相关论文: Division by zero in non-involutive meadows
Two notable examples of dual functionals in approximation theory and computer-aided geometric design are the blossom and the divided difference operator. Both of these dual functionals satisfy a similar set of formulas and identities.…
We consider finite range Gibbs fields and provide a purely combinatorial proof of the exponential tree decay of semi--invariants, supposing that the logarithm of the partition function can be expressed as a sum of suitable local functions…
We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
A proposal is made for a mathematically unambiguous treatment of evolution in the presence of closed timelike curves. In constrast to other proposals for handling the naively nonunitary evolution that is often present in such situations,…
The manuscript studies configurations of non-overlapping non-bonding dominoes on finite rectangular boards of unit squares characterized by row and column number. The non-bonding dominoes are defined here by the requirement that any domino…
We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds…
We investigate the concept of a ``Chevalley involution'' within the framework of root-graded Lie algebras with compatible grading. We provide a characterization of all centerless Lie tori of type $A_\ell(\ell\geq2)$ admitting a Chevalley…
A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflection from a boundary. For billiards in non-convex areas bounded by segments of confocal quadrics are studied. The topology…
In this article, we construct differential modular forms for compact Shimura curves over totally real fields bigger than rational of non-zero integral weights that is not classical (of order zero) generalizing the construction of Buium [8].
We study possible decompositions of totally decomposable algebras with involution, that is, tensor products of quaternion algebras with involution. In particular, we are interested in decompositions in which one or several factors are the…
We present families of combinatorial classes described as trees with nodes that can carry one of two types of "flowers": integer partitions or integer compositions. Two parameters on the flowers of trees will be considered: the number of…
For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…
The starting point of this work is that the class of evolution algebras over a fixed field is closed under tensor product. This arises questions about the inheritance of properties from the tensor product to the factors and conversely. For…
By means of the inverse techniques we analyse the evolution of purely spin-1/2 systems in homogeneous magnetic fields as well as the generation of exact solutions. Some ``evolution loops'', dynamical processes for which any state evolves…
Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of…
A non associative, noncommutative algebra is defined that may be interpreted as a set of vector modules over a noncommutative surface of rotation. Two of these vector modules are identified with the analogues of the tangent and cotangent…
We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differential equation whose solution can be described combinatorially. This yields a new formula for the number of NATs. We also obtain…
In system operations it is commonly assumed that arbitrary changes to a system can be reversed or `rolled back', when errors of judgement and procedure occur. We point out that this view is flawed and provide an alternative approach to…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…