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Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
We define a function by refining Stern's diatomic sequence. We name it the {\it assembly function}. It is strictly increasing continuous. The first and the second main theorems are on an action to the function. The third theorem is on…
This article presents an equivalent formulation of the implicit complementarity problem. We demonstrate that solution of the equivalent formulation is equivalent to the solution of the implicit complementarity problem. Moreover, we provide…
Program synthesis is the task of automatically deriving a program that has been specified by a user in advance. Combining automated theorem proving with program synthesis enables the automated construction of proven-to-be-correct programs,…
What are the necessary and sufficient conditions for a proposition to be called a requirement? In Requirements Engineering research, a proposition is a requirement if and only if specific grammatical and/or communication conditions hold. I…
Every function on a finite set defines an equivalence relation and, therefore, a partition called the kernel of the function. Automata such that every possible partition is the kernel of a word are called totally compatible. A…
Necessary conditions for a domain $\Omega\subset \mathbb C^n$ admitting a local plurisubharmonic defining function on the boundary are given. In tandem, we give an algorithm to construct a local plurisubharmonic defining function on the…
This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted…
In this paper, we discuss necessary and sufficient explanations for formal argumentation - the question whether and why a certain argument can be accepted (or not) under various extension-based semantics. Given a framework with which…
For a function defined on an arbitrary subset of a Riemann surface, we give conditions which allow the function to be extended conformally. One folkloric consequence is that two common definitions of an analytic arc in ${\mathbb C}$ are…
Computability theory is traditionally conceived as the theoretical basis of informatics. Nevertheless, numerous proposals transcend computability theory, in particular by emphasizing interaction of modules, or components, parts,…
We prove that the following problem is decidable: given a finite set of relations, decide whether this set admits a near-unanimity function.
This study considers the method to derive a ranking of alternatives by aggregating the rankings submitted by several individuals who may not evaluate all of them. The collection of subsets of alternatives that individuals (can) evaluate is…
Requirements engineering plays a critical role in developing software systems. One of the most difficult tasks in this process is identifying functional requirements. A critical problem in many projects is missing requirements until late in…
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…
What would you do if you were asked to "add" knowledge? Would you say that "one plus one knowledge" is two "knowledges"? Less than that? More? Or something in between? Adding knowledge sounds strange, but it brings to the forefront…
Existence of an increasing quasi-concave value function consistent with given preference information is an important issue in various fields including Economics, Multiple Criteria Decision Making, and Applied Mathematics. In this paper, we…
An example of a cocomplete abelian category that is not complete is constructed.
A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.
In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.