The Macneille Completion of a Uniquely Complemented Lattice

1994 ◽  
Vol 37 (2) ◽  
pp. 222-227 ◽  
Author(s):  
John Harding
Keyword(s):  
Lattice Theory ◽  
Macneille Completion ◽  
The Third ◽  
Uniquely Complemented ◽  
Complemented Lattice

AbstractProblem 36 of the third edition of Birkhoff's Lattice theory [2] asks whether the MacNeille completion of uniquely complemented lattice is necessarily uniquely complemented. We show that the MacNeille completion of a uniquely complemented lattice need not be complemented.

scholarly journals Preface

2015 ◽  
Vol 27 (4) ◽  
pp. 459-459
Author(s):  
ACHIM JUNG ◽  
GUO-QIANG ZHANG
Keyword(s):  
Lattice Theory ◽  
Process Algebra ◽  
Metric Spaces ◽  
Domain Theory ◽  
Conference Series ◽  
The Third ◽  
Language Semantics ◽  
And Mathematics ◽  
October 17 ◽  
Partial Logics

The International Symposium on Domain Theory (ISDT) is a conference series intended to be a forum for researchers in domain theory and its applications. Topics include topological and logical aspects of domains; categories of domains and powerdomains; continuous posets and their representations; partial orders, lattice theory and metric spaces; types, process algebra and concurrency; non-classical and partial logics; programming language semantics; applications in computer science and mathematics. This conference series was founded by Yingming Liu, Yixiang Chen, Klaus Keimel, and Guo-Qiang Zhang. All ISDT events have taken place in China. The first ISDT was held in Shanghai, October 17–24, 1999; the second ISDT was held in Chengdu, October 22–26, 2001; the third ISDT occurred in Xi'an, China, May 10–14, 2004; the fourth ISDT was held in Changsha, June 2–6, 2006; and the fifth ISDT took place in Shanghai, September 11–14, 2009.

Single identities forcing lattices to be Boolean

2018 ◽  
Vol 68 (4) ◽  
pp. 713-716
Author(s):  
Ivan Chajda ◽  
Helmut Länger ◽  
Ranganathan Padmanabhan
Keyword(s):  
Boolean Algebra ◽  
Unary Operation ◽  
Boolean Algebras ◽  
Uniquely Complemented ◽  
Complemented Lattice

Abstract In this note we characterize Boolean algebras among lattices of type (2, 2, 1) with join, meet and an additional unary operation by means of single two-variable respectively three-variable identities. In particular, any uniquely complemented lattice satisfying any one of these equational constraints is distributive and hence a Boolean algebra.

Postulates For Distributive Lattices

1951 ◽  
Vol 3 ◽  
pp. 28-30 ◽  
Author(s):  
Marlow Sholander
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Lattice Theory ◽  
Distributive Lattices ◽  
Intrinsic Interest ◽  
Binary Operations ◽  
The Third ◽  
Ternary Operation

Many sets of postulates have been given for distributive lattices and for Boolean algebra. For a description of some of the most interesting and for references to others the reader is referred to Birkhoff's “Lattice Theory”[1]. In this paper we give sets of postulates which have some intrinsic interest because of their simplicity. In the first two sections binary operations are used to describe a distributive lattice by 2 identities in 3 variables and a Boolean algebra by 3 identities in 3 variables. In the third section a ternary operation is used to describe distributive lattices with 0 and J by 2 identities in 5 variables.

scholarly journals The descending chain condition in join-continuous modular lattices

1969 ◽  
Vol 10 (1-2) ◽  
pp. 1-4 ◽  
Author(s):  
L. G. Kovács
Keyword(s):  
Distributive Lattice ◽  
Lattice Theory ◽  
Chain Condition ◽  
Modular Lattices ◽  
Algebraic Systems ◽  
The Third ◽  
Irreducible Elements ◽  
Descending Chain Condition ◽  
A Chain

If L is a distributive lattice in which every element is the join of finitely many join-irreducible elements, and if the set of join-irreducible elements of L satisfies the descending chain condition, then L satisfies the descending chain condition: this follows easily from the results of Chapter VIII, Section 2, in the Third (New) Edition of Garrett Birkhoff's ‘Lattice Theory’ (Amer. Math. Soc., Providence, 1967). Certain investigations (M. S. Brooks, R. A. Bryce, unpublished) on the lattice of all subvarieties of some variety of algebraic systems require a similar result without the assumption of distributivity. Such a lattice is always join-continuous: that is, it is complete and (∧X) ∨ y = ∧ {x ∨ y: x ∈ X} whenever X is a chain in the lattice (for, the dual of such a lattice is complete and ‘algebraic’, in Birkhoff's terminology). The purpose of this note is to present the result:

Progress report on 21-cm observations at low latitude between longitudes (l 11) 0° and 66°

1967 ◽  
Vol 31 ◽  
pp. 177-179
Author(s):  
W. W. Shane
Keyword(s):  
Preliminary Report ◽  
Progress Report ◽  
Galactic Centre ◽  
Low Latitude ◽  
The Third ◽  
Introductory Lecture ◽  
Centre Region

In the course of several 21-cm observing programmes being carried out by the Leiden Observatory with the 25-meter telescope at Dwingeloo, a fairly complete, though inhomogeneous, survey of the regionl11= 0° to 66° at low galactic latitudes is becoming available. The essential data on this survey are presented in Table 1. Oort (1967) has given a preliminary report on the first and third investigations. The third is discussed briefly by Kerr in his introductory lecture on the galactic centre region (Paper 42). Burton (1966) has published provisional results of the fifth investigation, and I have discussed the sixth in Paper 19. All of the observations listed in the table have been completed, but we plan to extend investigation 3 to a much finer grid of positions.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

The effects of Cyclosporin-A (CYA) on the Ultrastructure of Gingival Mast Cells (GMC) in Behcet's disease (BD)

1990 ◽  
Vol 48 (3) ◽  
pp. 358-359
Author(s):  
Oktay Arda ◽  
Ulkü Noyan ◽  
Selgçk Yilmaz ◽  
Mustafa Taşyürekli ◽  
İsmail Seçkin ◽  
...  
Keyword(s):  
Unknown Etiology ◽  
Control Group ◽  
Target Cells ◽  
Gingival Hyperplasia ◽  
Cellular Activity ◽  
Direct Relation ◽  
Immune Disease ◽  
Genital Ulceration ◽  
Functional Changes ◽  
The Third

Turkish dermatologist, H. Beheet described the disease as recurrent triad of iritis, oral aphthous lesions and genital ulceration. Auto immune disease is the recent focus on the unknown etiology which is still being discussed. Among the other immunosupressive drugs, CyA included in it's treatment newly. One of the important side effects of this drug is gingival hyperplasia which has a direct relation with the presence of teeth and periodontal tissue. We are interested in the ultrastructure of immunocompetent target cells that were affected by CyA in BD.Three groups arranged in each having 5 patients with BD. Control group was the first and didn’t have CyA treatment. Patients who had CyA, but didn’t show gingival hyperplasia assembled the second group. The ones displaying gingival hyperplasia following CyA therapy formed the third group. GMC of control group and their granules are shown in FIG. 1,2,3. GMC of the second group presented initiation of supplementary cellular activity and possible maturing functional changes with the signs of increased number of mitochondria and accumulation of numerous dense cored granules next to few normal ones, FIG. 4,5,6.

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