Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

Applications of Feller-Reuter-Riley transition functions

A Feller–Reuter–Riley function is a Markov transition function whose corresponding semigroup maps the set of the real-valued continuous functions vanishing at infinity into itself. The aim of this paper is to investigate applications of such functions in the dual problem, Markov branching processes, and the Williams-matrix. The remarkable property of a Feller–Reuter–Riley function is that it is a Feller minimal transition function with a stable q-matrix. By using this property we are able to prove that, in the theory of branching processes, the branching property is equivalent to the requirement that the corresponding transition function satisfies the Kolmogorov forward equations associated with a stable q-matrix. It follows that the probabilistic definition and the analytic definition for Markov branching processes are actually equivalent. Also, by using this property, together with the Resolvent Decomposition Theorem, a simple analytical proof of the Williams' existence theorem with respect to the Williams-matrix is obtained. The close link between the dual problem and the Feller–Reuter–Riley transition functions is revealed. It enables us to prove that a dual transition function must satisfy the Kolmogorov forward equations. A necessary and sufficient condition for a dual transition function satisfying the Kolmogorov backward equations is also provided.

Experimental study and theoretical analysis of signage legibility distances as a function of observation angle

Signage systems are widely used in buildings to provide information for wayfinding, thereby assisting in navigation during normal circulation of pedestrians and, more importantly, exiting information during emergencies. An important consideration in determining the effectiveness of signs is establishing the region from which the sign is visible to occupants, the so-called Visibility Catchment Area (VCA). This paper attempts to factor into the determination of the VCA of signs, the observation angle of the observer using both experimental and theoretical analysis.

Signage legibility distances as a function of observation angle

Signage systems are widely used in buildings to provide information for wayfinding, thereby assisting in navigation during normal circulation of pedestrians and, more importantly, exiting information during emergencies. An important consideration in determining the effectiveness of signs is establishing the region from which the sign is visible to occupants, the so-called visibility catchment area (VCA). This study attempts to factor into the determination of the VCA of signs, the observation angle of the observer. In building regulations, it is implicitly assumed that the VCA is independent of the observation angle. A theoretical model is developed to explain the relationship between the VCA and observation angle and experimental trials are performed in order to assess the validity of this model. The experimental findings demonstrate a consistency with the theoretical model. Given this result, the functionality of a comprehensive evacuation model is extended in accordance with the assumptions on which the theoretical model is based and is then demonstrated using several examples

A fast, streaming SIMD extensions 2, logistic squashing function

Schraudolph proposed an excellent exponential approximation providing increased performance particularly suited to the logistic squashing function used within many neural networking applications. This note applies Intel's streaming SIMD Extensions 2 (SSE2), where SIMD is single instruction multiple data, of the Pentum IV class processor to Schraudolph's technique, further increasing the performance of the logistic squashing function. It was found that the calculation of the new 32-bit SSE2 logistic squashing function described here was up to 38 times faster than the conventional exponential function and up to 16 times faster than a Schraudolph-style 32-bit method on an Intel Pentum D 3.6 GHz CPU.

Multi-function oxidases are responsible for the synergistic interactions occurring between repellents and insecticides in mosquitoes

Background: With the spread of pyrethroid resistance in mosquitoes, the combination of an insecticide (carbamate or organophosphate) with a repellent (DEET) is considered as a promising alternative strategy for the treatment of mosquito nets and other relevant materials. The efficacy of these mixtures comes from the fact that they reproduce pyrethroid features and that positive interactions occur between insecticides and repellent. To better understand the mechanisms involved and assess the impact of detoxifying enzymes (oxidases and esterases) in these interactions, bioassays were carried out in the laboratory against the main dengue vector Aedes aegypti. Methods: Topical applications of DEET and propoxur (carbamate), used alone or as a mixture, were carried out on female mosquitoes, using inhibitors of the two main detoxification pathways in the insect. PBO, an inhibitor of multi-function oxidases, and DEF, an inhibitor of esterases, were applied one hour prior to the main treatment. Results: Results showed that synergism between DEET and propoxur disappeared in the presence of PBO but not with DEF. This suggests that oxidases, contrary to esterases, play a key role in the interactions occurring between DEET and cholinesterase inhibitors in mosquitoes. Conclusion: These findings are of great interest for the implementation of "combination nets" in the field. They support the need to combine insecticide with repellent to overcome insecticide resistance in mosquitoes of public health importance.

Early growth and adult respiratory function in men and women followed from the fetal period to adulthood

While some studies suggest that poor fetal growth rate, as indicated by lower birth weight, is associated with poor respiratory function in childhood, findings among adults remain inconsistent. A study was undertaken to determine the association between early growth and adult respiratory function.