Donovan’s conjecture, blocks with abelian defect groups and discrete valuation rings

We give a reduction to quasisimple groups for Donovan’s conjecture for blocks with abelian defect groups defined with respect to a suitable discrete valuation ring O. Consequences are that Donovan’s conjecture holds for O-blocks with abelian defect groups for the prime two, and that, using recent work of Farrell and Kessar, for arbitrary primes Donovan’s conjecture for O-blocks with abelian defect groups reduces to bounding the Cartan invariants of blocks of quasisimple groups in terms of the defect. A result of independent interest is that in general (i.e. for arbitrary defect groups) Donovan’s conjecture for O-blocks is a consequence of conjectures predicting bounds on the O-Frobenius number and on the Cartan invariants, as was proved by Kessar for blocks defined over an algebraically closed field

Brain Fitness Program for Aging Individuals: Prevention Focused Program for Alzheimer’s Disease and Related Dementias

The culminating project for my capstone experience was the introduction of a Brain Fitness course. This literature review assessed the public’s knowledge regarding the etiology of Alzheimer’s disease and related dementias (ADRD) as well as the need for a program focused on prevention and intervention for cognitive related diseases, such as ADRD. Studies have shown an association between modifiable lifestyle factors and the development of ADRD, however, there is a lack of knowledge regarding available interventions and preventions. The number of individuals in the community with a diagnosis of ADRD has risen exponentially and so has the need for family caregivers and health care costs. The main objective of this literature review was to recognize the benefit of introducing a Brain Fitness course as a resource for the community

Impact of edge shape on the functionalities of graphene-based single-molecule electronics devices

We present an ab-initio analysis of the impact of edge shape and graphene-molecule anchor coupling on the electronic and transport functionalities of graphene-based molecular electronics devices. We analyze how Fano-like resonances, spin filtering and negative differential resistance effects may or may not arise by modifying suitably the edge shapes and the terminating groups of simple organic molecules. We show that the spin filtering effect is a consequence of the magnetic behavior of zigzag-terminated edges, which is enhanced by furnishing these with a wedge shape. The negative differential resistance effect is originated by the presence of two degenerate electronic states localized at each of the atoms coupling the molecule to graphene which are strongly affected by a bias voltage. The effect could thus be tailored by a suitable choice of the molecule and contact atoms if edge shape could be controlled with atomic precision.Comment: 11 pages, 20 figure

Arbitrarily large Morita Frobenius numbers

We construct blocks of finite groups with arbitrarily large Morita Frobenius numbers, an invariant which determines the size of the minimal field of definition of the associated basic algebra. This answers a question of Benson and Kessar. This also improves upon a result of the second author where arbitrarily large $\mathcal{O}$-Morita Frobenius numbers are constructed

Host Defense and the Airway Epithelium: Frontline Responses That Protect against Bacterial Invasion and Pneumonia

Airway epithelial cells are the first line of defense against invading microbes, and they protect themselves through the production of carbohydrate and protein matrices concentrated with antimicrobial products. In addition, they act as sentinels, expressing pattern recognition receptors that become activated upon sensing bacterial products and stimulate downstream recruitment and activation of immune cells which clear invading microbes. Bacterial pathogens that successfully colonize the lungs must resist these mechanisms or inhibit their production, penetrate the epithelial barrier, and be prepared to resist a barrage of inflammation. Despite the enormous task at hand, relatively few virulence factors coordinate the battle with the epithelium while simultaneously providing resistance to inflammatory cells and causing injury to the lung. Here we review mechanisms whereby airway epithelial cells recognize pathogens and activate a program of antibacterial pathways to prevent colonization of the lung, along with a few examples of how bacteria disrupt these responses to cause pneumonia

Molecular and cellular dynamics of the 26S proteasome

In eukaryotic cells, the ubiquitin-proteasome system serves to remove proteins that are either dysfunctional or no longer needed. The 26S proteasome is a 2.5 MDa multisubunit complex comprising the 20S core particle, where degradation is executed, and one or two regulatory particles which prepare substrates for degradation. Whereas the 20S core particles of several species had been studied extensively by X-ray crystallography, the 26S holocomplex structure had remained elusive for a long time. Recent advances in single-particle cryo-electron microscopy have changed the situation and provided atomic resolution models of this intriguing molecular machine and its dynamics. Besides, cryo-electron tomography enables structural studies in situ, providing molecular resolution images of macromolecules inside pristinely preserved cellular environments. This has greatly contributed to our understanding of proteasome dynamics in the context of cells

Correlation Studies of Zea mays under Field Conditions

This paper is a report of statistical studies involving correlations between various growth responses of corn plants and factor data obtained in the immediately vicinity of the growing plants. Weekly growth measurements of the corn plants were obtained and these were correlated with the factor data obtained from recording instruments. 22. The relation of moisture-Thermal conductivity of oats and other grain has received little if any attention. Employing the Stiles apparatus, an attempt has been made to ascertain the specific thermal conductivity of oats, having moisture contents up to maximum absorption. The thermal conductivity of a substance is the amount of heat which will pass per unit of time through unit area of a layer of the substance of unit thickness, the opposite faces of the layer having a temperature difference of one degree. 23. Some meotic-Refinements of the paraffin technique make it possible to demonstrate critical details of meiosis. The process yields figures that are comparable to the results of the smear process. Progressive synapsis during amphitene, and the tetrad structure of the chromosome at strepsiphase can be readily demonstrated

On tate duality and a projective scalar property for symmetric algebras

© 2018 Mathematical Sciences Publishers. We identify a class of symmetric algebras over a complete discrete valuation ring O of characteristic zero to which the characterisation of Knörr lattices in terms of stable endomorphism rings in the case of finite group algebras can be extended. This class includes finite group algebras, their blocks and source algebras and Hopf orders. We also show that certain arithmetic properties of finite group representations extend to this class of algebras. Our results are based on an explicit description of Tate duality for lattices over symmetric O-algebras whose extension to the quotient field of O is separable

On the Cost-of-Capital Rate under Incomplete Market Valuation

In this paper we discuss the concept of the cost-of-capital (CoC) rate for an insurance company as an equilibrium in the economic triangle of policyholders, shareholders, and the regulator. This provides a possible rationalization and an economic foundation for a quantity that is widely used in practice but whose value is typically neither technically nor economically well justified. We show how it can be well founded in such a triangular equilibrium. Under a simple one-period model and a valuation procedure of a two-price economy for illiquid assets we provide a corresponding economic-theoretical quantification for the CoC rate. The resulting rates are illustrated by a number of concrete numerical examples.ISSN:0022-4367ISSN:1539-697