where ki, i = 1, . . . , h, are loop momenta and the denominators Er are either quadratic of linear with respect to ki and external momenta q1, . . . , qN . By default, the integrals are dimensionally regularized with d = 4− 2ǫ. If the number of Feynman integrals needed for a given calculation is small or/and they are simple, one evaluates, by some methods, every scalar Feynman integral of the ...

We characterize continuity and compactness of the Volterra integral operator $T_g$ with non-constant analytic symbol $g$ between certain weighted Fréchet or (LB)-spaces functions on open unit disc, which arise as projective (resp. inductive) limits intersections unions) Bergman spaces order $1<p<\infty$ induced by standard radial weight $(1-|z|^2)^\alpha$ for $0<\alpha&...

Artificial Intelligence (AI) techniques are used for solving the intractable engineering problems. In this study, it is aimed to study the application of artificial bee colony algorithm for predicting the performance of circular diamond saw in sawing of hard rocks. For this purpose, varieties of fourteen types of hard rocks were cut in laboratory using a cutting rig at 5 mm depth of cut, 40 cm/...

surface roughness is a significant parameter which determines the efficiency of optical components. surface damages induced by grinding strongly influence the mechanical strength and optical quality of optical glasses. it is meaningful to rapid evaluate the surface roughness through the measurement of different grinding parameters. in this study, a cup diamond wheel (d64) is used in grinding pr...