Related papers: Construction schemes: transferring structures from…
We give a systematic and self-contained account of the construction of geometrically decomposed bases and degrees of freedom in finite element exterior calculus. In particular, we elaborate upon a previously overlooked basis for one of the…
We develop new techniques for constructing model structures from a given class of cofibrations, together with a class of fibrant objects and a choice of weak equivalences between them. As a special case, we obtain a more flexible version of…
In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…
We investigate several categories related to transition structures, using a mixture of algebraic and topological methods. We show how two such categories are connected by a contravariant adjunction. This is the most detailed of a family of…
In this paper, we study the random dynamical system $f_\omega^n$ generated by a family of maps $\{f_{\omega_0}: \mathbb{S}^1 \to \mathbb{S}^1\}_{\omega_0 \in [-\varepsilon,\varepsilon]},$ $f_{\omega_0}(x) = \alpha \xi (x+\omega_0) +a\…
The second class constraints algebra of the abelian Chern-Simons theory is rigorously studied in terms of the Hamiltonian embedding in order to obtain the first class constraint system. The symplectic structure of fields due to the second…
All known Moufang sets arise, in some way or another, from an algebraic structure which can be called `division' in some way. In this PhD dissertation, I made an attempt to develop a theory of local Moufang sets, which generalize Moufang…
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…
We study countable structures from the viewpoint of enumeration reducibility. Since enumeration reducibility is based on only positive information, in this setting it is natural to consider structures given by their positive atomic diagram…
Constructor theory is a meta-theoretic approach that seeks to characterise concrete theories of physics in terms of the (im)possibility to implement certain abstract "tasks" by means of physical processes. Process theory, on the other hand,…
We give a systematic approach to constructing non-reduced, locally Cohen-Macaulay schemes with reduced support a smooth projective variety. The hierarchy of such structures includes a lot of information about the underlying variety, its…
Recent experimental works reported observation of the {\omega} structure in steel. Here, stability of the {\omega} structure in steel is investigated based on first-principles with special interests in effects of interstitial C atoms. The…
We present the geometric solutions to some variational problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape…
In this essay we study various notions of projective space (and other schemes) over $\mathbb{F}_{1^\ell}$, with $\mathbb{F}_1$ denoting the field with one element. Our leading motivation is the "Hiden Points Principle," which shows a huge…
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
In this paper, we study shape functions depending on closed submanifolds. We prove a new structure theorem that establishes the general structure of the shape derivative for this type of shape function. As a special case we obtain the…
According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are…
A new construction of naturally reductive spaces is presented. This construction gives a large amount of new families of naturally reductive spaces. First the infinitesimal models of the new naturally reductive spaces are constructed. A…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
We answer an open question in the theory of transducer degrees initially posed in [1] on the existence of a diamond structure in the transducer hierarchy. Transducer degrees are the equivalence classes formed by word transformations which…