The infinitesimal characters of discrete series for real spherical spaces

Let $Z=G/H$ be the homogeneous space of a real reductive group and a unimodular real spherical subgroup, and consider the regular representation of $G$ on $L^2(Z)$. It is shown that all representations of the discrete series, that is, the irreducible subrepresentations of $L^2(Z)$, have infinitesimal characters which are real and belong to a lattice. Moreover, let $K$ be a maximal compact subgroup of $G$. Then each irreducible representation of $K$ occurs in a finite set of such discrete series representations only. Similar results are obtained for the twisted discrete series, that is, the discrete components of the space of square integrable sections of a line bundle, given by a unitary character on an abelian extension of $H$.Comment: To appear in GAF

Analyzing the Catalytic Role of Asp97 in the Methionine Aminopeptidase from \u3cem\u3eEscherichia coli\u3c/em\u3e

An active site aspartate residue, Asp97, in the methionine aminopeptidase (MetAPs) from Escherichia coli (EcMetAP-I) was mutated to alanine, glutamate, and asparagine. Asp97 is the lone carboxylate residue bound to the crystallographically determined second metal-binding site in EcMetAP-I. These mutant EcMetAP-I enzymes have been kinetically and spectroscopically characterized. Inductively coupled plasma–atomic emission spectroscopy analysis revealed that 1.0 ± 0.1 equivalents of cobalt were associated with each of the Asp97-mutated EcMetAP-Is. The effect on activity after altering Asp97 to alanine, glutamate or asparagine is, in general, due to a ∼ 9000-fold decrease in kca towards Met-Gly-Met-Met as compared to the wild-type enzyme. The Co(II) d–d spectra for wild-type, D97E and D97A EcMetAP-I exhibited very little difference in form, in each case, between the monocobalt(II) and dicobalt(II) EcMetAP-I, and only a doubling of intensity was observed upon addition of a second Co(II) ion. In contrast, the electronic absorption spectra of [Co_(D97N EcMetAP-I)] and [CoCo(D97N EcMetAP-I)] were distinct, as were the EPR spectra. On the basis of the observed molar absorptivities, the Co(II) ions binding to the D97E, D97A and D97N EcMetAP-I active sites are pentacoordinate. Combination of these data suggests that mutating the only nonbridging ligand in the second divalent metal-binding site in MetAPs to an alanine, which effectively removes the ability of the enzyme to form a dinuclear site, provides a MetAP enzyme that retains catalytic activity, albeit at extremely low levels. Although mononuclear MetAPs are active, the physiologically relevant form of the enzyme is probably dinuclear, given that the majority of the data reported to date are consistent with weak cooperative binding

Cost comparison of asthma treatments in 12-week study : caution about matching and short observational follow-up

This review was funded by Observational and Pragmatic Research Institute Pte Ltd.Peer reviewedPublisher PD

A Factorial Analysis Of The Barriers To Market Orientation Adoption Among Small And Medium Enterprises (SMEs) In A Developing Country

The purpose of the study was to examine the barriers of market orientation by SMEs in South Africa. Data were collected using the personal face-to-face interviews with the use of a structured questionnaire. A total of 350 SMES were selected randomly and visited within the various municipal areas in South Africa. Exploratory factor analysis was used to identify the dimensions using the principal component analysis. A four-factor structure emerged accounting for 62% of total variance. The reliability analysis, reflected coefficient values ranging from 0.743 to 0.893, indicating satisfactory internal consistency amongst variables within each dimension. By analysing the barriers, the adoption of market orientation among SMEs, managers, and marketers are presented with recommended strategies and implications on how to embrace market orientation for effective business performance. Marketing capacities of SMEs may be strengthened through the implementing of market orientation. SMEs are vital for socio-economic progress for developing economies. Effective implementation of market orientation can assist SMEs’ growth and development

Discrete Breathers in One-Dimensional Diatomic Granular Crystals

We report the experimental observation of discrete breathers in a one-dimensional diatomic granular crystal composed of compressed elastic beads that interact via Hertzian contact. We first characterize their effective linear spectrum both theoretically and experimentally. We then illustrate theoretically and numerically the modulational instability of the lower edge of the optical band. This leads to the dynamical formation of long-lived breather structures, whose families of solutions we compute throughout the linear spectral gap. Finally, we observe experimentally such localized breathing modes with quantitative characteristics that agree with our numerical results.Comment: 5 pages, 4 figure

Innovative Design and Evaluation of a Transmission Lifter

This study focuses on the design, fabrication, and evaluation of the Transmission Lifter, a specialized device tailored for the convenient, stable, and durable servicing of vehicle transmission assemblies. The research aims to address the prevalent challenges faced by automotive technicians and mechanics during transmission servicing, offering an innovative solution that meets the high-performance requirements of the automotive industry.The study meticulously follows industry standards and leverages expert feedback to ensure the Transmission Lifter's quality, performance, and safety. It goes through comprehensive testing, meticulous analysis, and critical evaluation to gauge the device's effectiveness. The results of the study lead to several key conclusions: The Transmission Lifter successfully meets industry standards and the expectations of automotive experts, ensuring that it aligns with the highest quality requirements. The device exhibits high performance efficiency as affirmed by expert evaluations, highlighting its superior capabilities. It boasts an impressive load capacity, accommodating medium to heavy-duty transmissions with ease. The device is adaptable to the diverse configurations of automobile transmissions. It maintains stability even during extended use and can handle a substantial load. The Transmission Lifter performs exceptionally well, earning an overall "Excellent" rating based on expert evaluations. This study's findings inform a set of valuable recommendations, including patent protection, material enhancements for portability, improved finishing and adherence to industry standards, instructional manuals for users, and a call for continued research in the field. The Transmission Lifter presents a significant advancement in the field of automotive technology, contributing to the safety, efficiency, and quality of transmission servicing. Its innovation serves as a testament to the commitment of the researcher and his desire to support fellow technicians and automotive enthusiasts. By addressing the critical needs of the automotive industry, the Transmission Lifter embodies innovation, safety, and a commitment to excellence, setting a benchmark for future developments in the field.As

Property Tax Lids and the Effect on Kansas

Cross sectional time series data in a partial adjustment model examine local government behavior under an aggregate property tax levy limit and under Truth in Taxation in Kansas. Results indicate that the aggregate levy limit would have continued to restrict property tax revenue and spending had it not been replaced.Public Economics,