scholarly journals The Coarse Structure of the Representation Algebra of a Finite Monoid

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mary Schaps

Let M be a monoid, and let L be a commutative idempotent submonoid. We show that we can find a complete set of orthogonal idempotents L^0 of the monoid algebra A of M such that there is a basis of A adapted to this set of idempotents which is in one-to-one correspondence with elements of the monoid. The basis graph describing the Peirce decomposition with respect to L^0 gives a coarse structure of the algebra, of which any complete set of primitive idempotents gives a refinement, and we give some criterion for this coarse structure to actually be a fine structure, which means that the nonzero elements of the monoid are in one-to-one correspondence with the vertices and arrows of the basis graph with respect to a set of primitive idempotents, with this basis graph being a canonical object.

1974 ◽  
Vol 56 ◽  
pp. 45-47
Author(s):  
R. B. Dunn ◽  
J. B. Zirker ◽  
J. M. Beckers

A number of observers have noted the presence of bright structures near the cores of the chromospheric rosettes when observed in the far wings of the Hα line (eg Hα ±7/8 Å). Dunn and Zirker observed these bright structures with the highest possible resolution using the Sacramento Peak vacuum solar telescope. They find that these bright regions exhibit a very intricate fine structure which can be followed out much further into the Hα line wing (eg Hα + 2 Å) and even into the continuum. They called this fine structure ‘solar filigree’, the name referring mainly to the collective appearance of the fine structure elements. The elements themselves appear as dot-like structures and frequently also as small wiggly structures called ‘crinkles’. The properties of the filigree structure are summarized as follows: (i)Size: Measured diameter of the crinkles and dots equals 0.25, 0.40 and 0.60″ at Hα + 2 Å, Hα ± 7/8 Å and Hα ±5/8 Å respectively. The telescope resolution equals 0.22″ so that at Hα + 2 Å the structure is extremely small. The drawings in Figure 1 show typical sizes of the crinkles and network patterns in the filigree.(ii)Contrast: Filigree is enhanced in the blue wing of the Hα line. Measured contrast, uncorrected for seeing, equals 5–10%.(iii)Relation to the Granulation: The filigree structures tend to lie between the granules. This is, however, not a strict rule. It seems that in the course of their lifetime the granules move the filigree structures around with velocities of about 1.5 km s-1. Some of the crinkles also seem to wash out temporarily until compressed again by a new granule. The detailed structure of the filigree, therefore, changes significantly over times comparable to the granule lifetime. The overall structure is, however, preserved over much longer periods of time. The granulation pattern when observed in the continuum well outside the Hα line appears very peculiar in that it has substantially decreased in contrast. It appears ‘soft’ similar to granulation washed-out by seeing. This abnormal granulation can be traced over long times (> 30 min) and coincides in location to the filigree location. It is, therefore, definitely real.(iv)Relation to the spicules: The filigree structure falls near the center of the Hα chromospheric rosettes. These rosettes consist of dark elongated mottles which should probably be identified with spicules. There is, therefore, at least a coarse relation between the occurrence of spicules and the filigree. There is no clear evidence that variations in the filigree pattern are related to the generation of spicules. Some spicules seem to originate from the spaces between the crinkles. Too few, however, to conclude a definite relation.(v)Relation to the magnetic field: Beckers studied the filigree with the Universal Birefringent Filter in the magnesium b1 and b2 lines. It is very well visible in the far wing of the lines (eg. b1 ±0.8 Å). When traced into the line core the structures increase somewhat in size, as they do in Hα, and form structures similar to, and perhaps identical with, the so-called photospheric network. In the magnetically sensitive b2 line one sees a one-to-one correspondence between these network structures and the magnetic field so that, at least in the layers seen near the core of the b2 line, there is a one-to-one correspondence between the filigree structures and the enhancements in the magnetic field. Simon and Zirker (Solar Physics, submitted for publication) using a spectrograph also found that the filigree occurs in regions of enhanced magnetic field. However, in contrast to the filter observations, they found the magnetic field regions to be much more diffuse (2–3″) so that there is not a one-to-one spatial correspondence between filigree and magnetic field structure.


2012 ◽  
Vol 05 (01) ◽  
pp. 1250002
Author(s):  
Pooja Grover ◽  
Ashwani K. Bhandari

In this paper minimal codes for several classes of non-cyclic abelian groups have been constructed by explicitly determining a complete set of primitive idempotents in the corresponding group algebras. Some classes of non-p-groups have also been considered. The minimum distances of such abelian codes have been discussed and compared to the minimum distances of cyclic codes of same lengths and dimensions over the same field.


Author(s):  
DIETER BRAUN ◽  
BRUNO C. TITECA ◽  
ARNOUT CEULEMANS

Sharp line emission spectra of the silicon phthalocyanine complex ((n- C 6 H 13)3 SiO )2 SiPc at low temperatures are resolved in multiple sites, and the vibronic fine structure of single-site emissions is identified. DFT methods are used to calculate the complete set of normal modes of the Cl 2 SiPc analogue. Geometry optimization of the excited state further yields the Franck–Condon and Jahn–Teller distortions in the emitting state. These results are combined to obtain theoretical Huang–Rhys factors for the active modes, which compare favourably with the experimental spectrum. The dominant satellites are a 675 cm−1 mode, which is identified as a totally symmetric bending of the four pyrrole rings, and a 1552 cm−1 mode, which is assigned to an antisymmetric stretching of the aza-nitrogens with tetragonal b 1 g symmetry.


2001 ◽  
Vol 11 (04) ◽  
pp. 405-445 ◽  
Author(s):  
S. MARGOLIS ◽  
M. SAPIR ◽  
P. WEIL

We relate the problem of computing the closure of a finitely generated subgroup of the free group in the pro-V topology, where V is a pseudovariety of finite groups, with an extension problem for inverse automata which can be stated as follows: given partial one-to-one maps on a finite set, can they be extended into permutations generating a group in V? The two problems are equivalent when V is extension-closed. Turning to practical computations, we modify Ribes and Zalesskiĭ's algorithm to compute the pro-p closure of a finitely generated subgroup of the free group in polynomial time, and to effectively compute its pro-nilpotent closure. Finally, we apply our results to a problem in finite monoid theory, the membership problem in pseudovarieties of inverse monoids which are Mal'cev products of semilattices and a pseudovariety of groups. Résumé: Nous établissons un lien entre le problème du calcul de l'adhéerence d'un sous-groupe finiment engendré du groupe libre dans la topologie pro-V, oú V est une pseudovariété de groupes finis, et un probléme d'extension pour les automates inversifs qui peut être énoncé de la faç con suivante: étant données des transformations partielles injectives d'un ensemble fini, peuvent-elles être étendues en des permutations qui engendrent un groupe dans V? Les deux problèmes sont équivalents si V est fermée par extensions. Nous intéressant ensuite aux calculs pratiques, nous modifions l'algorithme de Ribes et Zalesskiĭ pour calculer l'adhérence pro-p d'un sous-groupe finiment engendré du groupe libre en temps polynomial et pour calculer effectivement sa clôture pro-nilpotente. Enfin nous appliquons nos résultats à un problème de théorie des monoïdes finis, celui de de l'appartenance dans les pseudovariétés de monoïdes inversifs qui sont des produits de Mal'cev de demi-treillis et d'une pseudovariété de groupes.


1978 ◽  
Vol 26 (4) ◽  
pp. 410-418 ◽  
Author(s):  
J. C. Renaud

AbstractLet p,m be the modular representation algebra of the cyclic group of order pm over the prime field Zp. The characters of p, m are derived. For p = 2, this provides an alternative proof of a result due to Carlson (1975), tha 2,m is a local ring. It is shown that for p>2, p, m is a direct sum of 2m local rings. Their dimensions and primitive idempotents are derived.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 C 20, 12 C 05, 12 C 30, 33 A 65.


Author(s):  
W. H. Zucker ◽  
R. G. Mason

Platelet adhesion initiates platelet aggregation and is an important component of the hemostatic process. Since the development of a new form of collagen as a topical hemostatic agent is of both basic and clinical interest, an ultrastructural and hematologic study of the interaction of platelets with the microcrystalline collagen preparation was undertaken.In this study, whole blood anticoagulated with EDTA was used in order to inhibit aggregation and permit study of platelet adhesion to collagen as an isolated event. The microcrystalline collagen was prepared from bovine dermal corium; milling was with sharp blades. The preparation consists of partial hydrochloric acid amine collagen salts and retains much of the fibrillar morphology of native collagen.


Author(s):  
E. Horvath ◽  
K. Kovacs ◽  
G. Penz ◽  
C. Ezrin

Follicular structures, in the rat pituitary, composed of cells joined by junctional complexes and possessing few organelles and few, if any, secretory granules, were first described by Farquhar in 1957. Cells of the same description have since been observed in several species including man. The importance of these cells, however, remains obscure. While studying human pituitary glands, we have observed wide variations in the fine structure of follicular cells which may lead to a better understanding of their morphogenesis and significance.


Author(s):  
E. N. Albert

Silver tetraphenylporphine sulfonate (Ag-TPPS) was synthesized in this laboratory and used as an electron dense stain for elastic tissue (Fig 1). The procedures for the synthesis of tetraphenylporphine sulfonate and the staining method for mature elastic tissue have been described previously.The fine structure of developing elastic tissue was observed in fetal and new born rat aorta using tetraphenylporphine sulfonate, phosphotungstic acid, uranyl acetate and lead citrate. The newly forming elastica consisted of two morphologically distinct components. These were a central amorphous and a peripheral fibrous. The ratio of the central amorphous and the peripheral fibrillar portion changed in favor of the former with increasing age.It was also observed that the staining properties of the two components were entirely different. The peripheral fibrous component stained with uranyl acetate and/or lead citrate while the central amorphous portion demonstrated no affinity for these stains. On the other hand, the central amorphous portion of developing elastic fibers stained vigorously with silver tetraphenylporphine sulfonate, while the fibrillar part did not (compare figs 2, 3, 4). Based upon the above observations it is proposed that developing elastica consists of two components that are morphologically and chemically different.


Author(s):  
J. E. Lai-Fook

Dermal glands are epidermal derivatives which are reported to secrete either the cement layer, which is the outermost layer of the epicuticle or some component of the moulting fluid which digests the endocuticle. The secretions do not show well-defined staining reactions and therefore they have not been positively identified. This has contributed to another difficulty, namely, that of determining the time of secretory activity. This description of the fine structure of the developing glands in Rhodnius was undertaken to determine the time of activity, with a view to investigating their function.


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