An investigation of 2-critical sets in latin squares

In this paper we focus on the existence of 2-critical sets in the latin square corresponding to the elementary abelian 2-group of order 2(n). It has been shown by Stinson and van Rees that this latin square contains a 2-critical set of volume 4(n) - 3(n). We provide constructions for 2-critical sets containing 4(n) - 3(n) + 1 - (2(k-1) + 2(m-1) + 2(n-(k+m+1))) entries, where 1 less than or equal to k less than or equal to n and 1 less than or equal to m less than or equal to n - k. That is, we construct 2-critical sets for certain values less than 4(n) - 3(n) + 1 - 3 (.) 2([n /3]-1). The results raise the interesting question of whether, for the given latin square, it is possible to construct 2-critical sets of volume m, where 4(n) - 3(n) + 1 - 3 (.) 2([n/3]-1) < m < 4(n) - 3(n).

Elevated progesterone in yolk as a moderator of prenatal and postnatal auditory learning in bobwhite quail

Recent studies have established that yolk hormones of maternal origin have significant effects on the physiology and behavior of offspring in birds. Herrington (2012) demonstrated that an elevation of progesterone in yolk elevates emotional reactivity in bobwhite quail neonates. Chicks that hatched from progesterone treated eggs displayed increased latency in tonic immobility and did not emerge as quickly from a covered location into an open field compared to control groups. For the present study, three experimental groups were formed: chicks hatched from eggs with artificially elevated progesterone (P), chicks hatched from an oil-vehicle control group (V), and chicks hatched from a non-manipulated control group (C). Experiment 1 examined levels of progesterone with High Performance Liquid Chromatography/tandem Mass Spectroscopy (HPLC/MS) from prenatal day 1 to prenatal day 17 in bobwhite quail egg yolk. In Experiment 2, bobwhite quail embryos were passively exposed to an individual maternal assembly call for 24 hours prior to hatching. Chicks were then tested individually for their preference between the familiarized call and a novel call at 24 and 48 hours following hatching. For Experiment 3, newly hatched chicks were exposed to an individual maternal assembly call for 24-hrs. Chicks were then tested for their preference for the familiarized call at 24 and 48-hrs after hatch. Results of Experiment 1 showed that yolk progesterone levels were significantly elevated in treated eggs and were present in the egg yolk longer into prenatal development than the two control groups. Results from Experiment 2 indicated that chicks from the P group failed to demonstrate a preference for the familiar bobwhite maternal assembly call at 24 or 48-hrs after hatch following 24-hrs of prenatal exposure. In contrast, chicks from the C and V groups demonstrated a significant preference for the familiarized call. In Experiment 3, chicks from the P group showed an enhanced preference for the familiarized bobwhite maternal call compared to chicks from the C and V groups at 24 and 48-hrs after hatch. The results of these experiments suggest that elevated maternal yolk hormone levels in pre-incubated bobwhite quail eggs can influence auditory perceptual learning in embryos and neonates.^

The Evolution of Massive Young Stellar Objects in the Large Magellanic Cloud

This thesis presents an analysis of the largest catalog to date of infrared spectra of massive young stellar objects in the Large Magellanic Cloud. Evidenced by their very different spectral features, the luminous objects span a range of evolutionary states from those most embedded in their natal molecular material to those that have dissipated and ionized their surroundings to form compact HII regions and photodissociation regions. We quantify the contributions of the various spectral features using the statistical method of principal component analysis. Using this analysis, we classify the YSO spectra into several distinct groups based upon their dominant spectral features: silicate absorption (S Group), silicate absorption and fine-structure line emission (SE), polycyclic aromatic hydrocarbon (PAH) emission (P Group), PAH and fine-structure line emission (PE), and only fine-structure line emission (E). Based upon the relative numbers of sources in each category, we are able to estimate the amount of time massive YSOs spend in each evolutionary stage. We find that approximately 50% of the sources have ionic fine-structure lines, indicating that a compact HII region forms about half-way through the YSO lifetime probed in our study. Of the 277 YSOs we collected spectra for, 41 have ice absorption features, indicating they are surrounded by cold ice-bearing dust particles. We have decomposed the shape of the ice features to probe the composition and thermal history of the ice. We find that most the CO2 ice is embedded a polar ice matrix that has been thermally processed by the embedded YSO. The amount of thermal processing may be correlated with the luminosity of the YSO. Using the Australia Telescope Compact Array, we imaged the dense gas around a subsample of our sources in the HII complexes N44, N105, N113, and N159 using HCO+ and HCN as dense gas tracers. We find that the molecular material in star forming environments is highly clumpy, with clumps that range from subparsec to ~2 parsecs in size and with masses between 10^2 to 10^4 solar masses. We find that there are varying levels of star formation in the clumps, with the lower-mass clumps tending to be without massive YSOs. These YSO-less clumps could either represent an earlier stage of clump to the more massive YSO-bearing ones or clumps that will never form a massive star. Clumps with massive YSOs at their centers have masses larger than those with massive YSOs at their edges, and we suggest that the difference is evolutionary: edge YSO clumps are more advanced than those with YSOs at their centers. Clumps with YSOs at their edges may have had a significant fraction of their mass disrupted or destroyed by the forming massive star. We find that the strength of the silicate absorption seen in YSO IR spectra feature is well-correlated with the on-source HCO+ and HCN flux densities, such that the strength of the feature is indicative of the embeddedness of the YSO. We estimate that ~40% of the entire spectral sample has strong silicate absorption features, implying that the YSOs are embedded in circumstellar material for about 40% of the time probed in our study.

On the Compressibility of non-Abelian-Group Sources in a Distributed Source Coding Setting

We consider the problem of compression of a non-Abelian source.This is motivated by the problem of distributed function computation,where it is known that if one is only interested in computing a function of several sources, then one can often improve upon the compression rate required by the Slepian-Wolf bound. Let G be a non-Abelian group having center Z(G). We show here that it is impossible to compress a source with symbols drawn from G when Z(G) is trivial if one employs a homomorphic encoder and a typical-set decoder.We provide achievable upper bounds on the minimum rate required to compress a non-Abelian group with non-trivial center. Also, in a two source setting, we provide achievable upper bounds for compression of any non-Abelian group, using a non-homomorphic encoder.

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point.

A group topology on the free abelian group of cardinality c that makes its square countably compact

Under p = c, we prove that it is possible to endow the free abelian group of cardinality c with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.

Some classes of semisimple group (and loop) algebras over finite fields

We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components We apply our work to obtain similar information about the loop algebras of mdecomposable RA loops and to produce negative answers to the isomorphism problem over various fields (C) 2010 Elsevier Inc All rights reserved

Involutions and free pairs of bicyclic units in integral group rings

If * : G -> G is an involution on the finite group G, then * extends to an involution on the integral group ring Z[G] . In this paper, we consider whether bicyclic units u is an element of Z[G] exist with the property that the group < u, u*> generated by u and u* is free on the two generators. If this occurs, we say that (u, u*)is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, Z[G] contains a free bicyclic pair.

Finite group actions on products of spheres

In this work we make some contributions to the theory of actions of finite groups on products of spheres. Suppose that the group Z(q)(tau) acts freely on the product of k copies of spheres. Question: Is r less than or equal to k? We solve this question for several values of r and k.

Generalized soluble groups of finite co-central rank

Eine Gruppe G hat endlichen Prüferrang (bzw. Ko-zentralrang) kleiner gleich r, wenn für jede endlich erzeugte Gruppe H gilt: H (bzw. H modulo seinem Zentrum) ist r-erzeugbar. In der vorliegenden Arbeit werden, soweit möglich, die bekannten Sätze über Gruppen von endlichem Prüferrang (kurz X-Gruppen), auf die wesentlich größere Klasse der Gruppen mit endlichem Ko-zentralrang (kurz R-Gruppen) verallgemeinert.Für lokal nilpotente R-Gruppen, welche torsionsfrei oder p-Gruppen sind, wird gezeigt, dass die Zentrumsfaktorgruppe eine X-Gruppe sein muss. Es folgt, dass Hyperzentralität und lokale Nilpotenz für R-Gruppen identische Bediungungen sind. Analog hierzu sind R-Gruppen genau dann lokal auflösbar, wenn sie hyperabelsch sind. Zentral für die Strukturtheorie hyperabelscher R-Gruppen ist die Tatsache, dass solche Gruppen eine aufsteigende Normalreihe abelscher X-Gruppen besitzen. Es wird eine Sylowtheorie für periodische hyperabelsche R-Gruppen entwickelt. Für torsionsfreie hyperabelsche R-Gruppen wird deren Auflösbarkeit bewiesen. Des weiteren sind lokal endliche R-Gruppen fast hyperabelsch. Für R-Gruppen fallen sehr große Gruppenklassen mit den fast hyperabelschen Gruppen zusammen. Hierzu wird der Begriff der Sektionsüberdeckung eingeführt und gezeigt, dass R-Gruppen mit fast hyperabelscher Sektionsüberdeckung fast hyperabelsch sind.

On some Finite-Dimensional Representations of Artin Braid Group

Валентин В. Илиев - Авторът изучава някои хомоморфни образи G на групата на Артин на плитките върху n нишки в крайни симетрични групи. Получените пермутационни групи G са разширения на симетричната група върху n букви чрез подходяща абелева група. Разширенията G зависят от един целочислен параметър q ≥ 1 и се разцепват тогава и само тогава, когато 4 не дели q. В случая на нечетно q са намерени всички крайномерни неприводими представяния на G, а те от своя страна генерират безкрайна редица от неприводими представяния на групата на плитките.