Deterministic and non-deterministic hypersubstitutions for algebraic systems

2016 ◽  
Vol 09 (02) ◽  
pp. 1650047
Author(s):  
Jintana Joomwong ◽  
Dara Phusanga
Keyword(s):  
Deterministic Case ◽  
Operation Symbol ◽  
Algebraic Systems ◽  
Power Set

Hypersubstitutions for algebraic systems are mappings which send operation symbols to terms and relational symbols to formulas preserving arities (see [D. Phusanga, Derived Algebraic Systems, Ph.D. thesis, Potsdam (2013)]). In the non-deterministic case, i.e. if one operation symbol is sent to several terms of the same arity and also one relational symbol is sent to several quantifier free formulas of the same arity, we can consider a mapping from the set of operation symbols into the power set of the set of all terms and from the set of relational symbols into the power set of the set of all quantifier free formulas of the considered type. These mappings are called non-deterministic hypersubstitutions for algebraic systems. We consider sets of algebraic systems which are invariant under non-deterministic hypersubstitutions and apply the result to [Formula: see text]-[Formula: see text]-solid classes of algebraic systems. In this paper, we consider an extension of non-deterministic hypersubstitutions which is based on deterministic ones.

scholarly journals Green’s Relations on Regular Elements of Semigroup of Relational Hypersubstitutions for Algebraic Systems of Type ((m), (n))

2021 ◽  
Vol 53 ◽  
Author(s):  
Sorasak Leeratanavalee ◽  
Jukkrit Daengsaen
Keyword(s):  
Green’S Relations ◽  
Operation Symbol ◽  
Algebraic Systems ◽  
Regular Elements ◽  
Relational Term ◽  
Green's Relations ◽  
Algebraic Properties

Any relational hypersubstitution for algebraic systems of type (τ,τ′) = ((mi)i∈I,(nj)j∈J) is a mapping which maps any mi-ary operation symbol to an mi-ary term and maps any nj - ary relational symbol to an nj-ary relational term preserving arities, where I,J are indexed sets. Some algebraic properties of the monoid of all relational hypersubstitutions for algebraic systems of a special type, especially the characterization of its order and the set of all regular elements, were first studied by Phusanga and Koppitz[13] in 2018. In this paper, we study the Green’srelationsontheregularpartofthismonoidofaparticulartype(τ,τ′) = ((m),(n)), where m, n ≥ 2.

Migration and family change in Egypt: a comparative approach to social remittances

2013 ◽  
Vol 10 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Lucile Gruntz ◽  
Delphine Pagès-El Karoui
Keyword(s):  
Public Discourse ◽  
Comparative Approach ◽  
Structural Factors ◽  
Host Countries ◽  
Return Policies ◽  
Social Remittances ◽  
Power Set ◽  
Gender Ideals ◽  
Gulf States ◽  
And Gender

Based on two ethnographical studies, our article explores social remittances from France and from the Gulf States, i.e. the way Egyptian migrants and returnees contribute to social change in their homeland with a focus on gender ideals and practices, as well as on the ways families cope with departure, absence and return. Policies in the home and host countries, public discourse, translocal networks, and individual locations within evolving structures of power, set the frame for an analysis of the consequences of migration in Egypt. This combination of structural factors is necessary to grasp the complex negotiations of family and gender norms, as asserted through idealized models, or enacted in daily practices in immigration and back home.

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

scholarly journals Online Learning Algorithms for the Real-Time Set-Point Tracking Problem

2021 ◽  
Vol 11 (14) ◽  
pp. 6620
Author(s):  
Arman Alahyari ◽  
David Pozo ◽  
Meisam Farrokhifar
Keyword(s):  
Decision Making ◽  
Power Systems ◽  
Real Time ◽  
Demand Response ◽  
Tracking Problem ◽  
Smart Meters ◽  
Set Point ◽  
Point Tracking ◽  
Power Set ◽  
Decision Making Framework

With the recent advent of technology within the smart grid, many conventional concepts of power systems have undergone drastic changes. Owing to technological developments, even small customers can monitor their energy consumption and schedule household applications with the utilization of smart meters and mobile devices. In this paper, we address the power set-point tracking problem for an aggregator that participates in a real-time ancillary program. Fast communication of data and control signal is possible, and the end-user side can exploit the provided signals through demand response programs benefiting both customers and the power grid. However, the existing optimization approaches rely on heavy computation and future parameter predictions, making them ineffective regarding real-time decision-making. As an alternative to the fixed control rules and offline optimization models, we propose the use of an online optimization decision-making framework for the power set-point tracking problem. For the introduced decision-making framework, two types of online algorithms are investigated with and without projections. The former is based on the standard online gradient descent (OGD) algorithm, while the latter is based on the Online Frank–Wolfe (OFW) algorithm. The results demonstrated that both algorithms could achieve sub-linear regret where the OGD approach reached approximately 2.4-times lower average losses. However, the OFW-based demand response algorithm performed up to twenty-nine percent faster when the number of loads increased for each round of optimization.

scholarly journals Several results on compact metrizable spaces in $$\mathbf {ZF}$$

2021 ◽  
Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis ◽  
Eliza Wajch
Keyword(s):  
Continuum Hypothesis ◽  
Compact Spaces ◽  
Power Set ◽  
Compact Metrizable Space ◽  
Permutation Models ◽  
Independence Results ◽  
The Axiom Of Choice ◽  
Metrizable Spaces ◽  
Transfer Theorems ◽  
The Continuum

AbstractIn the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

Sign in / Sign up

Export Citation Format

Share Document