Consider a sequence {xn}n—Q in a normed space X converging to some x* £ X. It is shown that the sequence satisfies a condition of the type ||x* -x„|| < oi||xn xn_¡\\ for some constant a and every n > 1, if the associated null sequence {e„}„=q, en = x* — xn, is uniformly decreasing in norm or if it is alternating with respect to any ordering whose cone of positive elements is acute.

The light–cone lattice approach to the massive Thirring model is reformulated using a local and integrable lattice Hamiltonian written in terms of discrete fermi fields. Several subtle points concerning boundary conditions, normal–ordering, continuum limit, finite renormalizations and decoupling of fermion doublers are elucidated. The relations connecting the six–vertex anisotropy and the vario...

Abstract The aim of this paper is to extend some notions proper minimality from vector optimization set optimization. In particular, we focus our attention on the concepts Henig and Geoffrion minimality, which are well-known in We introduce a generalization both them with finite dimensional spaces, by considering also special class polyhedral ordering cone. framework, prove that these two equiv...

In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (Evans-Steuer) algorithm [12]. Different from it, the proposed algorithm works in the parameter space and does not aim to find the set of all efficient solutions. Instead, it finds a solution in the sense of Lö...

We consider the class of quantum spin chains with arbitrary Uq(sl2)-invariant nearest neighbor interactions, sometimes called SUq(2) for the quantum deformation of SU(2), for q > 0. We derive sufficient conditions for the Hamiltonian to satisfy the property we call Ferromagnetic Ordering of Energy Levels. This is the property that the ground state energy restricted to a fixed total spin subspac...

The notion of a strictly maximal point is a concept of proper maximality that plays an important role in the study of the stability of vector optimization problems. The aim of this paper is to study some properties of this notion with particular attention to geometrical aspects. More precisely, we individuate some relationships between strict maximality and the properties of the bases of the or...

Initially, second-order necessary and sufficient optimality conditions in terms of Hadamard type derivatives for the unconstrained scalar optimization problem φ(x)→ min, x ∈ R, are given. These conditions work with arbitrary functions φ, but they show inconsistency with the classical derivatives. This is a base to pose the question, whether the formulated optimality conditions remain true when ...

Let E be a real Banach space and P a cone in E which defines a partial ordering in E by x ≤ y if and only if y − x ∈ P . P is said to be normal if there exists a positive constant N such that θ ≤ x ≤ y implies ||x|| ≤ N||y||, where θ denotes the zero element of E and the smallest N is called the normal constant of P . If x ≤ y and x / y, we write x < y. For details on cone theory, see 1 . In pa...

Matrix data sets are common nowadays like in biomedical imaging where the Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) modality produces data sets of 3D symmetric positive definite matrices anchored at voxel positions capturing the anisotropic diffusion properties of water molecules in biological tissues. The space of symmetric matrices can be partially ordered using the Löwner ordering...

We survey recent results on first-passage processes in unbounded cones and their applications to ordering of particles undergoing Brownian motion in one dimension. We first discuss the survival probability S(t) that a diffusing particle, in arbitrary spatial dimension, remains inside a conical domain up to time t. In general, this quantity decays algebraically S ∼ t in the long-time limit. The ...