scholarly journals Semigroup varieties closed for the Bruck extension

1994 ◽  
Vol 36 (3) ◽  
pp. 371-380
Author(s):  
Francis Pastijn ◽  
Xiaoying Yan
Keyword(s):  
Semigroup Variety ◽  
Infinite Chain ◽  
Real Numbers ◽  
Chain Order ◽  
A Chain ◽  
Semigroup Varieties

We shall show that there exists a chain, order isomorphic to the chain of real numbers, of semigroup varieties closed for the Bruck extension. The least semigroup variety closed for the Bruck extension will be obtained as the union of varieties in an infinite chain of semigroup varieties.

A note on iterative arguments in a topos

1992 ◽  
Vol 111 (1) ◽  
pp. 57-62 ◽  
Author(s):  
J. J. C. Vermeulen
Keyword(s):  
Set Theory ◽  
Infinite Chain ◽  
Repetitive Process ◽  
A Chain

Intuitively, transfinite iteration is a repetitive process, which eventually reaches completion, but might need to progress through an infinite chain of steps before finally doing so. But whereas such a chain is always readily at hand in classical set theory in the form of ordinals, iterative arguments involving sets (i.e. objects) in a general topos have to depend on some intrinsic or naturally available inductive structure, say algebraic, which might not be associated with a (well-ordered) chain.

PERMUTATION IDENTITIES AND VARIETIES OF NILSEMIGROUPS

1993 ◽  
Vol 03 (02) ◽  
pp. 201-210
Author(s):  
XIAOYING YAN
Keyword(s):  
Equivalence Relation ◽  
Complete Lattice ◽  
Semigroup Variety ◽  
Infinite Subset ◽  
Equivalence Classes ◽  
Minimal Variety ◽  
Complete Sublattice ◽  
Countably Infinite ◽  
Semigroup Varieties

For any variety V of semigroups there exists a smallest semigroup variety PV containing V and closed for the construction of power semigroups. These varieties PV form a countably infinite subset PL(S) of the lattice L(S) of semigroup varieties. Though (PL(S), ⊆) is a complete lattice, it is not a complete sublattice of L(S). There exists however an interval in L(S) consisting of varieties of nilsemigroups which is isomorphic to (PL(S), ⊆). It will be shown that the equivalence classes of the equivalence relation induced by P: L(S)→PL(S), V↦PV, each contain a unique minimal variety consisting of nilsemigroups.

The Gap Between Partial and Full

1998 ◽  
Vol 08 (03) ◽  
pp. 399-430 ◽  
Author(s):  
J. Almeida ◽  
M. V. Volkov
Keyword(s):  
Partial Order ◽  
Finite Chain ◽  
Real Numbers ◽  
A Chain ◽  
Usual Order

We show that the interval of the lattice of semigroup pseudovarieties between the pseudovarieties generated by all semigroups of full and respectively, partial, order-preserving transformations of a finite chain, contains a chain isomorphic to the chain of real numbers (with the usual order). Similar results are proved for several related intervals.

PSEUDORECURSIVE VARIETIES OF SEMIGROUPS — II

2012 ◽  
Vol 22 (05) ◽  
pp. 1250042 ◽  
Author(s):  
BENJAMIN WELLS
Keyword(s):  
Equational Theory ◽  
Unary Operation ◽  
Finitely Based ◽  
New Techniques ◽  
Distinguished Element ◽  
A Chain ◽  
Rewriting Rules ◽  
Semigroup Varieties

Constructions that yield pseudorecursiveness in [I] (Int. J. Algebra Comput.6 (1996) 457–510) are extended in this article. Finitely based varieties of semigroups with increasingly strict expansions by additional unary operation symbols or individual constants are shown to have the pseudorecursive property: the equational theory is undecidable, but the subsets obtained by bounding the number of distinct variables are all recursive. The most stringent case considered here is the single unary operation or distinguished element. New techniques of stratified reducibility and interpretation via rewriting rules are employed to show the property inherits along a chain of theories. Pure semigroup varieties that are both finitely based and pseudorecursive will be discussed in a later paper.

scholarly journals Quantum dynamics of a domain wall in the presence of dephasing

2018 ◽  
Vol 52 (4) ◽  
pp. 487
Author(s):  
Claudio Castelnovo ◽  
Mark I. Dykman ◽  
Vadim N. Smelyanskiy ◽  
Roderich Moessner ◽  
Leonid P. Pryadko
Keyword(s):  
Domain Wall ◽  
Exact Solutions ◽  
Quantum Dynamics ◽  
Infinite Chain ◽  
Spectral Lines ◽  
A Chain

AbstractWe compare quantum dynamics in the presence of Markovian dephasing for a particle hopping on a chain and for an Ising domain wall whose motion leaves behind a string of flipped spins. Exact solutions show that on an infinite chain, the transport responses of the models are nearly identical. However, on finitelength chains, the broadening of discrete spectral lines is much more noticeable in the case of a domain wall.

scholarly journals Symmetric Chain Decompositions of Quotients by Wreath Products

10.37236/5073 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Dwight Duffus ◽  
Kyle Thayer
Keyword(s):  
Symmetric Group ◽  
Elementary Proof ◽  
Boolean Lattice ◽  
Wreath Products ◽  
Cyclic Groups ◽  
Chain Order ◽  
A Chain ◽  
Symmetric Chain ◽  
Symmetric Chain Order

Subgroups of the symmetric group $S_n$ act on $C^n$ (the $n$-fold product $C \times \cdots \times C$ of a chain $C$) by permuting coordinates, and induce automorphisms of the power $C^n$. For certain families of subgroups of $S_n$, the quotients defined by these groups can be shown to have symmetric chain decompositions (SCDs). These SCDs allow us to enlarge the collection of subgroups $G$ of $S_n$ for which the quotient $\mathbf{2}^n/G$ on the Boolean lattice $\mathbf{2}^n$ is a symmetric chain order (SCO). The methods are also used to provide an elementary proof that quotients of powers of SCOs by cyclic groups are SCOs.

ON MAXIMAL SUBGROUPS OF FREE OBJECTS OF CERTAIN COMPLETELY REGULAR SEMIGROUP VARIETIES

2011 ◽  
Vol 21 (03) ◽  
pp. 473-484
Author(s):  
IGOR DOLINKA
Keyword(s):  
Regular Semigroup ◽  
Semigroup Variety ◽  
Maximal Subgroups ◽  
Completely Regular Semigroup ◽  
Locally Finite ◽  
Completely Regular ◽  
Free Generators ◽  
Free Semigroups ◽  
Semigroup Varieties ◽  
Relatively Free Group

By adjusting a method of Kadourek and Polák developed for free semigroups satisfying xr ≏ x, we prove that if [Formula: see text] is a periodic group variety, then any maximal subgroup of the free object in the completely regular semigroup variety of the form [Formula: see text] is a relatively free group in [Formula: see text] over a suitable set of free generators. When [Formula: see text] is locally finite, we provide some bounds for the sizes of its finitely generated members.

Observation of Atom Rows in Thorium Pyromellitate Using a Field Emission STEM

1977 ◽  
Vol 35 ◽  
pp. 80-81
Author(s):  
H. Todokoro ◽  
S. Nomura ◽  
T. Komoda
Keyword(s):  
Field Emission ◽  
Amorphous Carbon ◽  
Carbon Film ◽  
Dark Field Image ◽  
Dark Field ◽  
Amorphous Carbon Film ◽  
Atomic Size ◽  
Wide Range ◽  
A Chain

It is interesting to observe polymers at atomic size resolution. Some works have been reported for thorium pyromellitate by using a STEM (1), or a CTEM (2,3). The results showed that this polymer forms a chain in which thorium atoms are arranged. However, the distance between adjacent thorium atoms varies over a wide range (0.4-1.3nm) according to the different authors.The present authors have also observed thorium pyromellitate specimens by means of a field emission STEM, described in reference 4. The specimen was prepared by placing a drop of thorium pyromellitate in 10-3 CH3OH solution onto an amorphous carbon film about 2nm thick. The dark field image is shown in Fig. 1A. Thorium atoms are clearly observed as regular atom rows having a spacing of 0.85nm. This lattice gradually deteriorated by successive observations. The image changed to granular structures, as shown in Fig. 1B, which was taken after four scanning frames.

Time-Resolved Cryo-Electron Microscopy of Oscillating Microtubules

1990 ◽  
Vol 48 (1) ◽  
pp. 502-503
Author(s):  
Eva-Maria Mandelkow ◽  
Ron Milligan
Keyword(s):  
Electron Microscopy ◽  
Dynamic Instability ◽  
Entire Solution ◽  
Reaction Scheme ◽  
Time Resolved ◽  
X Ray ◽  
X Ray Scattering ◽  
A Chain ◽  
Ray Scattering

Microtubules form part of the cytoskeleton of eukaryotic cells. They are hollow libers of about 25 nm diameter made up of 13 protofilaments, each of which consists of a chain of heterodimers of α-and β-tubulin. Microtubules can be assembled in vitro at 37°C in the presence of GTP which is hydrolyzed during the reaction, and they are disassembled at 4°C. In contrast to most other polymers microtubules show the behavior of “dynamic instability”, i.e. they can switch between phases of growth and phases of shrinkage, even at an overall steady state [1]. In certain conditions an entire solution can be synchronized, leading to autonomous oscillations in the degree of assembly which can be observed by X-ray scattering (Fig. 1), light scattering, or electron microscopy [2-5]. In addition such solutions are capable of generating spontaneous spatial patterns [6].In an earlier study we have analyzed the structure of microtubules and their cold-induced disassembly by cryo-EM [7]. One result was that disassembly takes place by loss of protofilament fragments (tubulin oligomers) which fray apart at the microtubule ends. We also looked at microtubule oscillations by time-resolved X-ray scattering and proposed a reaction scheme [4] which involves a cyclic interconversion of tubulin, microtubules, and oligomers (Fig. 2). The present study was undertaken to answer two questions: (a) What is the nature of the oscillations as seen by time-resolved cryo-EM? (b) Do microtubules disassemble by fraying protofilament fragments during oscillations at 37°C?

Do Event-Related Brain Potentials Reflect Mental (Cognitive) Operations?

2002 ◽  
Vol 16 (3) ◽  
pp. 129-149 ◽  
Author(s):  
Boris Kotchoubey
Keyword(s):  
Cognitive Processes ◽  
Point Of View ◽  
Internal Variables ◽  
Brain Potentials ◽  
Cognitive Operations ◽  
External Variables ◽  
Series Of Experiments ◽  
Mental Operations ◽  
A Chain ◽  
Processing Mechanisms

Abstract Most cognitive psychophysiological studies assume (1) that there is a chain of (partially overlapping) cognitive processes (processing stages, mechanisms, operators) leading from stimulus to response, and (2) that components of event-related brain potentials (ERPs) may be regarded as manifestations of these processing stages. What is usually discussed is which particular processing mechanisms are related to some particular component, but not whether such a relationship exists at all. Alternatively, from the point of view of noncognitive (e. g., “naturalistic”) theories of perception ERP components might be conceived of as correlates of extraction of the information from the experimental environment. In a series of experiments, the author attempted to separate these two accounts, i. e., internal variables like mental operations or cognitive parameters versus external variables like information content of stimulation. Whenever this separation could be performed, the latter factor proved to significantly affect ERP amplitudes, whereas the former did not. These data indicate that ERPs cannot be unequivocally linked to processing mechanisms postulated by cognitive models of perception. Therefore, they cannot be regarded as support for these models.

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