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Journal articles on the topic 'Invariant method'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Yu, Tong Lan, Xiao Hua Yang, Cai Chen, and Jie Liu. "Method of Detecting Unary Polynomial Inequality Likely Invariant." Applied Mechanics and Materials 373-375 (August 2013): 1894–99. http://dx.doi.org/10.4028/www.scientific.net/amm.373-375.1894.

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Many Studies has carried on the technology of detecting invariants, for example, Daikon can detect most of invariant by presetting some types of them. But unary polynomial inequality likely invariants are rarely discovered by traditional tools. An effective method to detect unary polynomial inequality likely invariant was proposed in this paper. Through analyzing the property of value ranges of unary polynomial inequality likely invariants, the algorithm set the threshold value and calculates neighbor distances to determine the form of invariants. Finally, experimental results are given to dem

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Zaitsev, P. L. "On Religious Invariant Y. Balakina: Comments From Reviewer." Herald of Omsk University. Series: Historical studies, no. 1 (2017): 15–17. http://dx.doi.org/10.24147/2312-1300.2017.1.15-17.

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The article analyzes the work of a famous religious studies Omsk Y. Balakina “Invariants of religious consciousness. From the history of the study. The problem of the method”. We pose the problem of religious invariants as invariant limit. Finds its explanation us gesture invariant and invariant words in Y. Balakina. It demonstrates heuristic opportunity to terminology mapping the concepts of “invariant religious” and “philosophical invariant”.

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Lai, Yi Qiang. "Rotation Moment Invariant Feature Extraction Techniques for Image Matching." Applied Mechanics and Materials 721 (December 2014): 775–78. http://dx.doi.org/10.4028/www.scientific.net/amm.721.775.

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In recently years, extracting images invariance features are gaining more attention in image matching field. Various types of methods have been used to match image successfully in a number of applications. But in mostly literatures, the rotation moment invariant properties of these invariants have not been studied widely. In this paper, we present a novel method based on Polar Harmonic Transforms (PHTs) which is consisted of a set of orthogonal projection bases to extract rotation moment invariant features. The experimental results show that the kernel computation of PHTs is simple and image f

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Fieker, Claus, and Jürgen Klüners. "Computation of Galois groups of rational polynomials." LMS Journal of Computation and Mathematics 17, no. 1 (2014): 141–58. http://dx.doi.org/10.1112/s1461157013000302.

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AbstractComputational Galois theory, in particular the problem of computing the Galois group of a given polynomial, is a very old problem. Currently, the best algorithmic solution is Stauduhar’s method. Computationally, one of the key challenges in the application of Stauduhar’s method is to find, for a given pair of groups $H<G$, a $G$-relative $H$-invariant, that is a multivariate polynomial $F$ that is $H$-invariant, but not $G$-invariant. While generic, theoretical methods are known to find such $F$, in general they yield impractical answers. We give a general method for computing invar

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Ohtsuki, Tomotada. "Invariants of 3-manifolds derived from universal invariants of framed links." Mathematical Proceedings of the Cambridge Philosophical Society 117, no. 2 (1995): 259–73. http://dx.doi.org/10.1017/s0305004100073102.

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Reshetikhin and Turaev [10] gave a method to construct a topological invariant of compact oriented 3-manifolds from a ribbon Hopf algebra (e.g. a quantum group Uq(sl2)) using finite-dimensional representations of it. In this paper we give another independent method to construct a topological invariant of compact oriented 3-manifolds from a ribbon Hopf algebra via universal invariants of framed links without using representations of the algebra. For Uq(sl2) these two methods give different invariants of 3-manifolds.

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Jinle, Zeng, Zou Yirong, Du Dong, Chang Baohua, and Pan Jiluan. "Research on a visual weld detection method based on invariant moment features." Industrial Robot: An International Journal 42, no. 2 (2015): 117–28. http://dx.doi.org/10.1108/ir-06-2014-0358.

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Purpose – This paper aims to develop a feasible visual weld detection method to solve the problems in multi-layer welding detection (e.g. cover pass welding detection) for seam tracking and non-destructive testing. It seeks for an adaptive and accurate way to determine the edge between the seam and the base metal in the grayscale image of weld automatically. This paper tries to contribute to next-generation real-time robotic welding systems for multi-layer welding. Design/methodology/approach – This paper opted for invariant moments to characterize the seam and the base metal for classificatio

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ZHANG, R. B., and H. C. LEE. "LICKORISH INVARIANT AND QUANTUM OSP(1|2)." Modern Physics Letters A 11, no. 29 (1996): 2397–406. http://dx.doi.org/10.1142/s0217732396002381.

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Lickorish’s method for constructing topological invariants of three-manifolds is generalized to the quantum supergroup setting. An invariant is obtained by applying this method to the Kauffman polynomial arising from the vector representation of U q( osp (1|2)). A transparent proof is also given showing that this invariant is equivalent to the U q( osp (1|2)) invariant obtained in an earlier publication.

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Kim, Joonoh, and Mihaw Shin. "An invariant of virtual knots using flat virtual knot diagrams." Journal of Knot Theory and Its Ramifications 27, no. 04 (2018): 1850024. http://dx.doi.org/10.1142/s0218216518500244.

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In this paper, we describe a method of making an invariant of virtual knots that is defined in terms of an integer labeling of the flat virtual knot diagram. We give an invariant of flat virtual knots using the invariant above. Moreover, we derive a relation of two invariants.

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ADAMS, COLIN, RACHEL HUDSON, RALPH MORRISON, et al. "The spiral index of knots." Mathematical Proceedings of the Cambridge Philosophical Society 149, no. 2 (2010): 297–315. http://dx.doi.org/10.1017/s0305004110000241.

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AbstractIn this paper, we introduce two new invariants that are closely related to Milnor's curvature-torsion invariant. The first, a particularly natural invariant called the spiral index of a knot, captures the number of local maxima in a knot projection that is free of inflection points. This invariant is sandwiched between the bridge and braid index of a knot, and captures more subtle properties. The second invariant, the projective superbridge index, provides a method of counting the greatest number of local maxima that occur in a given projection. In addition to investigating the relatio

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HAMACHI, KENTARO. "QUANTUM MOMENT MAPS AND INVARIANTS FOR G-INVARIANT STAR PRODUCTS." Reviews in Mathematical Physics 14, no. 06 (2002): 601–21. http://dx.doi.org/10.1142/s0129055x02001314.

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We study a quantum moment map and propose an invariant for G-invariant star products on a G-transitive symplectic manifold. We start by describing a new method to construct a quantum moment map for G-invariant star products of Fedosov type. We use it to obtain an invariant that is invariant under G-equivalence. In the last section we give two simple examples of such invariants, which involve non-classical terms and provide new insights into the classification of G-invariant star products.

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Sagaidak, A. I., and E. S. Borovkova. "Application of acoustic emission criteria for the study of deformation processes and destruction of reinforced concrete structures." Concrete and Reinforced Concrete 617, no. 3 (2023): 38–44. http://dx.doi.org/10.37538/0005-9889-2023-3(617)-38-44.

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Introduction. The main results of the application of the method of acoustic emission criteria for the diagnosis of the pre-destructive state of reinforced concrete structures are presented. The paper considers the relationship between the origin and growth of microcracks in reinforced concrete beams with deviations of invariant ratios from stable values of acoustic emission parameters.The aim of the research is evaluate the possibility of using the invariant method for the diagnosis of reinforced concrete structures. Refinement of numerical values of time and amplitude invariants, time and amp

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Mui, Yanping, Youzheng Zhang, and Guitao Cao. "Invariants of the Space Point Element Structure and Their Applications." Mathematical Problems in Engineering 2020 (October 19, 2020): 1–13. http://dx.doi.org/10.1155/2020/3295492.

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In this paper, a new geometric structure of projective invariants is proposed. Compared with the traditional invariant calculation method based on 3D reconstruction, this method is comparable in the reliability of invariant calculation. According to this method, the only thing needed to find out is the geometric relationship between 3D points and 2D points, and the invariant can be obtained by using a single frame image. In the method based on 3D reconstruction, the basic matrix of two images is estimated first, and then, the 3D projective invariants are calculated according to the basic matri

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Burde, Georgy I. "Partially Nonclassical Method and Conformal Invariance in the Context of the Lie Group Method." Symmetry 16, no. 7 (2024): 875. http://dx.doi.org/10.3390/sym16070875.

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The basic idea of the ‘partially nonclassical method’, developed in the present paper, is to apply the invariance requirement of the Lie group method using not all differential consequences of the invariant surface condition but only part of them. It differs from the ‘classical’ method, in which the invariant surface condition is not used, and from the ‘nonclassical’ method, in which all the differential consequences are used. It provides additional possibilities for the symmetry analysis of partial differential equations (PDEs), as compared with the ‘classical’ and ‘nonclassical’ methods, in

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Martínez, José A., Manuel Ruiz Marin, and Maria del Carmen Vivo Molina. "A Method to Analyse Measurement Invariance under Uncertainty in Between-Subjects Design." Spanish journal of psychology 15, no. 3 (2012): 1510–19. http://dx.doi.org/10.5209/rev_sjop.2012.v15.n3.39435.

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In this research we have introduced a new test (H-test) for analyzing scale invariance in between group designs, and considering uncertainty in individual responses, in order to study the adequacy of disparate rating and visual scales for measuring abstract concepts. The H-test is easy to compute and, as a nonparametric test, does not require any a priori distribution of the data nor conditions on the variances of the distributions to be tested. We apply this test to measure perceived service quality of consumers of a sports services. Results show that, without considering uncertainty, the 1-7

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Tur, A. V., and V. V. Yanovsky. "Invariants in dissipationless hydrodynamic media." Journal of Fluid Mechanics 248 (March 1993): 67–106. http://dx.doi.org/10.1017/s0022112093000692.

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We propose a general geometric method of derivation of invariant relations for hydrodynamic dissipationless media. New dynamic invariants are obtained. General relations between the following three types of invariants are established, valid in all models: Lagrangian invariants, frozen-in vector fields and frozen-in co-vector fields. It is shown that frozen-in integrals form a Lie algebra with respect to the commutator of the frozen fields. The relation between frozen-in integrals derived here can be considered as the Backlund transformation for hydrodynamic-type systems of equations. We derive

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HATAKENAKA, ERI. "Invariants of 3-manifolds derived from covering presentations." Mathematical Proceedings of the Cambridge Philosophical Society 149, no. 2 (2010): 263–95. http://dx.doi.org/10.1017/s0305004110000198.

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AbstractBy a covering presentation of a 3-manifold, we mean a labelled link (i.e., a link with a monodromy representation), which presents the 3-manifold as the simple 4-fold covering space of the 3-sphere branched along the link with the given monodromy. It is known that two labelled links present a homeomorphic 3-manifold if and only if they are related by a finite sequence of some local moves. This paper presents a method for constructing topological invariants of 3-manifolds based on their covering presentations. The proof of the topological invariance is shown by verifying the invariance

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Jia, Tianrui, Haoyang Li, Cheng Yang, Tao Tao, and Chuan Shi. "Graph Invariant Learning with Subgraph Co-mixup for Out-of-Distribution Generalization." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 8 (2024): 8562–70. http://dx.doi.org/10.1609/aaai.v38i8.28700.

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Graph neural networks (GNNs) have been demonstrated to perform well in graph representation learning, but always lacking in generalization capability when tackling out-of-distribution (OOD) data. Graph invariant learning methods, backed by the invariance principle among defined multiple environments, have shown effectiveness in dealing with this issue. However, existing methods heavily rely on well-predefined or accurately generated environment partitions, which are hard to be obtained in practice, leading to sub-optimal OOD generalization performances. In this paper, we propose a novel graph

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DE WIT, DAVID, JON R. LINKS, and LOUIS H. KAUFFMAN. "On the Links–Gould Invariant of Links." Journal of Knot Theory and Its Ramifications 08, no. 02 (1999): 165–99. http://dx.doi.org/10.1142/s0218216599000110.

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[Formula: see text] We introduce and study in detail an invariant of (1, 1) tangles. This invariant, derived from a family of four dimensional representations of the quantum superalgebra Uq[gl(2|1)], will be referred to as the Links–Gould invariant. We find that our invariant is distinct from the Jones, HOMFLY and Kauffman polynomials (detecting chirality of some links where these invariants fail), and that it does not distinguish mutants or inverses. The method of evaluation is based on an abstract tensor state model for the invariant that is quite useful for computation as well as theoretica

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Ravand, Hamdollah. "Assessing Measurement Invariance in a University Entrance Exam: A Comparison of Multigroup Confirmatory Factor Analysis Alignment Method vs. Multigroup Item Response Theory." Educational Methods & Psychometrics 2 (June 25, 2024): 11. https://doi.org/10.5281/zenodo.12819064.

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This study aimed to assess measurement invariance in a university entrance examination while comparing the effectiveness of multigroup item response theory (MGIRT) and multigroup confirmatory factor analysis (MGCFA) alignment methods in identifying non-invariant items. Data from four groups, representing different university types, were analyzed using the TAM package in R and Mplus. The findings indicated that both MGIRT and MGCFA alignment methods converged on one non-invariant item, with MGCFA alignment detecting an additional three cases of non-invariance. Sensitivity analyses revealed that

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ECKHARDT, ULRICH, and GERD MADERLECHNER. "INVARIANT THINNING." International Journal of Pattern Recognition and Artificial Intelligence 07, no. 05 (1993): 1115–44. http://dx.doi.org/10.1142/s021800149300056x.

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One of the most widely used methods for preprocessing binary images is thinning. The popularity of this method rests on the fact that considerable data reduction is achieved while retaining “essential” properties of the original image. Moreover, topological features, which cannot be verified by a genuinely parallel method (by Minsky and Papert22) are more easily treated in thinned images. For these reasons, many articles on this topic were published in the literature. Most of them are concerned with modifications of existing methods in order to yield “nicer” results out of the thinning process

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Dubois, Jérôme, and Christian Wegner. "Weighted L2-invariants and applications to knot theory." Communications in Contemporary Mathematics 17, no. 01 (2014): 1450010. http://dx.doi.org/10.1142/s0219199714500102.

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This paper deals with the study of a new family of knot invariants: the L2-Alexander invariant. A main result is to give a method of computation of the L2-Alexander invariant of a knot complement using any presentation of default 1 of the knot group.

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Liu, Yilin, Xuqiang Shao, and Zhaohui Wu. "Rotation Invariant Predictor-Corrector for Smoothed Particle Hydrodynamics Data Visualization." Symmetry 13, no. 3 (2021): 382. http://dx.doi.org/10.3390/sym13030382.

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In order to extract the vortex features more accurately, a new method of vortex feature extraction on the Smoothed Particle Hydrodynamics data is proposed in the current study by combining rotation invariance and predictor-corrector method. There is a limitation in the original rotation invariance, which can only extract the vortex features that perform equal-speed rotations. The limitation is slightly weakened to a situation that the rotation invariance can be used, given that a specific axis is existed in the fluid to replace the axis needed for it. Therefore, as long as the axis exists, the

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Sniders, Andris, and Toms Komass. "Invariant Method of Load Independent Pressure Control in Steam Boiler." Electrical, Control and Communication Engineering 1, no. 1 (2012): 5–10. http://dx.doi.org/10.2478/v10314-012-0001-4.

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Abstract The paper considers the possibility of steam production and supply process improvement by perfection of the steam boiler control system, applying invariance principle that makes possible preemptive compensation of the influence of steam expenditure as a disturbance on the control process quality and efficiency. For the development of invariant control system, the mathematical modeling and simulation in MATLAB - SIMULINK environment is made. The control unit is low pressure steam boiler with one input impact to control - the heat flow of burning gas mixture fuel, one measured output pa

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Yuldoshevich, Salomov Gulom. "CLASS HOURS FOR HIGH SCHOOL STUDENTS IN THE INVARIANT METHOD USE OF MOSAIC THERMAL WORK METHOD IN TRANSFER." Current Research Journal of Pedagogics 5, no. 10 (2024): 183–87. http://dx.doi.org/10.37547/pedagogics-crjp-05-10-31.

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In this article, special attention is paid to the issues of morally and morally mature education of high school students. The special features of organizing class hours in an invariant way, as well as the advantages of using innovative educational technologies in the educational process, were explained to high school students. Pedagogical principles of organizing the process using the mosaic term work method were presented to upper class students in invariant class hours. The main organizers of the educational process in general schools are class leaders and their role in organizing invariant

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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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GANGOPADHYAYA, ASIM, and JEFFRY V. MALLOW. "GENERATING SHAPE INVARIANT POTENTIALS." International Journal of Modern Physics A 23, no. 31 (2008): 4959–78. http://dx.doi.org/10.1142/s0217751x08042894.

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We transform the shape invariance condition, a difference-differential equation of supersymmetric quantum mechanics, into a local partial differential equation. We develop a new method for generating translationally shape invariant potentials from this equation. We generate precisely all the known shape invariant potentials, and argue that there are unlikely to be others.

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Isik, Leyla, Ethan M. Meyers, Joel Z. Leibo, and Tomaso Poggio. "The dynamics of invariant object recognition in the human visual system." Journal of Neurophysiology 111, no. 1 (2014): 91–102. http://dx.doi.org/10.1152/jn.00394.2013.

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The human visual system can rapidly recognize objects despite transformations that alter their appearance. The precise timing of when the brain computes neural representations that are invariant to particular transformations, however, has not been mapped in humans. Here we employ magnetoencephalography decoding analysis to measure the dynamics of size- and position-invariant visual information development in the ventral visual stream. With this method we can read out the identity of objects beginning as early as 60 ms. Size- and position-invariant visual information appear around 125 ms and 15

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AIZAWA, N., M. HARADA, M. KAWAGUCHI, and E. OTSUKI. "ALL LINK INVARIANTS FOR TWO DIMENSIONAL SOLUTIONS OF YANG–BAXTER EQUATION AND DRESSINGS." Journal of Knot Theory and Its Ramifications 15, no. 10 (2006): 1279–301. http://dx.doi.org/10.1142/s0218216506005147.

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All polynomial invariants of links for two dimensional solutions of Yang–Baxter equation is constructed by employing Turaev's method. As a consequence, it is proved that the best invariant so constructed is the Jones polynomial and there exist three solutions connecting to the Alexander polynomial. Invariants for higher dimensional solutions, obtained by the so-called dressings, are also investigated. It is observed that the dressings do not improve link invariant unless some restrictions are put on dressed solutions.

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Høier, R., C. R. Birkeland, R. Holmestad, and K. Marthinsen. "Three-phase structure invariants and structure factors determined with the quantitative convergent-beam electron diffraction method." Acta Crystallographica Section A Foundations of Crystallography 55, no. 2 (1999): 188–96. http://dx.doi.org/10.1107/s0108767398008903.

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Quantitative convergent-beam electron diffraction is used to determine structure factors and three-phase structure invariants. The refinements are based on centre-disc intensities only. An algorithm for parameter-sensitive pixel sampling of experimental intensities is implemented in the refinement procedure to increase sensitivity and computer speed. Typical three-beam effects are illustrated for the centrosymmetric case. The modified refinement method is applied to determine amplitudes and three-phase structure invariants in noncentrosymmetric InP. The accuracy of the results is shown to depe

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Kondratyev, Dmitry, Ilya Maryasov, and Valery Nepomniaschy. "The Automation of C Program Verification by Symbolic Method of Loop Invariants Elimination." Modeling and Analysis of Information Systems 25, no. 5 (2018): 491–505. http://dx.doi.org/10.18255/1818-1015-2018-5-491-505.

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During deductive verification of programs written in imperative languages, the generation and proof of verification conditions corresponding to loops can cause difficulties, because each one must be provided with an invariant whose construction is often a challenge. As a rule, the methods of invariant synthesis are heuristic ones. This impedes its application. An alternative is the symbolic method of loop invariant elimination suggested by V.A. Nepomniaschy in 2005. Its idea is to represent a loop body in a form of special replacement operation under certain constraints. This operation express

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Becker, D. A., and E. W. Richter. "Partially Invariant Solutions for Two-dimensional Ideal MHD Equations." Zeitschrift für Naturforschung A 45, no. 11-12 (1990): 1219–29. http://dx.doi.org/10.1515/zna-1990-11-1201.

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AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

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Winter, Sonja D., and Sarah Depaoli. "An illustration of Bayesian approximate measurement invariance with longitudinal data and a small sample size." International Journal of Behavioral Development 44, no. 4 (2019): 371–82. http://dx.doi.org/10.1177/0165025419880610.

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This article illustrates the Bayesian approximate measurement invariance (MI) approach in M plus with longitudinal data and small sample size. Approximate MI incorporates zero-mean small variance prior distributions on the differences between parameter estimates over time. Contrary to traditional invariance testing methods, where exact invariance is tested, this method allows for some “wiggle room” in the parameter estimates over time. The procedure is illustrated using longitudinal data on college students’ academic stress as it changes in the period leading up to and right after an important

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Pejkowski, Łukasz, and Dariusz Skibicki. "Multiaxial Fatigue Life Assessment Method Based on the Mean Value of Modified Second Invariant of the Deviatoric Stress." Solid State Phenomena 224 (November 2014): 15–20. http://dx.doi.org/10.4028/www.scientific.net/ssp.224.15.

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Stress invariants approach to the multiaxial fatigue life estimation is generally based on the root mean square value of second invariant of the deviatoric stress amplitude and the value of hydrostatic stress. Such an approach omits a significant part of the information about multiaxial load history. It is particularly noticeable in case of non-proportional loadings, which lead to a reduction of fatigue life (i.e. [1–3]). In this work a new method based on the mean value of modified second invariant of the deviatoric stress has been presented.

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TUZNIK, STANLEY L., PETER J. OLVER, and ALLEN TANNENBAUM. "Equi-affine differential invariants for invariant feature point detection." European Journal of Applied Mathematics 31, no. 2 (2019): 277–96. http://dx.doi.org/10.1017/s0956792519000020.

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Image feature points are detected as pixels which locally maximise a detector function, two commonly used examples of which are the (Euclidean) image gradient and the Harris–Stephens corner detector. A major limitation of these feature detectors is that they are only Euclidean-invariant. In this work, we demonstrate the application of a 2D equi-affine-invariant image feature point detector based on differential invariants as derived through the equivariant method of moving frames. The fundamental equi-affine differential invariants for 3D image volumes are also computed.

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Lei, Yuyao, Hongli Yang, and Ivan Ganchev Ivanov. "Characterization of Positive Invariance of Quadratic Convex Sets for Discrete-Time Systems Using Optimization Approaches." Mathematics 11, no. 11 (2023): 2419. http://dx.doi.org/10.3390/math11112419.

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A positively invariant set is an important concept in dynamical systems. The study of positively invariant set conditions for discrete-time systems is one interesting topic in both theoretical studies and practical applications research. Different methods for characterizing the invariance of different types of sets have been established. For example, the ellipsoidal and the Lorenz cone, which are quadratic convex sets, have different properties from a polyhedral set. This paper presents an optimization method and a dual optimization method to characterize the positive invariance of the ellipso

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SASTRY, CHALLA S., ARUN K. PUJARI, and B. L. DEEKSHATULU. "A FOURIER-RADIAL DESCRIPTOR ALGORITHM FOR INVARIANT FEATURE EXTRACTION." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 01 (2006): 197–212. http://dx.doi.org/10.1142/s0219691306001166.

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By integrating the Fourier techniques and the edge information obtained using the radial symmetric functions, we propose in this paper an invariant feature extraction algorithm. Unlike the Gabor feature extraction method, the present method does not use direction dependent filters, nor does it use the images in polar form, for rotation invariance. Besides, the present Fourier-Radial invariant feature extraction algorithm, suitable for both the texture and non-texture images, has functional analogy with the Gabor feature extraction method, and hence, is easily implementable. It is mathematicall

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Kurdyukov, Alexander P., and Victor A. Boichenko. "A Spectral Method of the Analysis of Linear Control Systems." International Journal of Applied Mathematics and Computer Science 29, no. 4 (2019): 667–79. http://dx.doi.org/10.2478/amcs-2019-0049.

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Abstract A spectral method of the analysis of linear control systems is considered. Within the framework of this approach the σ-entropy of input signals and the σ-entropy norm of systems are introduced. The invariance of the introduced norm makes it possible to get invariant results of σ-entropy analysis.

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Chris, Lina Arlends, Bagus Mulyawan, and Agus Budi Dharmawan. "A Leukocyte Detection System Using Scale Invariant Feature Transform Method." International Journal of Computer Theory and Engineering 8, no. 1 (2016): 69–73. http://dx.doi.org/10.7763/ijcte.2016.v8.1022.

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Gu, Feifei, Hong Zhao, Xiang Zhou, Jinjun Li, Penghui Bu, and Zixin Zhao. "Photometric invariant stereo matching method." Optics Express 23, no. 25 (2015): 31779. http://dx.doi.org/10.1364/oe.23.031779.

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Rota, G. C., and J. A. Stein. "Symbolic method in invariant theory." Proceedings of the National Academy of Sciences 83, no. 4 (1986): 844–47. http://dx.doi.org/10.1073/pnas.83.4.844.

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DURAND, F., B. HOST, and C. SKAU. "Substitutional dynamical systems, Bratteli diagrams and dimension groups." Ergodic Theory and Dynamical Systems 19, no. 4 (1999): 953–93. http://dx.doi.org/10.1017/s0143385799133947.

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We explore substitution minimal systems and their relation to stationary Bratteli diagrams and stationary dimension groups. The constructions involved are algorithmic and explicit and render an effective method to compute an invariant of (ordered) $K$-theoretic nature for these systems. This new invariant is independent of spectral invariants which have previously been extensively studied. Before we state the main results we give some background.

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Trofimov, Vyacheslav, and Maria Loginova. "Conservative Finite-Difference Schemes for Two Nonlinear Schrödinger Equations Describing Frequency Tripling in a Medium with Cubic Nonlinearity: Competition of Invariants." Mathematics 9, no. 21 (2021): 2716. http://dx.doi.org/10.3390/math9212716.

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Two 1D nonlinear coupled Schrödinger equations are often used for describing optical frequency conversion possessing a few conservation laws (invariants), for example, the energy’s invariant and the Hamiltonian. Their influence on the properties of the finite-difference schemes (FDSs) may be different. The influence of each of both invariants on the computer simulation result accuracy is analyzed while solving the problem describing the third optical harmonic generation process. Two implicit conservative FDSs are developed for a numerical solution of this problem. One of them preserves a diffe

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LEE, KYEONGHUI, and YOUNG HO IM. "GENERALIZED INDEX POLYNOMIALS FOR VIRTUAL LINKS." Journal of Knot Theory and Its Ramifications 21, no. 14 (2012): 1250128. http://dx.doi.org/10.1142/s0218216512501283.

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We construct some polynomial invariants for virtual links by the recursive method, which are different from the index polynomial invariant defined in [Y. H. Im, K. Lee and S. Y. Lee, Index polynomial invariant of virtual links, J. Knot Theory Ramifications19(5) (2010) 709–725]. We show that these polynomials can distinguish whether virtual knots can be invertible or not although the index polynomial cannot distinguish the invertibility of virtual knots.

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Yang, Jianwei, Ming Li, Zirun Chen, and Yunjie Chen. "Cutting Affine Moment Invariants." Mathematical Problems in Engineering 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/928161.

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The extraction of affine invariant features plays an important role in many fields of image processing. In this paper, the original image is transformed into new images to extract more affine invariant features. To construct new images, the original image is cut in two areas by a closed curve, which is called general contour (GC). GC is obtained by performing projections along lines with different polar angles. New image is obtained by changing gray value of pixels in inside area. The traditional affine moment invariants (AMIs) method is applied to the new image. Consequently, cutting affine m

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Pesina, S. A. "MULTI-LEVEL STRUCTURE OF POLISEMOUS WORD: INVARIANT-CLUSTER ANALYSIS." Voprosy Kognitivnoy Lingvistiki, no. 1 (2021): 60–69. http://dx.doi.org/10.20916/1812-3228-2021-1-60-69.

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Within the framework of the article, we have come up with a hypothesis of a polysemous word integrity as a multilevel structure, which is ensured by the dominant lexical invariant meaning. The analysis of the English polysemous word “key” is presented with the use of the empirical invariant-component method. Metaphorical clusters of meanings of this word and its lexical invariant are defined as a set of basic dominant components that form the semantic core of the word. The reasons for the ambiguity of the boundaries of the lexical meaning are substantiated, the patterns of schematization of th

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CHEN, JUN-HUA, and HONG-YI FAN. "THE ENERGY GAPS OF QUADRATIC HAMILTONIANS USING METHOD OF INVARIANT EIGENOPERATOR (IEO)." Modern Physics Letters B 24, no. 23 (2010): 2387–94. http://dx.doi.org/10.1142/s0217984910024766.

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Based on the invariant eigen-operator method3 we developed a general way to calculate the energy gaps of quadratic Boson or Fermion Hamiltonians. As an application, we calculated the energy gaps of an electron in uniform magnetic field (UMF) and a quadratic potential. We also checked the gauge invariance of electromagnetic field.

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Virdi, J. S., F. Chand, C. N. Kumar, and S. C. Mishra. "Complex dynamical invariants for two-dimensional nonhermitian Hamiltonian systems." Canadian Journal of Physics 90, no. 2 (2012): 151–57. http://dx.doi.org/10.1139/p11-152.

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Keeping in view the importance of dynamical invariants, attempts have been made to investigate complex invariants for two-dimensional Hamiltonian systems within the framework of the extended complex phase space approach. The rationalization method has been used to derive an invariant of a general nonhermitian quartic potential. Invariants for three specific potentials are also obtained from the general result.

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YANG, JIANWEI, LIANG ZHANG, and ZHENGDA LU. "THE MELLIN CENTRAL PROJECTION TRANSFORM." ANZIAM Journal 58, no. 3-4 (2017): 256–64. http://dx.doi.org/10.1017/s1446181116000341.

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The central projection transform can be employed to extract invariant features by combining contour-based and region-based methods. However, the central projection transform only considers the accumulation of the pixels along the radial direction. Consequently, information along the radial direction is inevitably lost. In this paper, we propose the Mellin central projection transform to extract affine invariant features. The radial factor introduced by the Mellin transform, makes up for the loss of information along the radial direction by the central projection transform. The Mellin central p

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Quesne, Christiane. "Deformed Shape Invariant Superpotentials in Quantum Mechanics and Expansions in Powers of ℏ". Symmetry 12, № 11 (2020): 1853. http://dx.doi.org/10.3390/sym12111853.

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We show that the method developed by Gangopadhyaya, Mallow, and their coworkers to deal with (translational) shape invariant potentials in supersymmetric quantum mechanics and consisting in replacing the shape invariance condition, which is a difference-differential equation, which, by an infinite set of partial differential equations, can be generalized to deformed shape invariant potentials in deformed supersymmetric quantum mechanics. The extended method is illustrated by several examples, corresponding both to ℏ-independent superpotentials and to a superpotential explicitly depending on ℏ.

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DANKOWICZ, HARRY, and GUNJAN THAKUR. "A NEWTON METHOD FOR LOCATING INVARIANT TORI OF MAPS." International Journal of Bifurcation and Chaos 16, no. 05 (2006): 1491–503. http://dx.doi.org/10.1142/s0218127406015441.

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This paper presents an iterative method for locating invariant tori of maps. Specifically, through the introduction of a shift function on the torus corresponding to the projection of the dynamics on the torus onto toral parameters, a discrete system of equations may be formulated whose solution approximates the spatial location of the torus. As invariant tori of continuous flows may be considered invariant under the application of the flow for a fixed time, or may correspond to invariant tori (of one less dimension) of suitably introduced Poincaré maps, the methodology applies to discrete and

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