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Journal articles on the topic 'Invariant properties'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Führ, Hartmut, and Jun Xian. "Quantifying invariance properties of shift-invariant spaces." Applied and Computational Harmonic Analysis 36, no. 3 (2014): 514–21. http://dx.doi.org/10.1016/j.acha.2013.08.002.

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2

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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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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4

Hertling, Peter, and Yongge Wang. "Invariance Properties of Random Sequences." JUCS - Journal of Universal Computer Science 3, no. (11) (1997): 1241–49. https://doi.org/10.3217/jucs-003-11-1241.

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We present invariance characterizations of different types of random sequences. We correct Schnorr's original, incorrect characterization of Martin-Loef ran dom sequences, compare it with Schnorr s corresponding characterization of his own randomness concept, and give a similar, new characterization of Kurtz random sequences. That is, we show that an infinite sequence is Kurtz random if and only if for every partial, computable, measure-invariant function the sequence is not recursive. 1.) Proceedings of the First Japan-New Zealand Workshop on Logic in Computer Science, special issue editors D

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Ohtsuki, Tomotada, and Shuji Yamada. "Quantum SU(3) Invariant of 3-Manifolds via Linear Skein Theory." Journal of Knot Theory and Its Ramifications 06, no. 03 (1997): 373–404. http://dx.doi.org/10.1142/s021821659700025x.

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The linear skein theory for the Kauffman bracket was introduced by Lickorish [11,12]. It gives an elementary construction of quantum SU(2) invariant of 3-manifolds. In this paper we prove basic properties of the linear skein theory for quantum SU(3) invariant. By using them we give an elementary construction of quantum SU(3) invariant of 3-manifolds and prove topological invariance of the invariant along the construction.

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MOHAPATRA, MANAS RANJAN, and SWADESH KUMAR SAHOO. "MAPPING PROPERTIES OF A SCALE INVARIANT CASSINIAN METRIC AND A GROMOV HYPERBOLIC METRIC." Bulletin of the Australian Mathematical Society 97, no. 1 (2017): 141–52. http://dx.doi.org/10.1017/s0004972717000570.

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We consider a scale invariant Cassinian metric and a Gromov hyperbolic metric. We discuss a distortion property of the scale invariant Cassinian metric under Möbius maps of a punctured ball onto another punctured ball. We obtain a modulus of continuity of the identity map from a domain equipped with the scale invariant Cassinian metric (or the Gromov hyperbolic metric) onto the same domain equipped with the Euclidean metric. Finally, we establish the quasi-invariance properties of both metrics under quasiconformal maps.

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Körding, Konrad P., and Peter König. "Neurons with Two Sites of Synaptic Integration Learn Invariant Representations." Neural Computation 13, no. 12 (2001): 2823–49. http://dx.doi.org/10.1162/089976601317098547.

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Neurons in mammalian cerebral cortex combine specific responses with respect to some stimulus features with invariant responses to other stimulus features. For example, in primary visual cortex, complex cells code for orientation of a contour but ignore its position to a certain degree. In higher areas, such as the inferotemporal cortex, translation-invariant, rotation-invariant, and even view point-invariant responses can be observed. Such properties are of obvious interest to artificial systems performing tasks like pattern recognition. It remains to be resolved how such response properties

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Cavallo, Alberto, and Carlo Collari. "Slice-torus Concordance Invariants and Whitehead Doubles of Links." Canadian Journal of Mathematics 72, no. 6 (2019): 1423–62. http://dx.doi.org/10.4153/s0008414x19000294.

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AbstractIn this paper we extend the definition of slice-torus invariant to links. We prove a few properties of the newly-defined slice-torus link invariants: the behaviour under crossing change, a slice genus bound, an obstruction to strong sliceness, and a combinatorial bound. Furthermore, we provide an application to the computation of the splitting number. Finally, we use the slice-torus link invariants and the Whitehead doubling to define new strong concordance invariants for links, which are proven to be independent of the corresponding slice-torus link invariant.

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Clark, W. Edwin, and Masahico Saito. "Algebraic properties of quandle extensions and values of cocycle knot invariants." Journal of Knot Theory and Its Ramifications 25, no. 14 (2016): 1650080. http://dx.doi.org/10.1142/s0218216516500802.

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Quandle 2-cocycles define invariants of classical and virtual knots, and extensions of quandles. We show that the quandle 2-cocycle invariant with respect to a non-trivial [Formula: see text]-cocycle is constant, or takes some other restricted form, for classical knots when the corresponding extensions satisfy certain algebraic conditions. In particular, if an abelian extension is a conjugation quandle, then the corresponding cocycle invariant is constant. Specific examples are presented from the list of connected quandles of order less than 48. Relations among various quandle epimorphisms inv

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10

SATO, CHIFUMI. "PERTURBATIVE INVARIANTS OF LENS SPACES ASSOCIATED WITH COHOMOLOGY CLASSES." Journal of Knot Theory and Its Ramifications 15, no. 07 (2006): 913–29. http://dx.doi.org/10.1142/s0218216506004786.

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The quantum SO(3)-invariants of ℚ-homology 3-spheres can be perturbatively expanded to the Ohtsuki invariant in number theory. On the other hand, it is known that the quantum SU(2)-invariants of 3-manifolds M admits a refinement involving a mod 2 cohomology class of M. A motivation of this paper is to study whether a perturbative expansion can be derived from the refinement. In this paper, we shall prove to be able to derive the perturbative expansion in the case of lens spaces by a concrete calculation, and shall define the perturbative invariant. Furthermore we obtain some properties for the

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11

Burigana, Luigi, and Michele Vicovaro. "“Invariants” in Koffka’s Theory of Constancies in Vision: Highlighting Their Logical Structure and Lasting Value." Gestalt Theory 39, no. 1 (2017): 6–29. http://dx.doi.org/10.1515/gth-2017-0004.

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SummaryBy introducing the concept of “invariants”, Koffka (1935) endowed perceptual psychology with a flexible theoretical tool, which is suitable for representing vision situations in which a definite part of the stimulus pattern is relevant but not sufficient to determine a corresponding part of the perceived scene. He characterised his “invariance principle” as a principle conclusively breaking free from the “old constancy hypothesis”, which rigidly surmised point-to-point relations between stimulus and perceptual properties. In this paper, we explain the basic terms and assumptions implici

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12

Tidor, Jonathan, and Yufei Zhao. "Testing Linear-Invariant Properties." SIAM Journal on Computing 51, no. 4 (2022): 1230–79. http://dx.doi.org/10.1137/21m1397246.

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13

Khaluf, Yara, Eliseo Ferrante, Pieter Simoens, and Cristián Huepe. "Scale invariance in natural and artificial collective systems: a review." Journal of The Royal Society Interface 14, no. 136 (2017): 20170662. http://dx.doi.org/10.1098/rsif.2017.0662.

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Self-organized collective coordinated behaviour is an impressive phenomenon, observed in a variety of natural and artificial systems, in which coherent global structures or dynamics emerge from local interactions between individual parts. If the degree of collective integration of a system does not depend on size, its level of robustness and adaptivity is typically increased and we refer to it as scale-invariant. In this review, we first identify three main types of self-organized scale-invariant systems: scale-invariant spatial structures, scale-invariant topologies and scale-invariant dynami

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14

Diehl, Joscha, Kurusch Ebrahimi-Fard, and Nikolas Tapia. "Time-Warping Invariants of Multidimensional Time Series." Acta Applicandae Mathematicae 170, no. 1 (2020): 265–90. http://dx.doi.org/10.1007/s10440-020-00333-x.

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Abstract In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe the data and to dampen the influence of noise. In some applications, these features are also required to satisfy some invariance properties. In this paper, we concentrate on time-warping invariants. We show that these correspond to a certain family of iterated sums of the increments of the time series, known as quasisymmetric function

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15

Balmaseda, Aitor, Fabio Di Cosmo, and Juan Manuel Pérez-Pardo. "On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits." Symmetry 11, no. 8 (2019): 1047. http://dx.doi.org/10.3390/sym11081047.

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An analysis of the invariance properties of self-adjoint extensions of symmetric operators under the action of a group of symmetries is presented. For a given group G, criteria for the existence of G-invariant self-adjoint extensions of the Laplace–Beltrami operator over a Riemannian manifold are illustrated and critically revisited. These criteria are employed for characterising self-adjoint extensions of the Laplace–Beltrami operator on an infinite set of intervals, Ω , constituting a quantum circuit, which are invariant under a given action of the group Z . A study of the different unitary

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16

KABLE, ANTHONY C. "AN ARITHMETICAL INVARIANT OF ORBITS OF AFFINE ACTIONS AND ITS APPLICATION TO SIMILARITY CLASSES OF QUADRATIC SPACES." International Journal of Number Theory 06, no. 06 (2010): 1215–53. http://dx.doi.org/10.1142/s1793042110003460.

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Given an action of an affine algebraic group on an affine variety and a relatively invariant regular function, all defined over the ring of integers of a number field and having suitable additional properties, an invariant of the rational orbits of the action is defined. This invariant, the reduced replete Steinitz class, takes its values in the reduced replete class group of the number field. The general framework is then applied to obtain an invariant of similarity classes of non-degenerate quadratic spaces of even rank. The invariant is related to more familiar invariants. It is shown that

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17

IM, YOUNG HO, and KYOUNG IL PARK. "A PARITY AND A MULTI-VARIABLE POLYNOMIAL INVARIANT FOR VIRTUAL LINKS." Journal of Knot Theory and Its Ramifications 22, no. 13 (2013): 1350073. http://dx.doi.org/10.1142/s0218216513500739.

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We introduce a parity of classical crossings of virtual link diagrams which extends the Gaussian parity of virtual knot diagrams and the odd writhe of virtual links that extends that of virtual knots introduced by Kauffman [A self-linking invariants of virtual knots, Fund. Math.184 (2004) 135–158]. Also, we introduce a multi-variable polynomial invariant for virtual links by using the parity of classical crossings, which refines the index polynomial introduced in [Index polynomial invariants of virtual links, J. Knot Theory Ramifications19(5) (2010) 709–725]. As consequences, we give some prop

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18

CHO, YONG SEUNG. "GENERATING SERIES FOR SYMMETRIC PRODUCT SPACES." International Journal of Geometric Methods in Modern Physics 09, no. 05 (2012): 1250045. http://dx.doi.org/10.1142/s0219887812500454.

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We consider the symmetric product spaces of closed manifolds. We introduce some geometric invariants and the topological properties of symmetric product spaces via the symmetric invariant ones of product spaces and apply to Gromov–Witten invariants. We examine the symmetric product spaces of the complex projective line, their Gromov–Witten invariants and compute the generating series induced by their Gromov–Witten invariants.

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19

Piccinini, Gualtiero. "An Egalitarian Account of Composition and Realization." Monist 105, no. 2 (2022): 276–92. http://dx.doi.org/10.1093/monist/onab035.

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Abstract I argue that wholes are neither identical to nor (completely) distinct from their parts. Instead, wholes are invariants under some transformations in their parts. Similarly, higher-level properties are neither identical to nor (completely) distinct from their lower-level realizers. Instead, higher-level properties are aspects of their realizers that are invariant under some transformations in their realizers. Nowhere in this picture is there any ontological hierarchy between levels of composition or realization. Neither wholes nor their parts are more fundamental. Neither is prior. Ne

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20

Neider, Daniel, P. Madhusudan, Shambwaditya Saha, Pranav Garg, and Daejun Park. "A Learning-Based Approach to Synthesizing Invariants for Incomplete Verification Engines." Journal of Automated Reasoning 64, no. 7 (2020): 1523–52. http://dx.doi.org/10.1007/s10817-020-09570-z.

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Abstract We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counterexample guided inductive synthesis principle and allows verification engines to communicate non-provability information to guide invariant synthesis. We show precisely how the verification engine can compute such non-provability information and how to build effective learning algorithms when invariants are expressed as Boolean combinations of a fixed set of predicates.

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21

Molchanov, Ilya, and Michael Schmutz. "Exchangeability-type properties of asset prices." Advances in Applied Probability 43, no. 3 (2011): 666–87. http://dx.doi.org/10.1239/aap/1316792665.

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Let η = (η1,…,ηn) be a positive random vector. If its coordinates ηi and ηj are exchangeable, i.e. the distribution of η is invariant with respect to the swap πij of its ith and jth coordinates, then Ef(η) = Ef(πijη) for all integrable functions f. In this paper we study integrable random vectors that satisfy this identity for a particular family of functions f, namely those which can be written as the positive part of the scalar product 〈u, η〉 with varying weights u. In finance such functions represent payoffs from exchange options with η being the random part of price changes, while from the

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Molchanov, Ilya, and Michael Schmutz. "Exchangeability-type properties of asset prices." Advances in Applied Probability 43, no. 03 (2011): 666–87. http://dx.doi.org/10.1017/s0001867800005097.

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Let η = (η1,…,ηn) be a positive random vector. If its coordinates ηiand ηjare exchangeable, i.e. the distribution of η is invariant with respect to the swap πijof itsith andjth coordinates, then Ef(η) = Ef(πijη) for all integrable functionsf. In this paper we study integrable random vectors that satisfy this identity for a particular family of functionsf, namely those which can be written as the positive part of the scalar product 〈u, η〉 with varying weightsu. In finance such functions represent payoffs from exchange options with η being the random part of price changes, while from the geometr

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23

Skinner, Joshua, and Anatoly Neishtadt. "Unusual properties of adiabatic invariance in a billiard model related to the adiabatic Piston problem." Theoretical and Applied Mechanics, no. 00 (2025): 6. https://doi.org/10.2298/tam241121006s.

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We consider the motion of two massive particles along a straight line. A lighter particle bounces back and forth between a heavier particle and a stationary wall, with all collisions being ideally elastic. This is one of canonical models in the theory of adiabatic invariants. It is known that if the lighter particle moves much faster than the heavier one, and the kinetic energies of the particles are of the same order, then the product of the speed of the lighter particle and the distance between the heavier particle and the wall is an adiabatic invariant: its value remains approximately const

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24

Honarvar Shakibaei, Barmak, and Peyman Jahanshahi. "Image Deconvolution by Means of Frequency Blur Invariant Concept." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/951842.

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Different blur invariant descriptors have been proposed so far, which are either in the spatial domain or based on the properties available in the moment domain. In this paper, a frequency framework is proposed to develop blur invariant features that are used to deconvolve a degraded image caused by a Gaussian blur. These descriptors are obtained by establishing an equivalent relationship between the normalized Fourier transforms of the blurred and original images, both normalized by their respective fixed frequencies set to one. Advantage of using the proposed invariant descriptors is that it

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Choi, Jeong Ryeol. "Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems." Advances in Mathematical Physics 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/120573.

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An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated us

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Rowe, Jonathan E., Michael D. Vose, and Alden H. Wright. "Representation Invariant Genetic Operators." Evolutionary Computation 18, no. 4 (2010): 635–60. http://dx.doi.org/10.1162/evco_a_00007.

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A genetic algorithm is invariant with respect to a set of representations if it runs the same no matter which of the representations is used. We formalize this concept mathematically, showing that the representations generate a group that acts upon the search space. Invariant genetic operators are those that commute with this group action. We then consider the problem of characterizing crossover and mutation operators that have such invariance properties. In the case where the corresponding group action acts transitively on the search space, we provide a complete characterization, including hi

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27

Sokolov, M. V. "The Turaev-viro Invariant for 3-Manifolds is a Sum of Three Invariants." Canadian Mathematical Bulletin 39, no. 4 (1996): 468–75. http://dx.doi.org/10.4153/cmb-1996-055-1.

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AbstractWe show that every Turaev-Viro invariant for 3-manifolds is a sum of three new invariants and discuss their properties. We also find a solution of a conjecture of L. H. Kauffman and S. Lins. Tables of the invariants for closed orientable 3-manifolds of complexity ≤ 3 are presented at the end of the paper.

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Ndogmo, J. C. "Properties of the Invariants of Solvable Lie Algebras." Canadian Mathematical Bulletin 43, no. 4 (2000): 459–71. http://dx.doi.org/10.4153/cmb-2000-054-0.

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AbstractWe generalize to a field of characteristic zero certain properties of the invariant functions of the coadjoint representation of solvable Lie algebras with abelian nilradicals, previously obtained over the base field ℂ of complex numbers. In particular we determine their number and the restricted type of variables on which they depend. We also determine an upper bound on the maximal number of functionally independent invariants for certain families of solvable Lie algebras with arbitrary nilradicals.

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Moyotl, A., H. Novales-Sanchez, J. J. Toscano, and E. S. Tututi. "Gauge invariant electromagnetic properties of fermions induced by CPT-violation in the Standard Model Extension." International Journal of Modern Physics A 29, no. 08 (2014): 1450039. http://dx.doi.org/10.1142/s0217751x14500390.

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Low-energy Lorentz-invariant quantities could receive contributions from a fundamental theory producing small Lorentz-violating effects. Within the Lorentz-violating extension of quantum electrodynamics, we investigate, perturbatively, the contributions to the one-loop ffγ vertex from the CPT-violating axial coupling of a vector background field to fermions. We find that the resulting vertex function has a larger set of Lorentz structures than the one characterizing the usual, Lorentz-invariant, parametrization of the ffγ vertex. We prove gauge invariance of the resulting one-loop expression t

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30

Lebiedowska, Maria K., and Malgorzata Syczewska. "Invariant sway properties in children." Gait & Posture 12, no. 3 (2000): 200–204. http://dx.doi.org/10.1016/s0966-6362(00)00080-1.

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31

Dahan, Xavier, Éric Schost, and Jie Wu. "Evaluation properties of invariant polynomials." Journal of Symbolic Computation 44, no. 11 (2009): 1592–604. http://dx.doi.org/10.1016/j.jsc.2008.12.002.

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32

Hedrick, J. K., and T. Butsuen. "Invariant Properties of Automotive Suspensions." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 204, no. 1 (1990): 21–27. http://dx.doi.org/10.1243/pime_proc_1990_204_128_02.

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Dynamic systems which are composed of interconnected sub-systems are subject to dynamic ‘constraint equations’ which are independent of the nature of the interconnections. A dynamic constraint equation is developed for a quarter car model of an automotive suspension. It is shown that only one of the three transfer functions (acceleration, suspension deflection and tyre deflection) can be independently specified and that the first two contain ‘invariant points’ at frequencies within the frequency range of interest. These constraint equations lead to conclusions with respect to trade-offs betwee

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Zhu, Yujun, Jinlian Zhang, and Yanping Guo. "Invariant properties of limit shadowing." Applied Mathematics-A Journal of Chinese Universities 19, no. 3 (2004): 279–87. http://dx.doi.org/10.1007/s11766-004-0036-7.

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Metafune, Giorgio, Diego Pallara, and Abdelaziz Rhandi. "Global properties of invariant measures." Journal of Functional Analysis 223, no. 2 (2005): 396–424. http://dx.doi.org/10.1016/j.jfa.2005.02.001.

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Dovgoshey, Oleksiy, and Juhani Riihentaus. "Bi-Lipschitz Mappings and Quasinearly Subharmonic Functions." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–8. http://dx.doi.org/10.1155/2010/382179.

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After considering a variant of the generalized mean value inequality of quasinearly subharmonic functions, we consider certain invariance properties of quasinearly subharmonic functions. Kojić has shown that in the plane case both the class of quasinearly subharmonic functions and the class of regularly oscillating functions are invariant under conformal mappings. We give partial generalizations to her results by showing that inℝn,n≥2, these both classes are invariant under bi-Lipschitz mappings.

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Kalitine, Boris S. "Pseudo-prolongations in the qualitative theory of dynamical systems." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (December 16, 2022): 45–53. http://dx.doi.org/10.33581/2520-6508-2022-3-45-53.

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This paper considers the qualitative behaviour of the flow in a neighbourhood of closed invariant sets of dynamical systems. The properties of compactness, invariance, and connectivity of pseudo-prolongations are investigated. A rather deep analysis of the flow in the vicinity of a compact invariant set of asymptotically compact phase spaces is presented. The connection of pseudo-prolongation with the first positive prolongation of T. Ura and the set of weakly elliptic points is refined.

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Balk, A. M. "The Rossby wave extra invariant in the dynamics of 3-D fluid layers and the generation of zonal jets." Nonlinear Processes in Geophysics 21, no. 1 (2014): 49–59. http://dx.doi.org/10.5194/npg-21-49-2014.

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Abstract. We consider an adiabatic-type (approximate) invariant that was earlier obtained for the quasi-geostrophic equation and the shallow water system; it is an extra invariant, in addition to the standard ones (energy, enstrophy, momentum), and it is based on the Rossby waves. The presence of this invariant implies the energy transfer from small-scale eddies to large-scale zonal jets. We show that this extra invariant can be extended to the dynamics of a three-dimensional (3-D) fluid layer on the beta plane. Combined with the investigation of other researchers, this 3-D extension implies e

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Xie, Wei, and Weijing Li. "Entanglement properties of random invariant quantum states." Quantum Information and Computation 22, no. 11&12 (2022): 901–23. http://dx.doi.org/10.26421/qic22.11-12-1.

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Entanglement properties of random multipartite quantum states which are invariant under global $\textnormal{SU}(d)$ action are investigated. The random states live in the tensor power of an irreducible representation of $\textnormal{SU}(d)$. We calculate and analyze the expectation and fluctuation of the second-order R\'enyi entanglement measure of the random invariant and near-invariant states in high dimension, and reveal the phenomenon of concentration of measure the random states exhibit. We show that with high probability a random SU($d$)-invariant state is close to being maximally entang

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Khorshidi, Maryam, Mehdi Nadjafikhah, Hossein Jafari, and Maysaa Al Qurashi. "Reductions and conservation laws for BBM and modified BBM equations." Open Mathematics 14, no. 1 (2016): 1138–48. http://dx.doi.org/10.1515/math-2016-0101.

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AbstractIn this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation laws of the BBM and MBBM equations are presented. Some aspects of their symmetry

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Zhao, Di, Tal-Yun Ho, Chol-Yong Jon, and Wanxiao Tang. "Geometric invariants under a SMRC-transformation group on manifolds and an application to asset pricing." Filomat 38, no. 29 (2024): 10303–21. https://doi.org/10.2298/fil2429303z.

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We investigate and confirm the geometric invariants under a SMRC-transformation group on manifolds and propose an interesting asset pricing model via the geometric invariant and martingale idea in a financial market. In this case we achieve, for the first time, an interesting example for the category of invariant geometries with respect to semi-symmetric connections. By virtue of the projective confor-mal semi-symmetric metric recurrent connection and the corresponding curvature tensors, the celebrated Schur?s theorem, which is used to characterize the geometric properties of spaces, is also o

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DUNDAR, ERDINC, UGUR ULUSU, and FATIH NURAY. "On ideal invariant convergence of double sequences and some properties." Creative Mathematics and Informatics 27, no. 2 (2018): 161–69. http://dx.doi.org/10.37193/cmi.2018.02.08.

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In this paper, we study the concepts of invariant convergence, p-strongly invariant convergence [V 2 σ ]p , I2-invariant convergence I σ 2 , I ∗ 2 - invariant convergence I σ∗ 2 of double sequences and investigate the relationships among invariant convergence, [V 2 σ ]p, I σ 2 and I σ∗ 2 . Also, we introduce the concepts of I σ 2 -Cauchy double sequence and I σ∗ 2 -Cauchy double sequen

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42

MARSHALL, T. J., and D. G. C. MCKEON. "RADIATIVE PROPERTIES OF THE STUECKELBERG MECHANISM." International Journal of Modern Physics A 23, no. 05 (2008): 741–48. http://dx.doi.org/10.1142/s0217751x08039499.

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We examine the mechanism for generating a mass for a U(1) vector field introduced by Stueckelberg. First, it is shown that renormalization of the vector mass is identical to the renormalization of the vector field on account of gauge invariance. We then consider how the vector mass affects the effective potential in scalar quantum electrodynamics at one-loop order. The possibility of extending this mechanism to couple, in a gauge invariant way, a charged vector field to the photon is discussed.

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Liu, Ping, Senyue Lou, and Lei Peng. "Second-Order Approximate Equations of the Large-Scale Atmospheric Motion Equations and Symmetry Analysis for the Basic Equations of Atmospheric Motion." Symmetry 14, no. 8 (2022): 1540. http://dx.doi.org/10.3390/sym14081540.

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In this paper, symmetry properties of the basic equations of atmospheric motion are proposed. The results on symmetries show that the basic equations of atmospheric motion are invariant under space-time translation transformation, Galilean translation transformations and scaling transformations. Eight one-parameter invariant subgroups and eight one-parameter group invariant solutions are demonstrated. Three types of nontrivial similarity solutions and group invariants are proposed. With the help of perturbation method, we derive the second-order approximate equations for the large-scale atmosp

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Semenov, Vladimir. "The 3D Navier–Stokes Equations: Invariants, Local and Global Solutions." Axioms 8, no. 2 (2019): 41. http://dx.doi.org/10.3390/axioms8020041.

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In this article, I consider local solutions of the 3D Navier–Stokes equations and its properties such as an existence of global and smooth solution, uniform boundedness. The basic role is assigned to a special invariant class of solenoidal vector fields and three parameters that are invariant with respect to the scaling procedure. Since in spaces of even dimensions the scaling procedure is a conformal mapping on the Heisenberg group, then an application of invariant parameters can be considered as the application of conformal invariants. It gives the possibility to prove the sufficient and nec

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Smith, Larry. "Modular Vector Invariants of Cyclic Permutation Representations." Canadian Mathematical Bulletin 42, no. 1 (1999): 125–28. http://dx.doi.org/10.4153/cmb-1999-014-5.

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AbstractVector invariants of finite groups (see the introduction for an explanation of the terminology) have often been used to illustrate the difficulties of invariant theory in the modular case: see, e.g., [1], [2], [4], [7], [11] and [12]. It is therefore all the more surprising that the unpleasant properties of these invariants may be derived from two unexpected, and remarkable, nice properties: namely for vector permutation invariants of the cyclic group of prime order in characteristic p the image of the transfer homomorphism is a prime ideal, and the quotient algebra is a polynomial alg

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Alotaibi, Abdullah, M. Mursaleen, and M. A. Alghamdi. "Invariant and Absolute Invariant Means of Double Sequences." Journal of Function Spaces and Applications 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/465364.

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We examine some properties of the invariant mean, define the concepts of strongσ-convergence and absoluteσ-convergence for double sequences, and determine the associated sublinear functionals. We also define the absolute invariant mean through which the space of absolutelyσ-convergent double sequences is characterized.

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SILVER, DANIEL S., and SUSAN G. WILLIAMS. "POLYNOMIAL INVARIANTS OF VIRTUAL LINKS." Journal of Knot Theory and Its Ramifications 12, no. 07 (2003): 987–1000. http://dx.doi.org/10.1142/s0218216503002901.

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Properties of polynomial invariants Δi for oriented virtual links are established. The effects of taking mirror images and reversing orientation of the link diagram are described. The relationship between Δ0(u,v) and an invariant of F. Jaeger, L. Kauffman, H. Saleur and J. Sawollek is discussed.

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Jaramillo-Quiceno, Julio C. "OPERADORES DE DIFERENCIALES q- Y DERIVACIONES DE LAS ALGEBRAS INVARIANTES RELATIVISTAS CUADRÁTICAS." MOMENTO, no. 69 (July 30, 2024): 116–36. http://dx.doi.org/10.15446/mo.n69.115338.

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This study aims to develop a new algebra based on the Minkowskian product or relativistic Lorentz invariants. This leads to the notion of q- invariant algebras, defining q- deformed quadratic relativistic algebras and establishing some q- differential operators and derivations. Then, from these algebras, we define the q- relativistic invariant function on a free algebra k⟨x, y, z, u⟩ with the objective of formulating the q- differential quadratic operators. On the other hand, we define the q- quadratic differential operators on the Clifford algebra Cl0,n. We consider the case of a polynomial f

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Maroto, Antonio L. "TDiff invariant field theories for cosmology." Journal of Cosmology and Astroparticle Physics 2024, no. 04 (2024): 037. http://dx.doi.org/10.1088/1475-7516/2024/04/037.

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Abstract We study scalar field theories invariant under transverse diffeomorphisms in cosmological contexts. We show that in the geometric optics approximation, the corresponding particles move along geodesics and contribute with the same active mass (energy) to the gravitational field as in Diff invariant theories. However, for low-frequency (super-Hubble) modes, the contributions to the energy-momentum tensor differ from that of Diff invariant theories. This opens up a wide range of possibilities for cosmological model building. As an example, we show that the simplest TDiff invariant scalar

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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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