ChemInform Abstract: Can F2H+ Exist in the Topological Form FHF+ ?

1986 ◽  
Vol 17 (50) ◽  
Author(s):  
R. L. DEKOCK ◽  
R. DUTLER ◽  
A. RAUK ◽  
R. D. VAN ZEE
Keyword(s):  
Topological Form

Can F2H+ exist in the topological form FHF+?

1986 ◽  
Vol 25 (18) ◽  
pp. 3329-3330 ◽  
Author(s):  
Roger L. DeKock ◽  
Remo Dutler ◽  
Arvi Rauk ◽  
Roger D. Van Zee
Keyword(s):  
Topological Form

scholarly journals Derived Categories and the Analytic Approach to General Reciprocity Laws—Part II

2007 ◽  
Vol 2007 ◽  
pp. 1-27 ◽  
Author(s):  
Michael C. Berg
Keyword(s):  
Number Field ◽  
Open Problem ◽  
Special Linear Group ◽  
Derived Categories ◽  
Topological Spaces ◽  
Base Field ◽  
Analytic Proof ◽  
Reciprocity Laws ◽  
Fold Cover ◽  
Topological Form

Building on the topological foundations constructed in Part I, we now go on to address the homological algebra preparatory to the projected final arithmetical phase of our attack on the analytic proof of general reciprocity for a number field. In the present work, we develop two algebraic frameworks corresponding to two interpretations of Kubota'sn-Hilbert reciprocity formalism, presented in a quasi-dualized topological form in Part I, delineating two sheaf-theoretic routes toward resolving the aforementioned (open) problem. The first approach centers on factoring sheaf morphisms eventually to yield a splitting homomorphism for Kubota'sn-fold cover of the adelized special linear group over the base field. The second approach employs linked exact triples of derived sheaf categories and the yoga of gluingt-structures to evolve a means of establishing the vacuity of certain vertices in diagrams of underlying topological spaces from Part I. Upon assigning properly designedt-structures to three of seven specially chosen derived categories, the collapse just mentioned is enough to yieldn-Hilbert reciprocity.

Topological form of a classical continuum theory of crystalline defects

2008 ◽  
Vol 5 (12) ◽  
pp. 3728-3731
Author(s):  
A. Belkadi ◽  
T. D. Young ◽  
P. Dłuzewski
Keyword(s):  
Continuum Theory ◽  
Crystalline Defects ◽  
Topological Form

A purely topological form of non-Aristotelian logic

1937 ◽  
Vol 2 (3) ◽  
pp. 97-112 ◽  
Author(s):  
Carl G. Hempel
Keyword(s):  
Truth Table ◽  
Aristotelian Logic ◽  
Truth Values ◽  
Symbolic Notation ◽  
Sentential Logic ◽  
New Type ◽  
Points Of View ◽  
Topological Form

1. The problem. The aim of the following considerations is to introduce a new type of non-Aristotelian logic by generalizing the truth-table methods so far employed for establishing non-Aristotelian sentential calculi. We shall expound the intended generalization by applying it to the particular set of pluri-valued systems introduced by J. Łukasiewicz. One will remark that the points of view illustrated by this example may serve to generalize quite analogously any other plurivalued systems, such as those originated by E. L. Post, by H. Reichenbach, and by others.2. J. Łukasiewicz's plurivalued systems of sentential logic. First of all, we consider briefly the structure of the Łukasiewicz systems themselves.As to the symbolic notation in which to represent those systems, we make the following agreements: For representing the expressions of the (two- or plurivalued) calculus of sentences, we make use of the Principia mathematica symbolism; however, we employ brackets instead of dots. We call the small italic letters “p”, “q”, “r”, … sentential variables or elementary sentences, and employ the term “sentence” as a general designation of both elementary sentences and the composites made up of elementary sentences and connective symbols (“~”, “ν” “.”, “⊃” “≡”).Now, the different possible sentences (or, properly speaking, the different possible shapes of sentences, such as “p”, “p∨q”, “~p.(q∨ r)”, etc.) are the objects to which truth-values are ascribed; and just as in every other case one wants a designation for an object in order to be able to speak of it, we want now a system of designations for the sentences with which we are going to deal in our truth-table considerations.

On topological form in structures

2005 ◽  
Vol 39 (1) ◽  
pp. 33-46 ◽  
Author(s):  
Michael J. Bucknum ◽  
Eduardo A. Castro
Keyword(s):  
Topological Form
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