Epimorphisms in the Category of ℓ-Groups

2009 ◽  
Vol 16 (01) ◽  
pp. 123-130
Author(s):  
Xinmin Lu ◽  
Hourong Qin
Keyword(s):  
Proper Subclass ◽  
Small Kernel

In the category of ℓ-groups, we introduce the concepts of Hopfian and generalized Hopfian ℓ-groups. An ℓ-group G is called Hopfian if every surjective ℓ-homomorphism f : G → G is an ℓ-isomorphism, and G is called generalized Hopfian if every surjective ℓ-homomorphism f : G → G has a small kernel in G. By an example we show that the class of generalized Hopfian ℓ-groups is a proper subclass of Hopfian ℓ-groups. In this paper, we establish some characterizations for them, which generalize some results in [9].

PERFECTLY BOUNDED CLASSES OF ABELIAN GROUPS

2013 ◽  
Vol 12 (05) ◽  
pp. 1250208 ◽  
Author(s):  
PATRICK W. KEEF
Keyword(s):  
Abelian Groups ◽  
Direct Sums ◽  
Proper Subclass ◽  
Infinite Height ◽  
Reduced Group

Let [Formula: see text] be the class of abelian p-groups. A non-empty proper subclass [Formula: see text] is bounded if it is closed under subgroups, additively bounded if it is also closed under direct sums and perfectly bounded if it is additively bounded and closed under filtrations. If [Formula: see text], we call the partition of [Formula: see text] given by [Formula: see text] a B/U-pair. We state most of our results not in terms of bounded classes, but rather the corresponding B/U-pairs. Any additively bounded class contains a unique maximal perfectly bounded subclass. The idea of the length of a reduced group is generalized to the notion of the length of an additively bounded class. If λ is an ordinal or the symbol ∞, then there is a natural largest and smallest additively bounded class of length λ, as well as a largest and smallest perfectly bounded class of length λ. If λ ≤ ω, then there is a unique perfectly bounded class of length λ, namely the pλ-bounded groups that are direct sums of cyclics; however, this fails when λ > ω. This parallels results of Dugas, Fay and Shelah (1987) and Keef (1995) on the behavior of classes of abelian p-groups with elements of infinite height. It also simplifies, clarifies and generalizes a result of Cutler, Mader and Megibben (1989) which states that the pω + 1-projectives cannot be characterized using filtrations.

On the short surface waves due to a half-immersed circular cylinder oscillating on water of infinite depth

1982 ◽  
Vol 384 (1787) ◽  
pp. 333-357 ◽  
Keyword(s):  
Circular Cylinder ◽  
Surface Waves ◽  
Usual Method ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Small Kernel ◽  
Rolling Mode ◽  
Incident Waves ◽  
Plausible Argument ◽  
Fixed Cylinder

In this paper we examine two-dimensional short surface waves in water of infinite depth produced by various modes of oscillation of a half-immersed circular cylinder. The usual method, which depends on finding the potential on the cylinder from an integral equation with a small kernel, is here replaced by one that uses instead the known value of the potential for incident waves in the presence of the fixed cylinder. Thus we are able to determine three-term asymptotic expansions for both the heaving and the swaying modes that improve on earlier forms, and, for the heaving mode, to refine the interpolation with previous numerical calculations and confirm in principle the result obtained elsewhere by a plausible argument. The rolling mode also can actually be included by superposition of the heaving and swaying modes for this cylinder.

scholarly journals Growth results for a subclass of Bazilevič functions

1985 ◽  
Vol 8 (4) ◽  
pp. 785-793
Author(s):  
Rabha Md. El-Ashwah ◽  
D. K. Thomas
Keyword(s):  
Unit Disc ◽  
Starlike Function ◽  
Area Function ◽  
Proper Subclass ◽  
Bazilevic Functions

Forα>0, letB(α)be the class of regular normalized Bazilevič functions defined in the unit disc. Choosing the associated starlike functiong(z)≡zgives a proper subclassB1(α)ofB(α). ForB(α), correct growth estimates in terms of the area function are unknown. Several results in this direction are given forB1(12).

scholarly journals Distributions with complete monotone derivative and geometric infinite divisibility

1990 ◽  
Vol 22 (3) ◽  
pp. 751-754 ◽  
Author(s):  
R. N. Pillai ◽  
E. Sandhya
Keyword(s):  
Infinite Divisibility ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Proper Subclass ◽  
Geometric Infinite Divisibility

It is shown that a distribution with complete monotone derivative is geometrically infinitely divisible and that the class of distributions with complete monotone derivative is a proper subclass of the class of geometrically infinitely divisible distributions.

scholarly journals Logarithmic (translationally) rapidly varying sequences and selection principles

2020 ◽  
Vol 107 (121) ◽  
pp. 45-51
Author(s):  
Dragan Djurcic ◽  
Nebojsa Elez ◽  
Valentina Timotic
Keyword(s):  
Information Theory ◽  
Basic Properties ◽  
Proper Subclass ◽  
Selection Principles

We introduce a proper subclass of the class of rapidly varying sequences (logarithmic (translationally) rapidly varying sequences), motivated by a notion in information theory (self-information of the system). We prove some of its basic properties. In the main result, we prove that Rothberger?s and Kocinac?s selection principles hold, when this class is on the second coordinate, and on the first coordinate we have the class of positive and unbounded sequences

scholarly journals Why We Still Do Not Know What a “Real” Argument Is

2014 ◽  
Vol 34 (1) ◽  
pp. 62 ◽  
Author(s):  
G.C. Goddu
Keyword(s):  
Theoretical Account ◽  
Proper Subclass ◽  
Real Argument ◽  
Significant Class

In his recent paper, “What a Real Argument is”, Ben Hamby attempts to provide an adequate theoretical account of “real” arguments. In this paper I present and evaluate both Hamby’s motivation for distinguishing “real” from non-“real” arguments and his articulation of the distinction. I argue that neither is adequate to ground a theoretically significant class of “real” arguments, for the articulation fails to pick out a stable proper subclass of all arguments that is simultaneously both theoretically relevant and a proper subclass of all arguments.

scholarly journals $${\mathcal {U}}$$-Bubble Model for Mixed Unit Interval Graphs and Its Applications: The MaxCut Problem Revisited

Algorithmica ◽  
2021 ◽  
Author(s):  
Jan Kratochvíl ◽  
Tomáš Masařík ◽  
Jana Novotná
Keyword(s):  
Unit Length ◽  
Algorithm Design ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Unit Interval ◽  
Interval Graphs ◽  
Induced Subgraph ◽  
Intersection Graphs ◽  
Proper Subclass ◽  
Maxcut Problem

AbstractInterval graphs, intersection graphs of segments on a real line (intervals), play a key role in the study of algorithms and special structural properties. Unit interval graphs, their proper subclass, where each interval has a unit length, has also been extensively studied. We study mixed unit interval graphs—a generalization of unit interval graphs where each interval has still a unit length, but intervals of more than one type (open, closed, semi-closed) are allowed. This small modification captures a richer class of graphs. In particular, mixed unit interval graphs may contain a claw as an induced subgraph, as opposed to unit interval graphs. Heggernes, Meister, and Papadopoulos defined a representation of unit interval graphs called the bubble model which turned out to be useful in algorithm design. We extend this model to the class of mixed unit interval graphs and demonstrate the advantages of this generalized model by providing a subexponential-time algorithm for solving the MaxCut problem on mixed unit interval graphs. In addition, we derive a polynomial-time algorithm for certain subclasses of mixed unit interval graphs. We point out a substantial mistake in the proof of the polynomiality of the MaxCut problem on unit interval graphs by Boyacı et al. (Inf Process Lett 121:29–33, 2017. 10.1016/j.ipl.2017.01.007). Hence, the time complexity of this problem on unit interval graphs remains open. We further provide a better algorithmic upper-bound on the clique-width of mixed unit interval graphs.

Modules in which every surjective endomorphism has a $$\mu $$-small kernel

2020 ◽  
Vol 66 (2) ◽  
pp. 325-337
Author(s):  
Abderrahim El Moussaouy ◽  
M’Hammed Ziane
Keyword(s):  
Small Kernel

Global Dimensions of Subidealizer Rings

1995 ◽  
Vol 2 (4) ◽  
pp. 419-424
Author(s):  
John Koker
Keyword(s):  
Global Dimension ◽  
Simple Modules ◽  
Proper Subclass

Abstract Recently, there have been many results which show that the global dimension of certain rings can be computed using a proper subclass of the cyclic modules, e.g., the simple modules. In this paper we view calculating global dimensions in this fashion as a property of a ring and show that this is a property which transfers to the ring's idealizer and subidealizer ring.

scholarly journals Distributions with complete monotone derivative and geometric infinite divisibility

1990 ◽  
Vol 22 (03) ◽  
pp. 751-754
Author(s):  
R. N. Pillai ◽  
E. Sandhya
Keyword(s):  
Infinite Divisibility ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Proper Subclass ◽  
Geometric Infinite Divisibility

It is shown that a distribution with complete monotone derivative is geometrically infinitely divisible and that the class of distributions with complete monotone derivative is a proper subclass of the class of geometrically infinitely divisible distributions.

Sign in / Sign up

Export Citation Format

Share Document