Related papers: Generalisation of an IMO Geometry Problem
In this lecture, we review some of the concepts of generalized geometry, as introduced by Hitchin and developed in the speaker's thesis. We also prove a Hodge decomposition for the twisted cohomology of a compact generalized K\"ahler…
A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.
A special formula for the total mean curvature of an ovaloid is derived. This formula allows us to extend the notion of the mean curvature to the class of boundaries of strictly convex sets. Moreover, some integral formula for ovaloids is…
Information geometric optimization (IGO) is a general framework for stochastic optimization problems aiming at limiting the influence of arbitrary parametrization choices. The initial problem is transformed into the optimization of a smooth…
We discuss new problems in universal algebraic geometry and explain them by boolean equations.
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…
A general method for analytic inversion of geometric integral transforms is proposed
Generalization, the ability to perform well beyond the training context, is a hallmark of biological and artificial intelligence, yet anticipating unseen failures remains a central challenge. Conventional approaches often take a…
We overview the main ideas and techniques of the functional-analytical approach to some extremal problems of convex geometry that stem from the Queen Dido problem.
We present a refinement, by selfimprovement, of the arithmetic geometric inequality.
In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find…
Geometric programming is an important class of optimization problems that enable practitioners to model a large variety of real-world applications, mostly in the field of engineering design. In many real life optimization problem…
A generalization of the concept of twisted internal coHom object in the category of conic quantum spaces (c.f. math.QA/0112233) was outlined in math.QA/0202205. The aim of this article is to discuss in more detail this generalization.
A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…
Coarse geometry, the branch of topology that studies the global properties of spaces, was originally developed for metric spaces and then Roe introduced coarse structures as a large-scale counterpart of uniformities. In the literature,…
Some extensions of an inequality from IMO'2001 are proven by means of the Lagrange multiplier criterion.
In this paper we present an introduction to morphological calculus in which geometrical objects play the rule of generalised natural numbers.
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed…
This is a corrected version of my paper "Application of integral geometry to minimal surfaces" appeared in International J. Math. vol. 4 Nr. 1 (1993), 89-111. The correction concerns Proposition 3.5. We discuss this correction in Appendix…