In an integrodifferential equation (IDE), the unknown function also appears under the integral sign, and it can be expressed in the formwhere u(x) is the unknown function and the parameter p denotes the degree of the derivative. The known functions K(x, t) and f(x) are referred to ...
Second, we present our main mathematical result showing sex gap unimodality in (strongly) coherent models under certain conditions; we discuss the intuition behind the conditions and show by example when multi-modality can occur. Third, we analyze a dynamic Gompertz model as a simple example of ...
For both points, the general growth conditions rule out deriving a PDE or the differentiability of by differentiating under the integral sign. For homogeneous integrands the Euler–Lagrange system can be derived using a Young-measure approach (see [8]), while for the heterogeneous case [4, Theor...
differential invariant as a function on a jet bundle that is invariant under the induced action of a certain group of transformations (see [5]), a second-order ODE is defined to be a section s of p21: J2(p) → J1(p), where p: R2 → R is the natural projection p(x, y) = x...
Under the assumption that (2) has no nontrivial solution satisfying given homogeneous two point boundary conditions it follows that the same is true for (1), provided certain sign and integral conditions hold. The criteria may be thought of as rather general extensions of the Hille-Wintner type...
Furthermore, in order to design fairly constructive stroboscopic strategies, we must determine the conditions under which the terminal set can be "taken out" of the integral sign. Such sufficient conditions can be described in terms of H-convex sets. Below we demonstrate that these conditions are...
One of the major concerns associated with the deceased individuals is the risk of pathogen transmission, and this may be particularly true for eusocial animals due to their enclosed living quarters1,2. In eusocial insects, corpse management is an integral part of the behavioural repertoire for ...
Optimal energy management of electric vehicles using slap swarm optimization and differential flatness control has been proposed. A battery–supercapacitor power system is adopted. Each source is connected in parallel to the DC-bus using DC–DC bidirecti
Ordinary Differential Equations We cannot use numerical quadrature directly to approximate the integral because we do not know the function y(s) and so cannot evaluate the integrand. Nevertheless, the basic idea is to choose a sequence of values of h so that this formula allows us to generate ...
Ordinary differential inclusions are closely related with control theory because Filippov and Ważewski proved that under very mild assumptions the control system x′=f(t,x,u(t)),u(t)∈U is measurable (1.6) may be reduced to the differential inclusion x′(t)∈F(t,x(t)) (see [3]...