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Quantum Dimension and Quantum Projective Spaces [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2014 We show that the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dabrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element $K_{2 }$ or its inverse. The spectral dimension computed in this sense coincides with the dimension
Matassa, Marco
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Algebraic invariants of the edge ideals of whisker graphs of cubic circulant graphs [PDF]
HeliyonLet Q be a polynomial ring over a field F and I be an edge ideal associated with the whisker graph of a cubic circulant graph. We discuss the regularity, depth, Stanley depth, and projective dimension of Q/I.
Mujahid Ullah Khan Afridi +2 more
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Geometry-Constrained Learning-Based Visual Servoing with Projective Homography-Derived Error Vector [PDF]
SensorsWe propose a novel geometry-constrained learning-based method for camera-in-hand visual servoing systems that eliminates the need for camera intrinsic parameters, depth information, and the robot’s kinematic model.
Yueyuan Zhang +5 more
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Big Finitistic Dimensions for Categories of Quiver Representations [PDF]
Mathematics Interdisciplinary Research, 2021 Assume that A is a Grothendieck category and R is the category of all A-representations of a given quiver Q. If Q is left rooted and A has a projective generator, we prove that the big finitistic flat (resp. projective) dimension FFD(A) (resp. FPD(A)) of
Roghayeh Bagherian, Esmaeil Hosseini
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Certifying dimension of quantum systems by sequential projective measurements [PDF]
Quantum, 2021 This work analyzes correlations arising from quantum systems subject to sequential projective measurements to certify that the system in question has a quantum dimension greater than some $d$.
Adel Sohbi +3 more
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Finitistic dimension conjectures via Gorenstein projective dimension [PDF]
Journal of Algebra, 2022 It is a well-known result of Auslander and Reiten that contravariant finiteness of the class $\mathcal{P}^{\mathrm{fin}}_\infty$ (of finitely generated modules of finite projective dimension) over an Artin algebra is a sufficient condition for validity of finitistic dimension conjectures.
Pooyan Moradifar, Jan Šaroch
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Quasi-projective dimension [PDF]
Pacific Journal of Mathematics, 2021 In this paper, we introduce a new homological invariant called quasi-projective dimension, which is a generalization of projective dimension. We discuss various properties of quasi-projective dimension. Among other things, we prove the following. (1) Over a quotient of a regular local ring by a regular sequence, every finitely generated module has ...
Gheibi, Mohsen +2 more
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A universal scheme for robust self-testing in the prepare-and-measure scenario [PDF]
Quantum, 2021 We consider the problem of certification of arbitrary ensembles of pure states and projective measurements solely from the experimental statistics in the prepare-and-measure scenario assuming the upper bound on the dimension of the Hilbert space. To this
Nikolai Miklin, Michał Oszmaniec
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S-FP-Projective Modules and Dimensions
Journal of Mathematics, 2023 Let R be a ring and let S be a multiplicative subset of R. An R-module M is said to be a u-S-absolutely pure module if ExtR1N,M is u-S-torsion for any finitely presented R-module N. This paper introduces and studies the notion of S-FP-projective modules,
Refat Abdelmawla Khaled Assaad +2 more
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Fractal Dimension of Fractal Functions on the Real Projective Plane
Fractal and Fractional, 2023 In this article, we consider an iterated functions system on the non-Euclidean real projective plane which has a linear structure. Then, we study the fractal dimension of the associated curve as a subset of the projective space and like a set of the ...
Alamgir Hossain +2 more
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