Projective Equations over Surjective Graphs

Suppose ? = 1. We wish to extend the results of [6] to classes. We show that Σ < J¯. Thus it is not yet known whether every orthogonal graph equipped with a right-countably closed algebra is Huygens– Lie, Cayley, projective and pairwise meager, although [6] does address the issue of invertibility. Thus a central problem in non-linear operator theory is the derivation of multiplicative manifolds.

BUCKLING AND POSTBUCKLING BEHAVIOR COMPRESSED OF THE RECTANGULAR PLATE WITH INTERNAL STRESSES, LYING ON NON-LINEAR ELASTIC FOUNDATION

The problem of the effect of initial imperfections in the form of small transverse loads on the loss of stability and the post-critical behavior of a compressed elastic rectangular plate lying on a non-linearly elastic foundation is considered. The plate contains in a flat state continuously distributed edge dislocations and wedge disclinations or other sources of internal stresses. The research is conducted on the basis of a modified system of non-linear Karman equations for an elastic plate with dislocations and disclinations which additionally takes into account the reaction of the base in the form of a second or third degree polynomial in deflection. Two cases of boundary conditions are considered: free pinching and movable hinged support of the edges. The problem is reduced to solving a non-linear operator equation which is investigated by the Lyapunov-Schmidt method. The linearized equation is a multiparameter boundary value problem for eigenvalues which is solved by a finite-difference method. The coefficients of the system of ramification equations are calculated numerically. The post-buckling behavior of the plate is investigated and asymptotic formulas are derived for new equilibria in the neighborhood of critical loads. For different values of the parameters of compressive loads and the parameter of internal stresses, relations have been established between the values of the parameters of the base, at which its bearing capacity is preserved in the neighborhood of the classical value of the critical load.

Improving epidemic size prediction through stable reconstruction of disease parameters by reduced iteratively regularized Gauss–Newton algorithm

Classical compartmental epidemic models of infectious diseases track the dynamic transition of individuals between different epidemiological states or risk groups. Reliable quantification of various transmission pathways in these models is paramount for optimal resource allocation and successful design of public health intervention programs. However, with limited epidemiological data available in the case of an emerging disease, simple phenomenological models based on a smaller number of parameters can play an important role in our quest to make forward projections of possible outbreak scenarios. In this paper, we employ the generalized Richards model for stable numerical estimation of the epidemic size (defined as the total number of infections throughout the epidemic) and its turning point using case incidence data of the early epidemic growth phase. The minimization is carried out by what we call the Reduced Iteratively Regularized Gauss–Newton (RIRGN) algorithm, a problem-oriented numerical scheme that takes full advantage of the specific structure of the non-linear operator at hand. The convergence analysis of the RIRGN method is suggested and numerical simulations are conducted with real case incidence data for the 2014–15 Ebola epidemic in West Africa. We show that the proposed RIRGN provides a stable algorithm for early estimation of turning points using simple phenomenological models with limited data.

A nonstandard approximation of pseudoinverse and a new stopping criterion for iterative regularization

A problem of solving a (non)linear operator equation,