Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse dimensionality is addressed by parametrizing many-body state in terms partially contracted tensors. These tensors form substantially reduced set effective degrees freedom. In practical algorithms, functionals like energy expectation values or overlaps optimized over certain sets TN...

The objective of this paper is to present a comprehensive study of dual representations of risk measures and convex functionals defined on an Orlicz space L or an Orlicz heart H. The first part of our study is devoted to the Orlicz pair (L, L). In this setting, we present a thorough analysis of the relationship between order closedness of a convex set C in L and the closedness of C with respect...

Let X be a topological space and let Φ ⊂ C(X). Then there exists a topological space Y containing X as a subspace and such that Φ = C(Y )|X, if and only if Φ is weakly composition closed, i.e., for any index set I, any fi ∈ Φ (i ∈ I) and any continuous map k : R → R we have k ◦ 〈fi〉 ∈ Φ, where 〈fi〉 : X → R is the map with i-th coordinate fi. The analogous statement is valid for functions to any...

where Ω is an ordinal (or the class of ordinals) and F is a family of (unary or finitary) operations on a topological space. The natural semantics is as follows: the modality 〈α〉 is interpreted by the αth iteration of the Cantor derivative, while the modalities 〈F 〉 and (F−1) are interpreted by the image and the preimage of the operation F . We describe logics in this language that are sound w....

We apply the existence and special properties of Gauduchon metrics to give several applications. The first one is concerned with implications algebro-geometric nature under a Hermitian metric nonnegative holomorphic sectional curvature. second show non-existence sections on vector bundles certain conditions. third restriction $\partial\bar{\partial}$-closedness some real $(n-1,n-1)$-forms compa...

In this paper, we first consider the class of minimal time functions in general setting locally convex topological vector (LCTV) spaces. The results obtained framework are based on a novel notion closedness target sets with respect to constant dynamics. Then, introduce and investigate new signed functions, which generalizations distance functions. Subdifferential formulas for under convexity as...

We study Blaschke-Santal\'o diagrams associated to the torsional rigidity and first eigenvalue of Laplacian with Dirichlet boundary conditions. work under convexity volume constraints, in both strong (volume exactly one) weak at most form. discuss some topological (closedness, simply connectedness) geometric (shape boundaries, slopes near point corresponding ball) properties these diagrams, als...

In this paper, we prove some common fixed point theorems for four weakly compatible self-maps along with (CLR) property in fuzzy 2- metric spaces. Our results are the improved version of proved by Shojaei et al. [1] 2013, since our does not require closedness ranges subsets X.

In this paper, we introduce techniques for producing normal square-free monomial ideals from old such ideals. These are then used to investigate the normality of cover under some graph operations. Square-free that come out as linear combinations two shown be not necessarily normal; a case integral closedness all powers these