scholarly journals GENERALIZATIONS OF THE RECURSION THEOREM

2018 ◽  
Vol 83 (04) ◽  
pp. 1683-1690 ◽  
Author(s):  
SEBASTIAAN A. TERWIJN
Keyword(s):  
Completeness Criterion ◽  
Recursion Theorem

AbstractWe consider two generalizations of the recursion theorem, namely Visser’s ADN theorem and Arslanov’s completeness criterion, and we prove a joint generalization of these theorems.

scholarly journals Some independence results for control structures in complete numberings

2001 ◽  
Vol 66 (1) ◽  
pp. 357-382 ◽  
Author(s):  
Sanjay Jain ◽  
Jochen Nessel
Keyword(s):  
General Setting ◽  
Programming System ◽  
Control Structures ◽  
Independence Results ◽  
Programming Systems ◽  
Recursion Theorem

AbstractAcceptable programming systems have many nice properties like s-m-n-Theorem, Composition and Kleene Recursion Theorem. Those properties are sometimes called control structures, to emphasize that they yield tools to implement programs in programming systems. It has been studied, among others by Riccardi and Royer, how these control structures influence or even characterize the notion of acceptable programming system. The following is an investigation, how these control structures behave in the more general setting of complete numberings as defined by Mal'cev and Eršov.

Some orthogonal and complete sets of Bessel functions associated with the vibrating plate

1982 ◽  
Vol 91 (3) ◽  
pp. 503-515 ◽  
Author(s):  
J. R. Higgins
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
Main Concern ◽  
Edge Type ◽  
Completeness Criterion ◽  
Complete Sets ◽  
Clamped Edge ◽  
Vibrating Plate

AbstarctSome orthogonal sets of Bessel functions of real order v are identified using the equation Δ2u = utt of the vibrating plate. Our main concern is with the L2 completeness of such sets, and we prove that the well known ‘clamped edge’ type is complete for v > -1, thus completing a result of E. Dahlberg. We also study a very closely related set and show that it needs an extra (non-Bessel) function for completeness.Our method for proving the completeness is based on one given by H. Hochstadt in connection with Dini functions. We have found it necessary to reorganize Hoch-stadt's method and correct some errors contained in it.Certain isolated values of v require special attention and we treat these by subjecting the Dalzell completeness criterion to a continuity argument.

scholarly journals On Well-Founded and Recursive Coalgebras

2020 ◽  
pp. 17-36
Author(s):  
Jiří Adámek ◽  
Stefan Milius ◽  
Lawrence S. Moss
Keyword(s):  
General Proof ◽  
Initial Algebra ◽  
Equivalent Characterization ◽  
Algebra Morphism ◽  
Recursion Theorem ◽  
The Relationship ◽  
Well Foundedness

AbstractThis paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving endofunctors on complete and well-powered categories every coalgebra has a well-founded part, and we provide a new, shorter proof that this is the coreflection in the category of all well-founded coalgebras. We present a new more general proof of Taylor’s General Recursion Theorem that every well-founded coalgebra is recursive, and we study conditions which imply the converse. In addition, we present a new equivalent characterization of well-foundedness: a coalgebra is well-founded iff it admits a coalgebra-to-algebra morphism to the initial algebra.

scholarly journals Kolmogorov Complexity and the Recursion Theorem

2006 ◽  
pp. 149-161 ◽  
Author(s):  
Bjørn Kjos-Hanssen ◽  
Wolfgang Merkle ◽  
Frank Stephan
Keyword(s):  
Kolmogorov Complexity ◽  
Recursion Theorem

Characterization of zigzag De Morgan functions

2016 ◽  
Vol 08 (02) ◽  
pp. 1650030
Author(s):  
V. A. Aslanyan
Keyword(s):  
Boolean Functions ◽  
Present Author ◽  
Completeness Theorem ◽  
Discrete Mathematics ◽  
Functional Completeness ◽  
Completeness Criterion ◽  
Appl Math

Post’s functional completeness theorem for Boolean functions plays an important role in discrete mathematics. In paper [A functional completeness theorem for De Morgan functions, Discrete Appl. Math. 162 (2014) 1–16, doi: 10.1016/j.dam.2013.08.006.] a functional completeness criterion for De Morgan functions is established by the present author and Yu. Movsisyan. Namely, the concepts of closed, complete and precomplete classes of De Morgan functions are introduced there and a functional completeness theorem for De Morgan functions is proven. As a result it is shown that there are five precomplete classes of De Morgan functions. Four of those are defined as sets of functions preserving some finitary relations. However, the fifth class — the class of zigzag De Morgan functions, is not defined by relations. In this paper, we prove that zigzag De Morgan functions can be defined as De Morgan functions preserving an atmost 16-ary relation.

PENERAPAN MODEL EXPERIENTIAL LEARNING UNTUK MENINGKATKAN KEMAMPUAN MENULIS PUISI SISWA KELAS VIII C SMPN 3 PENEBEL

2020 ◽  
Vol 9 (1) ◽  
pp. 46-56
Author(s):  
Ni Putu Ayu Ratih
Keyword(s):  
Action Research ◽  
Experiential Learning ◽  
Learning Model ◽  
Average Score ◽  
Language Teacher ◽  
Completeness Criterion ◽  
Classroom Action Research

This study aimed to know (1) students’ competence by implementing experiential learning model, (2) steps in implementing experiential learning model, and (3) students’ response after the experiential learning model is implemented in writing subject of VIII C students in SMPN 3 Penebel. This classroom action research was conducted in two cycles which consists of five components; design, implementation, observation, evaluation, and reflection. The subjects of this study were teacher and VIII C. Observation, test, and questionnaire were the collection technique. The data were analyzed qualitatively and quantitatively. It was found that; (1) students’ competence is improved after experiential learning model was implemented, it can be seen from the initial reflection which showed that the students’ average score is 65. Their average score in cycle I is 74.3. Their average score in cycle 2 is 86. Those have achieved the minimum completeness criterion, 75. (2) The learning steps of implementing the experiential learning are introduction, content, and conclusion. (3) The students’ response is improved in every cycle. In cycle I, students’ responses are 1243 with average 43 positive categories. In cycle II, the responses have increased into 1410 with average 49 very positive categories. Thus, experiential learning model can improve students’ competence in writing poem. It is suggested that; (1) Indonesian language teacher or other teacher can use this learning model as guidance in teaching; and (2) other researchers can conduct a continuation research related to experiential learning model.

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