Related papers: Weak approximation and rationally connected variet…
We generalize the notion of an exact category and introduce weakly exact categories. A proof of the snake lemma in this general setting is given. Some applications are given to illustrate how one can do homological algebra in a weakly exact…
Let $k$ be a field, $V$ be a $k$-vector space and $X\subset V$ an algebraic irreducible subvariety. We say that a function $f:X(k) \to k$ is weakly linear if its restriction to any two-dimensional linear subspace $W$ of $V$ contained in $X$…
In this paper we develop a Morse-like theory in order to decompose birational maps and morphisms of smooth projective varieties defined over a field of characteristic zero into more elementary steps which are locally \'etale isomorphic to…
The aim of this paper is to address an open problem given in [Kirk, W. A., Shahzad, Naseer, Normal structure and orbital fixed point conditions, J. Math. Anal. Appl. {\bf{vol 463(2)}}, (2018) 461--476]. We give a characterization of weak…
The problem is addressed of defining the values of functions, whose variables tend to infinity, from the knowledge of these functions at asymptotically small variables close to zero. For this purpose, the extrapolation by means of different…
We introduce a notion of quasi-weak equivalences associated with weak-equivalences in an exact category. It gives us a delooping for (idempotent complete) exact categories and a condition that the negative $K$-group of an exact category…
In this paper, rough approximations of Cayley graphs are studied and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition called pseudo-Cayley graphs containing Cayley graphs is proposed. Rough approximation is…
We analyze the partition function of two dimensional Yang-Mills theory on a family of surfaces of infinite genus. These surfaces have a recursive structure, which was used by one of us to compute the partition function that results in a…
We show that there exists, in quantum theory, a close relationship between the weak value and the correlation function, which sheds new lights on the concept of the weak value.
Ren and the second author established that the weakly optimal subvarieties (e.g. maximal weakly special subvarieties) of a subvariety $V$ of a Shimura variety arise in finitely many families. In this article, we refine this theorem by (1)…
We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth mappings by regular ones. They form a natural counterpart to…
In this paper, we investigate vector fields on polyhedral complexes and their associated trajectories. We study vector fields which are analogue of the gradient vector field of a function in the smooth case. Our goal is to define a nice…
We prove a generalization of the fact that periodic functions converge weakly to the mean value as the oscillation increases. Some convergence questions connected to locally periodic nonlinear boundary value problems are also considered.
We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…
We attempt to systematically derive perturbative quantum corrections to the Berry diagonal approximation of the two-level correlation function (TLCF) for chaotic systems. To this end, we develop a ``weak diagonal approximation'' based on a…
We discuss some topics concerning rational approximations in Quantum Chromodynamics, especially those related with the mathematical theory of Pad\'e Approximants. We focus on two kind of problems: the first one related with meromorphic…
We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves on a Riemann sphere which are invariant under a rational function.
An introduction to geography of log models with applications to positive cones of FT varieties and to geometry of minimal models and Mori fibrations.
We study the Fourier--Mukai numbers of rational elliptic surfaces. As its application, we give an example of a pair of minimal 3-folds with Kodaira dimensions 1, $h^1(\mc O)=h^2(\mc O)=0$ such that they are mutually derived equivalent,…
Using an alternative notion of good reduction, an analog of the Shafarevich theorem for elliptic curves is proved for morphisms of the projective line over number fields.