Related papers: A divisorial valuation with irrational volume
Valuation based systems verifying an idempotent property are studied. A partial order is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valuations: as infimum of…
The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise…
In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic…
We give upper bounds for volume of sublevel sets of real polynomials. Our method is to combine a version of global Lojasiewicz inequality with some well known estimate on volume of tubes around real algebraic sets. Some applications to…
We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for…
Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…
Interpretations for the q-binomial coefficient evaluated at -q are discussed. A (q,t)-version is established, including an instance of a cyclic sieving phenomenon involving unitary spaces.
This paper investigates the use of automatic continuity techniques in the context of valuations on convex bodies. We first provide an automatic continuity theorem for valuations restricted to parallelotopes with respect to a fixed basis.…
An application of (iterated) Bauer-Muir acceleration can give an Ap\'ery-like continued fraction for $\pi$ with irrational coefficients, and much faster convergence. It can be considered a generalized continued fraction with the same matrix…
The first part of the present article consists in a survey about the dynamical constructive method designed using dynamical theories and dynamical algebraic structures. Dynamical methods uncovers a hidden computational content for numerous…
We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…
In the paper, I considered construction of algebra of fractions of algebra with conjugation. I also considered algebra of polynomials and algebra of rational mappings over algebra with conjugation.
The aim of the paper is twofold. Firstly, by using the constant rank level set theorem from differential geometry, we establish sharp upper bounds for the dimensions of the solution sets of polynomial variational inequalities under mild…
Let $X$ be a smooth projective variety. The Iitaka dimension of a divisor $D$ is an important invariant, but it does not only depend on the numerical class of $D$. However, there are several definitions of ``numerical Iitaka dimension'',…
In this paper we develop the "local part" of our local/global approach to globally valued fields (GVFs). The "global part", which relies on these results, is developed in a subsequent paper.We study virtual divisors on projective varieties…
A new alternative volume operator is constructed for loop quantum gravity by using the so-called cotriad operators as building blocks. It is shown that the new volume operator shares the same qualitative properties with the standard volume…
We study several examples of surfaces with $p_g = q = 2$ and maximal Albanese dimension that are endowed with an irrational fibration.
We give a complete description of the behavior of the volume function at the boundary of the pseudoeffective cone of certain Calabi-Yau complete intersections known as Wehler N-folds. We find that the volume function exhibits a pathological…
In this article, the concept of $\mu-$ monotonic property of interval-valued function in higher dimension is introduced. Expansion of interval-valued function in higher dimension is developed using this property. Generalized Hukuhara…