Derived Smooth Manifolds

We define a simplicial category called the category of derived manifolds. It contains the category of smooth manifolds as a full discrete subcategory, and it is closed under taking arbitrary intersections in a manifold. A derived manifold is a space together with a sheaf of local $C^\infty$-rings that is obtained by patching together homotopy zero-sets of smooth functions on Euclidean spaces. We show that derived manifolds come equipped with a stable normal bundle and can be imbedded into Euclidean space. We define a cohomology theory called derived cobordism, and use a Pontrjagin-Thom argument to show that the derived cobordism theory is isomorphic to the classical cobordism theory. This allows us to define fundamental classes in cobordism for all derived manifolds. In particular, the intersection $A\cap B$ of submanifolds $A,B\subset X$ exists on the categorical level in our theory, and a cup product formula $$[A]\smile[B]=[A\cap B]$$ holds, even if the submanifolds are not transverse. One can thus consider the theory of derived manifolds as a {\em categorification} of intersection theory.Comment: 57 pages. Reformulation of author's PhD thesis. To appear in Duke Math J

Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

To-many or to-one? All-in-one! Efficient purely functional multi-maps with type-heterogeneous hash-tries

An immutable multi-map is a many-to-many map data structure with expected fast insert and lookup operations. This data structure is used for applications processing graphs or many-to-many relations as applied in compilers, runtimes of programming languages, or in static analysis of object-oriented systems. Collection data structures are assumed to carefully balance execution time of operations with memory consumption characteristics and need to scale gracefully from a few elements to multiple gigabytes at least. When processing larger in-memory data sets the overhead of the data structure encoding itself becomes a memory usage bottleneck, dominating the overall performance. In this paper we propose AXIOM, a novel hash-trie data structure that allows for a highly efficient and type-safe multi-map encoding by distinguishing inlined values of singleton sets from nested sets of multi-mappings

Computer theorem proving in math

We give an overview of issues surrounding computer-verified theorem proving in the standard pure-mathematical context. This is based on my talk at the PQR conference (Brussels, June 2003)

Special Libraries, January-February 1919

Volume 10, Issue 1https://scholarworks.sjsu.edu/sla_sl_1919/1000/thumbnail.jp

AXIOMATIC DESIGN OF BEARING PACKAGING AUTOMATION

QA bearing technologies Ltd. (hereafter QA) is a custom manufacturer of bearings in a variety of types and sizes. This research concerns one of the processes in QA’s bearing manufacturing in which the individual bearings, once assembled, are packaged to prevent corrosion and attack from any environmental influence. QA currently employs a manual process, which is time-consuming and significantly limits QA’s productivity. This greatly raises a need to improve this process through the design of an automated process for bearing packaging. Various kinds of packaging machine are available in the market for this application. However, most of them are designed for general packaging purpose and simply combining them may result in the functional overlap as applied to the packaging process. This research aims to design an automatic bearing packaging system (ABPS) based on an advanced design theory, i.e., Axiomatic Design Theory (ADT). In the first part of this research, a set of general functional requirements (FRs) and constraints (CONs) were defined specifically based on the needs from the customers. All FRs were maintained independent to each other such that the following design wouldn’t result in functional overlap. Then, design parameters (DPs) in general level were created to satisfy the defined FRs, each being a functionally independent subsystem consists of both custom-design components and products existing in the market. The second part of the research was to decompose the FRs and DPs based on independent axiom of ADT into further levels until the conceptual design was accomplished. In this process, acceptable alternatives in different hierarchies were proposed for comparison in the decision making process. Also, the relationship between FRs and DPs in the same level was always maintained one-to-one, which allows readily for modification in future, if needed. In the third part of this research, the information axiom of ADT was utilized to find the best solution from alternatives. For this, each alternative was evaluated in terms of the information content that reflects the possibility of satisfying the objective FR. The one with least information content was determined as the best alternative. As a result of this research, two solutions with different degree of automation were recommended for the bearing packaging system. The first solution is featured with higher degree of automation and capable of packaging bearings with limited human interface and as result, the total cost for its implementation is relatively high. The second solution integrates semi-automated machines and simplified sealing strategy and as such, the cost for its implementation is significantly reduced. After the conceptual design is complete, ADT is further applied in the detailed design level for oiling system with custom-designed components and mechanism. For the design of certain DPs, the design process applying ADT is used to compare with conventional methods, proved to be more efficient and simplified. Eventually, the final solution proposed for the detailed design of oiling system is consistent with independent axiom of ADT

Applications of Axiomatic Design in academic publications 2013-2018 : A Systematic Literature Review

Aksiomaattinen suunnitteluteoria on ollut kasvavan kiinnostuksen kohteena tiedeyhteisössä siitä lähtien, kun Nam P. Suh esitteli teorian 1990-luvulla. Siitä huolimatta, että aiheesta on tehty runsaasti aktiivista tutkimusta (muun muassa vuotuinen aksiomaattiseen suunnitteluteoriaan keskittynyt konferenssi), kattavia kirjallisuuskatsauksia on kirjoitettu vähän. Tämä tutkimus pyrkii osaltaan täyttämään edelläkuvattua aukkoa aksiomaattisen suunnitteluteorian tutkimuskentällä, keskittyen julkaisuihin vuodesta 2013 vuoteen 2018. Tutkimus on kirjoitettu jatkumoksi vuonna 2010 tutkijoiden Kulak, Cebi & Kahmaran (2010) julkaisemalle kirjallisuuskatsakuselle. Tämän vuoksi samankaltainen kategorisointi on implementoitu tähän tutkimukseen. Kategorisoinnin perusteina ovat käytetty aksiooma, sovellutusalue, metodologia ja määrittelytyyppi. Sovellutusalueisiin on tässä tutkimuksessa lisätty ’palvelut’ omana, uutena kategorianaan. Työssä esitellään lyhyesti aksiomaattinen suunnitteluteoria ja sen keskeiset osa- alueet, tärkeimpinä sunnnittelualueet, suunnitteluprosessi ja suunnitteluaksioomat. Metodologia-osiossa taustoitetaan systemaattisen kirjallisuuskatsauksen soveltamista tähän tutkimukseen ja kuvataan prosessin toteutus PRISMA-mallia käyttäen. Tutkimustulokset käydään lyhyesti läpi esimerkein kustakin kategoriasta. Tutkimusaineisto esitetään sekä lukuina, liitteenä että graaffeina. Näitä kirjallisuuskatsauksen tutkimustuloksia verrataan varhemman tutkimuksen vastaaviin. Sovelletun aksiooman suhteen merkittäviä muutoksia ei ole havaittavissa tämän tutkimuksen perusteella aikaisempaan kirjallisuuskatsaukseen verrattuna. Sovellutusaluessa, sitä vastoin, systeemisuunnittelun osuus on kasvanut merkittävästi edelliseen tutkimukseen verrattuna, kun taas ohjelmistosuunnittelun osuus on vastaavasti pienentynyt. Palvelusuunnittelun osuus on verrattain vaatimaton, joskin suurempi kuin esimerkiksi ohjelmistosuunnittelun. Tämän tutkimuksen perusteella suositellaan jatkotutkimuksia erityisesti aksiomaattisen suunitteluteorian sovellutuksista ohjelmisto- ja palvelusuunnitteluihin sekä mahdollisista syistä, miksi mainittujen sovellutusaljen osuus tutkimuskentässä on pienehkö.Axiomatic Design theory has been gaining growing interest within a design community since introduced by Nam P. Suh in 1990s. Despite an active research within the field, including yearly international conferences of Axiomatic Design, there is not many literature reviews made of academic publications of Axiomatic Design. This research aims to fulfil previously described gap on secondary research of Axiomatic Design, focusing on papers published between 2013 and 2018. The study is a continuum to previous paper published by Kulak, Cebi & Kahmaran (2010). Therefore, similar categorization based on applied axiom, application area, methodology and evaluation type is applied in this research. In application area, ‘services’ have been added as a new category for this research. Results are compared with previous study. In findings, no siginificant change has happened in applied axiom, Independece axiom still being clearly more popular within academic publications. In application area, however, there are noticeable changes compared to the previous study. Share of system design has increased while softare design has significantly decreased. Future research is recommended to further explore specifically applications of Axiomatic Design in software and in services