We prove several results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are quite short.

We consider the stability of the two branches of non-extremal enhançon solutions. We argue that one would expect a transition between the two branches at some value of the non-extremality, which should manifest itself in some instability. We study small perturbations of these solutions, constructing a sufficiently general ansatz for linearised perturbations of the non-extremal solutions, and sh...

The paper is devoted to a new approach for solution of some discrete extremal problems, such as the edge isoperimetric problem for graphs, the bisection width problem, the shadow and boundary minimization problems and others, on the carte-sian product of graphs and posets. The main aspect of the approach is in nding of some equivalence relations between the functions in the named problems via r...

The scattering of R-R gauge bosons off of Dirichlet p-branes is computed to leading order in the string coupling. The results are qualitatively similar to those found in the scattering of massless NS-NS bosons: all p-branes with p ≥ 0 exhibit stringy properties, in particular the Regge behavior. Both the R-R and NS-NS scattering amplitudes agree in the limit of small momentum transfer with scat...

We consider invariant measures for the stochastic Burgers equation on \({\mathbb {R}}\), forced by derivative of a spacetime-homogeneous Gaussian noise that is white in time and smooth space. An measure indecomposable, or extremal, if it cannot be represented as convex combination other measures. show each \(a\in {\mathbb there unique indecomposable law spacetime-stationary solution with mean a...

Some results on the existence of solution for certain fuzzy equations are revised and extended. In this paper, we establish the existence of a solution for the fuzzy equation Ex2 +Fx+G= x, where E, F, G, and x are positive fuzzy numbers satisfying certain conditions. To this purpose, we use fixed point theory, applying results such as the wellknown fixed point theorem of Tarski, presenting some...

We provide regularity results at the boundary for continuous viscosity solutions to nonconvex fully nonlinear uniformly elliptic equations and inequalities in Euclidian domains. We show that (i) any solution of two sided inequalities with Pucci extremal operators is C1,α on the boundary; (ii) the solution of the Dirichlet problem for fully nonlinear uniformly elliptic equations is C2,α on the b...

We study extremal and non-extremal generalizations of the regular non-abelian solution found by Chamseddine and Volkov in 5d N=4 gauged supergravity, which has been shown by Maldacena and Nastase to describe a system of NS5-branes wrapping an S dual to three-dimensional U(N) N = 1 supersymmetric Yang-Mills with Chern-Simons coupling k = N 2 . All black hole solutions have a temperature larger t...

In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. The optimal solution can be found as an extremal, solution of the Maximum Principle and analyzed with the techniques of geometric control. This leads to a numerical investigation based on so-called indirect methods using the HamPath software. The results are then compare...

Multidimensional minimax single facility location problems with Chebyshev distance are examined within the framework of idempotent algebra. A new algebraic solution based on an extremal property of the eigenvalues of irreducible matrices is given. The solution reduces both unconstrained and constrained location problems to evaluation of the eigenvalue and eigenvectors of an appropriate matrix. ...