Unified and explicit expressions of three-dimensional Green’s functions and their first derivatives for piezoelectric solids with general anisotropy
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DOI: 10.1016/j.ijsolstr.2018.05.009
Abstract: Abstract Unified and explicit expressions of static three-dimensional generally anisotropic Green’s functions and their first derivatives are presented. The application of residue calculus to the line integral form of the Green’s functions and their derivatives… read more here.
Keywords: three dimensional; explicit expressions; first derivatives; functions first ... See more keywords
New explicit expressions for Dirac bilinears
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DOI: 10.1103/physrevd.97.016005
Abstract: We derive new explicit expressions for the Dirac bilinears based on a generic representation of the massive Dirac spinors with canonical polarization. These bilinears depend on a direction n in Minkowski space which specifies the… read more here.
Keywords: explicit expressions; new explicit; dirac bilinears; expressions dirac ... See more keywords
Interesting Explicit Expressions of Determinants and Inverse Matrices for Foeplitz and Loeplitz Matrices
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DOI: 10.3390/math7100939
Abstract: Foeplitz and Loeplitz matrices are Toeplitz matrices with entries being Fibonacci and Lucas numbers, respectively. In this paper, explicit expressions of determinants and inverse matrices of Foeplitz and Loeplitz matrices are studied. Specifically, the determinant… read more here.
Keywords: explicit expressions; matrix; expressions determinants; determinants inverse ... See more keywords
Some Explicit Expressions for Twisted Catalan-Daehee Numbers
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DOI: 10.3390/sym14020189
Abstract: In this paper, the author considers the twisted Catalan numbers and the twisted Catalan-Daehee numbers, which are arisen from p-adic fermionic integrals and p-adic invariant integrals, respectively. We give some explicit identities and properties for… read more here.
Keywords: twisted catalan; explicit expressions; daehee numbers; catalan daehee ... See more keywords