[A]ll theſe Magiſtrates were elected by, and from, the whole promiſcuous Body of the People in their public Aſſemblies; that after the Inſtitution of Cenſors, it was look'd upon as a Matter of Form only, that they should enroll the new Senators at the next general Luſtrum, or Survey of the Commonwealth; […]
You [children] have been told, that Buonaparté is—“a very good?—man:”—that “A Chief-Conſul—” (self-appointed; and all but omnipotent)—“A Chief-Conſul, and proſtitute Conſuleſs, are far better than your old-faſhioned Kings and Queens.
The hysterical claims and missionary-like zeal exhibited by groups who wish to impose their vision of the good upon others is symptomatic of certain asocializing forces in our society.
The aim of this paper consists on the study of the following fourth-order operator: \begin{equation}\label{Ec::T4} T[M]\,u(t)\equiv u{(4)}(t)+p_1(t)\,u'(t)+p_2(t)\,u (t)+M\,u(t)\,,\ t\in I \equiv [a,b]\,, \end{equation} coupled with the two point boundary conditions: \begin{equation}\label{Ec::cf} u(a)=u(b)=u(a)=u (b)=0\,. \end{equation} So, we define the following space: \begin{equation}\label{Ec::esp} X=\left\lbrace u\in C4(I)\quad\mid\quad u(a)=u(b)=u(a)=u (b)=0 \right\rbrace \,. \end{equation} Here p_1∈C³(I) and p_2∈C²(I). By assuming that the second order linear differential equation \begin{equation}\label{Ec::2or} L_2\, u(t)\equiv u"(t)+p_1(t)\,u'(t)+p_2(t)\,u(t)=0\,,\quad t\in I, \end{equation} is disconjugate on I, we characterize the parameter's set where the Green's function related to operator T[M] in X is of constant sign on I⨯I.
