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Journal articles on the topic 'Spectral polytopes'

Author: Grafiati

Published: 30 June 2021

Last updated: 29 July 2025

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1

Greenfeld, Rachel, and Nir Lev. "Fuglede’s spectral set conjecture for convex polytopes." Analysis & PDE 10, no. 6 (2017): 1497–538. http://dx.doi.org/10.2140/apde.2017.10.1497.

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2

KIRAT, IBRAHIM, and ILKER KOCYIGIT. "REMARKS ON SELF-AFFINE FRACTALS WITH POLYTOPE CONVEX HULLS." Fractals 18, no. 04 (2010): 483–98. http://dx.doi.org/10.1142/s0218348x1000510x.

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Suppose that the set [Formula: see text] of real n × n matrices has joint spectral radius less than 1. Then for any digit set D = {d1, …, dq} ⊂ ℝn, there exists a unique non-empty compact set [Formula: see text] satisfying [Formula: see text], which is typically a fractal set. We use the infinite digit expansions of the points of F to give simple necessary and sufficient conditions for the convex hull of F to be a polytope. Additionally, we present a technique to determine the vertices of such polytopes. These answer some of the related questions of Strichartz and Wang, and also enable us to a

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3

Saldanha, Nicolau C., and Carlos Tomei. "Spectra of regular polytopes." Discrete & Computational Geometry 7, no. 4 (1992): 403–14. http://dx.doi.org/10.1007/bf02187851.

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4

Saldanha, Nicolau C., and Carlos Tomei. "Spectra of semi-regular polytopes." Boletim da Sociedade Brasileira de Matem�tica 29, no. 1 (1998): 25–51. http://dx.doi.org/10.1007/bf01245867.

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5

Douai, Antoine. "Global spectra, polytopes and stacky invariants." Mathematische Zeitschrift 288, no. 3-4 (2017): 889–913. http://dx.doi.org/10.1007/s00209-017-1918-8.

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6

Jungers, Raphaël M., Antonio Cicone, and Nicola Guglielmi. "Lifted Polytope Methods for Computing the Joint Spectral Radius." SIAM Journal on Matrix Analysis and Applications 35, no. 2 (2014): 391–410. http://dx.doi.org/10.1137/130907811.

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7

Queiró, João Filipe, and Ana Paula Santana. "The inverse Horn problem." Electronic Journal of Linear Algebra 39 (March 1, 2023): 90–93. http://dx.doi.org/10.13001/ela.2023.7539.

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Alfred Horn's conjecture on eigenvalues of sums of Hermitian matrices was proved more than 20 years ago. In this note, the problem is raised of, given an $n$-tuple $\gamma$ in the solution polytope, constructing Hermitian matrices with the required spectra such that their sum has eigenvalues $\gamma$.

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8

Paluri, Nataraj S. V., and Jayesh J. Barve. "A Reliable Algorithm to Compute the Spectral Set of a Polytope of Polynomials to Prescribed Accuracy." Journal of Dynamic Systems, Measurement, and Control 128, no. 2 (2005): 400–405. http://dx.doi.org/10.1115/1.2196416.

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We propose an algorithm to compute the spectral set of a polytope of polynomials. The proposed algorithm offers several key guarantees that are not available with existing techniques. It guarantees that the generated spectral set: (i) contains all the actual points, (ii) is computed to a prescribed accuracy, (iii) is computed reliably in face of all kinds of computational errors, and (iv) is computed in a finite number of algorithmic iterations. A further merit is that the computational complexity of the proposed algorithm is O(n) in contrast to O(n2) for existing techniques, where n is the de

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9

Samaresh, Ghosh. "Studies on the complexation behaviour of copper(II) ions with polyamidoamine (PAMAM) dendron." Journal Of Indian Chemical Society Vol. 84, Jan 2007 (2007): 93–95. https://doi.org/10.5281/zenodo.5811795.

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Department of Chemistry, Bankura Sammilani College, Bankura-722 102, West Bengal, India <em>E-mail </em>: gsamaresh@yahoo.com <em>Manuscript received 17 October 2006, accepted 27 October 2006</em> Spectral and electrochemical studies have been carried out for the investigation of the complexation behaviour of polytopic dendritic ligand (PAMAM) towards Cu<sup>II</sup> ion. Formation of the complex was clear from the UV-Vis <em>d</em>-<em>d</em> trasition band. Cyclic voltammetric study of the dendron-Cu<sup>II</sup> complex revealed chemically irreversible behaviour.

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10

Cerone, V. "A fast technique for the generation of the spectral set of a polytope of polynomials." Automatica 33, no. 2 (1997): 277–80. http://dx.doi.org/10.1016/s0005-1098(96)00196-3.

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11

Khatsymovsky, V. M. "Spectrum of area in the Faddeev formulation of gravity." Modern Physics Letters A 31, no. 19 (2016): 1650114. http://dx.doi.org/10.1142/s0217732316501145.

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Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual general relativity (GR). Earlier, we have proposed first-order representation of the minisuperspace model for the Faddeev formulation where the tetrad fields are piecewise constant on the polytopes like four-simplices or, say, cuboids into which [Formula: see text] can be decomposed, an analogue of the Cartan–Weyl connection-type form of the Hilbert–Einstein action in the usual conti

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12

Yu, Shiyong. "BEMMA: a hierarchical Bayesian end-member modeling analysis of sediment grain-size distributions." Mathematical Geosciences 48 (August 7, 2026): 723–41. https://doi.org/10.5281/zenodo.14675963.

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Sediment grain-size distributions provide rich information about sedimentary dynamics and potentially about environmental and climatic changes. However, entrainment, transport, and deposition, as a sequence of sorting process, modify original grain-size distributions of source materials, thereby resulting in complex distribution forms that are commonly multimodal and asymmetrical. However, neither traditional descriptive statistics nor curving fitting methods are able to address this complexity fully. End-member modeling analysis, essentially based on polytope expansion, stands out as a flexib

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13

Banigan, James R., Anindita Gayen, and Nathaniel J. Traaseth. "Correlating lipid bilayer fluidity with sensitivity and resolution of polytopic membrane protein spectra by solid-state NMR spectroscopy." Biochimica et Biophysica Acta (BBA) - Biomembranes 1848, no. 1 (2015): 334–41. http://dx.doi.org/10.1016/j.bbamem.2014.05.003.

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14

Wunsch, Patrick, and Walter G. Zumft. "Functional Domains of NosR, a Novel Transmembrane Iron-Sulfur Flavoprotein Necessary for Nitrous Oxide Respiration." Journal of Bacteriology 187, no. 6 (2005): 1992–2001. http://dx.doi.org/10.1128/jb.187.6.1992-2001.2005.

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ABSTRACT Bacterial nitrous oxide (N2O) respiration depends on the polytopic membrane protein NosR for the expression of N2O reductase from the nosZ gene. We constructed His-tagged NosR and purified it from detergent-solubilized membranes of Pseudomonas stutzeri ATCC 14405. NosR is an iron-sulfur flavoprotein with redox centers positioned at opposite sides of the cytoplasmic membrane. The flavin cofactor is presumably bound covalently to an invariant threonine residue of the periplasmic domain. NosR also features conserved CX3CP motifs, located C-terminally of the transmembrane helices TM4 and

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15

Stadler, Adrian-Mihail, Fausto Puntoriero, Francesco Nastasi, Sebastiano Campagna, and Jean-Marie Lehn. "RuIIMultinuclear Metallosupramolecular Rack-Type Architectures of Polytopic Hydrazone-Based Ligands: Synthesis, Structural Features, Absorption Spectra, Redox Behavior, and Near-Infrared Luminescence." Chemistry - A European Journal 16, no. 19 (2010): 5645–60. http://dx.doi.org/10.1002/chem.200900632.

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16

Teslyuk, O. I., S. V. Beltyukova, and O. O. Liventsova. "SORPTION-LUMINESCENT DETERMINATION OF MARKS OF TEA PRODUCTS QUALITY." Odesa National University Herald. Chemistry 29, no. 2(88) (2024): 142–55. https://doi.org/10.18524/2304-0947.2024.2(88).322137.

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Natural organic polyphenolic compounds are essential components of the diet. Determination of the presence and amount of dominant phenolic and polyphenolic components in food objects allows to assess the quality of products, which is important in food expertise. Luminescent sensors based on Ln(III) ion complexes are widely used for the highly sensitive determination of biologically active substances. The spectral and luminescent properties of polyphenolic substances – catechols, which are quality markers of tea products, have been studied. The diversity of isomers and the similarity of the str

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17

Rupa, Sharmin Akther, Md Rassel Moni, Md Abdul Majed Patwary, et al. "Synthesis of Novel Tritopic Hydrazone Ligands: Spectroscopy, Biological Activity, DFT, and Molecular Docking Studies." Molecules 27, no. 5 (2022): 1656. http://dx.doi.org/10.3390/molecules27051656.

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Polytopic organic ligands with hydrazone moiety are at the forefront of new drug research among many others due to their unique and versatile functionality and ease of strategic ligand design. Quantum chemical calculations of these polyfunctional ligands can be carried out in silico to determine the thermodynamic parameters. In this study two new tritopic dihydrazide ligands, N’2, N’6-bis[(1E)-1-(thiophen-2-yl) ethylidene] pyridine-2,6-dicarbohydrazide (L1) and N’2, N’6-bis[(1E)-1-(1H-pyrrol-2-yl) ethylidene] pyridine-2,6-dicarbohydrazide (L2) were successfully prepared by the condensation rea

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18

Loiseau, Frédérique, Cinzia Di Pietro, Scolastica Serroni, et al. "A New Polytopic Bis-diazacrown-ether-polypyridine Ligand and Its Complexes with Zn(II) Salts and Mononuclear and Dendritic Ru(II) Precursors. Synthesis, Absorption Spectra, Redox Behavior, and Luminescence Properties." Inorganic Chemistry 40, no. 27 (2001): 6901–9. http://dx.doi.org/10.1021/ic010338+.

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19

Lev, Nir, and Bochen Liu. "Spectrality of Polytopes and Equidecomposability by Translations." International Mathematics Research Notices, October 31, 2019. http://dx.doi.org/10.1093/imrn/rnz191.

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Abstract Let $A$ be a polytope in ${\mathbb{R}}^d$ (not necessarily convex or connected). We say that $A$ is spectral if the space $L^2(A)$ has an orthogonal basis consisting of exponential functions. A result due to Kolountzakis and Papadimitrakis (2002) asserts that if $A$ is a spectral polytope, then the total area of the $(d-1)$-dimensional faces of $A$ on which the outward normal is pointing at a given direction, must coincide with the total area of those $(d-1)$-dimensional faces on which the outward normal is pointing at the opposite direction. In this paper, we prove an extension of th

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20

Christandl, Matthias, Péter Vrana, and Jeroen Zuiddam. "Universal points in the asymptotic spectrum of tensors." Journal of the American Mathematical Society, November 23, 2021. http://dx.doi.org/10.1090/jams/996.

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Motivated by the problem of constructing fast matrix multiplication algorithms, Strassen (FOCS 1986, Crelle 1987–1991) introduced and developed the theory of asymptotic spectra of tensors. For any sub-semiring X \mathcal {X} of tensors (under direct sum and tensor product), the duality theorem that is at the core of this theory characterizes basic asymptotic properties of the elements of X \mathcal {X} in terms of the asymptotic spectrum of X \mathcal {X} , which is defined as the collection of semiring homomorphisms from X \mathcal {X} to the non-negative reals with a natural monotonicity pro

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21

Winter, Martin. "Capturing Polytopal Symmetries by Coloring the Edge-Graph." Discrete & Computational Geometry, September 27, 2023. http://dx.doi.org/10.1007/s00454-023-00560-7.

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AbstractA (convex) polytope $$P\subset \mathbb {R}^d$$ P ⊂ R d and its edge-graph $$G_P$$ G P can have very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$ G P , that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructe

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22

Narayanan, Hariharan, Rikhav Shah, and Nikhil Srivastava. "A Spectral Approach to Polytope Diameter." Discrete & Computational Geometry, March 16, 2024. http://dx.doi.org/10.1007/s00454-024-00636-y.

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23

Wang, Gang, Jian Meng, Ying Wang, and Liquan Mei. "A priori and a posteriori error estimates for a virtual element method for the non-self-adjoint Steklov eigenvalue problem." IMA Journal of Numerical Analysis, November 1, 2021. http://dx.doi.org/10.1093/imanum/drab079.

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Abstract In this paper we analyze a virtual element method (VEM) for the non-self-adjoint Steklov eigenvalue problem. The conforming VEM on polytopal meshes is used for discretization. We analyze the correct spectral approximation of the discrete scheme and prove an a priori error estimate for the discrete eigenvalues and eigenfunctions. The convergence order of a discrete eigenvalue may decrease if the corresponding eigenfunction has a singularity and it can be improved on a locally refined mesh. The VEM has great flexibility in handling computational meshes. These facts motivate us to constr

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24

Guglielmi, Nicola, and Vladimir Protasov. "Computing the spectral gap of a family of matrices." Mathematics of Computation, June 7, 2023. http://dx.doi.org/10.1090/mcom/3856.

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For a single matrix (operator) it is well-known that the spectral gap is an important quantity, as well as its estimate and computation. Here we consider, for the first time in the literature, the computation of its extension to a finite family of matrices, in other words the difference between the joint spectral radius (in short JSR, which we call here the first Lyapunov exponent) and the second Lyapunov exponent (denoted as SLE). The knowledge of joint spectral characteristics and of the spectral gap of a family of matrices is important in several applications, as in the analysis of the regu

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25

Wei, Xiaoqi, and Guo-Wei Wei. "Homotopy continuation for the spectra of persistent Laplacians." Foundations of Data Science, 2021, 0. http://dx.doi.org/10.3934/fods.2021017.

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<p style='text-indent:20px;'>The <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-persistent <inline-formula><tex-math id="M2">\begin{document}$ q $\end{document}</tex-math></inline-formula>-combinatorial Laplacian defined for a pair of simplicial complexes is a generalization of the <inline-formula><tex-math id="M3">\begin{document}$ q $\end{document}</tex-math></inline-formula>-combinatorial Laplacian. Given a filtration, the spectra of persistent combinatorial Lapla

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26

Nilsson, Erik, and Wietse Boon. "Nodal auxiliary space preconditioners for mixed virtual element methods." ESAIM: Mathematical Modelling and Numerical Analysis, November 13, 2024. http://dx.doi.org/10.1051/m2an/2024081.

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We propose nodal auxiliary space preconditioners for facet and edge virtual elements of lowest order by deriving discrete regular decompositions on polytopal grids and generalizing the Hiptmair-Xu preconditioner to the virtual element framework. The preconditioner consists of solving a sequence of elliptic problems on the nodal virtual element space, combined with appropriate smoother steps. Under assumed regularity of the mesh, the preconditioned system is proven to have bounded spectral condition number independent of the mesh size and this is verified by numerical experiments on a sequence

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27

Bies, Martin, Mirjam Cvetič, Ron Donagi, and Marielle Ong. "Brill-Noether-general limit root bundles: absence of vector-like exotics in F-theory Standard Models." Journal of High Energy Physics 2022, no. 11 (2022). http://dx.doi.org/10.1007/jhep11(2022)004.

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Abstract Root bundles appear prominently in studies of vector-like spectra of 4d F-theory compactifications. Of particular importance to phenomenology are the Quadrillion F-theory Standard Models (F-theory QSMs). In this work, we analyze a superset of the physical root bundles whose cohomologies encode the vector-like spectra for the matter representations (3,2)1/6, ($$ \overline{\textbf{3}} $$ 3 ¯ ,1)−2/3 and (1,1)1. For the family B3($$ {\Delta }_4^{{}^{\circ}} $$ ∆ 4 ° ) consisting of $$ \mathcal{O} $$ O (1011) F-theory QSM geometries, we argue that more than 99.995% of the roots in this su

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28

Oehlmann, Paul-Konstantin, and Thorsten Schimannek. "GV-spectroscopy for F-theory on genus-one fibrations." Journal of High Energy Physics 2020, no. 9 (2020). http://dx.doi.org/10.1007/jhep09(2020)066.

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Abstract We present a novel technique to obtain base independent expressions for the matter loci of fibrations of complete intersection Calabi-Yau onefolds in toric ambient spaces. These can be used to systematically construct elliptically and genus one fibered Calabi-Yau d-folds that lead to desired gauge groups and spectra in F-theory. The technique, which we refer to as GV-spectroscopy, is based on the calculation of fiber Gopakumar-Vafa invariants using the Batyrev-Borisov construction of mirror pairs and application of the so-called Frobenius method to the data of a parametrized auxiliary

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29

Guez, Jeremy, Guillaume Achaz, Francois Bienvenu, et al. "Cultural transmission of reproductive success impacts genomic diversity, coalescent tree topologies and demographic inferences." Genetics, February 14, 2023. http://dx.doi.org/10.1093/genetics/iyad007.

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Abstract Cultural transmission of reproductive success (CTRS) has been observed in many human populations as well as other animals. CTRS consists of a positive correlation of nongenetic origin between the progeny size of parents and children. This correlation can result from various factors, such as the social influence of parents on their children, the increase of children’s survival through allocare from uncles and aunts, or the transmission of resources. Here, we study the evolution of genomic diversity over time under CTRS. CTRS has a threefold impact on population genetics: (1) the effect

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