No abstract

Cauchy principal value is a standard method applied in mathematical applications by which an improper, and possibly divergent, integral is measured in a balanced way around singularities or at infinity. On the other hand, entropy prediction of systems behavior from a thermodynamic perspective commonly involves contour integrals. With the aim of facilitating the calculus of such integrals in this entropic scenario, we revisit the generalization of Cauchy principal value to complex contour integral, formalize its definition and-by using residue theory techniques-provide an useful way to evaluate them.

No abstract

If ( , , μ) is a finite measure space and X a Banach space whose dual has a countable norming set we provide a proof of the fact that the space of all weakly μ-measurable (classes of scalarly equivalent) Pettis integrable functions f : → X of finite variation, equipped with the variation norm, contains a copy of c 0 if and only if X does.

Given an unbounded non-decreasing positive function φ, we studied what the relations are between the growth order of any solution of a complex linear differential–difference equation whose coefficients are entire or meromorphic functions of finite φ-order. Our findings extend some earlier well-known results.