The formal axiomatic method popularized by Hilbert and recently defended by Hintikka is not fully adequate to the recent practice of axiomatizing mathematical theories. The axiomatic architecture of Topos theory and Homotopy type theory do not fit the pattern of the formal axiomatic theory in the standard sense of the word. However these theories fall under a more general and in some respects m...

The aim of this paper is to make progress towards a geometric model theory for non first order theories. The main difficulty is to work in an environment where the compactness theorem fails. This paper continues the work started in [GrLel]. The main result is an axiomatic approach to the Hrushovski-Zilber group configuration theorem.

The main result of this paper is an intersection representation for a class anisotropic vector-valued function spaces in axiomatic setting à la Hedberg and Netrusov (2007), which includes weighted mixed-norm Besov Lizorkin–Triebel spaces. In the special case classical spaces, gives improvement well-known Fubini property. has applications Lq-Lp-maximal regularity problem parabolic boundary value...

Following an acrimonious referendum on European Union membership, the UK was plunged into chaos as people attempted to negotiate a deeply divided domestic political landscape. In Scotland, things were further complicated by independence question and Scottish National Party’s (SNP) call for second referendum. light of Brexit result, since 2016 many citizens Scotland have re-thought their positio...

Investment and financing decisions are generally made under the assumption of a given objective function. Deriving growth from the value of a firm, however, requires the initial size and discount rates to be known a priori. The presentation of financial planning as a standard dynamic optimization problem usually works with overly restrictive assumptions. As an alternative, it is proposed to arr...

This paper examines the fundamental problem of identifying most important nodes in a network. To date, more than hundred centrality measures have been proposed, each evaluating position node network from different perspective. Our work focuses on PageRank which is one computer science used wide range scientific applications. build theoretical foundation for choosing (or rejecting) specific sett...

Axiomatic principles such as analyticity, unitarity, and crossing symmetry constrain the second derivative of the π π scattering amplitudes in some channels to be positive in a region of the Mandelstam plane. Since this region lies in the domain of validity of chiral perturbation theory, we can use these positivity conditions to bound linear combinations of l̄1 and l̄2. We compare our predictions...