arXiv research

The paper examines expectile quadrangle properties in risk management.

The paper introduces a new risk assessment framework using φ-divergence.

This paper extends the Risk Quadrangle framework for risk management and optimization.

Biased mean regression estimates factors exceeding expected loss or radiation release severity.

New risk measure and quadrangle improve financial decision-making.

The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.

SVR analyzed within RQ framework for risk management.

We give a geometric interpretation of the building associated to the real Lie group E_6(-14) in terms of its 54-dimensional module.

In this paper we discuss an extension of Perelman's comparison for quadrangles. Among applications of this new comparison theorem, we study the equidistance evolution of hypersurfaces in Alexandrov spaces with non-negative curvature. We show that, in certain cases, the equidistance evolution of hypersurfaces become tot…

A counterexample is given for the Knaster-like conjecture of Makeev for functions on $S^2$. Some particular cases of another conjecture of Makeev, on inscribing a quadrangle into a smooth simple closed curve, are solved positively.

We show existence of centrally symmetric maps on surfaces all of whose faces are quadrangles and pentagons for each orientable genus $g \geq 0$. We also show existence of centrally symmetric maps on surfaces all of whose faces are hexagons for each orientable genus $g = 2k-1$, $k\in \mathbb{N}$. We enumerate centrally …

In this paper we study geometric, algebraic, and computational aspects of flexibility and infinitesimal flexibility of Kokotsakis meshes. A Kokotsakis mesh is a mesh that consists of a face in the middle and a certain band of faces attached to the middle face by its perimeter. In particular any 3x3-mesh made of quadran…

Study on invariants of complex hyperbolic disc bundles over surfaces, proving a conjecture.

The paper studies quaternionic structures on GKM graphs and their relation to torus actions on quaternionic projective spaces.

New methods reduce bias in estimating optimality gaps for risk-averse stochastic programs.

The study establishes conditions for groups acting on polygonal complexes to contain virtually free subgroups.

Group lattices (Cayley digraphs) of a discrete group are in natural correspondence with differential calculi on the group. On such a differential calculus geometric structures can be introduced following general recipes of noncommutative differential geometry. Despite of the non-commutativity between functions and (gen…

Let M and N be even-dimensional oriented real manifolds, and $u:M \to N$ be a smooth mapping. A pair of complex structures at M and N is called u-compatible if the mapping u is holomorphic with respect to these structures. The quotient of the space of u-compatible pairs of complex structures by the group of u-equivaria…