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Journal articles on the topic 'Non-linear geometry'

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Author: Grafiati
Published: 8 June 2024

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1

Mourad, J. "Linear connections in non-commutative geometry." Classical and Quantum Gravity 12, no. 4 (April 1, 1995): 965–74. http://dx.doi.org/10.1088/0264-9381/12/4/007.

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2

BANKS, S. P. "On non-linear systems and algebraic geometry." International Journal of Control 42, no. 2 (August 1985): 333–52. http://dx.doi.org/10.1080/00207178508933367.

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3

Panchuk, K. L., and T. M. Myasoyedova. "The surface of non-linear rotation." Omsk Scientific Bulletin, no. 188 (2023): 5–12. http://dx.doi.org/10.25206/1813-8225-2023-188-5-12.

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The paper considers a geometric scheme, a mathematical model and an algorithm for shaping a non-linear rotation surface. It is known that in Euclidean geometry and mechanics the transformation of rotation is linear, while distance and angle are its invariants. The authors proposed a geometric scheme of non-linear rotation, in which the axis of rotation is a smooth spatial curve and the object of rotation is a smooth line. Several propositions, a lemma and a theorem are proved, which allow one to form the initial data in the problem of nonlinear rotation, the solution of which is the parametric equations of smooth surfaces. The research results make it possible to expand the variety of cyclic surfaces in the existing classification of analytic surfaces. They can also be useful in the creation of CAD, which provides for the design of surface forms of products for mechanical engineering, construction, architecture and other practical areas based on cyclic surfaces.
4

Ettinger, B., N. Sarig, and Y. Yomdin. "Linear versus Non-Linear Acquisition of Step-Functions." Journal of Geometric Analysis 18, no. 2 (March 4, 2008): 369–99. http://dx.doi.org/10.1007/s12220-008-9016-0.

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5

Samovol, V. S. "Power Geometry of a Non-Linear Differential Equation." Moscow Mathematical Journal 18, no. 2 (2018): 387–402. http://dx.doi.org/10.17323/1609-4514-2018-18-2-387-402.

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6

Destuynder, Philippe, and Michel Salaün. "Approximation of shell geometry for non-linear analysis." Computer Methods in Applied Mechanics and Engineering 152, no. 3-4 (January 1998): 393–430. http://dx.doi.org/10.1016/s0045-7825(97)00040-6.

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7

Nojima, Kôichirô. "Non-Linear Sigma Model in Semi-Infinite Geometry." Journal of the Physical Society of Japan 58, no. 5 (May 15, 1989): 1862–63. http://dx.doi.org/10.1143/jpsj.58.1862.

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8

Ragozini, Giancarlo. "A computational geometry approach for linear and non linear discriminant analysis." Computational Statistics 15, no. 1 (March 2000): 115–25. http://dx.doi.org/10.1007/s001800050042.

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9

Chu, Jianchun, and Nicholas McCleerey. "Fully non-linear degenerate elliptic equations in complex geometry." Journal of Functional Analysis 281, no. 9 (November 2021): 109176. http://dx.doi.org/10.1016/j.jfa.2021.109176.

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10

Brooke, John M., and David Moss. "Non-linear dynamos in torus geometry: transition to chaos." Monthly Notices of the Royal Astronomical Society 266, no. 3 (February 1994): 733–39. http://dx.doi.org/10.1093/mnras/266.3.733.

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11

Mazzeo, Rafe. "Book Review: Non-linear elliptic equations in conformal geometry." Bulletin of the American Mathematical Society 44, no. 02 (January 5, 2007): 323–31. http://dx.doi.org/10.1090/s0273-0979-07-01136-6.

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12

Leichtweiss, Kurt. "Linear combinations of convex hypersurfaces in non-Euclidean geometry." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 53, no. 1 (December 24, 2011): 77–88. http://dx.doi.org/10.1007/s13366-011-0080-4.

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13

Greb, U., and M. G. Rusbridge. "Non-linear interactions of drift-waves in quadrupole geometry." Plasma Physics and Controlled Fusion 30, no. 5 (May 1, 1988): 551–74. http://dx.doi.org/10.1088/0741-3335/30/5/006.

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14

Godefroy, G., G. Lancien, and V. Zizler. "The non-linear geometry of Banach spaces after Nigel Kalton." Rocky Mountain Journal of Mathematics 44, no. 5 (October 2014): 1529–83. http://dx.doi.org/10.1216/rmj-2014-44-5-1529.

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15

Grisaru, M. T., M. Massar, A. Sevrin, and J. Troost. "The quantum geometry of N = (2,2) non-linear σ-models." Physics Letters B 412, no. 1-2 (October 1997): 53–58. http://dx.doi.org/10.1016/s0370-2693(97)01053-8.

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16

Bergliaffa, Santiago E. Perez. "EFFECTIVE GEOMETRY IN ASTROPHYSICS." International Journal of Modern Physics D 13, no. 07 (August 2004): 1469–76. http://dx.doi.org/10.1142/s0218271804005705.

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The effective metric is introduced by means of two examples (non-linear electromagnetism and hydrodynamics), along with applications in Astrophysics. A sketch of the generality of the effect is also given.
17

AVRAMIDI, IVAN G. "DIRAC OPERATOR IN MATRIX GEOMETRY." International Journal of Geometric Methods in Modern Physics 02, no. 02 (April 2005): 227–64. http://dx.doi.org/10.1142/s0219887805000636.

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We review the construction of the Dirac operator and its properties in Riemannian geometry, and show how the asymptotic expansion of the trace of the heat kernel determines the spectral invariants of the Dirac operator and its index. We also point out that the Einstein–Hilbert functional can be obtained as a linear combination of the first two spectral invariants of the Dirac operator. Next, we report on our previous attempts to generalize the notion of the Dirac operator to the case of Matrix Geometry, where, instead of a Riemannian metric there is a matrix valued self-adjoint symmetric two-tensor that plays a role of a "non-commutative" metric. We construct invariant first-order and second-order self-adjoint elliptic partial differential operators, which can be called "non-commutative" Dirac operators and non-commutative Laplace operators. We construct the corresponding heat kernel for the non-commutative Laplace type operator and compute its first two spectral invariants. A linear combination of these two spectral invariants gives a functional that can be considered as a non-commutative generalization of the Einstein–Hilbert action.
18

GEGENBERG, J., P. F. KELLY, R. B. MANN, R. MCARTHUR, and D. VINCENT. "REINTERPRETATION OF THE NON-LINEAR SIGMA MODEL WITH TORSION." Modern Physics Letters A 03, no. 18 (December 1988): 1791–96. http://dx.doi.org/10.1142/s0217732388002154.

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It is shown that the bosonic non-linear sigma model with torsion may be reinterpreted as a non-linear sigma model formulated on an algebraically extended two-dimensional worldsheet. The torsion term arises naturally as a consequence of the extended geometry. The two models, while locally equivalent, have distinct global features.
19

Cheng, Ping-chin, and Wayne Y. Cheng. "Artifacts in Biological Confocal and Non-linear Microscopy." Microscopy and Microanalysis 7, S2 (August 2001): 1018–19. http://dx.doi.org/10.1017/s1431927600031160.

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Conventional histological sectioning and staining techniques produce tissue sections, by large, independent from each other (e.g. the staining intensity depends on the total stainable substance within the section, but not influence by the section above or below it). Although the hardness of the structure in a given section may influence the quality of the following sections, never the less, each physical section can be generally regarded as an independent sampling event. However, the image intensity and relative contrast in an optical section obtained from confocal or non-linear optical microscopy varies depending on the position of the section where it was obtained. Therefore, in sampling terms, optical sections are dependent sampling events. Artifacts caused by the geometry and optical properties (e.g. absorption, scattering, refractive index) of objects within a specimen can interfere the interpretation of the result and hinder the usefulness of three-dimension reconstruction. Figure 1 demonstrates intensity variation in confocal and multi-photon micrographs due to the geometry of the specimen. Depends on the absorption coefficient and path length of the illumination and the fluorescecent light, a solid spherical object produced a 3D data set, when reconstructed, resemble an inverted Chinese rice bowl. Figure 2 shows a 3D reconstruction of an Arabidopsis thaliana mesophyll protoplast; note only half of the spherical cell facing the illumination is imaged as shown in the cut-off view in FIG 3.
20

Coles, R. A., and G. Papadopoulos. "The geometry of the one-dimensional supersymmetric non-linear sigma models." Classical and Quantum Gravity 7, no. 3 (March 1, 1990): 427–38. http://dx.doi.org/10.1088/0264-9381/7/3/016.

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21

Ruschin-Rimini, Noa, Irad Ben-Gal, and Oded Maimon. "Fractal geometry statistical process control for non-linear pattern-based processes." IIE Transactions 45, no. 4 (April 2013): 355–73. http://dx.doi.org/10.1080/0740817x.2012.662420.

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22

Venkateshan, S. P., and V. R. Rao. "Approximate solution of non-linear transient heat conduction in cylindrical geometry." Wärme- und Stoffübertragung 26, no. 2 (March 1991): 97–102. http://dx.doi.org/10.1007/bf01590242.

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23

Ricci Maccarini, Roberto, Anna Saetta, and Renato Vitaliani. "A non-linear finite element formulation for shells of arbitrary geometry." Computer Methods in Applied Mechanics and Engineering 190, no. 37-38 (June 2001): 4967–86. http://dx.doi.org/10.1016/s0045-7825(00)00358-3.

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24

Ghorai, Debabrata, and Sunandan Gangopadhyay. "Non-linear effects on the holographic free energy and thermodynamic geometry." EPL (Europhysics Letters) 118, no. 3 (May 1, 2017): 31001. http://dx.doi.org/10.1209/0295-5075/118/31001.

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25

Nagy, P. T. "On non-linear covariant derivative in the General Geometry of Paths." Publicationes Mathematicae Debrecen 22, no. 1-2 (July 1, 2022): 115–22. http://dx.doi.org/10.5486/pmd.1975.22.1-2.15.

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26

Courty, Nicolas, Xing Gong, Jimmy Vandel, and Thomas Burger. "SAGA: sparse and geometry-aware non-negative matrix factorization through non-linear local embedding." Machine Learning 97, no. 1-2 (August 13, 2014): 205–26. http://dx.doi.org/10.1007/s10994-014-5463-y.

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27

Schulte, J. A. "Wavelet analysis for non-stationary, non-linear time series." Nonlinear Processes in Geophysics Discussions 2, no. 6 (December 21, 2015): 1705–37. http://dx.doi.org/10.5194/npgd-2-1705-2015.

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Abstract. Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the Quasi-biennial Oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysis were addressed by controlling the false discovery rate. A new local autobicoherence spectrum facilitated the detection of local nonlinearities and the quantification of cycle geometry. The local autobicoherence spectrum of the QBO time series showed that the QBO time series contained a mode with a period of 28 months that was phase-coupled to a harmonic with a period of 14 months. An additional nonlinearly interacting triad was found among modes with periods of 10, 16, 26 months. Local biphase spectra determined that the nonlinear interactions were not quadratic and that the effect of the nonlinearities was to produce non-smoothly varying oscillations. The oscillations were found to be skewed so that negative QBO regimes were preferred, and also asymmetric in the sense that phase transitions between the easterly and westerly phases occurred more rapidly than those from westerly to easterly regimes.
28

AÇIKTEPE, T., K. G. AKDENIZ, A. O. BARUT, and J. KALAYCI. "CONFORMALLY COVARIANT COUPLED NON-LINEAR FIELD THEORY ON THE HYPERCONE: VACUUM SOLUTIONS AND QUANTIZATION OF NORMAL MODES." Modern Physics Letters A 03, no. 02 (January 1988): 161–65. http://dx.doi.org/10.1142/s0217732388000192.

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For the conformally covariant coupled non-linear spinor-scalar fields of the σ -model type we show that the non-trivial vacuum instanton solutions have a geometric meaning as constant spinors on the five-dimensional hypercone. The quantized fields around these solutions correspond to the normal modes of the hypercone. A connection is thus established between field theory, particle spectrum of the fields and quantized excitations of a geometry (the hypercone).
29

Lelyukhin, Vladimir Egorovich, and Olga Valeryevna Kolesnikova. "Geometry of real objects in shipbuilding and ship repair." Vestnik of Astrakhan State Technical University. Series: Marine engineering and technologies 2020, no. 1 (February 17, 2020): 31–44. http://dx.doi.org/10.24143/2073-1574-2020-1-31-44.

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The article considers the modern engineering practice of designing and manufacturing that uses various analytical and graphic forms representing geometric objects. Both of these forms are characterized by the presence of two problems in terms of production practice: 1 - tools of modern geometry cannot operate with non-ideal forms and configurations of material objects; 2 - lack of methods and tools for describing patterns of generating geometric objects, from production lines to the structure that characterizes the relative location of surfaces. The generalized provisions of the geometry of non-ideal objects theoretically justified for formal synthesis and their elements have been presented, which avoids problems of geometric configuration in the practice of designing and developing manufacturing technologies in shipbuilding and ship repair. A special toolkit based on discrete mathematics is proposed for the formal description of the geometric configuration of non-ideal objects. The principles of geometry of real objects describe the structural-parametric representation of objects in a six-dimensional space that is defined by linear and angular vectors. The concepts of linear and angular vectors are analyzed. It has been stated that the presence of an angular vector simplifies the perception and makes easier calculating the processes of geometric transformations. A geometrical object refers to a closed subspace bounded by a single surface, a set of mating or intersecting surfaces. The examples of the real plane deviations from its reference, location of the planes for creating the ideal geometric configuration, variants of real images, forming the basis for six-dimensional space, structure of geometric configurations have been illustrated. It has been found that any specific part acting as a geometric object can be represented by a set of surfaces and the structure of their relationships, which contributes to the correctness of its manufacture. The use of six-dimensional space allows to describe the spatial geometric configurations of parts of various mechanisms with mathematical accuracy.
30

Maißer, P. "Multi-body dynamics and electromechanics: From a differential-geometric point of view." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 219, no. 2 (June 1, 2005): 147–58. http://dx.doi.org/10.1243/146441905x34135.

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Mechanics is the origin of physics. Almost any physical theory like electrodynamics stems from mechanical explanations. The mathematical-geometric considerations in mechanics serve as a prototype for other physical theories. Consequently, developments in modern physics in turn have a feedback to mechanics in terms of its representation. The laws of nature can be expressed as differential equations. The fact that these equations can be solved by average computers has led most engineers and many mathematical physicists to neglect geometrical aspects for solving and better understanding their problems. The intimate relation between geometry and analysis led to the differential geometry, which is a valuable tool for a better understanding in many physical disciplines like classical mechanics, electrodynamics, and nowadays in mechatronics. It has been the development of the theory of relativity that revealed the paramount importance of the differential geometry. Many problems in research and development can be studied by differential-geometric methods. Modern non-linear control theories, for instance, are entirely based on the differential geometry. This paper addresses some aspects in mathematical modelling of multi-body and electromechanical systems. The motivation for this research arises from applications of linear induction machines in modern transport technologies.
31

Varga, Rubem M. F., Augusto V. Cardona, Marco T. Vilhena, and Ricardo C. Barros. "On the decomposition method applied to linear and non-linear discrete ordinates problems in slab geometry." Progress in Nuclear Energy 42, no. 4 (January 2003): 439–56. http://dx.doi.org/10.1016/s0149-1970(03)90014-x.

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32

Frank, Philipp, Reimar Leike, and Torsten A. Enßlin. "Geometric Variational Inference." Entropy 23, no. 7 (July 2, 2021): 853. http://dx.doi.org/10.3390/e23070853.

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Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) techniques. While MCMC methods that utilize the geometric properties of continuous probability distributions to increase their efficiency have been proposed, VI methods rarely use the geometry. This work aims to fill this gap and proposes geometric Variational Inference (geoVI), a method based on Riemannian geometry and the Fisher information metric. It is used to construct a coordinate transformation that relates the Riemannian manifold associated with the metric to Euclidean space. The distribution, expressed in the coordinate system induced by the transformation, takes a particularly simple form that allows for an accurate variational approximation by a normal distribution. Furthermore, the algorithmic structure allows for an efficient implementation of geoVI which is demonstrated on multiple examples, ranging from low-dimensional illustrative ones to non-linear, hierarchical Bayesian inverse problems in thousands of dimensions.
33

Aulitto, Alessia, Avraham Hirschberg, Ines Lopez Arteaga, and Esmée L. R. H. Buijssen. "Effect of slit length on linear and non-linear acoustic transfer impedance of a micro-slit plate." Acta Acustica 6 (2022): 6. http://dx.doi.org/10.1051/aacus/2021059.

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The effect of the slit length on the acoustic transfer impedance of micro-slit plates (MSPs) is investigated in the linear and non-linear regime for a specific slit geometry. This geometry is inspired by slits obtained by cutting and bending the plate. MSPs are plates with arrays of slit-shaped perforations, with the width of the order of the acoustic viscous boundary layer thickness. Impedance tube measurements on two accurately manufactured plates are compared to numerical solution of the Linearized Navier-Stokes equations and to analytical limits. The impedance of the plate is obtained by the impedance of a single slit divided by the plate porosity. The resistance of a slit is independent on the slit length and on the plate porosity. In the linear regime the resistance is accurately predicted by a two-dimensional numerical model. In the non-linear regime, the resistance is strongly dependent on the amplitude of the acoustic waves. The inertance of the slit is weakly dependent on the slit length and on the plate porosity, for low and moderate amplitudes. For high amplitudes, a complicated amplitude dependency of the inertia of short slits is found. One expects that most of the conclusions obtained can be generalised to other slit geometries.
34

Casquilho, J. P., and J. L. Figueirinhas. "Linear analysis of transient pattern evolution in the non-Freedericksz twist geometry." Liquid Crystals 29, no. 1 (January 2002): 127–32. http://dx.doi.org/10.1080/02678290110093750.

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35

Schoen, R. M. "A report on some recent progress on non-linear problems in geometry." Surveys in Differential Geometry 1, no. 1 (1990): 201–41. http://dx.doi.org/10.4310/sdg.1990.v1.n1.a4.

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36

Mohammedi, N. "On the geometry of classically integrable two-dimensional non-linear sigma models." Nuclear Physics B 839, no. 3 (November 2010): 420–45. http://dx.doi.org/10.1016/j.nuclphysb.2010.06.005.

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37

Love, J. S., and M. J. Tait. "Non-linear multimodal model for tuned liquid dampers of arbitrary tank geometry." International Journal of Non-Linear Mechanics 46, no. 8 (October 2011): 1065–75. http://dx.doi.org/10.1016/j.ijnonlinmec.2011.04.028.

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38

Zhao, D., N. Wehres, H. Linnartz, and W. Ubachs. "Electronic spectra and molecular geometry of the non-linear carbon chain C9H3." Chemical Physics Letters 501, no. 4-6 (January 2011): 232–37. http://dx.doi.org/10.1016/j.cplett.2010.11.048.

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39

Howe, P. S., and G. Papadopoulos. "Further remarks on the geometry of two-dimensional non-linear σ-models." Classical and Quantum Gravity 5, no. 12 (December 1, 1988): 1647–61. http://dx.doi.org/10.1088/0264-9381/5/12/014.

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40

Tapia-McClung, Horacio, and Niels Grønbech-Jensen. "Non-iterative and exact method for constraining particles in a linear geometry." Journal of Polymer Science Part B: Polymer Physics 43, no. 8 (March 7, 2005): 911–16. http://dx.doi.org/10.1002/polb.20383.

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41

Bae, Ji-Hoon, Kyung-Tae Kim, Joon-Ho Lee, Hyo-Tae Kim, and Jae-Ick Choi. "Design of steerable non-uniform linear array geometry for side-lobe reduction." Microwave and Optical Technology Letters 36, no. 5 (February 5, 2003): 363–67. http://dx.doi.org/10.1002/mop.10765.

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42

Beji, S., and B. Barlas. "Boundary-fitted non-linear dispersive wave model for regions of arbitrary geometry." International Journal for Numerical Methods in Fluids 45, no. 6 (May 25, 2004): 643–57. http://dx.doi.org/10.1002/fld.721.

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43

Facchinetti, G., S. Giove, and N. Pacchiarotti. "Optimisation of a non linear fuzzy function." Soft Computing - A Fusion of Foundations, Methodologies and Applications 6, no. 6 (September 1, 2002): 476–80. http://dx.doi.org/10.1007/s00500-002-0164-z.

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44

Wanas, M. I., Samah A. Ammar, and Shymaa A. Refaey. "Teleparallel gravity with non-vanishing curvature." Canadian Journal of Physics 96, no. 12 (December 2018): 1373–83. http://dx.doi.org/10.1139/cjp-2017-0997.

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Guided by the rules of Einstein’s geometrization philosophy, a pure geometric field theory is constructed. The Lagrangian used to derive the field equations of the theory is a curvature scalar of a version of absolute parallelism (AP) geometry known in the literature as the parameterized absolute parallelism (PAP) geometry. The linear connection of this version has simultaneously non-vanishing curvature and torsion. Analysis of the theory obtained shows clearly that it is a pure gravity theory. The theory is a teleparallel one, since the building blocks of both PAP and AP geometries are the same. It is shown analytically that the theory has a trivial version in the AP-geometry, if gravity is attributed to curvature not to torsion. In the case of spherical symmetry, solutions of the field equations give rise to the Schwarzschild exterior field. The theory depends on two principles: covariance and unification. The weak equivalence principle is satisfied under a certain condition. The work preserves Einstein’s main idea that gravity is just space–time curvature, although it is not a metric theory. It is shown that the theory reduces to vacuum general relativity upon taking the parameter of the geometry b = 0.
45

Kabutey, Abraham, David Herak, Himsar Ambarita, and Riswanti Sigalingging. "Modeling of Linear and Non-linear Compression Processes of Sunflower Bulk Oilseeds." Energies 12, no. 15 (August 3, 2019): 2999. http://dx.doi.org/10.3390/en12152999.

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The present study aimed at describing the experimental and theoretical force-deformation curves of sunflower bulk oilseeds at varying initial pressing heights and vessel diameters as well as determining the theoretical pressure and energy along the screw press FL 200 pressing chambers. The design of efficient oil expression systems for industry and small-scale application remains a major challenge to engineers and researchers. In attempting to solve the problem, it is important to understand the linear compression process and to transfer the knowledge to the industry involving mechanical screw presses. The universal compression testing machine at a preset load of 200 kN and a speed of 5 mm·min−1, tangent curve model and the screw press FL 200 geometry parameters were applied. The obtained results of pressure and energy along the screw pressing chambers (1–7) ranged from 0.31 to 101.653 MPa and 12.616 to 1231.228 J. Applying the tangent model at n = 1 and n = 2, the cumulative pressure decreased with increasing vessel diameters while energy increased. The study provides useful information for the analysis of other bulk oilseeds and optimizing the processing parameters of screw press FL 200 and the design and development of new oil presses.
46

Alahmadi, Adel N., Husain S. Alhazmi, Hatoon Shoaib, David G. Glynn, Saeed Ur Rehman, and Patrick Solé. "Connections between Linear Complementary Dual Codes, Permanents and Geometry." Mathematics 11, no. 12 (June 20, 2023): 2774. http://dx.doi.org/10.3390/math11122774.

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Linear codes with complementary duals, or LCD codes, have recently been applied to side-channel and fault injection attack-resistant cryptographic countermeasures. We explain that over characteristic two fields, they exist whenever the permanent of any generator matrix is non-zero. Alternatively, in the binary case, the matroid represented by the columns of the matrix has an odd number of bases. We explain how Grassmannian varieties as well as linear and quadratic complexes are connected with LCD codes. Accessing the classification of polarities, we relate the binary LCD codes of dimension k to the two kinds of symmetric non-singular binary matrices, to certain truncated Reed–Muller codes, and to the geometric codes of planes in finite projective space via the self-orthogonal codes of dimension k.
47

Thiruthummal, Abhiram Anand, and Eun-jin Kim. "Monte Carlo Simulation of Stochastic Differential Equation to Study Information Geometry." Entropy 24, no. 8 (August 12, 2022): 1113. http://dx.doi.org/10.3390/e24081113.

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Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker–Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and to study Information Geometry using Monte Carlo (MC) simulation of SDEs. Specifically, we develop a new MC SDE method to overcome the challenges in calculating a time-dependent PDF and information geometric diagnostics and to speed up simulations by utilizing GPU computing. Using MC SDE simulations, we reproduce Information Geometric scaling relations found from the Fokker–Planck method for the case of a stochastic process with linear and cubic damping terms. We showcase the advantage of MC SDE simulation over FPE solvers by calculating unequal time joint PDFs. For the linear process with a linear damping force, joint PDF is found to be a Gaussian. In contrast, for the cubic process with a cubic damping force, joint PDF exhibits a bimodal structure, even in a stationary state. This suggests a finite memory time induced by a nonlinear force. Furthermore, several power-law scalings in the characteristics of bimodal PDFs are identified and investigated.
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Pantò, Bartolomeo, Marialaura Malena, and Gianmarco de Felice. "Non-Linear Modeling of Masonry Arches Strengthened with FRCM." Key Engineering Materials 747 (July 2017): 93–100. http://dx.doi.org/10.4028/www.scientific.net/kem.747.93.

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Recent seismic events, such as the Central Italy (2016), the Emilia (2012) and L’Aquila (2009) earthquake, have demonstrated the high vulnerability of cultural heritage represented by historical and monumental buildings. These structures are often characterized by the presence of elements with a curved geometry such as arches and vaults, which interact with the vertical elements (walls or columns) during the earthquake motion, producing a significant effect on the seismic response of the entire structure. Aiming at the reduction of the seismic vulnerability of curved masonry elements, several techniques of reinforcing based on composite fiber materials, have been recently developed and widely investigated by means of experimental tests and numerical simulations. The using of fiber reinforced systems, applied through cementitious mortar (FRCM), is becoming a very common technique of retrofitting for historical and monumental masonry buildings. This technique, if compared to the using of fiber polymeric materials (FRP), is more compatible with the mechanical properties of the masonry and more appropriate with the preservation needs of cultural heritage, associated to the historical constructions. A discrete macro-modeling approach, already available in the literature for modeling masonry structures with plane and curved geometry, is here employed to predict the non-linear behaviour of masonry arches strengthened with FRCM. In that approach the reinforcement is explicitly modeled by using a rigid plate, while the interaction between the reinforcement and the masonry support is governed by a discrete zero thickness interface. In this paper the interfacial behavior is updated with a more sophisticated bond-slip constitutive law specifically conceived for FRCM reinforcement within the framework of fracture mechanics; in particular the proposed calibration takes into account both the pure opening mode (mode I) and the in plane shear mode (mode II). The obtained numerical results are compared with an analytical closed form solution of the problem and validated by mean of experimental tests on prototypes, available in the literature.
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Asseo, E., G. Pelletier, and H. Sol. "A Non-Linear Emission Mechanism for Pulsar Radio Radiation." International Astronomical Union Colloquium 128 (1992): 322–25. http://dx.doi.org/10.1017/s0002731600155428.

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Among the various plasma instabilities which could be responsible for coherent pulsar radio emission, we investigate the two-stream instability, first introduced by Ruderman and Sutherland (1975) in order to account for the physical situation expected in the environment of neutron stars. They describe how, in a polar cap model, pair creation arises and leads to the formation of a very energetic beam of e+ (and/or e−) and of an e−e+ plasma, both with relativistic bulk motion along the bundle of dipolar magnetic field lines. The study of their interaction is limited to the cone of open B lines, a site which provides a natural geometry for the radio emission zone, observed as core and/or conal emission by Lyne and Manchester (1988) and Rankin (1983, 1986, 1990).
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AWADA, M. A. "GEOMETRY OF QUANTUM LOOPS AND KNOT THEORY." Modern Physics Letters A 04, no. 24 (November 20, 1989): 2409–16. http://dx.doi.org/10.1142/s0217732389002690.

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Starting from the linear quantum loop equation of non-abelian Chern-Simons theory in three dimensions, we prove that it yields precisely and to all loop orders in perturbation theory the exact skein relation satisfied by the Jones polynomial in knot theory.
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