Universal quadratic forms and indecomposables in number fields: A survey [PDF]
Communications in Mathematics, 2023 We give an overview of universal quadratic forms and lattices, focusing on the recent developments over the rings of integers in totally real number fields. In particular, we discuss indecomposable algebraic integers as one of the main tools.
Vítězslav Kala
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Gravitation and quadratic forms [PDF]
Journal of High Energy Physics, 2017 The light-cone Hamiltonians describing both pure ( N $$ \mathcal{N} $$ = 0) Yang-Mills and N $$ \mathcal{N} $$ = 4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity.
Sudarshan Ananth +4 more
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Quadratic Forms in Random Matrices with Applications in Spectrum Sensing [PDF]
EntropyQuadratic forms with random kernel matrices are ubiquitous in applications of multivariate statistics, ranging from signal processing to time series analysis, biomedical systems design, wireless communications performance analysis, and other fields ...
Daniel Gaetano Riviello +2 more
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Euclidean-Lorentzian Dichotomy and Algebraic Causality in Finite Ring Continuum [PDF]
EntropyWe present a concise and self-contained extension of the Finite Ring Continuum (FRC) program, showing that symmetry-complete prime shells Fp with p=4t+1 exhibit a fundamental Euclidean-Lorentzian dichotomy.
Yosef Akhtman
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Remarks on Limit Theorems for the Free Quadratic Forms [PDF]
EntropyIn 2021, Ejsmont and Biernacki showed that the free tangent distribution can be used to measure household satisfaction with durable consumer goods. This distribution arises as the limit of free random variables.
Wiktor Ejsmont +2 more
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Sharp deviation bounds for quadratic forms [PDF]
, 2013 This paper presents sharp inequalities for deviation probability of a general quadratic form of a random vector ξ with finite exponential moments. The obtained deviation bounds are similar to the case of a Gaussian random vector.
Vladimir Spokoiny
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On Kitaoka's conjecture and lifting problem for universal quadratic forms [PDF]
Bulletin of the London Mathematical Society, 2021 For a totally positive definite quadratic form over the ring of integers of a totally real number field K$K$ , we show that there are only finitely many totally real field extensions of K$K$ of a fixed degree over which the form is universal (namely ...
Vítězslav Kala, Pavlo Yatsyna
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K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories [PDF]
Categories and General Algebraic Structures with Applications, 2022 We build on previous work on multirings ([17]) that providesgeneralizations of the available abstract quadratic forms theories (specialgroups and real semigroups) to the context of multirings ([10], [14]).
Kaique Roberto, Hugo Mariano
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Universal quadratic forms, small norms and traces in families of number fields [PDF]
, 2020 We obtain good estimates on the ranks of universal quadratic forms over Shanks' family of the simplest cubic fields and several other families of totally real number fields. As the main tool we characterize all the indecomposable integers in these fields
V. Kala, M. Tinkov'a
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Highly reliable two-factor biometric authentication based on handwritten and voice passwords using flexible neural networks [PDF]
Компьютерная оптика, 2020 The paper addresses a problem of highly reliable biometric authentication based on converters of secret biometric images into a long key or password, as well as their testing on relatively small samples (thousands of images).
Alexey Sulavko
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