williams series are developed for mode III cracks, based on which the displacement field is defined in the singular region around the crack tip. The Williams element with generalized degrees of freedom (GDOFs) is proposed for analysis of stress intensity factor (SIF) of mode III crack. The SIF at the crack tip can be evaluated analytically by one of the undetermined constants of the Williams element. The influence of the relative length of the crack on the SIF is investigated. Three important parameters for the Williams element, including the radial scale factor, the number of subelements and the terms of the Williams series, are discussed in detail. Numerical example shows that the Williams element is of accuracy and efficiency.
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33

GU, XIAO-YAN, BIN DUAN, and ZHONG-QI MA. "SEPARATION OF ROTATIONAL DEGREES OF FREEDOM IN A QUANTUM THREE-BODY PROBLEM." International Journal of Modern Physics E 10, no. 01 (2001): 69–82. http://dx.doi.org/10.1142/s0218301301000411.

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We demonstrate explicitly how the rotational degrees of freedom in a quantum three-body problem is separated completely from the internal ones. It is shown that only finite partial angular momentum states are involved in constructing the base-functions with the given angular momentum and parity, and the contributions by the remaining partial angular momentum states are incorporated into the contributions by the generalized radial functions.
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34

Lee, Hsin-Sheng. "Creative Design of an Elliptical Trainer with Two Degrees of Freedom." International Journal of Mechanical Engineering Education 36, no. 4 (2008): 284–93. http://dx.doi.org/10.7227/ijmee.36.4.2.

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The elliptical trainer is a widely used piece of equipment for fitness and rehabilitation. An elliptical trainer with seven links and eight joints, and two degrees of freedom, can have its range of motion adjusted to match the user's stature, and the user can obtain different athletic effects. It allows for more adjustment than an elliptical trainer with one degree of freedom. In this paper, we refer to the present patents that specify the design requirements and constraints for an elliptical trainer. We then use Yan's creative mechanism design methods, which include generalized principles, number synthesis, specialization, and particularization, to obtain a practicable structure for an elliptical trainer with two degrees of freedom. We obtained five alternative kinds of mechanism. We chose one of them for a simulated kinematic analysis, and manufactured the prototype. This paper can serve not only as a reference for the development of fitness equipment but also as a teaching tool for creative mechanism design courses.
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35

Paul-Etienne, Vidal, Simon Cailhol, Frédéric Rotella, and Maurice Fadel. "Generic pulse width modulation model, based on generalized inverses and applied to voltage source inverters." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 38, no. 2 (2019): 845–61. http://dx.doi.org/10.1108/compel-07-2018-0291.

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Purpose This paper aims to develop a method for a unified model of pulse width modulation (PWM) voltage source inverters (VSI). This generic method, based on a common and easy-to-use carrier-based modulation, allows to generate the exhaustive solution set for a given PWM-VSI. Design/methodology/approach The use of the generalized inverse theory is developed to express the PWM solution set for the duty cycle. Indeed, the infinite number of PWM solutions is demonstrated. To explore this solution set, the unified model described exhibits degrees of freedom. The admissible margins to set the degree of freedom are highlighted. Some experimental results are presented. Findings It is demonstrated how the degree of freedom can be directly connected with efficiency indicators such as common mode voltage, inverter linearity and switching losses. The expression of the PWM solution set boundaries is clearly expressed. Research limitations/implications Further studies should explore how the degree of freedom can be connected with parameters associated with the current (and not the voltage as described in this paper). Practical implications The paper includes implications for the development of a more generic approach for PWM multilevel VSI. Originality/value This paper fulfils a mathematical frame to ease the expression of PWM scheme.
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36

Valencia, Angie, Oscar Aviles, and Mauricio Mauledoux. "Sliding Modes for a Manipulator Arm of 4 Degrees of Freedom." International Journal of Online Engineering (iJOE) 13, no. 10 (2017): 114. http://dx.doi.org/10.3991/ijoe.v13i10.7498.

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<p>The first step in designing a controller for a manipulating arm is to determine its configuration, which means, analyzing the main components that make up the mechanism. A manipulating arm is composed of joints, motors, sensors and other elements, which are linked to conform the different degrees of freedom (generalized coordinates: prismatic, rotational or a combination of both, which is presented as the most unusual), which allow the calculation of the dynamic model implemented to obtain the control specifications [1]. In this paper, the calculation of a controller by sliding modes for a manipulator arm with 4 rotational degrees of freedom will be done, showing the respective results and conclusions at the end.</p><p> </p>
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37

Xu, Hua, and Lu Feng Yang. "Mode-II Stress Intensity Factor by Triangular Williams Element with Generalized Degrees of Freedom." Applied Mechanics and Materials 204-208 (October 2012): 4391–95. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4391.

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A new triangular Williams element with generalized degrees of freedom (GDOFs) was proposed for analysis of stress intensity factor (SIF) of mode II crack. The singular region around the crack tip was evenly divided into a series of triangular elements, which could be approximated by the improved Williams series. On the basis of the principle, the displacement of local field must be compatible with that of the global one, so that the SIF at the crack tip can be directly evaluated by one of the undetermined constants of the Williams series. Three important parameters for the triangular Williams element, including the radial scale factor, the number of subelements and the terms of the Williams series, were discussed in detail. Numerical example shows that the triangular Williams elements with GDOFs can directly calculate the mode II SIF with high accuracy and efficiency.
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38

Karmakar, S., and M. K. Varanasi. "The Generalized Degrees of Freedom Region of the MIMO Interference Channel and Its Achievability." IEEE Transactions on Information Theory 58, no. 12 (2012): 7188–203. http://dx.doi.org/10.1109/tit.2012.2210191.

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39

Wong, Man-Yu, and Shuanglin Zhang. "Degrees of freedom and the likelihood ratio test for the generalized Behrens-Fisher problem." Journal of Applied Statistics 28, no. 8 (2001): 1067–74. http://dx.doi.org/10.1080/02664760120076715.

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40

Mohanty, Kaniska, and Mahesh K. Varanasi. "On the Generalized Degrees of Freedom of the MIMO Interference Channel With Delayed CSIT." IEEE Transactions on Information Theory 65, no. 5 (2019): 3261–77. http://dx.doi.org/10.1109/tit.2019.2891361.

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41

Xu, Hua, Quyang Wei, and Lufeng Yang. "Williams Element with Generalized Degrees of Freedom for Fracture Analysis of Multiple-Cracked Beam." IOP Conference Series: Materials Science and Engineering 250 (October 2017): 012059. http://dx.doi.org/10.1088/1757-899x/250/1/012059.

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42

TAKAHASHI, Kazunari, Yasushi NAKAUCHI, and Yasuchika MORI. "Two-Degree-of-Freedom Generalized Minimum Variance Control." Transactions of the Society of Instrument and Control Engineers 34, no. 6 (1998): 510–15. http://dx.doi.org/10.9746/sicetr1965.34.510.

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43

KLINKHAMER, F. R. "NEWTON'S GRAVITATIONAL COUPLING CONSTANT FROM A QUANTUM OF AREA." Modern Physics Letters A 26, no. 17 (2011): 1301–8. http://dx.doi.org/10.1142/s0217732311035729.

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A previous calculation of Newton's gravitational coupling constant G is generalized. This generalization makes it possible to have "atoms of two-dimensional space" with an integer dimension d atom of the internal space, where the case d atom = 1 is found to be excluded. Given the quantum of area l2, the final formula for G is inversely proportional to the logarithm of the integer d atom . The generalization used may be interpreted as a modification of the energy equipartition law of the microscopic degrees of freedom responsible for gravity, suggesting some form of long-range interaction between these degrees of freedom themselves.
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44

Nieto, J. A., P. A. Nieto-Marín, E. A. León, and E. García-Manzanárez. "Remarks on Plücker embedding and totally antisymmetric gauge fields." Modern Physics Letters A 35, no. 22 (2020): 2050184. http://dx.doi.org/10.1142/s0217732320501849.

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We make a number of comments about the way the Plücker embedding, which can be derived via the Grassmann-Plücker relations, can be associated to totally antisymmetric gauge fields. As a first step we discuss the case of the electromagnetic field strength, showing that the Plücker map implies both the true degrees of freedom of the electromagnetic field and the 1-brane (string) structure. The procedure is generalized in order to prove that the true degrees of freedom of a totally antisymmetric field and the p-brane structure are, in part, consequence of the Plücker coordinates.
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45

Griffith, Boyce E., and Sookkyung Lim. "Simulating an Elastic Ring with Bend and Twist by an Adaptive Generalized Immersed Boundary Method." Communications in Computational Physics 12, no. 2 (2012): 433–61. http://dx.doi.org/10.4208/cicp.190211.060811s.

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AbstractMany problems involving the interaction of an elastic structure and a viscous fluid can be solved by the immersed boundary (IB) method. In the IB approach to such problems, the elastic forces generated by the immersed structure are applied to the surrounding fluid, and the motion of the immersed structure is determined by the local motion of the fluid. Recently, the IB method has been extended to treat more general elasticity models that include both positional and rotational degrees of freedom. For such models, force and torque must both be applied to the fluid. The positional degrees of freedom of the immersed structure move according to the local linear velocity of the fluid, whereas the rotational degrees of freedom move according to the local angular velocity. This paper introduces a spatially adaptive, formally second-order accurate version of this generalized immersed boundary method. We use this adaptive scheme to simulate the dynamics of an elastic ring immersed in fluid. To describe the elasticity of the ring, we use an unconstrained version of Kirchhoff rod theory. We demonstrate empirically that our numerical scheme yields essentially second-order convergence rates when applied to such problems. We also study dynamical instabilities of such fluid-structure systems, and we compare numerical results produced by our method to classical analytic results from elastic rod theory.
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46

Xi, Ping, Yun-Long Jing, Wen-Dong Lü, and Xiang-Hua Zhai. "Statefinder diagnostic for a generalized Proca model." Modern Physics Letters A 32, no. 30 (2017): 1750160. http://dx.doi.org/10.1142/s0217732317501607.

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In this paper, we apply the statefinder diagnostic on the cosmology in the framework of the generalized Proca theories with derivative self-interactions possessing three propagating physical degrees of freedom. We discuss the evolving trajectories of the statefinder parameters with the parameter n of this model recently fitted as n = 0.254 and n = 0.16 by use of the current observational data and find that some typical characteristic of the evolution of statefinder parameters makes the model distinguishable between n = 0.254 case and n = 0.16 case and also from other dark energy models.
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47

Xu, Jinghua, Shuyou Zhang, Jianrong Tan, and Sheng Hongsheng. "Interruption performance design of variable freedom mechanism triggered by electro-mechanical-magnetic coupling." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 18 (2016): 3330–41. http://dx.doi.org/10.1177/0954406216646136.

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Coupling mechanism plays an important role in transmitting, motivating and actuating mechanical functions. However, it is difficult to obtain the transient dynamics performance of mechanism with variable degree of freedom precisely. Therefore, an interruption performance design method of variable freedom mechanism triggered by electro-magneto-thermo coupling is put forward. The Euler-Lagrange partial differential equations of variable freedom mechanism are built using generalized coordinates. Degree of freedom reduction rules are proposed to merge transformation or rotation constraints and obtain the total degrees of freedom of variable freedom mechanism at each transient status. Bivariate interpolating is employed to determine the electro-mechanical-magnetic coupled Lorentz force. Dynamics performance is simulated by iteration of linear algebraic equations using implicit predictor-corrector integration method. The design parameters such as stiffness and pre-tightening force of trigger spring, permissible dimension deviations and hole-shaft fit tolerance are determined and improved using the sensitivity analysis of simulation results. The pneumatic mechanical endurance and thermal infrared temperature rise experiments are accomplished to determine the infrared radiation energy distribution and transient working status of components. It gives an auxiliary thermo-visual approach for transient performance design of coupling mechanism.
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48

Olive, Keith A., and David Thomas. "Generalized limits to the number of light particle degrees of freedom from big bang nucleosynthesis." Astroparticle Physics 11, no. 4 (1999): 403–11. http://dx.doi.org/10.1016/s0927-6505(99)00009-2.

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49

Li, Q. S., L. F. Yang, X. D. Ou, G. Q. Li, and D. K. Liu. "The quintic finite element and finite strip with generalized degrees of freedom in structural analysis." International Journal of Solids and Structures 38, no. 30-31 (2001): 5355–72. http://dx.doi.org/10.1016/s0020-7683(00)00344-9.

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50

Gholami Davoodi, Arash, and Syed Ali Jafar. "Generalized Degrees of Freedom of the Symmetric $K$ User Interference Channel Under Finite Precision CSIT." IEEE Transactions on Information Theory 63, no. 10 (2017): 6561–72. http://dx.doi.org/10.1109/tit.2017.2736560.

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