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On the non-commutative neutrix product of the distributions x(+)(lambda) and x(+)(mu)
(Springer Heidelberg, 2006) Fisher, Brian; Taş, Kenan
Let f and g be distributions and let g(n) = (g * delta(n))(x), where delta(n)(x) is a certain sequence converging to the Dirac delta function. The non-commutative neutrix product f circle g of f and g is defined to be the limit of the sequence {fg(n)}, provided its limit h exists in the sense that [GRAPHICS] for all functions p in D. It is proved that (x(+)(lambda)ln(p)x(+)) circle (x(+)(mu)ln(q)x(+)) = x(+)(lambda+mu)ln(p+q)x(+), (x(-)(lambda)ln(p)x(-)) circle (x(-)mu ln(q)x(-)) = x(-)(lambda+mu)ln(p+q)x(-), for lambda + mu < -1; lambda,mu,lambda+mu not equal -1,-2,... and p,q = 0,1,2.....
On the symmetric space sigma-model kinematics
(World Scientific Publ CO PTE LTD, 2007) Yılmaz, Nejat T.
The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws.
Fractional differentiation and its applications (FDA08) PREFACE
(IOP Publishing LTD, 2009) Baleanu, Dumitru; Machado, J. A. Tenreiro

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