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Full-Text Articles in Physical Sciences and Mathematics
Sheaf Cohomology Of Conscious Entity, Goro Kato
Sheaf Cohomology Of Conscious Entity, Goro Kato
Mathematics
Awareness of a conscious entity can exist without elements; therefore, the general notion of an object of a category is employed. One of the characterization of understanding is: for a given local infonnation (awareness) there exists a global information whose restriction is the given information. For such mental activities, category and sheaf theories are employed to formulate consciousness. We will show that the cohomology (more general precohomology) object, a subquotient object, better represents the essence of a conscious entity than an object itself. We will also give a definition of an observation to fonnulate the collapse of the wave and …
Category Theory And Consciousness, Goro Kato, Daniele C. Struppa
Category Theory And Consciousness, Goro Kato, Daniele C. Struppa
Mathematics
No abstract provided.
Orbifold Homeomorphism And Diffeomorphism Groups, Joseph E. Borzellino, Victor Brunsden
Orbifold Homeomorphism And Diffeomorphism Groups, Joseph E. Borzellino, Victor Brunsden
Mathematics
In this paper we outline results on orbifold diffeomorphism groups that were presented at the International Conference on Infinite Dimensional Lie Groups in Geometry and Representation Theory at Howard University, Washington DC on August 17-21, 2000. Specifically, we define the notion of reduced and unreduced orbifold diffeomorphism groups. For the reduced orbifold diffeomorphism group we state and sketch the proof of the following recognition result: Let O1 and O2 be two compact, locally smooth orbifolds. Fix r ≥ 0. Suppose that Φ : Diffr (O1) → Diffr (O2) is a group isomorphism. Then Φ is induced by redred a (topological) …
Levy-Like Continuity Theorems For Convergence In Distribution, Theodore P. Hill, Ulrich Krengel
Levy-Like Continuity Theorems For Convergence In Distribution, Theodore P. Hill, Ulrich Krengel
Research Scholars in Residence
Levy’s classical continuity theorem states that if the pointwise limit of a sequence of characteristic functions exists, then the limit function itself is a characteristic function if and only if the limit function satisfies a single universal limit condition (in his case, the limit at zero is one), in which case the underlying measures converge weakly to the probability measure represented by the limit function. It is the purpose of this article to give a number of direct analogs of L´evy’s theorem for other probability-representing functions including moment sequences, maximal moment sequences, mean-residual-life functions, Hardy-Littlewood maximal functions, and failure-rate functions. …
Random Probability Measures With Given Mean And Variance Running Title: Random Probability Measures, Lisa Bloomer, Theodore P. Hill
Random Probability Measures With Given Mean And Variance Running Title: Random Probability Measures, Lisa Bloomer, Theodore P. Hill
Research Scholars in Residence
This article describes several natural methods of constructing random probability measures with prescribed mean and variance, and focuses mainly on a technique which constructs a sequence of simple (purely discrete, finite number of atoms) distributions with the prescribed mean and with variances which increase to the desired variance. Basic properties of the construction are established, including conditions guaranteeing full support of the generated measures, and conditions guaranteeing that the final measure is discrete. Finally, applications of the construction method to optimization problems such as Plackett’s Problem are mentioned, and to experimental determination of average-optimal solutions of certain control problems.