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Добірка наукової літератури з теми "Invariant cone"

Автор: Grafiati

Опубліковано: 11 березня 2023

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Статті в журналах з теми "Invariant cone"

1

Kasigwa, Michael, and Michael Tsatsomeros. "Eventual Cone Invariance." Electronic Journal of Linear Algebra 32 (February 6, 2017): 204–16. http://dx.doi.org/10.13001/1081-3810.3484.

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Eventually nonnegative matrices are square matrices whose powers become and remain (entrywise) nonnegative. Using classical Perron-Frobenius theory for cone preserving maps, this notion is generalized to matrices whose powers eventually leave a proper cone K â R^n invariant, that is, A^mK â K for all sufficiently large m. Also studied are the related notions of eventual cone invariance by the matrix exponential, as well as other generalizations of M-matrix and dynamical system notions.

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2

Parrilo, P. A., and S. Khatri. "On cone-invariant linear matrix inequalities." IEEE Transactions on Automatic Control 45, no. 8 (2000): 1558–63. http://dx.doi.org/10.1109/9.871772.

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3

Abbas, Mujahid, and Pasquale Vetro. "Invariant approximation results in‎ ‎cone metric spaces." Annals of Functional Analysis 2, no. 2 (2011): 101–13. http://dx.doi.org/10.15352/afa/1399900199.

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4

Westland, Stephen, and Caterina Ripamonti. "Invariant cone-excitation ratios may predict transparency." Journal of the Optical Society of America A 17, no. 2 (2000): 255. http://dx.doi.org/10.1364/josaa.17.000255.

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5

Chodos, Alan. "Tachyons as a Consequence of Light-Cone Reflection Symmetry." Symmetry 14, no. 9 (2022): 1947. http://dx.doi.org/10.3390/sym14091947.

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We introduce a new symmetry, light-cone reflection (LCR), which interchanges timelike and spacelike intervals. Our motivation is to provide a reason, based on symmetry, why tachyons might exist, with emphasis on application to neutrinos. We show that LCR, combined with translations, leads to a much larger symmetry. We construct an LCR-invariant Lagrangian and discuss some of its properties. In a simple example, we find complete symmetry in the spectrum between tachyons and ordinary particles. We also show that the theory allows for the introduction of a further gauge invariance related to chiral symmetry.

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6

Malesza, Wiktor, and Witold Respondek. "Linear cone-invariant control systems and their equivalence." International Journal of Control 91, no. 8 (2017): 1818–34. http://dx.doi.org/10.1080/00207179.2017.1333153.

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7

Hisabia, Aritra Narayan, and Manideepa Saha. "On Properties of Semipositive Cones and Simplicial Cones." Electronic Journal of Linear Algebra 36, no. 36 (2020): 764–72. http://dx.doi.org/10.13001/ela.2020.5553.

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Анотація:

For a given nonsingular $n\times n$ matrix $A$, the cone $S_{A}=\{x:Ax\geq 0\}$ , and its subcone $K_A$ lying on the positive orthant, called as semipositive cone, are considered. If the interior of the semipositive cone $K_A$ is not empty, then $A$ is named as semipositive matrix. It is known that $K_A$ is a proper polyhedral cone. In this paper, it is proved that $S_{A}$ is a simplicial cone and properties of its extremals are analyzed. An one-one relation between simplicial cones and invertible matrices is established. For a proper cone $K$ in $\mathbb{R}^n$, $\pi(K)$ denotes the collection of $n\times n$ matrices that leave $K$ invariant. For a given minimally semipositive matrix (no column-deleted submatrix is semipositive) $A$, it is shown that the invariant cone $\pi(K_A)$ is a simplicial cone.

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8

BRISUDOVA, MARTINA. "SMALL x DIVERGENCES IN THE SIMILARITY RG APPROACH TO LF QCD." Modern Physics Letters A 17, no. 02 (2002): 59–81. http://dx.doi.org/10.1142/s0217732302006308.

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We study small x divergences in boost invariant similarity renormalization group approach to light-front QCD in a heavy quark–antiquark state. With the boost invariance maintained, the infrared divergences do not cancel out in the physical states, contrary to previous studies where boost invariance was violated by a choice of a renormalization scale. This may be an indication that the zero mode, or nontrivial light-cone vacuum structure, might be important for recovering full Lorentz invariance.

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9

Kosheleva, Olga, and Vladik Kreinovich. "ON GEOMETRY OF FINSLER CAUSALITY: FOR CONVEX CONES, THERE IS NO AFFINE-INVARIANT LINEAR ORDER (SIMILAR TO COMPARING VOLUMES)." Mathematical Structures and Modeling, no. 1 (May 30, 2020): 49–55. http://dx.doi.org/10.24147/2222-8772.2020.1.49-55.

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Some physicists suggest that to more adequately describe the causal structure of space-time, it is necessary to go beyond the usual pseudoRiemannian causality, to a more general Finsler causality. In this general case, the set of all the events which can be influenced by a given event is, locally, a generic convex cone, and not necessarily a pseudo-Reimannian-style quadratic cone. Since all current observations support pseudo-Riemannian causality, Finsler causality cones should be close to quadratic ones. It is therefore desirable to approximate a general convex cone by a quadratic one. This can be done if we select a hyperplane, and approximate intersections of cones and this hyperplane. In the hyperplane, we need to approximate a convex body by an ellipsoid. This can be done in an affine-invariant way, e.g., by selecting, among all ellipsoids containing the body, the one with the smallest volume; since volume is affine-covariant, this selection is affine-invariant. However, this selection may depend on the choice of the hyperplane. It is therefore desirable to directly approximate the convex cone describing Finsler causality with the quadratic cone, ideally in an affine-invariant way. We prove, however, that on the set of convex cones, there is no affine-covariant characteristic like volume. So, any approximation is necessarily not affine-invariant.

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10

HATZINIKITAS, AGAPITOS, and IOANNIS SMYRNAKIS. "CLOSED BOSONIC STRING PARTITION FUNCTION IN TIME INDEPENDENT EXACT pp-WAVE BACKGROUND." International Journal of Modern Physics A 21, no. 05 (2006): 995–1013. http://dx.doi.org/10.1142/s0217751x06025493.

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Анотація:

The modular invariance of the one-loop partition function of the closed bosonic string in four dimensions in the presence of certain homogeneous exact pp -wave backgrounds is studied. In the absence of an axion field, the partition function is found to be modular invariant and equal to the free field partition function. The partition function remains unchanged also in the presence of a fixed axion field. However, in this case, the covariant form of the action suggests summation over all possible twists generated by the axion field. This is shown to modify the partition function. In the light-cone gauge, the axion field generates twists only in the worldsheet σ-direction, so the resulting partition function is not modular invariant, hence wrong. To obtain the correct partition function one needs to sum over twists in the t-direction as well, as suggested by the covariant form of the action away from the light-cone gauge.

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