Archimedean Cones in Vector Spaces

In the case of an ordered vector space (briefly, OVS) with an order unit, the Archimedeanization method was recently developed by Paulsen and Tomforde [4]. We present a general version of the Archimedeanization which covers arbitrary OVS. Also we show that an OVS (V, V+) is Archimedean if and only if inf(tau is an element of{tau}), y is an element of L(x(tau) - y) = 0 for any bounded below decreasing net {x(tau)}(tau) in V, where L is the collection of all lower bounds of {x(tau)}(tau), and give characterization of the almost Archimedean property of V+ in terms of existence of a linear extension of an additive mapping T : U+ -> V+.


Nonstandard hulls of lattice-normed ordered vector spaces
Aydin, Abdullah; Gorokhova, Svetlana; Gul, Hasan (2018-01-01)
Nonstandard hulls of a vector lattice were introduced and studied in many papers. Recently, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach-Kantorovich space due to Emelyanov, we describe and investigate the nonstandard hull of a lattice-normed space, which is the foregoing generalization of Luxemburg's nonstandard hull of a normed space.
Series solution of the wave equation in optic fiber
Çıldır, Sema; Çakır, Serhat; Department of Physics (2007)
In this study, the mapped Galerkin method was applied to solve the vector wave equation based on H field and to obtain the propagation constant in x y space. The vector wave equation was solved by the transformation of the infinite x y plane onto a unit square. Two-dimensional Fourier series expansions were used in the solutions. Modal fields and propagation constants of dielectric waveguides were calculated. In the first part of the study, all of the calculations were made in step index fibers. Transvers...
BASKAL, S; ERIS, A; SATIR, A (1994-12-19)
The symmetries and associated conservation laws of the SO(2,1) invariant non-linear sigma model equations in 1+1 dimensions are investigated. An infinite family of generalized local symmetries is presented and the uniqueness of these solutions is discussed.
uτ-Convergence in locally solid vector lattices
Dabboorasad, Yousef A M; Emel’yanov, Eduard; Department of Mathematics (2018)
We say that a net (xα) in a locally solid vector lattice (X,τ) is uτ-convergent to a vector x ∈ X if
Nonstandard hulls of ordered vector spaces
Emelyanov, Eduard (2016-06-01)
This paper undertakes the investigation of ordered vector spaces by applying nonstandard analysis. We introduce and study two types of nonstandard hulls of ordered vector spaces. Norm-nonstandard hulls of ordered Banach spaces are also investigated.
Citation Formats
E. Emelyanov, “Archimedean Cones in Vector Spaces,” JOURNAL OF CONVEX ANALYSIS, pp. 169–183, 2017, Accessed: 00, 2020. [Online]. Available: