Related papers: On identity theorem for real functions
We explore a quantitative interpretation of 2-dimensional intuitionistic type theory (ITT) in which the identity type is interpreted as a "type of differences". We show that a fragment of ITT, that we call difference type theory (dTT),…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
This article shows a very elementary and straightforward proof of the Implicit Function Theorem for differentiable maps $F(x,y)$ defined on a finite-dimensional Euclidean space. There are no hypothesis on the continuity of the partial…
We describe a new logical data model, called the concept-oriented model (COM). It uses mathematical functions as first-class constructs for data representation and data processing as opposed to using exclusively sets in conventional…
Database analytics algorithms leverage quantifiable structural properties of the data to predict interesting concepts and relationships. The same information, however, can be represented using many different structures and the structural…
Often in language and other areas of cognition, whether two components of an object are identical or not determine whether it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from…
Set functions are a feature of functional logic programming to encapsulate all results of a non-deterministic computation in a single data structure. Given a function $f$ of a functional logic program written in Curry, we describe a…
The standard literature on special functions contains a lot of hypergeometric identities involving products and quotients of gamma functions, but still the occurrence of such identities is a sporadic phenomenon. This is because the…
The notion of pairable functions is introduced and some of its properties are developed. In this connection the famous Euler identity is interpreted as a property of certain pairable functions and finite cyclic groups.
Universal identifiers and hashing have been widely adopted in computer science from distributed financial transactions to data science. This is a consequence of their capability to avoid many shortcomings of relative identifiers, such as…
We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre…
Intuitive Set Theory (IST) is defined as the theory we get, when we add Axiom of Monotonicity and Axiom of Fusion to Zermelo-Fraenkel set theory. In IST, Continuum Hypothesis is a theorem, Axiom of Choice is a theorem, Skolem paradox does…
This paper develops a unified identification framework for counterfactual analysis in incomplete models characterized by support and moment restrictions. I demonstrate that identifying structural parameters and conducting counterfactual…
We present a theorem of resolution of singularities for real analytic constrained differential systems $A(x)\dot{x} = F(x)$ defined on a 2-manifold with corners having impasse set $\{x; \det A(x) = 0\}$. This result can be seen as a…
A new integral identity for functions with continuous second partial derivatives is derived. It is shown that the value of any function f(r,t) at position r and time t is completely determined by its previous values at all other locations…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
The edge-of-the-wedge theorem in several complex variables gives the analytic continuation of functions defined on the poly upper half plane and the poly lower half plane, the set of points in $\mathbb{C}^d$ with all coordinates in the…
We investigate the problem of cryptanalysis as a problem belonging to the class NP. A class of problems UF is defined for which the time constructing any feasible solution is polynomial. The properties of the problems of NP, which may be…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
We present an algorithmic approach to the verification of identities on multiple theta functions in the form of products of theta functions $[(-1)^{\delta}a_1^{\alpha_1}a_2^{\alpha_2}\cdots a_r^{\alpha_r}q^{s}; q^{t}]_\infty$, where…