scholarly journals Boolean algebras in algebraic topology

2007 ◽  
pp. 135-139
Author(s):  
Zoran Petrovic

The appearance of the complete Heyting algebra in the realm of Algebraic Topology is the main topic of the paper.

1969 ◽  
Vol 34 (3) ◽  
pp. 475-480 ◽  
Author(s):  
Alfred Horn

Dummett's LC [1] is a system which characterizes all formulas of the propositional calculus which are valid in every chain (for definitions and notation see the first section of [2]). An L-algebra is a Heyting algebra in which (x → y) + (y → x) = 1 for all x, y. L-algebras bear the same relation to LC as Boolean algebras to the classical propositional calculus and Heyting algebras to the intuitionist propositional calculus.


2009 ◽  
Vol 16 (1) ◽  
pp. 29-47
Author(s):  
Guram Bezhanishvili ◽  
Patrick J. Morandi

Abstract This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to the profinite completion of a Heyting algebra (resp. bounded distributive lattice). This results in simple examples of profinite bounded distributive lattices that are not isomorphic to the profinite completion of any bounded distributive lattice. We also show that each profinite Boolean algebra is isomorphic to the profinite completion of some Boolean algebra. It is still an open question whether each profinite Heyting algebra is isomorphic to the profinite completion of some Heyting algebra.


2018 ◽  
Vol 35 (1-2) ◽  
pp. 125-134
Author(s):  
Anālayo Bhikkhu

With the present paper I study and translate a discourse in the Ekottarika-?gama preserved in Chinese of which no parallel in other discourse collections is known. This situation relates to the wider issue of what significance to accord to the absence of parallels from the viewpoint of the early Buddhist oral transmission. The main topic of the discourse itself is perception of impermanence, which is of central importance in the early Buddhist scheme of the path for cultivating liberating insight. A description of the results of such practice in this Ekottarika-?gama discourse has a somewhat ambivalent formulation that suggests a possible relation to the notion of rebirth in the Pure Abodes, suddh?v?sa. This notion, attested in a P?li discourse, in turn might have provided a precedent for the aspiration, prominent in later Buddhist traditions, to be reborn in the Pure Land.


2019 ◽  
pp. 326-329 ◽  
Author(s):  
Nico Antens

As in the rest of Europe beet cultivation and the related beet quality was the main topic at Suiker Unie this campaign due to the very dry weather conditions. With a rather low beet yield as a result it was a short campaign of only 120 days in the Netherlands and 100 days at the Anklam factory in Germany. Despite the unusual beet quality and its related impact on the process, all factories had rather stable beet slicing rates. The beet cultivation and harvest, main investments and process disturbances of the 2018/19 campaign at the three factories Anklam (D), Dinteloord (NL) and Vierverlaten (NL) are discussed.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tun-Wei Hsu ◽  
Jong-Ling Fuh ◽  
Da-Wei Wang ◽  
Li-Fen Chen ◽  
Chia-Jung Chang ◽  
...  

AbstractDementia is related to the cellular accumulation of β-amyloid plaques, tau aggregates, or α-synuclein aggregates, or to neurotransmitter deficiencies in the dopaminergic and cholinergic pathways. Cellular and neurochemical changes are both involved in dementia pathology. However, the role of dopaminergic and cholinergic networks in metabolic connectivity at different stages of dementia remains unclear. The altered network organisation of the human brain characteristic of many neuropsychiatric and neurodegenerative disorders can be detected using persistent homology network (PHN) analysis and algebraic topology. We used 18F-fluorodeoxyglucose positron emission tomography (18F-FDG PET) imaging data to construct dopaminergic and cholinergic metabolism networks, and used PHN analysis to track the evolution of these networks in patients with different stages of dementia. The sums of the network distances revealed significant differences between the network connectivity evident in the Alzheimer’s disease and mild cognitive impairment cohorts. A larger distance between brain regions can indicate poorer efficiency in the integration of information. PHN analysis revealed the structural properties of and changes in the dopaminergic and cholinergic metabolism networks in patients with different stages of dementia at a range of thresholds. This method was thus able to identify dysregulation of dopaminergic and cholinergic networks in the pathology of dementia.


1979 ◽  
Vol 2 (1) ◽  
pp. 17-41
Author(s):  
Michał Jaegermann

In the paper is developed a theory of information storage and retrieval systems which arise in situations when a whole possessed information amounts to a fact that a given document has some feature from properly chosen set. Such systems are described as suitable maps from descriptor algebras into sets of subsets of sets of documents. Since descriptor algebras turn out to be pseudo-Boolean algebras, hence an “inner logic” of our systems is intuitionistic. In the paper is given a construction of systems and are considered theirs properties. We will show also (in Part II) a formalized theory of such systems.


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