We develop a level set method for the computation of multivalued solutions to quasi-linear hyperbolic partial differential equations and Hamilton-Jacobi equations in any number of space dimensions. We use the classic idea of Courant and Hilbert to define the solution of the quasi-linear hyperbolic PDEs or the gradient of the solution to the Hamilton-Jacobi equations as zero level sets of level ...

The exact stability condition for certain class of fractional-order multivalued transfer functions is presented. Unlike the conventional case that the stability is directly studied by investigating the poles of the transfer function, in the systems under consideration, the branch points must also come into account as another kind of singularities. It is shown that a multivalued transfer functio...

Next-to-MHV one-loop amplitudes in N = 4 gauge theory can be written as a linear combination of known multivalued functions, called scalar box functions, with coefficients that are rational functions. We consider the localization of these coefficients in twistor space and prove that all of them are localized on a plane. The proof is done by studying the action of differential operators that tes...

In this paper we investigate minimal pairs of continuous selections of four linear functions in R3. Our purpose is to find minimal pairs of compact convex sets (polytops) which represent all 166 (see [2]) continuous selections in CS(y1, y2, y3,− ∑3 i=1 yi) in R 3. We find that these 166 selections are represented by 16 essentialy different minimal pairs which were studied in [5], [9]. Three out...

in this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in cat(0) spaces as well as in uced banach spaces. moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...