<mods:mods version="3.3" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-3.xsd" xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><mods:titleInfo><mods:title>Solutions for PDEs with constant coefficients&#13;
and derivability of functions ranged in&#13;
commutative algebras</mods:title></mods:titleInfo><mods:name type="personal"><mods:namePart type="given">А. А.</mods:namePart><mods:namePart type="family">Pogoruі</mods:namePart><mods:role><mods:roleTerm type="text">author</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart type="given">Ramón М.</mods:namePart><mods:namePart type="family">Rodríguez-Dagnіno</mods:namePart><mods:role><mods:roleTerm type="text">author</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart type="given">Мichael</mods:namePart><mods:namePart type="family">Shapіro</mods:namePart><mods:role><mods:roleTerm type="text">author</mods:roleTerm></mods:role></mods:name><mods:abstract>It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper,&#13;
we extend this idea to finite-dimensional commutative algebras; that is, we prove that if some basis of a subspace of a commutative&#13;
algebra satisfies a polynomial equation, then the components of a monogenic function on the subspace are solutions of the respective&#13;
partial differential equation (PDE). We illustrate these concepts with a few examples.</mods:abstract><mods:classification authority="lcc">Mathematical Analysis</mods:classification><mods:originInfo><mods:dateIssued encoding="iso8061">2013</mods:dateIssued></mods:originInfo><mods:originInfo><mods:publisher>John Wiley &amp; Sons</mods:publisher></mods:originInfo><mods:genre>Article</mods:genre></mods:mods>