A geometric Ginzburg–Landau problem

Geometric Programming Problem with Trapezoidal Fuzzy Variables

Nowadays Geometric Programming (GP) problem is a very popular problem in many fields. Each type of Fuzzy Geometric Programming (FGP) problem has its own solution. Sometimes we need to use the ranking function to change some part of GP to the linear one. In this paper, first, we propose a method to solve multi-objective geometric programming problem with trapezoidal fuzzy variables; then we use ...

A geometric problem and the Hopf Lemma

A classical result of A. D. Alexandrov states that a connected compact smooth n-dimensional manifold without boundary, embedded in Rn+1, and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of M in a hyperplane Xn+1 = const in case M satisfies: for any two points (X, Xn+1), (X , X̂n+1) on M , with Xn+1 > X̂n+1, the mean curvature at the first is not gre...

A Non-geometric Switch Toggling Problem

Switch toggling games such as Lights Out and the σ-game are widely studied in mathematics and have been applied to model a variety of situations such as genetic networks and cellular automata. This paper introduces a class of toggling games where at each iteration a fixed number of switches is chosen to be toggled where the only switches changed are the switches chosen to be toggled. The switch...

On a Bernoulli problem with geometric constraints

A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane {x1 = 0} where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition...

A Geometric Shortest Path Problem , with Application