Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

2013 ◽  
Author(s):  
Friedhelm Waldhausen ◽  
Bjørn Jahren ◽  
John Rognes
Keyword(s):  
Main Tool ◽  
Homotopy Equivalence ◽  
Classifying Space ◽  
Deformation Retract ◽  
Simplicial Sets ◽  
Full Proof

Since its introduction by the author in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing the author's program from more than thirty years ago. The main result is a stable parametrized h-cobordism theorem, derived from a homotopy equivalence between a space of PL h-cobordisms on a space X and the classifying space of a category of simple maps of spaces having X as deformation retract. The smooth and topological results then follow by smoothing and triangulation theory. The proof has two main parts. The essence of the first part is a “desingularization,” improving arbitrary finite simplicial sets to polyhedra. The second part compares polyhedra with PL manifolds by a thickening procedure. Many of the techniques and results developed should be useful in other connections.

Application of Monoterpenoids and their Derivatives for Treatment of Neurodegenerative Disorders

2019 ◽  
Vol 25 (39) ◽  
pp. 5327-5346 ◽  
Author(s):  
Konstantin P. Volcho ◽  
Sergey S. Laev ◽  
Ghulam Md Ashraf ◽  
Gjumrakch Aliev ◽  
Nariman F. Salakhutdinov
Keyword(s):  
Alzheimer’S Disease ◽  
Clinical Trials ◽  
Huntington's Disease ◽  
Neurodegenerative Disorders ◽  
Heterogeneous Group ◽  
Neuroprotective Activity ◽  
Severe Loss ◽  
Neurotrophic Activity ◽  
Full Proof ◽  
Effective Treatments

Neurodegenerative disorders (NDDs) like Alzheimer's disease, Parkinson’s disease and Huntington’s disease are a heterogeneous group of disorders with the progressive and severe loss of neurons. There are no full proof cures for these diseases, and only medicines are available that can alleviate some of the symptoms. Developing effective treatments for the NDDs is a difficult but necessary task. Hence, the investigation of monoterpenoids which modulate targets applicable to many NDDs is highly relevant. Many monoterpenoids have demonstrated promising neuroprotective activity mediated by various systems. It can form the basis for elaboration of agents which will be useful both for the alleviation of symptoms of NDDs and for the treatment of diseases progression and also for prevention of neurodegeneration. The further developments including detections of monoterpenoids and their derivatives with high neuroprotective or neurotrophic activity as well as the results of qualified clinical trials are needed to draw solid conclusions regarding the efficacy of these agents.

scholarly journals Uniqueness, continuity and the existence of implicit functions in constructive analysis

2011 ◽  
Vol 14 ◽  
pp. 127-136 ◽  
Author(s):  
H. Diener ◽  
P. Schuster
Keyword(s):  
Implicit Function Theorem ◽  
A Priori ◽  
Implicit Function ◽  
Implicit Functions ◽  
Unique Existence ◽  
Constructive Analysis ◽  
Full Proof

AbstractWe extract a quantitative variant of uniqueness from the usual hypotheses of the implicit function theorem. Not only does this lead to an a priori proof of continuity, but also to an alternative, full proof of the implicit function theorem. Additionally, we investigate implicit functions as a case of the unique existence paradigm with parameters.

Towards Full Proof Automation in Frama-C Using Auto-active Verification

2019 ◽  
pp. 88-105 ◽  
Author(s):  
Allan Blanchard ◽  
Frédéric Loulergue ◽  
Nikolai Kosmatov
Keyword(s):  
Proof Automation ◽  
Full Proof

scholarly journals Deriving session and union types for objects

2013 ◽  
Vol 23 (6) ◽  
pp. 1163-1219
Author(s):  
LORENZO BETTINI ◽  
SARA CAPECCHI ◽  
MARIANGIOLA DEZANI-CIANCAGLINI ◽  
ELENA GIACHINO ◽  
BETTI VENNERI
Keyword(s):  
Large Scale ◽  
Type System ◽  
Object Oriented Programming ◽  
Type Safety ◽  
Network Applications ◽  
Session Types ◽  
Safety Property ◽  
Core Language ◽  
Structured Communication ◽  
Full Proof

Guaranteeing that the parties of a network application respect a given protocol is a crucial issue.Session typesoffer a method for abstracting and validating structured communication sequences (sessions).Object-oriented programmingis an established paradigm for large scale applications.Union types, which behave as the least common supertypes of a set of classes, allow the implementation of unrelated classes with similar interfaces without additional programming. We have previously developed an integration of the features above into a class-based core language for building network applications, and this successfully amalgamated sessions and methods so that data can be exchanged flexibly according to communication protocols (session types).The first aim of the work reported in this paper is to provide a full proof of the type safety property for that core language by renewing syntax, typing and semantics. In this way, static typechecking guarantees that after a session has started, computation cannot get stuck on a communication deadlock.The second aim is to define a constraint-based type system that reconstructs the appropriate session types of session declarations instead of assuming that session types are explicitly given by the programmer. Such an algorithm can save programming work, and automatically presents an abstract view of the communications of the sessions.

The Proof of the Feynman–Kac Formula for Heat Equation on a Compact Riemannian Manifold

2003 ◽  
Vol 06 (02) ◽  
pp. 311-320 ◽  
Author(s):  
Oleg O. Obrezkov
Keyword(s):  
Riemannian Manifold ◽  
Heat Equation ◽  
Compact Riemannian Manifold ◽  
Type Formula ◽  
Chernoff Theorem ◽  
Common Lines ◽  
Full Proof

A full proof of the Feynman–Kac-type formula for heat equation on a compact Riemannian manifold is obtained using some ideas originating from the papers of Smolyanov, Truman, Weizsaecker and Wittich.1-3 In particular, the technique exploited in the paper has some common lines with Chernoff theorem, which is one of the basic points of the approach to the topics undertaken in the above-mentioned papers.

scholarly journals Notes on Absolute Hodge Classes

2017 ◽  
Author(s):  
Franc¸ois Charles ◽  
Christian Schnell
Keyword(s):  
Abelian Varieties ◽  
Hodge Conjecture ◽  
De Rham Cohomology ◽  
Galois Action ◽  
De Rham ◽  
Definition Of ◽  
Full Proof

This chapter surveys the theory of absolute Hodge classes. First, the chapter recalls the construction of cycle maps in de Rham cohomology, which is then used in the definition of absolute Hodge classes. The chapter then deals with variational properties of absolute Hodge classes. After stating the variational Hodge conjecture, the chapter proves Deligne's principle B and discusses consequences of the algebraicity of Hodge bundles and of the Galois action on relative de Rham cohomology. Finally, the chapter provides some important examples of absolute Hodge classes: a discussion of the Kuga–Satake correspondence as well as a full proof of Deligne's theorem which states that Hodge classes on abelian varieties are absolute.

scholarly journals Blockchain Technology Concept for Improving Supply Chain Traceability in the Ivory Market

2021 ◽  
Vol 8 (1) ◽  
pp. 1-14
Author(s):  
Norman Gwangwava
Keyword(s):  
Supply Chain ◽  
Literature Review ◽  
Blockchain Technology ◽  
Modeling Techniques ◽  
Ivory Trade ◽  
Full Proof

Supply chain traceability is gaining momentum as a means to gain visibility across the supply chain. In order to curb poaching in wildlife sector and harvesting of resources such as ivory, there is need to introduce full proof technologies. This article proposes use of blockchain in tracing the supply chain of ivory and other wildlife products, from source to destination. The article is based on literature review on wildlife practices. Ivory trade participants were identified and mapped into a blockchain model using blockchain modeling techniques. The proposed blockchain approach allows transaction recording as blocks and visibility to relevant participants.

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