This paper deals with the boundary value problem involving the differential equation begin{equation*}     ell y:=-y''+qy=lambda y,  end{equation*}  subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$  begin{equation*}     y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0), end{equation*} where $q(x),  a_1 , a_2$ are  rea...

This note studies a network of agents having continuous-time dynamics with quantized interactions and time-varying directed topology. Due to the discontinuity of the dynamics, solutions of the resulting ODE system are intended in the sense of Krasovskii. A limit connectivity graph is defined, which encodes persistent interactions between nodes: if such graph has a globally reachable node, Kraso...

This note studies a network of agents having continuous-time dynamics with quantized interactions and time-varying directed topology. Due to the discontinuity of the dynamics, solutions of the resulting ODE system are intended in the sense of Krasovskii. A limit connectivity graph is defined, which encodes persistent interactions between nodes: if such graph has a globally reachable node, Kraso...

The discovery of conductivity and magnetism at the polar-nonpolar interfaces of insulating nonmagnetic oxides such as LaAlO3 and SrTiO3 has raised prospects for attaining interfacial functionalities absent in the component materials. Yet, the microscopic origin of such emergent phenomena remains unclear, posing obstacles to design of improved functionalities. Here we present first principles ca...

The available experimental data and steady-state calculations make it difficult to explain the M discontinuity beneath both oceans and continents on the basis of the same phase change. The oceanic M discontinuity may be a chemical discontinuity between basalt and peridotite , and a similar chemical discontinuity ma,y thus be expected b�neath the conti­ nents. Since ayailable experimental data p...

Models of dream analysis either assume a continuum of waking and dreaming or the existence of two dissociated realities. Both approaches rely on different methodology. Whereas continuity models are based on content analysis, discontinuity models use a structural approach. In our study, we applied both methods to test specific hypotheses about continuity or discontinuity. We contrasted dream rep...

In the absence of a randomized control trial, regression discontinuity (RD) designs can produce plausible estimates of the treatment effect on an outcome for individuals near a cutoff score. In the standard RD design, individuals with rating scores higher than some exogenously determined cutoff score are assigned to one treatment condition; those with rating scores below the cutoff score are as...

The mission of Wageningen UR (University & Research centre) is ‘To explore the potential of nature to improve the quality of life’. Within Wageningen UR, nine specialised research institutes of the DLO Foundation have joined forces with Wageningen University to help answer the most important questions in the domain of healthy food and living environment. With approximately 30 locations, 6,000 m...

In the current study, the effect of such parameters as the length, position and angle of crack on free vibrations of a cracked plate was examined by finite element method. The assumed crack was internal and through and its growth was ignored. In the proposed finite element model, crack was considered as a discontinuity on the plate surface and the results were compared with the results of other...

We consider, in an open subset Ω of R , energies depending on the perimeter of a subset E ⊂ Ω (or some equivalent surface integral) and on a function u which is defined only on E. We compute the lower semicontinuous envelope of such energies. This relaxation has to take into account the fact that in the limit, the “holes” Ω \ E may collapse into a discontinuity of u, whose surface will be count...