Comparison of numerical performances of two methods for coefficient inverse problems is described. The first one is the classical Gel’fand-Levitan-Krein equation method, and the second one is the recently developed approximately globally convergent numerical method. This comparison is performed for both computationally simulated and experimental data. 2010 AMS subject classification: 35R25, 35R30

This paper extends Krein-Rutman's theorem on linear operators leaving an invariant cone in infinite-dimensional Banach spaces to multivalued convex functions. The result is applied to obtain necessary and sufficient conditions for global controllability and reachability of nonlinear discrete-time systems described by convex processes.

BRANKO CURGUS and BRANKO NAJMAN Deenitizable operators in Krein spaces have spectral properties similar to those of selfadjoint operators in Hilbert spaces. A suucient condition for deenitizability of a selfadjoint operator A with a nonempty resolvent set (A) in a Krein space (H; j ]) is the niteness of the number of negative squares of the form Axjy] (see 10, p. 11]). In this note we consider ...

Krein space operator-theoretic methods are used to prove that the operator (sgnx)-j-j is similar to a selfadjoint operator in the Hubert space ¿2(R) • Let L be a symmetric ordinary differential expression. Spectral properties of the operators associated with the weighted eigenvalue problem Lu = Xwu have been studied extensively. When w is positive, this problem leads to a selfadjoint problem in...

It was shown that linked systems of symmetric designs with a1 = 0 and mutually unbiased bases (MUBs) are triply regular association schemes. In this paper, we characterize triple regularity of linked systems of symmetric designs by its Krein number. And we prove that a maximal set of MUBs carries a quadruply regular association scheme and characterize the quadruple regularity of MUBs by its par...

Motivated by the concept of complete pairs, which was introduced by Krein and Langer, we present the concepts of an almost complete pair of matrices and a complete triple of matrices. It is proved that an almost complete pair of matrices can be extended to a complete triple. An application of the result to differential equations is also given.

G. Žitković defined the notion of a convexly compact set in a topological space and, among other things, used it to give an extension of the Walrasian excess-demand theorem. We continue the study of convexly compactness in LCS spaces and prove a Krein-Milman theorem in this setting.

In this paper, we consider two new uniqueness results for fuzzy fractional differential equations (FFDEs) involving Riemann-Liouville generalized H-differentiability with the Nagumo-type condition and the Krasnoselskii-Krein-type condition. To this purpose, the equivalent integral forms of FFDEs are determined and then these are used to study the convergence of the Picard successive approximati...