Multiplicative Number - Theoretic Functions

Quite frequently in the study of number theory we become acquainted with special functions which are defined on the set of positive integers. These functions are known as Number-theoretic functions or Arithmetical functions. This report will give some of the general ideas of the multipli­cative number-theoretic functions. The first part of this report will be devoted to the general develop­ment of such functions by means of definitions and theorems. The second part will consist of generalizations of a particular function, the -r-function. Throughout this paper, lower case Greek letters will represent real numbers and lower case English letters will represent integers. Also the basic ideas of summation and product will be assumed as already familiar to the reader

Analysis of Factors Influencing Termination of Leadership by Selected 4-H Leaders in the Northeast Wyoming 4-h District Between the Years 1974-1976

Agricultural Educatio

Optical Manufacturing and Testing Requirements Identified by the NASA Science Instruments, Observatories and Sensor Systems Technology Assessment

In August 2010, the NASA Office of Chief Technologist (OCT) commissioned an assessment of 15 different technology areas of importance to the future of NASA. Technology assessment #8 (TA8) was Science Instruments, Observatories and Sensor Systems (SIOSS). SIOSS assess the needs for optical technology ranging from detectors to lasers, x-ray mirrors to microwave antenna, in-situ spectrographs for on-surface planetary sample characterization to large space telescopes. The needs assessment looked across the entirety of NASA and not just the Science Mission Directorate. This paper reviews the optical manufacturing and testing technologies identified by SIOSS which require development in order to enable future NASA high priority missions

Hydrogen bonded complexes between nitrogen dioxide, nitric acid, nitrous acid and water with SiH3OH and Si(OH)4

The inter-conversion of nitrogen oxides and oxy acids on silica surfaces is of major atmospheric importance. As a preliminary step towards rationalising experimental observations, and understanding the mechanisms behind such reactions we have looked at the binding energies of NO2, N2O4, HNO3, HONO and H2O with simple proxies of a silica surface, namely SiH3OH and Si(OH)4 units. The geometries of these molecular clusters were optimised at both HF/6-311+G(d) and B3LYP/6-311+G(d) level of theory. The SCF energies of the species were determined at the HF/6-311++G(3df,2pd) and B3LYP/6-311++G(3df,2pd) level. The values indicate that nitric acid is by far the most strongly bound species, in agreement with experimental observations. It was also found that the dimer N2O4 is significantly more strongly bound to the Si(OH)4 and SiH3OH units than NO2 itself. The vibrational frequencies calculated for the hydrogen-bonded complexes are compared to the experimentally observed frequencies of the adsorbed species where possible

On the feasibility of N2 fixation via a single-site FeI/FeIV cycle: Spectroscopic studies of FeI(N2)FeI, FeIV=N, and related species

The electronic properties of an unusually redox-rich iron system, [PhBPR 3]FeNx (where [PhBPR 3] is [PhB(CH2PR2)3]−), are explored by Mössbauer, EPR, magnetization, and density-functional methods to gain a detailed picture regarding their oxidation states and electronic structures. The complexes of primary interest in this article are the two terminal iron(IV) nitride species, [PhBPiPr 3]FeN (3a) and [PhBPCH2Cy 3]FeN (3b), and the formally diiron(I) bridged-Fe(μ-N2)Fe species, {[PhBPiPr 3]Fe}2(μ-N2) (4). Complex 4 is chemically related to 3a via a spontaneous nitride coupling reaction. The diamagnetic iron(IV) nitrides 3a and 3b exhibit unique electronic environments that are reflected in their unusual Mössbauer parameters, including quadrupole-splitting values of 6.01(1) mm/s and isomer shift values of −0.34(1) mm/s. The data for 4 suggest that this complex can be described by a weak ferromagnetic interaction (J/D < 1) between two iron(I) centers. For comparison, four other relevant complexes also are characterized: a diamagnetic iron(IV) trihydride [PhBPiPr 3]Fe(H)3(PMe3) (5), an S = 3/2 iron(I) phosphine adduct [PhBPiPr 3]FePMe3 (6), and the S = 2 iron(II) precursors to 3a, [PhBPiPr 3]FeCl and [PhBPiPr 3]Fe-2,3:5,6-dibenzo-7-aza bicyclo[2.2.1]hepta-2,5-diene (dbabh). The electronic properties of these respective complexes also have been explored by density-functional methods to help corroborate our spectral assignments and to probe their electronic structures further

Cavitation in soft matter

Cavitation is the sudden, unstable expansion of a void or bubble within a liquid or solid subjected to a negative hydrostatic stress. Cavitation rheology is a field emerging from the development of a suite of materials characterization, damage quantification, and therapeutic techniques that exploit the physical principles of cavitation. Cavitation rheology is inherently complex and broad in scope with wide-ranging applications in the biology, chemistry, materials, and mechanics communities. This perspective aims to drive collaboration among these communities and guide discussion by defining a common core of high-priority goals while highlighting emerging opportunities in the field of cavitation rheology. A brief overview of the mechanics and dynamics of cavitation in soft matter is presented. This overview is followed by a discussion of the overarching goals of cavitation rheology and an overview of common experimental techniques. The larger unmet needs and challenges of cavitation in soft matter are then presented alongside specific opportunities for researchers from different disciplines to contribute to the field

Alkali environments in tellurite glasses

Neutron diffraction measurements are reported for five binary alkali tellurite glasses, xM2O · (100 − x)TeO2 (containing 10 and 20 mol% K2O, 10 and 19 mol% Na2O, and 20 mol% 7Li2O), together with 23Na MAS NMR measurements for the sodium containing glasses. Differences between neutron correlation functions are used to extract information about the local environments of lithium and sodium. The Na–O bond length is 2.37(1) Å and the average Na–O coordination number, nNaO, decreases from 5.2(2) for x = 10 mol% Na2O to 4.6(1) for x = 19 mol% Na2O. The average Li–O coordination number, nLiO, is 3.9(1) for the glass with x = 20 mol% Li2O and the Li–O bond length is 2.078(2) Å. As x increases from 10 to 19 mol% Na2O, the 23Na MAS NMR peak moves downfield, confirming an earlier report of a correlation of peak position with sodium coordination number. The close agreement of the maximum in the Te–O bond distribution for sodium and potassium tellurite glasses of the same composition, coupled with the extraction of reasonable alkali coordination numbers using isostoichiometric differences, gives strong evidence that the tellurium environment in alkali tellurites is independent of the size of the modifier cation used

The impact of external pressure and sustainable management practices on manufacturing performance and environmental outcomes

Purpose: The study investigates the direct effect of external pressure on environmental outcomes and manufacturing performance and examines the mediating effect of sustainable management practice. Design/methodology/approach: This study draws upon Institutional Theory and Resource Based View to understand how factors such as external pressure and sustainable management relate with environmental outcomes and manufacturing performance. The model specifies previously unexplored direct and mediating relationships between external pressure, sustainable management, environmental outcomes and manufacturing performance. The empirical analysis is based on data collected from the sixth edition of the International Manufacturing Strategy Survey (IMSS). The research hypotheses were tested using Structural Equation Modelling. Findings: Results show that while there is a significant direct and mediating relationship between external pressure, adoption of formal sustainability programs and environmental outcomes, such significant relationships do not exist with manufacturing performance. Practical implications: The study shows that external pressure can influence the adoption of sustainable practices but the adoption of formal sustainable practices does not necessarily lead to an improvement in manufacturing performance. The implication therefore is that managers need to clearly understand what the actual benefits of sustainability are and where financial advantage, other than manufacturing cost, may be gained. Originality/value: The relationship between the adoption of sustainable practices and organisational performance is a complex one. In contrast to previous studies, this study found that while external pressure and sustainable management relate positively with environmental outcomes, no such relationship exists with manufacturing performance. This raises a number of questions over naively following such strategies