In this article, our goal is to prove the existence and uniqueness of solution for 1D and 2D semi-linear hyperbolic equations in a bounded domain with a monotone nonlinear term. We use elliptic regularization and a finite difference scheme in time to build the approximate solutions for the semi-linear hyperbolic equations, and we utilize the regularization method together with the monotonicity ...

This paper deals with approximate solutions of general (that is, without any convexity assumption) multi-objective optimization problems (MOPs). In this text, by reviewing some standard scalarization techniques we are interested in finding the relationships between ε-(weakly, properly) efficient points of an MOP and ε-optimal solutions of the related scalarized problem. For this purpose, the re...

A set K of nodes of a graph G is geodesically convex (respectively, monophonically convex) if K contains every node on every shortest (respectively, chordless) path joining nodes in K. We investigate the classes of graphs which are characterized by certain local convexity conditions with respect to geodesic convexity, in particular, those graphs in which balls around nodes are convex, and those...

Based on a classic paper by Ginibre [Commun. Math. Phys. 8, 26 (1968)] it is shown that, whenever Bogoliubov's approximation, that is, the replacement of a(0) and a*(0) by complex numbers in the Hamiltonian, asymptotically yields the right pressure, it also implies the asymptotic equality of |a(0)|(2)/V and a*(0)a(0)/V in symmetry breaking fields, irrespective of the existence or absence of Bos...

Abstract This paper is devoted to a game-theoretic approach the level-set curvature flow equation with nonlinear dynamic boundary conditions. Under comparison principle for problem, we construct family of deterministic discrete games, whose value functions approximate unique viscosity solution. We also apply game approximation study convexity preserving properties and fattening phenomenon this ...

We characterize the open sets in the sphere that are geodesically convex in any containing domain with respect to various conformal metrics.

Based on the definition of approximate solution (also known as $ \varepsilon $-solution), we propose idea generalized convexity semi-infinite optimization in this research. The nonsmooth sufficient and necessary criteria resilient solutions are then provided. Additionally, it is demonstrated that approximative assumption holds for both strong weak robust dual theorems. efficient cardinality/mea...

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

We discuss several known formulas that use the Macaulay duration and convexity of commonly used cash flow streams to approximate their net present value, compare them with a new approximation formula involves hyperbolic functions. Our objective is assess reliability each under different scenarios. The results in this note should be interest actuarial candidates educators as well analysts workin...