Results 41 to 50 of about 796,048 (181)

Properties of Generalized Polyhedral Convex Multifunctions [PDF]

arXiv, 2023
This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral convexity under sums and compositions of multifunctions, the domains and ranges of generalized polyhedral convex multifunctions, and the direct and inverse images of sets under such mappings ...
arxiv  

On linearization and uniqueness of preduals

Mathematische Nachrichten, Volume 298, Issue 3, Page 955-975, March 2025.
Abstract We study strong linearizations and the uniqueness of preduals of locally convex Hausdorff spaces of scalar‐valued functions. Strong linearizations are special preduals. A locally convex Hausdorff space F(Ω)$\mathcal {F}(\Omega)$ of scalar‐valued functions on a nonempty set Ω$\Omega$ is said to admit a strong linearization if there are a ...
Karsten Kruse
wiley   +1 more source

Reconstruction of the core convex topology and its applications in vector optimization and convex analysis [PDF]

arXiv, 2017
In this paper, the core convex topology on a real vector space $X$, which is constructed just by $X$ operators, is investigated. This topology, denoted by $\tau_c$, is the strongest topology which makes $X$ into a locally convex space. It is shown that some algebraic notions $(closure ~ and ~ interior)$ existing in the literature come from this ...
arxiv  

Estimating National and Foreign Trade Elasticities Using Generalized Transport Costs

Journal of Regional Science, Volume 65, Issue 2, Page 471-496, March 2025.
ABSTRACT We introduce the definition of two distinct trade elasticities corresponding to imports from regions located in the same country (national elasticities) and foreign regions located in other countries (foreign elasticities). We resort to a three‐tier nested CES utility structure to derive the corresponding demand gravity equations.
José L. Zofío, Jorge Díaz‐Lanchas, Damiaan Persyn, Javier Barbero   +3 more
wiley   +1 more source

Examples of differentiable mappings into non-locally convex spaces [PDF]

arXiv, 2003
Examples of differentiable mappings into real or complex topological vector spaces with specific properties are given, which illustrate the differences between differential calculus in the locally convex and the non-locally convex case. In particular, for a suitable non-locally convex space E, we describe a smooth injection of R into E whose derivative
arxiv  

Affine Non‐Reductive GIT and moduli of representations of quivers with multiplicities

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non‐Reductive GIT. Our quotients come with explicit projective completions, whose boundaries we interpret in terms of the original action.
Eloise Hamilton, Victoria Hoskins, Joshua Jackson   +2 more
wiley   +1 more source

Willmore‐type inequality in unbounded convex sets

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract In this paper, we prove the following Willmore‐type inequality: on an unbounded closed convex set K⊂Rn+1$K\subset \mathbb {R}^{n+1}$ (n⩾2$(n\geqslant 2$), for any embedded hypersurface Σ⊂K${\Sigma }\subset K$ with boundary ∂Σ⊂∂K$\partial {\Sigma }\subset \partial K$ satisfying a certain contact angle condition, there holds 1n+1∫ΣHndA⩾AVR(K)|Bn+
Xiaohan Jia, Guofang Wang, Chao Xia, Xuwen Zhang   +3 more
wiley   +1 more source

Remarks on the $Γ$-regularization of Non-convex and Non-semi-continuous Functions on Topological Vector Spaces [PDF]

Journal of Convex Analysis 19(2):467-483 (2012), 2016
We show that the minimization problem of any non-convex and non-lower semi-continuous function on a compact convex subset of a locally convex real topological vector space can be studied via an associated convex and lower semi-continuous function $\Gamma \left( h\right) $. This observation uses the notion of $\Gamma $-regularization as a key ingredient.
arxiv  

Substitutions on compact alphabets

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract We develop a systematic approach to continuous substitutions on compact Hausdorff alphabets. Focussing on implications of irreducibility and primitivity, we highlight important features of the topological dynamics of their (generalised) subshifts.
Neil Mañibo, Dan Rust, James J. Walton
wiley   +1 more source

On the Nuclearity of Dual Groups [PDF]

arXiv, 2012
We prove that the dual space of a locally convex nuclear $k_\omega$ vector space endowed with the compact--open topology is a locally convex nuclear vector space. An analogous result is shown for nuclear groups. As a consequence of this, we obtain that nuclear $k_\omega$--groups are strongly reflexive.
arxiv