We present the integral decomposition for fundamental solution of generalized Cattaneo equation with both time derivatives smeared through convoluting them some memory kernels. For power-law kernels ${t}^{\ensuremath{-}\ensuremath{\alpha}}, \ensuremath{\alpha}\ensuremath{\in}(0,1]$ this becomes fractional one governed by Caputo in which highest order is 2. To invert solutions from Fourier-Lapla...

We present a systematic method for reducing an arbitrary one−loop N(≥ 5)−point massless Feynman integral with generic 4−dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D = 6, a triangle integral in D = 4, and a general two−point integral in D = 4 + 2ε space time dimensions. All IR divergences present in the original integral are contained in th...

Singular integral equation that has enormous applications in applied problems including fluid mechanics, biomechanics, electromagnetic theory and chemistry applications such as heat conduction, crystal growth and electrochemistry. An integral equation is called a singular integral equation if one or both limits of integration become infinite, or if the kernel of the equation becomes infinite at...

We work over C, the field of complex numbers. The Prym variety of a double cover C → D of a smooth connected projective curve D by a smooth connected curve C is defined (see [7]) as the identity component of the kernel of the norm homomorphism N : J(C) → J(D) between the Jacobians of the curves. This is an abelian variety polarised by the restriction of the canonical polarisation on J(C); we de...