The norm of polynomials in large random and deterministic matrices

Let X_N= (X_1^(N), ..., X_p^(N)) be a family of N-by-N independent, normalized random matrices from the Gaussian Unitary Ensemble. We state sufficient conditions on matrices Y_N =(Y_1^(N), ..., Y_q^(N)), possibly random but independent of X_N, for which the operator norm of P(X_N, Y_N, Y_N^*) converges almost surely for all polynomials P. Limits are described by operator norms of objects from free probability theory. Taking advantage of the choice of the matrices Y_N and of the polynomials P we get for a large class of matrices the "no eigenvalues outside a neighborhood of the limiting spectrum" phenomena. We give examples of diagonal matrices Y_N for which the convergence holds. Convergence of the operator norm is shown to hold for block matrices, even with rectangular Gaussian blocks, a situation including non-white Wishart matrices and some matrices encountered in MIMO systems.Comment: 41 pages, with an appendix by D. Shlyakhtenk

Preignition-limited performance of several fuels

Preignition-limited performance data were obtained on a supercharged CFR engine at two sets of operating conditions over a wide range of fuel-air ratios to determine the preignition characteristics for the following five fuels: s-3 reference fuel, s-3 plus 4 ml. tel per gallon, afd-33(140-p), benzene, and diisobutylene. Maximum thermal-plug temperatures at constant intake-air pressures were also determined to correlate the preignition characteristics of each fuel with its ability to increase general engine-temperature levels. Additional runs were made to compare the preignition-limited performance of triptane, triptane plus 4 ml. tel per gallon, and an-f-28r fuel

Spectral fluctuations of tridiagonal random matrices from the beta-Hermite ensemble

A time series delta(n), the fluctuation of the nth unfolded eigenvalue was recently characterized for the classical Gaussian ensembles of NxN random matrices (GOE, GUE, GSE). It is investigated here for the beta-Hermite ensemble as a function of beta (zero or positive) by Monte Carlo simulations. The fluctuation of delta(n) and the autocorrelation function vary logarithmically with n for any beta>0 (1<<n<<N). The simple logarithmic behavior reported for the higher-order moments of delta(n) for the GOE (beta=1) and the GUE (beta=2) is valid for any positive beta and is accounted for by Gaussian distributions whose variances depend linearly on ln(n). The 1/f noise previously demonstrated for delta(n) series of the three Gaussian ensembles, is characterized by wavelet analysis both as a function of beta and of N. When beta decreases from 1 to 0, for a given and large enough N, the evolution from a 1/f noise at beta=1 to a 1/f^2 noise at beta=0 is heterogeneous with a ~1/f^2 noise at the finest scales and a ~1/f noise at the coarsest ones. The range of scales in which a ~1/f^2 noise predominates grows progressively when beta decreases. Asymptotically, a 1/f^2 noise is found for beta=0 while a 1/f noise is the rule for beta positive.Comment: 35 pages, 10 figures, corresponding author: G. Le Cae

Pressurised membrane bioreactor treatment of an inhibitory petrochemical wastewater

Please read the abstract in the section front of this documentDissertation (M Eng (Chemical Engineering))--University of Pretoria, 2007.Chemical Engineeringunrestricte

A COMPREHENSIVE REVIEW ON COMPARISON OF GDOCP IN PHARMACEUTICAL MANUFACTURING UNIT AS PER EUROPEAN AND WHO GUIDELINES

To review the good documentation practices in the pharmaceutical industry as per the guidelines provided in the European Commission and WHO (World Health Organisation). GDocP is a systematic method of planning, evaluating, approving, issuing, documenting, preserving, and archiving records. GDocP is a must when operating in an atmosphere of existing GMP. To provide an overview of good documentation practices for those employed in the pharmaceutical and healthcare sectors. The GDocP stands for good documentation practice which can be described as an integral part of quality assurance (QA) and thus related to all aspects of GMP. There are very few articles related to the comparison of GDocP in the pharmaceutical manufacturing unit as per European and WHO guidelines hence we are trying to develop a study on the comparison of GDocP guidelines. Public and private organizations, institutions, and regulatory authorities working and cooperating and with the pharmaceutical industry are involved at the international and national level to reach a consensus on the guidelines and laws for the production of medicinal products for human. This article explains how these participants work and cooperate and set out current regulations along the lines of the European community and WHO referencing, where appropriate, the practiced guidelines, outside space regulatory action referred to above. In this way, the goal is to achieve exceptional standards of quality, protection, and efficacy in the manufacture of health products

Pedagogical leadership: A comparative study from England, Greece and Sweden

Current international research addresses the complexities, challenges and barriers that impact formal accountable leadership in the field of Early Childhood Education and Care (ECEC) as well as its conceptualisations (e.g. Nicholson and Maniates 2016, Caroll-Lind et al 2016, Nicholson et al 2020). For example, a literature review of English ECEC found that there is a distinction between organisational leadership and pedagogical leadership (Pascal et al 2020). Pedagogical leaders are the ones who might not have any organisational responsibilities but lead the direct interactions between children and adults and the educational elements that constitute the pedagogy. They also highlight that in England there is no clear route to a leadership qualification for staff in ECEC

\u3ci\u3eThemeda triandra\u3c/i\u3e as a Perennial Seed Crop in South-Eastern Australia: What are the Agronomic Possibilities and Constraints, and Future Research Needs?

In Australia, the development of native perennial seed crops is an area of increasing interest. Reasons for this include the production of high-value seed, the significance of native plants to Aboriginal people and the importance of diversified cropping in building more resilient farming systems. One species of interest is Themeda triandra, a C4 perennial tussock grass that dominated grasslands and woodlands across Australia prior to European invasion. Djaara, the traditional owner group representing the Dja Dja Wurrung people of Djandak (Dja Dja Wurrung country in central Victoria), is one group who seek to return T. triandra to the landscape as a seed-producing crop. This is due to the species holding for them significant cultural and social value, along with envisioned future economic opportunities. As such, this review is targeted towards temperate grasslands of south-eastern Australia where Djandak is located. This review summarises the agronomic possibilities and constraints relating to production of a T. triandra as a seed crop via an understanding of the genetic, environmental and management factors that influence the growth, development, and seed yield of this species. Future research and development needs are also identified

Novel enantiopure bis(pyrrolo)tetrathiafulvalene donors exhibiting chiral crystal packing arrangements

Two novel enantiopure bis(pyrrolo[3,4-d])tetrathiafulvalene derivatives, substrates for preparing chiral conducting materials, show chiral crystal packing arrangements in which successive layers are rotated in accordance with an exact or approximate 43 axis. The corresponding donors containing fused dihydropyrrolegroups, and thus four more hydrogen atoms, form stacks along a crystal axis