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Formalization of Integral Linear Space [PDF]
Formalized Mathematics, 2011 Summary: In this article, we formalize integral linear spaces, that is a linear space with integer coefficients. Integral linear spaces are necessary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm that outputs short lattice base and cryptographic systems with lattice.
Futa, Yuichi +2 more
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CrystalsThe six-dimensional framework of the integral formalism for line defects (straight dislocations and line forces) in anisotropic elasticity has been extended to a 2n-dimensional integral formalism for line defects in quasicrystals (n=4,5,6 for one-, two-,
Markus Lazar
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An operational calculus formulation of fractional calculus with general analytic kernels
Electronic Research Archive, 2022 Fractional calculus with analytic kernels provides a general setting of integral and derivative operators that can be connected to Riemann–Liouville fractional calculus via convergent infinite series.
Noosheza Rani , Arran Fernandez
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Line Defects in One-Dimensional Hexagonal Quasicrystals
MathematicsUsing the eight-dimensional framework of the integral formalism of one-dimensional quasicrystals, the analytical expressions for the displacement fields and stress functions of line defects, which are dislocations and line forces, in one-dimensional ...
Markus Lazar
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Path integrals: From quantum mechanics to photonics
APL Photonics, 2021 The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its dynamical evolution,
Charles W. Robson +3 more
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Virtual Residue and an Integral Formalism [PDF]
The Journal of Geometric Analysis, 2018 We generalize Grothendieck's residues $Res\frac {s}$ to virtual cases, namely cases when the zero loci of the section $s$ has dimension larger than the expected dimension(zero). We also provide an exponential type integral formalism for the virtual residue, which can be viewed as an analogue of the Mathai-Quillen formalism for localized Euler classes.
Huai-Liang Chang, Mu-Lin Li
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Self dual models and mass generation in planar field theory [PDF]
, 2001 We analyse in three space-time dimensions, the connection between abelian self dual vector doublets and their counterparts containing both an explicit mass and a topological mass.
A. Coste +25 more
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Challenges to Path Integral Formulations of Quantum Theories
, 2007 The functional integral has many triumphs in elucidating quantum theory. But incorporating charge fractionalization into that formalism remains a challenge.Comment: 8 pages, 5 ...
Jackiw, R.
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Anomaly and Condensate in the Light-Cone Schwinger Model [PDF]
, 1996 The axial anomaly and fermion condensate in the light cone Schwinger model are studied following path integral methods. This formalism allows for a simple and direct calculation for these and other vacuum dependent phenomena.Comment: 10pp ...
Adler +13 more
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The Lamb-Bateman integral equation and the fractional derivatives
, 2010 The Lamb-Bateman integral equation was introduced to study the solitary wave diffraction and its solution was written in terms of an integral transform. We prove that it is essentially the Abel integral equation and its solution can be obtained using the
Babusci, D., Dattoli, G., Sacchetti, D.
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