Branching Processes in Autoregressive Random Environment

2000 Mathematics Subject Classification: 60J80, 60K05.

Extremes of Bivariate Geometric Variables with Application to Bisexual Branching Processes

2000 Mathematics Subject Classification: 60J80, 60G70.

O paradoxo da superdifusão de uma caminhada aleatória com memória exponencial

The random walk models with temporal correlation (i.e. memory) are of interest in the study of anomalous diffusion phenomena. The random walk and its generalizations are of prominent place in the characterization of various physical, chemical and biological phenomena. The temporal correlation is an essential feature in anomalous diffusion models. These temporal long-range correlation models can be called non-Markovian models, otherwise, the short-range time correlation counterparts are Markovian ones. Within this context, we reviewed the existing models with temporal correlation, i.e. entire memory, the elephant walk model, or partial memory, alzheimer walk model and walk model with a gaussian memory with profile. It is noticed that these models shows superdiffusion with a Hurst exponent H > 1/2. We study in this work a superdiffusive random walk model with exponentially decaying memory. This seems to be a self-contradictory statement, since it is well known that random walks with exponentially decaying temporal correlations can be approximated arbitrarily well by Markov processes and that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. The solution to the apparent paradox is that the model is genuinely non-Markovian, due to a time-dependent decay constant associated with the exponential behavior. In the end, we discuss ideas for future investigations.

Limit sets and the Poincare-Bendixson Theorem in impulsive semidynamical systems

We consider semidynamical systems with impulse effects at variable times and we discuss some properties of the limit sets of orbits of these systems such as invariancy, compactness and connectedness. As a consequence we obtain a version of the Poincare-Bendixson Theorem for impulsive semidynamical systems. (C) 2008 Elsevier Inc. All rights reserved.

Free groups in central simple algebras without Tits` theorem

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality \k\ (which need not be open).

Does low phosphorus supply limit seedling establishment and tree growth in groves of ectomycorrhizal trees in a central African rainforest?

In a forest grove at Korup dominated by the ectomycorrhizal species Microberlinia bisulcata, an experiment tested whether phosphorus (P) was a limiting nutrient. P-fertilization of seven subplots 1995-97 was compared with seven controls. It led to large increases in soil P concentrations. Trees were measured in 1995 and 2000. M. bisulcata and four other species were transplanted into the treatments, and a wild cohort of M. bisulcata seedlings was followed in both. Leaf litter fall from trees and seedlings were analysed for nutrients. Growth of trees was not affected by added P. Transplanted seedlings survived better in the controls than added-P subplots: they did not grow better with added-P.M. bisulcata wildlings survived slightly better in the added-P subplots in yr 1 but not later. Litter fall and transplanted survivors had much higher concentrations of P (not N) in the added-P than control subplots. Under current conditions, it appears that P does not limit growth of trees or hinder seedling establishment, especially of M. bisculcata, in these low-P grove soils.

Climate-pollen relationships AD 1901-1996 in two small mires near the forest limit in the northern and central Swiss Alps

Climatic relationships were established in two 210Pb dated pollen sequences from small mires closely surrounded by forest just below actual forest limits (but about 300 m below potential climatic forest limits) in the northern Swiss Alps (suboceanic in climate; mainly with Picea) and the central Swiss Alps (subcontinental; mainly Pinus cembra and Larix) at annual or near-annual resolution from ad 1901 to 1996. Effects of vegetational succession were removed by splitting the time series into early and late periods and by linear detrending. Both pollen concentrations detrended by the depth-age model and modified percentages (in which counts of dominant pollen types are down-weighted) are correlated by simple linear regression with smoothed climatic parameters with one-and two-year timelags, including average monthly and April/September daylight air temperatures and with seasonal and annual precipitation sums. Results from detrended pollen concentrations suggest that peat accumulation is favoured in the northern-Alpine mire either by early snowmelt or by summer precipitation, but in the central-Alpine mire by increased precipitation and cooler summers, suggesting a position of the northern-Alpine mire near the upper altitudinal limit of peat formation, but of the central-Alpine mire near the lower limit. Results from modified pollen percentages indicate that pollen pro duction by plants growing near their upper altitudinal limit is limited by insufficient warmth in summer, and pollen production by plants growing near their lower altitudinal limit is limited by too-high temperatures. Only weakly significant pollen/climate relationships were found for Pinus cembra and Larix, probably because they experience little climatic stress growing 300 m below the potential climatic forest limit.

Uppermost Limit, Extent, and Fluctuations of the Timberline and Treeline Ecocline in the Swiss Central Alps during the past 11,500 Years

Pollen and macrofossils were analyzed at two sites above today's treeline (or tree limit) in the Swiss Central Alps (Gouillé Loéré, 2503 m a.s.l., and Lengi Egga, 2557 m a.s.l.) to test two contrasting hypotheses about the natural formation of timberline (the upper limit of closed forest) in the Alps. Our results revealed that Pinus cembra--Larix decidua forests near timberline were rather closed between 9000 and 2500 B.C. (9600-4000 ¹⁴C yr BP), when timberline fluctuations occurred within a belt 100-150 m above today's tree limit. The treeline ecocline above timberline was characterized by the mixed occurrence of tree, shrub, dwarf-shrub, and herbaceous species, but it did not encompass more than 100-150 altitudinal meters. The uppermost limit reached by timberline and treeline during the Holocene was ca. 2420 and 2530 m, respectively, i.e., about 120 to 180 m higher than today. Between 3500 and 2500 B.C. (4700-4000 ¹⁴C yr BP) timberline progressively sank by about 300 m, while treeline was lowered only ca. 100 m. This change led to an enlargement of the treeline-ecocline belt (by ca. 300 m) after 2500 B.C. (4000 ¹⁴C yr BP). Above the treeline ecocline, natural meadows dominated by dwarf shrubs (e.g., Salix herbacea) and herbaceous species (e.g., Helianthemum, Taraxacum, Potentialla, Leontodon t., Cerastium alpinum t., Cirsium spinosissimum, Silene exscapa t., and Saxifraga stellaris) have been present since at least 11,000 cal yr ago. In these meadows tree and tall shrub species (>0.5 m) never played a major role. These results support the conventional hypothesis of a narrow ecocline with rather sharp upper timberline and treeline boundaries and imply that today's treeless alpine communities in the Alps are close to a natural stage. Pollen (percentages and influx), stomata, and charcoal data may be useful for determining whether or not a site was treeless. Nevertheless, a reliable and detailed record of past local vegetation near and above timberline is best achieved through the inclusion of macrofossil analysis.

Elasto-plastic stress analysis of an insulated rail joint (IRJ) with a loading below shakedown limit

A finite element numerical simulation is carried out to examine stress distributions on railhead in the vicinity of the endpost of a insulated rail joint. The contact patch and pressure distribution are considered using modified Hertzian formulation. A combined elasto-plastic material modelling available in Abaqus is employed in the simulation. A dynamic load factor of 1.21 is considered in modelling for the wheel load based on a previous study as part of this on going research. Shakedown theorem is employed in this study. A peak pressure load which is above the shakedown limit is determined as input load. As a result, a progressive damage in the railhead has been captured as depicted in the equivalent plastic strain plot.

Ultimate flexural limit states analysis of prestressed concrete sleeper

Railway is one of the most important, reliable and widely used means of transportation, carrying freight, passengers, minerals, grains, etc. Thus, research on railway tracks is extremely important for the development of railway engineering and technologies. The safe operation of a railway track is based on the railway track structure that includes rails, fasteners, pads, sleepers, ballast, subballast and formation. Sleepers are very important components of the entire structure and may be made of timber, concrete, steel or synthetic materials. Concrete sleepers were first installed around the middle of last century and currently are installed in great numbers around the world. Consequently, the design of concrete sleepers has a direct impact on the safe operation of railways. The "permissible stress" method is currently most commonly used to design sleepers. However, the permissible stress principle does not consider the ultimate strength of materials, probabilities of actual loads, and the risks associated with failure, all of which could lead to the conclusion of cost-ineffectiveness and over design of current prestressed concrete sleepers. Recently the limit states design method, which appeared in the last century and has been already applied in the design of buildings, bridges, etc, is proposed as a better method for the design of prestressed concrete sleepers. The limit states design has significant advantages compared to the permissible stress design, such as the utilisation of the full strength of the member, and a rational analysis of the probabilities related to sleeper strength and applied loads. This research aims to apply the ultimate limit states design to the prestressed concrete sleeper, namely to obtain the load factors of both static and dynamic loads for the ultimate limit states design equations. However, the sleepers in rail tracks require different safety levels for different types of tracks, which mean the different types of tracks have different load factors of limit states design equations. Therefore, the core tasks of this research are to find the load factors of the static component and dynamic component of loads on track and the strength reduction factor of the sleeper bending strength for the ultimate limit states design equations for four main types of tracks, i.e., heavy haul, freight, medium speed passenger and high speed passenger tracks. To find those factors, the multiple samples of static loads, dynamic loads and their distributions are needed. In the four types of tracks, the heavy haul track has the measured data from Braeside Line (A heavy haul line in Central Queensland), and the distributions of both static and dynamic loads can be found from these data. The other three types of tracks have no measured data from sites and the experimental data are hardly available. In order to generate the data samples and obtain their distributions, the computer based simulations were employed and assumed the wheel-track impacts as induced by different sizes of wheel flats. A valid simulation package named DTrack was firstly employed to generate the dynamic loads for the freight and medium speed passenger tracks. However, DTrack is only valid for the tracks which carry low or medium speed vehicles. Therefore, a 3-D finite element (FE) model was then established for the wheel-track impact analysis of the high speed track. This FE model has been validated by comparing its simulation results with the DTrack simulation results, and with the results from traditional theoretical calculations based on the case of heavy haul track. Furthermore, the dynamic load data of the high speed track were obtained from the FE model and the distributions of both static and dynamic loads were extracted accordingly. All derived distributions of loads were fitted by appropriate functions. Through extrapolating those distributions, the important parameters of distributions for the static load induced sleeper bending moment and the extreme wheel-rail impact force induced sleeper dynamic bending moments and finally, the load factors, were obtained. Eventually, the load factors were obtained by the limit states design calibration based on reliability analyses with the derived distributions. After that, a sensitivity analysis was performed and the reliability of the achieved limit states design equations was confirmed. It has been found that the limit states design can be effectively applied to railway concrete sleepers. This research significantly contributes to railway engineering and the track safety area. It helps to decrease the failure and risks of track structure and accidents; better determines the load range for existing sleepers in track; better rates the strength of concrete sleepers to support bigger impact and loads on railway track; increases the reliability of the concrete sleepers and hugely saves investments on railway industries. Based on this research, many other bodies of research can be promoted in the future. Firstly, it has been found that the 3-D FE model is suitable for the study of track loadings and track structure vibrations. Secondly, the equations for serviceability and damageability limit states can be developed based on the concepts of limit states design equations of concrete sleepers obtained in this research, which are for the ultimate limit states.

Evaluating legume species as alternative trap crops to chickpea for management of Helicoverpa spp. (Lepidoptera: Noctuidae) in central Queensland cotton cropping systems

Mounting levels of insecticide resistance within Australian Helicoverpa spp. populations have resulted in the adoption of non-chemical IPM control practices such as trap cropping with chickpea, Cicer arietinum (L.). However, a new leaf blight disease affecting chickpea in Australia has the potential to limit its use as a trap crop. Therefore this paper evaluates the potential of a variety of winter-active legume crops for use as an alternative spring trap crop to chickpea as part of an effort to improve the area-wide management strategy for Helicoverpa spp. in central Queensland’s cotton production region. The densities of Helicoverpa eggs and larvae were compared over three seasons on replicated plantings of chickpea, Cicer arietinum (L.), field pea Pisum sativum (L), vetch, Vicia sativa (L.) and faba bean, Vicia faba (L.). Of these treatments, field pea was found to harbour the highest densities of eggs. A partial life table study of the fate of eggs oviposited on field pea and chickpea suggested that large proportions of the eggs laid on field pea suffered mortality due to dislodgment from the plants after oviposition. Plantings of field pea as a replacement trap crop for chickpea under commercial conditions confirmed the high level of attractiveness of this crop to ovipositing moths. The use of field pea as a trap crop as part of an areawide management programme for Helicoverpa spp. is discussed.

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem o limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (xi(gamma)) is determined. On account of interference, the magnitude of xi(gamma) is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.