Related papers: Operations for D-Algebraic Functions
We are interested in differential forms on mixed-dimensional geometries, in the sense of a domain containing sets of $d$-dimensional manifolds, structured hierarchically so that each $d$-dimensional manifold is contained in the boundary of…
A characterization of multiplicative (and additive) arithmetical functions is given. Using this characterization, we show that the group of multiplicative arithmetical functions is isomorphic to the group of additive arithmetical functions.
Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
This paper continues the author's previous work on a limit-free algebraic-geometric construction of the derivative in the class of polynomial functions and extends the proposed framework to elementary functions. Derivatives of rational…
Based on results about open string correlation functions, a nonassociative algebra was proposed in a recent paper for D-branes in a background with nonvanishing $H$. We show that our associative algebra obtained by quantizing the endpoints…
We recall that diagonals of rational functions naturally occur in lattice statistical mechanics and enumerative combinatorics. We find that a seven-parameter rational function of three variables with a numerator equal to one (reciprocal of…
We introduce a new diagrammatic notation for representing the result of (algebraic) effectful computations. Our notation explicitly separates the effects produced during a computation from the possible values returned, this way simplifying…
In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…
This paper provides a general operadic definition for the notion of splitting the operations of algebraic structures. This construction is proved to be equivalent to some Manin products of operads and it is shown to be closely related to…
Let $M$ be a commutative homogeneous space of a compact Lie group $G$ and $A$ be a closed $G$-invariant subalgebra of the Banach algebra $C(M)$. A function algebra is called antisymmetric if it does not contain nonconstant real functions.…
We introduce and discuss a new class of (multivalued analytic) transcendental functions which still share with algebraic functions the property that the number of their isolated zeros can be explicitly counted. On the other hand, this class…
Let $f$ be a real polynomial of $x = (x_1,\dots,x_n)$ and $\varphi$ be a locally integrable function of $x$ which satisfies a holonomic system of linear differential equations. We study the distribution $f_+^\lambda\varphi$ with a…
In this article, we show that the algebraic degree in semidefinite programming can be expressed in terms of the coefficient of a certain monomial in a doubly symmetric polynomial. This characterization of the algebraic degree allows us to…
A universal differential equation is a nontrivial differential equation the solutions of which approximate to arbitrary accuracy any continuous function on any interval of the real line. On the other hand, there has been much interest in…
Trigonometric formulas are derived for certain families of associated Legendre functions of fractional degree and order, for use in approximation theory. These functions are algebraic, and when viewed as Gauss hypergeometric functions,…
A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this…
We strengthen certain known results saying that separately regular functions are rational and separately Nash functions are semialgebraic. The approach presented here unifies and highlights the similarities between the two problems.
The second derivative of a function r(t) with respect to a variable t is equal to -n times the function raised to the 2n-1 power of r(t); using this definition, an ordinary differential equation is constructed. Graphs with the horizontal…