Problem of identity transformations of nondeterministic program shcemes in algorithmic algebra systems

Cybernetics ◽  
1983 ◽  
Vol 18 (3) ◽  
pp. 334-341 ◽  
Author(s):  
Yu. A. Yushchenko
Keyword(s):  
Algorithmic Algebra ◽  
Identity Transformations ◽  
Nondeterministic Program

PAL – Propositional Algorithmic Logic

1981 ◽  
Vol 4 (3) ◽  
pp. 675-760
Author(s):  
Grażyna Mirkowska
Keyword(s):  
Data Structures ◽  
Completeness Theorem ◽  
Natural Numbers ◽  
First Order ◽  
Algorithmic Logic ◽  
Axiomatic Systems ◽  
Nondeterministic Program ◽  
Basic Sets

The aim of propositional algorithmic logic is to investigate the properties of program connectives. Complete axiomatic systems for deterministic as well as for nondeterministic interpretations of program variables are presented. They constitute basic sets of tools useful in the practice of proving the properties of program schemes. Propositional theories of data structures, e.g. the arithmetic of natural numbers and stacks, are constructed. This shows that in many aspects PAL is close to first-order algorithmic logic. Tautologies of PAL become tautologies of algorithmic logic after replacing program variables by programs and propositional variables by formulas. Another corollary to the completeness theorem asserts that it is possible to eliminate nondeterministic program variables and replace them by schemes with deterministic atoms.

scholarly journals Working in Increasing Isolation? How an International MOOC for Career Professionals Supports Peer Learning across Distance

2018 ◽  
Vol 11 (1) ◽  
pp. 23
Author(s):  
Barbara Kieslinger ◽  
Juliet Tschank ◽  
Teresa Schaefer ◽  
Claudia Magdalena Fabian
Keyword(s):  
Online Community ◽  
Career Guidance ◽  
Work Experiences ◽  
Collaborative Reflection ◽  
Employment Services ◽  
Daily Work ◽  
Organizational Settings ◽  
Work Related ◽  
Identity Transformations ◽  
Opening Up

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>In this contribution we provide an assessment of an international MOOC that was designed specifically for professionals in employment services and career guidance. The six-week course was implemented in the context of a wider spanning project on the study of professional identity transformations and was building on the experience of smaller courses provided in closed organizational settings. By opening up the course and transferring it into a MOOC format, almost 90 professionals from around 20 countries were able to share their work experiences and discuss challenges in their daily work related to demographic change, digitalization and organizational change. Amongst the most active contributors were those participants, who were confronted with an increasing isolation at work: being either placed in remote areas, part of a distributed team or a “functional” island. For them, learning from and with others as part of an online community, becomes increasingly important, as reflected by the participants’ feedback and their comments during the course. The analysis clearly stresses the importance of the exchange of experiences with colleagues and peers. While tutor input was also appreciated, participants especially appreciate the learning from their peers. A MOOC or online community can serve an important role in collaborative reflection and social learning. Given this experience, MOOCs could be offered specifically for certain professions where people work in isolation, either in geographical terms or in terms of the topics they are covering. </span></p></div></div></div>

Analyst: A program package for proving identities (theorems) in axiomatic algorithmic-algebra systems

Cybernetics ◽  
1980 ◽  
Vol 15 (4) ◽  
pp. 467-473
Author(s):  
G. M. Kirsanov ◽  
G. E. Tseitlin ◽  
E. L. Yushchenko
Keyword(s):  
Program Package ◽  
Algorithmic Algebra

STABILITY COMPUTATIONS FOR NILPOTENT HOPF BIFURCATIONS IN COUPLED CELL SYSTEMS

2007 ◽  
Vol 17 (08) ◽  
pp. 2595-2603 ◽  
Author(s):  
M. GOLUBITSKY ◽  
M. KRUPA
Keyword(s):  
Hopf Bifurcations ◽  
Cell Systems ◽  
Codimension One ◽  
Partial Stability ◽  
Branching Patterns ◽  
Coupled Cell Systems ◽  
The Stability ◽  
Identity Transformations ◽  
Partial Synchrony ◽  
Stability Results

Vanderbauwhede and van Gils, Krupa, and Langford studied unfoldings of bifurcations with purely imaginary eigenvalues and a nonsemisimple linearization, which generically occurs in codimension three. In networks of identical coupled ODE these nilpotent Hopf bifurcations can occur in codimension one. Elmhirst and Golubitsky showed that these bifurcations can lead to surprising branching patterns of periodic solutions, where the type of bifurcation depends in part on the existence of an invariant subspace corresponding to partial synchrony. We study the stability of some of these bifurcating solutions. In the absence of partial synchrony the problem is similar to the generic codimension three problem. In this case we show that the bifurcating branches are generically unstable. When a synchrony subspace is present we obtain partial stability results by using only those near identity transformations that leave this subspace invariant.

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