In this paper, we show that the infinite generalised Stirling matrices associated with boson strings with one annihilation operator are projective limits of approximate substitutions, the latter being characterised by a finite set of algebraic equations. 1. Introduction The series of papers [1, 2, 3] had two sequels. First one, algebraic, was the construction of a Hopf algebra of Feynman-Bender...

This paper proposes a novel stochastic process that represents the arbitrary rectangular partitioning of an infinite-dimensional matrix as the conditional projective limit. Rectangular partitioning is used in relational data analysis, and is classified into three types: regular grid, hierarchical, and arbitrary. Conventionally, a variety of probabilistic models have been advanced for the first ...

For the smooth normalization f : X → X of a singular variety X over a field k of characteristic zero, we show that for any conducting subscheme Y for the normalization, and for any i ∈ Z, the natural map Ki(X, X, nY ) → Ki(X, X, Y ) is zero for all sufficiently large n. As an application, we prove a formula for the Chow group of zero cycles on a quasi-projective variety X over k with Cohen-Maca...

We develop techniques for obtaining the mirror of Calabi-Yau supermanifolds as super Landau-Ginzburg theories. In some cases the dual can be equivalent to a geometry. We apply this to some examples. In particular we show that the mirror of the twistorial Calabi-Yau CP becomes equivalent to a quadric in CP×CP as had been recently conjectured (in the limit where the Kähler parameter of CP, t → ±∞...

The volume of a line bundle is defined in terms limsup. It fundamental question whether this limsup limit. has been shown that always the case on generically reduced schemes. We show volumes are limits two classes schemes not necessarily reduced: codimension one subschemes projective varieties such their components maximal dimension contain normal points and whose nilradical squared equals zero.

In this paper, we discuss the theories of admissible covers (HarrisMumford) and limit linear series (Eisenbud-Harris), two techniques for using degenerations to study maps between curves. While the theories are superficially very similar, they have certain fundamental differences which we will also explore. 1. Motivational problems We begin by laying out a number of questions on curves which sh...

Work fluctuation theorems have been one of the important achievements in field nonequilibrium Statistical Physics, both classical and quantum regimes. Conventionally, work done on a system is defined by means two-point measurement scheme, where projective Hamiltonian performed at beginning end process. Recently, context generalized measurements received lot attention. Here, we define weak value...

let $g$ be a finite group and $pi_{e}(g)$ be the set of element orders of $g $. let $k in pi_{e}(g)$ and $s_{k}$ be the number of elements of order $k $ in $g$. set nse($g$):=${ s_{k} | k in pi_{e}(g)}$. in this paper, it is proved if $|g|=|$ pgl$_{2}(q)|$, where $q$ is odd prime power and nse$(g)= $nse$($pgl$_{2}(q))$, then $g cong $pgl$_

Let F be a flat family of projective schemes, whose geometric generic fiber is reduced and irreducible. We give conditions on a special fiber (a “limit” of the family) to guarantee that it too is reduced. These conditions often imply also that the generic fiber is normal. The conditions are particularly easy to check in the setup of a “geometric vertex decomposition” [Knutson-Miller-Yong ’07]. ...