Search results for "Mathematical proof"

Existence of competitive equilibrium in a non-optimal one-sector economy without conditions on the distorted marginal product of capital

2012

Abstract This paper develops a method for proving the existence of competitive equilibrium in a distorted/non-optimal one-sector economy–a discrete time variant of the Romer model–without conditions on the equilibrium value of the marginal product of capital. Existence is obtained under weaker conditions than in Le Van et al. (2002) . Moreover, we provide an existence result for an economy with a regressive tax studied in Santos (2002) . The proofs rely on ideas of Becker and Boyd (1997) .

Multi-Skill Call Center as a Grading from “Old” Telephony

2009

We explore parallels between the older telephony switches and the multi-skill call centers. The numerical results have shown that a call center with equally distributed skills is preferable compared to traditional grading-type design. The annex contains a short version of mathematical proof on limited availability schemes design for small call flow intensity *** and for large *** . The proof explores one excellent V. Benes' paper (from Bell Labs). On its own merit, the annex could initiate new mathematical research in call center area, more by now the powerful software for numerical analysis is available. Main conclusion is the following: numerical analysis of simple multi-skill call center…

Phenomenological-Semantic Investigations into Incompleteness

2000

When today the phenomenologist surveys the history of the philosophical comprehension of Godel’s theorems, he is confronted with the realization that the decisive publications come almost exclusively from the sphere of analytic philosophy.1 But does phenomenology in the spirit of Husserl not mean to keep in step with the epochal results of the special sciences by working on the phenomenological understanding of them? Phenomenological research of this kind means the same as development of phenomenological theory of science (Wissenschaftstheorie). In connection with the incompleteness theorems, the latter would be confronted with fundamental questions such as, “To what extent can mathematical…

Resource Quantification for the No-Programming Theorem

2018

The no-programming theorem prohibits the existence of a Universal Programmable Quantum Processor. This statement has several implications in relation to quantum computation, but also to other tasks of quantum information processing, making this construction a central notion in this context. Nonetheless, it is well known that even when the strict model is not implementable, it is possible to conceive of it in an approximate sense. Unfortunately, the minimal resources necessary for this aim are still not completely understood. Here, we investigate quantitative statements of the theorem, improving exponentially previous bounds on the resources required by such a hypothetical machine. The proof…

Finitary formal topologies and Stone’s representation theorem

2008

AbstractWe study the concept of finitary formal topology, a point-free version of a topological space with a basis of compact open subsets. The notion of finitary formal topology is defined from the perspective of the Basic Picture (introduced by the second author) and thus it is endowed with a binary positivity relation. As an application, we prove a constructive version of Stone’s representation theorem for distributive lattices. We work within the framework of a minimalist foundation (as proposed by Maria Emilia Maietti and the second author). Both inductive and co-inductive methods are used in most proofs.

Epistemic and didactic values of the demonstrative process in different cultures: a case study in Geometry with Chinese and Italian students

2011

Lead Poisoning in France around 1840: Managing Proofs and Uncertainties in Laboratories, Courtrooms, and Workplaces.

2021

This article reviews one of the most famous cases of lead poisoning in France, the Ponchon affair, which occurred in 1843 during a crucial period for French toxicology. The trial attracted public attention and inflamed controversy among medical and legal experts. The debate involved toxicological methods and their reliability, and gave rise to more general questions about the value of expert evidence, the way it was presented in court, and its relationship to other forms of legal evidence. I begin with a general overview of lead poisoning and toxicological research on lead compounds around 1840. I then discuss different toxicological proofs employed for detecting or preventing lead poisonin…

Whitney forms and their extensions

2021

Whitney forms are widely known as finite elements for differential forms. Whitney’s original definition yields first order functions on simplicial complexes, and a lot of research has been devoted to extending the definition to nonsimplicial cells and higher order functions. As a result, the term Whitney forms has become somewhat ambiguous in the literature. Our aim here is to clarify the concept of Whitney forms and explicitly explain their key properties. We discuss Whitney’s initial definition with more depth than usually, giving three equivalent ways to define Whitney forms. We give a comprehensive exposition of their main properties, including the proofs. Understanding of these propert…

Stability of stochastic nonlinear systems with state-dependent switching

2013

In this paper, the problem of stability on stochastic systems with state-dependent switching is investigated. To analyze properties of the switched system by means of Itô’s formula and Dynkin’s formula, it is critical to show switching instants being stopping times. When the given active-region set can be replaced by its interior, the local solution of the switched system is constructed by defining a series of stopping times as switching instants, and the criteria on global existence and stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily have solutions, thereby quasi-…

Teaching and Learning of Geometry as a process of Objectification: conditions and obstacles to argumentation and proof. The role of natural language,…

2021

This paper examines some examples (taken from research conducted over the years) that show students’ linguistic attitudes in geometry tasks. The examples are framed within the Theory of Objectification with reference to the notion of sensuous cognition, semiotic means of objectification and levels of generality. We show the struggle students live, at higher levels of generality, in intertwining natural language, specific language and the spontaneous use of geometrical figures, bound to perception and kinaesthetic activity. Within the networking paradigm, we coordinate the Theory of Objectification and Duval’s semio-cognitive approach to frame the interplay between the ideal and the material…