Varieties of involution monoids with extreme properties

2019 ◽  
Vol 70 (4) ◽  
pp. 1157-1180
Author(s):  
Edmond W H Lee
Keyword(s):  
The Other ◽  
Sufficient Condition ◽  
Finitely Based ◽  
Finitely Based Variety ◽  
Lattice Of Subvarieties ◽  
Power Set ◽  
Cross Variety ◽  
Positive Integers

Abstract A variety that contains continuum many subvarieties is said to be huge. A sufficient condition is established under which an involution monoid generates a variety that is huge by virtue of its lattice of subvarieties order-embedding the power set lattice of the positive integers. Based on this result, several examples of finite involution monoids with extreme varietal properties are exhibited. These examples—all first of their kinds—include the following: finite involution monoids that generate huge varieties but whose reduct monoids generate Cross varieties; two finite involution monoids sharing a common reduct monoid such that one generates a huge, non-finitely based variety while the other generates a Cross variety; and two finite involution monoids that generate Cross varieties, the join of which is huge.

scholarly journals FRAGMENTS OF FREGE’SGRUNDGESETZEAND GÖDEL’S CONSTRUCTIBLE UNIVERSE

2016 ◽  
Vol 81 (2) ◽  
pp. 605-628 ◽  
Author(s):  
SEAN WALSH
Keyword(s):  
Set Theory ◽  
The Other ◽  
Structure Theory ◽  
Sufficient Condition ◽  
Weak Version ◽  
Power Set ◽  
Consistency Problem ◽  
Universe Of Sets ◽  
The 19Th Century ◽  
Abstraction Principles

AbstractFrege’sGrundgesetzewas one of the 19th century forerunners to contemporary set theory which was plagued by the Russell paradox. In recent years, it has been shown that subsystems of theGrundgesetzeformed by restricting the comprehension schema are consistent. One aim of this paper is to ascertain how much set theory can be developed within these consistent fragments of theGrundgesetze, and our main theorem (Theorem 2.9) shows that there is a model of a fragment of theGrundgesetzewhich defines a model of all the axioms of Zermelo–Fraenkel set theory with the exception of the power set axiom. The proof of this result appeals to Gödel’s constructible universe of sets and to Kripke and Platek’s idea of the projectum, as well as to a weak version of uniformization (which does not involve knowledge of Jensen’s fine structure theory). The axioms of theGrundgesetzeare examples ofabstraction principles, and the other primary aim of this paper is to articulate a sufficient condition for the consistency of abstraction principles with limited amounts of comprehension (Theorem 3.5). As an application, we resolve an analogue of the joint consistency problem in the predicative setting.

scholarly journals Dynamics of Boundary Graphs

2013 ◽  
Vol 5 (3) ◽  
pp. 447-455
Author(s):  
G. Mariumuthu ◽  
M. S. Saraswathy
Keyword(s):  
Simple Graph ◽  
The Other ◽  
Boundary Vertex ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Periodic Graph ◽  
Vertex Set ◽  
Necessary And Sufficient ◽  
Positive Integers ◽  
Boundary Graph

In a graph G, the distance d(u,v) between a pair of vertices u and v is the length of a shortest path joining them. A vertex v is a boundary vertex of a vertex u if for all The boundary graph B(G) based on a connected graph G is a simple graph which has the vertex set as in G. Two vertices u and v are adjacent in B(G) if either u is a boundary of v or v is a boundary of u. If G is disconnected, then each vertex in a component is adjacent to all other vertices in the other components and is adjacent to all of its boundary vertices within the component. Given a positive integer m, the mth iterated boundary graph of G is defined as A graph G is periodic if for some m. A graph G is said to be an eventually periodic graph if there exist positive integers m and k >0 such that We give the necessary and sufficient condition for a graph to be eventually periodic.  Keywords: Boundary graph; Periodic graph. © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v5i3.14866 J. Sci. Res. 5 (3), xxx-xxx (2013) 

A JUST NON-FINITELY BASED VARIETY OF BIGROUPS

2001 ◽  
Vol 29 (9) ◽  
pp. 4011-4046 ◽  
Author(s):  
C. K. Gupta* ◽  
A. N. Krasilnikov
Keyword(s):  
Finitely Based ◽  
Finitely Based Variety

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

scholarly journals Equipartitioning and balancing points of polygons

Pythagoras ◽  
2010 ◽  
Vol 0 (71) ◽  
Author(s):  
Shunmugam Pillay ◽  
Poobhalan Pillay
Keyword(s):  
General Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Sufficient Condition ◽  
Centre Of Mass ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The centre of mass G of a triangle has the property that the rays to the vertices from G sweep out triangles having equal areas. We show that such points, termed equipartitioning points in this paper, need not exist in other polygons. A necessary and sufficient condition for a quadrilateral to have an equipartitioning point is that one of its diagonals bisects the other. The general theorem, namely, necessary and sufficient conditions for equipartitioning points for arbitrary polygons to exist, is also stated and proved. When this happens, they are in general, distinct from the centre of mass. In parallelograms, and only in them, do the two points coincide.

scholarly journals Two examples related to conical energies

2022 ◽  
Vol 47 (1) ◽  
pp. 261-281
Author(s):  
Damian Dąbrowski
Keyword(s):  
Singular Integral ◽  
Recent Article ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
The Other ◽  
Independent Interest ◽  
Sufficient Condition ◽  
Lipschitz Graphs ◽  
Big Pieces

In a recent article (2021) we introduced and studied conical energies. We used them to prove three results: a characterization of rectifiable measures, a characterization of sets with big pieces of Lipschitz graphs, and a sufficient condition for boundedness of nice singular integral operators. In this note we give two examples related to sharpness of these results. One of them is due to Joyce and Mörters (2000), the other is new and could be of independent interest as an example of a relatively ugly set containing big pieces of Lipschitz graphs.

scholarly journals On the Turán Properties of Infinite Graphs

10.37236/771 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Andrzej Dudek ◽  
Vojtěch Rödl
Keyword(s):  
Infinite Graph ◽  
Infinite Graphs ◽  
The Other ◽  
Other Hand ◽  
Turan's Theorem ◽  
Vertex Set ◽  
Turán’S Theorem ◽  
Positive Integers

Let $G^{(\infty)}$ be an infinite graph with the vertex set corresponding to the set of positive integers ${\Bbb N}$. Denote by $G^{(l)}$ a subgraph of $G^{(\infty)}$ which is spanned by the vertices $\{1,\dots,l\}$. As a possible extension of Turán's theorem to infinite graphs, in this paper we will examine how large $\liminf_{l\rightarrow \infty} {|E(G^{(l)})|\over l^2}$ can be for an infinite graph $G^{(\infty)}$, which does not contain an increasing path $I_k$ with $k+1$ vertices. We will show that for sufficiently large $k$ there are $I_k$–free infinite graphs with ${1\over 4}+{1\over 200} < \liminf_{l\rightarrow \infty} {|E(G^{(l)})|\over l^2}$. This disproves a conjecture of J. Czipszer, P. Erdős and A. Hajnal. On the other hand, we will show that $\liminf_{l\rightarrow \infty} {|E(G^{(l)})|\over l^2}\le{1\over 3}$ for any $k$ and such $G^{(\infty)}$.

Interface acoustic waves in piezoelectric bi-crystalline structures of specific types

2005 ◽  
Vol 461 (2056) ◽  
pp. 895-911 ◽  
Author(s):  
A. N Darinskii ◽  
M Weihnacht
Keyword(s):  
Acoustic Waves ◽  
The Other ◽  
Imaginary Component ◽  
Sufficient Condition ◽  
Bulk Wave ◽  
Piezoelectric Crystal ◽  
Piezoelectric Media ◽  
Crystalline Structures ◽  
Material Constants ◽  
Bulk Waves

The paper discusses the properties of the acoustic waves guided by an interface inside piezoelectric media. The interfaces of two types have been considered: (i) an infinitesimally thin metallic layer inserted into homogeneous piezoelectric crystal of arbitrary symmetry; (ii) rigidly bonded crystals whose piezoelectric coefficients differ by sign while the other material constants are identical. Several general theorems have been proved regarding the existence of interface acoustic waves (IAWs) propagating more slowly than bulk waves. In particular, a sufficient condition for the existence of such ‘slow’ IAWs has been derived. The propagation of leaky IAWs has been studied. Special attention has been paid to the analysis of the situation when the imaginary component of the leaky IAW velocity vanishes, resulting in the appearance of non-attenuating IAWs travelling faster than the slow transverse bulk wave. The computations performed for LiNbO 3 and LiTaO 3 illustrate general conclusions.

scholarly journals On some varieties of ai-semirings satisfying xp+1 ≈ x

2018 ◽  
Vol 16 (1) ◽  
pp. 913-923
Author(s):  
Aifa Wang ◽  
Yong Shao
Keyword(s):  
Distributive Lattice ◽  
Finitely Based ◽  
Finitely Generated ◽  
Lattice Of Subvarieties

AbstractThe aim of this paper is to study the lattice of subvarieties of the ai-semiring variety defined by the additional identities$$\begin{array}{} \displaystyle x^{p+1}\approx x\,\,\mbox{and}\,\,zxyz\approx(zxzyz)^{p}zyxz(zxzyz)^{p}, \end{array} $$wherepis a prime. It is shown that this lattice is a distributive lattice of order 179. Also, each member of this lattice is finitely based and finitely generated.

Trustworthy Government and Legitimating Beliefs

2019 ◽  
pp. 362-384
Author(s):  
Margaret Levi
Keyword(s):  
Decision Making ◽  
State Building ◽  
The Other ◽  
Sufficient Condition ◽  
Goods And Services ◽  
Moral Economies ◽  
The Government ◽  
The Relationship ◽  
Advanced Democracies

A trustworthy government is one that keeps its promises (or has exceptionally good reasons why it fails to), is relatively fair in its decision-making and enforcement processes, and delivers goods and services. A legitimate government is one that appeals to widely accepted justifications for its selection, maintenance, and policies. Investigations across history and countries reveal that the more trustworthy the government, the more likely it is to evoke observation of its laws and acquiescence to policies. Less clear is the link between perceptions that government is trustworthy and beliefs that it is legitimate, at least in countries claiming or trying to be democratic. Being trustworthy in practices and outcomes may contribute to perceptions of government legitimacy. However, trustworthiness is, at best, a necessary but not sufficient condition for legitimating beliefs. This chapter explores the relationship between the trustworthiness of government and its legitimacy by considering cases from both advanced democracies and state-building efforts. It argues that current democracies may need to refashion their moral economies—the extra-market reciprocal rights and obligations that link populations, governments, corporations, and all the other various organizations that make up the society—if they are to reestablish strong grounds for legitimacy.

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