Let |·| be the standard Euclidean norm on ℝ n and let X=(ℝ ,∥·∥) a normed space. A subspace Y⊂X is strongly α-Euclidean if there constant t such that t|y|≤∥y∥≤αt|y| for every y∈Y, say it α-complemented ∥P Y ∥≤α, where P orthogonal projection from X to ∥ denotes operator of with respect X. We give an example space arbitrarily high dimension 2-Euclidean but contains no 2-dimensional both (1+ϵ)-Eu...

In previous work we established a multilinear duality and factorisation theory for norm inequalities pointwise weighted geometric means of positive linear operators defined on normed lattices. this paper extend the reach first time to setting general spaces. The scope includes Fourier restriction-type inequalities. We also sharpen our operators. Our results all share common theme: estimates mea...

in this paper, we introduce the notion of an action $y_x$as a generalization of the notion of a module,and the notion of a norm $vt: y_xto f$, where $f$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: y_xto [0, 1]subseteq {bf r}$, with $bf r$  the set of all real numbers. a great many standard mappings on algebr...

Strictly proper kernel scores are well-known tools in probabilistic forecasting, while characteristic kernels have been extensively investigated machine learning. We show that both notions coincide, so insights from one part of the literature can be used other. metric induced by a cannot reliably distinguish between distributions far apart total variation norm as soon underlying space measures ...

Researchers have long been interested in the role that norms can play governing agent actions multi-agent systems. Much work has done on formalising normative concepts from human society and adapting them for government of open software systems, simulation processes artificial societies. However, there comparatively little applying MAS mechanisms to understanding society. This investigates this...

In this work, we investigate measurement incompatibility in general probabilistic theories (GPTs). We show several equivalent characterizations of compatible measurements. The first is terms the positivity associated maps. second relates compatibility to inclusion certain generalized spectrahedra. For this, extend theory free spectrahedra ordered vector spaces. third characterization connects d...

assessment of the correlation between rock brittleness and rock fracture toughness has been the subject of extensive research works in the recent years. unfortunately, the brittleness measurement methods have not yet been standardized, and rock fracture toughness cannot be estimated satisfactorily by the proposed indices. in the present study, statistical analyses are performed on some data col...

one of the main distinctions between geomaterials and other engineering materials is the spatial variation of their properties in different directions. this characteristic of geomaterials -so called heterogeneity- is studied herewith. several spatial distributions are introduced to describe probabilistic variation of geotechnical properties of soils. among all, the absolute normal distribution ...