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Journal articles on the topic 'Transformation invariance'

Author: Grafiati

Published: 10 December 2022

Last updated: 25 July 2025

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1

Wagner, Jenny. "Generalised model-independent characterisation of strong gravitational lenses." Astronomy & Astrophysics 620 (December 2018): A86. http://dx.doi.org/10.1051/0004-6361/201834218.

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Based on the standard gravitational lensing formalism with its effective, projected lensing potential in a given background cosmology, we investigated under which transformations of the source position and of the deflection angle the observable properties of the multiple images remain invariant. These observable properties are time delay differences, the relative image positions, relative shapes, and magnification ratios. As they only constrain local lens properties, we derive general, local invariance transformations in the areas covered by the multiple images. We show that the known global i

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DAS, ASHOK, and MARCELO HOTT. "CHIRAL INVARIANCE OF MASSIVE FERMIONS." Modern Physics Letters A 09, no. 24 (1994): 2217–25. http://dx.doi.org/10.1142/s0217732394002070.

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We show that a massive fermion theory, while not invariant under the conventional chiral transformation, is invariant under a m-deformed chiral transformation. These transformations and the associated conserved charges are nonlocal but reduce to the usual transformations and charges when m=0. The m-deformed charges commute with helicity and satisfy the conventional chiral algebra.

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3

Miao, Xu, and Rajesh P. N. Rao. "Learning the Lie Groups of Visual Invariance." Neural Computation 19, no. 10 (2007): 2665–93. http://dx.doi.org/10.1162/neco.2007.19.10.2665.

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A fundamental problem in biological and machine vision is visual invariance: How are objects perceived to be the same despite transformations such as translations, rotations, and scaling? In this letter, we describe a new, unsupervised approach to learning invariances based on Lie group theory. Unlike traditional approaches that sacrifice information about transformations to achieve invariance, the Lie group approach explicitly models the effects of transformations in images. As a result, estimates of transformations are available for other purposes, such as pose estimation and visuomotor cont

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CHIMENTO, LUIS P., and WINFRIED ZIMDAHL. "DUALITY INVARIANCE AND COSMOLOGICAL DYNAMICS." International Journal of Modern Physics D 17, no. 12 (2008): 2229–54. http://dx.doi.org/10.1142/s0218271808013820.

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A duality transformation that interrelates expanding and contracting cosmological models is shown to single out a duality invariant, interacting two-component description of any irrotational, geodesic and shear-free cosmic medium with vanishing three-curvature scalar. We have applied this feature to a system of matter and radiation, to a mixture of dark matter and dark energy, to minimal and conformal scalar fields, and to an enlarged Chaplygin gas model of the cosmic substratum. We have extended the concept of duality transformations to cosmological perturbations and demonstrated the invarian

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HO, S. H. "ALTERNATIVE CONFORMAL QUANTUM MECHANICS." International Journal of Modern Physics A 26, no. 16 (2011): 2735–42. http://dx.doi.org/10.1142/s0217751x11053547.

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We investigate a one-dimensional quantum mechanical model, which is invariant under translations and dilations but does not respect the conventional conformal invariance. We describe the possibility of modifying the conventional conformal transformation such that a scale invariant theory is also invariant under this new conformal transformation.

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Perju, Veaceslav, and Vladislav Cojuhari. "CENTRAL AND LOGARITHMIC CENTRAL IMAGE CHORD TRANSFORMATIONS FOR INVARIANT OBJECT RECOGNITION." Journal of Engineering Science XXVIII (1) (March 15, 2021): 38–46. https://doi.org/10.52326/jes.utm.2021.28(1).03.

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Pattern descriptors invariant to rotation, scaling, and translation represents an important direction in the elaboration of the real time object recognition systems. In this article, the new kinds of object descriptors based on chord transformation are presented. There are described new methods of image presentation - Central and Logarithmic Central Image Chord Transformations (CICT and LCICT). It is shown that the CICT operation makes it possible to achieve invariance to object rotation. In the case of implementation of the LCICT transformation, invariance to changes in the rotation and scale

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Salosin, Evgeny Georgievich. "LORENTZ TRANSFORMATION CHANGE." Globus 8, no. 1(66) (2022): 36–40. http://dx.doi.org/10.52013/2658-5197-66-1-9.

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For relativistic velocities, Galileo’s principle of addition of four-dimensional velocities is valid, and not the Lorentz transformation. In this case, it is impossible to write down the law of conservation of energy with Newton’s potential using the Lorentz transformation. And with the proposed transformation it is possible. In addition, the invariance of the wave equation with respect to the Galilean transformation with four-dimensional velocity is obtained. The GR equation is also invariant under the Galileo transformations of the four-vector. This transformation is a more general case of i

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King, J. R. "Local transformations between some nonlinear diffusion equations." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 33, no. 3 (1992): 321–49. http://dx.doi.org/10.1017/s0334270000007074.

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AbstractWe derive local transformations mapping radially symmetric nonlinear diffusion equations with power law or exponential diffusivities into themselves or into other equations of a similar form. Both discrete and continuous transformations are considered. For the cases in which a continuous transformation exists, many additional forms of group-invariant solution may be constructed; some of these solutions may be written in closed form. Related invariance properties of some multidimensional diffusion equations are also exploited.

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9

Földiák, Peter. "Learning Invariance from Transformation Sequences." Neural Computation 3, no. 2 (1991): 194–200. http://dx.doi.org/10.1162/neco.1991.3.2.194.

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The visual system can reliably identify objects even when the retinal image is transformed considerably by commonly occurring changes in the environment. A local learning rule is proposed, which allows a network to learn to generalize across such transformations. During the learning phase, the network is exposed to temporal sequences of patterns undergoing the transformation. An application of the algorithm is presented in which the network learns invariance to shift in retinal position. Such a principle may be involved in the development of the characteristic shift invariance property of comp

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10

HAMMOND, RICHARD T. "THE NECESSITY OF TORSION IN GRAVITY." International Journal of Modern Physics D 19, no. 14 (2010): 2413–16. http://dx.doi.org/10.1142/s0218271810018554.

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It is shown that torsion is required for a complete theory of graviation, and that without it, the equations of gravitation violate fundamental laws. In the first case, we are reminded that, in the absence of external forces, the correct conservation law of total angular momentum arises only if torsion, whose origin is intrinsic spin, is included into gravitation. The second case considers the "mass reversal" transformation. It has been known that under a global chiral transformation and "mass to negative mass" transformation, the Dirac equation is invariant. But global transformations violate

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11

Alsing, P. M., and G. Milburn. "Lorentz Invariance of Entanglement." Quantum Information and Computation 2, no. 6 (2002): 487–512. http://dx.doi.org/10.26421/qic2.6-4.

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We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipar

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12

Frank, Steven A., and Jordi Bascompte. "Invariance in ecological pattern." F1000Research 8 (December 12, 2019): 2093. http://dx.doi.org/10.12688/f1000research.21586.1.

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Background: The abundance of different species in a community often follows the log series distribution. Other ecological patterns also have simple forms. Why does the complexity and variability of ecological systems reduce to such simplicity? Common answers include maximum entropy, neutrality, and convergent outcome from different underlying biological processes. Methods: This article proposes a more general answer based on the concept of invariance, the property by which a pattern remains the same after transformation. Invariance has a long tradition in physics. For example, general relativi

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Organista, José Orlando, Marek Nowakowski, and H. C. Rosu. "Shape invariance through Crum transformation." Journal of Mathematical Physics 47, no. 12 (2006): 122104. http://dx.doi.org/10.1063/1.2397556.

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14

Eichhorn, Ralf, Stefan J. Linz, and Peter Hänggi. "Transformation invariance of Lyapunov exponents." Chaos, Solitons & Fractals 12, no. 8 (2001): 1377–83. http://dx.doi.org/10.1016/s0960-0779(00)00120-x.

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Even-Tzur, Gilad. "Invariance property of coordinate transformation." Journal of Spatial Science 63, no. 1 (2017): 23–34. http://dx.doi.org/10.1080/14498596.2017.1316688.

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16

Bez, H. E. "Conceptual aspects of transformation invariance." Computer-Aided Design 19, no. 9 (1987): 475–78. http://dx.doi.org/10.1016/0010-4485(87)90232-6.

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Dai, Gaole, and Jun Wang. "On Transformation Form-Invariance in Thermal Convection." Materials 16, no. 1 (2022): 376. http://dx.doi.org/10.3390/ma16010376.

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Over the past two decades, effective control of physical fields, such as light fields or acoustics fields, has greatly benefited from transforming media. One of these rapidly growing research areas is transformation thermotics, especially embodied in the thermal conductive and radiative modes. On the other hand, transformation media in thermal convection has seldom been studied due to the complicated governing equations involving both fluid motion and heat transfer terms. The difficulty lies in the robustness of form invariance in the Navier–Stokes equations or their simplified forms under coo

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JOGLEKAR, SATISH D., and A. MISRA. "WILSON LOOP AND THE TREATMENT OF AXIAL GAUGE POLES." Modern Physics Letters A 15, no. 08 (2000): 541–46. http://dx.doi.org/10.1142/s0217732300000530.

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We consider the question of gauge invariance of the Wilson loop in the light of a new treatment of axial gauge propagator proposed recently based on a finite field-dependent BRS (FFBRS) transformation. We remark that under the FFBRS transformation as the vacuum expectation value of a gauge-invariant observable remains unchanged, our prescription automatically satisfies the Wilson loop criterion. Furthermore, we give an argument for direct verification of the invariance of Wilson loop to O(g4) using the earlier work by Cheng and Tsai. We also note that our prescription preserves the thermal Wil

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19

Zhang, Yunsheng, Zijing Ren, Zichen Ding, Hong Qian, Haiqiang Li, and Chao Tao. "Co-ECL: Covariant Network with Equivariant Contrastive Learning for Oriented Object Detection in Remote Sensing Images." Remote Sensing 16, no. 3 (2024): 516. http://dx.doi.org/10.3390/rs16030516.

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Contrastive learning allows us to learn general features for downstream tasks without the need for labeled data by leveraging intrinsic signals within remote sensing images. Existing contrastive learning methods encourage invariant feature learning by bringing positive samples defined by random transformations in feature spaces closer, where transformed samples of the same image at different intensities are considered equivalent. However, remote sensing images differ from natural images in their top-down perspective results in the arbitrary orientation of objects and in that the images contain

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Pal, Dipan K., and Marios Savvides. "Non-Parametric Transformation Networks for Learning General Invariances from Data." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 4667–74. http://dx.doi.org/10.1609/aaai.v33i01.33014667.

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ConvNets, through their architecture, only enforce invariance to translation. In this paper, we introduce a new class of deep convolutional architectures called Non-Parametric Transformation Networks (NPTNs) which can learn general invariances and symmetries directly from data. NPTNs are a natural generalization of ConvNets and can be optimized directly using gradient descent. Unlike almost all previous works in deep architectures, they make no assumption regarding the structure of the invariances present in the data and in that aspect are flexible and powerful. We also model ConvNets and NPTN

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SAMARSKII, A. A., V. I. MAZHUKIN, P. P. MATUS, V. G. RYCHAGOV, and I. SMUROV. "INVARIANT DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS WITH TRANSFORMATIONS OF INDEPENDENT VARIABLES." Mathematical Models and Methods in Applied Sciences 09, no. 01 (1999): 93–110. http://dx.doi.org/10.1142/s0218202599000075.

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In this paper, invariant difference schemes for nonstationary equations under independent variables transformation constructed and investigated. Under invariance of difference scheme we mean its ability to preserve basic properties (stability, approximation, convergency, etc.) in various coordinate systems. Difference schemes of the second-order approximation that satisfy the invariance property are constructed for equations of parabolic type. Stability and convergency investigation of correspondent difference problems are carried out; a priori estimates in various grid norms are obtained.

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Kudari, Medha, Shivashankar S., and Prakash S. Hiremath. "Illumination and Rotation Invariant Texture Representation for Face Recognition." International Journal of Computer Vision and Image Processing 10, no. 2 (2020): 58–69. http://dx.doi.org/10.4018/ijcvip.2020040105.

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This article presents a novel approach for illumination and rotation invariant texture representation for face recognition. A gradient transformation is used as illumination invariance property and a Galois Field for the rotation invariance property. The normalized cumulative histogram bin values of the Gradient Galois Field transformed image represent the illumination and rotation invariant texture features. These features are further used as face descriptors. Experimentations are performed on FERET and extended Cohn Kanade databases. The results show that the proposed method is better as com

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23

CASTELLANA, MICHELE, and GIOVANNI MONTANI. "BRST SYMMETRY TOWARDS THE GAUSS CONSTRAINT FOR GENERAL RELATIVITY." International Journal of Modern Physics A 23, no. 08 (2008): 1218–21. http://dx.doi.org/10.1142/s0217751x08040093.

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Quantization of systems with constraints can be carried on with several methods. In the Dirac's formulation the classical generators of gauge transformations are required to annihilate physical quantum states to ensure their gauge invariance. Carrying on BRST symmetry it is possible to get a condition on physical states which, differently from the Dirac's method, requires them to be invariant under the BRST transformation. Employing this method for the action of general relativity expressed in terms of the spin connection and tetrad fields with path integral methods, we construct the generator

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24

Webber, Chris J. S. "Predictions of the Spontaneous Symmetry-Breaking Theory for Visual Code Completeness and Spatial Scaling in Single-Cell Learning Rules." Neural Computation 13, no. 5 (2001): 1023–43. http://dx.doi.org/10.1162/08997660151134316.

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This article shows analytically that single-cell learning rules that give rise to oriented and localized receptive fields, when their synaptic weights are randomly and independently initialized according to a plausible assumption of zero prior information, will generate visual codes that are invariant under two-dimensional translations, rotations, and scale magnifications, provided that the statistics of their training images are sufficiently invariant under these transformations. Such codes span different image locations, orientations, and size scales with equal economy. Thus, single-cell rul

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Alinea, Allan L., and Takahiro Kubota. "Transformation of primordial cosmological perturbations under the general extended disformal transformation." International Journal of Modern Physics D 30, no. 08 (2021): 2150057. http://dx.doi.org/10.1142/s0218271821500577.

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Primordial cosmological perturbations are the seeds that were cultivated by inflation and the succeeding dynamical processes, eventually leading to the current universe. In this work, we investigate the behavior of the gauge-invariant scalar and tensor perturbations under the general extended disformal transformation, namely, [Formula: see text], where [Formula: see text] and [Formula: see text], with [Formula: see text] and [Formula: see text] being a general functional of [Formula: see text]. We find that the tensor perturbation is invariant under this transformation. On the other hand, the

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26

Hill, James M. "Lorentz Invariance in Relativistic Particle Mechanics." Symmetry 16, no. 12 (2024): 1691. https://doi.org/10.3390/sym16121691.

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The notion of invariance under the Lorentz transformation is fundamental to special relativity and its continuation beyond the speed of light. Theories and solutions with this characteristic are stronger and more powerful than conventional theories or conventional solutions because the Lorentz-invariant approach automatically embodies the conventional approach. We propose a Lorentz-invariant extension of Newton’s second law, which includes both special relativistic mechanics and Schrödinger’s quantum wave theory. Here, we determine new general expressions for energy–momentum, which are Lorentz

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27

Mei, Xiaochun, and Canlun Yuan. "Three Serious Mistakes in Einstein’s Original Paper of Special Relativity in 1905." Applied Physics Research 15, no. 2 (2023): 80. http://dx.doi.org/10.5539/apr.v15n2p80.

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It is revealed in this paper that there were three serious mistakes in the Einstein&rsquo;s original paper in 1905. Einstein did not prove that the motion equation of classical electromagnetic field could satisfy the invariance of the Lorentz coordinate transformation. The Einstein&rsquo;s derivations on the formulas of transverse and longitudinal masses, as well as the calculation on the mass-energy relation are wrong. 1. In order to prove that the classical Maxwell electromagnetic field equation satisfied the invariance of Lorentz transformation in free space without charged and curr

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Pestman, Wiebe R. "Creating and classifying measures of linear association by optimization techniques." MATHEMATICA SCANDINAVICA 106, no. 1 (2010): 67. http://dx.doi.org/10.7146/math.scand.a-15125.

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The idea of measures of linear association, such as Pearson's correlation coefficient, can be put in a general framework by axiomization. Groups of linear transformations on $\mathsf{R}^n$ can be exploited to create new and classify existing measures according to their invariance properties. Thus invariance under the Euclidean transformation group leads to the class of so-called geometric measures. Similarly, a measure is called algebraic if it is invariant under scalings. Pearson's coefficient is an example of an algebraic measure; it is not geometric. It is proved that, generally, a measure

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Heydeman, J., and W. W. Schongs. "Power Invariance Transformation in Power Systems." International Journal of Electrical Engineering & Education 37, no. 2 (2000): 180–89. http://dx.doi.org/10.7227/ijeee.37.2.7.

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Many textbooks describe a balanced three-phase circuit by a single-phase equivalent representation. Confusion may arise amongst students regarding per-unit values of line-to-line voltages and phase voltages and, therefore, about the magnitudes of currents and powers. This paper proposes that students must first be taught symmetrical components based on power invariance transformation. A balanced three-phase circuit is to be described only in terms of positive sequence components. In the authors' experience, students understand this approach better and make fewer errors in per-unit calculation

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Bartlett, D. F., and W. F. Edwards. "Invariance of charge to Lorentz transformation." Physics Letters A 151, no. 6-7 (1990): 259–62. http://dx.doi.org/10.1016/0375-9601(90)90279-w.

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31

Rigolin, Gustavo. "On Lorentz Invariant Complex Scalar Fields." Advances in High Energy Physics 2022 (February 28, 2022): 1–58. http://dx.doi.org/10.1155/2022/5511428.

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We obtain a Lorentz covariant wave equation whose complex wave function transforms under a Lorentz boost according to the following rule, Ψ x ⟶ e i / ℏ f x Ψ x . We show that the spacetime-dependent phase f x is the most natural relativistic extension of the phase associated with the transformation rule for the nonrelativistic Schrödinger wave function when it is subjected to a Galilean transformation. We then generalize the previous analysis by postulating that Ψ x transforms according to the above rule under proper Lorentz transformations (boosts or spatial rotations). This is the most gener

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PITMAN, JIM. "Poisson–Dirichlet and GEM Invariant Distributions for Split-and-Merge Transformations of an Interval Partition." Combinatorics, Probability and Computing 11, no. 5 (2002): 501–14. http://dx.doi.org/10.1017/s0963548302005163.

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This paper introduces a split-and-merge transformation of interval partitions which combines some features of one model studied by Gnedin and Kerov [12, 11] and another studied by Tsilevich [30, 31] and Mayer-Wolf, Zeitouni and Zerner [21]. The invariance under this split-and-merge transformation of the interval partition generated by a suitable Poisson process yields a simple proof of the recent result of [21] that a Poisson–Dirichlet distribution is invariant for a closely related fragmentation–coagulation process. Uniqueness and convergence to the invariant measure are established for the s

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Siahaan, Haryanto M., and Triyanta Triyanta. "On the Napsuciale-Kirchbach Formalism for Spin 3/2 Field Theory." Indonesian Journal of Physics 19, no. 2 (2016): 51–54. http://dx.doi.org/10.5614/itb.ijp.2008.19.2.3.

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We consider the newly approach by Napsuciale and Kirchbach as an alternative formalism for spin-3/2 fields. The Feynman rules for interacting case are derived. Gauge invariance property in this formalism is shown from the corresponding invariant Compton scattering amplitude related to gauge transformation of the polarization vector.

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Gionti, Gabriele, and Andronikos Paliathanasis. "Duality transformation and conformal equivalent scalar–tensor theories." Modern Physics Letters A 33, no. 16 (2018): 1850093. http://dx.doi.org/10.1142/s0217732318500931.

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We deal with the duality symmetry of the dilaton field in cosmology and specifically with the so-called Gasperini–Veneziano duality transformation. In particular, we determine two conformal equivalent theories to the dilaton field, and we show that under conformal transformations Gasperini–Veneziano duality symmetry does not survive. Moreover, we show that those theories share a common conservation law, of Noetherian kind, while the symmetry vector which generates the conservation law is an isometry only for the dilaton field. Finally, we show that the Lagrangian of the dilaton field is equiva

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Zhang, Feng, Yuru Hu, and Xiangpeng Xin. "Lie Symmetry Analysis, Exact Solutions, and Conservation Laws of Variable-Coefficients Boiti-Leon-Pempinelli Equation." Advances in Mathematical Physics 2021 (November 29, 2021): 1–14. http://dx.doi.org/10.1155/2021/6227384.

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In this article, we study the generalized ( 2 + 1 )-dimensional variable-coefficients Boiti-Leon-Pempinelli (vcBLP) equation. Using Lie’s invariance infinitesimal criterion, equivalence transformations and differential invariants are derived. Applying differential invariants to construct an explicit transformation that makes vcBLP transform to the constant coefficient form, then transform to the well-known Burgers equation. The infinitesimal generators of vcBLP are obtained using the Lie group method; then, the optimal system of one-dimensional subalgebras is determined. According to the optim

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Abreu, Everton M. C., Rafael L. Fernandes, Albert C. R. Mendes, Jorge Ananias Neto, and Mario Jr Neves. "Duality and gauge invariance of non-commutative spacetime Podolsky electromagnetic theory." Modern Physics Letters A 32, no. 03 (2017): 1750019. http://dx.doi.org/10.1142/s0217732317500195.

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The interest in higher derivative field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. In this paper, we have introduced the non-commutative (NC) version of the Podolsky theory and we investigated the effect of the non-commutativity over its original gauge invariance property. We have demonstrated precisely that the non-commutativity spoiled the primary gauge invariance of the original action under this primary gauge transformation. After that we have used the Noether dualization technique to

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BONINI, MARISA. "WILSON RENORMALIZATION GROUP FOR GAUGE THEORIES." International Journal of Modern Physics A 16, no. 11 (2001): 1847–59. http://dx.doi.org/10.1142/s0217751x01004517.

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The Wilson renormalization group formulation of gauge theories is reviewed. In particular, the fine tuning procedure needed to recover the gauge invariance broken by the infrared cutoff is discussed. When the cutoff is larger than any physical scale, this procedure determines the finite non-invariant couplings of the ultraviolet action. These couplings are used to build up a local field transformation which allows to write a BRS invariant ultraviolet action.

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Sallhofer, Hans. "The Inversion Invariance of the Lorentz Transformation." Zeitschrift für Naturforschung A 52, no. 8-9 (1997): 678. http://dx.doi.org/10.1515/zna-1997-8-922.

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HAMADA, KEN-JI. "CONFORMAL FIELD THEORY ON R × S3 FROM QUANTIZED GRAVITY." International Journal of Modern Physics A 24, no. 16n17 (2009): 3073–110. http://dx.doi.org/10.1142/s0217751x0904422x.

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Conformal algebra on R × S3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess–Zumino action managing nonperturbative dynamics of the conformal factor in the metric field. It is shown that the residual diffeomorphism invariance in the radiation+ gauge is equal to the conformal symmetry, and the conformal transformation preserving the gauge-fixing condition that forms a closed algebra quantum mechanically i

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Qiu, Dong, and Weiquan Zhang. "Convexity Invariance of Fuzzy Sets under the Extension Principles." Journal of Function Spaces and Applications 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/849104.

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We discuss the convexity invariance of fuzzy sets under the extension principles. Particularly, we give a necessary and sufficient condition for a mapping to be an inverse *-convex transformation, and also obtain some sufficient conditions for a mapping to be an *-convex transformation. Two applications are given to illustrate the obtained results. Finally, we give some applications of the main results to the hyperstructure convexity invariance of type 2 fuzzy sets under hyperalgebra operations, and to the convexity invariance of fuzzy numbers under basic arithmetic operations.

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Razina, O. V., P. Yu Tsyba, and N. T. Suikimbayeva. "Application of the form invariance transformations of the scalar cosmological model in inflation theory." Journal of Physics: Conference Series 2090, no. 1 (2021): 012054. http://dx.doi.org/10.1088/1742-6596/2090/1/012054.

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Abstract In this work, it is shown that the equations of motion of the scalar field for spatially flat, homogeneous, and isotropic space-time Friedmann-Robertson-Walker have a form-invariance symmetry, which is arising from the form invariance transformation. Form invariance transformation is defined by linear function ρ = n 2 ρ in general case. It is shown the method of getting potential and the scalar field for the power law scale factor. The initial model is always stable at exponent of the scale factor α > 1, but stability of the transformation model depends on index n. Slow roll parame

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SUGI, T., DEJEY, and R. S. RAJESH. "GEOMETRIC ATTACK RESISTANT ROBUST IMAGE WATERMARKING SCHEME." International Journal of Information Acquisition 09, no. 01 (2013): 1350008. http://dx.doi.org/10.1142/s0219878913500083.

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A new watermarking approach based on affine Legendre moment invariants (ALMIs) and local characteristic regions (LCRs) which allows watermark detection and extraction under affine transformation attacks is presented in this paper. It is a non-blind watermarking scheme. Original image color image is converted into HSV color space and divided into four parts. LCR is constructed and a set of affine invariants are derived on LCRs based on Legendre moments for each part. These invariants can be used for estimating the affine transform coefficients on the LCRs. ALMIs are used for watermark embedding

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Mubarak, Dirar Abdallah*1 Elnabgha Mohamed Nageeb Mohamed Ali2 Sawsan Ahmed Elhouri Ahmed3 Fatma Medani4 &. Ahmed Elfaki5. "THE EQUIVALENCE PRINCIPLE ON THE BASIS OF FIELD DEPENDENT LORENTZ TRANSFORMATION." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, no. 1 (2018): 1–6. https://doi.org/10.5281/zenodo.1134757.

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The equality of gravitational and inertial mass within the framework of equivalence principle was investigated. The gravitational mass is expressed in terms of speed and potential by using velocity invariance and curved space Lorentz transformation. The same transformations were used to express inertial mass in terms of acceleration and potential. The gravitational mass and the inertial one are shown to be equal.

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Hill, James M. "Three-Dimensional Lorentz-Invariant Velocities." Symmetry 16, no. 9 (2024): 1133. http://dx.doi.org/10.3390/sym16091133.

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Lorentz invariance underlies special relativity, and the energy formula and relative velocity formula are well known to be invariant under a Lorentz transformation. Here, we determine the functional forms in terms of four arbitrary functions for those three dimensional velocity fields that are automatically invariant under the most general fully three-dimensional Lorentz transformation. For general three-dimensional motion, using rectangular Cartesian coordinates (x,y,z), we determine the first-order partial differential equations for the three velocity components u(x,y,z,t), v(x,y,z,t) and w(

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Rawat, Seema. "CPT Invariance of Quaternion Dirac equation." International Journal for Research in Applied Science and Engineering Technology 10, no. 1 (2022): 961–66. http://dx.doi.org/10.22214/ijraset.2022.39956.

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Abstract: In this paper the invariance of Quaternion Dirac equation under Lorentz Transformation, Charge conjugation, Parity transformation and Time reversal operation has been discussed successfully. The invariance under the combined operation of Charge conjugation, Parity and Time reversal (CPT) has also been discussed and expression for C, P, T and combined CPT operators have been obtained in terms of quaternions. Invariance condition for electric and magnetic field has also been obtained. It has been concluded that the Quaternion Dirac equation dominates over ordinary Dirac equation becaus

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Carruthers, Isaac M., Diego A. Laplagne, Andrew Jaegle, et al. "Emergence of invariant representation of vocalizations in the auditory cortex." Journal of Neurophysiology 114, no. 5 (2015): 2726–40. http://dx.doi.org/10.1152/jn.00095.2015.

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An essential task of the auditory system is to discriminate between different communication signals, such as vocalizations. In everyday acoustic environments, the auditory system needs to be capable of performing the discrimination under different acoustic distortions of vocalizations. To achieve this, the auditory system is thought to build a representation of vocalizations that is invariant to their basic acoustic transformations. The mechanism by which neuronal populations create such an invariant representation within the auditory cortex is only beginning to be understood. We recorded the

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Polihronov, J. "Incompressible flows: Relative scale invariance and isobaric polynomial fields." AIP Advances 12, no. 8 (2022): 085022. http://dx.doi.org/10.1063/5.0101855.

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This article examines the Bouton–Lie group invariants of the Navier–Stokes equation (NSE) for incompressible fluids. The theory is applied to the general scaling transformation admitted by the NSE: it adds new partial differential equations to the Navier–Stokes system of equations and is used to derive all self-similar solutions. This method can be applied to any differential equation exhibiting scaling invariance. The solutions are found to be based on isobaric polynomials, which can be smooth and nonzero at the initial moment. The non-self-similar velocity and pressure fields in the case of

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Bhutani, O. P., and K. Vijayakumar. "On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 32, no. 4 (1991): 457–68. http://dx.doi.org/10.1017/s0334270000008535.

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AbstractAfter formulating the alternate potential principle for the nonlinear differential equation corresponding to the generalised Emden-Fowler equation, the invariance identities of Rund [14] involving the Lagrangian and the generators of the infinitesimal Lie group are used for writing down the first integrals of the said equation via the Noether theorem. Further, for physical realisable forms of the parameters involved and through repeated application of invariance under the transformation obtained, a number of exact solutions are arrived at both for the Emden-Fowler equation and classica

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Webber, Chris J. S. "Self-Organization of Symmetry Networks: Transformation Invariance from the Spontaneous Symmetry-Breaking Mechanism." Neural Computation 12, no. 3 (2000): 565–96. http://dx.doi.org/10.1162/089976600300015718.

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Symmetry networks use permutation symmetries among synaptic weights to achieve transformation-invariant response. This article proposes a generic mechanism by which such symmetries can develop during unsupervised adaptation: it is shown analytically that spontaneous symmetry breaking can result in the discovery of unknown invariances of the data's probability distribution. It is proposed that a role of sparse coding is to facilitate the discovery of statistical invariances by this mechanism. It is demonstrated that the statistical dependences that exist between simple-cell-like threshold featu

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Khokhlov, S. V., and L. A. Ignatochkina. "Invariance of some classes of almost Hermitian structures concerning to the one-parameter group of diffeomorphisms generated by the Lie vector field." Differential Geometry of Manifolds of Figures, no. 53 (2022): 127–34. http://dx.doi.org/10.5922/0321-4796-2022-53-12.

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Finding the conditions for the invariance of geometric objects under the action of transformation groups is one of the main objects of geometric research. Almost Hermitian structures and structures of the Gray — Hervella classification on smooth manifolds are considered in this paper. All arguments are given using invariant Koszul’s calculus. Conditions for the invariance of the Kähler form in type structures are investigated and it is shown that the Kähler form is covariantly constant with respect to the Lie vector field. Conditions for the invariance of the Riemannian metric under the acti

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