Explicit particular solutions have been found for any angle Θ∈ 0,2π]; this is distinct from [1,2] where the explicit solutions only with Θ="π and Θ="2π can be obtained.
The technique of separation of variables is used to derive explicit particular solutions for constant coefficient, singularly perturbed partial differential equations (PDEs) on a rectangular domain with Dirichlet boundary conditions.
Motivated by some of these potentially useful developments, many authors have recently demonstrated the usefulness of fractional calculus in the derivation of explicit particular solutions of a number of linear ordinary and partial differential equations of the second and higher orders.
The problem has not yet received a general precise solution, but explicit particular solutions have been found.
The methodology presented here is based chiefly upon some general theorems on (explicit) particular solutions of some families of fractional differential equations with the Laplace transform and the expansion coefficients of binomial series.
The purpose of this paper is to present a certain class of the explicit particular solutions of the associated Cauchy-Euler fractional partial differential equation of arbitrary real or complex orders and their applications as follows: where u = u ( x, t ) ; A, B, C, M, N, α and β are arbitrary constants.
He has made explicit no particular vision of London; the previous mayor was vociferous in his enthusiasm for a multicultural capital and his glee at finance-driven London's transformation into a de facto city-state increasingly detached from the rest of Britain ("a Singapore of the West", in Mr Livingstone's words).
The first are those whose main verb, called 'performative verb,' makes explicit the particular act that the speaker is performing in producing the utterance.
Rather, they are open to the legitimacy of censorship because they think that the production and consumption of certain sorts of sexually explicit material in particular, violent pornography and non-violent but degrading pornography may in fact cause sufficiently significant harm to others, particularly women.
The germane issue for improvement practitioners, therefore, is not whether they use theory but whether they make explicit the particular theory or theories, informal and formal, they actually use.
Given the complex processes of policymaking, content analysis of policy documents and stakeholder interviews was selected to find how tacit (unspoken), implicit, and indirect knowledge and opinions shaped the policymaking processes and how more explicit and particular use of research evidence was integrated into policymaking processes.
