scholarly journals The system of sets of lengths and the elasticity of submonoids of a finite-rank free commutative monoid

2019 ◽  
Vol 19 (07) ◽  
pp. 2050137 ◽  
Author(s):  
Felix Gotti
Keyword(s):  
Finite Rank ◽  
Convex Cone ◽  
The Other ◽  
Extremal System ◽  
Commutative Monoid ◽  
Commutative Monoids ◽  
Other Hand ◽  
Sets Of Lengths

Let [Formula: see text] be an atomic monoid. For [Formula: see text], let [Formula: see text] denote the set of all possible lengths of factorizations of [Formula: see text] into irreducibles. The system of sets of lengths of [Formula: see text] is the set [Formula: see text]. On the other hand, the elasticity of [Formula: see text], denoted by [Formula: see text], is the quotient [Formula: see text] and the elasticity of [Formula: see text] is the supremum of the set [Formula: see text]. The system of sets of lengths and the elasticity of [Formula: see text] both measure how far [Formula: see text] is from being half-factorial, i.e. [Formula: see text] for each [Formula: see text]. Let [Formula: see text] denote the collection comprising all submonoids of finite-rank free commutative monoids, and let [Formula: see text]. In this paper, we study the system of sets of lengths and the elasticity of monoids in [Formula: see text]. First, we construct for each [Formula: see text] a monoid in [Formula: see text] having extremal system of sets of lengths. It has been proved before that the system of sets of lengths does not characterize (up to isomorphism) monoids in [Formula: see text]. Here we use our construction to extend this result to [Formula: see text] for any [Formula: see text]. On the other hand, it has been recently conjectured that the elasticity of any monoid in [Formula: see text] is either rational or infinite. We conclude this paper by proving that this is indeed the case for monoids in [Formula: see text] and for any monoid in [Formula: see text] whose corresponding convex cone is polyhedral.

scholarly journals Characteristic subgroups of relatively free groups

1992 ◽  
Vol 46 (3) ◽  
pp. 497-507
Author(s):  
Roger M. Bryant
Keyword(s):  
Nilpotent Group ◽  
Finite Rank ◽  
Free Groups ◽  
Nilpotency Class ◽  
The Other ◽  
Power Exponent ◽  
Free Nilpotent Group ◽  
Other Hand

A simple new proof is given of a result of Vaughan-Lee which implies that if G is a relatively free nilpotent group of finite rank k and nilpotency class c with c < k then the characteristic subgroups of G are all fully invariant. It is proved that the condition c < k can be weakened to c < k + p − 2 when G has p–power exponent for some prime p. On the other hand it is shown that for each prime p there is a 2-generator relatively free p-group G which is nilpotent of class 2p such that the centre of G is not fully invariant.

The Generalized Rank of Trace Languages

2019 ◽  
Vol 30 (01) ◽  
pp. 135-169
Author(s):  
Michal Kunc ◽  
Jan Meitner
Keyword(s):  
Infinite Sequence ◽  
Fixed Number ◽  
The Other ◽  
Direct Products ◽  
Commutative Monoids ◽  
Free Products ◽  
Free Monoids ◽  
Other Hand ◽  
Rational Series ◽  
Regular Sets

Given a partially commutative alphabet and a set of words [Formula: see text], the rank of [Formula: see text] expresses the amount of shuffling required to produce a word belonging to [Formula: see text] from two words whose concatenation belongs to the closure of [Formula: see text] with respect to the partial commutation. In this paper, the notion of rank is generalized from concatenations of two words to an arbitrary fixed number of words. In this way, an infinite sequence of non-negative integers and infinity is assigned to every set of words. It is proved that in the case of alphabets defining free commutative monoids, as well as in the more general case of direct products of free monoids, sequences of ranks of regular sets are exactly non-decreasing sequences that are eventually constant. On the other hand, by uncovering a relationship between rank sequences of regular sets and rational series over the min-plus semiring, it is shown that already for alphabets defining free products of free commutative monoids, rank sequences need not be eventually periodic.

On surjunctive monoids

2015 ◽  
Vol 25 (04) ◽  
pp. 567-606 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Michel Coornaert
Keyword(s):  
Cellular Automata ◽  
The Other ◽  
Finite Alphabet ◽  
Finitely Generated ◽  
Commutative Monoids ◽  
Residually Finite ◽  
Finite Monoids ◽  
Other Hand ◽  
Bicyclic Monoid

A monoid M is called surjunctive if every injective cellular automata with finite alphabet over M is surjective. We show that all finite monoids, all finitely generated commutative monoids, all cancellative commutative monoids, all residually finite monoids, all finitely generated linear monoids, and all cancellative one-sided amenable monoids are surjunctive. We also prove that every limit of marked surjunctive monoids is itself surjunctive. On the other hand, we show that the bicyclic monoid and, more generally, all monoids containing a submonoid isomorphic to the bicyclic monoid are non-surjunctive.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

Life Beyond 1MeV

1980 ◽  
Vol 38 ◽  
pp. 30-33
Author(s):  
K.H. Westmacott
Keyword(s):  
Electron Microscopy ◽  
Past Experience ◽  
The Other ◽  
Good Case ◽  
Other Hand ◽  
The U.S

Life beyond 1MeV – like life after 40 – is not too different unless one takes advantage of past experience and is receptive to new opportunities. At first glance, the returns on performing electron microscopy at voltages greater than 1MeV diminish rather rapidly as the curves which describe the well-known advantages of HVEM often tend towards saturation. However, in a country with a significant HVEM capability, a good case can be made for investing in instruments with a range of maximum accelerating voltages. In this regard, the 1.5MeV KRATOS HVEM being installed in Berkeley will complement the other 650KeV, 1MeV, and 1.2MeV instruments currently operating in the U.S. One other consideration suggests that 1.5MeV is an optimum voltage machine – Its additional advantages may be purchased for not much more than a 1MeV instrument. On the other hand, the 3MeV HVEM's which seem to be operated at 2MeV maximum, are much more expensive.

Can the Academic Self-Concept be Positive and Realistic?

2005 ◽  
Vol 19 (3) ◽  
pp. 129-132 ◽  
Author(s):  
Reimer Kornmann
Keyword(s):  
Academic Performance ◽  
Opposite Effect ◽  
Self Esteem ◽  
Point Of View ◽  
The Other ◽  
Self Concept ◽  
High Ability ◽  
Self Image ◽  
Other Hand

Summary: My comment is basically restricted to the situation in which less-able students find themselves and refers only to literature in German. From this point of view I am basically able to confirm Marsh's results. It must, however, be said that with less-able pupils the opposite effect can be found: Levels of self-esteem in these pupils are raised, at least temporarily, by separate instruction, academic performance however drops; combined instruction, on the other hand, leads to improved academic performance, while levels of self-esteem drop. Apparently, the positive self-image of less-able pupils who receive separate instruction does not bring about the potential enhancement of academic performance one might expect from high-ability pupils receiving separate instruction. To resolve the dilemma, it is proposed that individual progress in learning be accentuated, and that comparisons with others be dispensed with. This fosters a self-image that can in equal measure be realistic and optimistic.

Stories and the Self

2020 ◽  
Vol 32 (2) ◽  
pp. 47-58 ◽  
Author(s):  
Stefan Krause ◽  
Markus Appel
Keyword(s):  
Meta Analysis ◽  
The Self ◽  
The Other ◽  
Lower Degree ◽  
Contrast Effects ◽  
Self Perception ◽  
Self Perceptions ◽  
Other Hand ◽  
The One ◽  
Implicit And Explicit

Abstract. Two experiments examined the influence of stories on recipients’ self-perceptions. Extending prior theory and research, our focus was on assimilation effects (i.e., changes in self-perception in line with a protagonist’s traits) as well as on contrast effects (i.e., changes in self-perception in contrast to a protagonist’s traits). In Experiment 1 ( N = 113), implicit and explicit conscientiousness were assessed after participants read a story about either a diligent or a negligent student. Moderation analyses showed that highly transported participants and participants with lower counterarguing scores assimilate the depicted traits of a story protagonist, as indicated by explicit, self-reported conscientiousness ratings. Participants, who were more critical toward a story (i.e., higher counterarguing) and with a lower degree of transportation, showed contrast effects. In Experiment 2 ( N = 103), we manipulated transportation and counterarguing, but we could not identify an effect on participants’ self-ascribed level of conscientiousness. A mini meta-analysis across both experiments revealed significant positive overall associations between transportation and counterarguing on the one hand and story-consistent self-reported conscientiousness on the other hand.

Don’t Put Me in This Group

2019 ◽  
Vol 50 (2) ◽  
pp. 80-93
Author(s):  
Jort de Vreeze ◽  
Christina Matschke
Keyword(s):  
Positive Emotions ◽  
Negative Emotions ◽  
Negative Information ◽  
The Self ◽  
The Other ◽  
Other Hand ◽  
Group Memberships

Abstract. Not all group memberships are self-chosen. The current research examines whether assignments to non-preferred groups influence our relationship with the group and our preference for information about the ingroup. It was expected and found that, when people are assigned to non-preferred groups, they perceive the group as different to the self, experience negative emotions about the assignment and in turn disidentify with the group. On the other hand, when people are assigned to preferred groups, they perceive the group as similar to the self, experience positive emotions about the assignment and in turn identify with the group. Finally, disidentification increases a preference for negative information about the ingroup.

ON THE OTHER HAND

1961 ◽  
Vol 6 (6) ◽  
pp. 222-223
Author(s):  
Edwin G. Boring
Keyword(s):  
The Other ◽  
Other Hand
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