“…A76, 318–327] presented an enumeration of the 41 physical quantity types in non-relativistic physics, in arbitrary dimensions, based on the formalism of Clifford algebra. Gopalan considered three antisymmetries: spatial inversion, 1, time reversal, 1′, and wedge reversion, 1(†). …”
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“…Instead of describing the detailed analytic procedures of in vivo ligand-receptor imaging, the authors provide a pragmatic approach, along with personal perspectives, for conducting positron emission tomography imaging for receptor occupancy, and systematically elucidate the mathematics of receptor occupancy calculations in practical ways that can be understood with elementary algebra. The authors also share insights regarding positron emission tomography imaging for receptor occupancy to facilitate applications for the development of drugs targeting receptors in the central nervous system.…”
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“…We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N(4/3) for N computational cells used and with N(2/3) (sublinear) when magnetization is given in canonical tensor format. …”
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“…To perform some of the heavy computations, we use the computer algebra package Sigma.…”
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“…A new error bound for the linear complementarity problem when the matrix involved is a B-matrix is presented, which improves the corresponding result in (Li et al. in Electron. J. Linear Algebra 31(1):476-484, 2016). In addition some sufficient conditions such that the new bound is sharper than that in (García-Esnaola and Peña in Appl. …”
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“…In this paper, we demonstrate a complete version of the convergence theory of the modulus-based matrix splitting iteration methods for solving a class of implicit complementarity problems proposed by Hong and Li (Numer. Linear Algebra Appl. 23:629-641, 2016). New convergence conditions are presented when the system matrix is a positive-definite matrix and an [Formula: see text] -matrix, respectively.…”
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“…In this paper, we use the algebra methods, the properties of the r-circulant matrix and the geometric circulant matrix to study the upper and lower bound estimate problems for the spectral norms of a geometric circulant matrix involving the generalized k-Horadam numbers, and we obtain some sharp estimations for them. …”
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“…We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. …”
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“…We prove that for every Bushnell–Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces a bijection between irreducible unitary representations in the two categories. …”
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“…We investigate the action of this group of affine transformations on Legendrian submanifolds of [Formula: see text] by giving a detailed overview of the structure of the algebra of scalar differential invariants, and we show how the scalar differential invariants can be constructed from the central moments. …”
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“…Within the standard missing-data framework, we give a novel characterization of the observed data as a stopping-set sigma algebra. We demonstrate that the usual missingness-at-random conditions are equivalent to requiring particular stochastic processes to be adapted to a set-indexed filtration. …”
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“…Autocatalytic reactions are in certain contrast with the linear algebra of reaction stoichiometry, on which rate equations respecting the permanence of atoms are constructed. …”
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“…After identifying causal structures on groupoids with a particular class of subcategories, called causal categories accordingly, it will be shown that causal structures can be recovered from a particular class of non-selfadjoint class of algebras, known as triangular operator algebras, contained in the von Neumann algebra of the groupoid of the quantum system. …”
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“…Whereas previous proofs of this result used explicit computations of the cardinalities of these groups, we instead use their structure as modules for the Hecke algebra.…”
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“…In addition, the book provides some mathematical developments, such as the detailed analysis of the Lorentz group and its Lie algebra. The book is suitable for students in the third year of a physics degree or on a masters course, as well as researchers and any reader interested in relativity. …”
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“…It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. …”
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“…We present a systematic study on the consequence of the Adler’s zero condition in correlation functions of nonlinear sigma models, by deriving the conserved current and the Ward identity associated with the nonlinear shift symmetry, and demonstrate how the old-fashioned current algebra emerges. The Ward identity leads to a new representation of on-shell amplitudes, which amounts to bootstrapping the higher point amplitudes from lower point amplitudes and adding new vertices to satisfy the Adler’s condition. …”
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“…He has published more than 50 research papers in international journals on topics such as Computability Theory, Machine Learning, Fuzzy Measures and Computational Algebra. His current research focuses on the application Quantum Computing to algebraic, optimization and machine learning problems. …”
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“…He has published more than 50 research papers in international journals on topics such as Computability Theory, Machine Learning, Fuzzy Measures and Computational Algebra. His current research focuses on the application Quantum Computing to algebraic, optimization and machine learning problems. …”
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