Related papers: Fonctions constructibles et int\'egration motiviqu…

We show that a large class of formal groups can be realised functorially by even periodic ring spectra. The main advance is in the construction of morphisms, not of objects.

We prove the version of Joyce-Song formula for the Behrend function identities in the motivic setting. The main method we use is the proof of Kontsevich-Soibelman conjecture about the motivic Milnor fibers by Q. T. Le, who uses the method…

We compute the motivic nearby cycles of functions obtained by composition of two functions with distinct sets of variables with a two variable function

This paper deals with some special integral transforms of Bargmann-Fock type in the setting of quaternionic valued slice hyperholomorphic and Cauchy-Fueter regular functions. The construction is based on the well-known Fueter mapping…

Categories of lenses/optics and Dialectica categories are both comprised of bidirectional morphisms of basically the same form. In this work we show how they can be considered a special case of an overarching fibrational construction,…

For functions of two quaternionic variables that are regular in the sense of Fueter, we establish a result similar in spirit to the Hanges and Tr\`eves theorem. Namely, we show that a ball contained in the boundary of a domain is a…

In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…

We use the properties of Hermite and Kamp\'e de F\'eriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of…

The theory of integrals is used to analyse the structure of Hopf algebroids, introduced in math.QA/0302325. We prove that the total algebra of the Hopf algebroid is a separable extension of the base algebra if and only if it is a…

In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook…

The aim of this paper is to generalize Grothendieck's theory of smooth functors in order to include within this framework the theory of fibered categories. We obtain in particular a new characterization of fibered categories.

The First and Second Liouville's Theorems provide correspondingly criterium for integrability of elementary functions "in finite terms" and criterium for solvability of second order linear differential equations by quadratures. The…

We show that in the theory of Daniell integration iterated integrals may always be formed, and the order of integration may always be interchanged. By this means, we discuss product integrals and show that the related Fubini theorem holds…

We show that the framing of $2$-sequences whose generating functions are rational integrate to $3$-sequences. To do so, we give a generalization of Wolstenholme's Theorem.

In this paper, we present new applications of our general minimax theorems. In particular, one of them concerns the multiplicity of global minima for the integral functional of the Calculus of Variations.

We introduce a formalism based on a combinatorial notion of cell complex subject to an inclusion-reversing duality operation. Our main goal is to open the way for a functorial definition of field theories in a context where no manifold or…

This article is first in a series of papers where we reprove the statements in constructing the Enhanced Operation Map and the abstract six-functor formalism developed by Liu-Zheng. In this paper, we prove a theorem regarding constructing…

We shall present and analyze two examples of extended theories of gravitation in Palatini formalism with matter that couples to the connection. This will show that the class of Further Extended Theories of Gravitation introduced in ref. [1]…

We define and study Gysin morphisms on mixed motives over a perfect field. Our construction extends the case of closed immersions, already known from results of Voevodsky, to arbitrary projective morphisms. We prove several classical…

In this paper, an open problem in the multidimensional complex analysis is pesented that arises in the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential…