On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

An improved simulation model to predict pre-harvest aflatoxin risk in maize

Aflatoxin is a potent carcinogen produced by Aspergillus flavus, which frequently contaminates maize (Zea mays L.) in the field between 40° north and 40° south latitudes. A mechanistic model to predict risk of pre-harvest contamination could assist in management of this very harmful mycotoxin. In this study we describe an aflatoxin risk prediction model which is integrated with the Agricultural Production Systems Simulator (APSIM) modelling framework. The model computes a temperature function for A. flavus growth and aflatoxin production using a set of three cardinal temperatures determined in the laboratory using culture medium and intact grains. These cardinal temperatures were 11.5 °C as base, 32.5 °C as optimum and 42.5 °C as maximum. The model used a low (≤0.2) crop water supply to demand ratio—an index of drought during the grain filling stage to simulate maize crop's susceptibility to A. flavus growth and aflatoxin production. When this low threshold of the index was reached the model converted the temperature function into an aflatoxin risk index (ARI) to represent the risk of aflatoxin contamination. The model was applied to simulate ARI for two commercial maize hybrids, H513 and H614D, grown in five multi-location field trials in Kenya using site specific agronomy, weather and soil parameters. The observed mean aflatoxin contamination in these trials varied from <1 to 7143 ppb. ARI simulated by the model explained 99% of the variation (p ≤ 0.001) in a linear relationship with the mean observed aflatoxin contamination. The strong relationship between ARI and aflatoxin contamination suggests that the model could be applied to map risk prone areas and to monitor in-season risk for genotypes and soils parameterized for APSIM.

An improved simulation model to predict pre-harvest aflatoxin risk in maize

Aflatoxin is a potent carcinogen produced by Aspergillus flavus, which frequently contaminates maize (Zea mays L.) in the field between 40° north and 40° south latitudes. A mechanistic model to predict risk of pre-harvest contamination could assist in management of this very harmful mycotoxin. In this study we describe an aflatoxin risk prediction model which is integrated with the Agricultural Production Systems Simulator (APSIM) modelling framework. The model computes a temperature function for A. flavus growth and aflatoxin production using a set of three cardinal temperatures determined in the laboratory using culture medium and intact grains. These cardinal temperatures were 11.5 °C as base, 32.5 °C as optimum and 42.5 °C as maximum. The model used a low (≤0.2) crop water supply to demand ratio—an index of drought during the grain filling stage to simulate maize crop's susceptibility to A. flavus growth and aflatoxin production. When this low threshold of the index was reached the model converted the temperature function into an aflatoxin risk index (ARI) to represent the risk of aflatoxin contamination. The model was applied to simulate ARI for two commercial maize hybrids, H513 and H614D, grown in five multi-location field trials in Kenya using site specific agronomy, weather and soil parameters. The observed mean aflatoxin contamination in these trials varied from <1 to 7143 ppb. ARI simulated by the model explained 99% of the variation (p ≤ 0.001) in a linear relationship with the mean observed aflatoxin contamination. The strong relationship between ARI and aflatoxin contamination suggests that the model could be applied to map risk prone areas and to monitor in-season risk for genotypes and soils parameterized for APSIM.

Spatiotemporal aspects of Hendra Virus infection in Pteropid Bats (Flying-Foxes) in Eastern Australia

Hendra virus (HeV) causes highly lethal disease in horses and humans in the eastern Australian states of Queensland (QLD) and New South Wales (NSW), with multiple equine cases now reported on an annual basis. Infection and excretion dynamics in pteropid bats (flying-foxes), the recognised natural reservoir, are incompletely understood. We sought to identify key spatial and temporal factors associated with excretion in flying-foxes over a 2300 km latitudinal gradient from northern QLD to southern NSW which encompassed all known equine case locations. The aim was to strengthen knowledge of Hendra virus ecology in flying-foxes to improve spillover risk prediction and exposure risk mitigation strategies, and thus better protect horses and humans. Monthly pooled urine samples were collected from under roosting flying-foxes over a three-year period and screened for HeV RNA by quantitative RT-PCR. A generalised linear model was employed to investigate spatiotemporal associations with HeV detection in 13,968 samples from 27 roosts. There was a non-linear relationship between mean HeV excretion prevalence and five latitudinal regions, with excretion moderate in northern and central QLD, highest in southern QLD/northern NSW, moderate in central NSW, and negligible in southern NSW. Highest HeV positivity occurred where black or spectacled flying-foxes were present; nil or very low positivity rates occurred in exclusive grey-headed flying-fox roosts. Similarly, little red flying-foxes are evidently not a significant source of virus, as their periodic extreme increase in numbers at some roosts was not associated with any concurrent increase in HeV detection. There was a consistent, strong winter seasonality to excretion in the southern QLD/northern NSW and central NSW regions. This new information allows risk management strategies to be refined and targeted, mindful of the potential for spatial risk profiles to shift over time with changes in flying-fox species distribution.

Changes in energy efficiency in Australia: A decomposition of aggregate energy intensity using logarithmic mean Divisia approach

This paper provides an empirical estimation of energy efficiency and other proximate factors that explain energy intensity in Australia for the period 1978-2009. The analysis is performed by decomposing the changes in energy intensity by means of energy efficiency, fuel mix and structural changes using sectoral and sub-sectoral levels of data. The results show that the driving forces behind the decrease in energy intensity in Australia are efficiency effect and sectoral composition effect, where the former is found to be more prominent than the latter. Moreover, the favourable impact of the composition effect has slowed consistently in recent years. A perfect positive association characterizes the relationship between energy intensity and carbon intensity in Australia. The decomposition results indicate that Australia needs to improve energy efficiency further to reduce energy intensity and carbon emissions. © 2012 Elsevier Ltd.

Cognitive function in schizophrenia: Conflicting findings and future directions

Introduction Schizophrenia is a severe mental disorder with multiple psychopathological domains being affected. Several lines of evidence indicate that cognitive impairment serves as the key component of schizophrenia psychopathology. Although there have been a multitude of cognitive studies in schizophrenia, there are many conflicting results. We reasoned that this could be due to individual differences among the patients (i.e. variation in the severity of positive vs. negative symptoms), different task designs, and/or the administration of different antipsychotics. Methods We thus review existing data concentrating on these dimensions, specifically in relation to dopamine function. We focus on most commonly used cognitive domains: learning, working memory, and attention. Results We found that the type of cognitive domain under investigation, medication state and type, and severity of positive and negative symptoms can explain the conflicting results in the literature. Conclusions This review points to future studies investigating individual differences among schizophrenia patients in order to reveal the exact relationship between cognitive function, clinical features, and antipsychotic treatment.

Periodic oscillations in feedback systems with combined pulse modulation

This paper presents a systematic method of investigating the existence of limit cycle oscillations in feedback systems with combined integral pulse frequency-pulse width (IPF-P/V) modulation. The method is based on the non-linear discrete equivalence of the continuous feedback system containing the IPF-PW modulator.

Excel’s Sumif and Sumifs function

As accountants, we are all familiar with the SUM function, which calculates the sum in a range of numbers. However, there are instances where we might want to sum numbers in a given range based on a specified criteria. In this instance the SUM IF function can achieve this objective.

Ternary function and circuit design using ternary multiplexers

The recent trend towards minimizing the interconnections in large scale integration (LSI) circuits has led to intensive investigation in the development of ternary circuits and the improvement of their design. The ternary multiplexer is a convenient and useful logic module which can be used as a basic building block in the design of a ternary system. This paper discusses a systematic procedure for the simplification and realization of ternary functions using ternary multiplexers as building blocks. Both single level and multilevel multiplexing techniques are considered. The importance of the design procedure is highlighted by considering two specific applications, namely, the development of ternary adder/subtractor and TCD to ternary converter.

The effect of internal audit function quality and internal audit contribution to external audit on audit fees

Corporate governance mandates and listing rules identify internal audit functions (IAF) as a central internal control mechanism. External audits are expected to assess the quality of IAF before placing reliance on its work. We provide evidence on the effect of IAF quality and IAF contribution to external audit on audit fees. Using data from a matched survey of both external and internal audits, we extend prior research which is based mainly on internal audits' assessment and conducted predominantly in highly developed markets. We find a positive relationship between IAF quality and audit fees as well as a reduction in audit fees as a result of external auditors' reliance on IAF. The interaction between IAF quality and IAF contribution to external audit suggests that high quality IAF induces greater external auditor reliance on internal auditors' work and thus result in lower external audit fees.

Application of the Conjugate Gradient Method to a Problem on Minimum Time Orbit Transfer

This correspondence considers the problem of optimally controlling the thrust steering angle of an ion-propelled spaceship so as to effect a minimum time coplanar orbit transfer from the mean orbital distance of Earth to mean Martian and Venusian orbital distances. This problem has been modelled as a free terminal time-optimal control problem with unbounded control variable and with state variable equality constraints at the final time. The problem has been solved by the penalty function approach, using the conjugate gradient algorithm. In general, the optimal solution shows a significant departure from earlier work. In particular, the optimal control in the case of Earth-Mars orbit transfer, during the initial phase of the spaceship's flight, is found to be negative, resulting in the motion of the spaceship within the Earth's orbit for a significant fraction of the total optimized orbit transfer time. Such a feature exhibited by the optimal solution has not been reported at all by earlier investigators of this problem.

'A responsible nuclear weapons power' : Nuclear Weapons and Indian Foreign Policy

This thesis examines the interrelationship and dynamics between the Indian United Progressive Alliance government’s foreign policy and its nuclear weapons policy. The purpose of the study is to situate nuclear policy within a foreign policy framework, and the fundamental research problem is thus how does the Indian nuclear policy reflect and respond to the Indian foreign policy? The study examines the intentions in the Indian foreign and nuclear policies, and asks whether these intentions are commensurable or incommensurable. Moreover, the thesis asks whether the UPA government differs from its predecessors, most notably the Bharatiya Janata Party-led National Democratic Alliance government in its foreign and nuclear policies. Answers to these questions are based on the interpretation of political texts and speeches as suggested by Quentin Skinner’s notion of meaning3, what does a writer or speaker mean by what he or she says in a given text, and by J.L. Austin’s speech act theory. This linguistic perspective and the approach of intertextualizing, place the political acts within their contingent intellectual and political contexts. The notion of strategic culture is therefore introduced to provide context for these juxtapositions. The thesis firstly analyses the societal, historical and intellectual context of India’s foreign and nuclear policy. Following from this analysis the thesis then examines the foreign and nuclear policies of Prime Minister Manmo-han Singh’s UPA government. This analysis focuses on the texts, speeches and statements of Indian authorities between 2004 and 2008. This study forwards the following claims: firstly, the UPA Government conducts a foreign policy that is mainly and explicitly inclusive, open and enhancing, and it conducts a nuclear policy that is mainly and implicitly excluding, closed and protective. Secondly, despite the fact that the notion of military security is widely appreciated and does not, as such, necessarily collide with foreign policy, the UPA Government conducts a nuclear policy that is incommensurable with its foreign policy. Thirdly, the UPA Gov-ernment foreign and nuclear policies are, nevertheless, commensurable re-garding their internal intentions. Finally, the UPA Government is conduct-ing a nuclear policy that is gradually leading India towards having a triad of nuclear weapons with various platforms and device designs and a function-ing and robust command and control system encompassing political and military planning, decision-making and execution. Regarding the question of the possible differences between the UPA and NDA governments this thesis claims that, despite their different ideological roots and orientations in domestic affairs, the Indian National Congress Party conducts, perhaps surprisingly, quite a similar foreign and nuclear policy to the Bharatiya Janata Party.

A method for the experimental evaluation of the acoustic characteristics of an engine exhaust system in the presence of mean flow

The paper deals with an exact analysis of standing waves in an impedance tube with mean flow. A method is offered for the experimental evaluation of the various wave parameters. Navier–Stokes equations have been solved for evaluating the volume velocity taking into account mean flow, viscosity, etc. The engine exhaust system has been characterized as an acoustic source with an acoustic pressure and internal impedance. A method is suggested for the evaluation of these hypothetical parameters using the exhaust pipe as an impedance tube.Subject Classification: [43]85.20; [43]20.40.

Velocity ratio-cum-transfer matrix method for the evaluation of a muffler with mean flow

The paper deals with a method for the evaluation of exhaust muffers with mean flow. A new set of variables, convective pressure and convective mass velocity, have been defined to replace the acoustic variables. An expression for attenuation (insertion loss) of a muffler has been proposed in terms of convective terminal impedances and a velocity ratio, on the lines of the one existing for acoustic filters. In order to evaluate the velocity ratio in terms of convective variables, transfer matrices for various muffler elements have been derived from the basic relations of energy, mass and momentum. Finally, the velocity ratiocum-transfer matrix method is illustrated for a typical straight-through muffler.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.