scholarly journals Equationally complete varieties of generalized groups

1975 ◽  
Vol 13 (1) ◽  
pp. 75-83 ◽  
Author(s):  
W.F. Page
Keyword(s):  
Commutative Case ◽  
Universal Algebras ◽  
Associative Operation ◽  
Infinite Sets ◽  
University Of Miami ◽  
Phd Thesis ◽  
Special Case

In previous work, Page and Butson [Algebra Universalis 3 (1973), 112–126] characterized all equationally complete classes (atoms) of m–semigroups (universal algebras with one m–ary associative operation), and hence m–groups, in the commutative case. The further characterization of the non-commutative m-group atoms was thought to hinge upon a conjecture by Page [PhD thesis, University of Miami, 1973] that a weaker form of commutativity held true. In this paper that conjecture is proved and then used to study the special case m = 4. Two additional infinite sets of atoms are thereby determined, although it is not proved that these examples exhaust the remaining atoms for m = 4.

scholarly journals Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach

2021 ◽  
Author(s):  
Yves Achdou ◽  
Jiequn Han ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions ◽  
Benjamin Moll
Keyword(s):  
Continuous Time ◽  
Wealth Distribution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Heterogeneous Agent ◽  
Saving Behavior ◽  
Income And Wealth Distribution ◽  
Heterogeneous Agent Models ◽  
Special Case

Abstract We recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time. This workhorse model – as well as heterogeneous agent models more generally – then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (i) an analytic characterization of the consumption and saving behavior of the poor, particularly their marginal propensities to consume; (ii) a closed-form solution for the wealth distribution in a special case with two income types; (iii) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including – but not limited to – the Aiyagari-Bewley-Huggett model.

scholarly journals Congruence pairs of principal MS-algebras and perfect extensions

2020 ◽  
Vol 70 (6) ◽  
pp. 1275-1288
Author(s):  
Abd El-Mohsen Badawy ◽  
Miroslav Haviar ◽  
Miroslav Ploščica
Keyword(s):  
Boolean Algebra ◽  
Congruence Lattices ◽  
Descriptive Solution ◽  
The One ◽  
Special Case ◽  
Congruence Pair

AbstractThe notion of a congruence pair for principal MS-algebras, simpler than the one given by Beazer for K2-algebras [6], is introduced. It is proved that the congruences of the principal MS-algebras L correspond to the MS-congruence pairs on simpler substructures L°° and D(L) of L that were associated to L in [4].An analogy of a well-known Grätzer’s problem [11: Problem 57] formulated for distributive p-algebras, which asks for a characterization of the congruence lattices in terms of the congruence pairs, is presented here for the principal MS-algebras (Problem 1). Unlike a recent solution to such a problem for the principal p-algebras in [2], it is demonstrated here on the class of principal MS-algebras, that a possible solution to the problem, though not very descriptive, can be simple and elegant.As a step to a more descriptive solution of Problem 1, a special case is then considered when a principal MS-algebra L is a perfect extension of its greatest Stone subalgebra LS. It is shown that this is exactly when de Morgan subalgebra L°° of L is a perfect extension of the Boolean algebra B(L). Two examples illustrating when this special case happens and when it does not are presented.

Intersections of quotient rings and Prüfer v-multiplication domains

2016 ◽  
Vol 15 (08) ◽  
pp. 1650149 ◽  
Author(s):  
Said El Baghdadi ◽  
Marco Fontana ◽  
Muhammad Zafrullah
Keyword(s):  
Integral Domain ◽  
Algebraic Approach ◽  
Quotient Field ◽  
Topological Characterization ◽  
Locally Finite ◽  
Star Operation ◽  
Star Operations ◽  
Quotient Rings ◽  
Special Case

Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an overring [Formula: see text] of [Formula: see text] a subring of [Formula: see text] containing [Formula: see text] as a subring. A family [Formula: see text] of overrings of [Formula: see text] is called a defining family of [Formula: see text], if [Formula: see text]. Call an overring [Formula: see text] a sublocalization of [Formula: see text], if [Formula: see text] has a defining family consisting of rings of fractions of [Formula: see text]. Sublocalizations and their intersections exhibit interesting examples of semistar or star operations [D. D. Anderson, Star operations induced by overrings, Comm. Algebra 16 (1988) 2535–2553]. We show as a consequence of our work that domains that are locally finite intersections of Prüfer [Formula: see text]-multiplication (respectively, Mori) sublocalizations turn out to be Prüfer [Formula: see text]-multiplication domains (PvMDs) (respectively, Mori); in particular, for the Mori domain case, we reobtain a special case of Théorème 1 of [J. Querré, Intersections d’anneaux intègers, J. Algebra 43 (1976) 55–60] and Proposition 3.2 of [N. Dessagnes, Intersections d’anneaux de Mori — exemples, Port. Math. 44 (1987) 379–392]. We also show that, more than the finite character of the defining family, it is the finite character of the star operation induced by the defining family that causes the interesting results. As a particular case of this theory, we provide a purely algebraic approach for characterizing P vMDs as a subclass of the class of essential domains (see also Theorem 2.4 of [C. A. Finocchiaro and F. Tartarone, On a topological characterization of Prüfer [Formula: see text]-multiplication domains among essential domains, preprint (2014), arXiv:1410.4037]).

scholarly journals Characterization of Self-Adjoint Domains for Two-Interval Even Order Singular C-Symmetric Differential Operators in Direct Sum Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Qinglan Bao ◽  
Xiaoling Hao ◽  
Jiong Sun
Keyword(s):  
Boundary Conditions ◽  
Differential Operators ◽  
Direct Sum ◽  
Even Order ◽  
Special Case ◽  
Symmetric Differential Operators

This paper is concerned with the characterization of all self-adjoint domains associated with two-interval even order singular C-symmetric differential operators in terms of boundary conditions. The previously known characterizations of Lagrange symmetric differential operators are a special case of this one.

Quadratic-monomial generated domains from mixed signed, directed graphs

2019 ◽  
Vol 29 (02) ◽  
pp. 279-308
Author(s):  
Michael A. Burr ◽  
Drew J. Lipman
Keyword(s):  
Directed Graphs ◽  
Complete Characterization ◽  
Combinatorial Structure ◽  
Signed Directed Graph ◽  
Odd Cycle ◽  
Combinatorial Classification ◽  
Special Case ◽  
Text Condition

Determining whether an arbitrary subring [Formula: see text] of [Formula: see text] is a normal or Cohen-Macaulay domain is, in general, a nontrivial problem, even in the special case of a monomial generated domain. We provide a complete characterization of the normality, normalizations, and Serre’s [Formula: see text] condition for quadratic-monomial generated domains. For a quadratic-monomial generated domain [Formula: see text], we develop a combinatorial structure that assigns, to each quadratic monomial of the ring, an edge in a mixed signed, directed graph [Formula: see text], i.e. a graph with signed edges and directed edges. We classify the normality and the normalizations of such rings in terms of a generalization of the combinatorial odd cycle condition on [Formula: see text]. We also generalize and simplify a combinatorial classification of Serre’s [Formula: see text] condition for such rings and construct non-Cohen–Macaulay rings.

scholarly journals Full Characterization of Act-and-wait Control for First-order Unstable Lag Processes

2010 ◽  
Vol 16 (7-8) ◽  
pp. 1209-1233 ◽  
Author(s):  
T. Insperger ◽  
P. Wahi ◽  
A. Colombo ◽  
G. Stépán ◽  
M. Di Bernardo ◽  
...  
Keyword(s):  
Time Delay ◽  
Feedback Systems ◽  
Periodic Control ◽  
First Order ◽  
Full Characterization ◽  
The Stability ◽  
And Control ◽  
Time Periodic ◽  
Special Case

Act-and-wait control is a special case of time-periodic control for systems with feedback delay, where the control gains are periodically switched on and off in order to stabilize otherwise unstable systems. The stability of feedback systems in the presence of time delay is a challenging problem. In this paper, we show that the act-and-wait type time-periodic control can always provide deadbeat control for first-order unstable lag processes with any (large but) fixed value of the time delay in the feedback loop. A full characterization of this act-and-wait controller with respect to the system and control parameters is given based on performance and robustness against disturbances.

Sets which do not have subsets of every higher degree

1978 ◽  
Vol 43 (1) ◽  
pp. 135-138 ◽  
Author(s):  
Stephen G. Simpson
Keyword(s):  
Similar Degree ◽  
Theoretic Analysis ◽  
Natural Numbers ◽  
Ramsey's Theorem ◽  
Ramsey’S Theorem ◽  
Infinite Sets ◽  
Special Case

Let A be a subset of ω, the set of natural numbers. The degree of A is its degree of recursive unsolvability. We say that A is rich if every degree above that of A is represented by a subset of A. We say that A is poor if no degree strictly above that of A is represented by a subset of A. The existence of infinite poor (and hence nonrich) sets was proved by Soare [9].Theorem 1. Suppose that A is infinite and not rich. Then every hyperarith-metical subset H of ω is recursive in A.In the special case when H is arithmetical, Theorem 1 was proved by Jockusch [4] who employed a degree-theoretic analysis of Ramsey's theorem [3]. In our proof of Theorem 1 we employ a similar, degree-theoretic analysis of a certain generalization of Ramsey's theorem. The generalization of Ramsey's theorem is due to Nash-Williams [6]. If A ⊆ ω we write [A]ω for the set of all infinite subsets of A. If P ⊆ [ω]ω we let H(P) be the set of all infinite sets A such that either [A]ω ⊆ P = ∅. Nash-Williams' theorem is essentially the statement that if P ⊆ [ω]ω is clopen (in the usual, Baire topology on [ω]ω) then H(P) is nonempty. Subsequent, further generalizations of Ramsey's theorem were proved by Galvin and Prikry [1], Silver [8], Mathias [5], and analyzed degree-theoretically by Solovay [10]; those results are not needed for this paper.

THE BANACH-LIE *-ALGEBRA OF MULTIPLICATION OPERATORS ON A W*-ALGEBRA

2011 ◽  
Vol 04 (02) ◽  
pp. 235-261
Author(s):  
Maysaa Alqurashi ◽  
Najla A. Altwaijry ◽  
C. Martin Edwards ◽  
Christopher S. Hoskin
Keyword(s):  
State Space ◽  
Lie Algebra ◽  
The State ◽  
Multiplication Operators ◽  
Dual Cone ◽  
Positive Real ◽  
Linear Isometry ◽  
Real Linear ◽  
Special Case

The hermitian part [Formula: see text] of the Banach-Lie *-algebra [Formula: see text] of multiplication operators on the W *-algebra A is a unital GM-space, the base of the dual cone in the dual GL-space [Formula: see text] of which is affine isomorphic and weak*-homeomorphic to the state space of [Formula: see text]. It is shown that there exists a Lie *-isomorphism ϕ from the quotient (A ⊕∞ Aop)/K of an enveloping W *-algebra A ⊕∞ Aop of A by a weak*-closed Lie *-ideal K onto [Formula: see text], the restriction to the hermitian part ((A ⊕∞ Aop)/K)h of which is a bi-positive real linear isometry, thereby giving a characterization of the state space of [Formula: see text]. In the special case in which A is a W *-factor this leads to a further identification of the state space of [Formula: see text] in terms of the state space of A. For any W *-algebra A, the Banach-Lie *-algebra [Formula: see text] coincides with the set of generalized derivations of A, and, as an application, a formula is obtained for the norm of an element of [Formula: see text] in terms of a centre-valued 'norm' on A, which is similar to that previously obtained by non-order-theoretic methods.

MASS TRANSPORTATION IN GROUPS OF TYPE H

2005 ◽  
Vol 07 (04) ◽  
pp. 509-537 ◽  
Author(s):  
S. RIGOT
Keyword(s):  
Cost Function ◽  
Optimal Transport ◽  
Transport Problem ◽  
Mass Transportation ◽  
Heisenberg Groups ◽  
The One ◽  
Carathéodory Distance ◽  
The Cost ◽  
Special Case

We give a solution of the optimal transport problem in groups of type H when the cost function is the square of either the Carnot–Carathéodory or Korányi distance. This generalizes results previously proved for the Heisenberg groups. We use the same strategy that the one which was developed in that special case together with slightly refined technicalities that essentially reflect the fact that the center of the group can be of dimension larger than one. For each distance we prove existence, uniqueness and give a characterization of the optimal transport. In the case of the Carnot–Carathéodory distance we also prove that the optimal transport arises as the limit of the optimal transports in natural Riemannian approximations.

Sign in / Sign up

Export Citation Format

Share Document