Related papers: Real coextensions as a tool for constructing trian…
We propose a compositional approach to construct subspaces consisting entirely of r-uniform states, including the ones in heterogeneous systems. The approach allows one to construct new objects from old ones: it combines encoding isometries…
We describe a prescription for constructing conformal blocks in conformal field theories in any space-time dimension with arbitrary quantum numbers. Our procedure reduces the calculation of conformal blocks to constructing certain group…
We set up a general framework to study Tate cohomology groups of Galois modules along $\mathbb{Z}_p$-extensions of number fields. Under suitable assumptions on the Galois modules, we establish the existence of a five-term exact sequence in…
The left and right diameters of a monoid are topological invariants defined in terms of suprema of lengths of derivation sequences with respect to finite generating sets for the universal left or right congruences. We compute these…
This is the second paper in a series that aims to provide mathematical descriptions of objects and constructions related to the first few steps of the semantical theory of dependent type systems. We construct for any pair $(R,LM)$, where…
We describe those complete linearly ordered topological spaces $X$ which are homogeneous (=CHLOTS). That is, $X$ is order isomorphic with any nonempty open interval in $X$. Using countable tail-like ordinals as indices, we build towers of…
This article introduces continuous $H^2$-nonconforming finite elements in two and three space dimensions which satisfy a strong discrete Miranda--Talenti inequality in the sense that the global $L^2$ norm of the piecewise Hessian is bounded…
A natural framework for real-time specification is monadic first-order logic over the structure $(\mathbb{R},<,+1)$---the ordered real line with unary $+1$ function. Our main result is that $(\mathbb{R},<,+1)$ has the 3-variable property:…
In this paper, we use the properties of the self-polar triangle to not only show a novel method for a basic point-line enumerative problem of conics, but also present a series of closed-form solutions to the conics from all minimal…
Three kinds of universal central extension are considered for a perfect Lie algebra. More precisely, one can consider such a Lie algebra as a Lie triple system, or a Leibniz algebra and construct appropriate central extensions. We show that…
This paper addresses sharpness conditions for constructing $C^r$ conforming finite element spaces from a superspline spaces on general simplicial triangulations. We introduce the concept of extendability for the pre-element spaces, which…
For a fix modular form g and a non negative ineteger {\nu}, by using Rankin-Cohen bracket we first define a linear map $T_{g,{\nu}}$ on the space of modular forms. We explicitly compute the adjoint of this map and show that the n-th Fourier…
Consider a linear ordering equipped with a finite sequence of monadic predicates. If the ordering contains an interval of order type \omega or -\omega, and the monadic second-order theory of the combined structure is decidable, there exists…
With a view to proving the conjecture of "dlt extension" related to the abundance conjecture, a sequence of potential candidates for replacing the Ohsawa measure in the Ohsawa-Takegoshi $L^2$ extension theorem, called the "lc-measures",…
We introduce several new constructions of finite posets with the number of linear extensions given by generalized continued fractions. We apply our results to the problem of the minimum number of elements needed for a poset with a given…
Commutative totally ordered monoids abound, number systems for example. When the monoid is not assumed commutative, one may be hard pressed to find an example. One suggested by Professor Orr Shalit are the countable ordinals with addition.…
The present paper contains a systematic study of the structure of metric Lie algebras, i.e., finite-dimensional real Lie algebras equipped with a non-degenerate invariant symmetric bilinear form. We show that any metric Lie algebra without…
The aim of this paper is to provide an answer to the $\mathbb{C}[\partial]$-split extending structures problem for Leibniz conformal algebras, which asks that how to describe all Leibniz conformal algebra structures on $E=R\oplus Q$ up to…
A number of constructions in function field arithmetic involve extensions from linear objects using digit expansions. This technique is described here as a method of constructing orthonormal bases in spaces of continuous functions. We…
We generalise work of Young-Eun Choi to the setting of ideal triangulations with vertex links of arbitrary genus, showing that the set of all (possibly incomplete) hyperbolic cone-manifold structures realised by positively oriented…